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The true toughness of human cortical bone measured with realistically short cracks
Abstract
Bone is more difficult to break than to split. Although this is well known, and many studies exist on the behaviour of long cracks in bone, there is a need for data on the orientation-dependent crack-growth resistance behaviour of human cortical bone that accurately assesses its toughness at appropriate size scales. Here, we use in situ mechanical testing to examine how physiologically pertinent short (<600 microm) cracks propagate in both the transverse and longitudinal orientations in cortical bone, using both crack-deflection/twist mechanics and nonlinear-elastic fracture mechanics to determine crack-resistance curves. We find that after only 500 microm of cracking, the driving force for crack propagation was more than five times higher in the transverse (breaking) direction than in the longitudinal (splitting) direction owing to major crack deflections/twists, principally at cement sheaths. Indeed, our results show that the true transverse toughness of cortical bone is far higher than previously reported. However, the toughness in the longitudinal orientation, where cracks tend to follow the cement lines, is quite low at these small crack sizes; it is only when cracks become several millimetres in length that bridging mechanisms can fully develop leading to the (larger-crack) toughnesses generally quoted for bone.
... This results in anisotropic fracture toughness [21]. Crack deflections in weak cement line interfaces, seen as irregular and tortuous crack paths, have been 115 identified as important toughening mechanisms particularly when cracks propagate perpendicular to the long axis of osteons in transverse (breaking) directions [22][23][24], but also in the radial (anti-plane longitudinal) [18,25] direction. Furthermore, lower fracture toughness in aged [18,25,26] or irradiated [20] bone tissue, and in bone tested at high loading rates [27,28], has been associated with smoother crack surfaces compared to young or quasi-statically loaded tissue. ...
... Fracture toughness and toughening mechanisms in cortical bone have been studied extensively using both linear and nonlinear fracture mechanics. In the longitudinal orientation, intact ligaments bridging 370 the crack are the main toughening mechanisms while crack deflection is found to be the predominant toughening mechanisms in radial and transverse orientations [16,21,22,25,55]. However, most studies focused on one or two orientations and due to the lack of standardized tests for bone, it is difficult to compare data from different studies. ...
... With these settings, the crack was typically 480 identified at the same location for two to four consecutive images during stable crack growth ( Figure 3A), which shows that the image acquisition frequency was not the limiting factor. The crack tip detection was comparable to conventional methods using the unloading compliance for analyzing the Jintegral [11,22,71]. Future studies could try to improve the speckle pattern for DIC by decreasing the size of the speckles and increasing the contrast, possibly trying out other methods than an airbrush for 485 applying the speckles. ...
... The central characteristic of these third-generation biomineralized ELMs is the use of a biological scaffold. Most mineralized materials that occur in nature such as bone, coral, and nacre are generated from the mineralization of a biological scaffold consisting of biopolymers and other proteins 19,20 . One motivation for using a biological scaffold within ELMs is that they have the potential to be more durable than hydrogels, which degrade at ranges of humidities and temperatures common with outdoor use cases. ...
... One desirable internal geometry would be the osteonal structure of cortical bone. Osteons are ring-like structures with plies of biomineralized collagen, centered around an internal channel, that considerably toughen cortical bone 20,43 and permit nutrition/waste exchange and cellular communication 44 . ...
... We also demonstrated that mycelium scaffolds can permit the construction of specimens with complex internal microarchitectures. Osteonal bone was chosen as a demonstration since this microarchitecture is well-known to contribute to bone's excellent properties while provide important physiological functions 20,22,24,43,44 . Mycelium scaffolds were bacteriallybiomineralized into concentric rings that mimic the lamellae within osteons, and then were mineralized together with a dispersed sand phase within a beam-shaped mold. ...
Engineered living materials (ELMs) are garnering considerable attention as a promising alternative to traditional building materials because of their potentially lower carbon footprint and additional functionalities conferred by living cells. However, biomineralized ELMs designed for load-bearing purposes are limited in their current design and usage for several reasons, including (1) low microbial viability and (2) limited control of specimen internal microarchitecture. We created ‘third generation’ biomineralized ELMs from fungal mycelium scaffolds that were mineralized either by the fungus itself or by ureolytic bacteria. Both self-mineralized (i.e. fungally-mineralized) and bacterially-mineralized scaffolds retained high microbial viability for at least four weeks in room temperature or accelerated dehydration storage conditions, without the addition of protectants against desiccation. The microscale modulus of calcium carbonate varied with the different biomineralized scaffold conditions, and moduli were largest and stiffest for bacterial biomineralization of fungal mycelium. As an example of how mycelium scaffolds can enable the design of complex internal geometries of biomineralized materials, osteonal-bone mimetic architectures were patterned from mycelium and mineralized using ureolytic bacteria. These results demonstrate the potential for mycelium scaffolds to enable new frontiers in the design of biomineralized ELMs with improved viability and structural complexity.
Progress and Potential
Biomineralized engineered living materials (ELMs) offer new approaches for increasing the sustainability of building materials and processes. However, the design and usage of biomineralized ELMs is constrained by several important limitations, including low microbial viability and limited ability to control internal microarchitecture. Fungal mycelium scaffolds, biomineralized by either fungi or bacteria, achieve much higher viability of ureolytic microorganisms than what has been reported for biomineralized ELMs. Further, mycelium scaffolds permit the manufacturing of complex architectures, such as inspired by the structure of osteonal bone. Mycelium scaffolds have the potential to enable new frontiers in the design and use of biomineralized ELMs.
Graphical Abstract
... Linear elastic fracture mechanics (LEFM) has typically been used to report fracture behavior in bone, either through stress intensity factors, critical distance theory, or via the J-integral. Stress intensity factors are a common tool for characterizing toughness and have been used in several studies with a variety of tissues and experimental methods with a large range in results [7]. The theory of critical distances, derived from LEFM, has been previously applied in fracture mechanics of bone and suggests that the microstructure influences toughness [8]. ...
... Fracture toughness of bone has been found to differ with respect to age [12,13,14,15], disease [16], and anatomical direction [7]. Regardless, bone exhibits exceptional toughness and resistance to fracture due to the extrinsic and intrinsic toughening mechanisms present across hierarchical length scales [17]. ...
... After an initial settling period, the response of the specimen is linear, followed by a nonlinear response initiating around P 3 with a load maximum, and subsequent load reduction to failure. Figure 3 depicts the reconstruction of the 3D X-ray image at load stage P 6 = 62.3 N. Movies depicting the reconstructed Haversian Canal and crack structure are provided as Supplementary Material. Reconstructed images provided here are larger than others have reported using smaller samples with cross-sections on the scale of 2 mm or less [37,7,38,14] The crack becomes fully separated from the induced notch at peak load (P 5 ), at which point the fracture process zone is fully developed and of constant length. Observed in 3D, the crack is shown to be tortuous and interacts with the microstructure at the length scale of On.Dm. ...
... Crack resistance curve (R-curve) measurements using J-integral methodologies that are based on elastic-plastic fracture mechanics incorporate intrinsic and extrinsic toughening mechanisms. They enable determining the fracture toughness of the material while simultaneously allowing to distinguish between crack initiation and crack growth toughness Busse et al., 2013;Carlton et al., 2010;Koester et al., 2008Koester et al., , 2011Launey et al., 2010;Zimmermann et al., 2011). ...
... R-curve measurements have been successfully applied to bone studies of various species. They were first utilized by Vashishth et al. (1997) to investigate the fracture resistance of human cortical bone in the longitudinal cracking orientation and later by Koester et al., in 2008 to investigate the transverse cracking orientation (i.e., perpendicular to the bone axis). Studying the transverse testing orientation is experimentally challenging and thus tests were conducted in situ inside of a scanning electron microscope (SEM) allowing direct observation of crack growth during testing and visualization of deformation mechanisms and failure characteristics such as crack deflection and twisting Launey et al., 2010). ...
... Moreover, our crack initiation toughness numbers of both the airtested (hydrated) and dehydrated samples (Table 2) are comparable to previously reported results (Carlton et al., 2010;Gauthier et al., 2017;Koester et al., 2008Koester et al., , 2011Nalla et al., 2003;Willett et al., 2019;Zioupos and Currey, 1998) from tests on fully hydrated and dehydrated/dried bones, respectively, and as shown in Table 3. Unlike human bone, fracture toughness data of sheep bone has, to the knowledge of the authors, not been reported despite their frequent use in orthopedic research. The trend to lower crack initiation toughness with SEM based vacuum testing conditions ( Fig. 2b and Table 2), is, however, comparable to human bone. ...
... Previous studies showed that osteonal area, size, and density as well as intracortical porosity alter fracture toughness (Granke et al., 2016;Yeni et al., 1997). Crack deflection at cement lines was shown to be a major mechanism of fracture resistance (Burr et al., 1988;Koester et al., 2008) which deteriorated with aging (Chan et al., 2009;Koester et al., 2011). In addition, aspects of bone tissue composition such as collagen maturity, carbonate substitution, and crystallinity were associated with fracture incidence in human bone biopsies (Boskey et al., 2016;Gourion-Arsiquaud et al., 2009) indicating that compositional changes may modify local material properties and fracture resistance of bone. ...
... Specifically, the interstitial bone and osteons were modeled by a 3D cohesive XFEM formulation, which permits cracks to form within elements, and cement lines were modeled as 2D cohesive interface elements (Section 2.3.3). In the enriched region, cracks may propagate through any elements within the interstitial and osteonal bone and deflect at cement lines, as observed experimentally, in the entire detailed microstructure region (Koester et al., 2008;Lloyd et al., 2017). Material properties were assigned to the models based on experimental measurements (Section 2.3.2, ...
... This scaling utilized a direct relationship between elastic modulus and ultimate strength (Duchemin et al., 2008) and an inverse relationship between elastic modulus and fracture toughness (Singleton et al., 2021) following experimental findings in the literature. The base values for the normal and shear ultimate strengths and critical energy release rates used in the scaling were taken from the literature (Koester et al., 2008;Reilly and Burstein, 1975) as outlined in our previous studies (Demirtas et al., 2016;Demirtas and Ural, 2018b). The models explicitly incorporate the microstructure, which captures the directional dependence of fracture toughness and ultimate strength as an outcome of the simulations. ...
Microstructural and compositional changes that occur due to aging, pathological conditions, or pharmacological
treatments alter cortical bone fracture resistance. However, the relative importance of these changes to the
fracture resistance of cortical bone has not been quantified in detail. In this technical note, we developed an
integrated experimental-computational framework utilizing human femoral cortical bone biopsies to advance the
understanding of how fracture resistance of cortical bone is modulated due to modifications in its microstructure
and material properties. Four human biopsy samples from individuals with varying fragility fracture history and
osteoporosis treatment status were converted to finite element models incorporating specimen-specific material
properties and were analyzed using fracture mechanics-based modeling. The results showed that cement line
density and osteonal volume had a significant effect on crack volume. The removal of cement lines substantially
increased the crack volume in the osteons and interstitial bone, representing straight crack growth, compared to
models with cement lines due to the lack of crack deflection in the models without cement lines. Crack volume in
the osteons and interstitial bone increased when mean elastic modulus and ultimate strength increased and mean
fracture toughness decreased. Crack volume in the osteons and interstitial bone was reduced when material
property heterogeneity was incorporated in the models. Although both the microstructure and the heterogeneity
of the material properties of the cortical bone independently increased the fracture toughness, the relative
contribution of the microstructure was more significant. The integrated experimental-computational framework
developed here can identify the most critical microscale features of cortical bone modulated by pathological
processes or pharmacological treatments that drive changes in fracture resistance and improve our understanding
of the relative influence of microstructure and material properties on fracture resistance of cortical
bone.
... Bone tissue exhibits a rising fracture resistance with crack extension, thus, toughness measurements should be described as a function of crack extension [52,85]. Here, as cracks were barely detectable at load step 2, we were not able to analyse changes with increasing crack size. ...
... Therefore, we could not quantify differences between indenter geometry, either material orientation. While it is well known that the driving force for crack propagation is higher in the transverse direction than in the longitudinal direction [52,64], the complex crack growth pattern observed here, both axially and radially to the indentation axis, makes it difficult to assign an unique crack propagation direction to our specimens, for which traditional fracture toughness mechanical testing on compact-tension samples may be more appropriate. ...
... The absence of cement sheaths results in the loss of one of the major extrinsic toughening mechanisms in bone: crack deflection and twisting at the cement lines [64]. As such, we did not observe major deflections as reported for human cortical bone [52], and most cracks penetrated the osteons. This allowed us to simply calculate crack opening displacements by taking two planes parallel to the main crack direction. ...
The development of treatment strategies for skeletal diseases relies on the understanding of bone mechanical properties in relation to its structure at different length scales. At the microscale, indention techniques can be used to evaluate the elastic, plastic, and fracture behaviour of bone tissue. Here, we combined in situ high-resolution SRμCT indentation testing and digital volume correlation to elucidate the anisotropic crack propagation, deformation, and fracture of ovine cortical bone under Berkovich and spherical tips. Independently of the indenter type we observed significant dependence of the crack development due to the anisotropy ahead of the tip, with lower strains and smaller crack systems developing in samples indented in the transverse material direction, where the fibrillar bone ultrastructure is largely aligned perpendicular to the indentation direction. Such alignment allows to accommodate the strain energy, inhibiting crack propagation. Higher tensile hoop strains generally correlated with regions that display significant cracking radial to the indenter, indicating a predominant Mode I fracture. This was confirmed by the three-dimensional analysis of crack opening displacements and stress intensity factors along the crack front obtained for the first time from full displacement fields in bone tissue. The X-ray beam significantly influenced the relaxation behaviour independent of the tip. Raman analyses did not show significant changes in specimen composition after irradiation compared to non-irradiated tissue, suggesting an embrittlement process that may be linked to damage of the non-fibrillar organic matrix. This study highlights the importance of three-dimensional investigation of bone deformation and fracture behaviour to explore the mechanisms of bone failure in relation to structural changes due to aging or disease. STATEMENT OF SIGNIFICANCE: : Characterising the three-dimensional deformation and fracture behaviour of bone remains essential to decipher the interplay between structure, function, and composition with the aim to improve fracture prevention strategies. The experimental methodology presented here, combining high-resolution imaging, indentation testing and digital volume correlation, allows us to quantify the local deformation, crack propagation, and fracture modes of cortical bone tissue. Our results highlight the anisotropic behaviour of osteonal bone and the complex crack propagation patterns and fracture modes initiating by the intricate stress states beneath the indenter tip. This is of wide interest not only for the understanding of bone fracture but also to understand other architectured (bio)structures providing an effective way to quantify their toughening mechanisms in relation to their main mechanical function.
... It results in isotropic material properties of a tissue formed from intrinsically anisotropic building blocks, but more importantly such twisted layers are excellent in resisting the propagation of cracks, which explains the high fracture toughness in so many biological materials (3,(6)(7)(8)(9). A well-studied example is compact bone in which mineralized fibers of collagen type I build up ~ 5 µm wide lamellae with an alternating twisting angle to form a plywood-like material with high toughness (9)(10)(11)(12)(13). Despite the well-known connection between structure and mechanical function, the processes causing the emergence of twisted plywood structures in Nature remain unclear. ...
... As the chosen MC3T3-E1 cells are preosteoblastic, it is remarkable that the observed tissue twisting presents similarities of what is found in bone. Osteons located in human long bone for example exhibit a typical lamellar plywood-like structure with around 5 µm thick lamellae of mineralized collagen fibers (9)(10)(11)(12)(13). Despite the different tissue compositions (a highly mineralized collagen extracellular matrix vs. a loosely packed cell-collagen tissue) it is likely that our in vitro results showing the emergence of a chiral tissue structure are triggered by similar processes responsible for the twisted plywood structure in the in vivo case. ...
Little is known about the contribution of 3D surface geometry on the development of multi-layered tissues containing fibrous extracellular matrix components such as those found in bone. Here we elucidate the role of curvature in the formation of chiral, twisted plywood-like structures. Tissues consisting of murine pre-osteoblast cells (MC3T3-E1) were grown on 3D scaffolds with constant mean curvature and negative Gaussian curvature for up to 32 days. Using 3D fluorescence microscopy, the influence of surface curvature on actin stress-fiber alignment and chirality was investigated. To gain mechanistic insights, also MC3T3-E1 cells deficient in nuclear A-type lamins or treated with drugs targeting cytoskeleton proteins were used in our study. We find that wild type cells grow multilayered tissue with fibers predominantly aligned along directions of negative curvature, but where subsequent layers twist in orientation with respect to older tissues with time. Fiber orientation is conserved below the tissue surface thus creating a twisted plywood like material. We further show that this directional organization strongly depends on structural components of the cells (A-type lamins, actin and myosin). Our data indicate the importance of substrate curvature in the formation of 3D tissues and provides new insights into the emergence of chirality.
Significance Statement
Biological tissues (like compact bone) often consist of multiple fibrous layers which are staggered with a twisting angle relative to each other, thereby improving mechanical performance. The underlying principles of how such tissues are formed and what determines the fiber direction are still debated. Here we report the formation of a twisted plywood-like tissue grown in vitro on constant mean and negative Gaussian curvature substrates and present evidence that for tissue consisting of pre-osteoblast like cells, surface curvature is a main determinant for fiber orientation.
... Then, the "fracture work" was divided by the surface area of the skin samples to obtain the energy required for the crack to expand on the uni area, which could be approximately regarded as the fracture toughness of the skin speci mens. The average fracture toughness of the fish skin samples was 22.67 ± 1.23 kJ/m 2 which was in the same order of magnitude as the cortical bone (~10 kJ/m 2 ) [25] and some tough mammalian skin (~20 kJ/m 2 ) [26], indicating that the Chinese sturgeon skin had superior fracture toughness. ...
... Then, the "fracture work" was divided by the surface area of the skin samples to obtain the energy required for the crack to expand on the unit area, which could be approximately regarded as the fracture toughness of the skin specimens. The average fracture toughness of the fish skin samples was 22.67 ± 1.23 kJ/m 2 , which was in the same order of magnitude as the cortical bone (~10 kJ/m 2 ) [25] and some tough mammalian skin (~20 kJ/m 2 ) [26], indicating that the Chinese sturgeon skin had superior fracture toughness. ...
Fish skin is a biological material with high flexibility and compliance and can provide good mechanical protection against sharp punctures. This unusual structural function makes fish skin a potential biomimetic design model for flexible, protective, and locomotory systems. In this work, tensile fracture tests, bending tests, and calculation analyses were conducted to study the toughening mechanism of sturgeon fish skin, the bending response of the whole Chinese sturgeon, and the effect of bony plates on the flexural stiffness of the fish body. Morphological observations showed some placoid scales with drag-reduction functions on the skin surface of the Chinese sturgeon. The mechanical tests revealed that the sturgeon fish skin displayed good fracture toughness. Moreover, flexural stiffness decreased gradually from the anterior region to the posterior region of the fish body, which means that the posterior region (near the tail) had higher flexibility. Under large bending deformation, the bony plates had a specific inhibition effect on the bending deformation of the fish body, especially in the posterior region of the fish body. Furthermore, the test results of the dermis-cut samples showed that the sturgeon fish skin had a significant impact on flexural stiffness, and the fish skin could act as an external tendon to promote effective swimming motion.
... In this study, crack growth from the EUC method was compared to crack growth measurements from images taken during the fracture test with a digital camera attached to an optical microscope. Another approach that has been used to assess crack growth during cortical bone fracture is scanning electron microscopy (SEM) [84,85]. However, a recent study [86] showed that the use of SEM leads to lower fracture toughness values due to dehydration of the cortical bone samples. ...
... Note that this dominant orientation is consistent with the anisotropy of fracture toughness. It is much easier to split bone (propagate a crack along the long axis, between osteons and other microstructures) with as little as one-fifth of the energy required to break bone (grow a crack perpendicular to the long axis, in the transverse plane, across the microstructure) [84]. ...
Purpose of review:
This review surveys recent literature related to cortical bone fracture mechanics and its application towards understanding bone fragility and hip fractures.
Recent findings:
Current clinical tools for hip fracture risk assessment have been shown to be insensitive in some cases of elevated fracture risk leading to the question of what other factors account for fracture risk. The emergence of cortical bone fracture mechanics has thrown light on other factors at the tissue level that are important to bone fracture resistance and therefore assessment of fracture risk. Recent cortical bone fracture toughness studies have shown contributions from the microstructure and composition towards cortical bone fracture resistance. A key component currently overlooked in the clinical evaluation of fracture risk is the importance of the organic phase and water to irreversible deformation mechanisms that enhance the fracture resistance of cortical bone. Despite recent findings, there is an incomplete understanding of which mechanisms lead to the diminished contribution of the organic phase and water to the fracture toughness in aging and bone-degrading diseases. Notably, studies of the fracture resistance of cortical bone from the hip (specifically the femoral neck) are few, and those that exist are mostly consistent with studies of bone tissue from the femoral diaphysis. Cortical bone fracture mechanics highlights that there are multiple determinants of bone quality and therefore fracture risk and its assessment. There is still much more to learn concerning the tissue-level mechanisms of bone fragility. An improved understanding of these mechanisms will allow for the development of better diagnostic tools and therapeutic measures for bone fragility and fracture.
... At the macroscopic scale, bone is composed of cortical bone and trabecular bone. Encouraged by the idea that an accurate evaluation of bone quality could potentially be a predictor of risk of bone fracture, recent studies on the fracture properties of bone have focused on understanding the origin of bone toughness and its resistance to crack propagation in relation to bone's multi-scale structure [2], [3]. Despite the current understanding of the origins and mechanisms of toughening in human bone, it is still not fully understood how specific disease states can affect these mechanisms and how certain therapies can improve bone toughness to reduce the fracture risk. ...
... In the study, the behaviour of all specimens was predominantly non-elastic [5]. Therefore, an elastic-plastic fracture mechanics (EPFM) parameter, J-integral was calculated based on British Standard BS 7448-1 [6]: (2) where S is the bending span, F is the applied force, f(a o /W) is a function of (a o /W) , v is Poisson's ratio, E is elastic modulus, U p is the plastic part of area under plot of force versus specimen displacement along the load-line, B is the specimen's thickness, W is the effective width of the test specimen and a 0 the average original crack length. ...
Bones are the main structural components of a skeleton in our body. They run as a special role in the body providing its shape maintenance, protection of internal organs and transmission of forces. Their structural integrity is essential for the quality of life. Unfortunately, bones can only sustains loads until it reach a certain limit. Understanding fracture behaviour of bone is necessary for prevention and diagnosis of trauma. This paper aims to review and update readers on current published research explicitly related to bone fracture analysis conducted by three point bending test. Past studies have shown that most analysis have been done on fracture mechanism and how to find fracture toughness of the bone. Besides using an experimental approached, some of the research used Finite Element (FE) as a tool to investigate the fracture mechanism.
... Mechanical energy absorption materials such as cast-iron, steel, and foam [1][2][3] have been widely used. Interestingly, nature has provided energy absorption materials (EAM) such as bones [4] and nacre [5], which have inspired the development of novel materials with greater energy absorption capacities, such as steel foam with a mechanical energy absorption capacity of about 183.23 MJ/m 3 [2]. However, these energy absorption capacities may not be sufficient for the urgent needs of the current industry. ...
The C3B, C3N, and NB-based honeycomb structures (GBNHs) are promising candidates for creating parts that can absorb energy when subjected to external forces. However, the mechanical energy absorption capacity of GBNHs can be changed significantly under different temperatures. In this study, we focus on investigating the effect of temperature on the energy absorption capacity and mechanical properties of GBNHs via molecular dynamics (MD). The obtained results show that the energy absorption capacity of GBNHs sharply increases with the decrease in temperature. At room temperature, the average mechanical energy absorption capacity of GBNHs is over about 5500 MJ/m3 and the everage anti-penetration ability can reach over 9300 MJ/m3. The potential of GBHNs exceed the graphene-based carbon honeycombs (GCHs) by about 5440 MJ/m3. Besides, the temperature also affects the mechanical properties of GBNHs. The critical strain is
decreased with increasing temperature. These obtained results provide important bases for GBNH in the production of energy-absorbing components.
... Drawing inspiration from natural materials like bone, nacre, tooth enamel, and sponge spicules, the "topologically interlocked concept" involves assembling hard and stiff building blocks along weaker interfaces [6] [7] [8] [9]. This strategy provides a means to transform inherently brittle and rigid components into materials with enhanced toughness and durability [10][11][12][13][14][15][16]. ...
Precise material architectures and interfaces can render conventional ceramics tough, deformable and damage-resistant, offering a wide range of possibilities beyond those provided by conventional ones. This study explores the mechanical properties of topologically interlocked ceramic panels by systematically varying architectural parameters (i.e., interlocking angles and building block sizes) using a combination of experimental testing and finite element modeling based on COMSOL Multiphysics®. Three distinct designs were fabricated using digital laser manufacturing, categorized as designs with constant interlocking angles and tile sizes, constant interlocking angles and variable tile sizes, and variable interlocking angles and tile sizes and subjected them to out-of-plane quasi-static loads. The results show substantial enhancements in toughness (up to 110%) and strength (up to 120%) for ceramics with varying building block sizes, compared to those with constant block sizes. Additionally, these ceramics exhibit increased flexibility (up to 130%) compared to plain ceramics. Larger interlocking angles contribute to superior mechanical properties, fostering increased energy absorption and stability. The study also investigates post-failure behavior, revealing that increasing length ratios consistently augment the energy absorption. This research highlights the potential of these materials for flexible protection and the importance of controlling architectural parameters based on the interlocking angle and building block size to optimize performance while minimizing damage.
... Thus, the effective tangent operator is defined as: Table 1 summarizes the equations of the proposed model, and Fig. 3 details the algorithm of the Impl-Ex scheme. [7]; c [63]; d [64]; e [65]; f [32]; g [37]; h [11] i [66,67] ** The Haversian canal is considered as a structural void ***The Poisson's ratio is 0.3 for all the components ...
The cortical bone is a hierarchical composite material that, at the microscale, is segmented in an interstitial matrix, cement line, osteons, and Haversian canals. The cracking of the structure at this scale directly influences the macro behavior, and, in this context, the cement line has a protagonist role. In this sense, this work aims to simulate the crack initiation and propagation processes via cortical bone microstructure modeling with a two-dimensional mesh fragmentation technique that captures the mechanical relevance of its constituents. In this approach, high aspect ratio elements are inserted between the regular constant strain triangle finite elements to define potential crack paths a priori. The crack behavior is described using a composed damage model with two scalar damage variables, which is integrated by an implicit-explicit (Impl-Ex) scheme to avoid convergence problems usually found in numerical simulations involving multiple cracks. The approach's capability of modeling the failure process in cortical bone microstructure is investigated by simulating four conceptual problems and one example based on a digital image of an experimental test. The results obtained in terms of crack pattern and failure mechanisms agree with those described in the literature, demonstrating that the numerical tool is promising to simulate the complex failure mechanisms in cortical bone, considering the properties of its distinct phases.
... Interestingly, similar mechanisms have been reported at higher length scales of the tissue, where osteons have been reported to deflect the crack path under longitudinal loading at the microscale (Mohsin et al., 2006). Surprisingly, at that scale, cracks tended to propagate in cement lines, which were reported to have lower toughness due to hyper-mineralization (lower Vf MCF ) (Koester et al., 2008;Nalla et al., 2003;Zimmermann et al., 2009). Our findings have observed (and enumerated) that MCFs have similar capacity for acting as barriers to crack propagation at the ultrastructural level and can ultimately increase the toughness of tissue. ...
Bone is a naturally occurring composite material composed of a stiff mineral phase and a compliant organic matrix of collagen and non-collagenous proteins (NCP). While diverse mineral morphologies such as platelets and grains have been documented, the precise role of individual constituents, and their morphology, remains poorly understood. To understand the role of constituent morphology on the fracture behaviour of lamellar bone, a damage based representative volume element (RVE) was developed, which considered various mineral morphologies and mineralised collagen fibril (MCF) configurations. This model framework incorporated a novel phase-field damage model to predict the onset and evolution of damage at mineral-mineral and mineral-MCF interfaces. It was found that platelet-based mineral morphologies had superior mechanical performance over their granular counterparts, owing to their higher load-bearing capacity, resulting from a higher aspect ratio. It was also found that MCFs had a remarkable capacity for energy dissipation under axial loading, with these fibrillar structures acting as barriers to crack propagation, thereby enhancing overall elongation and toughness. Interestingly, the presence of extrafibrillar platelet-based minerals also provided an additional toughening through a similar mechanism, whereby these structures also inhibited crack propagation. These findings demonstrate that the two primary constituent materials of lamellar bone play a key role in its toughening behaviour, with combined effect by both mineral and MCFs to inhibit crack propagation at this scale. These results have provided novel insight into the fracture behaviour of lamellar bone, enhancing our understanding of microstructure-property relationships at the sub-tissue level.
... For the composites with weak interfaces, interfacial debonding contributes to energy dissipation, which serves as a source of toughening in composites (Chua and Piggott 1985;Dastjerdi et al. 2013). In addition, crack interaction with weak interfaces in fiber reinforced composites leads to crack deflection, which reduces stress levels at the crack tip and enhances fracture resistance (He and Hutchinson 1989;Koester et al. 2008;Parmigiani and Thouless 2006). ...
Intermittent beading is a novel design that holds great potential for simultaneous improvement of strength and toughness of composites. Despite the progress in fabrication of beaded fiber composites, the mechanisms of fracture in such composites are largely unknown. In this study, calculations are carried out for interfacial debonding in a beaded fiber composite subjected to tensile loading. The post-yield strain softening followed by strain hardening of polymer matrix, and debonding of the fiber-bead, bead-matrix and fiber-matrix interfaces are accounted for in the numerical analyses. It is found that interfacial debonding can activate plastic deformation in the bead and polymer matrix, contributing to toughening of the beaded fiber composite. We have identified that the bead-matrix interfacial debonding is the major mechanism controlling plastic deformation in the matrix. The low cohesive strength of the bead-matrix interface plays a role in suppressing development of shear bands in the polymer matrix, enhancing plastic dissipation of the composite. The high toughness of the bead-matrix interface enables large plastic zone in the matrix, promoting plastic dissipation. For the fiber-bead interface, there is an increase in plastic dissipation of the composite with decreasing cohesive strength, while high interface toughness can amplify plastic dissipation. In addition, we reveal that weak fiber-matrix interface is capable of spreading plastic deformation in the matrix, increasing plastic dissipation of the composite. The findings of this study can shed new light on the fracture mechanisms of beaded fiber composites.
... Stiff biological materials (SBMs), such as nacre and bone, are natural layered composites that are known for having remarkable fracture toughness that can be orders of magnitude higher than that of the brittle ceramics that dominates their composition (Jackson et al., 1988;Currey, 1977;Sarikaya, 1994;Menig et al., 2000;Koester et al., 2008;Wegst et al., 2015). The key to such enhancement in fracture toughness lies in their lamellar architectures, which are the intricate arrangements of ceramic and organic phases at the sub-micron scales (see Fig. 1(A) & (B)). ...
Layered architectures are prevalent in tough biological composites, such as nacre and bone. Another example of a biological composite with layered architecture is the skeletal elements—called spicules—from the sponge Euplectella aspergillum. Based on the similarities between the architectures, it has been speculated that the spicules are also tough. Such speculation is in part supported by a sequence of sudden force drops (sawtooth patterns) that are observed in the spicules' force-displacement curves from flexural tests, which are thought to reflect the operation of fracture toughness enhancing mechanisms. In this study, we performed three-point bending tests on the spicules, which also yielded the aforementioned sawtooth patterns. However, based on the analysis of the micrographs obtained during the tests, we found that the sawtooth patterns were in fact a consequence of slip events in the flexural tests. This is put into perspective by our recent study, in which we showed that the spicules' layered architecture contributes minimally to their toughness, and that the toughness enhancement in them is meager in comparison to what is observed in bone and nacre [Monn MA, Vijaykumar K, Kochiyama S, Kesari H (2020): Nat Commun 11:373]. Our past and current results underline the importance of inferring a material's fracture toughness through direct measurements, rather than relying on visual similarities in architectures or force-displacement curve patterns. Our results also suggest that since the spicules do not possess remarkable toughness, re-examining the mechanical function of the spicule's intricate architecture could lead to the discovery of new engineering design principles.
... It can provide detailed information on the behavior of materials during mechanical testing that static observation cannot. Some studies performed in situ SEM mechanical tests on transverse and longitudinal bone specimens to further verify the anisotropy of bone mechanical properties and proposed that the mechanical properties of the longitudinal and transverse orientations of the bone were different, which could be attributed to differences in the direction of microcracks [138]. Furthermore, a study reported a novel device with a confocal Raman microscope that enables uniaxial stretching of microfibers ranging in diameter from 10 to 100 microns in length [135]. ...
Bone has a special structure that is both stiff and elastic, and the composition of bone confers it with an exceptional mechanical property. However, bone substitute materials that are made of the same hydroxyapatite (HA) and collagen do not offer the same mechanical properties. It is important for bionic bone preparation to understand the structure of bone and the mineralization process and factors. In this paper, the research on the mineralization of collagen is reviewed in terms of the mechanical properties in recent years. Firstly, the structure and mechanical properties of bone are analyzed, and the differences of bone in different parts are described. Then, different scaffolds for bone repair are suggested considering bone repair sites. Mineralized collagen seems to be a better option for new composite scaffolds. Last, the paper introduces the most common method to prepare mineralized collagen and summarizes the factors influencing collagen mineralization and methods to analyze its mechanical properties. In conclusion, mineralized collagen is thought to be an ideal bone substitute material because it promotes faster development. Among the factors that promote collagen mineralization, more attention should be given to the mechanical loading factors of bone.
... Trabeculae crossarrange in the internal bone to generate cancellous bone, which has a loose structure, but its arrangement and thickness are crucial for the bone to withstand pressure and weight. [23][24][25][26] Bone tissue is made up of bone matrix and other cells at the microscopic structure. The bone matrix is composed of both inorganic and organic substances. ...
Bone tumors, including primary bone tumors, invasive bone tumors, metastatic bone tumors, and others, are one of the most clinical difficulties in orthopedics. Once these tumors have grown and developed in the bone system, they will interact with osteocytes and other environmental cells in the bone system's microenvironment, leading to the eventual damage of the bone's physical structure. Surgical procedures for bone tumors may result in permanent defects. The dual-efficacy of tissue regeneration and tumor treatment has made biomaterial scaffolds frequently used in treating bone tumors. 3D printing technology, also known as additive manufacturing or rapid printing prototype, is the transformation of 3D computer models into physical models through deposition, curing, and material fusion of successive layers. Adjustable shape, porosity/pore size, and other mechanical properties are an advantage of 3D-printed objects, unlike natural and synthetic material with fixed qualities. Researchers have demonstrated the significant role of diverse 3D-printed biological scaffolds in the treatment for bone tumors and the regeneration of bone tissue, and that they enhanced various performance of the products. Based on the characteristics of bone tumors, this review synthesized the findings of current researchers on the application of various 3D-printed biological scaffolds including bioceramic scaffold, metal alloy scaffold and nano-scaffold, in bone tumors and discussed the advantages, disadvantages, and future application prospects of various types of 3D-printed biological scaffolds. Finally, the future development trend of 3D-printed biological scaffolds in bone tumor is summarized, providing a theoretical foundation and a larger outlook for the use of biological scaffolds in the treatment of patients with bone tumors.
Nacre is a classic model, providing an inspiration for fabricating high‐performance bulk nanocomposites with the two‐dimensional platelets. However, the “brick” of nacre, aragonite platelet, is an ideal building block for making high‐performance bulk nanocomposites. Herein, we demonstrated a strong and tough conductive nacre through reassembling aragonite platelets with bridged by MXene nanosheets and hydrogen bonding, not only providing high mechanical properties but also excellent electrical conductivity. The flexural strength and fracture toughness of the obtained conductive nacre reach ~282 MPa and ~6.3 MPa m 1/2 , which is 1.6 and 1.6 times higher than that of natural nacre, respectively. These properties are attributed to densification and high orientation degree of the conductive nacre, which is effectively induced by the combined interactions of hydrogen bonding and MXene nanosheets bridging. The crack propagations in conductive nacre are effectively inhibited through crack deflection with hydrogen bonding, and MXene nanosheets bridging between aragonite platelets. In addition, our conductive nacre also provides a self‐monitoring function for structural damage and offers exceptional electromagnetic interference shielding performance. Our strategy of reassembling the aragonite platelets exfoliated from waste nacre into high‐performance artificial nacre, provides an avenue for fabricating high‐performance bulk nanocomposites through the sustainable reutilization of shell resources.
Nacre is a classic model, providing an inspiration for fabricating high‐performance bulk nanocomposites with the two‐dimensional platelets. However, the “brick” of nacre, aragonite platelet, is an ideal building block for making high‐performance bulk nanocomposites. Herein, we demonstrated a strong and tough conductive nacre through reassembling aragonite platelets with bridged by MXene nanosheets and hydrogen bonding, not only providing high mechanical properties but also excellent electrical conductivity. The flexural strength and fracture toughness of the obtained conductive nacre reach ~282 MPa and ~6.3 MPa m1/2, which is 1.6 and 1.6 times higher than that of natural nacre, respectively. These properties are attributed to densification and high orientation degree of the conductive nacre, which is effectively induced by the combined interactions of hydrogen bonding and MXene nanosheets bridging. The crack propagations in conductive nacre are effectively inhibited through crack deflection with hydrogen bonding, and MXene nanosheets bridging between aragonite platelets. In addition, our conductive nacre also provides a self‐monitoring function for structural damage and offers exceptional electromagnetic interference shielding performance. Our strategy of reassembling the aragonite platelets exfoliated from waste nacre into high‐performance artificial nacre, provides an avenue for fabricating high‐performance bulk nanocomposites through the sustainable reutilization of shell resources.
When porous materials are subjected to compressive loads, localized failure chains, commonly termed as anticracks, can occur and cause large-scale structural failure. Similar to tensile and shear cracks, the resistance to anticrack growth is governed by fracture toughness. Yet, nothing is known about the mixed-mode fracture toughness for highly porous materials subjected to shear and compression. We present novel fracture mechanical field experiments tailored for weak layers in a natural snowpack. Using a mechanical model for interpretation, we calculate the fracture toughness for anticrack growth for the full range of mode interactions, from pure shear to pure collapse. The measurements show that fracture toughness values are significantly larger in shear than in collapse, and suggest a power-law interaction between the anticrack propagation modes. Our results reveal new insights into the fracture characteristics of anticracks in highly porous materials and provide important benchmarks for computational modeling.
Little is known about the contribution of 3D surface geometry on the development of multi-layered tissues containing fibrous extracellular matrix components such as those found in bone. Here we elucidate the role of curvature in the formation of chiral, twisted plywood-like structures. Tissues consisting of murine pre-osteoblast cells (MC3T3-E1) were grown on 3D scaffolds with constant mean curvature and negative Gaussian curvature for up to 32 days. Using 3D fluorescence microscopy, the influence of surface curvature on actin stress-fiber alignment and chirality was investigated. To gain mechanistic insights, we did experiments with MC3T3-E1 cells deficient in nuclear A-type lamins or treated with drugs targeting cytoskeleton proteins. We find that wild type cells form a thick tissue with fibers predominantly aligned along directions of negative curvature, but exhibiting a twist in orientation with respect to older tissues. Fiber orientation is conserved below the tissue surface thus creating a twisted plywood like material. We further show that this alignment pattern strongly depends on structural components of the cells (A-type lamins, actin and myosin), showing a role of mechanosensing on tissue organisation. Our data indicate the importance of substrate curvature in the formation of 3D tissues and provides new insights into the emergence of chirality.
This review discusses recent advances, challenges, future research directions and perspectives in biomineralized tissues, providing in-depth insights into derived guidelines for design and preparation of high-performance biomimetic materials.
Fatigue failure is invariably the most crucial failure mode for metallic structural components. Most microstructural strategies for enhancing fatigue resistance are effective in suppressing either crack initiation or early-stage crack propagation, but often do not work for both synergistically. Here, we demonstrate that this challenge can be overcome by architecting a gradient structure consisting of a surface layer of nacre-like nanolaminates followed by multi-variant twinned structure in pure titanium. The surface nanolaminates are featured by regulated horizontal (lamellar parallel) high-angle grain boundaries and vertical (lamellar perpendicular) low-angle grain boundaries. The polarized accommodation of different types of grain boundaries to cyclic loading enhances the structural stability of surface nanolaminates against grain thickening and microstructure softening, thereby delaying surface roughening and thus crack nucleation. The decohesion of the nanolaminated grains along horizonal high-angle grain boundaries gives rise to an extraordinarily high frequency (~ 1.7×10 ³ times per mm) of fatigue crack deflection, which effectively reduces the fatigue crack propagation rate (by 2 orders of magnitude lower than the homogeneous coarse-grained counterpart). These intriguing features of the surface nanolaminates, along with the various toughening mechanisms activated in the subsurface twinned structure, result in a fatigue resistance that is far superior to the homogeneous and gradient structures with equiaxed grains. Our work on architecting the surface nanolaminates in gradient structure provides a scalable and sustainable strategy in designing fatigue-resistant alloys by structuring gradients/heterogeneity.
Carbonate source rock reservoirs often exhibit pronounced lamination, resulting in fine-scale facies and rock property variations that are not adequately captured by open hole logs. Precise characterization of reservoir heterogeneity across multiple scales is essential for accurate hydraulic fracture design, landing zone optimization, and ultimately enhancing well productivity. This paper presents a comprehensive workflow that utilizes specialized core-logging equipment to precisely define the thinly layered nature of the cored section, enabling centimeter-scale resolution analysis of vertical heterogeneity. The acquired data allow us to define distinct rock classes with unique and characteristics behaviors, based on multi-dimensional data patterns that mirror their unique and characteristic behaviors in rock properties. The rock classification facilitates the quantitative definition of vertical heterogeneity, capturing the fine-scale property variations within the core section. It also informs the selection of core samples for laboratory rock property characterization, ensuring that the representation of the observed variability is maximized. By integrating the multidimensional core-logging data with the discrete laboratory rock property results, we construct centimeter-resolution petrophysical and geomechanical models that result in higher fidelity reservoir characterization of thinly layered carbonate source reservoirs and more representative numerical simulations, thereby enhancing our ability to optimize hydraulic fracturing and well productivity. The workflow also includes upscaling the resolution of downhole wireline log measurements, utilizing image log measurements as structural constraints to the process, thereby enabling the derivation of high-resolution petrophysical and geomechanical properties in non-cored sections of the same well and in neighboring wells without core data. The study revealed cyclic reservoir and mechanical property variability, particularly in intervals with higher organic content, which were critical for understanding productivity, evaluating the in-situ stress, and for hydraulic fracture modeling. This level of detail in reservoir characterization is not achievable when using conventional resolution wireline logs.
Intermittent beading is a promising design strategy that enables simultaneous improvement of strength and toughness of fiber-reinforced composites. In spite of the potential for amplification in mechanical properties, the failure mechanisms of beaded fiber composites are not fully understood. In this study, calculations are carried out for breakage of beaded fibers in the polymer matrix composites. The plastic deformation of polymer matrix and debonding of the bead-matrix, fiber-bead and fiber-matrix interfaces are accounted for in the numerical analyses. It is found that the location of fiber break is governed by toughness of the fiber-bead interface and fiber strength. The low toughness of fiber-bead interface promotes the emergence of break inside bead, and high fiber strength is capable of activating break outside bead. The break at the edge of bead prevails in most cases. We have further revealed that the fiber-matrix interface with high strength and enhanced toughness can give rise to large amount of fiber breaks, while low degree of fiber cracking emerges in the case of strong fiber-bead interface. For the bead-matrix interface, the intermediate interfacial strength generates a high degree of fiber breaks and low interfacial toughness suppresses fiber cracking, leading to small amount of fiber breaks. In addition, the dependence of plastic dissipation in the polymer matrix on fiber breakage is elucidated.
Composites with high strength and high fracture resistance are desirable for structural and protective applications. Most composites, however, suffer from poor damage tolerance and are prone to unpredictable fractures. Understanding the behavior of materials with an irregular reinforcement phase offers fundamental guidelines for tailoring their performance. Here, we study the fracture nucleation and propagation in two phase composites, as a function of the topology of their irregular microstructures. We use a stochastic algorithm to design the polymeric reinforcing network, achieving independent control of topology and geometry of the microstructure. By tuning the local connectivity of isodense tiles and their assembly into larger structures, we tailor the mechanical and fracture properties of the architected composites, at the local and global scale. Finally, combining different reinforcing networks into a spatially determined meso‐scale assembly, we demonstrate how the spatial propagation of fractures in architected composite materials can be designed and controlled a priori.
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Nature with its abundant source offers numerous inspirations for structural and engineering designs. The oriented membranes stacked with bouligand structures in the fish scales show an outstanding combination of high strength and crack‐resistance. Although the applications of hard biomimetic composites have been reported, the structures have not been utilized in soft materials. Inspired by the scales of various fishes, we use and stack electrospun membranes to fabricate bouligand elastomers, including orthogonal‐plywood, single‐bouligand, and double‐bouligand structures. We systematically investigated the effects of different structures on the properties of elastomers and explained possible mechanism using finite element analysis. The stiffness and fatigue characteristics of these biomimetic elastomers with the above structures were improved compared with the original membranes, especially the elastomers with a single‐bouligand structure, which can undergo 5000 cycles at a maximum strain of 35% without complete failure. The crack only propagates to half of the width of the elastomer with a remaining strength of 50% of its original strength. Moreover, the mechanical performance can be adjusted by regulating the proportion of the components. The excellent crack‐resistant properties and transparency promote its various potential applications.
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Ceramic materials are widely used in engineering field because of their good physical and chemical properties. The poor mechanical properties of traditional ceramics seriously limit the development of ceramic materials and have attracted extensive attention since its birth. The development of high toughness, light weight, and functional ceramic materials has long been the pursuit of materials scientists. Since ancient times, nature has been the source of all kinds of human technological ideas, engineering principles, and major inventions. The functional structure of biology provides a good research object for the bionic design and preparation of ceramic materials. Therefore, it is necessary to summarize the functional structures and mechanisms in nature and biomimetic preparation technology. The purpose of this review is to provide guidance for the functionalized biomimetic design and efficient preparation of ceramic materials. Some typical functional examples in nature are introduced in detail, and several representative biomimetic preparation methods are listed. Finally, the performance and application status of biomimetic ceramics are summarized, and the future development direction of biomimetic ceramic materials is prospected.
Bone has a complex hierarchical structure with structural integration from nm to cm. The understanding of bone structure is developing rapidly due to improvements in available methodologies that allow unravelling structures across several length scales. These methods include advances in electron microscopy, in particular, focused ion beam scanning electron microscopy (FIB‐SEM), confocal laser scanning microscopy techniques, X‐ray imaging, X‐ray diffraction tomography (XRD‐CT), and tensor tomography (small angle X‐ray scattering tensor tomgraphy, SAXS‐TT and wide angle X‐ray scattering tensor tomgraphy, WAXS‐TT). Special emphasis is placed on the latter X‐ray techniques that are emerging into powerful tools. Through a review of selected recent results on the structure of the bone matrix as well as the lacuno‐canalicular network housing the osteocyte cells of bone, it is proposed that bone is more heterogeneous than typically described and that local variation in composition and crystallography may play a significant role in bone biology in health and disease.
Multilayer structures are not only applied to manipulate properties of synthetic polymer materials such as rainbow films and barrier films but also widely discovered in natural materials like nacre. In this work, in situ formation of an interconnected multi-nanolayer (IMN) structure in poly(butylene adipate-co-terephthalate) (PBAT)/poly(butylene succinate) (PBS) cocontinuous blends is designed by an extensional flow field during a "casting-thermal stretching" process, combining the properties of two components to a large extent. Hierarchical structures including phase morphology, crystal structure, and lamellar crystals in IMN films have been revealed, which clearly identifies the crucial role of extensional flow. The oriented PBAT phase in the IMN structure can be beneficial to the epitaxial growth of PBS crystals onto the PBAT nanolayers, thus improving interfacial adhesions. Furthermore, intense extensional stress can also promote crystallinity and thicken the lamellar structure. Given such distinct features in the fully biodegradable films, a simultaneous enhancement in tear strength, tensile strength, and puncture resistance has been achieved. To the best of our knowledge, the tear strength of IMN films about 285.9 kN/m is the highest level in the previous works of this system. Moreover, the proposed fabrication way of the IMN structure is facile and scalable, which is highly expected to be an efficient strategy for development of structured biodegradable polymers with excellent comprehensive properties.
Organisms use gene and cell engineering to tailor the mineralization process and synthesize structure composites with special functions and favorable properties. This spurs scientists to design functional materials based on learning from nature. Herein, a systematic review of the biomimetic synthesis and hierarchical structure design of calcium carbonate–based minerals is presented. First, biomimetic synthesis strategies, including additive‐induced, template‐oriented, and gel‐mediated routes to direct the construction of the hierarchical structure, are reviewed. The molecular‐recognition technique and directional assembly pathway are then summarized to precisely describe the interactions between inorganic minerals and organic matter, and direct the mineral growth. Next, the underlying mineralization mechanisms governing the evolution of the complex morphology and structure are discussed. Nonclassical pathways that control mineral growth, including the theories of the amorphous phase, oriented attachment, mesocrystal formation, and liquid precursor, are concluded. Finally, herein, the applications of calcium carbonate–based minerals are discussed. Unique hierarchical structure endows minerals with special functions, including optical performance, biomedical applications, and environmental and ecological restoration. Overall, in this report, the biomimetic synthesis of calcium carbonate–based minerals is reviewed, covering the fundamental principles, construction of the hierarchical structure, underlying mechanisms of mineral growth, and functional designs.
Compact, mineralized cortical bone tissues are often concealed on magnetic resonance (MR) images. Recent development of MR instruments and pulse techniques has yielded significant advances in acquiring anatomical and physiological information from cortical bone despite its poor ¹H signals. This work demonstrates the first MR research on cortical bones under an ultrahigh magnetic field of 14 T. The ¹H signals of different mammalian species exhibit multi‐exponential decays of three characteristic T2 or T2* values: 0.1–0.5 ms, 1–4 ms, and 4–8 ms. Systematic sample comparisons attribute these T2/T2* value ranges to collagen‐bound water, pore water, and lipids, respectively. Ultrashort echo time (UTE) imaging under 14 T yielded spatial resolutions of 20–80 microns, which resolves the 3D anatomy of the Haversian canals. The T2* relaxation characteristics further allow spatial classifications of collagen, pore water and lipids in human specimens. The study achieves a record of the spatial resolution for MR imaging in bone and shows that ultrahigh‐field MR has the unique ability to differentiate the soft and organic compartments in bone tissues.
The denaturation of collagen at the molecular level in bone and dentin can impact their structure and properties, leading to increased brittleness in pathological diseases such as osteogenesis imperfecta, dentinogenesis imperfecta, diabetes, and cancer. This study investigates the relationship between collagen denaturation and the macroscale resistance of bone and dentin. Through heat treatment at \(160{^{\circ }}\hbox {C}\) on bovine bone and human dentin, the effects of collagen denaturation on macroscale flexural strength, scanning electron microscopy, and transmission electron microscopy imaging of micro- and nanostructure were studied. The results show that collagen denaturation decreases the resistance of bone and dentin to fracture, even though collagen denaturation did not impact the mineral organization around and inside collagen fibrils. This is attributable to (1) a reduction in bone and dentin ability to deform (e.g., 40–75% decrease in strain to failure) and to resist fracture (e.g., 83–95% decrease in work to fracture) properties and (2) to a smoother crack path with less crack deflection around microstructural features. Reduction in deformation and toughness not only removed plastic deformation but also drastically decreased elastic deformation and elastic work to fracture in all tissues. However, the elastic modulus was only affected in radial-oriented bone samples where collagen fibrils are oriented perpendicularly to crack opening forces. This study highlights the crucial role of collagen molecule integrity and orientation in bone/dentin deformability and resistance.
Biological materials such as skins, bones, teeth or seashells boast remarkable structures and mechanisms, many of them unmatched by engineering materials. In these materials, fracture toughness is key to achieve high strength, reliability, robustness, damage tolerance and notch performance, and to fulfil critical structural functions in the organism. In this chapter, we review and discuss some of the main strategies found in biological materials to resist the propagation of cracks and to reach high toughness. We discuss six major groups of natural materials through specific examples: a uniaxial fiber composite (tendon), a laminated composite (fish scales), a natural elastomer (skin), a mineralized brick and mortar composite (nacre), three-dimensional mineralized cross plies (conch shells, tooth enamel) and a complex hierarchical material (bone). The composition, architecture, mechanics of deformation and fracture, and overall performance is reviewed for each of these materials. The chapter concludes with a summary of the broad strategies deployed in biological materials to manage damage and prevent crack propagation. These lessons are now inspiring the next generation of structural materials.
Physiological and pathological processes such as aging, diseases, treatments, and lactation can alter lacunar-canalicular network (LCN) morphology and perilacunar region properties. These modifications can impact the mechanical environment of osteocytes which in turn can influence osteocyte mechanosensitivity and the remodeling process. In this study, we aim to evaluate how the modifications in the canalicular morphology, lacunar density, and the perilacunar region properties influence the local mechanical environment of LCN and the apparent bone properties using 3D finite element (FE) modeling. The simulation results showed that reduced perilacunar region elastic modulus led to a detectable change in apparent elastic modulus of the bone. The increase in canalicular density, length, and diameter did not influence the strain amplification in the models but they increased the amount of highly strained bone around LCN. Change in lacunar density did not influence the strain amplification and the amount of highly strained regions on LCN surfaces. Reduction in perilacunar elastic modulus increased both the strain amplification and the volume of highly strained tissue around and on the surface of LCN. The FE models of LCN in this study can be utilized to quantify the influence of modifications in canalicular morphology, lacunar density, and perilacunar region properties on the apparent bone properties and the local mechanical environment of LCN. This information is important in gaining a better understanding of how mechanical environment of osteocytes is influenced by the modifications in LCN morphology and perilacunar region properties due to physiological and pathological processes.
There has been growing interest of late in the fracture properties of human bone. As understanding such properties in the context of the hierarchical microstructure of bone is of obvious importance, this study addresses the evolution of the in vitro fracture toughness with crack extension (Resistance-curve behavior) in terms of the salient mechanisms involved. Fracture-mechanics based measurements were performed on compact-tension specimens hydrated in Hanks' Balanced Salt Solution using cortical bone from mid-diaphyses of 34-41 year-old human humeri. Post-test observations of the crack path were made by optical microscopy and three-dimensional X-ray computed tomography. The fracture toughness was found to rise linearly with crack extension with a mean crack-initiation toughness of Ko ∼ 2.0 MPa√m for crack growth in the proximal-distal direction. The increasing cracking resistance had its origins in several toughening mechanisms, most notably crack bridging by uncracked ligaments. Uncracked-ligament bridging, which was observed by tomography in the wake of the crack, was identified as the dominant toughening mechanism responsible for the observed Rcurve behavior through compliance-based experiments. The extent and nature of the bridging zone was examined quantitatively using multi-cutting compliance experiments in order to assess the bridging stress distribution. The results obtained in this study provide an improved understanding of the mechanisms associated with the failure of cortical bone, and as such are of importance from the perspective of developing a realistic framework for fracture risk assessment, and for determining how the increasing propensity for fracture with age can be prevented.
A solution is presented for the elastic stress intensity factors at the tip of a slightly curved or kinked two-dimensional crack. The solution is accurate to first order in the deviation of the crack surface from a straight line and is carried out by perturbation procedures analogous to those of Banichuk [1] and Goldstein and Salganik [2, 3]. Comparison with exact solutions for circular arc cracks and straight cracks with kinks indicates that the first order solution is numerically accurate for considerable deviations from straightness. The solution is applied to fromulate an equation for the path of crack growth, on the assumption that the path is characterized by pure Mode I conditions (i.e., K II=0) at the advancing tip. This method confirms the dependence of the stability, under Mode I loading, of a straight crack path on the sign of the non-singular stress term, representing tensile stress T acting parallel to the crack, in the Irwin-Williams expansion of the crack tip field. The straight path is shown to be stable under Mode I loading for TT>0.
A line integral is exhibited which has the same value for all paths surrounding the tip of a notch in the two-dimensional strain field of an elastic or deformation-type elastic-plastic material. Appropriate integration path choices serve both to relate the integral to the near tip deformations and, in many cases, to permit its direct evaluation. This averaged measure of the near tip field leads to approximate solutions for several strain-concentration problems. Contained perfectly plastic deformation near a crack tip is analyzed for the plane-strain case with the aid of the slip-line theory. Near tip stresses are shown to be significantly elevated by hydrostatic tension, and a strain singularity results varying inversely with distance from the tip in centered fan regions above and below the tip. Approximate estimates are given for the strain intensity, plastic zone size, and crack tip opening displacement, and the important role of large geometry changes in crack blunting is noted. Another application leads to a general solution for crack tip separations in the Barenblatt-Dugdale crack model. A proof follows on the equivalence of the Griffith energy balance and cohesive force theories of elastic brittle fracture, and hardening behavior is included in a model for plane-stress yielding. A final application leads to approximate estimates of strain concentrations at smooth-ended notch tips in elastic and elastic-plastic materials.
Our bones are full of cracks, which form and grow as a result of daily loading activities. Bone is the major structural material in our bodies. Although weaker than many engineering materials, it has one trick that keeps it ahead - it can repair itself. Small cracks, which grow under cyclic stresses by the mechanism of fatigue, can be detected and removed before they become long enough to be dangerous. This article reviews the work that has been done to understand how cracks form and grow in bone, and how they can be detected and repaired in a timely manner. This is truly an interdisciplinary research field, requiring the close cooperation of materials scientists, biologists and engineers.
Age-related changes in the skeleton often lead to an increase in the susceptibility of bone to fracture. The purpose of this study was to determine whether differences in material properties between the osteonal and interstitial regions of bone have an effect on bone fracture properties. Parameters such as longitudinal fracture toughness, transverse fracture toughness, porosity, interstitial microhardness, osteonal microhardness, bone density, and weight fractions of the mineral and organic phases of bone were examined as a function of age using female baboon femurs. With increasing age, the longitudinal fracture toughness decreased significantly as did transverse fracture toughness, whereas the interstitial microhardness increased. However, no significant differences in the other parameters were observed as a function of age. Using the ratio of interstitial microhardness to osteonal microhardness as a measure of the differences in the material properties in these two regions, correlation analysis revealed that the longitudinal fracture toughness of bone has a significant correlation with the microhardness ratio. Localized differences in material properties between osteonal and interstitial regions of bone increase with age; such differences may result in high stress concentrations at cement lines and facilitate longitudinal crack propagation.
Properties of the organic matrix of bone as well as its function in the microstructure could be the key to the remarkable mechanical properties of bone. Previously, it was found that on the molecular level, calcium-mediated sacrificial bonds increased stiffness and enhanced energy dissipation in bone constituent molecules. Here we present evidence for how this sacrificial bond and hidden length mechanism contributes to the mechanical properties of the bone composite, by investigating the nanoscale arrangement of the bone constituents and their interactions. We find evidence that bone consists of mineralized collagen fibrils and a non-fibrillar organic matrix, which acts as a 'glue' that holds the mineralized fibrils together. We believe that this glue may resist the separation of mineralized collagen fibrils. As in the case of the sacrificial bonds in single molecules, the effectiveness of this mechanism increases with the presence of Ca2+ ions.
Bone, with a hierarchical structure that spans from the nano-scale to the macro-scale and a composite design composed of nano-sized mineral crystals embedded in an organic matrix, has been shown to have several toughening mechanisms that increases its toughness. These mechanisms can stop, slow, or deflect crack propagation and cause bone to have a moderate amount of apparent plastic deformation before fracture. In addition, bone contains a high volumetric percentage of organics and water that makes it behave nonlinearly before fracture. Many researchers used strength or critical stress intensity factor (fracture toughness) to characterize the mechanical property of bone. However, these parameters do not account for the energy spent in plastic deformation before bone fracture. To accurately describe the mechanical characteristics of bone, we applied elastic-plastic fracture mechanics to study bone's fracture toughness. The J integral, a parameter that estimates both the energies consumed in the elastic and plastic deformations, was used to quantify the total energy spent before bone fracture. Twenty cortical bone specimens were cut from the mid-diaphysis of bovine femurs. Ten of them were prepared to undergo transverse fracture and the other 10 were prepared to undergo longitudinal fracture. The specimens were prepared following the apparatus suggested in ASTM E1820 and tested in distilled water at 37 degrees C. The average J integral of the transverse-fractured specimens was found to be 6.6 kPa m, which is 187% greater than that of longitudinal-fractured specimens (2.3 kPa m). The energy spent in the plastic deformation of the longitudinal-fractured and transverse-fractured bovine specimens was found to be 3.6-4.1 times the energy spent in the elastic deformation. This study shows that the toughness of bone estimated using the J integral is much greater than the toughness measured using the critical stress intensity factor. We suggest that the J integral method is a better technique in estimating the toughness of bone.
Based on the microscopic analyses of cracks and correlational studies demonstrating evidence for a relationship between fracture toughness and microstructure of cortical bone, an equation was derived for bone fracture toughness in longitudinal crack growth, using debonding at osteonal cement lines and weakening effect of pores as main crack mechanisms. The correlation between the measured and predicted values of fracture toughness was highly significant but weak for a single optimal value of matrix to cement line fracture toughness ratio. Using fracture toughness values and histomorphometrical parameters from an available data set, matrix to cement Line fracture toughness ratio was calculated for human femoral bone. Based on these calculations it is suggested that the effect of an osteon on fracture toughness will depend on the cement line's ability to compensate for the pore in an osteon. Matrix to cement line fracture toughness ratio significantly increased with increasing age, suggesting that the effectiveness of osteons in energy absorption may be reduced in the elderly due to a change in cement line properties. (C) 2000 John Wiley & Sons, Inc.
The fracture toughness of the right femoral neck, femoral shaft, and tibial shaft of matched cadaveric bones, ages 50 to 90 years, was compared. Results of this study indicate that tensile (G(Ic)) and shear (G(IIc)) fracture toughness vary depending on bone location. The femoral neck has the greatest resistance to crack initiation for both tension and shear loading while the femoral shaft has the least. The relationship between age and the fracture toughness of the femoral neck and shaft was investigated. G(c) of the femoral shaft significantly decreased with age for mode I and was nearly significant for mode II. Fracture toughness of the femoral neck did not change with age for the later decades of life. Implications of these findings are discussed. (C) 2000 John Wiley & Sons, Inc.
A molecular energy dissipation mechanism in the form of sacrificial bonds and hidden length was previously found in bone constituent molecules of which the efficiency increased with the presence of Ca^2+ ions in the experimental solution. Here we present evidence for how this sacrificial bond-hidden length mechanism contributes to the mechanical properties of the bone composite. From investigations into the nanoscale arrangement of the bone constituents in combination with pico-Newton adhesion force measurements between mineralized collagen fibrils, based on single molecule force spectroscopy, we find evidence that bone consists of mineralized collagen fibrils and a non fibrillar organic matrix which acts as a ``glue'' that holds the mineralized fibrils together. We propose that this ``glue'' resists the separation of mineralized collagen fibrils. Like in the case of the sacrificial bonds in single molecules, the effectiveness of this ``glue'' increases with the presence of Ca^2+ ions. We further investigate how this molecular scale strengthening mechanism increases the fracture toughness of the macroscopic material.
The stress distribution close to the tip of a crack which has a finite tip radius and which is being opened either by means of a remotely applied tension field sigmay,0 or by means of a concentrated force (e.g. a wedge driven into the crack) has been computed. It is shown that there exist tensile stresses (sigma_x) parallel to the plane of the crack and ahead of the crack tip. The maximum value of the tension sigma_x is an approximately constant fraction (~1/5) of the peak stress concentration sigmay,max. which usually causes crack propagation. Inside a brittle solid, if a plane of weakness or potential cleavage is present and is roughly normal to the plane of the original crack, this interface may break and produce a secondary crack in such a manner as to interfere with the progress of the primary crack. If the ratio of the adhesive strength of the interface to the general cohesive strength of the solid is in the right range large increases in the strength and toughness of otherwise brittle solids may result.
A fracture mechanics approach has been used to predict fracture toughness increases due to crack deflection around second phase particles. The analysis is based on a determination of the initial tilt and the maximum twist of the crack front between particles, which provides the basis for evaluating the deflection-induced reduction in crack driving force. Features found to be important in determining the toughness increase include the volume fraction of second phase, the particle morphology and aspect ratio, and the distribution of interparticle spacing. Predictions are compared with expected surface area increases.
A mechanics model of microcrack toughening is presented. The model predicts the magnitude of microcrack toughening as well as the existence of R -curve effects. The toughening is predicated on both the elastic modulus diminution in the microcrack process zone and the dilatation induced by microcracking. The modulus effect is relatively small and process-zone-size-independent. The dilatational effect is potentially more substantial, as well as being the primary source of the R curve. The dilatational contribution is also zone-size-dependent. The analysis demonstrates that microcrack toughening is less potent than transformation toughening.
The mechanisms of fatigue-crack propagation in ceramics and intermetallics are examined through a comparison of cyclic crack-growth behavior in ductile and brittle materials. Crack growth is considered to be a mutual competition between intrinsic mechanisms of crack advance ahead of the crack tip, which promote crack growth, and extrinsic mechanisms of crack-tip shielding behind the tip, which impede it. In this paper, we examine and model the widely differing nature of these mechanisms, with emphasis on behavior in ceramics at ambient and elevated temperatures, and compare their specific dependencies upon the alternating and maximum driving forces (e.g., ΔK and Kmax), thereby providing a useful distinction of the process of fatigue-crack propagation in these different classes of materials.
A fracture mechanics approach has been used to predict fracture toughness increases due to crack deflection around second phase particles. The analysis is based on a determination of the initial tilt and the maximum twist of the crack front between particles, which provides the basis for evaluating the deflection-induced reduction in crack driving force. Features found to be important in determining the toughness increase include the volume fraction of second phase, the particle morphology and aspect ratio, and the distribution of interparticle spacing. Predictions are compared with expected surface area increases.
The fracture mechanics parameters associated with the fracture of transversely oriented bovine femur compact tension specimens have been determined for a slowly propagating and stable crack, as a function of cross head speed. It was found that an increase in cross head speed from 1.7-33 × 10-6 m sec-1 produced an increase in the crack velocity from 2.1-27 × 10-5 m sec-1 and an associated increase in the critical strain energy release rate (Gc) from 920 to 2780 J m-2 and in the critical stress intensity factor (Kc) from 2.4 to 5.2 MN m- 3 2.
Linear elastic fracture mechanics was used to study longitudinal crack propagation in bovine compact bone. The resistance to crack initiation in slotted specimens was examined by measuring both the critical stress intensity factor, Kc, and the critical strain energy release rate, Gc. A change in specimen thickness (from 0.185 to 0.380 cm) did not affect the value of Kc (or Gc). A significant positive correlation (P < 0.01) was found between Kc (or Gc) and dry density. A comparison of the experimentally determined effective modulus (relating Kc and Gc) with an effective modulus calculated from the transversely isotropic model for bone showed good agreement.
The tensile fracture stress (σfr) of longitudinal bovine tibia compact bone specimens was measured as a function of the length (c) and radius of curvature (r) of machined edge cracks. It was established that, for a given value of r, then where A and B are constants. A fracture mechanics method was utilised to derive values of the fracture toughness (as defined by the critical stress intensity factor, KIC), the specific surface energy (γ) and the “intrinsic” flaw size (c0). The advantages and limitations of this approach are discussed.
The fracture mechanics parameter of the critical stress intensity factor (Kc) was determined by a modified compact tension test method, for the fracture of bovine tibia cortical bone at orientations of 0 degrees, 15 degrees, 30 degrees, 45 degrees, 75 degrees and 90 degrees to the bone axis. It was established that, for a given loading rate, a variation in orientation from 0-90 degrees produced average increases in Kc from 3.2 to 6.5 MN m-3/2.
Linear elastic fracture mechanics predicts that the fracture stress of precracked materials is dependent on the length of the initial crack tip radius of curvature, as supported by the Griffith and Inglis equations. In order to determine the applicability of these equations and the effects of other variables, tensile specimens of bovine tibia were produced with edge cracks of known dimensions and tested to fracture. Longitudinal sheet tensile specimens were taken from the midposterior diaphysis of bovine tibiae that had been kept frozen in saline soaked towels. Each specimen had a milled gauge length of 25 mm, 16 mm width and 2 mm thickness. All specimen preparation was performed under a saline drip. An edge crack, centered along the gauge length, was milled in the specimen perpendicular to its long axis. The crack lengths used were 4, 6, 8, 10 and 12 mm. The crack tip was formed with drill bits having nominal diameters of 1/32, 1/16, and 3/32 in. All the combinations of crack length and crack tip radius were repeated five times for a total of 75 specimens. The testing order was randomly selected. Each specimen was tested in tension to fracture at a constant deformation rate of 7.5 X 10(-3) mm s-1, on an Instron mechanical testing device, and the fracture stress was measured. A linear load-deflection curve to fracture was exhibited by all of the specimens. The weight percent calcium of each specimen was determined by atomic absorption spectrophotometry. Microradiographs were used to determine the fractional void area and to histologically evaluate each bone sample.(ABSTRACT TRUNCATED AT 250 WORDS)
The fracture mechanics parameters of critical stress intensity factor (Kc) and critical strain energy release rate (Gc) for longitudinal fracture of bovine tibia cortical bone were determined by the compact tension method. It was demonstrated that, for a given bone density, Kc and Gc depended on the loading rate, and resultant crack velocity, with a maximum in fracture toughness (Kc approximately 6.3 MNm-3/2, Gc approximately 2900 Jm-2) at a crack velocity approximately 10(-3) ms-1. For a given loading rate, or crack velocity, an increase in bone density, in the range from 1.92 to 2.02 Mgm-3, produced increases in Kc and Gc, but a variation in specimen thickness (from 0.5 to 2 mm) had no effect on the measured fracture mechanics parameters.
The longitudinal fracture toughnesses of human cortical bone were compared to those of bovine cortical bone to test the hypothesis that although human osteonal bone is significantly weaker and more compliant than primary (plexiform) bone, it is not less tough than primary bone. The fracture toughness indices, critical strain energy release rate (Gc) and critical stress intensity factor (Kc), were determined for human Haversian bone and bovine bone under tension (Mode I) loading using the compact tension method. The effects of thickness, crack growth range and anisotropy on fracture indices for slow stable crack growth in cortical bone were determined. Plane strain assumptions required for application of linear elastic fracture mechanics (LEFM) to bone were investigated. Longitudinal oriented fracture toughness tests were used to assess the crack inhibiting effect of human bone microstructure on fracture resistance. Human bone Kc calculated from the stress concentration formula for 2 and 3 mm thick specimens equaled 4.32 and 4.05 MN m-3/2, respectively. Human bone Gc calculated from the compliance method equaled 827 N m-1 for 2 mm thick specimens and 595 N m-1 for 3 mm thick specimens. It was found that crack growth range, thickness and material assumptions affect fracture toughness. Kc calculated from Gc using an anisotropic relation provided the lowest estimate of Kc and equaled 3.31 MN m-3/2 for 2 mm thick specimens and 2.81 MN m-3/2 for 3 mm thick specimens. Both Kc and Gc were significantly reduced after being adjusted to ASTM standard thickness using ratios determined from bovine bone. The fracture toughness of bovine bone relative to human bone ranged from 1.08 to 1.66. This was compared to the longitudinal strength of bovine bone relative to the longitudinal strength of human bone which is approximately equal to 1.5. We found that even though human bone is significantly weaker than bovine bone, relative to its strength, the toughness of human and bovine bone are roughly similar, but the data were not sufficiently definitive to answer the question of which is tougher.
This paper explores the assumptions and limitations of the probability calculation that led to the conclusion by Burr et al. (1985) that microcracks initiate new remodeling events. It also corrects several minor errors in the calculation in the original manuscript. The results show that the probability that cracks and resorption spaces are associated depends heavily on a factor, F, that accounts for the possibility that some osteons that contain both a crack and a resorption space share a cement line with an adjacent osteon to which the crack more properly 'belongs.' F in turn depends on (1) the measurement criteria for cracks and resorption spaces, (2) the osteon population density in the bone, and (3) the mechanism by which cracks initiate remodeling. The theoretical maximum number of osteons that can contain both a crack and a resorption space (nmax) increases as the number of resorption spaces (r), the number of cracks (c), and F increase, but decreases as the osteon population density (d) increases. A larger nmax makes a direct association between cracks and resorption spaces more difficult to demonstrate experimentally.
The role of microcracking in cortical bone as a toughening mechanism has been investigated in conjunction with the variation in fracture toughness with crack length. Fracture toughness tests were conducted on miniaturised compact tension specimens made from human and bovine cortical bone and the resultant microstructural damage, present in the form of microcracking on the surface, was analysed around the main propagating crack. It was found that the fracture toughness (Kc) and the cumulative number of microcracks increased linearly with crack extension in human and bovine cortical bone, although both Kc and number of microcracks were considerably higher in the latter case. Based on these results, a mechanism, derived from the resistance (R) curve concept developed for microcracking brittle solids, is proposed to explain the fracture of cortical bone, with microcracking distributed between a frontal process zone and a significant process zone wake. Evidence to support this mechanism is given from the existing bone literature, detailed scanning electron microscopical observations and the distribution of microcracks in the process zone wake.
Aging adversely affects the elastic and ultimate properties of human cortical bone as seen in uniaxial tests in quasi static loading, high strain rate impact or fatigue. Little is known about the full effects of aging on toughness and its relationship with strength. In the present article the elastic modulus (E), strength (sigma f), fracture toughness (KC and J-integral), and work of fracture (Wf) were determined in specimens of male human femoral bone aged between 35-92 years. In this way we investigated whether fracture of bone in three situations, allowing various amounts of damage prior to fracture, can provide a better insight into the fracture process and also the relative importance of these experimental methods for assessing the soundness of bone material. We found a steady and significant decrease with age for all these mechanical measures. E fell by 2.3%, from its value of 15.2 GPa at 35 years of age, per decade of later life; sigma f fell similarly from 170 MPa by 3.7%; KC from 6.4 MPa m1/2 by 4.1%; J-integral from 1.2 kJ m-2 by 3%, and the Wf from 3.4 kJ m-2 by 8.7%. In aging bone there was a deterioration in the elastic properties of the material. This reduced the (elastically calculated) critical stress intensity level (KC) required to initiate a macrocrack, or the nonlinear energy associated with the onset of fracture (J). The macrocrack was preceded by less damage, and once created needed less energy to drive through the tissue (Wf).
The fracture toughness of the right femoral neck, femoral shaft, and tibial shaft of matched cadaveric bones, ages 50 to 90 years, was compared. Results of this study indicate that tensile (G(Ic)) and shear (G(IIc)) fracture toughness vary depending on bone location. The femoral neck has the greatest resistance to crack initiation for both tension and shear loading while the femoral shaft has the least. The relationship between age and the fracture toughness of the femoral neck and shaft was investigated. G(c) of the femoral shaft significantly decreased with age for mode I and was nearly significant for mode II. Fracture toughness of the femoral neck did not change with age for the later decades of life. Implications of these findings are discussed.
Based on the microscopic analyses of cracks and correlational studies demonstrating evidence for a relationship between fracture toughness and microstructure of cortical bone, an equation was derived for bone fracture toughness in longitudinal crack growth, using debonding at osteonal cement lines and weakening effect of pores as main crack mechanisms. The correlation between the measured and predicted values of fracture toughness was highly significant but weak for a single optimal value of matrix to cement line fracture toughness ratio. Using fracture toughness values and histomorphometrical parameters from an available data set, matrix to cement line fracture toughness ratio was calculated for human femoral bone. Based on these calculations it is suggested that the effect of an osteon on fracture toughness will depend on the cement line's ability to compensate for the pore in an osteon. Matrix to cement line fracture toughness ratio significantly increased with increasing age, suggesting that the effectiveness of osteons in energy absorption may be reduced in the elderly due to a change in cement line properties.
The hypothesis of this study is that the mechanical integrity of the collagen network in bone deteriorates with age, and such adverse changes correlate with the decreased toughness of aged bone. To test the hypothesis, 30 human cadaveric femurs from donors ranging from 19 to 89 years of age were tested to determine the age-related changes in the mechanical properties of demineralized bone and fresh bone samples. Along with bone porosity, bone density, and weight fractions of the mineral and organic phases, collagen denaturation and concentrations of collagen cross-links (HP, hydroxylysylpyridinoline; LP, lysylpyridinoline; PE, pentosidine) were determined for these bone specimens as a function age. Analysis of variance (ANOVA) showed that age-dependent changes were reflected in the decreased strength, work to fracture, and fracture toughness of bone; in the decreased strength, elastic modulus, and work to fracture of the collagen network; as well as in the increased concentration of pentosidine (a marker of nonenzymatic glycation) and increased bone porosity. Regression analyses of the measured parameters showed that the age-related decrease in work to fracture of bone (especially its postyield portion) correlated significantly with deterioration in the mechanical integrity of the collagen network. The results of this study indicate that the adverse changes in the collagen network occur as people age and such changes may lead to the decreased toughness of bone. Also, the results suggest that nonenzymatic glycation may be an important contributing factor causing changes in collagen and, consequently, leading to the age-related deterioration of bone quality.
It has been proposed that cortical bone derives its toughness by forming microcracks during the process of crack propagation (J. Biomech. 30 (1997) 763; J. Biomech. 33 (2000) 1169). The purpose of this study was to experimentally validate the previously proposed microcrack-based toughening mechanism in cortical bone. Crack initiation and propagation tests were conducted on cortical bone compact tension specimens obtained from the antlers of red deer. For these tests, the main fracture crack was either propagated to a predetermined crack length or was stopped immediately after initiating from the notch. The microcracks produced in both groups of specimens were counted in the same surface area of interest around and below the notch, and crack growth resistance and crack propagation velocity were analyzed. There were more microcracks in the surface area of interest in the propagation than in initiation specimens showing that the formation of microcracks continued after the initiation of a fracture crack. Crack growth resistance increased with crack extension, and crack propagation velocity vs. crack extension curves demonstrated the characteristic jump increase and decrease pattern associated with the formation of microcracks. The scanning electron micrographs of crack initiation and propagation displayed the formation of a frontal process zone and a wake, respectively. These results support the microcrack-based toughening mechanism in cortical bone. Bone toughness is, therefore, determined by its ability to form microcracks during fracture.
A mechanistic understanding of fracture in human bone is critical to predicting fracture risk associated with age and disease. Despite extensive work, a mechanistic framework for describing how the microstructure affects the failure of bone is lacking. Although micromechanical models incorporating local failure criteria have been developed for metallic and ceramic materials, few such models exist for biological materials. In fact, there is no proof to support the widely held belief that fracture in bone is locally strain-controlled, as for example has been shown for ductile fracture in metallic materials. In the present study, we provide such evidence through a novel series of experiments involving a double-notch-bend geometry, designed to shed light on the nature of the critical failure events in bone. We examine how the propagating crack interacts with the bone microstructure to provide some mechanistic understanding of fracture and to define how properties vary with orientation. It was found that fracture in human cortical bone is consistent with strain-controlled failure, and the influence of microstructure can be described in terms of several toughening mechanisms. We provide estimates of the relative importance of these mechanisms, such as uncracked-ligament bridging.
Although there are empirical correlations between strain rate, cortical and cancellous bone apparent stiffness, apparent yield strength, apparent ultimate strength and cortical bone fracture toughness, a mechanistic description for these phenomena is lacking. Microcracking is a major mechanism in cortical and cancellous bone failure, however, microdamage content alone cannot explain the strain rate dependence of bone strength without considering time-dependent behavior of the crack. Using a rate-dependent model of a fiber-bridged microcrack and data from the literature, we demonstrate that the experimental apparent yield strength of bone can be predicted directly from measurements of apparent moduli of elasticity of bone constituents and failure strain of the collagenous matrix. Yield strength predictions for estrogen depleted bone were made using the model and data from ovariectomized sheep. It was predicted that the yield strength of estrogen-deficient bone is comparable to that of normal bone within strain rates associated with physiological activities. For high strain rates, however, the strength of estrogen-depleted bone was predicted to be much weaker than normals suggesting a higher fracture risk due to impact from falls, for individuals with estrogen-depleted bones such as in post-menopausal osteoporosis.
Previous studies of the fracture properties of cortical bone have suggested that the fracture toughness increases with crack length, which is indicative of rising R-curve behavior. Based on this indirect evidence and the similarity of bone to ceramic matrix composites, we hypothesized that bone would exhibit rising R-curve behavior in the transverse orientation and that the characteristics of the R-curves would be regionally dependent within the cortex due to variations in bone microstructure and toughening mechanisms. To test these hypotheses, we conducted R-curve experiments on specimens from equine third metacarpal bones using standard fracture mechanics testing methods. Compact type specimens from the dorsal and lateral regions in the middle of the diaphysis were oriented for crack propagation transverse to the longitudinal axis of the bone. The test results demonstrate that equine cortical bone exhibits rising R-curve behavior during transverse crack propagation as hypothesized. Statistical analyses of the crack growth initiation toughness, K0, the peak toughness, Kpeak, and the crack extension at peak toughness, deltaa, revealed significant regional differences in these characteristics. Specifically, the lateral cortex displayed higher crack growth initiation and peak toughnesses. The dorsal cortex exhibited greater crack extension at the peak of crack growth resistance. Scanning electron microscopy revealed osteon pullout on fracture surfaces from the dorsal cortex and but not in the lateral cortex. Taken together, the significant differences in R-curves and the SEM fractography indicate that the fracture mechanisms acting in equine cortical bone are regionally dependent.
An understanding of the evolution of toughness is essential for the mechanistic interpretation of the fracture of cortical bone. In the present study, in vitro fracture experiments were conducted on human cortical bone in order to identify and quantitatively assess the salient toughening mechanisms. The fracture toughness was found to rise linearly with crack extension (i.e., rising resistance- or R-curve behavior) with a mean crack-initiation toughness, K0 of approximately 2 MPa square root m for crack growth in the proximal-distal direction. Uncracked ligament bridging, which was observed in the wake of the crack, was identified as the dominant toughening mechanism responsible for the observed R-curve behavior. The extent and nature of the bridging zone was examined quantitatively using multi-cutting compliance experiments in order to assess the bridging zone length and estimate the bridging stress distribution. Additionally, time-dependent cracking behavior was observed at stress intensities well below those required for overload fracture; specifically, slow crack growth occurred at growth rates of approximately 2 x 10(-9) m/s at stress intensities approximately 35% below the crack-initiation toughness. In an attempt to measure slower growth rates, it was found that the behavior switched to a regime dominated by time-dependent crack blunting, similar to that reported for dentin; however, such blunting was apparent over much slower time scales in bone, which permitted subcritical crack growth to readily take place at higher stress intensities.
This study was concerned with the mechanics and micromechanisms of diffuse (ultrastructural) damage occurrence in human tibial cortical bone specimens subjected to tension-tension fatigue. A nondestructive technique was developed for damage assessment on the surfaces of intact compact tension specimens using laser scanning confocal microscopy. Results indicated that diffuse damage initiates as a result of fractures in the inter-canalicular regions. Subsequent growth of those microscopic flaws demonstrated multiple deflections from their paths due to 3D spatial distribution of microscopic porosities (lacunae-canalicular porosities) and the stress-concentrating effects of lacunae. Damage dominating effects in the early stages of fatigue had been verified by the observed variations of the fracture toughness due to artificially induced amounts of damage. Toughening behavior was observed as a function of diffuse damage.
Mechanical fatigue of bone leads to micro-cracking which is associated with remodeling, establishing a balance in the microcrack population of the living tissue, thus, in the steady-state, the microstructure of bone provides sites of discontinuity acting as stress raisers. Hence fracture toughness plays a decisive role in bone functionality by determining the level to which the material can be stressed in the presence of cracks, or, equivalently, the magnitude of cracking which can be tolerated at a given stress level. Cortical bone, which behaves as a quasi-brittle solid when fractured, was tested as short-rod chevron-notched tension specimens (CNT). The main features of the CNT specimen are its geometry and the V shaped notch. The notch leads to steady-state crack propagation whilst the requested geometry allows a diameter 40% smaller than the thickness of a standard compact tension specimens (CT). These features are essential to distinguish the inhomogeneties in the fracture properties of materials like bone. Bone structure and crack propagation of the CNT specimens were analyzed using X-ray computed micro-tomography (XMT), which is a non-invasive imaging technique. The unique feature of the micro-CT is the high resolution three-dimensional image which consists of multi-sliced tomographs taken in a fine pitch along the rotational axis. Fracture toughness (K(IC)) computed according to the peak load was 4.8 MNm(-3/2) while that derived from experimental calibration tests using XMT was 4.9 MNm(-3/2).
Age-related deterioration of the fracture properties of bone, coupled with increased life expectancy, is responsible for increasing incidence of bone fracture in the elderly, and hence, an understanding of how its fracture properties degrade with age is essential. The present study describes ex vivo fracture experiments to quantitatively assess the effect of aging on the fracture toughness properties of human cortical bone in the longitudinal direction. Because cortical bone exhibits rising crack-growth resistance with crack extension, unlike most previous studies, the toughness is evaluated in terms of resistance-curve (R-curve) behavior, measured for bone taken from wide range of age groups (34-99 years). Using this approach, both the ex vivo crack-initiation and crack-growth toughness are determined and are found to deteriorate with age; the initiation toughness decreases some 40% over 6 decades from 40 to 100 years, while the growth toughness is effectively eliminated over the same age range. The reduction in crack-growth toughness is considered to be associated primarily with a degradation in the degree of extrinsic toughening, in particular, involving crack bridging in the wake of the crack.
Micromechanical models for fracture initiation that incorporate local failure criteria have been widely developed for metallic and ceramic materials; however, few such micromechanical models have been developed for the fracture of bone. In fact, although the fracture event in "hard" mineralized tissues such as bone is commonly believed to be locally strain-controlled, only recently has there been experimental evidence (using double-notched four-point bend testing) to support this widely held belief. In the present study, we seek to shed further light on the nature of the local cracking events that precede catastrophic fracture in human cortical bone, and to define their relationship to the microstructure. Specifically, numerical computations are reported that demonstrate that the stress and strain states ahead of such a notch are qualitatively similar irrespective of the deformation mechanism (pressure-insensitive plasticity vs. pressure-sensitive microcracking). Furthermore, we use the double-notched test to examine crack-microstructure interactions from a perspective of determining the salient toughening mechanisms in bone and to characterize how these may affect the anisotropy in fracture properties. Based on preliminary micromechanical models of these processes, the relative contributions of various toughening mechanisms are established. In particular, crack deflection and uncracked-ligament bridging are identified as the major mechanisms of toughening in cortical bone.
Data for fracture in human humeral cortical bone are re-analyzed to assess the validity for this material of linear-elastic fracture mechanics (LEFM), which is the standard method of analyzing toughness and one basis for analyzing clinical data relating to bone quality. A nonlinear fracture model, which is based on representing the damage zone in the bone by a cohesive model, is calibrated against a number of sets of test data for normal (not diseased or aged) human cortical bone taken from cadavers. The data consist of load vs. load-point displacement measurements from standard compact-tension fracture tests. Conventional LEFM is unable to account for the shape of the load-displacement curves, but the nonlinear model overcomes this deficiency. Calibration of the nonlinear model against one data curve leads to predictions of the peak load and the displacement to peak load for two other data curves that are, for this limited test set, more accurate than those made using LEFM. Furthermore, prior observations of damage mechanisms in bone are incompatible with the modeling assumption of LEFM that all nonlinearity is confined to a zone much smaller than the specimen and the crack length. The predictions of the cohesive model and the prior observations concur that the length of the nonlinear zone in human cortical bone varies in the range 3-10 mm, which is comparable to or larger than naturally-occurring bones and the specimens used to test them. We infer that LEFM is not an accurate model for cortical bone. The fracture toughness of bone deduced via LEFM from test data will not generally be a material constant, but will take different values for different crack lengths and test configurations. The accuracy of using LEFM or single-parameter fracture toughness for analyzing the significance of data from clinical studies is called into question. The nonlinear cohesive zone model is proposed to be a more accurate model of bone and the traction-displacement or cohesive law is hypothesized to be a material property. The cohesive law contains a more complete representation of the mechanics of material failure than the single-parameter fracture toughness and may therefore provide a superior measure of bone quality, e.g., for assessing the efficacy of therapy for osteoporosis.
Toughness is crucial to the structural function of bone. Usually, the toughness of a material is not just determined by its composition, but by the ability of its microstructure to dissipate deformation energy without propagation of the crack. Polymers are often able to dissipate energy by viscoplastic flow or the formation of non-connected microcracks. In ceramics, well-known toughening mechanisms are based on crack ligament bridging and crack deflection. Interestingly, all these phenomena were identified in bone, which is a composite of a fibrous polymer (collagen) and ceramic nanoparticles (carbonated hydroxyapatite). Here, we use controlled crack-extension experiments to explain the influence of fibre orientation on steering the various toughening mechanisms. We find that the fracture energy changes by two orders of magnitude depending on the collagen orientation, and the angle between collagen and crack propagation direction is decisive in switching between different toughening mechanisms.
Osteoporosis is a major health problem characterized by compromised bone strength that predisposes patients to an increased risk of fracture. Osteoporotic patients differ from normal subjects in bone mineral composition, bone mineral content, and crystallinity. Poor bone quality in patients with osteoporosis presents the surgeon with difficult treatment decisions. Much effort has been expended on improving therapies that are expected to preserve bone mass and thus decrease fracture risk. Manipulation of both the local fracture environment in terms of application of growth factors, scaffolds and mesenchymal cells, and systemic administration of agents promoting bone formation and bone strength has been considered as a treatment option from which promising results have recently been reported. Surprisingly, less importance has been given to investigating fracture healing in osteoporosis. Fracture healing is a complex process of bone regeneration, involving a well-orchestrated series of biological events that follow a definable temporal and spatial sequence that may be affected by both biological factors, such as age and osteoporosis, and mechanical factors such as stability of the osteosynthesis. Current studies mainly focus on preventing osteoporotic fractures. In recent years, the literature has provided evidence of altered fracture healing in osteoporotic bone, which may have important implications in evaluating the effects of new osteoporosis treatments on fracture healing. However, the mechanics of this influence of osteoporosis on fracture healing have not yet been clarified and clinical evidence is still lacking.
The purpose of this work is to investigate the use of indentation fracture as a method of measuring toughness at the microscale in cortical bone. Indentation fracture employs sharp indenters to initiate cracks, whose length can be used to calculate the toughness of the material. Only a cube corner indenter tip is found to initiate cracks at a suitable size scale for microstructural measurement. Cracks from 7 to 56 microm in length are produced using loads from 0.05 to 3N. Preliminary data predicts rising toughness with increasing crack length (rising R-curve behaviour) at the microscale. This technique provides a new insight into fracture in cortical bone since it allows the investigator to observe mechanisms and measure toughness at a size scale at which in vivo damage is known to exist.
Crack-growth experiments in human dentin have been performed in situ in an environmental scanning electron microscope to measure, for the first time, the crack-growth resistance curve (R-curve) for clinically relevant (<250 microm) crack extensions and to simultaneously identify the salient toughening mechanisms. "Young" dentin from donors 19-30 years in age and "aged" dentin from donors 40-70 years in age were evaluated. The "young" group had 0-4% of its tubules filled with apatite; the "aged" group was subdivided into "opaque" with 12-32% filled tubules and "transparent" with 65-100% filled tubules. Although crack-initiation toughnesses were similar, the crack-growth resistance of "young" dentin was higher by about 40% compared to "aged" dentin. Mechanistically, this behavior is interpreted in terms of three phenomena: (i) gross crack deflection of the growing crack, (ii) microcracks which initiated at unfilled tubules in the high stress region in the vicinity of a propagating crack (no microcracks formed at filled tubules), and (iii) crack propagation which followed a local trajectory through unfilled tubules and deflected around filled tubules. The higher toughness of the "young" dentin was related to enhanced microcracking (at unfilled tubules) ahead of the growing crack, which (i) shields the crack by activating multiple crack tips and by reducing the local stress intensity through crack deflection and (ii) leads to the formation of crack bridges from "uncracked ligaments" due to the incomplete coalescence of these microcracks with the main crack tip. With age, the role of these toughening mechanisms was diminished primarily to the lower fraction of unfilled, and hence microcracked, tubules.
had full access to the experimental data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis. Data acquisition was carried out by K Study design, interpretation and analysis of data and preparation of the manuscript were performed jointly by
- R O R Author
Author contributions
R.O.R. had full access to the experimental data in the study and takes responsibility for the integrity of
the data and the accuracy of the data analysis. Data acquisition was carried out by K.J.K. Study design,
interpretation and analysis of data and preparation of the manuscript were performed jointly by K.J.K.,
J.W.A. and R.O.R.
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Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions.
Correspondence and requests for materials should be addressed to R.O.R.
nature materials VOL 7 AUGUST 2008 www.nature.com/naturematerials
- T L Norman
- D Vashishth
- D Burr
Norman, T. L., Vashishth, D. & Burr, D. B. in Advances in Bioengineering Vol. 20 (ed. Vanerby, R.)
361–364 (ASME, New York, 1991).