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Delamination, Fiber Bridging and Toughness of Ceramic Matrix Composites
Abstract
Delamination cracks in long-fibre reinforced ceramic matrix composites are found to be bridged by fibres which span the crack wake at a shallow angle. The in situ observation of bridging fibres reveals that these are subject to considerable tensile forces, giving rise to a substantial crack closure force. The overall crack closure force is determined by the number of bridging fibres, steadily reduced by fibre failure caused by high bending moments at the root of each fibre. This leads to a model for crack closing forces combining simple mechanics and Weibull statistics. The model relates these forces to the properties of fibres, matrix and their interface.
... (1). From in-situ examinations on the damage evolution in this phenomenon, it demonstrated that fiber bridging could experience bending, peeling and breakage with crack opening [47]. Based on this observation, Kaute [47] proposed a micromechanical model to explore the bridging stress in quasi-static delamination growth and the bridging stress in the first two stages, i.e., bending and peeling. ...
... From in-situ examinations on the damage evolution in this phenomenon, it demonstrated that fiber bridging could experience bending, peeling and breakage with crack opening [47]. Based on this observation, Kaute [47] proposed a micromechanical model to explore the bridging stress in quasi-static delamination growth and the bridging stress in the first two stages, i.e., bending and peeling. Particularly, the first right term represents closure force related to zero crack opening (i. ...
... The hybrid fiber bridging zone model developed in the previous section was implemented using experimental data on mode I delamination growth. It is assumed in present study that damage mechanisms in bridging fiber remain similar in fatigue delamination, as that discussed by Kaute et al. [47] in quasi-static delamination. Table 1 shows the mechanical properties for each reinforcement used in this study, applied in the determination of peel-off energy and fiber bridging stress energy. ...
A mechanistic model for mode I fatigue delamination growth based on the hybrid fiber bridging zone was developed and is described herein. The model is based on the microfracture mechanisms of striation, fiber peel-off and fiber bridging stress, measured through scanning electron microscopy analysis. The effects of the carbon and glass fiber delamination features at the microscopic level were also considered to predict the crack propagation behavior in a hybrid laminate. The experimental SERR based on the fiber bridging zone model was used as the similitude parameter for the crack growth rate, following power law.
... At large opening displacements the bridging ligament becomes slender as it peels off the fracture surface, and shear deforma-tions become negligible. Kaute et al. [8] proposed a model where only the axial stiffness of the bridging fiber is considered. They assumed the fiber to be straight and long in comparison with its diameter. ...
... The fiber was assumed to be straight and only transfer longitudinal forces. More recently, Daneshjoo et al. [11] published a model building on the work by Kaute [8]. Their model considers matrix spalling, fiber pull-out and fiber fracture as the main failure mechanisms. ...
... Both these models are limited to infinitesimally small deflections of the bridging ligament, i.e. when the local normal opening displacement is much smaller than the height of the bridging ligament. The models proposed by Kaute et al. [8], Ivens et al. [9] and Daneshjoo et al. [11], on the other hand, are only applicable when the local normal opening displacement is several orders of magnitude larger than the height of the bridging ligament. A comprehensive review of fiber bridging investigations, including micromechanical models for crossover fiber bridging in the wake of a delamination front under different modes, is given by Khan [12]. ...
A micromechanical model of cross-over fiber bridging is developed for the prediction of macroscopic mixed-mode bridging laws (traction-separation laws). The model is based on non-linear beam theory and takes into account debonding between fiber and matrix as well as buckling of fibers in compression. Further, it is shown how failure of the bridging fibers can be taken into account through a Weibull distributed failure strain. Predictions made by the proposed model are compared with predictions made by detailed 3D finite element models, and a very good agreement was observed. It is shown that models based on linear beam theory are only valid for small transverse deflections of the bridging ligament and greatly underestimate the force transferred by ligaments subjected to moderately large deflections. The novel model, on the other hand, is applicable in the entire range where the bridging problem transitions from a beam bending problem to a bar-like problem. Finally, an example of how the proposed model can be used for parameter/sensitivity studies is given. A conclusion from this study is that reducing the fracture toughness, Gc, of the interface between fibers and matrix may lead to increased energy dissipation through cross-over fiber bridging as more fibres remain intact longer.
... Furthermore, there is a number of micromechanical models [36,37] developed to investigate the delamination by considering fiber bridging effects. Sørensen et al. [38] proposed a micromechanical model for prediction of the mixed mode I/II bridging laws based on the observed bridging mechanism during crack growth in a unidirectional carbon/ epoxy composite. ...
... While the number of fiber failures is negligible until bending stress at the fiber roots does not exceed the mean fiber strength. The bridging fibers start to fail by increasing the bending stress at fiber roots, which means that the number of bridging fibers decreases due to the fiber failure [37]. Daneshjoo et al. [39] developed a mixed mode I/II micromechanical bridging model based on the breakdown of the failure micro-mechanisms involved during the fiber bridging phenomenon such as the fiber peel-off, matrix spalling, fiber-matrix debonding, fiber pull-out and fiber fracture. ...
... The energy contribution of bridging fibers was obtained by substitution of Eqs. (37) and (38) into Eq. (34) and performing an integration [39]. ...
In this paper, by considering the absorbed energy in the fracture process zone and extension of the minimum strain energy density theory for orthotropic materials, a new mixed mode I/II failure criterion was proposed. The applicability of the new criterion, to predict the crack growth in both laminated composites and wood species, was investigated. By defining a suitable damage factor and using the mixed mode I/II micromechanical bridging model, the absorbed energy in the fracture process zone was considered. It caused the new criterion to be more compatible with the nature of the failure phenomena in orthotropic materials, unlike available ones that were conservative. A good agreement was obtained between the fracture limit curves extracted by the present criterion and the available experimental data. The theoretical results were also compared with those of the minimum strain energy density criterion to show the superiority of the newly proposed criterion.
... Bridging laws can be extracted via experiments or micromechanical models. A number of micromechanical models have been developed for the mode I delamination with considering fiber bridging effects [5,11,12]. Spearing and Evans [5] predicted a relationship between the normal stress and the normal opening by modeling of the bridged fibers as short rectangular cross section beams which overcome the fracture resistance through peeling away from the crack faces. Their model was based on the classical beam theory in which the fiber sliding with friction (observed experimentally [13]) has been ignored. ...
... Their model was based on the classical beam theory in which the fiber sliding with friction (observed experimentally [13]) has been ignored. Kaute et al. [11] presented a model based on in situ observation of the fiber pull-out from the matrix during testing of ceramic matrix composites. Their model presented a relation for crack closure force as a function of the crack opening and predicted a decrease of bridging stress due to the fiber failure using the Weibull statistics. ...
... As the crack opening increases, the number of bridged fibers decreases due to fiber fracture [11,18]. One difference is that the fibers, during the crack bridging phenomenon under mixed mode I/II, are subjected to a compressive or a tensile load according to their bridging direction. ...
In unidirectional laminated composites, fiber bridging as a toughening mechanism has a significant effect on the behavior of mixed mode I/II delamination. In the present paper, effects of fiber bridging and related micro-mechanisms were investigated quantitatively. To this end, a novel micromechanical model called “mixed mode I/II micromechanical bridging model” was proposed based on the calculation of the delamination crack bridging zone energy absorption. Firstly, different failure micro-mechanisms, occurring during the fiber bridging process, were identified. Then, different loading conditions on the bridged fibers were applied. In the next step, the absorbed energy of each failure micro-mechanisms was calculated. Finally, the energy absorbed by the fiber bridging zone was obtained by summation of the absorbed energy of each failure micro-mechanisms. The traction-separation behaviors in both the normal and tangential directions of the crack plane are the outcome of the proposed model. Moreover, the mixed mode I/II delamination failure response of the laminated composite was extracted by plotting GI versus GII and compared with the available experimental data. The results show that the proposed model is able to predict the mixed mode I/II delamination behavior of laminated composites considering fiber bridging effects.
... Fiber misalignment controls compressive failure and fatigue life under aligned cyclic loads [12,13]. Fiber meandering leads to oblique bridging fibers traversing delamination cracks, a major source of delamination fracture resistance [14]. Variations in fiber positioning, especially clusters of unusually close fibers, are associated with variations in the strength of a composite under loads applied normal to the fiber direction [15]. ...
... When a crack in a composite material propagates along the fiber direction, splitting a fiber bundle in two, a small number of fibers are often found bridging the crack, forming beam-like structures whose ends are embedded in the two opposing surfaces. In nominally unidirectional materials or plies, these so-called ''oblique bridging fibers'' form shallow angles with the fracture surfaces (Fig. 21a) [14]. The angle of the bridging fibers to the fracture surface typically maximizes at approximately 10°as the crack opens before the fibers break. ...
... We refer to this effect as ''topological frustration'': the frustration of splitting fracture by the topology of the fiber bundle. (Table 2) and r f = 7.5 lm (for the SiC fibers in the material studied in [14]), we estimate 300-1000 pairs of map changes per mm 2 . ...
Data acquired from synchrotron-based X-ray computed tomography provide complete descriptions of the stochastic positions of each fiber in large bundles within composite samples. The data can be accumulated for distances along the nominal fiber direction that are long enough to reveal meandering or misalignment. Data are analyzed for a single fiber bundle consolidated as a mini-composite specimen and a block of fibers embedded within a single ply in a tape laminate specimen. The fibers in these materials differ markedly in their
departure from alignment and the patterns formed by fiber deviations. The tape laminate specimen exhibits evidence of fibers that have slipped laterally through the bundle in narrow shear bands, which may be a mechanism of bundle deformation under transverse compression and shear. This pattern is absent in the single-tow specimen, which was not subject to transverse loads in processing. We propose a combination of topological and Euclidean metrics to quantify these and other stochastic bundle characteristics. Topological metrics are based on the neighbor map of fibers, which is constructed on cross-sections of the bundle by Delaunay triangulation (or Voronoi tessellation). Variations of the neighbor map along the fiber direction describe fiber meandering, twist, etc. Euclidean metrics include factors such as local fiber density and fiber orientation. The metrics distinguish bundle types, enable quantification of the effects of the manufacturing history of bundles, and provide target statistics to be matched by virtual specimens that might be generated for use in fiber-scale virtual tests.
... The specimen most commonly used for Mode I fracture is the double cantilever beam (DCB) [3]. Other types of composite laminates and adhesively-bonded joints were also examined [11][12][13][14][15] based on existing standards and protocols. Their applicability for the interpretation of the fracture mechanics data obtained from non-standardized asymmetric fracture joints has been validated in [16]. ...
... This increasing SERR is usually described by the resistance curve (R-curve) describing the relationship between the crack length and the corresponding SERR. Extensive experiments have been performed involving ceramic [13,14] and polymer matrix composites [9,10,13] in order to examine the effect of fiber bridging on the SERR. The results showed that fiber bridging is observed in both delamination and crack propagation perpendicular to the fiber direction and affects the shape of the R-curve. ...
... Modeling of the fiber bridging effects on delamination resistance has also been performed and the results are presented in [14,15]. Kaute et al. [14] observed fiber bridging and attributed it to fiber waviness. ...
... Fibre bridging in unidirectional fibre composites is traditionally divided into two basic cracking modes: crack bridging by fibres oriented perpendicular to the crack plane (Marshall et al., 1985;McCartney, 1987;Hutchinson and Jensen, 1990;Zok and Hom, 1990; Thouless and Evans, 1988;Deve and Maloney, 1991;Kardomateas and Carlson, 1996) and crack bridging by fibres oriented parallel to the cracking plane, denoted fibre cross-over bridging Spearing and Evans, 1992;Kaute et al., 1993;Shercliff et al., 1994;Sørensen and Jacobsen, 1998). The present paper focuses at the latter. ...
... A number of micromechanical models have been developed for Mode I cracking with fibre cross-over bridging (Spearing and Evans, 1992;Kaute et al., 1993;Ivens et al., 1995). Spearing and Evans (1992) modelled cross-over bridging by a beam peeling off along an interface. ...
... The agreement between the measured and predicted bridging law shapes suggests that a micromechanical model based on simple beam theory may be adequate to represent cross-over bridging. The model by Kaute et al. (1993) is based on fibre pull out from the matrix. This mechanism was observed in situ during testing of ceramic matrix composites (Kaute et al., 1993;Shercliff et al., 1994). ...
The fracture resistance of fibre composites can be greatly enhanced by crack bridging. In situ observations of mixed mode crack growth in a unidirectional carbon-fibre/epoxy composite reveal crack bridging by single fibres and by beam-like ligaments consisting of several fibres. Based on the observed bridging mechanism, a micromechanical model is developed for the prediction of macroscopic mixed mode bridging laws (stress-opening laws). The model predicts a high normal stress for very small openings, decreasing rapidly with increasing normal and tangential crack opening displace- ments. In contrast, the shear stress increases rapidly, approaching a constant value with increasing normal and tangential openings. The solutions for the bridging laws and the resulting toughening due to the bridging stresses are obtained in closed analytical form. ! 2007 Elsevier Ltd. All rights reserved.
... The cohesive zone model incorporates a detailed description of the processes occurring during crack bridging (Cox, 1999), i.e. ÿber pull-out, matrix spalling and ÿber breakage. Thereby, the cohesive constitutive relations derived here extend earlier work by Llorca and Elices (1992) and Kaute et al. (1993) to mixed-mode loading condition. In the thermal part, the cohesive zone model incorporates a description of crack conductance in dependence of the current local condition within the bridged crack. ...
... The model describing the load transfer across the ÿber bridging zone is an extension of the mode I crack bridging model of Kaute et al. (1993). The present work generalizes this model to deal with arbitrary values of mode mixity. ...
... As the displacement jump across the crack increases, the forces carried by the bridging ÿbers increase until spalling of the matrix initiates and imposes an upper limit on the forces that can be carried by the ÿbers. An approximate expression linking the maximum value of the normal component of the ÿber force, max(f n ), to the fracture toughness of the matrix, K m IC , (Kaute et al., 1993), can be obtained based on results of Tada et al. (1973) as ...
The coupled thermomechanical numerical analysis of composite laminates with bridged delamination cracks loaded by a temperature gradient is described. The numerical approach presented is based on the framework of a cohesive zone model. A traction–separation law is presented which accounts for breakdown of the micromechanisms responsible for load transfer across bridged delamination cracks. The load transfer behavior is coupled to heat conduction across the bridged delamination crack. The coupled crack–bridging model is implemented into a finite element framework as a thermomechanical cohesive zone model (CZM). The fundamental response of the thermomechanical CZM is described. Subsequently, bridged delamination cracks of fixed lengths are studied. Values of the crack tip energy release rate and of the crack heat flux are computed to characterize the loading of the structure. Specimen geometries are considered that lead to crack opening through bending deformation and buckling delamination. The influence of critical mechanical and thermal parameters of the bridging zone on the thermomechanical delamination behavior is discussed. Bridging fibers not only contribute to crack conductance, but by keeping the crack opening small they allow heat flux across the delamination crack to be sustained longer, and thereby contribute to reduced levels of thermal stresses. The micro-mechanism based cohesive zone model allows the assessment of the effectiveness of the individual mechanisms contributing to the thermomechanical crack bridging embedded into the structural analysis.
... It is appropriate here to comment on a study by Kaute et al. [27], who determined the cohesive law of a ceramic matrix composite subjected to fibre cross-over bridging. The mechanism is similar to the mechanism identified here for the polymer matrix composite, but differ in details, e.g. because the ceramic matrix composite has a weak fibre/matrix interface that facilitates fibre pull out. ...
... Nevertheless, the two materials systems are expected to possess fairly similar cohesive laws. The experimental approach taken by Kaute et al. [27] can be summarised as follows: first, they loaded DCB specimens by wedge forces until a mid-plane crack had propagated along the entire length of the specimen (''pre-cracking''). The two half parts were held together only by bridging ligaments. ...
... This behaviour is quite different from the cohesive law that we have determined. We believe that the initial linear part of the cohesive law obtained by Kaute et al. [27] is an artefact of the precracking: during the initial splitting of the specimen into two parts, the bridging ligaments must have been subjected to some opening, denoted d i . Knowing that the bridging mechanism consists of the formation of bridging ligaments we expect that the ligaments would already have developed some splitting during the pre-cracking. ...
The determination of cohesive laws for describing large scale failure process zones is discussed. Firstly, a general approach for determination of cohesive laws, by the measurement of the J integral and end-opening of the cohesive zone of double cantilever beam specimens loaded with pure bending moments, is described. Next, two case stories are reviewed: failure of adhesive joints and splitting of a unidirectional carbon fibre/epoxy composite. For the adhesive joints, measured failure strengths of bonded panels having a central notch were found to in very good agreement with predictions from cohesive law parameters determined on test specimens. For the problem of splitting of unidirectional composites, micromechanisms were observed in situ during cracking. A cohesive law shape, predicted by a micromechanics model, was found to agree well with macroscopic cohesive law determined by the J integral approach. The cohesive law was used for predicting effect of specimen shape on strength; predictions were confirmed by experiments. Finally, some ideas regarding determination of mixed mode cohesive laws are discussed.
... This condition imposes an upper limit on the forces that can be carried by the fibers. An approximate expression linking the maximum value of the normal component of the fiber force, max ((,), to the fracture toughness of the matrix, K7c , (Kaute et al., 1993), can be obtained based on results ofTada et al., (1973) as: ...
... The thermomechanical CZM requires information on fiber, matrix, fiber-matrix interface properties, statistical information on fiber failure and reference parameters for size effects. The default parameters used in the present study are given in Table 4, compiled from data given in Kaute et al. (1993Kaute et al. ( , 1995, , Heredia et al. (1995) and Munro (1997). Basic cohesive zone model response. ...
The coupled thermomechanical numerical analysis of damaged composite structures loaded by temperature transients and gradients is described. The numerical approach presented is based on the framework of cohesive zone models. Traction-separation laws are coupled to heat conduction across the cracks. An implementation of the model into a finite element framework is described. Three examples of application are discussed: (i) interface crack growth; (ii) crack bridging; (iii) application to photothermal imaging.
... A considerable literature exists on experiments that identify local damage mechanisms in ceramic composites and monitor the evolution of such mechanisms during mechanical loading by a variety of in situ measurements. Such measurements include those via optical microscopy (108)(109)(110)(111)(112)(113), scanning electron microscopy (114)(115)(116)(117)(118)(119), speckle interferometry (120-122), acoustic waves (123)(124)(125), and electrical resistance (126,127). Most of these measurements were at room temperature; only a few studies tackled in situ measurements at high temperatures (e.g., References 114 and 128). ...
... Even in fiber bundles that appear well aligned to the eye, some fibers meander within the bundle, with important implications for material processing and failure. For example, bundles with greater degrees of meandering are expected to be compacted to lower volume fractions but exhibit enhanced fracture resistance under transverse loads, because meandering fibers bridge splitting cracks (117). ...
We review the development of virtual tests for high-temperature ceramic matrix composites with textile reinforcement. Success hinges on understanding the relationship between the microstructure of continuous-fiber composites, including its stochastic variability, and the evolution of damage events leading to failure. The virtual tests combine advanced experiments and theories to address physical, mathematical, and engineering aspects of material definition and failure prediction. Key new experiments include surface image correlation methods and synchrotron-based, micrometer-resolution 3D imaging, both executed at temperatures exceeding 1,500 degrees C. Computational methods include new probabilistic algorithms for generating stochastic virtual specimens, as well as a new augmented finite element method that deals efficiently with arbitrary systems of crack initiation, bifurcation, and coalescence in heterogeneous materials. Conceptual advances include the use of topology to characterize stochastic microstructures. We discuss the challenge of predicting the probability of an extreme failure event in a computationally tractable manner while retaining the necessary physical detail.
... Adopting the bridging law as the basic material law, a number of studies [1,[3][4][5][6][7][8][9][10][11][12][13] have predicted the fracture behaviour of test specimens or components by the use of idealised bridging laws, e.g. rectilinear or linear bridging laws. ...
... rectilinear or linear bridging laws. Studies that focus on the measurement of real bridging laws are, for example, those of Li and Ward [12], Kaute et al. [13], Brenet et al. [14], Sørensen and Jacobsen [2], Lindhagen [15] and Andersson and Stigh [16]. A discussion of these experimental methods can be found in Sørensen and Jacobsen [17]. ...
In this paper R-curves for mode I crack growth in composites are modelled based on measured bridging laws. It is shown that simulated and measured R-curves are in good agreement. Simulations show that variations in the measured bridging law parameters can explain the scatter in overall R-curves. Finite element procedures for treating a generalised nonlinear law for intra-laminar fibre bridging (longitudinal splitting) in combination with R-curve modelling are demonstrated for mode I loading. The difference between calculating the crack growth resistance by linear elastic fracture mechanics and by the J integral for the double cantilever beam specimen loaded by wedge forces is elucidated. It is shown that calculating the crack growth resistance by linear elastic fracture mechanics results in overestimation of the steady-state crack growth resistance.
... It has been observed [1,2] that when a delamination crack grows in a laminated composite, fibers in the upper and lower laminas may cross the opposite surfaces thereby bridging the two laminas (see Fig. 1) and increasing the crack growth resistance. In the mean time, Z-fibers have been introduced to reinforce laminates in the transverse direction (see Fig. 2) and to enhance the delamination resis- tance [3,4]. ...
... In both cases, the crack growth behavior may be studied using the stress singularity based linear elastic fracture mechanics and a crack bridging model that describes the relationship between the fiber bridging trac- tion and the crack opening displacement. For example, crack bridging models and cantilever beam specimens have been used to investigate the delamination crack growth resistance in [1,2,[5][6][7]. ...
The present work studies the modeling aspect of composite fracture in the presence of crack face fiber bridging using both a combined cohesive/bridging zone model and a standard bridging model. It is found that when the bridging energy density is comparable to or less than the critical energy release rate the peak load predicted from the combined cohesive/bridging model is generally significantly lower than that obtained from the standard bridging zone/crack tip energy release approach if the peak cohesive traction is not significantly higher than the peak bridging traction. Hence, care must be exercised when combining the bridging and cohesive zones into to a single cohesive zone for evaluating crack growth behavior.
... The toughness enhancing mechanisms of crack-arrest/trap and bridging by tough particles ( Mower and Argon, 1995;Bower and Ortiz, 1991 ) or fibers ( Kaute et al., 1993;Sørensen and Jacobsen, 1998 ) in the case of two-or multiple-phase heterogeneous materials, i.e ., composites, have been extensively discussed ( Tan et al., 2019;Kim et al., 2019;Mohamed et al., 2018;Sun et al., 2018;Naya et al., 2019 ). More generally, the strength and the fracture toughness of solids exhibiting heterogeneity in material properties have been discussed and the related stress dislocalization and crack-trap mechanisms have been investigated analytically and numerically ( Dimas et al., 2016;. ...
Spatial heterogeneity of adhesion properties is known to result in bridging during debonding of secondary bonded composite joints. The ligaments that bridge both substrates have crack-arrest features and thus significantly enhance the fracture resistance of joints. We have investigated the effect of randomly distributed adhesion properties between the adhesive layer and each composite substrate in previous works; however, the spatial correlation of adhesion heterogeneity within or between the substrates and how it effects the failure of secondary bonded composites is still poorly understood. In this current work, we assume that the spatial heterogeneity of adhesion follows a log-normal distribution. The Napierian logarithm of interface toughness Gc and separating strength S can thus be described by a Gaussian Process. We investigate in detail the effect of spatial correlation both within each substrate and between opposite substrates. Finally, we predict the crack resistance of such joints with adhesives of different mechanical properties. We find that the failure strain of adhesives is important through varying the elongation of ligaments and thus the associated extra dissipated energy. This work represents the first critical step for designing tougher secondary bonded composite joints by triggering and controlling adhesive ligament bridging.
... Fiber bridging can be caused by continuous fibers, whiskers, ductile ligaments, or even individual grains in a polycrystal [4] as well as the inserts of DCB specimen [5]. The modeling of the bridging mechanism is, depending on the considered material system, focused on either general bridging [4], bridging of fibers between sandwich facesheet and sandwich core [6][7][8][9][10][11], bridging of fibers perpendicular to the crack plane [12,13], or the bridging of fibers which are aligned with the crack plane [14][15][16][17][18][19][20][21]. The focus of this work is on the latter. ...
A recently developed cohesive zone traction-separation formulation for mode I facesheet to core disbonding, which includes the effects of fiber bridging in a novel way, is extended to account for mode II and mixed mode delamination. The pure mode I and mode II behavior of the model is calibrated based on traction separation curves which are extracted from Double Cantilever Beam (DCB) and End Notched Flexure (ENF) experiments utilizing the J integral. An existing mixed mode framework, which requires no further parameters, is used to predict the load displacement curves of Mixed ode Bending (MMB) tests. Very close agreement between numerical predictions and experimental results is observed for all demonstrated mixed mode ratios.
... The adhesive ligament is a phenomenon that is analogous to the fiber bridging regularly observed in laminate delamination. Fiber bridging is a typical mechanism due to variability in the material properties induced by micro effects, e.g ., weak bonding and fiber misalignments ( Kaute et al., 1993 ). Canal et al. (2017Canal et al. ( , 2016 applied connector elements with randomly distributed strong and weak strengths along the crack path to reproduce microscale imperfections and explore the mechanisms of fiber bridging. ...
Toughening strategies are needed to design high performance secondary bonded joints. Although adhesively bonded joints present a promising solution for cost-saving assembly, they are however among the most vulnerable parts in composite structures. Due to the inherent heterogeneity of composite substrates and the infeasibility of ideal surface pretreatments, the bonding properties of composite joints feature a spatial variability that can result in a wide variety of debonding phenomenology, such as crack tip transfer, crack bifurcation or ligament bridging. In the present work, we apply a cohesive zone model with spatially stochastic interfacial properties to model the physical behaviors that take place during debonding of an adhesively bonded composite joint. The joint distribution of the two essential bonding properties, namely, the critical separating stress σm and the strain energy release rate Gc, follows a bivariate lognormal probability distribution. The proposed model captures the mechanisms of crack-tip transfer and the failure of bridging adhesive ligaments between the composite adherends, as well as the associated toughening of joints. We find that the extrinsic dissipation attributed to extra debonding areas and plastic-damage mechanisms of ligaments may be one of the primary causes for the thickness effect of bondline on the fracture toughness, commonly observed for adhesively bonded joints. Through a parametric study, we discuss the effect of variability in interfacial properties on the enhancement of toughness of bonded composite joints. The outcomes of this work may provide insights into the fundamental failure mechanisms of secondary bonded composite joints.
... In composite materials, the rising R-curve behavior is often attributed to fiber bridging. 12,[26][27][28][29][30] However, in the presented work, all tested specimens showed signs of fiber bridging, even the specimens with a flat R-curve. To understand this difference in mode I energy release rate between the H and V specimens, one specimen from each group (tested with the DCB method) was pulled until separated into two pieces. ...
Interlaminar fracture properties of melt‐infiltrated woven SiC/SiC ceramic matrix composites were investigated using traditional and wedge‐loaded double cantilever beam methods. The two methods produced comparable GIC results for some specimens. The difference in boundary conditions between the two methods appeared to influence the crack propagation path. The DCB method, having free‐end boundary condition, allowed more interaction between the crack and the composite microstructure than the wedge method did. The effect of fiber tow layout sequence had an effect on the interlaminar properties. Higher toughness was observed for the orientation where crack propagation occurs between planes with more transverse tows. Jump‐arrest phenomenon was found to have higher significance on the rising R‐curve behavior than fiber bridging.
... It follows that, in order to obtain realistic results, the appropriate shape must be used. 55 Analytical models have been proposed to obtain cohesive laws accounting for fiber bridging [27,28,29,30]. However, these simplified models are not able to capture some of the experimentally observed features like the thickness effect. ...
A cohesive zone model (CZM) is proposed to assess the thickness scaling effect associated with fiber bridging during fracture. The CZM was developed through a multi-scale simulation approach and utilizes an embedded cell model of the Double Cantilever Beam (DCB) that explicitly accounts for the bridging bundles on the fracture plane. In particular, micromechanical simulations of failure were carried out, for varying arms thickness, in order to determine the homogenized fracture behavior. To model the observed scaling effect, the conventional cohesive law, formulated as an opening-stress law, is enriched with information on the crack opening angle. Continuum finite element simulations indicated that the proposed CZM was able to mimic very well the essential features observed in the experiments, raising R-curve behavior and thickness scaling effect on the energy dissipated at steady state.
... In fact, extensive fiberbridging between crack faces and slight tortuous crack path can be observed, rendering difficult in the clear identification of the crack tip by conventional observation methods via magnified lenses. Fiber-bridging is an important damage mechanism contributing to toughness increase [29]. This damage mechanism emerges in the DCB test. ...
A miniaturized version of the double cantilever beam (DCB) test is used to determine the fracture energy in human cortical bone under pure mode I loading. An equivalent crack length based data reduction scheme is used with remarkable advantages relative to classical methods. Digital image correlation technique is employed to determine crack opening displacement at the crack tip being correlated with the evolution of fracture energy. A method is presented to obtain the cohesive law (trapezoidal bilinear softening) mimicking the mechanical behavior observed in bone. Cohesive zone modelling (finite element method) was performed to validate the procedure showing excellent agreement.
... Three mechanisms are responsible for load transfer characteristics across bridged delamination cracks, i.e.: (1) fiber pull-out, (2) matrix spalling -the growth of cracks in the matrix due to stress concentrations caused by the presence of the bridging fibers, and (3) fiber fracture due to combined bending and axial loading, with a Weibull distribution describing the fiber failure statistics. The model describing the load transfer across the fiber bridging zone is an extension of the mode I crack bridging model of Kaute et al. [1]. The present work generalizes this model to deal with arbitrary values of mode mixity [2]. ...
High temperature ceramic matrix composites (CMCs) are material considered in many applications where high heat fluxes constitute a significant contribution to loading. The laminates can fulfill their function as thermal protection layers only if they stay intact, i.e. without internal delaminations or spalling, such that the heat flux remains undisturbed by such events. Crack bridging is an important effect in CMCs, and its implication to CMC laminates under thermal loading is investigated.
... If the fibre is metallic, however, then there is the potential for energy absorption, not only from fibre pull-out, but also as a result of plastic deformation of the fibre (assuming that fracture occurs such that fibres bridge the crack plane, which in general will require a certain minimum fibre aspect ratio and also at least some fibre debonding). This potential for energy absorption via fibre plasticity has been highlighted by several researchers [20][21][22][23][24][25] with particular attention having been drawn by Ashby and coworkers [20] to the concept of the constraint imposed by the surrounding matrix having an influence on the volume of fibre in which plastic deformation can occur, and hence on its effective ductility (and on the total plastic work). This is clearly dependent on the interfacial bond strength, which thus affects both fibre pull-out and fibre plasticity. ...
A model is presented for prediction of the fracture energy of ceramic–matrix composites containing dispersed metallic fibres. It is assumed that the work of fracture comes entirely from pull-out and/or plastic deformation of fibres bridging the crack plane. Comparisons are presented between these predictions and experimental measurements made on a commercially-available composite material of this type, containing stainless steel (304) fibres in a matrix predominantly comprising alumina and alumino-silicate phases. Good agreement is observed, and it’s noted that there is scope for the fracture energy levels to be high (∼20 kJ m−2). Higher toughness levels are both predicted and observed for coarser fibres, up to a practical limit for the fibre diameter of the order of 0.5 mm. Other deductions are also made concerning strategies for optimisation of the toughness of this type of material.
Description
This concise, archival reference examines the results of the latest research and development programs on continuous fiber ceramic composites (CFCCs). It examines specific issues, such as thermal stresses, stress gradients, measurement capabilities, gripping methods, environmental effects, statistical considerations, and limited material quantities.
22 peer-reviewed papers are divided into 4 major categories:
• Room-Temperature Test Results/Methods
• Test Results/Methods Related to Design Implications
• Environmental Effects and Characterization
• Damage Accumulation and Material Development
Please note: This volume serves as an excellent companion to STP 1309/Thermal and Mechanical Test Methods and Behavior of Continuous-Fiber Ceramic Composites.
This publication will be of value to
• Gas Turbine Designers
• Materials Scientists
• Ceramicists
• Power Systems Engineers
• Mechanical and Design Engineers
Damage mechanisms in composite laminates are quite complex, and it is necessary to perceive their effects on the degradation of laminate mechanical properties. This work employs acoustic emission (AE) and digital image correlation (DIC) techniques to describe the evolution of intra/inter-laminar damage modes in the CFRP laminates under in-plane/out-of-plane loading conditions. In this study, laminates of stacking sequences [900]8, [450]8, [450/−450]2s, and [00]8 under tensile load are investigated to distinguish the intra-laminar damages like matrix cracking, fiber–matrix debond, and fiber breakage. Double cantilever beam, end notch flexure, and mixed-mode bending specimens are used to characterize delamination failure in the laminate. An unsupervised k-means clustering technique is used to classify the AE data based on peak frequency and amplitude. The surface displacement and strain data are evaluated using the DIC technique to understand the damage evolution in the laminates. Post failure analysis is carried out using a digital microscope, and fractography studies are used to identify and assign the damages to different AE clusters. This investigation yields a taxonomy of damage modes, their sequence of occurrence, and failure strains that can be used for structural health monitoring and progressive damage modeling of composite laminates.
A strain-based criterion is presented in this paper to investigate mixed-mode I/II fracture behavior in orthotropic materials. The maximum principal strain component, in the vicinity of a crack existing in an orthotropic medium, is formulated considering the T-stress effect as well as the singular terms. The criterion predicts the onset of mixed-mode I/II fracture when the maximum principal strain reaches its critical value. The role of T-stress, calculated for an orthotropic domain, in the mixed-mode I/II fracture toughness assessment is explored theoretically. Along with other criteria, the accuracy of the proposed criterion is evaluated by predicting the fracture test data in the literature for wood species and laminated composites. The developed criterion is shown to be superior to other criteria in predicting the onset of mixed-mode I/II fracture in orthotropic materials.
Adhesive bonding community shows a continued interest in using bridging mechanisms to toughen the interface of secondary bonded joints, especially in the case of laminated composites. Due to snap-back instability that occurs during fracture, confusions may exist when identifying the toughening effect experimentally. The true toughening effect may be overestimated by lumping all energy contributions (kinetic energy included) in an overall effective toughness. Here, fundamentals for bridging to enhance fracture resistance are explored through the theoretical analysis of the delamination of a composite double cantilever beam (DCB) with bridging. Specifically, we establish a theoretical framework on the basis of Timoshenko beam theory and linear elastic fracture mechanics to solve the fracture response of DCB in the presence of discrete bridging phases. We elucidate the crack trapping and the snap-back instability in structural response during the crack propagation. We identify the contribution to the overall toughness observed numerically/experimentally of both the physical fracture energy and other types of dissipation. The associated toughening mechanisms are then unveiled. Furthermore, we study the effects of property of the bridging phases on the snap-back instability, based on which, we propose a dimensionless quantity that can be deployed as an indicator of the intensity of snap-back instability. Finally, we identify the role of geometrical properties, i.e. the substrate thickness and the arrangement spacing of the bridging phases, in the snap-back instability and the macroscopic fracture toughness of a DCB. This work provides, from a theoretical point of view, an essential insight into the physics related to the structural response of DCB with discrete toughening elements.
Fiber-reinforced polymer composites are widely used in the aerospace industry due to their high stiffness and strength-to-weight ratios. However, their applicability can be limited by their relatively low interlaminar properties when compared to metallic alternatives. Through-thickness reinforcement approaches, such as stitching, z-pinning, needling, tufting, and three-dimensional weaving, have been developed in recent decades to enhance the interlaminar properties of composites. Stitching is considered to be an efficient and cost-effective method to reinforce composites in the through-thickness direction. Additionally, stitch parameters (stitch density, linear thread density, thread material, pretension, etc.) highly influence the in-plane and out-of-plane properties. This paper summarizes results from over one hundred papers on the influence of stitch parameters on fracture energy, interlaminar strength, and impact characteristics of stitched composite laminates, sandwich composites, and high-temperature composites. Much of the research on the influence of stitch parameters has focused on thermoset polymer matrix composites (PMCs), while fewer studies have investigated the impact of stitch parameters on high temperature or sandwich composites. Modification of existing and new test methods have been developed to adequately measure the effectiveness of stitching on the out-of-plane behavior of PMC panels. Results demonstrate that out-of-plane properties of PMCs are highly dependent on stitch parameters and can be enhanced by through-thickness stitching.
A combined stress/energy-based (CSE) criterion is developed to predict mixed mode I/II fracture behavior in laminated composites by taking into account the effect of fiber bridging toughening. Following the proposed criterion, first, the absorbed energy resulting from fiber bridging micro-mechanisms is obtained and translated into a defined effective critical distance (i.e., the size of the crack tip micro-cracking zone). Then, the maximum principal stress is evaluated at the calculated effective critical distance around the crack tip to predict the onset of fracture. The CSE criterion is employed, along with other criteria, to predict experimental data reported in the literature on the onset of mixed mode I/II fracture in laminated composites and wood species (i.e. orthotropic composites). A higher correlation is found between the theoretical results predicted by the CSE criterion and the test data, as compared to other criteria. The stress-based formulation of the CSE criterion offers more computational simplicity as compared to the energy-based criteria while providing an acceptable accuracy and taking into account the effects of absorbed energy resulting from the micromechanical fiber bridging in the solution.
Traction-separation relations due to large scale bridging in composites are very important in modeling their fracture response. Several works demonstrated that such relations are dependent upon the specimen's stiffness and loading conditions. Experimental data and micromechanics of bridging suggested that, in addition to the crack opening displacement (COD), the local curvature can be used as an additional kinematic parameter to incorporate the stiffness dependence on traction-separation-angle relations. In this work, analysis of data from DCB specimens with different stiffness, in three different materials, subjected to monotonic end opening forces, demonstrates that when the tractions are correlated with the product of local angle and COD, a stiffness independent traction-separation-angle relation is obtained, and can be implemented in an FE scheme. The methodology is further exemplified by fatigue data and fracture under pure moments that highlight the importance of the second kinematic parameter and the soundness of the approach.
Fiber reinforced composites are quickly replacing their metal counterparts in the structural applications due to their higher specific strength and stiffness. The fiber bridging increases the fracture toughness of the composites several times. At the same time, the characterization of the composites is challenging due to fiber bridging. Large number of studies has been devoted to investigate various aspects of fiber bridging phenomenon in the composites. This paper is a comprehensive review of the literature studies on fiber bridging. The paper is mainly focused on the origin of fiber bridging, bridging laws, experimental investigations and cohesive zone modeling of the delamination in the presence of fiber bridging. The fatigue delamination growth characterization in the presence of fiber bridging and the significance of stitching/z-pinning are also briefly discussed in this literature review.
Mode-I delamination crack growth in Ceramic Matrix Composite (CMC) materials is studied using experiments and associated numerical modeling. Double cantilever beam tests were conducted to measure delamination growth characteristics and the associated mode-I critical energy release rate. The tests revealed significant crack growth resistance (R-curve) behavior with the load carrying capacity increasing with the delamination growth. The experimentally observed load-displacement response could not be explained by linear elastic fracture mechanics or by a two-parameter triangular cohesive finite element models. The observed crack growth resistance behavior is explained by incorporating cohesive traction-separation relationship with a bilinear softening resulting in a long “tail”, which is interpreted and modeled as a superposition of two traction-separation relationships representing mechanisms associated with near crack-tip region and fiber-bridging in the crack-wake, respectively.
It is well known that large-scale bridging accompanying delamination and fracture in layered composites is among the most important toughening mechanisms. The resulting resistance to fracture, however, is dependent on the specimen geometry rendering its modeling difficult. As a consequence, characterization of the tractions on the wake of the crack, the so-called bridging zone, is very important in the efforts to predict the loading response of composite structures. In this chapter, experimental results and modeling of delamination and fracture in layered composite specimens are discussed. The experimental part consists of displacement-controlled monotonic tests of interlaminar and intralaminar fracture. Selected specimens are equipped with wavelength-multiplexed fiber Bragg grating (FBG) sensors to monitor crack propagation and strains over several millimeters in the wake of the crack. The modeling part involves an iterative scheme to calculate the traction-separation relation, due to bridging, using the strains from the FBG sensors, parametric finite elements, and optimization. The experimental results demonstrate an important effect of specimen thickness in interlaminar and intralaminar fracture: the bridging zone length at steady state linearly increases with specimen thickness, while the maximum bridging stress is independent of thickness in each case. Results of a similar study in cross ply specimens, limited to a selected specimen thickness, show important effects of specimen width on the extent of large-scale bridging. The obtained traction-separation relations for each investigated case are employed in cohesive zone simulations to predict the corresponding load-displacement curves. On the basis of the experimental results, a micromechanics model is used, based on an embedded-cell model, to predict the observed specimen thickness effects on large-scale bridging. The results of the reported studies demonstrate that the so-called bridging law is not a material parameter and the proposed methods of analysis, predict very well the load-displacement response.
The toughening behaviour of a number of SiC fibre reinforced glass-ceramic systems was evaluated in terms of the crack growth resistance curve by performing three point bend tests on notched samples. During testing the initiation and growth of delamination cracks were observed. Afterwards a model was developed that describes the crack growth resistance of the materials. The basic assumption of the model is that the cracks are of mixed mode. They initiate from the notch in mode II, but as the crack proceeds the mode I-component becomes more important. At large crack lengths, the cracks consist almost entirely of a mode I-component. A comparison of theory and experiment shows that the model offers a reasonable description of the crack growth resistance of the composites.
Fiber reinforced composites can develop large scale bridging upon mode I fracture. This toughening mechanism depends on the constituents and the geometry of the specimen, and is especially important in unidirectional laminates when fracture is parallel to the fibers. The mode I intralaminar fracture behavior of unidirectional carbon-epoxy laminates was investigated by means of a three-dimensional multiscale model based on an embedded-cell approach. A double cantilever beam specimen was represented by an anisotropic homogeneous solid, while the bridging bundles ahead of the crack tip were included as beam elements. The failure micro-mechanisms controlling the crack propagation (namely, decohesion and subsequent failure of the bridging bundles) were included in the behavior of the different constituents. Numerical simulations were able to predict the macroscopic response, as well as the development of bridging and the growth of the crack. These results demonstrated the ability of the virtual testing approach to study complex fracture processes in composite materials. Finally, the developed model was employed to study the thickness effect and ascertain the influence of the constituents’ properties on the energy released during fracture.
A study was conducted to improve upon currently used test procedures for determining the Mode I, Mode II and mixed-mode delamination toughness of ceramic matrix composite materials. Test methods and specimen geometries were chosen that may be used to test unidirectional or multidirectional layups. The test methods consisted of the Mode I double cantilever beam test, the Mode II end-notched flexure test and the mixed-mode single leg bending test. Procedures for these tests were developed that could be used at room or elevated temperature and for which a compliance calibration method of data reduction could be employed. These procedures were then used to perform a study on a Nicalon/MAS-5 fiber-reinforced ceramic to determine the effects of mode ratio, temperature and layup on delamination toughness. It was concluded that the three test methods combined can be used to provide sufficient information on the variation of toughness with mode mix for most design purposes.
Low temperature regimes impose various constraints with regard to structural material performance. In this context, advanced composite materials and fiber-reinforced metal laminates (FML) have been considered to be appropriate candidates, and in some cases even a favored choice. As such, FML GLARE 2 was selected, as it has recently been examined for some applications in the aerospace industry.
GLARE 2 was mechanically characterized with regard to low temperatures and orientation effects by monotonic loading of uniform and notched specimens, and by some results from cyclic loading. The mechanical tests were accompanied by supplementary characterization techniques [optical and SEM microscopy, acoustic emission (AE) combined with stress wave emission (SWE) monitoring, and fast Fourier transform (FFT) analysis] in order to clarify the controlled fracture mechanisms and the damage build-up profile, with regard to the dominant variables (temperature and orientation).
The experimental results emphasized the anisotropic mechanical behavior of GLARE 2 in terms of tensile and fracture toughness properties. The distinct mechanical response at the various orientations was reflected by other supporting findings such as SWE shapes and the frequency of their appearance, event count rates, characteristic frequency, and fracture modes at some stress levels and at failure. These comprehensive data make it possible to point out the main fracture mechanisms, which govern damage accumulation, including temperature effects; these may be helpful in the composite processing design. In addition, it has been shown that the degree and progression of damage can be associated with AE event count rates. Similar tendency related to crack density has also been assessed using damage mechanics models.
Photothermal non-destructive evaluation (NDE) of solids is a powerful method to detect subsurface cracks, inclusions and delaminations. To fully explore the use of this method, and to expand its capabilities a quantitative measurement model is required. Such a model provides the link between the actual damage processes in the material or structure under investigation and the measurement system response. In the proposed paper a numerical simulations of the photothermal non-destructive evaluation of unidirectionally reinforced composite materials. In the investigation, special focus is placed on the description of the interaction of the thermal field with the delamination to be detected. The model consists of two main parts: (1) a probabilistic crack advance and crack bridging model embedded in a full field solution of the actual loaded structure, and (2) a model describing the thermal characteristics of the bridged delamination in dependence of the loading state and the probabilistic fiber failure model. The paper will describe results on computationally predicted thermal response data in dependence of the type and magnitude of the applied loading for the case of ceramic matrix composite materials.
Large scale bridging is an important toughening mechanism in composite laminates that depends on the
specimen geometry as well as the constituent materials. In this work, an iterative approach is applied to
identify the effect of specimen thickness on traction–separation behavior in the bridging zone. Double
cantilever beam specimens (DCB) with embedded arrays of wavelength-multiplexed fiber Bragg grating
(FBG) sensors are subjected to monotonic mode I fracture loading. As processed specimens with thicknesses
h = 2, 4, 8 and 10 mm as well as specimens of h = 4 mm milled down from the 8 and 10 mm are
tested. Non-homogeneous strain distributions in the vicinity of the interlaminar crack plane are locally
monitored by means of embedded FBGs. The measured strain data are used to quantify the bridging tractions
associated with each specimen thickness and consequently the energy release rate (ERR) due to the
bridging. The results show that the bridging zone length and the ERR at the plateau level increase with
specimen thickness while the results for all specimens with h = 4 are the same thus excluding any processing
effects. Moreover, the maximum stress of traction-opening in the bridging zone and crack opening
displacement at the end of the zone are independent of thickness. In contrast, the rate of tractions
decay depends on the specimen thickness in that it decreases with thickness scaling. Thus the so-called
bridging law is not a material parameter. The identified traction–separation relations are employed in a
cohesive zone model to predict fracture of DCB specimens with different thicknesses.
Large scale bridging in mode-I delamination of layered composites is an important toughening mechanism. While its extent depends on constituent materials, it is also influenced by specimen geometry. Here, an analytical approach is adopted to express the through the thickness longitudinal strains in a double cantilever beam (DCB) specimen with the applied load and bridging tractions. The expression for the strains is confronted with strain data from embedded Bragg grating sensors to obtain bridging tractions in specimens with different thickness. The results show that the maximum stress of traction-separation in the bridging zone and maximum crack opening displacement at the end of the bridging zone are independent of thickness. However, the form of the bridging traction depends on thickness and is not a material property. The identified bridging relations are appended in a cohesive zone model to simulate delamination. The proposed approach predicts fracture of DCB specimens with different thicknesses.
Bridging by intact fibers is an important toughening mechanism in composite materials. However, a direct experimental evaluation of its contribution is difficult to achieve and in the case of large scale bridging the thickness, h, may have an important influence on the energy release rate (ERR). In this work a semi-experimental method is adopted to quantify the effects of thickness to fracture of unidirectional glass fiber reinforced polymer (GFRP) double cantilever beam specimens in mode I fracture under monotonic loads. Several specimens with thickness in the range of h = 3.5–19 mm are tested. In two selected specimens, embedded optical fibers with an array of eight or ten wavelength division multiplexed fiber Bragg gratings were are to measure local strains close to the crack plane and employed in an inverse identification procedure to determine the bridging tractions. The results suggest that the stress at the start of the bridging zone and the crack opening displacement at its end are independent of the specimen thickness. However, the rate of change of the tractions with crack length depends on the specimen thickness. While the initiation value of the ERR is independent of h, at the steady state it varies from 900 (h = 3.5 mm) to 2100 J/m2 (h = 19 mm). Using the identified tractions, the total stress intensity factor (SIF) and the corresponding ERR are calculated. The results show that the SIF approach gives similar results. Thus thickness, via the bridging fibers, is responsible for the effects on steady state ERR observed in the specimens used herein.
This paper makes a critique of the double torsion (DT) test technique in studying the transverse fracture behavior of SiC/CAS-I1 glass-ceramic composite. Previous to this study, there has not been much work on high temperature transverse properties of this composite. The applicability of the DT method to elevated temperatures was demonstrated. Test rate had a considerable effect on the compliance for the DT tests performed at high temperatures. This is believed to be due to the thermal expansion/shrinkage of the metals used in the DT test system. However, this did not appear to be a problem for the purposes of this study. Transverse fracture toughness data, coupled with scanning electron microscopy and microdebonding analysis of the fracture surfaces, indicated no significant effect of high temperature oxidative environment on cracking parallel to the fibers in SiC/CAS-I composite.
In many materials, ligaments form upon crack extension and cause toughening by a crack bridging mechanism. Such materials include composites, layered systems and certain single crystals. Analysis of the phenomenon has revealed microstructural requirements for optimum combinations of toughening and strengthening. The preference is for ligaments that achieve high yield strength, exhibit high touchness, small size large area fraction. Ligament plasticity amends these requirements to a preference for larger ligaments: unless there are unchartered effects of the ligament size on their yield strength and rupture strain. These effects are discussed and quantified. © 1997 Acta Metallurgica Inc.
A fiber bridging model has been created to examine the effects of bridging on Mode I delamination fatigue fracture in a carbon fiber polymer–matrix composite. The model uses a cohesive zone law that is derived from quasi-static R-curves to determine the bridging energy applied in the bridged region. Timoshenko beam theory and an iterative self-consistent scheme are used to calculate the bridging tractions and displacements. After applying the bridging model to crack propagation data the scatter in the data was significantly reduced and clear trends were observed as a function of temperature that were not apparent previously. This indicated that the model appropriately accounted for the bridging in the experiments. Scanning electron microscopy crack opening displacement measurements were performed to validate the model’s predictions. The measurements showed that the predictions were close to the actual bridging levels in the specimen.
Problems arising during characterisation of fracture resistance due to fibre bridging are reviewed and discussed. A distinction is made between small scale bridging and large scale bridging. Simple criteria are used to distinguish between the two types of bridging. Under small scale bridging the crack growth resistance can be characterised by an R-curve. However, under large scale bridging the shape of the R-curve depends on specimen geometry. Therefore, it is preferable to characterise large scale bridging by a bridging law. Methods for determining bridging laws are discussed. Experimental results indicate that the bridging law is independent of specimen geometry, i.e. a material property. Finite element procedures for implementation of bridging laws in component design are outlined.
Cracking parallel to the fibers in off-axis plies is usually the initial form of damage in composite laminates. This cracking process has been associated with the (transverse) fracture toughness, defined by the critical strain energy release rate, GIc. The measurement of GIc provides basic information about the transverse crack resistance. In this study, the utility of the double torsion (DT) test technique to determine GIc in a glass-ceramic matrix composite (Nicalon/CAS-II) at temperatures up to 1000°3C has been demonstrated. GIc did decrease moderately with increasing temperature (as does the bulk matrix); however, no evidence of an interphase oxidizing effect on crack growth (parallel to the fibers) could be found. The inevitable misalignment of fibers in the material was not very efficient at bridging the crack in the DT specimens, in contrast to the significant matrix crack interactions with the fibers reported for other geometries such as double cantilever beam and flexure specimens.
An approach for the coupled thermomechanical analysis of composite structures with bridged cracks is described. A crack bridging law is presented that accounts for breakdown of load as well as of heat transfer across the crack with increasing crack opening. The crack bridging law is implemented into a finite element framework as a cohesive zone model and is used for the investigation of unidirectional laminates under prescribed temperature gradients. The effects of crack bridging parameters on energy release rates, mode mixity and crack heat flux is discussed for boundary conditions which lead to crack opening either through bending deformation or delamination buckling.
The fracture of ceramic-matrix composites is frequently complex, involving the evolution of subcritical damage which strongly affects the final failure process, and which is very specimen dependent. In this and a companion paper, observations of fracture mechanisms are described for a calcium-alumino-silicate (CAS) glass reinforced with SiC fibres. The tests were principally undertaken dynamically in situ within a scanning electron microscope. This technique enables detailed characterization of the subcritical damage and of the crack interactions which occur prior to final failure. It is shown that meaningful modelling of fracture processes in these materials generally requires this level of detail in identifying the micromechanisms. This paper describes a preliminary evaluation of the unnotched tensile response of the material, followed by in situ observations on two common delamination geometries: four-point bending and double cantilever beam. The tensile behaviour of edge-notched specimens is described in the companion paper.
We propose a hybrid technique to extract cohesive fracture properties of a quasi-brittle (not exhibiting bulk plasticity)
material using an inverse numerical analysis and experimentation based on the optical technique of digital image correlation
(DIC). Two options for the inverse analysis were used—a shape optimization approach, and a parameter optimization for a potential-based
cohesive constitutive model, the so-called PPR (Park-Paulino-Roesler) model. The unconstrained, derivative free Nelder-Mead
algorithm was used for optimization in the inverse analysis. The two proposed schemes were verified for realistic cases of
varying initial guesses, and different synthetic and noisy displacement field data. As proof of concept, both schemes were
applied to a Polymethyl-methacrylate (PMMA) quasi-static crack growth experiment where the near tip displacement field was
obtained experimentally by DIC and was used as input to the optimization schemes. The technique was successful in predicting
the applied load-displacement response of a four point bend edge cracked fracture specimen.
KeywordsCohesive zone model (CZM)–Digital image correlation (DIC)–Park-Paulino-Roesler (PPR) model–Nelder-Mead scheme
Guided by the orthotropy rescaling technique and other available analytic results, a systematic analysis is conducted for commonly used fracture specimens to investigate the role of material orthotropy in fracture behavior of unidirectional composites. Included are notched bars, delamination beams and hybrid sandwiches, of many varieties All numerical calibrations are presented with fitting formulae in the relevant parameter regimes. The effect of material orthotropy on fracture behavior of unidirectional composites is thus quantified, which significantly reduces the complexities involved in both experimental investigation and theoretical modelling. A summary of the orthotropy rescaling concepts, with some extensions, is also included.
This article summarizes the current understanding of relationships between microstructure and mechanical properties in ceramics reinforced with aligned fibers. Emphasis is placed on definition of the micromechanical properties of the interface that govern the composite toughness. Issues such as the debond and sliding resistance of the interface are discussed based on micromechanics calculations and experiments conducted on both model composites and actual composites.RésuméCet article résume la compréhension courante des relations qui existent entre microstructure et propriétés mécaniques dans les céramiques renforcées par des fibres alignées. L'accent est mis sur la définition des propriétés mécaniques de l'interface qui régissent la résistance du composite. On discute les conséquences telles que la résistance à l'arrachement et au glissement à l'interface, en se basant sur des calculs de micromécanique et sur des expériences réalisées à la fois sur des composites modèles et sur des composites réels.ZusammenfassungDieser Artikel stellt den gegenwärtigen Stand im Verständnis des Zusammehanges zwischen Mikrostruktur und mechanischen Eigenschaften von Keramiken, die mit ausgerichteten Fasern verstärkt sind, zusammen. Besonderer Wert wird auf die Definition der mikromechanischen Eigenschaften der Grenzfläche gelegt, welche die Zähigkeit des Werkstoffes bestimmen. Bestimmte Fragenkreise, wie die Ablösung oder der Gleitwiderstand an der Grenzfläche, werden auf der Grundlage von mikromechanischen Rechnungen und von Experimenten, die an Modell- und echten Werkstoffen durchgeführt wurden, diskutiert.
The article draws upon recent work by us and our colleagues on metal and ceramic matrix composites for high temperature engines. The central theme here is to deduce mechanical properties, such as toughness, strength and notch-ductility, from bridging laws that characterize inelastic processes associated with fracture. A particular set of normalization is introduced to present the design charts, segregating the roles played by the shape, and the scale, of a bridging law. A single material length, γâE/Ïâ, emerges, where γâ is the limiting-separation, Ïâ the bridging-strength, and E the Young`s modulus of the solid. It is the huge variation of this length-from a few manometers for atomic bond, to a meter for cross-over fibers - that underlies the richness in material behaviors. Under small-scale bridging conditions, γâE/Ïâ is the only basic length scale in the mechanics problem and represents, with a pre-factor about 0.4, the bridging zone size. A catalog of small-scale bridging solutions is compiled for idealized bridging laws. Large-scale bridging introduces a dimensionless group, a/(γâE/Ïâ), where a is a length characterizing the component. The group plays a major role in all phenomena associated with bridging, and provides a focus of discussion in this article. For example, it quantifies the bridging scale when a is the unbridged crack length, and notch-sensitivity when a is hole radius. The difference and the connection between Irwin`s fracture mechanics and crack bridging concepts are discussed. It is demonstrated that fracture toughness and resistance curve are meaningful only when small-scale bridging conditions prevail, and therefore of limited use in design with composites. Many other mechanical properties of composites, such as strength and notch-sensitivity, can be simulated by invoking large-scale bridging concepts. 37 refs., 21 figs., 3 tabs.
An experimental investigation has been carried out on the mechanical
properties of unidirectional (0)12, (0, 90)3S,
(± 45, 02)S, and (± 45)3S
composites consisting of CAS glass ceramic reinforced with Nicalon SiC
fibres. Measurements have been made of the elastic properties and of the
tensile, compression and shear strengths of the composites, and these
have been supported by a detailed study of the damage which occurs
during monotonic and repeated loading. These damage studies have been
carried out by means of edge replication microscopy and acoustic
emission monitoring. The elastic properties of the composites are, by
and large, close to the values that would be predicted from the
constituent properties and lay-up sequences, but their strengths are
lower than expected, and it appears that the Nicalon reinforcing fibre
has been seriously degraded during manufacture. The fracture energy is
much higher than predicted from observations of fibre pull-out, and it
is suggested that the energy required to form a close three-dimensional
network of matrix cracks could account for the high apparent toughness.
The matrix cracking stress can be predicted reasonably closely by the
Aveston, Cooper and Kelly model of cracking in brittle matrix
composites, but it is shown that subcritical microcracks can form and/or
grow at stresses well below the predicted critical values without
affecting composite properties.
The interlaminar fracture behaviour of AS4/PES (poly(ether sulphone)) composite has been investigated in Mode I, Mode II and for fixed Mode I to Mode II ratios of 0·84, 1·33 and 2·13. The data obtained from these tests have been analysed using several different analytical approaches. The results obtained show that in Mode I the interlaminar crack growth in double cantilever beam (DCB) specimens is accompanied by fibre bridging behind the crack tip and by splitting at the crack tip, and in Mode II by the formation of a damage zone at the crack tip. These failure mechanisms are shown to increase the value of the interlaminar fracture energy considerably as the crack propagates through the composite, i.e. a rising ‘R-curve’ is measured. It is shown also that the value of the interlaminar fracture energy at crack initiation in Mode I, (init), increases as the length of the initial precrack is increased. The lowest (init) value obtained for the poly(ether sulphone) (PES) composite in this study is 0·8 kJm−2, and this value was ascertained from a specimen with the precrack being grown by about 2 mm ahead of the initial crack (). The typical Mode II steady-state propagation energy, (s/s-prop), value obtained for the specimens was about 2·0 kJm−2. The length of the initial precrack had no significant effect on the (init) and (init) values. The Mode II tests gave values of and of . Finally, the failure loci for the PES composite have been constructed and theoretical expressions to describe these data considered.
The characteristics of the toughening of brittle matrices by ductile inclusions are demonstrated by model experiments, and analysed using recently developed techniques. Design considerations, and the transition from single-crack mechanics to the regime of multiple cracking, or “continuum damage” mechanics are described.RésuméOn étudie les caractéristiques de l'augmmentation de ténacité des matrices fragiles par les inclusions ductiles grâce à des expériences modèles; elles sont analysées en utilisant de techniques récemment développées. On dérit des considérations de conceptio, et la transition de la mécanique à une seule fissure au régime à fissures multiples, ou mécanique du “dégât continu”.ZusammenfassungDie Charakteristika der Zähigkeitsverbesserung spröder Matrix-Materialien durch duktile Einshls̈se werden mit Modell-Experimenten gezeigt und mit kürzlich entwickelten Methoden analysiert. Überlergungen zur Auslegung und der Übergang von der Ein-Riβ-Mechanik zum Bereich vieler Risse oder der “Kontinuums-Schädigungs”-Mechanik werden beschrieben.
The pullout of fibers in the crack wake makes an important contribution to the toughness of ceramic-matrix composites. The pullout is, in turn, influenced by the properties of the fibers and by the sliding resistance of the interface. Basic relationships governing the pullout are developed analytically and investigated experimentally using a lithium aluminum silicate/silicon carbide (LAS/SIC) composite subjected to various heat treatments. The experiments involve determining the strengths of single fibers and then measuring the pullout distributions. The results are used to provide a consistent view of the pullout process and related changes in mechanical properties.
An exact theory is developed to describe the evolution of fibre fragmentation in a single-filament composite test as a function of the underlying fibre statistical strength and fibre/matrix interfacial shear stress, . The fragment distribution is a complicated function of fibre strength and because the stress around breaks which do occur recovers to the applied value, , over a length () determined by . Therefore, no other breaks can occur within () of an existing break. To account for this effect, the fibre fragment distribution is decomposed into two parts; fragments formed by breaks separated by more than () at stress , and fragments smaller than () which were formed at some prior stress when a smaller () () prevailed. The distribution of fragments larger than () is identical to that of a fibre with a unique non-statistical strength and is known exactly. The distribution of fragments smaller than () can then be determined from the distribution of the longer fragments. Predictions of the theory are compared to simulations of fibre fragmentation for several common models of stress recovery around fibre breaks with excellent agreement obtained. The present theory can be utilized to thus derive both thein situ fibre strength at short gauge lengths and the from experimentally obtained fragment distributions, and an unambiguous inversion procedure is briefly discussed. The application of the theory to other multiple-cracking phenomena in composites is also discussed.
An investigation of the structure and properties of a calcium aluminosilicate glass-ceramic reinforced with Nicalon fibres is described. Microstructural analysis of the interface showed that during manufacture of the composite a reaction zone rich in carbon formed between the Nicalon fibre and the anorthite matrix. Tensile strengths were approximately 330 MPa for unidirectional material and around 210 MPa for a (0/90)3s. composite, little more than half that predicted by the mixtures rule. Flexural strengths were, however, higher than tensile strengths, by a factor 1.5–2.5 depending on lay-up. Studies carried out on specimens heat treated in air for 24 h at temperatures in the range 600–1200 C showed a progressive change of interface microstructure in the outermost regions of the specimens due to oxidation of the carbon-rich layer; at 1000 C and above the carbon had disappeared to leave voids and silica-rich bridges between fibre and matrix. These changes affected the strength of the interfacial bond, as measured by an micro-indentation technique, and also the degree of fibre pull-out produced in mechanical tests. Thus as-received material exhibited appreciable pull-out whilst heattreated samples were characterized by brittle behaviour in the outer (oxidized) regions. Nevertheless, the composites whilst in the unstressed condition appeared to survive these short-term exposures to oxidizing environments. An interfacial shear stress of around 5 MPa was calculated by applying the Aveston, Cooper and Kelly theory to crack spacings measured in our room-temperature deformation experiments, a value which agreed well with the 3–5 MPa obtained by the micro-indentation method.
The use of silicon carbide-type fibres to reinforce lithium aluminosilicate glass ceramics results in composites with exceptional
levels of strength and toughness. It is demonstrated that composite strength and stress-strain behaviour depend onin situ fibre strength, matrix composition, test technique and atmosphere of test. Both linear and non-linear tensile stress-strain
curves are obtained with ultimate strengths at 22° C approaching 700 MPa and failure strains of 1%. Flexure tests performed
at up to 1000° C in air are compared with data obtained in argon to demonstrate a significant dependence of strength and failure
mode on test atmosphere. Finally, glass ceramic matrix composite performance is compared with a silicon carbide fibre-reinforced
epoxy system to demonstrate the importance of matrix failure strain on strength and stress-strain behaviour.
Delamination cracks in composites may interact with misaligned or inclined fibers. Such interactions often lead to fiber bridging, which causes the nominal delamination resistance to increase as the crack "tends. Substantial specimen geometry effects are also involved. An experimental investigation of the role of fiber bridging has been conducted for three different composites. The results are compared with fiber bridging models based on a softening traction law, leading to schemes for predicting trends in delamination resistance with specimen geometry and crack length. Implications for utilizing this effect to suppress the growth of delaminations are presented.
Brittle solids can be toughened by incorporating ductile inclusions into them. The inclusions bridge the crack and are stretched as the crack opens, absorbing energy which contributes to the toughness. To calculate the contribution to the toughness it is necessary to know the force-displacement curve for an inclusion, constrained (as it is) by the stiff, brittle matrix. Measured force-displacement curves for highly constrained metal wires are described and related to the unconstrained properties of the wire. The constraint was achieved by bonding the wire into a thick-walled glass capillary, which was then cracked in a plane normal to the axis of the wire and tested in tension. Constraint factors as high as 6 were found, but a lesser constraint gives a larger contribution to the toughness. The diameter of the wires (or of the inclusions) plays an important role. Simple, approximate, models for the failure of the wires are developed. The results allow the contribution of ductile particles to the toughness of a brittle matrix composite to be calculated.
Fiber failure locations with respect to a given matrix crack are determined for single and multiple matrix cracking in ceramic composites by defining a pointwise failure probability in terms of the Weibull strength theory. The composite is assumed to be reinforced with uniaxially aligned continuous fibers with frictionally constrained interfaces. The average fiber pullout lengths after complete and partial fiber failure are given for both single and multiple matrix cracking. Previous results reported by Sutcu [(J. Mater. Sci. 23, 928 (1988)] for the work of fracture are refined, and the composite strength beyond matrix cracking is estimated for multiple matrix cracking, assuming that all matrix cracks behave in a similar manner throughout the composite volume. The frictional stress caused by bridging fibers is considered in the strength computation in order to improve the strength prediction, especially beyond the ultimate load. The predicted results are compared to experimental results on LAS-Glass/Nicalon fiber composite.
Mode I fracture properties, in particular the critical strain energy release rate GIC, of a unidirectional glass/epoxy composite for crack growth parallel to the fibres, were studied in two ways using double cantilever beam specimen geometry. In the first case, a crack was propagated by repeated loading-unloading cycles. The specimens deviated from linear elastic beam and linear elastic fracture mechanics predictions with respect to their compliance and load at crack propagation, and GIC showed a continuous increase with crack growth, owing to the progressive build-up of a fibre-bridged zone behind the crack tip. In the second case, the crack was propagated in a similar manner but the bridging fibres were removed periodically using a stress corrosion treatment in a solution of 2n HCl. This treatment effectively restored the linear elastic beam behaviour and reduced GIC to an unbridged value which is independent of crack length.
A review of the state of the art in the subject of interlaminar fracture toughness (ift), its relation to structural performance and the damage tolerance of polymeric composite materials is presented. The sources of low ift (high brittleness) of existing materials and methods to im4prove it by introducing tough interlayers or by using thermoplastic matrices are discussed. The IFT test methods, their analytical basis and utilization are described. Comprehensive ift data for GIc and GIIc for different composite systems and test methods, which was extracted from numerous publications, are presented.
This paper reviews the formulation of the problem of a bridged crack in an elastic medium as an integral equation, noting explicit forms for specimens of various common shapes. Numerical methods are provided for the convenient and efficient self-consistent solution of the integral equation when the bridging tractions, p, are a function of crack opening displacement, u, rather than an explicit function of position in the crack. Methods are presented for determining physically and computationally unstable crack configurations for various forms of p(u), including functions possessing a peak. Knowledge of both stable and unstable solutions is essential to demarking the transition from noncatastrophic (or ductile) failure to catastrophic (or brittle) failure.
The Mode I delamination failure of fibre-reinforced epoxy laminates was characterized using the uniform double cantilever beam test specimen and scanning electron microscopy. Generally, this failure appeared in a variety of forms, depending on ply orientation, test-specimen geometry and matrix toughness. The calculated fracture energy heavily depended on the fracture surface morphology. By defining interlaminar fracture strictly as an interlaminar separation including no fibre breakage, pull-out, etc, a material property independent of test-specimen geometry and orientation of the plies constituting the delaminating interface was elucidated. Since this quantity dissipated the least amount of energy possible during crack growth, it is the controlling factor for laminate toughness.
The dominant influence of fiber coatings on the mechanical performance of brittle matrix composites is addressed. These effects are described in terms of two independent mechanical parameters, the debond energy, , and the sliding resistance along the debond, τ. Complications associated with mode mixity, roughness and coating microstructure are emphasized. A mechanics of composite behavior based on these parameters is described, together with measurement approaches that allow and τ to be evaluated either in situ or in model composites. Key problems associated with fiber coatings are identified and discussed.
The influence of fiber pull-out on the mechanical properties of fiber reinforced ceramics has been analyzed using an approach based on weakest-link statistics. The essential physics contributed by the statistics is the establishment of a relationship between the fiber failure site, which governs the pull-out length, and the properties of the fibers, the matrix, and the interface. This analysis involves the development of a stress/displacement law for fibers in the bridging zone of a matrix crack, thereby permitting a discussion of the crack growth resistance and its dependence on relevant microstructural variables.
The far-reaching effects of such extrinsic factors as specimen shape and load distribution on bridged crack propagation, in cases where bridging-zone length is comparable to any of the crack and/or specimen dimensions, are presently demonstrated in view of calculation results for single-edge-notch specimens under uniform remote tension. The inherent risk of nonconservative predictions or reliability and strength may be reduced by considering the relationship between the bridging tractions and the crack-opening displacement as a fundamental material property. The fundamentality of the 'bridging length scale', or initial crack extension over which the bridging zone matures, is demonstrated.