Fig 5 - uploaded by Zaloa Arechabaleta
Content may be subject to copyright.
The relation between the anelastic strain at the yield stress and the characteristics ρ and L of the dislocation network. The solid line shows the linear relation expressed by Eq. (9).
Source publication
Understanding the intricate structure of dislocations in metals is a major issue in materials science. In this paper we present a comprehensive approach for the characterisation of dislocation networks, resulting in accurate quantification and significantly increasing the insight into the dislocation structure. Dislocation networks in metals consis...
Context in source publication
Context 1
... interest, but also at the basis of the magnitude of springback, a technologically important phenomenon. In the present study, the anelastic strain at the yield stress has been experimentally determined from each loading curve by subtracting the elastic strain σ E / y from the total strain at = σ σ y . Its relation with the product ρL is shown in Fig. 5. The figure shows that indeed a linear relation is found, albeit with a slight de- viation at low values of ρL . The slope of the line fitted with Eq. (9) is (0.047 ± 0.002) nm for the two steels. This implies, using the pre- viously given values for b and M ...
Similar publications
High temperature annealing of thick (40–100 nm) Ge layers deposited on Si(100) at ∼400 °C leads to the formation of continuous films prior to their transformation into porous-like films due to dewetting. The evolution of Si-Ge composition, lattice strain, and surface morphology caused by dewetting is analyzed using scanning electron microscopy, Ram...
Citations
... In reality, crystal lattices are not perfect like the standard ones, as shown in Fig. 1(A) but contain different types of defects such as vacancy, interstitial and dislocations (edge, screw) [35]. Interestingly, materials that contain many dislocations have improved mechanical strength as dislocations can get tangled, preventing each other from propagating through the crystal lattice. ...
... Fabrication of Zne1.2 Mg alloy by extrusion has produced medical implants with higher yield strength, ultimate tensile strength, and hardness than pure zinc, leading to improved hemocompatibility and cytocompatibility [35]. Although the fabricated alloy was composed of an Mg 2 Zn 11 , a precipitated phase beside the Zn matrix phase, the grain size became smaller and more homogeneous after the extrusion process. ...
Along the way, investigations over the past few years have focused on developing new Zn-based alloys as future materials for medical implants due to the poor mechanical and degradation properties. Effective grain size control is a fundamental property of Zn-based alloys that has a significant impact on their mechanical properties and degradation rate through various methodical adjustments of the microstructure. In particular, these critical properties of Zn-based alloys largely depend on grains' size and distribution in the respective microstructures. The review article critically analyzes the influence of grain refinement and microstructure on the mechanical properties, biodegradability, and biocompatibility of Zn-based alloys. The article establishes the interdependence between microstructure, mechanical properties, degradation rate, and biocompatibility of both Zn and its alloys. We conclude integration of alloying and fabrication techniques can significantly control grain refinement in Zn-based alloys, and the use of innovative techniques such as dynamic recrystallization and inoculation can further improve the grain refinement process.
... Hence hardening is commonly associated with plasticity. A lesser studied type of deformation is anelasticity, i.e. recoverable nonlinear mechanical behaviour, as observed by [1][2][3][4][5][6][7]. Anelastic deformation is an additional strain component on top of the elastic lattice strain during loading and unloading. ...
... The aforementioned dislocation bow-out models [4,7] excel in capturing the dissipative and mechanically reversible pre-yield deformation, however omit significant mechanically irreversible dislocation motion, that is at the origin of plastic strain and hardening. The flow strength description in current hardening models juxtaposed to bow-out models [4][5][6][7] leads to solely linear elastic behaviour; the majority of work-hardening models lacks a description of reversible dislocation motion and bow-out models [4][5][6][7] omit significant irreversible dislocation motion. From an engineering perspective, the total recoverable strain during loading and unloading governs the apparent elastic modulus [1][2][3]31,32], which is essential for materials models of cyclic loading and precision engineering [4,7,33], and in spring-back and thermomechanical processing of metals alloys [5,30,34]. ...
... The aforementioned dislocation bow-out models [4,7] excel in capturing the dissipative and mechanically reversible pre-yield deformation, however omit significant mechanically irreversible dislocation motion, that is at the origin of plastic strain and hardening. The flow strength description in current hardening models juxtaposed to bow-out models [4][5][6][7] leads to solely linear elastic behaviour; the majority of work-hardening models lacks a description of reversible dislocation motion and bow-out models [4][5][6][7] omit significant irreversible dislocation motion. From an engineering perspective, the total recoverable strain during loading and unloading governs the apparent elastic modulus [1][2][3]31,32], which is essential for materials models of cyclic loading and precision engineering [4,7,33], and in spring-back and thermomechanical processing of metals alloys [5,30,34]. ...
Modelling dislocation glide over the initial part of a stress–strain curve of metals received little attention up to now. However, dislocation glide is essential to ones understanding of the fundamental relationship between inelastic deformation and the evolution of the dislocation network structure. Therefore, we present a model of dislocation-driven deformation under static loading conditions.
We reproduce repeated cyclic uniaxial tensile tests on Interstitial-Free and Low-Alloy steels. The elastic mechanical behaviour is described by isotropic linear elasticity, pre-yield anelastic mechanical behaviour by a dislocation bow-out model with dissipation, and the post-yield evolution of dislocation network structure by a statistical storage model. We hypothesise that when the local anelastic compliance is lower than the global plastic compliance, deformation is mechanically recoverable, and vice versa. This hypothesis is corroborated with the classical Taylor relation. We report the relation between stable and unstable dislocation glide using this prototypical modelling framework.
We find four structural variables, that are based on dislocation physics, to describe the stress–strain curve: total dislocation density, average dislocation segment length, dislocation junction formation rate, and average dislocation junction length. Firstly, we quantify the dislocation network evolution during uniaxial monotonic loading, and verify work-hardening by dislocation junction formation and a Taylor-type equation for flow. Finally, we present a semi-empirical relation for the evolution of the dislocation network structure. Which allows us to: refine the physical interpretation of the Taylor relationship, and rationalise experimental observations on apparent modulus degradation by thermomechanical processing. Both these findings circumvent the limitations of current, physics-based hardening models.
... The yield stress at deformation start σ 0 , also called proof stress, was determined at the intersection point of the stress-strain curve and the proportional line offset to 0.002 true strain. Although more physical approaches are provided in literature concerning the initiation of dislocation motion (e.g., by Arechabaleta et al. [74]), the well-established 0.002 strain offset method was applied for the determination of σ 0 in order to assure comparability with previous findings on the basis of the same approach. ...
Microalloyed steels offer a good combination of desirable mechanical properties by fine-tuning grain growth and recrystallization dynamics while keeping the carbon content low for good weldability. In this work, the dislocation density evolution during hot rolling was correlated by materials modeling with flow curves. Single-hit compression tests at different temperatures and strain rates were performed with varying isothermal holding times prior to deformation to achieve different precipitation stages. On the basis of these experimental results, the dislocation density evolution was evaluated using a recently developed semi-empirical state-parameter model implemented in the software MatCalc. The yield stress at the beginning of the deformation σ0, the initial strain hardening rate θ0, and the saturation stress σ∞-as derived from the experimental flow curves and corresponding Kocks plots-were used for the calibration of the model. The applicability for industrial processing of many microalloyed steels was assured by calibration of the model parameters as a function of temperature and strain rate. As a result, it turned out that a single set of empirical equations was sufficient to model all investigated microalloyed steels since the plastic stresses at high temperatures did not depend on the precipitation state.
... where φ is a material constant (in the range of 0.15-0.4 [28]) estimated as 0.15 for coherent and 0.4 for semi-coherent Si precipitates, G is the shear modulus of the Al matrix (~26.5 ...
The AlSi10Mg alloy is characterized by a high strength-to-weight ratio, good formability, and satisfying corrosion resistance; thus, it is very often used in automotive and aerospace applications. However, the main limitation of using this alloy is its low yield strength and ductility. The equal-channel angular pressing is a processing tool that allows one to obtain ultrafine-grained or nanomaterials, with exceptional mechanical and physical properties. The purpose of the paper was to analyze the influence of the ECAP process on the structure and hardness of the AlSi10Mg alloy, obtained by the selective laser melting process. Four types of samples were examined: as-fabricated, heat-treated, and subjected to one and two ECAP passes. The microstructure analysis was performed using light and electron microscope systems (scanning electron microscope and transmission electron microscope). To evaluate the effect of ECAP on the mechanical properties, hardness measurements were performed. We found that the samples that underwent the ECAP process were characterized by a higher hardness than the heat-treated sample. It was also found that the ECAP processing promoted the formation of structures with semicircular patterns and multiple melt pool boundaries with a mean grain size of 0.24 μm.
... Lesser studied is the contribution of dislocations to the pre-yield constitutive behaviour. The nonlinear pre-yield mechanical behaviour, as observed by [6][7][8][9][10] , is due to an additional strain component on top of the elastic lattice strain during loading and unloading. First Eshelby [11] and later Koehler and DeWit [6] connected the apparent elastic constants, which are lower than the theoretical constants, to the bowing out of pinned dislocation segments. ...
... Recently, Van Liempt and Sietsma [8] showed that the pre-yield mechanical behaviour is a measure for the average properties of the dislocation network which they characterized by the total dislocation density and the average dislocation segment length. The method championed by Arechabaleta et al. [9,10] allows for obtaining information on the characteristics of a dislocation network via mechanical testing. However, the crystallographic texture of a polycrystalline material is only taken into account by the Taylor factor and the assumed circular dislocation loop shape is only valid for materials with Poisson's ratio = 0 , i.e. highly compressible materials. ...
... We envision a dislocation network as a continuous structure consisting of discrete dislocation segments delimited by microstructural features like precipitates, solute atoms, grain boundaries and interaction interacting with adjacent dislocation segments within the same net [10,22] . Those points of interaction, which include all microstructural defects that impede local dislocation motion, are commonly known as pinning points where dislocation motion is locally impeded. ...
Intricate knowledge of dislocation networks in metals has proven paramount in understanding the constitutive behaviour of these materials but current experimental methods yield limited information on the characteristics of these networks. Recently, the isotropic anelastic response of metals has been used to investigate complex dislocation networks through the well-known phenomenon that the observed elastic constants are influenced by dislocations. Considering the dependence of the behaviour of a Frank-Read (FR) source on its initial dislocation character and using discerning characteristics of dislocations, i.e. Burgers vector, line sense and slip system, the present paper takes dislocation character, crystal structure and dislocation network geometry into account and obtains the anisotropic mechanical response for a generic Poisson’s ratio. In this work, the tensile test tangent moduli and yield points are presented for spatially uniform and nonuniform dislocation distributions across slip systems. First, the reversible shear strain of the FR source is derived as a function of initial dislocation character. The area swept by a mobile and initially straight dislocation segment pinned at both ends is given as an explicit function of the line stress. Secondly, the anisotropic anelastic strain ontribution of FR sources to the total pre- and at-yield strain in single crystallites is alculated. For a given normal stress and superposition of the principal infinitesimal linear elastic lattice strain and anelastic dislocation strain, the tangent moduli are presented.
The moduli and the inception of plastic flow have a notable dependence on initial dislocation character, spatial dislocation distribution and loading direction.
... ....... 26 specimens. The literature data is taken from [11,24,204,136,161,162,168,171,188,202,203] The purity of the sample was ~99.17% and the annealing was performed at 620 o C for 500 h. for NaCl [153,164,225,226]. ...
... for NaCl [153,164,225,226]. The n = 1 line, as prescribed by Banerdt and Sammis [164] [11,24,234,34,35,136,168,171,202,232,233]. The studies marked with '*' in the legend The dislocations were observed using etch-pit method and the evolution of dislocation density xxix was recorded by observing the iso-thermally annealed sample at regular intervals. ...
... A Frank network of dislocations appears to be observed. The term 'Frank network' was given by Cottrell [202] which is a continuous network of dislocations inside a crystalline structure where three dislocations meet at a node for minimizing the energy. Fig. 32b shows the dislocation structure in Al single crystal annealed at 920 K (~0.99Tm) for one month. ...
... With further increasing strain to ∼3% ( figure 5(b)), more dislocation were activated and with a much higher density. Further increasing the strain to 6.2% ( figure 5(c)), it can be seen that dislocation networks were formed and appeared hexagonal mainly, it is generally accepted that dislocations rearranged and transformed to dislocation networks are beneficial to lower the defect energy so as to enhance the ductility [30]. ...
To surmount the longstanding puzzle of strength-ductility trade-off, efforts had been made to apply Mg - Ag microalloying on 5%TiB2/Al-4.5%Cu composites by in situ molten salt reaction and subsequent heat treatment. The obtained composites achieve an eye-catching tensile elongation (δ) of 6.1 ± 0.4%, while maintaining elevated ultimate tensile strength (UTS) of 497 ± 4 MPa and yield strength (YS) of 401 ± 3MPa. Comprehensive characterization demonstrated that the uniformly distributed TiB2 particles together with semi-coherent grain boundaries between the α-Al matrix and reinforcement phase (TiB2 particles, Ω-Al2Cu, σ-Al5Cu6Mg2) facilitated the dislocation motion integrally, which eliminated the stress concentrations, may be the main reason for amelioration in the strength-ductility trade-off of the composites when subject to rigorous multi-step heat treatment.
... Parameter α describes the interaction between dislocations. It is dependent on the strength of dislocation junctions [61] and the average pinning distance [62], and therefore it is also dependent on the geometrical arrangement of dislocations [20]. The strengthening coefficient is lower if cells are formed in comparison to random dislocation distribution [20]. ...
This study investigates differences in the deformation mechanisms between room temperature (296 K) and cryogenic temperatures (77 K) and their advantages for low temperature formability in alloys EN AW 1085, EN AW 5182 and EN AW 6016. Compared to room temperature behaviour, tensile tests showed an overall increase in yield strength, ultimate tensile strength and uniform elongation with differences among the principal alloy types. In general, the improved mechanical properties result from higher strain hardening rates at lower temperatures. The application of an extended Kocks-Mecking approach showed a significant reduction of the dynamic recovery and suggested higher dislocation densities upon cryogenic deformation. This was confirmed via in-situ synchrotron experiments, which also reveal a higher proportion of screw dislocations. Moreover, kernel average misorientation maps from electron backscattered diffraction and in-situ cryogenic deformation in a transmission electron microscope displayed a more uniform dislocation arrangement with a reduction of slip lines and less highly misaligned areas after deformation at lower temperatures. Supported by a detailed characterization of the microstructure and its dislocation structure, the associated fundamental mechanisms we reveal, which are at the origin of the exceptional improvement in mechanical properties, are extensively discussed.
... Even though the current simulations do not consider the plastic deformation in the WEL region, very large stress over 1.1 GPa still exists as shown in Fig. 5(a). In a recent study, Arechabaleta et al. [53] have reported the dislocation evolutions in a low-alloy and interstitial-free steels in the pre-yield range of a tensile test. Their theory can explain the formation of high dislocation density in region-I after a large number of wheel-rail contact cycles. ...
The existence of narrow and brittle white etching layers (WELs) on the rail surface is often linked with the formation of rail defects such as squats and studs, which play the key roles in rail surface degradation and tribological performance. In the present study, a systematic investigation on stress/strain distribution and fatigue life of the WEL during wheel-rail rolling contact was conducted based on a numerical model considering the realistic wheel geometry. This is the first study considering the influence of rail materials, loading pressure, frictional condition, WEL geometry (a/b), and slip ratio (Sr) in the practical service conditions at the same time. The results revealed much higher residual stress in WEL than in rail matrix. Stress changes along the rail depth matched with the previously reported microstructure evolutions. The current work revealed that the maximum difference in contact stress between the wheel passages of rail matrix and the WEL region (noted as stress variation) rises with the increase of loading pressure, the value of a/b, and Sr; but drops with the friction coefficient (μ). In addition, a critical length-depth ratio of 5 for a/b has been found. The fatigue parameter, FP, of the WEL decreased quickly with the length-depth ratio when it was less than 5 and then increased slightly when it was larger than 5. This study also revealed that the fatigue life of the WEL was reduced for high strength head hardened (HH) rail compared with standard carbon (SC) rail.
... The dislocation density within the cell walls is high, while it is low within the cell interiors, which facilitates the slip of mobile dislocations. The cell-type of dislocation structure provides a heterogeneous spatial distribution of dislocation pinning points (dislocation segment lengths), which requires a gradient of shear stresses to bow them out and produce plastic deformation [47]. This would explain the continuous yielding effect observed in the microstructures austenitised at 0.1°C/s. ...
This study unravels the microstructural mechanisms controlling the mechanical behaviour and austenite mechanical stability in ultrafine grained austenite/martensite (α′/γ) microstructures, created varying the austenitisation heating rate (0.1–10 °C/s) and temperature within the start-finish austenite formation temperatures (AS − AF) in a cold-rolled semi-austenitic stainless steel. A wide spectrum of strength-ductility combinations; i.e. strengths of 900–2100 MPa and elongations up to 25%, were characterised by sub-size tensile testing. The nanoprecipitation of Ni3(Ti,Al) in martensite during heating to low austenitisation temperatures rises the strength, while the martensite recovery, enhanced at low heating rates, improves the work-hardening. The high strength of martensite partially suppresses the formation of mechanically-induced martensite during loading, which is enabled with the increase of austenite volume fraction and contributes positively to the work-hardening. The heating rate barely affects the mechanical properties of microstructures austenitised close to AF. The austenite ultrafine grain size controls the yield strength, while the decrease in austenite mechanical stability and the α′/γ composite effect increase remarkably the work-hardening with respect to dual (α′/γ) microstructures with larger martensite volume fractions and fully austenitised microstructures. These results will enable the design of microstructures with controlled mechanical behaviour for a wider spread use of similar steel grades.
