Elasto-plastic Self-consistent Model Research Articles

Utilizing integrated neutron diffraction and elastoplastic self-consistent crystal plasticity model to quantitatively assess the strengthening mechanism in Al–12.5Ce and Al–12.5Ce–0.4Mg alloys

An integrated in-situ neutron diffraction and elastic plastic self-consistent crystal plasticity (EPSC-CP) modeling scheme is performed on a binary Al–12Ce alloy and a ternary Al–12Ce–0.4Mg alloys. Using this scheme, the constitutive parameters, i.e. elastic constants and slip system parameters of individual phases can be calibrated which can be used in microstructure-based CP models to predict materials performance. From this study, it is shown that the elastic constants of Al11Ce3 intermetallics calculated from density function theory calculation in the literature are rather accurate. When applied to the EPSC-CP model, the lattice strains of both the binary and ternary alloys are correctly predicted as compared with experiments, and large lattice strain differences between Al (100) plane and Al11Ce3 (010) plane are demonstrated. The slip system parameters calibrated by the scheme shows that the addition of 0.4 wt% Mg in the alloy has little influence on the critical resolved shear stress of initial dislocation glide in the Al matrix which caused plastic yield in the material. This can be explained by the very dilute Mg solute content in the Al solid solution, causing large spacing of Al–Mg lattice misfit sites and little impact on resistance of dislocation glide at initial yield. The 0.4 wt% Mg addition, on the other hand, has a large influence on the hardening term in the slip system parameters, indicating those Al–Mg misfit sites do help dislocation accumulation during the deformation. The impact of dilute Mg addition on the Al slip system parameters is also reflected in the flow behavior of the ternary alloy: little impact on the yield stress, but a large impact on working hardening and tensile strength of the materials which is consistent with the literature.

Analysis of Phase-Specific Strain Pole Figures for Duplex Steels under Elasto-Plastic Uniaxial Tension—Experiment vs. EPSC Modelling

For the duplex stainless steel X2CrNiMoN22-5-3, phase-specific strain pole figures (strain PFs) for the phases ferrite (bcc) and austenite (fcc) were analysed under uniaxial tensile loading for various loading states in purely elastic and elasto-plastic regimes. Experimentally, strain PFs were determined by means of in situ neutron diffraction strain measurements under defined uniaxial loading. These experimental results were compared with strain PFs calculated using elasto-plastic self-consistent (EPSC) modelling. The comparison was performed for two different {hkl} planes per phase. While classic load stress and load partitioning analyses for multi-phase materials are often limited to the load direction and a selected direction transverse to it, the results illustrate the added value of determining a strain PF, especially when a phase-specific texture is present. The comparison with experimental data shows how well the load partitioning behaviour can be predicted using common EPSC models, using the example of a duplex stainless steel. The EPSC model used was validated with the software ISODEC in its elastic range. Based on the results of the EPSC model, and taking into account the local phase-specific crystallographic texture, a prediction can be made as to what extent intergranular stresses and phase-specific textures could affect the results of a (residual) stress analysis by means of the diffraction method. This makes it possible to assess whether, for technical applications, meaningful residual stress results can be expected in certain component directions.

Investigation of residual stresses and modeling of tensile deformation in wire-arc additive manufactured 6061 aluminum alloy: Diffraction and elastoplastic self-consistent model

The aim of this work is to study the mechanical behavior of 6061 aluminum walls produced by Wire Arc Additive Manufacturing at the different scales of the material. The residual stresses of the parts are characterized on the surface and in the bulk thanks to X-ray and neutron diffraction techniques, respectively. Although the residual stress values determined in the close-surface are low (40 MPa for the maximum value), the mechanical state is different in depth with significant maximum residual stress levels ( ± 100 MPa). Tensile tests carried out on samples extracted from a WAAM wall in three orientations reveal that the mechanical properties of the manufactured material are slightly better compared to conventional material in T6 state. In situ X-ray diffraction experiments have also been performed under uniaxial tensile testing in order to determine strain pole figures. An elasto-plastic self-consistent model considering the microstructural characteristics and the main physical phenomena governing the material behavior, is proposed. The model agrees with the experimental data and the simulations reproduce the main features observed at the scale of the diffracting volume.

Effect of pre-strain on springback behavior after bending in AA 6016-T4: Experiments and crystal plasticity modeling

Modeling springback in sheet materials is challenging in aluminum alloys, especially when a complex strain path is applied. This paper presents results from pure bending experiments on AA 6016-T4 sheet material, where various plastic pre-strains were first applied prior to bending. A crystal plasticity based elasto-plastic self-consistent (EPSC) model that includes the effect of backstress in the hardening law was used to predict final part shape after unloading. The backstress term in the model was calibrated using geometrically necessary dislocation (GND) content, measured experimentally by high resolution electron backscattered diffraction (HREBSD). The EPSC model predicted springforward angles for unstrained 1 mm AA 6016-T4 sheet with an error of 0.4% (0.3°) in the worst case, while the J2 plasticity isotropic model overpredicted springforward angles by as much as 2.4% (2°). For cases where uniaxial, plane-strain, and biaxial pre-strains were first imparted to the sheets before bending, the EPSC model with backstress accurately predicted the transition from springforward to springback, while the EPSC model without backstress did not. Backstress influence on model accuracy, which increased with greater pre-strain levels, appears to be correlated to the statistically stored dislocation (SSD) density computed by the model at the end of each pre-strain step.

Origins of improved elongation to fracture in cyclic bending under tension of AA6022-T4 sheets as revealed using crystal plasticity modeling

Plastic instabilities can be suppressed by imposing cyclic bending during tension to increase elongation-to-fracture (ETF) of metallic sheets. This work is a combined experimental and modeling study into the origins of the improved ETF in cyclic bending during tension facilitated by a continuous-bending-under-tension (CBT) test. Load-displacement is measured during the CBT test under an optimized combination of band depth and pull speed process parameters for aluminum alloy (AA) 6022-T4. Monotonic and load reversal response of the alloy is also characterized under strain histories that resemble the history in CBT. Electron-backscattered diffraction and neutron diffraction are employed to characterize the initial microstructure and texture evolution of the alloy after CBT and simple tension (ST). Monotonic, load reversal, and texture data are used to adjust and verify the parameters of an elasto-plastic self-consistent crystal plasticity-based finite element model for simulating CBT. Additionally, a flow stress curve based on a bulge test is used to calibrate the model to capture the large strain hardening behavior of the alloy. The model is then used to simulate the CBT test while predicting the load-displacement and texture evolution data. The model successfully reproduced the succession of spikes and plateaus during CBT validating the prediction of the extrapolated hardening. After the validation, the development of stress and strain is probed through the sheet thickness to determine the underlying profiles as well as along the sheet to elucidate the location and onset of failure axially. The model reveals the development of more strain and dislocation density at the surface then at the center of the sheet and correctly predicts the strain localizations. Comparisons of texture evolution and mechanical fields developed in ST and CBT reveal very similar mechanical states in the sheet. These results in combination with experimental results suggest that the origins of improved ETF during CBT pertain primarily to the incremental deformation structural effects and secondary to the microstructural evolution effects.

Crystal plasticity modeling of strain-induced martensitic transformations to predict strain rate and temperature sensitive behavior of 304 L steels: Applications to tension, compression, torsion, and impact

This paper advances crystallographically-based Olson-Cohen (direct γ → α’) and deformation mechanism (indirect γ→ε→α’) phase transformation models for predicting strain-induced austenite to martensite transformation. The advanced transformation models enable predictions of not only strain-path sensitive, but also of strain-rate and temperature sensitive deformation of polycrystalline stainless steels (SSs). The deformation of constituent grains in SSs is modeled as a combination of anisotropic elasticity, crystallographic slip, and phase transformation, while the hardening is based on the evolution of dislocation density and explicit shifts in phase fractions. Such grain-scale deformation is implemented within the meso‑scale elasto-plastic self-consistent (EPSC) homogenization model, which is coupled with the implicit finite element (FE) method to provide a constitutive response at each FE integration point for solving boundary value problems at the macro-scale. Parameters pertaining to the hardening and transformation models within FE-EPSC are calibrated and validated on a suite of data including flow curves and phase fractions for monotonic compression, tension, and torsion as a function of strain-rate and temperature for wrought and additively manufactured (AM) SS304L. To illustrate the potential and accuracy of the integrated multi-level FE-EPSC simulation framework, geometry, mechanical response, phase fractions, and texture evolution are simulated during gas-gun impact deformation of a cylinder and quasi-static tension of a notched specimen made of AM SS304L. Details of the simulation framework, comparison between experimental and simulation results, and insights from the results are presented and discussed.

DISEMM: a tool for the investigation of elasto-plastic behaviour on polycrystalline samples using X-ray and neutron diffraction.

The software DISEMM is designed to analyse diffraction data from in situ loading experiments on polycrystalline samples for the determination of single-crystal elastic constants (SECs) and elasto-plastic self-consistent (EPSC) modelling of lattice strains. The SECs can be obtained from powder-diffraction elastic constants using a variety of grain-to-grain interaction models, namely Voigt, Reuss, Hill, Kröner, de Wit and Matthies approaches. The texture of the polycrystalline sample can be taken into account using the orientation distribution function of the grains. For the analysis of two-phase materials, an approach was implemented to calculate the stress transfer between the phases and its impact on the apparent elastic properties. The calculated SECs can then be used as input into the EPSC model, which allows the user to predict the elasto-plastic behaviour for comparison with experimental lattice strain data and to investigate the activation of individual slip systems. For this purpose, critical resolved shear stresses and hardening parameters are adapted iteratively.

Experimental characterization and crystal plasticity modeling of dual-phase steels subjected to strain path reversals

This paper is concerned with monotonic and load reversal deformation of four dual-phase (DP) 590, 780, 980, 1180 and one martensitic (MS) 1700 steel sheets. While the monotonic data are presented for all steels, the load reversal data are provided for DP 590, DP 780, and DP 1180. Particularities pertaining to the reversal deformation including the decreasing hardening rate during forward tension, a linear and then a non-linear unloading, followed by the Bauschinger effect, and a shift in the hardening rate during continuous straining were quantified and discussed as a function of loading history. Moreover, parameters such as the reloading stress differential, reloading softening stress, ratcheting strain, and unloading deviation stress were determined and discussed as a function of martensite fraction. The data were interpreted and predicted using an elasto-plastic self-consistent (EPSC) crystal plasticity model incorporating anisotropic elasticity, a dislocation density based hardening law, and a slip system backstress law. The model parameters associated with the slip strengths of ferrite and martensite and backstress were established. This work demonstrated the ability of crystal plasticity modeling to account for the co-dependent nature of crystallographic slip in ferrite and martensite and the sources of hardening caused by history-dependent dislocation density evolution and backstress to predict not only monotonic but also hysteresis in plastic response during the forward-reversal cycles. The combination of comprehensive experimental data and modeling results allowed us to infer that the tradeoff between the magnitude of backstress per phase and the volume fraction of ferrite versus martensite per steel governs the unloading and subsequent yielding per steel, while the dissolution of dislocations facilitates capturing the hardening rates during load reversal deformation.

Experimental characterization and crystal plasticity modeling for predicting load reversals in AA6016-T4 and AA7021-T79

The detailed contribution of microstructural-level phenomena, such as dislocation structure development and annihilation, as well as inter-granular and intra-granular backstress fields, to reverse loading behavior in metal alloys remains an area of active research and debate. The ability to predict unloading nonlinearities, the Bauschinger effect (BE), and changes in hardening rates during reverse loading is necessary for accurate modeling of deformation and springback in forming operations that involve strain path changes. This paper applies a recently developed elasto-plastic self-consistent (EPSC) crystal plasticity model to predict and interpret reverse loading in two commercially sensitive aluminum alloys (AA): 6016-T4 and 7021-T79. Model calibration and verification was enabled by an extensive experimental campaign of cyclic loading applied to the two alloys. The experimental data included hardening rates during monotonic tension, linear followed by non-linear unloading, the BE, and hardening rate changes during reverse loading that induce permanent softening. By considering anisotropic elasticity, dislocation density-based hardening, intra-granular slip system-level backstress fields, and inter-granular stress fields, the model predicted and quantified the contribution of different micro-scale phenomena to the observed behavior. The ability of the model to capture contrasting characteristics of the two alloys, particularly the distinct permanent softening and reloading yield stresses, demonstrated its ability to account for the co-dependent nature of crystallographic glide and the sources of hardening originating from the deformation history-dependent dislocation density evolution and backstress fields. Comparison of the experimental and modeling results revealed that the unloading behavior is primarily driven by backstress, the BE is governed by backstress and inter-granular stresses, and the hardening rates upon load reversals are controlled primarily by the strain-path sensitive evolution of dislocation density.

Multi-strain path deformation behavior of AA6016-T4: Experiments and crystal plasticity modeling

The development of backstresses that occur during a strain path change when forming sheet metal renders final part geometry prediction, after springback, difficult using conventional models. Most deformation models do not explicitly account for the influence of these stresses. A more recently developed elasto-plastic self-consistent (EPSC) model incorporates the backstresses to influence the activation of slip systems for more accurate simulations of the complex material response. The current study assesses the performance of the EPSC model for deformation response of AA6016-T4 via multiple biaxial, plane-strain, and uniaxial tension strain paths. The response to complex strain paths was examined by first pre-straining under uniaxial, biaxial, and plane-strain tension, then by loading in uniaxial tension. The EPSC model predictions closely matched experimental results. The model correctly predicted the highest yield stress and sharpest transition from elastic to plastic deformation for uniaxial tension after an initial uniaxial pre-strain. Lower yield stress for uniaxial tension after first pre-straining in biaxial and plane-strain tension is also correctly predicted, along with a smoother transition from elastic to plastic behavior. A linear geometrically necessary dislocation (GND) development, with strain, was observed using high-resolution electron backscattered diffraction (HREBSD) while a quadratic statistically stored dislocation (SSD) development was predicted by the model. The comparison revealed an expected transition from kinematic to isotropic hardening at higher strains. Finally, at higher strain levels the backstress accounted for around 15% of the total subsequent flow stress in all pre-strain cases.

Lattice strain development in an alpha titanium alloy studied using synchrotron and neutron diffraction

Neutron and high-energy X-ray diffraction methods have been used to investigate deformation mechanisms (slip and twinning activities) during uniaxial tensile tests of Grade 1 commercially pure titanium (Ti-α). These two diffraction techniques have provided valuable and complementary information. The predictions made by an Elasto-Plastic Self-Consistent (EPSC) model, taking into account grain reorientation and stress relaxation induced by twinning activity, have been compared with the experimental data. Results clearly demonstrate that there is a good agreement between simulations and diffraction measurements. The EPSC model enables accurate predictions of: (i) the lattice strains developed in variously oriented {hk.l} grain families within the bulk material, (ii) the grain reorientation induced by twinning activity and (iii) the macroscopic stress-strain response. Two different textured products were studied in order to evaluate the influence of texture on the mesoscopic and macroscopic responses of Ti-α alloy.

Modeling of plasticity-induced martensitic transformation to achieve hierarchical, heterogeneous, and tailored microstructures in stainless steels

While stainless steels (SS) have excellent corrosion resistance for use in industries such as chemical and food processing, medical implants made of such steels require more stringent specifications, e.g., high strength while maintaining a low weight. A way to design and manufacture such behavior of SS is through the intentional deformation induced manipulation of constituent phases to achieve heterogeneous and hierarchical microstructures. In this paper, an elasto-plastic self-consistent modeling framework incorporating a strain-induced austenite-to-martensite transformation kinetic sub-model is calibrated using a set of SS304L data from the literature to capture stress-strain response and volume fraction of phases. The model is then validated by predicting the mechanical responses of SS316L using a new data set recorded as a function of strain-rate and temperature. By accurately predicting the material behavior, the modeling results can guide the manufacturing process to achieve the desired final part properties.

Adjustment of the Mechanical Properties of Mg2Nd and Mg2Yb by Optimizing Their Microstructures

The deformation behavior of the extruded magnesium alloys Mg2Nd and Mg2Yb was investigated at room temperature. By using in situ energy-dispersive synchrotron X-ray diffraction compression and tensile tests, accompanied by Elasto-Plastic Self-Consistent (EPSC) modeling, the differences in the active deformation systems were analyzed. Both alloying elements change and weaken the extrusion texture and form precipitates during extrusion and subsequent heat treatments relative to common Mg alloys. By varying the extrusion parameters and subsequent heat treatment, the strengths and ductility can be adjusted over a wide range while still maintaining a strength differential effect (SDE) of close to zero. Remarkably, the compressive and tensile yield strengths are similar and there is no mechanical anisotropy when comparing tensile and compressive deformation, which is desirable for industrial applications. Uncommon for Mg alloys, Mg2Nd shows a low tensile twinning activity during compression tests. We show that heat treatments promote the nucleation and growth of precipitates and increase the yield strengths isotopically up to 200 MPa. The anisotropy of the yield strength is reduced to a minimum and elongations to failure of about 0.2 are still achieved. At lower strengths, elongations to failure of up to 0.41 are reached. In the Mg2Yb alloy, adjusting the extrusion parameters enhances the rare-earth texture and reduces the grain size. Excessive deformation twinning is, however, observed, but despite this the SDE is still minimized.

Origins of high ductility exhibited by an extruded magnesium alloy Mg-1.8Zn-0.2Ca: Experiments and crystal plasticity modeling

Low ductility and strength are major bottlenecks against Mg alloys’ wide applications. In this work, we systematically design the composition and fabrication process for a low-alloyed Mg-Zn-Ca alloy, showing that it can be extruded at low temperatures (∼250 ℃) and high speeds (∼2 mm/s). After the extrusion, this alloy exhibits a substantially weakened basal texture, relatively small grain size, very high tensile elongation (∼30%), and good strength. The origin of the considerably improved ductility was studied using a combination of three-dimensional atom probe tomography (3D-APT), transmission electron microscopy (TEM), electron backscattered diffraction (EBSD) in conjunction with surface slip trace analysis, in-situ synchrotron X-ray diffraction, and elasto-plastic self-consistent (EPSC) modeling. Co-segregation of Zn and Ca atoms at a grain boundary is observed and associated with texture weakening and grain boundary mediated plasticity, both improving the ductility. While basal slip and prismatic slip are identified as the dominant deformation systems in the alloy, the ratio between their slip resistances is substantially reduced relative to pure Mg and most other Mg alloys, significantly contributing to the improved ductility of the alloy. This Mg-Zn-Ca alloy exhibiting excellent mechanical properties and low fabrication cost is a promising candidate for industrial productions.

Stress-assisted (γ→α′) and strain-induced (γ→ε→α′) phase transformation kinetics laws implemented in a crystal plasticity model for predicting strain path sensitive deformation of austenitic steels

This paper formulates stress-assisted and strain-induced austenite to martensite transformation kinetics laws within a crystal plasticity framework to enable modeling of strain path sensitive elasto-plastic deformation of austenitic steels taking into account the evolution of crystallographic texture and the directionality of deformation mechanisms in the constituent phases. Consistent with experimental observations for mechanically induced martensitic transformation, the stress-assisted transformation is modeled as direct from γ-austenite to α' -martensite, while the strain-induced transformation is modeled as indirect through an intermediate ε-martensite phase, which subsequently transforms to α' -martensite. While the stress-assisted transformation law is conceived based on an energy criterion, the strain-induced transformation law relies on the local stress state sensitive motion of partial dislocations forming shear bands of ε-martensite phase, which after intersecting with other shear bands give rise to α' -martensite. The kinetic models are implemented in the elasto-plastic self-consistent polycrystal plasticity model to facilitate modeling of strain path and crystallographic texture dependence of martensitic transformation, while predicting deformation behavior of metastable austenitic steels. Due to its morphology, the ε-martensite is modeled using a flat ellipsoid approximation, which is a new numerical feature in the model. Simple tension, simple compression, and simple shear data of an austenitic steel have been used to calibrate and to illustrate predictive characteristics of the overall implementation. In doing so, stress-strain response, texture, and phase fractions of γ-austenite, intermediate ε-martensite, and α′-martensite are all calculated, while fully accounting for the crystallography of the transformation mechanisms. It is demonstrated that the appropriate modeling of phase fractions and crystallography facilitates predicting the experimentally measured data. The implementation and insights from these predictions are presented and discussed in this paper.

An elasto-plastic self-consistent model for damaged polycrystalline materials: Theoretical formulation and numerical implementation

Elasto-plastic multiscale approaches are known to be suitable to model the mechanical behavior of metallic materials during forming processes. These approaches are classically adopted to explicitly link relevant microstructural effects to the macroscopic behavior. This paper presents a finite strain elasto-plastic self-consistent model for damaged polycrystalline aggregates and its implementation into ABAQUS/Standard finite element (FE) code. Material degradation is modeled by the introduction of a scalar damage variable at each crystallographic slip system for each individual grain. The single crystal plastic flow is described by both the classical and a regularized version of the Schmid criterion. To integrate the single crystal constitutive equations, two new numerical algorithms are developed (one for each plastic flow rule). Then, the proposed single crystal modeling is embedded into the self-consistent scheme to predict the mechanical behavior of elasto-plastic polycrystalline aggregates in the finite strain range. This strategy is implemented into ABAQUS/Standard FE code through a user-defined material (UMAT) subroutine. Special attention is paid to the satisfaction of the incremental objectivity and the efficiency of the convergence of the global resolution scheme, related to the computation of the consistent tangent modulus. The capability of the new constitutive modeling to capture the interaction between the damage evolution and the microstructural properties is highlighted through several simulations at both single crystal and polycrystalline scales. It appears from the numerical tests that the use of the classical Schmid criterion leads to a poor numerical convergence of the self-consistent scheme (due to the abrupt changes in the activity of the slip systems), which sometimes causes the computations to be prematurely stopped. By contrast, the use of the regularized version of the Schmid law allows a better convergence of the self-consistent approach, but induces an important increase in the computation time devoted to the integration of the single crystal constitutive equations (because of the high value of the power-law exponent used to regularize the Schmid yield function). To avoid these difficulties, a numerical strategy is built to combine the benefits of the two approaches: the classical Schmid criterion is used to integrate the single crystal constitutive equations, while its regularized version is used to compute the microscopic tangent modulus required for solving the self-consistent equations. The robustness and the accuracy of this novel numerical strategy are particularly analyzed through several numerical simulations (prediction of the mechanical behavior of polycrystalline aggregates and simulation of a circular cup-drawing forming process).

Size effect in stainless steel thin wires under tension

Miniaturization of modern devices drives the exploration into how materials behave in small dimensions. However, the mechanical behaviors of micro-scale specimens under varied loading conditions are still challenging to characterize and predict. In this work, specimen size-dependent weakening effect was experimentally revealed in 316L stainless steel thin wires under tension with wire diameter decreasing from 200 μm down to 61 μm. The underlying mechanisms were primarily associated with surface grain softening and strain localization, which were largely dependent on the number of grains across wire diameter. Through an analog composite model with surface and interior grains that follows the Hall-Petch relation, the extent of surface grain softening was found to coincide with the flow stress reduction due to lack of boundary strengthening. Further using elasto-plastic self-consistent polycrystal modeling, the stress-strain behaviors of interior and surface grains were well described in analogy to those of bulk materials with similar-size grains and extremely large grains, respectively. Subsequently, the analog composite model well simulated the specimen size-dependent weakening effect under tension. This work provided more insights into the size effect exploration and proposed a practical model for describing size-dependent mechanical behaviors of small-scale materials to be applied to miniaturized devices.

A comparative study between elasto-plastic self-consistent crystal plasticity and anisotropic yield function with distortional hardening formulations for sheet metal forming

A comparative study between micro- and macro-mechanical constitutive models is carried out while predicting deformation behavior of an aluminum alloy (AA) 6022-T4 during several loading scenarios of increasing complexity including monotonic tension, large strain cyclic deformation, and drawing of a cylindrical cup. The micro-model is a recently developed implicit formulation of the elasto-plastic self-consistent (EPSC) crystal plasticity, which is coupled with the implicit finite element method (FEM) through a user material subroutine in Abaqus. In the coupled formulation, every finite element integration point embeds the implicit EPSC constitutive law that accounts for the directionality of deformation mechanisms and microstructural evolution. The crystallography based EPSC model integrates a dislocation-based hardening law and accounts for inter-granular and slip system level back-stresses, which make it capable of capturing non-linear unloading and the Bauschinger effect. The macro-model is a recently developed anisotropic yield function incorporating distortional hardening using the homogeneous anisotropic hardening (HAH) approach. The model is also implemented as a user material subroutine in Abaqus. Parameters pertaining to the micro and macro models are identified using experimental data from a set of monotonic and cyclic tests performed for AA6022-T4. Additional experimental data for the alloy in terms of flow stress curves, R-value, and anisotropic yield surface evolution are used to verify the models. Finally, the cup drawing simulations are carried out in the FEM using the two constitutive formulations and geometrical changes including the earing profile and sheet thinning/thickening are compared against each other and with experiments to further verify the predictive characteristics of the models. The two formulations and results are discussed in terms of accuracy and computational efficiency.

Effect of heat treatment on the tensile behavior of selective laser melted Ti-6Al-4V by in situ X-ray characterization

Selective Laser Melted Ti-6Al-4V (as-SLMed) exhibits decreased yield strength, increased work hardening, and increased ductility after heat treatment at 730 °C (HT-730) or 900 °C (HT-900) for 2 h. To understand the change of mechanical properties, in situ high energy X-ray diffraction (HEXRD) is used to examine the phase composition, load partitioning, slip system activity, and dislocation density evolution in all three specimens. The as-SLMed specimen is dominated by martensitic α΄. After heat treatment, α΄ partly or fully decomposes into α+β, reducing the yield strength. In HT-730, β precipitates with confined size show much higher lattice strain than the α΄/α matrix during deformation; in HT-900, the lattice strain difference is mostly eliminated. This is a key reason for the increased ductility in HT-900. From the anisotropic lattice strain development, basal slip is identified as the easiest slip system in α΄/α. Using an elasto-plastic self-consistent (EPSC) model, the critical resolved shear stress ratio between prismatic slip and basal slip (CRSSprism/CRSSbasal) is estimated to be 1.31 and 1.16 in the as-SLMed and the HT-900 specimens, respectively. The α phase in HT-900 is able to activate multiple slip systems and accumulate more dislocations during plastic deformation. This explains why HT-900 has better ductility and higher work hardening rate than the other two specimens.

Predicting deformation behavior of α-uranium during tension, compression, load reversal, rolling, and sheet forming using elasto-plastic, multi-level crystal plasticity coupled with finite elements

An elasto-plastic self-consistent (EPSC) polycrystal plasticity formulation is adapted to model deformation of wrought α-uranium (α-U) accommodated by a combination of elasticity, dislocation glide, and deformation twinning. The EPSC model incorporates a strain-path, strain rate, and temperature sensitive dislocation density-based hardening law for the evolution of resistance to slip, twinning, and de-twinning and a slip system-level kinematic back-stress law to influence the driving force for activation. The model is used to interpret the complex deformation behavior of α-U as a function of strain-path and temperature. Samples of α-U with different initial orientation distributions are experimentally evaluated in simple compression, tension, and load reversal at room temperature and in compression and rolling at 573 K under a quasi-static deformation rate. Evolution of texture and twinning is characterized using electron backscattered diffraction and in-situ and ex-situ neutron diffraction during deformation. It is observed that the behavior of the material is highly anisotropic owing to its low-symmetry orthorhombic crystal structure and different activation stresses for crystallographic deformation modes. The model is calibrated and validated under these deformation conditions and predicts the stress-strain responses, amount of twinning, texture evolution, and lattice strains with one set of parameters for the hardening and back-stress evolution laws. Subsequently, the developed model is used as a constitutive law in the implicit finite element (FE) framework to simulate drawing of a hemispherical part from a rolled sheet of α-U. Here, the FE-EPSC model is a two-level homogenization scheme with EPSC relating the grain-level to the polycrystalline aggregate-level response, while the FE framework scales the polycrystalline to the part-level response. The simulation results and insights from the calculations, such as location dependent texture evolution is in good agreement with experiments.