•Strain rate and temperature sensitive strain-induced austenite to martensite transformation laws are developed.•The laws are incorporated into an elasto-plastic self-consistent crystal ...plasticity-based finite element model.•The model is used to simulate deformation of wrought and additively manufactured 304 L steels during tension, compression, torsion, and impact.•Geometrical features, strength, and microstructures in terms of spatial fields of phase fraction and texture evolution are predicted.•Strain path, strain-rate, temperature, triaxiality, and initial microstructure and texture sensitivity of martensitic transformation is interpreted.
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.
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.
•Stress-assisted and strain-induced austenite to martensite transformation kinetics laws are formulated.•The strain-induced law is driven by partial dislocations, while the stress-assisted law involves an energy criterion.•The kinetic laws are implemented in a crystal plasticity model for predicting the transformation-induced plasticity.•The laws capture the role of crystallographic texture and grain scale stress state on martensite formation.•Case studies involving different stress states demonstrate utility of the model in predicting the deformation behavior.
A set of constitutive model parameters along with crystallography governs the activation of deformation mechanisms in crystal plasticity. The constitutive parameters are typically established by ...fitting of mechanical data, while microstructural data is used for verification. This paper develops a Pareto-based multi-objective machine learning methodology for efficient identification of crystal plasticity constitutive parameters. Specifically, the methodology relays on a Gaussian processes-based surrogate model to limit the number of calls to a given crystal plasticity model, and, consequently, to increase the computational efficiency. The constitutive parameters pertaining to an Elasto-Plastic Self-Consistent (EPSC) crystal plasticity model including a dislocation density-based hardening law, a backstress law, and a phase transformations law are identified for two materials, a dual phase (DP) steel, DP780, subjected to load reversals and a stainless steel (SS), 316L, subjected to strain rate and temperature sensitive deformation. The latter material undergoes plasticity-induced martensitic phase transformations. The optimization objectives were the quasi static flow stress data for the DP steel case study, while a set of strain-rate and temperature sensitive flow stress and phase volume fraction data for the SS case study. The procedure and results for the two case studies are presented and discussed illustrating advantages and versatility of the developed methodology. In particular, the efficiency of the developed methodology over an existing genetic algorithm methodology is discussed. Additionally, the parameters identified for the SS case study were utilized to simulate three biaxial tensile loading paths using a finite element implementation of EPSC for further verification.
•A Pareto-based multi-objective machine learning procedure for parameters is developed.•A budgeted infilling algorithm is based on Gaussian processes surrogate models.•Employed crystal plasticity model is physically based and features several sub-models.•The developed procedure is used to identifying model parameters for two steel alloys.•The procedure is two orders of magnitude faster than genetic algorithm procedures.
Crystal plasticity models evolve a polycrystalline yield surface using meso-scale descriptions of deformation mechanisms. The activation of deformation mechanisms is governed by crystallography and a ...set of model parameters, which are typically calibrated through the fitting of mechanical data such as stress–strain curves and elastic lattice strains. Microstructural data such as phase fractions and texture evolution are used for verifying crystal plasticity parameters. In this work, we use a multi-objective genetic algorithm to identify hardening parameters from flow stress curves with an option to incorporate texture into the optimization approach. Robust, generalized objective functions are developed and used to identify sets of parameters pertaining to dislocation density-based hardening laws in visco-plastic and elasto-plastic self-consistent (VPSC and EPSC) homogenization models. First, the parameters are identified for pure Nb directly from texture using an objective function based on generalized spherical harmonics. Since texture evolution is driven by the relative contribution of active slip systems, the parameters governing the evolution of slip resistance ratios can be recovered from fitting discrete textures at a series of strains. Next, a comprehensive set of load reversal data for dual phase (DP) 780 steel is used to fit a hardening law and a back-stress law in EPSC. Finally, parameters pertaining to a complex hardening law for the evolution of slip and twinning in pure α-Ti are identified. Remarkably, using texture as an objective in combination with stress–strain objectives constrains the model of Ti to fully reproduce not only stress–strain and texture evolution but also hierarchical twinning measurements as a function of initial grain size and texture. Furthermore, given an appropriate model fit to representative experimental texture evolution, underlying twin volume fractions contributing to texture evolution can be predicted.
•A multi-objective optimization is developed to fit parameters for crystal plasticity.•Utility of the optimization procedure is illustrated on Nb, DP780, and Ti data.•A texture objective function based on generalized spherical harmonics is formulated.•Hardening and back-stress parameters are adjusted to fit load reversal data for DP780.•Fitting of Ti data partitioned barrier effects from dislocation and twinning effects.
•Crystal Plasticity captures effect of crystal orientation of Ta Taylor cylinders.•Strong variations in final shapes predicted with crystal plasticity finite elements.•Calibrated strain hardening and ...adiabatic heating constitutive laws were required.•Results emphasize the need of microstructure-aware models for engineering design.
Recent Taylor cylinder impact tests carried out for Ta single crystals showed strong variations in dimensional changes for different crystallographic directions aligned with the cylindrical axis. In order to capture the effect of crystallography on the deformation characteristics and final shapes of the impacted cylinders, a single crystal material subroutine is adapted and embedded in the solid mechanics/dynamics Finite Element solver Abaqus to simulate the aforementioned single crystal Ta Taylor impact experiments. Details of the coupled model implementation, and insights on the role played by single crystal anisotropic flow on the deformation behavior across a broad range of strain rates and temperatures for different single crystal orientations are presented and discussed. We demonstrate the predictive capability of the adopted crystal plasticity model to capture the significant role played by crystal orientation-induced anisotropy, as well as strain hardening and adiabatic heating, on the dynamic deformation response of crystalline materials. This re-emphasizes the need of microstructure-aware models to improve the accuracy of simulations for high-consequence engineering design.
Crystallographic texture in metals influences material properties, e.g., r-value. In this work, a moderately strong texture is obtained in AA5182-O through continuous-bending-under-tension processing ...followed by a recovery heat treatment from the initial weak cube texture. EBSD scans confirm that the texture is retained after heat treating. The processed material exhibits increased strength and reduced planar anisotropy, providing benefits to subsequent forming operations, compared to the as-received material. Crystal plasticity simulations confirm the texture change during deformation and predict the flow stress response. Such simulations can be used for stress superposition process design to intentionally manipulate material properties.
•Elasto-plastic self-consistent (EPSC) and homogeneous anisotropic hardening (HAH) models are adjusted for alloy AA6022-T4.•The models capture nonlinear unloading, Bauschinger effect, and anisotropic ...hardening behavior of the alloy.•The models are used to simulate drawing of a cylindrical cup in implicit finite elements to facilitate comparisons.•Both formulations achieve acceptable accuracy in terms of simulating geometrical changes of the cup during forming.•The HAH model is significantly faster, while the EPSC model is much easier to adjust and calibrate.
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.
•In-situ high energy synchrotron X-ray diffraction is used to characterize the evolution of texture, twinning, lattice strains, and flow stress for Be.•Compressive loading and cross-reloading tests ...are performed to observe transients in the flow stress and microstructure.•An advanced elastic-plastic self-consistent crystal plasticity model is used to predict and interpret the data.•Shifts in active deformation mechanisms are responsible for the transients from one deformation path to another and hardening.•Role of twinning/de-twinning along with slip during compressive deformation of beryllium as a function of strain rate is discussed.
Deformation behavior of beryllium during compressive loading and cross-reloading is studied using in-situ high energy synchrotron X-ray diffraction microscopy and crystal plasticity modeling. The evolution of texture, twinning, elastic lattice strains, and flow stress are measured and compared with the predictions of an advanced elastic-plastic self-consistent (EPSC) crystal plasticity model. The model is initialized with the experimentally measured texture and residual stress produced by a simulation of cooling and calibrated to establish a set of model parameters using a portion of the measured data. The rest of the measured data is used for validation of the model. It is shown that the model is sufficiently flexible to reproduce the particularities pertaining to the complex strain-path-change and strain rate sensitive deformation of the material including the evolution of texture, twinning, lattice strains, transients in the stress-strain response, and anisotropic hardening with great accuracy using a single set of model parameters. From the comparison of the experimental data and predictions, we infer that the shifts in active deformation mechanisms between the slip systems from soft to hard and vice versa as well as between twinning to de-twinning are primarily responsible for drastic changes in the flow stress from one path to another. In particular, deformation twins form during compressive in-plane loading followed either by de-twinning during compressive cross-reloading in the through-thickness direction or by forming additional twin variants with some de-twinning of the existing variants during a compressive cross-reloading in another in-plane direction. The shifts in active deformation mechanisms are a consequence of changes in texture relative to the compression direction mediated with the deformation history and strain rate dependent dislocation density evolution governing hardening. The secondary effects improving the predictions come from accounting for residual stress, slip system-level backstress, and latent hardening.
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.
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