Polycrystal Plasticity Model Research Articles

A Transition State Theory-Based Continuum Plasticity Model Accounting for the Local Stress Fluctuation

Based on the transition state theory, a continuum plasticity theory is developed for metallic materials. Moreover, the nature of local stress fluctuation within a material point is considered by incorporating the probability distribution of the stresses. The model is applied to investigate the mechanical behaviors of 316 L stainless steel under various loading cases. The simulated results closely match the results obtained by the polycrystal plasticity model and experiments. The mechanical behaviors associated with strain rate sensitivity, temperature dependence, stress relaxation, and strain creep are correctly captured by the model. Furthermore, the proposed model successfully characterizes the Bauschinger effect, which is challenging to capture with a conventional continuum model without additional assumptions. The proposed model could be further employed in the design, manufacturing, and service of engineering components.

Fast-throughput simulations of laser-based additive manufacturing in metals to study the influence of processing parameters on mechanical properties

Laser-powder bed fusion additive manufacturing (LPBF-AM) of metals is rapidly becoming one of the most important materials processing pathways for next-generation metallic parts and components in a number of important applications. However, the large parametric space that characterizes laser-based LPBF-AM makes it challenging to understand what are the variables controlling the microstructural and mechanical property outcomes. Sensitivity studies based on direct LPBF-AM processing are costly and lengthy to conduct, and are subjected to the specifications and variability of each printer. Here we develop a fast-throughput numerical approach that simulates the LPBF-AM process using a cellular automaton model of dynamic solidification and grain growth. This is accompanied by a polycrystal plasticity model that captures grain boundary strengthening due to complex grain geometry and furnishes the stress-strain curves of the resulting microstructures. Our approach connects the processing stage with the mechanical testing stage, thus capturing the effect of processing variables such as the laser power, laser spot size, scan speed, and hatch width on the yield strength and tangent moduli of the processed materials. When applied to pure Cu and stainless 316L steel, we find that laser power and scan speed have the strongest influence on grain size in each material, respectively.

The strain rate sensitive and anisotropic behavior of rare-earth magnesium alloy ZEK100 sheet

To overcome the limitation in formability at room temperature, manufacturers have developed magnesium alloys with remarkable properties by adding rare-earth elements. The rare-earth magnesium alloys behave differently from the conventional alloys, especially with respect to their coupled anisotropic and strain rate sensitive behavior. In the current work, such behavior of the rare-earth Mg alloy ZEK100 sheet at room temperature is investigated with the aid of the elastic viscoplastic self-consistent polycrystal plasticity model. Different strain rate sensitivities (SRSs) for various deformation modes are employed by the model to simulate the strain rate sensitive behaviors under different loading directions and loading rates. Good agreement between the experiments and simulations reveals the importance and necessity of using different SRSs for each deformation mode in hexagonal close-packed metals. Furthermore, the relative activities of each deformation mode and the texture evolution during different loadings are discussed. The anisotropic and strain rate sensitive behavior is ascribed to the various operating deformation modes with different SRSs during loading along different directions.

Multi‐scale composite finite element modeling of three‐dimensional prestressed reinforced concrete structural members: Part I—A comprehensive framework

AbstractThe goal of this work is to develop a complete theoretical framework for the numerical modeling of three‐dimensional prestressed reinforced concrete structural members, soil mixture, and their interactions. This numerical formulation is based on the construction of a new composite finite element, in order to tackle the multi‐scale problem. For this purpose, the mechanical behavior of each microstructure component material will be modeled as follows: (a) for the plain concrete (PC) and the soil mixture, an anisotropic‐damage‐elastoplastic model equipped with the strong discontinuity approach will be taken into account; (b) a polycrystal plasticity model, for the steel rebars and prestrssed tendons will be captured through a new strategy solution of discontinuous bifurcation problem, with the main objective to represent the multi‐cracking phenomenon; (c) regarding the mechanical behavior of the aggregates and rocks (skeleton—hydro mechanic problem) in the PC and soil mixture, respectively, an anisotropic‐damage‐double‐poro‐polycrystal plasticity model equipped with softening material will be considered. An advanced failure algorithm based on the marching tetrahedron and the pseudo‐termic problem will be developed. Finally, the zone that characterizes the interaction between the structural member and the soil mixture will be encrusted inside the composite finite element.

Role of anisotropy in the ballistic response of rolled magnesium

Rolled magnesium alloys exhibit pronounced tension-compression asymmetry as well as anisotropy in yield and strain-hardening behavior. Although differences in the mechanical response are reasonably well-understood, it is not clear to what extent anisotropy alters the deformation and failure of plates subjected to ballistic loading conditions. In this work, the role of texture and anisotropy in the ballistic response is investigated using a combined experimental–computational approach. Sphere impact experiments are performed on rolled magnesium plates cut from orientations that exhibit differing mechanical responses. The complex failure process is characterized by in situ diagnostics, including ultra-high-speed Digital Image Correlation and Photonic Doppler Velocimetry, and compared with simulations performed on polycrystalline aggregates using a polycrystal plasticity model for hcp metals. The anisotropic deformation behavior arises from deformation mechanisms with disparate strength and strain hardening behavior, which is well captured in the model. The occurrence of low-strength extension twinning is shown to govern the initial anisotropic deformation and bulging of the plate. When compared with post-mortem 3D X-ray microscopy, regions that experience intense basal slip are shown to be sites for damage initiation that leads to eventual fracture. The combination of experiments and simulations suggest that at low to intermediate ballistic loading rates, material orientation plays a crucial role in dictating eventual fracture and failure in strongly anisotropic metals such as in rolled magnesium alloys.

Exploring stress equivalence for solid solution strengthened Mg alloy polycrystals

The principle of “stress equivalence” proposed by Basinski et al. offers insight regarding the nature of thermally activated plasticity of solid solution alloys of FCC and HCP (Mg) crystal structures at low temperatures. More recently, Leyson and Curtin have developed a theoretical framework which builds upon the Labusch solute strengthening model. The current work analyzes some recent results from the literature (for single crystal Mg–Zn, Mg–Y, and Mg–Dy) which permit a further examination of the concept of “stress equivalence.” Then, using an effective Taylor factor obtained from polycrystal plasticity modeling of textured Mg, the results of cryogenic mechanical tests of polycrystalline Mg–Sc and Mg–Y alloys are analyzed to test their adherence to the principle of “stress equivalence.” The analysis accounts for the truly long-range strengthening effect of grain boundaries through established, temperature dependent Hall-Petch relationships, but makes no other assumption of an “athermal stress” that is frequently mentioned in the literature. The results emphasize the broad applicability of Basinski's principle of stress equivalence, by showing that the low temperature thermally activated tensile response of textured, polycrystalline Mg alloys can be predicted once the flow stress at a single rate and temperature is known.

Correction to: Multi-Island Genetic-Algorithm-Based Approach to Uniquely Calibrate Polycrystal Plasticity Models for Magnesium Alloys

Correction to: Multi-Island Genetic-Algorithm-Based Approach to Uniquely Calibrate Polycrystal Plasticity Models for Magnesium Alloys

Three-dimensional crystal plasticity simulations using peridynamics theory and experimental comparison

A three-dimensional (3D) peridynamics (PD) model of crystal plasticity (CP) is presented for predicting the fine-scale localization in polycrystalline microstructures undergoing elastoplastic deformation. Microscale data from electron microscopy and digital image correlation have indicated that slip localizations arise early in deformation and act as precursors to mechanical failure and fracture. However, classical numerical approaches such as crystal plasticity finite element methods (CPFEM) are generally unable to predict the emergence and distribution of such localizations. Alternatively, the PD formulation has attracted significant attention for its unique treatment of deformation in the presence of high strain gradient fields. In this paper, a mesh-free non-ordinary state-based PD technique is developed for simulating the elasto-plastic deformation of 3D polycrystalline aggregates of a magnesium alloy. This work presents the details of 3D polycrystal plasticity modeling using PD theory with experimental and CPFEM comparisons. The results from this model are validated against published experimental data for the stress-strain response and texture evolution. The crystal plasticity peridynamic (CPPD) models are successful in simulating grain averaged strains seen in the experiment and depict well-resolved regions of strain localization.

The effect of Mg and Si content on the microstructure, texture and bendability of Al–Mg–Si alloys

In this paper, four model Al–Mg–Si automotive sheet alloys with different Mg and Si contents were prepared and heated treated to the same T4P temper (solution treated and pre-aged for 8 h at 75 °C and aged for 1 week at room temperature). The influence of the Mg and Si content on microstructure, crystallographic texture, tensile behavior and bendability was investigated. The evolution of microstructure and texture during thermomechanical processing was characterized. It was found that the bendability of sheets in the T4P temper decreases with raising Mg and Si content. The deterioration of bendability can be related to the decreased true fracture strain measured in tension. The fracture mode in the bend tests was found to be predominately transgranular. Crack initiation was observed at α-Al(FeMn)Si constituent particles and the propagation of cracks proceeded by a combination of shear bands and void growth/coalescence. Finally, the strength of the recrystallization texture increases was observed to increase with increasing Mg and Si contents and it was found that the relationship between crystallographic texture and the plastic anisotropy, e.g. r-value, could be predicted using the visco-plastic self-consistent (VPSC) polycrystal plasticity model. • The bendability of Al–Mg–Si alloys sheets after solution treatment decreases with raising Mg and Si contents. • The transgranular fracture mode is mainly account for the bending of Al–Mg–Si alloys sheets in T4P temper. • Cracks initiate at α-Al(FeMn)Si constituent particles and propagate by a combination of shear bands and void growth.

Self-consistent, polycrystal rate-independent crystal plasticity modeling for yield surface determination

The evolution of the macroscopically observed yield surface has been the subject of many studies due to its significant effect on the numerical simulation of metal forming processes. Although macroscopic models exist that aim to define this evolution accurate data for calibration as well as validation of these models are difficult to obtain. One common approach is to use crystal plasticity simulations for analyzing the mesoscopic behavior followed by a homogenization scheme for gathering the aggregate behavior. In this study a similar approach is followed the difference being the choice of the crystal plasticity and homogenization methods. A rate-independent crystal plasticity framework where all slip system activities are solved implicitly using a backward Euler approach in combination with an interior point method for constrained optimization is used for single crystal behavior. The aggregate behavior is obtained using a self-consistent analytical homogenization scheme. The results of the homogenization scheme are compared against full-field crystal plasticity finite element simulations. The determination of the yield surface is done by considering the macroscopic behavior where the strain rate direction and magnitude changes over a threshold during stress-based loading.

Multi-Island Genetic-Algorithm-Based Approach to Uniquely Calibrate Polycrystal Plasticity Models for Magnesium Alloys

The single-crystal yielding and hardening behavior of polycrystals is important for understanding their mechanical behavior. Many parameters (> 10) are usually required to achieve this for magnesium alloys based on physics-based models. However, the efficient and precise determination of these parameters is a very challenging task. An efficient and practical method is proposed herein to determine the parameter set by dividing the parameters into those for yielding and hardening, thereby significantly reducing the time cost of automatic parameter calibration. This method is then applied to calibrate the parameter set used in the viscoplastic self-consistent (VPSC) model to describe the mechanical behavior of the rare-earth magnesium alloy ZEK100 from multiple mechanical test data. The obtained best-fit parameters can be considered realistic and nearly unique, and can successfully reproduce the mechanical behavior and textural evolution. This procedure can be generally applied to calibrate near-unique parameters in other materials and constitutive models.

Material testing of magnesium alloy AZ31B using a finite element polycrystal method based on a rate independent crystal plasticity model

Magnesium and its alloys are attractive structural light materials because they have a high spe-cific strength and high specific stiffness. That is why their usage in high performance automotive and aerospace applications has been increased. However, their high anisotropy and low ductility could bring to forming failure, to avoid these a better accuracy for metal forming simulation is re-quired. The identification of macroscopic parameters is expensive due to the experiments needed to find them, the use of multi-scale approach allows to find parameters for the model through easier experiments. A finite element polycrystal method, based on a rate independent polycrystal plasticity model, is implemented in order to perform the material testing of a cast magnesium alloy AZ31B. The parameters of the model are adjusted to better fit the experimental data through a trial and error process.

Porous polycrystal plasticity modeling of neutron-irradiated austenitic stainless steels

A micromechanical model for quantifying the simultaneous influence of irradiation hardening and swelling on the mechanical stiffness and strength of neutron-irradiated austenitic stainless steels is proposed. The material is regarded as an aggregate of equiaxed crystalline grains containing a random dispersion of pores (large voids due to large irradiation levels) and exhibiting elastic isotropy but viscoplastic anisotropy. The overall properties are obtained via a judicious combination of various bounds and estimates for the elastic energy and viscoplastic dissipation of voided crystals and polycrystals. Reference results are generated with full-field numerical simulations for dense and voided polycrystals with periodic microstructures and crystal plasticity laws accounting for the evolution of dislocation and Frank loop densities. These results are calibrated with experimental data available from the literature and are employed to assess the capabilities of the proposed model to describe the evolution of mechanical properties of highly irradiated Solution Annealed 304L steels at 330oC. The agreement between model predictions and simulations is seen to be quite satisfactory over the entire range of porosities and loadings investigated. The expected decrease of overall elastic properties and strength for porosities observed at large irradiation levels is reported. The mathematical simplicity of the proposed model makes it particularly apt for implementation into finite-element codes for structural safety analyses.

Temperature-dependence of plasticity and fracture in an Al-Cu-Li alloy

ABSTRACT The microstructure of an Al-Cu-Li alloy sheet is characterised in the solution treated, underaged, and peak aged tempers. Its mechanical response under uniaxial tension is measured at , , and along , , and to the rolling direction. The anisotropic stress-strain curves are interpreted using a polycrystal plasticity model, which implements three hardening modes suggested by the microstructure, viz., matrix hardening, hardening due to isotropic precipitates, and hardening due to anisotropic precipitates. Phenomenological activation theory based analysis of the work hardening suggests that the physical mechanism underlying work hardening due to anisotropic precipitates remains constant over the temperature range studied, while the mechanism underlying matrix hardening varies strongly with temperature.

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.

Size effect on the subsequent yield and hardening behavior of metal foil

With the growing demand for miniaturized and integrated products, the metal foils have been extensively applied in the field of aerospace, electronics, medical equipment, and microsystem technology. However, the deformation process is usually under the complex stress status for the fabrication of the micropart. In addition, size effect dramatically impact the microforming process and therefore the well-developed metal forming theory established at macroscale is inapplicable at the grain level. To further investigate the size effect on the subsequent yield and hardening behavior, the biaxial tests of stainless-steel foils with diverse grain sizes and thicknesses were conducted under different stress states. The initial and subsequent yield loci are computed under various loading histories according to the plastic work per unit volume principle. It is found that the evolution of yield loci from initial to the subsequent state shows a remarkable difference for metal foils with different grain sizes. Based on Yld2000-2d yield criterion, the theoretical yield loci based on three different hardening models, including isotropic, kinetic, and isotropic-kinetic mixed hardening models, were acquired to explore and evaluate their applicability at microscale. Results indicated that the isotropic-kinetic mixed hardening model can better describe the evolution of subsequent yield locus than the individual hardening model. In addition, the back stress is shifted down with the increase of grain size for the foils with a certain thickness. Based on the Taylor-Bishop-Hill (TBH) polycrystal plasticity model, the evolution of subsequent yield surface is interpreted by the transformation of grain orientation.

Correction to: An EBSD Evaluation of the Microstructure of Crept Nimonic 101 for the Validation of a Polycrystal–Plasticity Model

Correction to: An EBSD Evaluation of the Microstructure of Crept Nimonic 101 for the Validation of a Polycrystal–Plasticity Model

Micromechanical approaches to understand dwell fatigue: from titanium a-b microstructures to disc thermal alleviation

Micro-pillar tests on α and α-β colony Ti alloys in combination with crystal plasticity finite element analysis has enabled the extraction of a and b phase slip strength and rate sensitivity properties. Faithfully representative α-β microstructure polycrystal plasticity models have then been established in order to investigate dwell fatigue in isothermal rig test behaviour and anisothermal thermomechanical flight loading conditions. The role of thermal alleviation in diminishing dwell sensitivity has been demonstrated.

Crystal plasticity modeling and neutron diffraction measurements of a magnesium AZ31B plate: Effects of plastic anisotropy and surrounding grains

This study used in-situ neutron diffraction measurements and Elastic ViscoPlastic Self-Consistent polycrystal plasticity model, which incorporates a Twinning and DeTwinning scheme (denoted by EVPSC-TDT), to examine the macro-and micro-mechanical behaviors of a rolled AZ31B plate subjected to uniaxial tension. Three specimens were specifically designed for minimum, maximum and intermediate twinning: (1) loading along the rolling direction, (2) loading along the plate normal, and (3) loading along the direction 45° with respect to the plate normal. Apart from the macroscopic stress strain response, the measured diffraction intensities and internal elastic strains were obtained to examine the activities of the deformation modes at the grain level. The diffraction intensity evolution signaled the volume fraction change of twinning, while the internal elastic strain evolution designated the stress partitioning among the grain orientations. The effect of the surrounding grains on the development of the internal elastic strain was investigated by identifying the corresponding deformation mechanisms. Notably, the corresponding modeling work revealed that the EVPSC-TDT model permitted the prediction of the strain hardening and anisotropic behavior along the directions with minimum, maximum and intermediate twinning at the macroscale, and the evolution of the diffraction intensities and internal strains at the microscale. The results provide a physical understanding of the effects of the load direction, texture and surrounding grains on the role of the deformation modes in hexagonal close-packed polycrystalline materials.

Analysis of Grain-Resolved Data from Three-Dimensional X-Ray Diffraction Microscopy in the Elastic and Plastic Regimes

The combination of experimental data and polycrystal plasticity modeling is a powerful tool to advance our understanding of the behavior of individual grains and how these interact. The present paper illustrates how much information a single three-dimensional x-ray diffraction experiment contains and how this may be analyzed and compared with model predictions. The data cover the elastic and plastic regimes (0.1%, 1%, and 5% strain) of a tensile experiment on a fully recrystallized stainless-steel sample. The number of bulk grains analyzed is on the order of 200. Specific phenomena considered are stress correlations across twin boundaries, stress states, and resolved shear stresses in the elastic and plastic regimes along with lattice rotations.