Crystal Plasticity Finite Element Simulations Research Articles

Influence of slip system combination models on crystal plasticity finite element simulation of NiTi shape memory alloy undergoing uniaxial compression

The influence of various slip system combination models on crystal plasticity finite element simulation of NiTi shape memory alloy subjected to uniaxial compression deformation is investigated according to three combinations of slip systems, including combination of {010}〈100〉 and {110}〈111〉 slip modes, combination of {110}〈100〉 and {110}〈111〉 slip modes and combination of {110}〈100〉, {010}〈100〉 and {110}〈111〉 slip modes, which consist of 18, 18 and 24 slip systems, respectively. By means of simulating mechanical response, strain distribution, stress distribution and Schmid factor, it can be found that in terms of simulation accuracy, combination of {110}〈100〉 and {110}〈111〉 slip modes is in good agreement with combination of {110}〈100〉, {010}〈100〉 and {110}〈111〉 slip modes. The contribution of {110}〈100〉 slip mode to plastic strain is primary in plastic deformation of NiTi shape memory alloy, whereas {010}〈100〉 slip mode, which makes small contribution to plastic deformation, can be regarded as the unfavorable slip mode. In the case of large plastic strain, the {010}〈100〉 slip mode contributes to the formation of (001) [01¯0] texture component, while {110}〈100〉 and {110}〈111〉 slip modes facilitate the formation of γ-fibre (〈111〉) texture.

Molecular dynamics investigation of c-axis deformation of single crystal Ti under uniaxial stress conditions: Evolution of compression twinning and dislocations

Twinning plays an important role on the microstructure evolution of HCP metals. In this work, we perform c-axis compression of single crystal Ti under uniaxial stress conditions using molecular dynamics simulations. The objective is to demonstrate activation and evolution of compression twins along with dislocations when Ti single crystals are loaded in uniaxial stress conditions using two commonly utilized interatomic potentials. We find that activation of only {101¯1} compression twins with the Kim potential is inconsistent with the Schmid criterion while activation of both {101¯1} and {112¯2} compression twins with the Hennig potential is consistent with the Schmid criterion. Twin variants activated do not contribute equally to the total twinned volume even with equal Schmid factor for both potentials and thereby demonstrating inability of the Schmid criterion to predict dominance and evolution of twin variants. The Kim potential shows large amount of dislocation density in comparison to the Hennig potential. The strain rate sensitivity on activation of compression twin systems is observed with the Hennig potential. The study can be utilized to further investigate the evolution of compression twins required to develop/improve twin volume fraction evolution laws for crystal plasticity finite element simulations.

Grain rotations during uniaxial deformation of gradient nano-grained metals using crystal plasticity finite element simulations

Gradient nano-grained (GNG) metals have great application potential due to its outstanding performance in both strength and ductility. In this paper, we investigate the uniaxial deformation response of GNG Cu utilizing the developed size-dependent crystal plasticity model with random initial grain lattice orientation implemented by the user-material subroutine of ABAQUS. The results show that the grain size gradient leads to gradient distribution of stress and strain, consistent with the results in the literature. In addition, the Lode parameter also shows a gradient distribution with the value closer to zero at the small-grained surface regions. Importantly, we discover that the magnitude of grain rotation strongly depends on the initial lattice orientation of the grain, but does not depend on the grain size in the current crystal plasticity finite element framework. Furthermore, we gave a reasonable explanation for the distribution of grain rotation magnitudes. Our study provides insights into the outstanding mechanical properties of GNG metals and the evolution of texture.

Sparse and scalable eigenstrain-based reduced order homogenization models for polycrystal plasticity

In this manuscript, accelerated, sparse and scalable eigenstrain-based reduced order homogenization models have been developed for computationally efficient multiscale analysis of polycrystalline materials. The proposed model is based on the eigenstrain-based reduced order homogenization (EHM) approach, and provides significant efficiency in analysis of structures composed of complex polycrystalline microstructures. The acceleration is achieved by introducing sparsity into the linearized reduced order system through selectively considering the interactions between grains based on the idea of grain clustering. The proposed approach results in a hierarchy of reduced models that recovers eigenstrain-based homogenization, when full range of interactions are considered, and degrades to the Taylor model, when all inter-grain interactions are neglected. The resulting sparse system is solved efficiently using both direct and iterative sparse solvers, both of which show significant efficiency improvements compared to the full EHM. A layer-by-layer neighbor grain clustering scheme is proposed and implemented to define ranges of grain interactions. Performance of the proposed approach is evaluated by comparing the results against the full EHM and crystal plasticity finite element (CPFE) simulations.

Micromechanical modeling approach to derive the yield surface for BCC and FCC steels using statistically informed microstructure models and nonlocal crystal plasticity

In order to describe irreversible deformation during metal forming processes, the yield surface is one of the most important criteria. Because of their simplicity and efficiency, analytical yield functions along with experimental guidelines for parameterization become increasingly important for engineering applications. However, the relationship between most of these models and microstructural features are still limited. Hence, we propose to use micromechanical modeling, which considers important microstructural features, as a part of the solution to this missing link. This study aims at the development of a micromechanical modeling strategy to calibrate material parameters for the advanced analytical initial yield function Barlat YLD 2004-18p. To accomplish this, the representative volume element is firstly created based on a method making use of the statistical description of microstructure morphology as input parameter. Such method couples particle simulations to radical Voronoi tessellations to generate realistic virtual microstructures as representative volume elements. Afterwards, a nonlocal crystal plasticity model is applied to describe the plastic deformation of the representative volume element by crystal plasticity finite element simulation. Subsequently, an algorithm to construct the yield surface based on the crystal plasticity finite element simulation is developed. The primary objectives of this proposed algorithm are to automatically capture and extract the yield loci under various loading conditions. Finally, a nonlinear least square optimization is applied to determine the material parameters of Barlat YLD 2004-18p initial yield function of representative volume element, mimicking generic properties of bcc and fcc steels from the numerical simulations.

Adaptive multi-time-domain subcycling for crystal plasticity FE modeling of discrete twin evolution

Crystal plasticity finite element (CPFE) models that accounts for discrete micro-twin nucleation-propagation have been recently developed for studying complex deformation behavior of hexagonal close-packed (HCP) materials (Cheng and Ghosh in Int J Plast 67:148–170, 2015, J Mech Phys Solids 99:512–538, 2016). A major difficulty with conducting high fidelity, image-based CPFE simulations of polycrystalline microstructures with explicit twin formation is the prohibitively high demands on computing time. High strain localization within fast propagating twin bands requires very fine simulation time steps and leads to enormous computational cost. To mitigate this shortcoming and improve the simulation efficiency, this paper proposes a multi-time-domain subcycling algorithm. It is based on adaptive partitioning of the evolving computational domain into twinned and untwinned domains. Based on the local deformation-rate, the algorithm accelerates simulations by adopting different time steps for each sub-domain. The sub-domains are coupled back after coarse time increments using a predictor-corrector algorithm at the interface. The subcycling-augmented CPFEM is validated with a comprehensive set of numerical tests. Significant speed-up is observed with this novel algorithm without any loss of accuracy that is advantageous for predicting twinning in polycrystalline microstructures.

Investigation of fatigue crack incubation and growth in cast MAR-M247 subjected to low cycle fatigue at room temperature

MC carbide particles (with Hafnium and/or Tantalum as constituent metallic element, M) were observed to crack extensively in a cast polycrystalline nickel-base superalloy, MAR-M247, when subjected to low-cycle fatigue loading at room temperature. High resolution secondary electron images taken on the surface of a double edge notch test specimen revealed that approximately half the carbide particles cracked in the highly-strained notch section of the specimen. These images further illustrated that the average surface area of cracked particles was approximately three times that of the uncracked particles. Additional analysis illustrated that the cracks within a large number of particles aligned nearly perpendicular to the loading direction. However, high aspect ratio particles (with aspect ratio $${>}3$$ ) were prone to incubate cracks aligned along its major axis, independent of the loading direction. Additionally, forward-scattered imaging often showed a high density of slip bands interaction with most of the particles which cracked. The life limiting crack growth in MAR-M247 was observed to be crystallographic in nature, as the crack grew along slip bands as measured by high-resolution electron backscatter diffraction, even after spanning many grains. Statistically representative microstructure models of MAR-M247 were generated and used in the crystal plasticity finite element simulations. As expected, there was a significant variation in the computed stress state among constituent carbide particles. The stress state of the carbide particles was found to be heavily influenced by the stress in surrounding grains and the orientation of the major axis of the particles with respect to applied load direction. For particles that intersect the free-surface, stress was found to be highly concentrated at the free surface and a positive correlation between the magnitude of free-surface area and the maximum principal stress was found. Additionally, high stress concentrations were observed in regions where carbide particles intersect grain boundaries.

Laue micro-diffraction and crystal plasticity finite element simulations to reveal a vein structure in fatigued Cu

The formation of a vein during cyclic shearing of a single copper crystal oriented for single slip can be followed in transmission Laue diffraction by analyzing the spatially resolved lattice rotation evolution. Because Laue transmission integrates the signal over the thickness of the sample, the structure of the vein in the beam direction is a priori believed to be inaccessible. Here we show that the vein geometry in the beam direction can be retrieved by comparing lattice curvature tensor components from crystal plasticity finite element simulations with those experimentally derived. Virtual sectional analysis facilitates the interpretation of the measured lattice curvatures of quasi-2D dislocation structures, allowing identifying a vein morphology that is slightly vertically and horizontally inclined in the through thickness direction.

High Temperature Deformation Mechanism in Hierarchical and Single Precipitate Strengthened Ferritic Alloys by In Situ Neutron Diffraction Studies

The ferritic Fe-Cr-Ni-Al-Ti alloys strengthened by hierarchical-Ni2TiAl/NiAl or single-Ni2TiAl precipitates have been developed and received great attentions due to their superior creep resistance, as compared to conventional ferritic steels. Although the significant improvement of the creep resistance is achieved in the hierarchical-precipitate-strengthened ferritic alloy, the in-depth understanding of its high-temperature deformation mechanisms is essential to further optimize the microstructure and mechanical properties, and advance the development of the creep resistant materials. In the present study, in-situ neutron diffraction has been used to investigate the evolution of elastic strain of constitutive phases and their interactions, such as load-transfer/load-relaxation behavior between the precipitate and matrix, during tensile deformation and stress relaxation at 973 K, which provide the key features in understanding the governing deformation mechanisms. Crystal-plasticity finite-element simulations were employed to qualitatively compare the experimental evolution of the elastic strain during tensile deformation at 973 K. It was found that the coherent elastic strain field in the matrix, created by the lattice misfit between the matrix and precipitate phases for the hierarchical-precipitate-strengthened ferritic alloy, is effective in reducing the diffusional relaxation along the interface between the precipitate and matrix phases, which leads to the strong load-transfer capability from the matrix to precipitate.

Discontinuous yielding in wrought magnesium

Recent reports of discontinuous yielding in the uniaxial compression of extruded magnesium suggest that twinning is accompanied by a significant stress decrease in the parent grain, leading to corresponding stress concentrations. We performed crystal plasticity finite element simulations using a simple twinning implementation that includes this “softening” effect for tensile twinning. With this method we were able to reproduce the experimentally observed yield point elongation and the Lüders-like propagation of strain and twinning over the sample. Twin variant selection was analysed in detail at various stages of deformation. Although lower rank variants were found to be activated, most of the twinning activity occurred on variants with the highest global Schmid factor. The stress fluctuations arising from the stress relaxation due to twinning did not appear to alter the dominance of the highest Schmid factor variant significantly. However, when twin softening is included, the twinning strain is dominated by a single variant. Despite giving rise to the highest stress fluctuations during yielding, simulations using the twin stress relaxation implementation actually showed less heterogeneity in stress after yielding. The results of our simple model suggest that “twin softening” could be key to the development of discontinuous yielding in extruded magnesium alloys.

Indentation Pileup Behavior of Ti-6Al-4V Alloy: Experiments and Nonlocal Crystal Plasticity Finite Element Simulations

This study reports on the indentation pileup behavior of Ti-6Al-4V alloy. Berkovich nanoindentation was performed on a specimen with equiaxed microstructure. The indented area was characterized by electron backscattered diffraction (EBSD) to obtain the indented grain orientations. Surface topographies of several indents were measured by atomic force microscopy (AFM). The pileup patterns on the indented surfaces show significant orientation dependence. Corresponding nonlocal crystal plasticity finite element (CPFE) simulations were carried out to predict the pileup patterns. Analysis of the cumulative shear strain distributions and evolutions for different slip systems around the indents found that the pileups are mainly caused by prismatic slip. The pileup patterns evolve with the loading and unloading process, and the change in pileup height due to the elastic recovery at unloading stage is significant. The density distributions of geometrically necessary dislocations (GNDs) around the indent were predicted. Simulation of nanoindentation on a tricrystal model was performed.

Three dimensional simulations of texture and triaxiality effects on the plasticity of magnesium alloys

We investigate the synergistic effects of texture and intrinsic plastic anisotropy (at the level of single crystal) on the deformation of polycrystalline magnesium using three-dimensional crystal plasticity finite element simulations. Using rolled plate texture as a basis, we simulate the deformation using a range of synthetic textures. Smooth and notched round bar specimens are considered to achieve different levels of stress triaxiality. Two sets of constituent single crystal properties, representative of an Mg alloy and pure Mg respectively, are adopted in order to investigate the role of intrinsic plastic anisotropy. Our results reveal that textural variations couple into the intrinsic plastic anisotropy and triaxiality to determine the active deformation mechanisms. When loaded along the rolling direction of the plate, the deformation is accommodated by prismatic slip at low triaxiality and pyramidal 〈c+a〉 slip at high triaxiality. Softer mechanisms such as basal slip and extension twinning, which are not favored by the loading orientation, are activated due to the intergranular stresses. The smooth specimens show macroscopic strain localization the onset of which depends on initial texture. The deformed textures are strongly modulated by both triaxiality and intrinsic plastic anisotropy. We also briefly discuss the potential role of twinning in damage evolution.

Crystal Plasticity Finite-element Simulation on Development of Dislocation Structures in BCC Ferritic Single Crystals

Crystal Plasticity Finite-element Simulation on Development of Dislocation Structures in BCC Ferritic Single Crystals

Crystal plasticity finite element modeling of discrete twin evolution in polycrystalline magnesium

This paper develops an advanced, image-based crystal plasticity finite element (CPFE) model, for predicting explicit twin formation and associated heterogeneous deformation in single crystal and polycrystalline microstructures of hexagonal close-packed or hcp materials, such as magnesium. Twin formation is responsible for premature failure of many hcp materials. The physics of nucleation, propagation and growth of explicit twins are considered in the CPFE formulation. The twin nucleation model is based on dissociation of sessile dislocations into stable twin loops, while propagation is assumed by atoms shearing on twin planes and shuffling to reduce the thermal activation energy barrier. The explicit twin evolution model however has intrinsic issues of low computational efficiency. Very fine simulation time steps with enormous computation costs are required to simulate the fast propagating twin bands and associated strain localization. To improve the computational efficiency, a multi-time scale subcycling algorithm is developed. It decomposes the computational domain into sub-domains of localized twins requiring very fine time-steps and complementary domains of relatively low resolution. Each sub-domain updates the stress and the deformation-dependent variables in different rates, followed by a coupling at the end of every coarse time step to satisfy global equilibrium. A 6-fold increase in computing speed is obtained for a polycrystalline Mg microstructure simulation in this paper. CPFE simulations of high purity Mg microstructures are compared with experiments with very good agreement in stress-strain response as well as heterogeneous twin formation with strain localization.

Effects of grain-to-grain interactions on shear strain localization in Al–Cu–Li rolled sheets

Crystal plasticity finite element simulations of tensile tests on thin polycrystalline samples with grain orientations representative of the microstructure in Al–Cu–Li rolled sheets are carried out to study the influence of grain-to-grain interactions on plastic strain localization. Anisotropic work-hardening and rate-sensitivity of the material behavior are assumed. The grains are modeled as thin platelets in the through-thickness direction, elongated in the rolling and transverse directions. The only distinctive feature of the present simulations with respect to standard crystal plasticity calculations is the enforcement of tangential continuity conditions on the elastic and plastic distortion rates along grain boundaries, which introduces grain-to-grain interactions and renders the simulations nonlocal. Whereas standard crystal plasticity calculations do not predict any significant plastic strain pattern, slanted shear bands spontaneously emerge throughout the sample in the simulations involving tangential continuity, in agreement with experimental observations. Also in agreement with experimental data, shear banding is delayed when the tensile axis shifts from rolling to transverse direction, and the trend to shear banding is enhanced when grain thickness is decreased, particularly in loading along the rolling direction.

Effects of void fraction on void growth and linkage in commercially pure magnesium

Void growth and linkage in magnesium is strongly influenced by the local microstructure. An innovative approach is used which allows for a quantitative analysis of the microstructural features that play a significant role in the deformation and fracture processes. Several hole configurations were investigated in order to determine the effects of void fraction on the growth and linkage processes. The samples were pulled in uniaxial tension under both an optical microscope and SEM. The digital image correlation method was used to obtain strain distributions. Furthermore, the experimental results were compared to crystal plasticity finite element simulations in order to determine the role of the various deformation mechanisms on the fracture behavior. It was established that the void fraction did not have a significant impact on the growth and linkage behavior of the holes. Interactions between the holes and the microstructure were observed for all of the configurations analyzed. The strain distributions revealed that twin and grain boundaries produce strain concentrations an order of magnitude larger than the macroscopic strain. Furthermore, the results show that there is likely a critical strain required to initiate fracture in these boundaries.

Miniaturization of Micro-Solder Bumps and Effect of IMC on Stress Distribution

As the joints become smaller in more advanced packages and devices, intermetallic (IMCs) volume ratio increases, which significantly impacts the overall mechanical behavior of joints. The existence of only a few grains of Sn (Tin) and IMC materials results in anisotropic elastic and plastic behavior which is not detectable using conventional finite element (FE) simulation with average properties for polycrystalline material. In this study, crystal plasticity finite element (CPFE) simulation is used to model the whole joint including copper, Sn solder and Cu6Sn5 IMC material. Experimental lap-shear test results for solder joints from the literature were used to validate the models. A comparative analysis between traditional FE, CPFE and experiments was conducted. The CPFE model was able to correlate the experiments more closely compared to traditional FE analysis because of its ability to capture micro-mechanical anisotropic behavior. Further analysis was conducted to evaluate the effect of IMC thickness on stress distribution in micro-bumps using a systematic numerical experiment with IMC thickness ranging from 0% to 80%. The analysis was conducted on micro-bumps with single crystal Sn and bicrystal Sn. The overall stress distribution and shear deformation changes as the IMC thickness increases. The model with higher IMC thickness shows a stiffer shear response, and provides a higher shear yield strength.

In-situ SEM observation and crystal plasticity finite element simulation of fretting fatigue crack formation in Ni-base single-crystal superalloys

Fretting fatigue behavior of Ni-base single crystal (NBSX) superalloys was investigated based on in-situ scanning electron microscope (SEM) observations. Evolutions of slip lines and initiations of cracks were observed. Slip lines were found on specimen free surface along three typical directions. Short cracks were observed to initiate along the slip line. Crystal plasticity constitutive model considering cyclic hardening effect was employed. Crystal plasticity finite element method (CPFEM) simulation showed the activations of crystallographic slip systems at contact region. The slip plane with the maximum plastic slip was determined as dominate slip plane. Equivalent plastic strain was proved effective to predict crack initiation. The simulation results including predicted slip lines, crack initiation locations and orientations were in good agreements with observations.

Crystal plasticity modeling of size effects in rolled multilayered Cu-Nb composites

We present size-dependent crystal plasticity finite element simulations of the deformation microstructure, plastic flow and texture evolution in multilayered Cu-Nb composites during cold rolling. The model is based on a constitutive framework incorporating thermally activated dislocation slip, mechanical twinning and non-crystallographic shear banding. It also accounts for the dislocation density evolution and its dependence on initial grain size. By performing a series of quadricrystal simulations considering characteristic heterophase microstructures, the underlying micromechanics and texture of the composites are explored. Significant shear banding occurs in both phases, primarily determined by their initial orientations. For each phase, the activation of shear banding is also affected by the mechanical properties and orientations of the adjacent phase. For composites with an initial single layer thickness of 35 μm or 4 μm, the layer thickness reduction after rolling is non-uniform and the typical rolling textures for bulk pure metals develop in the respective phases. For the 75 nm initial single layer thickness composite, both phases are reduced uniformly in thickness and the initial orientations prevail. The predictions agree well with experimental observations in cold-rolled Cu-Nb thin films. The simulations reveal that for the composites with initial single layer thickness of micrometer scale, dislocation slip is the dominant deformation mechanism although shear banding increasingly carries the deformation at larger strains. For the samples with initial single layer thickness of a few tens of nanometers, shear banding and dislocation slip are the dominant mechanisms. This transition in deformation characteristics leads to different textures in micrometer- and nanometer-scaled multilayers.

Investigation of grain-scale microstructural variability in tantalum using crystal plasticity-finite element simulations

In this work, a crystal plasticity-finite element (CP-FE) model is used to investigate the effects of microstructural variability at a notch tip in tantalum single crystals and polycrystals. It is shown that at the macroscopic scale, the mechanical response of single crystals is sensitive to the crystallographic orientation while the response of polycrystals shows relatively small susceptibility to it. However, at the microscopic scale, the local stress and strain fields in the vicinity of the crack tip are completely determined by the local crystallographic orientation at the crack tip for both single and polycrystalline specimens with similar mechanical field distributions. Variability in the local metrics used (maximum von Mises stress and equivalent plastic strain at 3% deformation) for 100 different realizations of polycrystals fluctuates by up to a factor of 2–7 depending on the local crystallographic texture. Comparison with experimental data shows that the CP model captures variability in stress–strain response of polycrystals that can be attributed to the grain-scale microstructural variability. This work provides a convenient approach to investigate fluctuations in the mechanical behavior of polycrystalline materials induced by grain morphology and crystallographic orientations.