Crystal Plasticity Finite Element Analysis Research Articles

On the plastic driving force of grain boundary migration: A fully coupled phase field and crystal plasticity model

Dislocations stored in heavily deformed materials play an important role in driving microstructure evolution. Here, we developed a full coupling model that concurrently couples the phase field method with crystal plasticity finite element analysis to study grain boundary (GB) migration under a plastic driving force. In our model, we describe multiple active grains in GB regions with crystal plasticity theory and use a weighted sum of their properties (i.e., stress and elastic/plastic potentials, etc.) to evaluate the plastic driving force for GB migration. The model can qualitatively capture the absorption of dislocations by mobile GBs through re-initialization of slip system resistances of newly active grains. A finite element based preconditioned Jacobian-free Newton-Krylov approach is used to simultaneously solve all the nonlinear partial differential equations for the coupled physics models. Determining model parameters and validation of the model are accomplished by simulating copper bicrystals and comparing the results to available experiments. This model provides a useful tool for effectively simulating GB migration in metals undergoing large plastic deformation. All the developments have been implemented in the MOOSE/MARMOT simulation package.

Stabilized tetrahedral elements for crystal plasticity finite element analysis overcoming volumetric locking

Image-based CPFE modeling involves computer generation of virtual polycrystalline microstructures from experimental data, followed by discretization into finite element meshes. Discretization is commonly accomplished using three-dimensional four-node tetrahedral or TET4 elements, which conform to the complex geometries. It has been commonly observed that TET4 elements suffer from severe volumetric locking when simulating deformation of incompressible or nearly incompressible materials. This paper develops and examines three locking-free stabilized finite element formulations in the context of crystal plasticity finite element analysis. They include a node-based uniform strain (NUS) element, a locally integrated B-bar (LIB) based element and a F-bar patch (FP) based element. All three formulations are based on the partitioning of TET4 element meshes and integrating over patches to obtain favorable incompressibility constraint ratios without adding large degrees of freedom. The results show that NUS formulation introduces unstable spurious energy modes, while the LIB and FP elements stabilize the solutions and are preferred for reliable CPFE analysis. The FP element is found to be computationally efficient over the LIB element.

イメージベース結晶塑性有限要素解析における幾何モデルの粗視化の影響

イメージベース結晶塑性有限要素解析における幾何モデルの粗視化の影響

集合組織を持つTi合金多結晶材料の変形に関する結晶塑性有限要素解析

Plastic slip deformation in textured α phase Ti alloy polycrystal models is studied by a crystal plasticity finite element analysis. Models consist of 57 crystal grains and their crystal orientations are defined in accordance to existing experimental data. Crystal orientation of the texture is called TD-split type where the normal to the basal plane inclines about +/- 40 degree from ND toward TD. Critical resolved shear stress for prismatic slip systems is the lowest and that for basal systems is slightly higher than that for the prismatic ones. Results show that slip deformation is highly non-uniform at the deformation stage of macroscopic yielding point and two prismatic systems operate depending on the inclination of + or - 40 degree to TD. After some amount of deformation, activation of slip systems multiply in crystal grains.

<i>α</i>-Ti合金多結晶材料のモデル化および弾塑性変形に関する結晶塑性有限要素解析

<i>α</i>-Ti合金多結晶材料のモデル化および弾塑性変形に関する結晶塑性有限要素解析

Orientation dependence of the deformation kink band formation behavior in Zn single crystal

Variations in deformation kink band formation behavior with loading orientation were examined by the combination of experiment and computer simulation, using the Zn single crystal as a model material. Based on the results, the controlling factors for the formation behavior of deformation kink bands and its general features were discussed. Due to compression parallel to the basal plane, several deformation bands formed in the Zn single crystal. By the examination of the crystallographic nature of the deformation bands, they were found to exhibit three characteristic features: an ambiguous crystal rotation axis on the [0001] zone axis, an arbitrary rotation angle with a wide variation, and a variation in the crystal rotation angle within the deformation band boundary itself. In addition, an analysis protocol to classify the nature of the deformation bands via the observation on (0001) was newly proposed. As a result, the deformation bands formed in the Zn single crystal were confirmed to be predominantly deformation kink bands rather than deformation twining.Among the abovementioned three crystallographic features, we first experimentally confirmed by using the single crystal that the variations in the rotation axis in deformation kink bands exhibit a strong dependence on loading orientation. Using computer simulation based on the crystal plasticity finite element analysis, the origin of the variation in rotation axis in deformation kink bands was clarified to be due to the initiation of different types of basal dislocations that construct the deformation kink band boundaries, which depends on the loading orientation. In addition, the variations in types of the dislocations owing to the internal stress were found to cause the significant waviness of the deformation band boundaries on (0001) specimen surface.

Crystal plasticity finite element analysis for René88DT statistical volume element generation

This work focuses on the major cause of life limiting behavior in Ni-based superalloys for high pressure and temperature turbine disks applications in low cycle fatigue. Specific ideas of local microstructure features, such as the role of as large as (ALA) grains, in promoting slip localization in directly measured 3D microstructures were tested with finite element method (FEM) simulations with crystal plasticity. Synthetic microstructures with experimentally determined microstructurally small fatigue crack weakest link features of ALA grains comprise the test cases. A René88 damage tolerant (R88DT) dataset, from electron backscatter diffraction, was used to instantiate approximately 1.5 million elements and 200 grains from FEM sensitivity studies. Changing mesh resolution minimally impacted global damage response, but local convergence required the maximum resolution. The present results help to quantify the deleterious impact of ALA grains in Ni-based superalloys to extend service life.

Effect of realistic 3D microstructure in crystal plasticity finite element analysis of polycrystalline Ti-5Al-2.5Sn

The effect of constitutive parameters and microstructure on the kinematic and constitutive responses within grains in a crystal plasticity finite element (CPFE) simulation of a polycrystalline titanium alloy are compared with experimental results. The simulation of a Ti-5Al-2.5Sn sample deformed in uniaxial tension at room temperature used a phenomenological power-law based CPFE model, which includes four families of slip systems commonly observed in structural metals with a hexagonal lattice structure. The experimentally characterized microstructure patch was approximated by a quasi-3D columnar grain structure and by a more realistic 3D representation. The quasi-3D microstructure was generated by extending the EBSD characterized surface microstructure in the depth direction, while the 3D microstructure was built based on subsurface orientation information acquired using differential-aperture X-ray microscopy (DAXM). The effect of grain morphology and constitutive parameters on simulation results are compared in terms of stress–strain responses and lattice reorientation.

Effects of subgrain size and static recrystallization on the mechanical performance of polycrystalline material: A microstructure-based crystal plasticity finite element analysis

In this paper, the effects of subgrain size and static recrystallization on the mechanical performance of polycrystalline material were investigated using a microstructure-based crystal plasticity finite element (CPFE) model. Firstly, polycrystalline microstructures with different mean subgrain sizes were prepared using simple assumption based on experimental observations, and intermediate microstructures during static recrystallization (SRX) were simulated by a cellular automata model adopting curvature driven grain/subgrain growth mechanism. Then, CPFE method was applied to perform stress analysis of plane strain tension on these virtual microstructures. The results show that the subgrains inside pre-existing grains have an effect on the heterogeneity of the stress distributions. The average stress decreases with increasing the mean subgrain radius. As grain/subgrain grows during SRX, the average stress also decreases. It can be deduced that well-defined and finer subgrain structure may strengthen the polycrystalline material, while grain/subgrain growth during SRX process will degrade the strength.

OS0109-168 Ti-6Al-4V合金多結晶体のすべり変形と転位蓄積に関する結晶塑性有限要素解析

OS0109-168 Ti-6Al-4V合金多結晶体のすべり変形と転位蓄積に関する結晶塑性有限要素解析

Three-dimensional crystal plasticity finite element analysis of microstructure and texture evolution during channel die compression of IF steel

In the present study, three-dimensional crystal plasticity finite element method (CPFEM) is used to simulate microstructure and texture evolution during channel die compression of a body-centered cubic (BCC) polycrystalline material of interstitial free (IF) steel. Microstructural heterogeneity and anisotropy were taken into account by assigning a crystal orientation to each integration point of the element and determining the stiffness matrix of the individual crystal. A numerical technique for direct data mapping of Euler angles and critical resolved shear stress is also suggested. Based on the experimental observation by electron backscatter diffraction (EBSD) measurement of an as-received IF steel sheet, representative volume element (RVE) of the initial microstructure was generated by using the Voronoi tessellation scheme. The microstructure and texture evolution during channel die compression of IF steel is investigated by comparing results numerically predicted by the CPFEM with the microstructure experimentally measured by the EBSD. From the contour maps and distributions of the rotation and misorientation angles, it was revealed that the rotation of crystals is apparently influenced by both the individual orientation itself and the interaction with neighboring crystals. Furthermore, the orientations, which exhibit small rotation and misorientation angles, are the ones initially oriented along the α- and γ-fibers and hardly change despite the increase in the plastic deformation.

A peridynamic implementation of crystal plasticity

This paper presents the first application of peridynamics theory for crystal plasticity simulations. A state-based theory of peridynamics is used (Silling et al., 2007) where the forces in the bonds between particles are computed from stress tensors obtained from crystal plasticity. The stress tensor at a particle, in turn, is computed from strains calculated by tracking the motion of surrounding particles. We have developed a quasi-static implementation of the peridynamics theory. The code employs an implicit iterative solution procedure similar to a non-linear finite element implementation. Peridynamics results are compared with crystal plasticity finite element (CPFE) analysis for the problem of plane strain compression of a planar polycrystal. The stress, strain field distribution and the texture formation predicted by CPFE and peridynamics were found to compare well. One particular feature of peridynamics is its ability to model fine shear bands that occur naturally in deforming polycrystalline aggregates. Peridynamics simulations are used to study the origin and evolution of these shear bands as a function of strain and slip geometry.

The effects of regularity on the geometrical properties of Voronoi tessellations

This study comprehensively quantifies the effects of regularity on the geometrical properties of a random three-dimensional Voronoi tessellation (VT), where regularity was defined as the ratio of the minimum seed distance to the seed distance of the correlated body-centred cubic lattice. A scheme to generate Voronoi tessellations with controlled regularity is proposed, which was used to simulate 106 cells for a series of regularities. The results were used to derive probability distributions for the properties of the tessellation, including faces and edges per cell, vertex and dihedral cell angles, cell areas and volumes, etc. An understanding of the relation between a simple, measurable parameter characterizing the degree of regularity of a Voronoi tessellation and its geometrical properties is essential in generating virtual microstructures that are statistically representative of reality; the statistical results are also relevant to all other applications involving random Voronoi tessellations. Finally, an application is presented of the proposed Voronoi tessellation generation scheme applied to micromechanical modelling of grain structures with defined regularities for crystal plasticity finite element analysis.

Crystal Plasticity Finite Element Analysis Based on Crystal Orientation Mapping with Three-Dimensional X-Ray Diffraction Microscopy

In other study we examined the plastic behavior for polycrystalline iron by three-dimensional x-ray diffraction (3DXRD) experiment. In this study we analyze the behavior by crystal plasticity finite element (CPFE) analysis, to confirm the validity of application to the deformation analysis of engineering steels of a couple of constitutive models. In the CPFE analysis, the observed microstructure and its crystal orientation are modeled with finite elements to take the inter-granular and intra-granular interactions into consideration. The plastic deformation state of the finite element model was computed by means of CPFE analysis based on the {110}<111> slip system in body centered cubic (BCC) crystal. The experiment showed that the most of the grains rotated toward the preferred orientation <110> along the tensile axis and that intra-granular orientation spread and multi-directionally rotated as the tensile strain increased. These results are reproduced by the CPFE analysis, in which the influence of interaction between neighboring grains is taken into consideration.

OS1202 走査型3DXRD顕微鏡法及び結晶塑性有限要素解析による多結晶鉄の変形挙動の考察

OS1202 走査型3DXRD顕微鏡法及び結晶塑性有限要素解析による多結晶鉄の変形挙動の考察

アルミニウム合金板の二軸引張変形の均質化結晶塑性有限要素解析と実験検証

アルミニウム合金板の二軸引張変形の均質化結晶塑性有限要素解析と実験検証

OS0108 AZ91鋳造材における双晶頻度に及ぼす時効の影響

Effect of aging on activity of twinning in magnesium alloy AZ91 was investigated. The experimental results showed that stress-strain curves during reversed loadings were different between tension after compression and compression after compression. The difference in stress-strain behavior decreased with the increase in aging time. Crystal plasticity finite element analysis revealed that the difference of activities of twinning and detwinning resulted in the difference in stress-strain behavior during reversed loadings, which suggested that the decrease of difference in the stress-strain curves with the increase in aging time related to the decrease in the activity of twinning.

ジルコニウムの塑性変形挙動の結晶塑性有限要素解析

ジルコニウムの塑性変形挙動の結晶塑性有限要素解析

Three-dimensional crystal plasticity finite element simulation of nanoindentation on aluminium alloy 2024

Crystal plasticity finite element (CPFE) simulations of AA2024 under nanoindentation at six different depths are performed. The model parameters are calibrated through a representative volume element model fitting the stress–strain curves obtained from tensile tests performed at 0, 45 and 90° from the rolling direction. The simulated force–displacement curves and indentation moduli match the experimental data very well. The simulated results indicated that the local deformation in the indentation zone strongly depends on the grain properties. The significant difference in pile-up pattern due to the crystallographic orientation under the indenter is captured by the simulations. The simulation results for the stress and misorientation distributions reveal that low angle grain boundaries allow stress and misorientation continuity from grain to grain whereas high angle grain boundaries act as barriers, which causes stress concentrations at the grain boundaries. It appears that the proposed CPFE analysis approach can provide detailed three-dimensional microstructure information including misorientation map after deformation, which cannot be easily obtained from experiments.

Crystal Plasticity Finite Element Analysis of Texture Evolution during Rolling of fcc Polycrystalline Metal

Localized strain and crystallographic orientation distribution during rolling process have a significant effect on anisotropic flow behavior in sheet forming of aluminum alloy, resulting in local thinning. In this study, crystal plasticity finite element method (CPFEM), which incorporates a crystal plasticity constitutive law into the three-dimensional finite element method, was used to investigate strain localization and textural evolution during the flat rolling process of the face-centered-cubic material. A rate-dependent polycrystalline theory based on the Taylor model was fully implemented into an in-house program, CAMProll3D. The through-thickness texture evolution depending on the degree of draught was predicted by using the developed CPFEM program and compared well with the experimental data available in the literature. The orientation distributions not only in the thickness direction but also in the width direction of the flat rolled sheet were investigated depending on the amount of reduction during the multi-pass flat rolling in terms of pole figure, orientation distribution function and flow potential surface in the 3-plane. Finally, the effect of friction condition between the rolls and the material on rotation about the transverse direction was found to be important to determine the texture evolution at the surface of the rolled sheet. [doi:10.2320/matertrans.M2012346]