Three-dimensional Crystal Plasticity Finite Element Research Articles

Anisotropic formability and deformation mechanism of near-α titanium alloy sheet under continuous nonlinear strain paths at high temperature

In the present study, the anisotropic formability and underlying deformation mechanism of near-α TA32 titanium alloy sheet under continuous nonlinear strain paths (CNSPs) at high temperature were investigated in depth. To achieve this goal, a new experimental method combining hot gas bulging with step-combined dies was proposed, and the hot CNSPs of metal sheets can be flexibly and conveniently realized by changing the number and shape of step-combined dies. Based on this method, the anisotropic deformation behavior and forming limits of TA32 sheet under fifteen CNSPs were tested at 800 ℃ with a strain rate of 0.001 s−1. Then, two advanced constitutive models with different scales were embedded into the classical Marciniak-Kuczyński (M-K) theory to predict the forming limits of TA32 sheet under different strain paths: the macro-scale viscoplastic model coupled with Hill48 yield criterion and non-associated flow rule (NAFR) as well as the meso-scale three-dimensional crystal plasticity finite element (CPFE) model coupled with cellular automata (CA). The results demonstrate that the CPFE-CA-MK coupled model exhibits higher accuracy in predicting the forming limits of TA32 sheet under linear and continuous nonlinear strain paths. Especially for the tension-tension strain paths, the CPFE-CA-MK coupled model improves accuracy by at least 3.1 % compared to macro-scale models. Due to the material anisotropy, the initial inclination angle of the groove in the CPFE-CA-MK model is closely related to the strain path and significantly affects the prediction accuracy. Based on the CPFE simulation, the effects of anisotropy and strain path change on the dislocation slip mode of different texture components was analyzed in depth, which provides a theoretical guidance for the optimization of hot forming process of TA32 titanium alloy complex components.

Formation of plate-like high-strain region in polycrystalline α-titanium and its relation to high-strain bands on surface

The investigation of heterogeneous deformation mechanisms in materials is important for understanding fracture mechanisms. In this study, uniaxial tensile deformation of polycrystalline α-titanium was numerically reproduced by three-dimensional crystal plasticity finite element analysis, and the following were revealed for the first time: (i) plate-like high-strain regions form inside the specimen, which are typically observed as band-like high-strain regions (high-strain bands: HSBs) on the surface of and cross-sections in α-titanium specimen, and (ii) the formation of HSBs also affects the work-hardening rate near the yielding point. The reasons for the difference in the formation mechanism of HSBs between the surface and inside were also discussed. The results obtained showed that active slip systems that contribute to the formation of HSBs may differ between the surface and inside of specimen, and strain in HSBs on the specimen surface is higher than that inside. The distributions of HSBs at the surface of and inside the specimen are determined by distributions of resolved shear stress. These results are important for understanding the differences in the fracture mechanisms between the surface and interior of materials.

Meso-modelling study of the mechanical response and texture evolution of magnesium alloy during hot compression

The mechanical response and texture evolution of magnesium alloy during hot deformation are closely related to the heterogeneous meso-deformation. The improved Voce hardening law was developed and introduced into the crystal plasticity (CP) theory, and a reconstruction method of textured representative polycrystal was proposed. Three-dimensional crystal plasticity finite element model (3D-CPFEM) was established to meso-simulate the hot compression deformation of ZK61 Mg alloy. The influence of the temperature and strain rate on mechanical response was investigated, and the corresponding texture evolution and the texture transformation mechanism was revealed through meso-simulation. The results show that the 3D-CPFEM with the improved Voce hardening law and the initial texture characteristic can well predict the mechanical response and texture evolution under different temperatures and strain rates during hot compression of ZK61 Mg alloy. The basal plane texture of the ZK61 tubular blank is transformed into the basal fiber texture after hot compression, where the basal plane of grains is deflected gradually from the radial-axial plane to the radial-tangential plane. The texture transformation is attributed to two reasons, i.e., the orientation deflection of the grains with larger basal slip systems Schmid factor (SF) and the orientation retention of the grains whose c-axis tends to be parallel to the axial direction (AD) of the tubular blank. The change of the grain orientation corresponding to the basal plane texture component of the tubular blank has little contribution to the formed basal fiber texture.

On the Influence of Grain Boundary Misorientation on the Severe Plastic Deformation of Aluminum Bicrystals: A Three-Dimensional Crystal Plasticity Finite Element Method Study

A three-dimensional crystal plasticity finite element method model is developed to investigate the influence of the grain boundary (GB) misorientation on the equal-channel angular pressing deformation of aluminum bicrystals. Aluminum bicrystals with symmetric 〈112〉 tilt boundaries and misorientations of 9 deg (low angle), 15 deg (transitional), and 30 deg (high angle) have been designed to study the influence of GB misorientations on the deformed areas near GBs. The numerical results indicate that a high-angle grain boundary acts as a barrier in terms of Mises stress distribution, plastic slip, and lattice rotation, while the aluminum bicrystal with low-angle grain boundary still behaves similarly to a single crystal. An intermediate configuration is found for the aluminum bicrystal with transitional grain boundary. It is also found that the geometry of the GB after deformation depends on the initial orientation of the grain at the lower part of the billet.

Explicit modeling of double twinning in AZ31 using crystal plasticity finite elements for predicting the mechanical fields for twin variant selection and fracture analyses

A number of studies have found that the formation of double twins in low symmetry metals can lead to the onset of strain localizations, leading further to void nucleation and ultimately fracture. This work extends a recently developed three-dimensional crystal plasticity finite element framework [1] to explicitly model kinematics and kinetics of nucleation/formation, propagation, and thickening/growth of a discrete double twin lamella ({101¯1}−{101¯2}) in a magnesium alloy AZ31. With this approach, morphological and crystallographic reorientations as well as the shear transformation strains associated with strain accommodation by the double twinning sequence are modeled during simple compression and tension. The simulations predict that the distribution of local stress-strain fields during formation and growth of primary contraction twin creates the driving force for the formation of a secondary extension twin variant, which is consistent with experimental observations in both compression and tension. In particular, the contraction twin variant (01¯11)[01¯12¯] is predicted to form an internal extension twin variant (011¯2)[01¯11]. Furthermore, the prediction of the underlining crystallographic slip deformation mechanism reveals a substantial activity of basal slip within the contraction portion of the double twin, causing strain localization in its vicinity. Finally, the simulations reveal a gradient in the traction force field across twin-parent interface, suggesting that contraction twin-parent boundaries are weak links in the microstructure where voids can nucleate.

Three-dimensional quantification of texture heterogeneity in single-crystal aluminium subjected to equal channel angular pressing

A three-dimensional crystal plasticity finite element method (3D CPFEM) modelling of a real equal channel angular pressing (ECAP) process for investigating the mechanical properties and texture evolutions of single-crystal aluminium has been developed for the first time. The challenge of modelling such a severe plastic deformation via 3D CPFEM is how to accurately predict the deformation mechanism under the complicated contact conditions between a billet and a die. The validation by comparison with experimental observations demonstrates that the developed 3D CPFEM ECAP model is able to precisely capture the deformation characteristics at the microscale. Furthermore, this research clarified the previously remaining disputes such as the microstructural formation mechanism in the deformed area and the deformation nature in the plastic deformation zone. It is also the first time to extensively discuss the orientation-dependent deformation feature of the ECAP-processed billets, including morphology, lattice rotation angle and grain refinement.

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.

A study on the texture evolution mechanism of nickel single crystal deformed by high pressure torsion

High pressure torsion (HPT) is one of the most promising severe plastic deformation (SPD) techniques to produce ultrafine-grained (UFG) or nano-grained (NG) materials via introducing very large plastic strain. This study aims to understand the texture evolution mechanism during HPT by examining the nickel single crystal. The predicted textures after different HPT rotation angles based on a three-dimensional crystal plasticity finite element method (CPFEM) model agree well with the experimental measurements. Both the modelling and experiment show that the crystallographic orientation rotates gradually towards different ideal torsion texture components during HPT deformation, and three steady-state stages and two transition stages can be divided according to the texture evolution history. The crystal rotation during HPT process has been partitioned into three components around the radial direction, tangential direction, and axial direction, respectively. The texture evolution history and mechanism have been examined and discussed in details.

Orientation dependent deformation by slip and twinning in magnesium during single crystal indentation

We present the orientation dependent indentation response of pure magnesium during single grain indentation. A conical indenter and maximum loads between 50mN and 900mN were employed. Indent topographies were acquired by confocal microscopy. The indents were also characterized by electron backscatter orientation microscopy for their microstructures. Pronounced activation of specific twinning systems was observed around the impressions. The resulting data were compiled into the inverse pole figure presentation of indent microstructures and topographies after Zambaldi and Raabe, Acta Mater. (2010). Three-dimensional crystal plasticity finite element simulation of the indentation deformation supports the interpretation of the orientation dependent slip and twinning patterns around the indents. The match between the activation of observed and simulated twinning variants is discussed with respect to the conditions for nucleation and growth of extension twins. Furthermore, the compatibility of the twinning strains with the imposed deformation is discussed based on the expanding cavity model of indentation. The orientation dependent response of magnesium during indentation is compared to the literature data for indentation of alpha-titanium and beryllium. Recommendations are given on how to exploit the characteristic nature of the observed indentation patterns to rapidly assess the relative activity of deformation mechanisms and their critical shear stresses during alloy development.

Three-Dimensional Crystal Plasticity Finite Element Simulation of Hot Compressive Deformation Behaviors of 7075 Al Alloy

Three-dimensional crystal plasticity finite element (CPFE) method is used to investigate the hot compressive deformation behaviors of 7075 aluminum alloy. Based on the grain morphology and crystallographic texture of 7075 aluminum alloy, the microstructure-based representative volume element (RVE) model was established by the pole figure inversion approach. In order to study the macroscopic stress-strain response and microstructural evolution, the CPFE simulations are performed on the established microstructure-based RVE model. It is found that the simulated stress-strain curves and deformation texture well agree with the measured results of 7075 aluminum alloy. With the increasing deformation degree, the remained initial weak Goss texture component tends to be strong and stable, which may result in the steady flow stress. The grain orientation and grain misorientation have significant effects on the deformation heterogeneity during hot compressive deformation. In the rolling-normal plane, the continuity of strain and misorientation can maintain across the low-angle grain boundaries, while the discontinuity of strain and misorientation is observed at the high-angle grain boundaries. The simulated results demonstrate that the developed CPFE model can well describe the hot compressive deformation behaviors of 7075 aluminum alloy under elevated temperatures.

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.

Modeling Twin Clustering and Strain Localization in Hexagonal Close-Packed Metals

It has been suggested that microtextures related to deformation twinning can affect the stretch formability of hexagonal close-packed (hcp) metals. We study the evolution of strain localization and the formation of twin clusters in hcp polycrystals due to softening induced by twinning reorientation of the crystal lattice. We performed three-dimensional crystal plasticity finite element simulations of uniaxial and biaxial deformation using basal starting textures of various strengths. Weaker textures resulted in relatively homogeneous deformation, strong textured systems, however, showed significant shear band formation in biaxial tension. In this case, highly strained regions coincided very well with dense clusters of twins. Due to the scarcity of available slip systems, such shear localization due to twin clustering may lead to eventual crack initiation and failure. The spatial correlation of twins was analyzed and was found to be significantly affected by texture. The decay of the correlation function was well approximated by a power law, a characteristic of a wide range of phenomena associated with self-organized criticality.

Finite Element Simulation of the Hot Deformation Behavior of AA7075 Using a Coupled Thermo-Mechanical Crystal Plasticity Constitutive Model

Three-dimensional crystal plasticity finite element (CPFE) simulations are performed to study the coupled thermo-mechanical response of aluminium alloy 7075 under hot compression loadings. To improve the computational efficiency, a grain-scale representative volume element model with periodic boundary conditions is adopted to represent the macroscopic response. The initial grains are created using Voronoi tessellation method, and the grain orientations are obtained from the electron back-scatter diffraction test. The simulated results indicate that the effects of the grain properties on the local deformation and temperature distribution of the alloy are significant during the hot deformation. The temperature continuity can be found across some grain boundaries while there is a temperature gap at other grain boundaries. The proposed coupled thermo-mechanical CPFE model is able to provide detailed microstructure evolution and temperature distribution in the studied alloy during the hot deformation, which cannot be easily obtained by experiments.

Indentation in F.C.C. Single Crystals

A three-dimensional crystal-plasticity finite element model of nano-indentation is developed in this paper to analyze deformation of a face-centred cubic (f.c.c.) high-purity single crystal of copper. This model was implemented as a user-defined subroutine in the commercial finite element software ABAQUS/Standard and used to study cases with different crystallographic orientations of the single crystal. The effects of various factors – crystallographic orientation of the indented material, an indenter angle and contact conditions between the indenter and workpiece material – on the load-displacement characteristics are studied. The obtained results show an anisotropic nature of surface topography around the obtained indents.

The effects of load condition on void coalescence in FCC single crystals

To investigate the effects of load condition on void coalescence in FCC crystals, void coalescence under constant strain control was studied by using three-dimensional crystal plasticity finite element method, which was implemented with rate dependent crystal plasticity theory as user material subroutine. By comparison the width of inter-void ligament in single crystals, significant effects of load condition on void coalescence were revealed: (1) Crystallographic orientation plays a role in void coalescence, and the role is different under various load conditions. (2) The deformation is localized around voids under triaxial applied strain load condition, and the slip systems in soft orientation are easy to be activated, so voids in soft orientation grains tend to coalesce much easier than that in hard orientation, and the void growth direction has only a minor role in influencing the coalescence effect for different crystallographic orientations. (3) Under low biaxial applied strain load condition, the deformation localization is not serious, and the global deformation of soft orientation is homogeneous, so soft orientation shows less coalescence effect in general.

FEM simulation of void coalescence in FCC crystals

To investigate the coalescence behaviors of voids in FCC crystals, three bicrystal models were used to study the coalescence of voids in single crystals, voids at grain boundary and voids in two grains by using three-dimensional crystal plasticity finite element method, which was implemented with rate dependent crystal plasticity theory as user material subroutine. By comparison the width of inter-void ligament in bicrystals, significant effects of orientation factor and high-angle grain boundary on void coalescence were revealed: (1) Voids in soft orientation grains tend to coalesce much easier than that in hard orientation under the strain controlled boundary condition. (2) For void coalescence at grain boundary, with the orientation factor’s difference between the two grains increasing, larger deformation mismatch is induced between grains, and the void prefers to grow along grain boundary. (3) Large orientation factor’s difference accelerate void coalescence at grain boundary, but decelerate void coalescence between grains.

Crystal plasticity modelling and experiments for deriving microstructure-property relationships in γ-TiAl based alloys

Single-crystals of γ-TiAl cannot be grown for the compositions present inside the two-phase γ/α2-microstructures that show good mechanical properties. Therefore the single crystal constitutive behaviour of γ-TiAl was studied by nanoindentation experiments in single phase regions of these microstructures. The experiments were extensively characterized by a combined experimental approach to clarify the orientation dependent mechanical response during nanoindentation. They further were analyzed by a three-dimensional crystal plasticity finite element model that incorporated the deformation behaviour of γ-TiAl. The spatially resolved activation of competing deformation mechanisms during indentation was used to assess their relative strengths. On the length-scale of multi-grain aggregates two kinds of microstructures were investigated. The lamellar microstructure was analyzed in terms of kinematic constraints perpendicular to densely spaced lamellar boundaries which lead to pronounced plastic anisotropy. Secondly, the mechanical behaviour of massively transformed microstructures was modelled by assuming a lower degree of kinematic constraints. This resulted in less plastic anisotropy on a single grain scale and lower compatibility stresses in a 64-grain aggregate. On the macroscopic length scale, the results could possibly explain the pre-yielding of lamellar microstructures.

Plastic anisotropy of γ-TiAl revealed by axisymmetric indentation

Single crystals of γ-TiAl cannot be grown in the near-stoichiometric compositions that are present inside two-phase γ / α 2 -microstructures with attractive mechanical properties. Therefore, the single-crystal constitutive behavior of γ-TiAl was studied by nanoindentation experiments in single-phase regions of these γ / α 2 -microstructures. The experiments were characterized by orientation microscopy and atomic force microscopy to quantify the orientation-dependent mechanical response during nanoindentation. Further, they were analyzed by a three-dimensional crystal plasticity finite element model that incorporated the deformation behavior of γ-TiAl. The spatially resolved activation of competing deformation mechanisms during indentation was used to assess their relative strengths. A convention was defined to unambiguously relate any indentation axis to a crystallographic orientation. Experiments and simulations were combined to study the orientation-dependent surface pile-up. The characteristic pile-up topographies were simulated throughout the unit triangle of γ-TiAl and represented graphically in the newly introduced inverse pole figure of pile-up patterns. Through this approach, easy activation of ordinary dislocation glide in stoichiometric γ-TiAl was confirmed independently from dislocation observation by transmission electron microscopy.

Effect of Grain Boundary Characteristics on Lattice Orientations

Grain boundary characteristics are defined by five parameter, grain boundary plane normal and misorientation angle/axis between two adjacent grains. The influence of the grain boundary character distribution on lattice evolution during deformation was investigated using three-dimensional crystal plasticity finite element method (CPFEM). Various combinations of grain boundaries were modeled systematically. In analyzing the numerical microstructural characterization obtained by the simulation, orientation average scheme and correlation parameters between misorientation and its special distribution are used. Inter- and intra-grain structures were investigated using the spatial distribution of lattice orientation. Main emphasis was placed on misorientation distributions around grain boundaries, where grain interaction mainly occurred.

A combined experimental and computational study of deformation in grains of biomedical grade 316LVM stainless steel

In this work three-dimensional crystal plasticity finite element models are used to simulate the tensile deformation of a thin 316LVM stainless steel specimen. Such models are of interest for predicting the mechanical response of cardiovascular stents, typically made from thin struts of this material. Detailed experimental analysis of the mechanical response of the specimen during deformation is performed using scanning electron microscopy, digital photogrammetry and orientation imaging microscopy to examine microscale strain distribution, plastic slip and grain reorientation. At the macroscale, the models are found to give good predictions of the stress–strain response of the specimen, and at the microscale the models are found to give good predictions of the strain distribution and the active slip systems in the different grains. The models are less successful in predicting grain reorientations. This, however, is shown to be quite sensitive to the choice of latent hardening ratio.