An integrated crystal plasticity-phase field model for spatially resolved twin nucleation, propagation, and growth in hexagonal materials (original) (raw)
Related papers
Acta Materialia, 2023
Twin, dislocation, and grain boundary interaction in hexagonal materials, such as Mg, Ti, and Zr, has critical influence on the materials' mechanical properties. The development of a microstructure-sensitive constitutive model for these deformation mechanisms is the key to the design of high-strength and ductile alloys. In this work, we have developed a mechanical formulation within the finite strain framework for modeling dislocation slip-and deformation twinning-induced plasticity. A dislocation density-based crystal plasticity model was employed to describe the dislocation activities, and the stress and strain distributions. The model was coupled with a multi-phase-field model to predict twin formation and twin-twin interactions. The coupled model was then employed to study twin, dislocation, and grain boundary interactions in Mg single-and polycrystals during monotonic and cyclic deformation. The results show that twin-twin interactions can enhance the strength by impeding twin propagation and growth. The role of dislocation accommodation on twin-twin interactions was twofold. Dislocation slip diminished twin-twin hardening by relieving the development of back-stresses, while it effectively relaxed the stress concentration near twin-twin intersections and thus may alleviate crack nucleation. The plastic anisotropy in each grain and the constraints imposed by the local boundary conditions resulted in stress variations among grains. This stress heterogeneity was responsible for the observed anomalous twinning behaviour. That is, low Schmid factor twins were activated to relax local stresses and accommodate the strain incompatibility, whereas the absence of high Schmid factor twins was associated with slip band-induced stress relaxation.
Explicit incorporation of deformation twins into crystal plasticity finite element models
Computer Methods in Applied Mechanics and Engineering, 2015
Deformation twinning is a subgrain mechanism that strongly influences the mechanical response and microstructural evolution of metals especially those with low symmetry crystal structure. In this work, we present an approach to modeling the morphological and crystallographic reorientation associated with the formation and thickening of a twin lamella within a crystal plasticity finite element (CPFE) framework. The CPFE model is modified for the first time to include the shear transformation strain associated with deformation twinning. Using this model, we study the stress-strain fields and relative activities of the active deformation modes before and after the formation of a twin and during thickening within the twin, and in the parent grain close to the twin and away from the twin boundaries. These calculations are carried out in cast uranium (U), which has an orthorhombic crystal structure and twins predominantly on the < > systems under ambient conditions. The results show that the resolved shear stresses on a given twin system on the twin-parent grain interface and in the parent are highly inhomogeneous. We use the calculated mechanical fields to determine whether the twin evolution occurs via thickening of the existing twin lamella or formation of a second twin lamella. The analysis suggests that the driving force for thickening the existing twin lamella is low and that formation of multiple twin lamellae is energetically more favorable. The overall modeling framework and insight into why twins in U tend to be thin are described and discussed in this paper.
Computational Materials Science, 2020
We perform molecular dynamics simulations to investigate the microstructural evolution and role of twinning on ω-phase transformation in single crystal Ti for loading perpendicular to the c-axis under uniaxial strain conditions. We find that both tension twinning and ω-phase evolve simultaneously and compete with each other. The number of activated tension twin variants not only affects the overall twin volume fraction but also the ω-phase volume fraction. For the case where four twin variants activate, the overall twin volume fraction is lowest and ω-phase volume fraction is highest in comparison to the case where only two twin variants activate. Significant amount of unconsumed parent HCP structure occurs for the case where four twin variants activate in comparison to the case where only two twin variants activate. This suggests that the number of activated twin variants and the spatial distribution of twins belonging to these variants play an important role on the amount of unconsumed parent HCP structure. The presence of high dislocation density for the case where four twin variants activate in comparison to the case where only two variants activate indicates that the number of activated twin variants also affects the overall dislocation density. The foregoing observations can be useful to develop a dynamic material strength model which can account for the coupled evolution of plasticity and phase transformation.
2019
One ambitious objective of Integrated Computational Materials Engineering (ICME) is to shorten the materials development cycle by using computational materials simulation techniques at different length scales. In this regard, the most important aspects are the prediction of the microstructural evolution during material processing and the understanding of the contributions of microstructural features to the mechanical response of the materials. One possible solution to such a challenge is to apply the Phase Field (PF) method because it can predict the microstructural evolution under the influence of different internal or external stimuli, including deformation. To accomplish this, it is necessary to take into account plasticity or, specifically, non-homogeneous plastic deformation, which is particularly important for investigating the size effects in materials emerging at the micron length scale. In this work, we present quasi-2D simulations of plastic deformation in a face centred c...
Incorporation of deformation twinning in crystal plasticity models
Journal of the Mechanics and Physics of Solids, 1998
A new constitutive framework, together with an efficient time-integration scheme, is presented for incorporating the crystallography of deformation twinning in polycrystal plasticity models. Previous approaches to this problem have required generation of new crystal orientations to reflect the orientations in the twinned regions or implementation of "volume fraction transfer" schemes, both of which require an update of the crystal orientations at the end of each time step in the simulation of the deformation process. In the present formulation, all calculations are performed in a relaxed configuration in which the lattice orientation of the twinned and the untwinned regions are pre-defined based on the initial lattice orientation of the crystal. The validity of the proposed constitutive framework and the time-integration procedures has been demonstrated through comparisons of predicted rolling textures in low stacking fault energy fee metals and in hcp metals with the corresponding predictions from the earlier approaches as well as through qualitative comparisons with the measurements reported previously. I('>
Modeling the effect of twinning and detwinning during strain-path changes of magnesium alloy AZ31
International Journal of Plasticity, 2009
Hexagonal materials deform plastically by activating diverse slip and twinning modes. The activation of such modes depends on their relative critical stresses, and the orientation of the crystals with respect to the loading direction. To be reliable, a constitutive description of these materials has to account for texture evolution associated with reorientations due to both dislocation slip and twinning, and for the effect of the twin boundaries as barriers to dislocation propagation. We extend a previously introduced twin model, which accounts explicitly for the composite character of the grain formed by a matrix with embedded twin lamellae, to describe the influence of twinning on the mechanical behavior of the material. The role of the twins as barriers to dislocations is explicitly incorporated into the hardening description of slip deformation via a directional Hall-Petch mechanism. We introduce here an improved hardening law for twinning, which discriminates for specific twin/dislocation interactions, and a detwinning mechanism. We apply this model to the interpretation of compression and tension experiments done in rolled magnesium alloy AZ31B at room temperature. Particularly challenging cases involve strain-path changes that force strong interactions between twinning, detwinning, and slip mechanisms.
In this work, the viscoplastic self-consistent based All Twin Variant (ATV) polycrystal modelling was employed to decipher the deformation behaviour of Mg-3Al-0.3Mn Magnesium alloy that develops f1012g1011-extension twins profoundly during ambient temperature compression. Twinning was considered by taking into account all the potential f1012g twin variants, and hence called here as the 'ATV' approach. The model treats each twin variant as a grain with increasing volume fraction transferred from the respective parent grain according to its pseudo-slip shear-rate. The slip and twin-induced strain hardening were simulated by adopting a classical phenomenological hardening model while assigning a higher hardening coefficient for the twins relative to the parent matrix. The viscoplastic self-consistent polycrystal homogenisation scheme combined with the ATV approach permitted to reproduce with high precision the experimentally measured strain hardening behaviour, crystallographic texture and twin volume fraction evolution. Beyond these average measures, the activities of twin variants in individual grains could be predicted in good agreement with Electron Back-Scattered Diffraction measurements. The ATV approach permits also to examine the matrix and twin phases separately in terms of textures and misorientation distributions.
International Journal of Plasticity, 2017
In this work, we employ the recently developed framework for the explicit modeling of discrete twin lamellae within a three-dimensional (3D) crystal plasticity finite element (CPFE) model to examine the effects of dislocation densities in the twin domain on twin thickening. Simulations are carried out for 1 012 〈101 1〉 extension twins in a magnesium AZ31 alloy. The model for the twin lamellae accounts for the crystallographic twin-matrix orientation relationship and characteristic twin shear transformation strain. The calculations for the mechanical fields as a result of twinning consider that one of three types of twin-dislocation density interactions have occurred. One case assumes that the expanding twin retains in its domain the same dislocation density as the parent. The second one considers that twin expansion has lowered the dislocation density as the twin thickens, and the last one, the Basinski effect, assumes that when twin sweeps the region, the dislocation density incorporated in the twin domain is amplified. In the modeling approach, the twin is thickened according to a criterion that maintains the stress state in the vicinity of the grain at a pre-defined characteristic twin resistance. The calculations show that most of the averaged properties, such as the rate of dislocation storage in the entire twin grain, the twin growth rate, the stress field in the twinned grain and neighboring grains, and the slip activity in the parent matrix are not significantly altered by dislocation storage in the twin. The results indicate that, however, the slip activity in the twinned domain is affected. In particular, in the increased dislocation density case, the rate of dislocation density in the twin domain increases at low strains when the twin is first growing from 2% to 5% volume fraction. This initial boost in the dislocation density storage rate causes the newly expanded dislocation twin to contain more stored dislocations than the other cases for all strain levels. Another interesting difference concerns the preference for one or two twins for the same total twin volume fraction; for the increased dislocation twin or twin that retains the dislocation density as it grows, formation of two twins is favored. For a twin that removes dislocation density, only one twin is preferred. The results imply that in the case with reduced dislocation density leads to lower stored dislocations and dislocation storage rates, and lower pyramidal slip activity.
International Journal of Plasticity, 2010
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 timesteps 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.