Comparison of mechanical behaviour of thin film simulated by discrete dislocation dynamics and continuum crystal plasticity

3D finite element simulations of 9-grain multicrystalline aggregates are performed within the framework of the classical continuum crystal plasticity and discrete dislocation dynamics. The results are processed in a statistical way by ensemble averaging. The comparison is made at three levels: macroscopic stress–strain curves, average stress values per grain, local values of stress and plastic strain. The comparison shows that some similarities are observed in the stress and strain distributions in both simulations approaches. But there are also large discrepancies caused by the discrete nature of plasticity in DDD. The DDD simulations provide higher stress levels in the aggregate due to the small number of dislocation sources and to the stress field induced by individual dislocations.

Prediction of FLD of sheet metals based on crystal plasticity model

 In some advanced sheet metal forming processes such as the incremental forming process, a local fracture strain after necking is very important. In order to accurately predict necking and fracture phenomena, a crystal plasticity model is introduced in the finite element analysis of tensile tests. A tensile specimen is modeled by many grains that have their own crystalline orientation. And each of the grains is discretized by many elements. Using this analysis, necking behavior of a tensile specimen can be predicted without any initial imperfections. A damage model is also implemented to predict sudden drops of load carrying capacity after necking and to reflect the void nucleation and growth of the severely deformed region. From an analysis of the tensile test, the necking behavior is well predicted. Finally, analyses are carried out for various strain paths, and FLDs up to necking and fracture are predicted.

Texture, twinning and uniform elongation of wrought magnesium

A small number of crystal plasticity simulations and tensile tests are carried out with the aim of demonstrating that control of twinning can improve the uniform elongation of magnesium based alloys, It is suggested that this can be accomplished through texture manipulation because texture influences both the fraction of grains that undergo twinning and the strain required for the twinning reaction to go to completion.

Application of radial return mapping algorithm for finite strain elastoplasticity in a hybrid finite element and particle-in-cell model

The radial return mapping algorithm within the computational context of a hybrid Finite Element and Particle-In-Cell (FE/PIC) method is constructed to allow a fluid flow FE/PIC code to be applied solid mechanic problems with large displacements and large deformations. The FE/PIC method retains the robustness of an Eulerian mesh and enables tracking of material deformation by a set of Lagrangian particles or material points. In the FE/PIC approach the particle velocities are interpolated from nodal velocities and then the particle position is updated using a suitable integration scheme, such as the 4th order Runge-Kutta scheme[1]. The strain increments are obtained from gradients of the nodal velocities at the material point positions, which are then used to evaluate the stress increment and update history variables. To obtain the stress increment from the strain increment, the nonlinear constitutive equations are solved in an incremental iterative integration scheme based on a radial return mapping algorithm[2]. A plane stress extension of a rectangular shape J2 elastoplastic material with isotropic, kinematic and combined hardening is performed as an example and for validation of the enhanced FE/PIC method. It is shown that the method is suitable for analysis of problems in crystal plasticity and metal forming. The method is specifically suitable for simulation of neighbouring microstructural phases with different constitutive equations in a multiscale material modelling framework.

Characteristics of the contraction twins formed close to the fracture surface in Mg-3A1-1Zn alloy deformed in tension

Characteristics of the “contraction” twins, formed close to the fracture surface in Mg–3Al–1Zn alloy deformed in tension approximately perpendicular to the grain c-axes, are investigated using transmission electron microscopy. The grain c-axis contractions were largely accommodated by {1011}-{1012} source double-twins in a variant characterized by 38° ⟨1210⟩ source twin/matrix misorientation in conjunction with dislocation slip. A possible interpretation of the observed preference for this variant formation is given and some crystal plasticity modelling is performed to elucidate the matter.

Identification and rationalization of secondary twin variants in a magnesium alloy

The present work combines electron backscatter diffraction, transmission electron microscopy and Schmid analysis to investigate secondary twinning in the magnesium alloy Mg-3AI-1Zn. Inspection of the misorientations between the parent matrix and {1011} - {1012} doubly twinned volumes reveals that there are four possible variants. One of these variants characterized by 38°< 1210 > misorientation with the matrix is favoured much more than the others. This variant involves activation of the secondary twinning systems that are quite inconsistent with the Schmid-type behaviour. For the secondary twin to grow significantly it must take on a shape enforced by the primary twin, however, this is not optimal for strain compatibility. It is argued that the 38° < 1210 > variant occurs most frequently because it provides the closest match between the primary and secondaty twinning planes, thus minimizing the compatibility strain. This conjecture is confirmed by the simulations of twin activity m ellipsoidal grains performed using the visco-plastic self-consistent crystal plasticity model.

Finite element simulations of the cyclic elastoplastic behaviour of copper thin films

A large-scale computational and statistical strategy is presented to investigate the development of plastic strain heterogeneities and plasticity induced roughness at the free surface in multicrystalline films subjected to cyclic loading conditions, based on continuum crystal plasticity theory. The distribution of plastic strain in the grains and its evolution during cyclic straining are computed using the finite element method in films with different ratios of in-plane grain size and thickness, and as a function of grain orientation (grains with a {1 1 1} or a {0 0 1} plane parallel to the free surface and random orientations). Computations are made for 10 different realizations of aggregates containing 50 grains and one large aggregate with 225 grains. It is shown that overall cyclic hardening is accompanied by a significant increase in strain dispersion. The case of free-standing films is also addressed for comparison. The overall surface roughness is shown to saturate within 10 to 15 cycles. Plasticity induced roughness is due to the higher deformation of {0 0 1} and random grains and due to the sinking or rising at some grain boundaries.

Modelling the combined effect of grain size and grain shape on plastic anisotropy of metals

Within each columnar grain of a metallic film, the resistance to dislocation glide varies in function of the orientation of the slip plane with regard to the grain long axis. Plastic slip is impeded across grain boundaries and this contributes to the anisotropy of the overall mechanical response. A simplified (Taylor-type) crystal plasticity model is proposed that accounts for such effect of grain shape on the slip system selection. Assuming that dislocation density gradients are normal to the grain boundaries, backstresses developed at the onset of plasticity are estimated based on two definitions of the effective grain boundary spacing ‘‘seen’’ by individual slip systems. The first one reduces to the mean area-to-perimeter ratio of cross-sections of the grain cut parallel to the slip plane. Closed-form expressions of the average backstresses developed inside grains with spheroidal shapes are introduced in the crystal hardening law. The model reproduces the very high plastic anisotropy of electro-deposited pure iron with a strong c-fiber and a refined columnar grain structure [Yoshinaga, N., Sugiura, N., Hiwatashi, S., Ushioda, K., Kada, O., 2008. Deep drawability of electro-deposited pure iron having an extremely sharp h111i//ND texture. ISIJ Int. 48, 667–670]. It also provides valid estimates of the texture development and the influence of grain size on the yield strength.

Texture selection mechanisms in uniaxially extruded magnesium alloys

Extrusion textures in magnesium alloys are of high interest due to their influence on yield asymmetry. This data supports work describing three mechanisms of texture selection that may play a role during extrusion. These mechanisms involve localized differences in deformation at the grain level, the change in local environment experienced by grain boundary bulges and shear banding. The work employs visco-plastic crystal plasticity and electron backscattering diffraction.