Modeling of polycrystals with gradient crystal plasticity: A comparison of strategies

This paper treats the computational modeling of size dependence in microstructure models of metals. Different gradient crystal plasticity strategies are analyzed and compared. For the numerical implementation, a dual-mixed finite element formulation which is suitable for parallelization is suggested. The paper ends with a representative numerical example for polycrystals.     

Plastic shear deformation of a thin strain-hardening disc: variational principles

An analytical solution is derived for the problem of shearing of a thin disc of incompressible rigid, plastic strain-hardening material. The solution is obtained by a methodology introduced by the author in previous publications, relying fundamentally on continuity of the rotation-rate vector field. A variational theorem is derived which shows that the velocity vector field is unique if the boundary values are properly prescribed. The derived solution is compared to experiments, with which it shows good agreement.     

Crystal plasticity-based constitutive modelling of irradiated bcc structures

A constitutive crystal plasticity model is proposed and developed for the inelastic deformation of irradiated bcc ferritic/martensitic steels. Defects found in these irradiated materials are used as substructure variables in the model. Insights from lower length- and time-scale simulations are used to frame the kinematic and substructure evolution relations of the governing deformation mechanisms. Models for evolution of mobile and immobile dislocations, as well as interstitial loops (formed due to irradiation), are developed. A rate theory-based approach is used to model the evolution of point defects generated during irradiation. The model is used to simulate the quasi-static tensile and creep response of a martensitic steel over a range of loading histories.     

Crystal plasticity modeling of irradiation growth in Zircaloy-2

Abstract

A physically based reaction-diffusion model is implemented in the visco-plastic self-consistent (VPSC) crystal plasticity framework to simulate irradiation growth in hcp Zr and its alloys. The reaction-diffusion model accounts for the defects produced by the cascade of displaced atoms, their diffusion to lattice sinks and the contribution to crystallographic strain at the level of single crystals. The VPSC framework accounts for intergranular interactions and irradiation creep, and calculates the strain in the polycrystalline ensemble. A novel scheme is proposed to model the simultaneous evolution of both, number density and radius, of irradiation-induced dislocation loops directly from experimental data of dislocation density evolution during irradiation. This framework is used to predict the irradiation growth behaviour of cold-worked Zircaloy-2 and trends compared to available experimental data. The role of internal stresses in inducing irradiation creep is discussed. Effects of grain size, texture and external stress on the coupled irradiation growth and creep behaviour are also studied and compared with available experimental data.     

Dislocation-based plasticity model and micro-beam Laue diffraction analysis of polycrystalline Ni foil: A forward prediction

A physically-based, rate and length-scale dependent strain gradient crystal plasticity framework was employed to simulate the polycrystalline plastic deformation at the microscopic level in a large-grained, commercially pure Ni sample. The latter was characterised in terms of the grain morphology and orientation (in the bulk) by micro-beam Laue diffraction experiments carried out on beamline B16 at Diamond Light Source. The corresponding finite element model was developed using a grain-based mesh with the specific grain orientation assignment appropriate for the sample considered. Sample stretching to 2% plastic strain was simulated, and a post-processor was developed to extract the information about the local lattice misorientation (curvature), enabling forward-prediction of the Laue diffraction patterns. The ‘streaking’ phenomenon of the Laue spots (anisotropic broadening of two-dimensional (2D) diffraction peaks observed on the 2D detector) was correctly captured by the simulation, as constructed by direct superposition of reflections from different integration points within the diffraction gauge volume. Good agreement was found between the images collected from experiments and simulation patterns at various positions in the sample.     

Pressure-enforced plasticity in MAX phases: from single grain to polycrystal investigation

Ti₄AlN₃, Ti₃AlC₂ and Ti₃Al_0.8Sn_0.2C₂ MAX phases were plastically deformed at room temperature (RT) under gaseous confining pressure. Microstructures of as-grown and deformed samples are carefully analysed using scanning electron microscopy (SEM), atomic force microscopy (AFM) and transmission electron microscopy (TEM). It is demonstrated that high level of plastic deformation can be reached under confining gas pressure; the later suppresses the brittle failure at RT to the profit of plasticity. Multiscale characterization techniques are shown to provide a unique insight into all the scales of the plastic deformation; in particular, the effect of the mesoscale. Indeed, grain shape and orientation relative to the compression axis are shown to play a key role in the deformation process, intergranular stresses leading to a complex stress field in the polycrystalline samples. The TEM results show that dislocation activity highly depends on the grain orientation. The observation of dislocation entanglements unambiguously demonstrates that dislocations may be organized in such a configuration so that their glide in the basal plane can be hindered when deep plastic regime is reached.     

The effect of the location of stage-I fatigue crack across the persistent slip band on its growth rate – A 3D dislocation dynamics study

Abstract

A 3D dislocation dynamics study to ascertain the probable path of stage-I fatigue crack propagation across the persistent slip band (PSB) in austenitic stainless steel is presented. Cyclic plasticity and the resulting crack tip slip displacement (CTSD) are evaluated for cracks of varying length introduced at PSB-center and at two PSB-matrix interfaces. CTSD attains high value at either of the two interfaces irrespective of the proximity of crack front to the grain boundary. Further, a difference in microcrack propagation rate is also observed among the two interfaces. The present results assert microcrack propagation preferrentially along one of the two PSB-matrix interfaces rather than at the PSB-center. A pre-existing PSB dislocation structure localises the cyclic slip for crack lengths up to approximately half of the grain depth for an applied strain range of 2 × 10^?4.     

Berkovich nanoindentation study of monocrystalline tungsten: a crystal plasticity study of surface pile-up deformation

Abstract

In this paper, it was investigated whether Berkovich indentation test with a triangular-based pyramidal imprint would exhibit the same surface pile-up deformation behaviour as in Vickers or spherical indentation tests. The characteristic correlation between the pile-up patterns of monocrystalline tungsten and the geometry of slip systems was examined both experimentally and computationally. Surface pile-up patterns for three different crystallographic orientations of specimens with corresponding rotational crystal symmetry were characterised. In addition, the effect of the varying azimuthal orientation of the indenter on the pile-up patterns was also discussed. Predictions from finite element simulation based on the crystal plasticity theory are also presented and compared with the measured results. It was found that the surface pile-up patterns of Berkovich indentation did not necessarily reflect the rotational crystal symmetry of tungsten single crystal specimens. The pile-up patterns were affected by the variation of the indenter’s azimuthal orientation. The height of the pile-up hillocks was often highly non-uniform even on the same surface plane indicating strong influence of slip geometry leading to the plastic anisotropy.     

Crack growth on the basal plane in single crystal zinc: experiments and computations

Crack propagation on the basal planes in zinc was examined by means of in situ fracture testing of pre-cracked single crystals, with specific attention paid to the fracture mechanism. During quasistatic loading, crack propagation occurred in short bursts of dynamic crack extension followed by periods of arrests, the latter accompanied by plastic deformation and blunting of the crack-tip. In situ observations confirmed nucleation and propagation of microcracks on parallel basal planes and plastic deformation and failure of the linking ligaments. Pre-existing twins in the crack path serve as potent crack arrestors. The crystallographic orientation of the crack growth direction on the basal plane was found to influence both the fracture load as well as the deformation at the crack-tip, producing fracture surfaces of noticeably different appearances. Finite element analysis incorporating crystal plasticity was used to identify dominant slip systems and the stress distribution around the crack-tip in plane stress and plane strain. The computational results are helpful in rationalizing the experimental observations including the mechanism of crack propagation, the orientation dependence of crack-tip plasticity and the fracture surface morphology.     

A dislocation dynamics study of the strength of stacking fault tetrahedra. Part I: interactions with screw dislocations

We present a comprehensive dislocation dynamics (DD) study of the strength of stacking fault tetrahedra (SFT) to screw dislocation glide in fcc Cu. Our methodology explicitly accounts for partial dislocation reactions in fcc crystals, which allows us to provide more detailed insights into the dislocation–SFT processes than previous DD studies. The resistance due to stacking fault surfaces to dislocation cutting has been computed using atomistic simulations and added in the form of a point stress to our DD methodology. We obtain a value of 1658.9 MPa, which translates into an extra force resolved on the glide plane that dislocations must overcome before they can penetrate SFTs. In fact, we see they do not, leading to two well differentiated regimes: (i) partial dislocation reactions, resulting in partial SFT damage, and (ii) impenetrable SFT resulting in the creation of Orowan loops. We obtain SFT strength maps as a function of dislocation glide plane-SFT intersection height, interaction orientation, and dislocation line length. In general SFTs are weaker obstacles the smaller the encountered triangular area is, which has allowed us to derive simple scaling laws with the slipped area as the only variable. These laws suffice to explain all strength curves and are used to derive a simple model of dislocation–SFT strength. The stresses required to break through obstacles in the 2.5–4.8-nm size range have been computed to be 100–300 MPa, in good agreement with some experimental estimations and molecular dynamics calculations.