Anxin Ma

On the influence of isotropic and kinematic hardening caused by strain gradients on the deformation behaviour of polycrystals

During the deformation of polycrystals, pronounced strain gradients may occur at grain boundaries between grains whose misorientations lead to a large mismatch in their deformation behaviour. Hence, even under globally uniaxial and homogeneous strains, internal stresses will arise that must be characterized by nonlocal plasticity models. In this work, such a nonlocal constitutive model is formulated based on the concept of densities of geometrically necessary superdislocations in an isotropic elastic-plastic medium. Since the deformation of individual grains is considered, crystal plasticity models are applied that take into account plastic slip on crystallographic planes. This new nonlocal constitutive model is applied to describe the deformation of a polycrystal under the influence of plastic strain gradients caused by isotropic and kinematic strain hardening. It is found that isotropic hardening originating from plastic strain gradients amplifies deformation heterogeneities stemming from different Schmid factors in neighbouring grains. However, the kinematic hardening resulting from plastic strain gradients tends to reduce such deformation heterogeneity. Thus, the capability of a polycrystal to deform uniformly is determined by the competition between isotropic and kinematic hardening. Finally, the model is applied to explain why grain refinement is an efficient way to improve material strength and ductility at the same time.

Multiscale Modeling of Nanoindentation: From Atomistic to Continuum Models

Nanoindentation revealed a number of effects, like pop-in behavior or indentation size effects, that are very different from the classical mechanical behavior of bulk materials and that have therefore sparked a lot of research activities. In this contribution a multiscale approach is followed to understand the mechanisms behind this peculiar material behavior during nanoindentation. Atomistic simulations reveal the mechanisms of dislocation nucleation and multiplication during the very start of plastic deformation. From mesoscale dislocation density based models we gain advanced insight into how plastic zones develop and spread through materials with heterogeneous dislocation microstructures. Crystal plasticity models on the macroscale, finally, are able to reproduce load-indentation curves and remaining imprint topologies in a way that is directly comparable to experimental results and, thus, allows for the determination of true material properties by inverse methods. The complex interplay of the deformation mechanisms occurring on different length scales is described and the necessity to introduce the knowledge about fundamental deformation mechanisms into models on higher length scales is highlighted.

Scale Bridging Modeling of Plastic Deformation and Damage Initiation in Polycrystals

Plastic deformation of polycrystalline materials includes dislocation slip, twinning, grain boundary sliding and eigenstrain produced by phase transformations and diffusion. These mechanisms are often alternative and competing in different loading conditions described by stress level, strain rate and temperature. Modelling of plasticity in polycrystalline materials has a clear multiscale character, such that plastic deformation has been widely studied on the macro-scale by the finite element methods, on the meso-scale by representative volume element approaches, on the micro-scale by dislocation dynamics methods and on the atomic scale by molecular dynamics simulations. Advancement and further improvement of the reliability of macro-scale constitutive models is expected to originate from developments at microstructural or even smaller length scales by transfering the observed mechanisms to the macro-scale in a suited manner. Currently efficient modelling tools have been developed for different length scales and there still exists a challenge in passing relevant information between models on different scales. This chapter aims at overviewing the current stage of modelling tools at different length scales, discussing the possible approaches to bridge different length scales, and reporting successful multiscale modelling applications.

A crystal plasticity smooth-particle hydrodynamics approach and its application to equal-channel angular pressing simulation

A crystal plasticity (CP) modelling approach based on smooth-particle hydrodynamics (SPH) has been developed to study severe plastic deformation of crystalline materials. The method has been implemented and validated by comparing the stress distribution and stress evolution of several SPH and FEM simulations for an anisotropic elastic material. The findings show that the SPH method produces an efficient and numerically robust solution for solid-mechanics boundary value problems. Furthermore, the approach has been extended to incorporate a CP model and employed to simulate FCC polycrystals under the equal-channel angular pressing (ECAP) condition. It was found that the polycrystal contains four distinct regions with different deformation mechanisms. For the case that friction between deformable particles and boundary particles was neglected, more than one half of the grains suffered severe plastic deformation. The CP-SPH developed here thus is demonstrated to be a powerful tool to study grain refinement under severe plastic deformation.

Micromechanical modeling approach to derive the yield surface for BCC and FCC steels using statistically informed microstructure models and nonlocal crystal plasticity

In order to describe irreversible deformation during metal forming processes, the yield surface is one of the most important criteria. Because of their simplicity and efficiency, analytical yield functions along with experimental guidelines for parameterization become increasingly important for engineering applications. However, the relationship between most of these models and microstructural features are still limited. Hence, we propose to use micromechanical modeling, which considers important microstructural features, as a part of the solution to this missing link. This study aims at the development of a micromechanical modeling strategy to calibrate material parameters for the advanced analytical initial yield function Barlat YLD 2004-18p. To accomplish this, the representative volume element is firstly created based on a method making use of the statistical description of microstructure morphology as input parameter. Such method couples particle simulations to radical Voronoi tessellations to generate realistic virtual microstructures as representative volume elements. Afterwards, a nonlocal crystal plasticity model is applied to describe the plastic deformation of the representative volume element by crystal plasticity finite element simulation. Subsequently, an algorithm to construct the yield surface based on the crystal plasticity finite element simulation is developed. The primary objectives of this proposed algorithm are to automatically capture and extract the yield loci under various loading conditions. Finally, a nonlinear least square optimization is applied to determine the material parameters of Barlat YLD 2004-18p initial yield function of representative volume element, mimicking generic properties of bcc and fcc steels from the numerical simulations.

Plastic deformation modelling of tempered martensite steel block structure by a nonlocal crystal plasticity model

The plastic deformations of tempered martensite steel representative volume elements with different martensite block structures have been investigated by using a nonlocal crystal plasticity model which considers isotropic and kinematic hardening produced by plastic strain gradients. It was found that pronounced strain gradients occur in the grain boundary region even under homogeneous loading. The isotropic hardening of strain gradients strongly influences the global stress–strain diagram while the kinematic hardening of strain gradients influences the local deformation behaviour. It is found that the additional strain gradient hardening is not only dependent on the block width but also on the misorientations or the deformation incompatibilities in adjacent blocks.

Influence of Microstructural Features on the Propagation of Microstructurally Short Fatigue Cracks in Structural Steels

Cyclically loaded structural steel components are usually designed to endure macroscopic stress amplitudes close to the material’s endurance strength where microcracks initiate due to microstructural inhomogeneities and exhibit strong interactions with the various microstructural features in their neighborhood upon propagating. The current study presents a microstructural model with a capability to quantitatively describe the influence of microstructural features on the growth of cyclic cracks in the decisive, very early fatigue behavior stage. The FE model is based on the crystal plasticity theory and accounts for relative grain orientations. Both the extended finite element method (XFEM) and a coupled damage mechanics approach are used to describe crack opening behavior. The model is implemented to simulate real microcracking events produced in interrupted cyclic multiple-step tests under metallographic observation with temperature change measurements. Furthermore, the model is implemented on virtually created microstructures with altered grain sizes and orientations based on statistical EBSD analysis.