Roland E. Logé

Finite element model of primary recrystallization in polycrystalline aggregates using a level set framework

The paper describes a robust finite element model of interface motion in media with multiple domains and junctions, as is the case in polycrystalline materials. The adopted level set framework describes each domain (grain) with a single level set function, while avoiding the creation of overlap or vacuum between these domains. The finite element mesh provides information on stored energies, calculated from a previous deformation step. Nucleation and growth of new grains are modelled by inserting additional level set functions around chosen nodes of the mesh. The kinetics and topological evolutions induced by primary recrystallization are discussed from simple test cases to more complex configurations and compared with the Johnson–Mehl–Avrami–Kolmogorov theory.

Development of numerical tools for the multiscale modelling of recrystallization in metals, based on a digital material framework

This work is currently under development within the framework of an American‐European project (Digimat Project). The paper details the development of some numerical tools dedicated to the digital representation of metallic materials structures, to the finite element modelling of the polycrystalline microstructure deformation under large strains and to the subsequent recrystallization. The level set method used for the description of the microstructure interfaces is shown to represent a common base to all these developments.

3D elastic-plastic finite element simulation of cold pilgering of zircaloy tubes

In cold pilgering of tubes, a material element undergoes a series of small incremental deformations (≈100 strokes), alternatively under tensile and compressive stresses. This complex history sometimes results in surface damage, seemingly by low-cycle fatigue. Prior to studying the resistance of diverse potential materials to this kind of complex, non-proportional multi-axial, and non-periodic cycling, a thorough mechanical analysis of the stress states is necessary: the finite element method (FEM) software Forge3(®) has been used, with updated Lagrangian formulation due to the transient character of strains and stresses. The process is periodical, except for the ends of a given preform, which are cut off afterwards. One stroke only should thus be sufficient to analyse the whole process, provided the correct initialisations are done in terms of shape, strains and stresses, but these are parts of the unknown of the problem. This point will be particularly addressed in the following, where it is shown that in the non-work hardening case at least, simulating three strokes leads to an invariant geometry and state of stress, starting from a reasonable estimate of the geometry. Strains and stresses thus obtained will be discussed in detail, together with their probable consequences on the damage and fatigue of the material, to be later correlated with defects.

On the mechanical behaviour of AA 7075-T6 during cyclic loading

The mechanical behavior of an aluminum alloy during uniaxial cyclic loading is examined using finite element simulations of aggregates with individually resolved crystals. The aggregates consist of face centered cubic (FCC) crystals with initial orientations assigned by sampling the orientation distribution function (ODF) determined from the measured crystallographic texture. The simulations show that the (elastic) lattice strains within the crystals evolve as the number of cycles increases. This evolution is attributed to the interactions between grains driven by the local plasticity. Under constant amplitude strain cycles, the average (macroscopic) stress decays with increasing number of cycles in concert with the evolution of the lattice strains. Further, the average number of active slip systems also decreases with increasing cycles, eventually reaching zero as the material response becomes totally elastic at the grain level. During much of the cyclic history only a single slip system is activated in most grains. The simulation results are compared to experimental data for the macroscopic stress and for lattice strains in the unloaded state after 1, 30 and 1000 cycles.

Adaptive mesh refinement and automatic remeshing in crystal plasticity finite element simulations

In finite element simulations dedicated to the modelling of microstructure evolution, the mesh has to be fine enough to: (i) accurately describe the geometry of the constituents; (ii) capture local strain gradients stemming from the heterogeneity in material properties. In this paper, 3D polycrystalline aggregates are discretized into unstructured meshes and a level set framework is used to represent the grain boundaries. The crystal plasticity finite element method is used to simulate the plastic deformation of these aggregates. A mesh sensitivity analysis based on the deformation energy distribution shows that the predictions are, on average, more sensitive near grain boundaries. An anisotropic mesh refinement strategy based on the level set description is introduced and it is shown that it offers a good compromise between accuracy requirements on the one hand and computation time on the other hand. As the aggregates deform, mesh distortion inevitably occurs and ultimately causes the breakdown of the simulations. An automatic remeshing tool is used to periodically reconstruct the mesh and appropriate transfer of state variables is performed. It is shown that the diffusion related to data transfer is not significant. Finally, remeshing is performed repeatedly in a highly resolved 500 grains polycrystal subjected to about 90% thickness reduction in rolling. The predicted texture is compared with the experimental data and with the predictions of a standard Taylor model.

A multiscale approach to model the anisotropic deformation of lithospheric plates

The association of experimental data showing that the plastic deformation of olivine, the main constituent of the upper mantle, is highly anisotropic and the ubiquitous seismic anisotropy in the upper mantle, which indicates that olivine crystals show coherent orientations over scales of tens to hundreds of kilometers, implies that the long-term deformation in the upper mantle is anisotropic. We propose a multiscale approach, based on a combination of finite element and homogenization techniques, to model the deformation of a lithospheric plate while fully considering the mechanical anisotropy stemming from a strain-induced orientation of olivine crystals in the mantle. This multiscale model explicitly takes into account the evolution of crystal preferred orientations (CPO) of olivine and of the mechanical anisotropy during the deformation. We performed a series of numerical experiments simulating the uniaxial extension of a homogeneous (100% olivine) but anisotropic plate to test the role of the olivine CPO on the plate mechanical behavior and the link between CPO and mechanical anisotropy evolution. Even for this simple solicitation, different orientations and intensity of the initial olivine CPO result in variable plate strengths and deformation regimes. A plate with an initial CPO where the olivine [100] and [010] axes are concentrated at 45 degrees to the extension direction has high resolved shear stresses on the easy (010)[100] and (001)[100] slip systems of olivine. This results in low strength and in deformation by transtension. Plates with an initial CPO where the maximum of [100] axes is parallel or normal to the extension direction show a high initial strength. Isotropic plates have an intermediate behavior. The progressive rotation of olivine [100] axes toward the imposed stretching direction results in hardening in all models, except in those characterized by an initial concentration of olivine [100] axes normal to the imposed extension, in which softening is followed by hardening.

Prediction of intergranular strains in cubic metals using a multisite elastic-plastic model

A novel approach is adopted for determining the elastic and plastic strains of individual grains within a deformed polycrystalline aggregate. In this approach, termed “multisite modeling”, the deformation of a grain does not merely depend on the grain lattice orientation. It is also significantly influenced by the interaction with one or several of the surrounding grains. The elastic-plastic constitutive law is integrated by identifying iteratively which dislocation slip systems are activated within the grains, and the local stress tensor is shown to be the solution of a linear equation set. Several micro–macro averaging schemes are considered for the distribution of the macroscopic load over the polycrystalline aggregate. These averaging schemes are tested by simulating the development of intergranular strains during uniaxial tension of MONEL-400 as well as commercial purity aluminium. Neutron diffraction measurements of the elastic lattice strains are used as a reference in order to discriminate between the various predictions. The results demonstrate the relevance of “multisite” grain interactions in f.c.c. polycrystals.

Sensitivity of α-ZY4 high-temperature deformation textures to the β-quenched precipitate structure and to recrystallization: Application to hot extrusion

Hot extrusion of Zircaloy-4 tubes usually starts from β-quenched microstructures and induces strong textures. Individual crystallographic orientations were investigated by transmission electron microscopy using the electron backscatter pattern (EBSP) technique as well as Kikuchi patterns. Basal poles were found close to the tangential direction of the tubes in regions exhibiting fine and homogeneously distributed precipitates (FHDPs). In contrast, regions with large and isolated precipitates (LIPs) had more variable orientations. Laboratory plane strain compression tests were performed and the induced textures were compared with numerical simulations using a polycrystalline viscoplastic self-consistent model. The β-quenched material was modeled as a mixture of LIP and FHDP regions, each having a different set of slip system hardnesses, with a volume fraction depending on the previous thermal history. The model was subsequently applied to predict the texture evolution during extrusion with metadynamic recrystallization taking place thereafter. The calculation suggests that recrystallization modifies the orientation of those grains where 〈c+a〉 crystallographic slip has been significantly activated during deformation.

Simulation of cup-drawing based on crystal plasticity applied to reduced grain samplings

This paper presents a means of reducing the computational cost of finite element (FE) simulations coupled to polycrystal plasticity theory. One typically assumes that a polycrystal with a large number of grains underlies every integration point of the FE mesh. Instead, it is suggested here using reduced samplings of grains which differ from one integration point to another. On average, every set of 5 to 25 finite elements contains a variety of lattice orientations that is representative of the macroscopic texture. The model is applied to deep-drawing of a cylindrical cup made of steel. In a first set of simulations, grains are assigned orientations representative of a cold rolling texture and the “earing” profile is compared to experiment. In a second set of simulations, lattice orientations are random and an isotropic deep-drawing result is expected. It is demonstrated that using a minimum of 20 grains per integration point allows properly predicting the final shape of the cup and the texture development.

Strain Induced Abnormal Grain Growth in Nickel Base Superalloys

Under certain circumstances abnormal grain growth occurs in Nickel base superalloys during thermomechanical forming. Second phase particles are involved in the phenomenon, since they obviously do not hinder the motion of some boundaries, but the key parameter is here the stored energy difference between adjacent grains. It induces an additional driving force for grain boundary migration that may be large enough to overcome the Zener pinning pressure. In addition, the abnormal grains have a high density of twins, which is likely due to the increased growth rate.