A. J. Beaudoin

Grain-size effect in viscoplastic polycrystals at moderate strains

Abstract This work deals with the prediction of grain-size dependent hardening in FCC and BCC polycrystalline metals at moderately high strains (2–30%). The model considers 3–D, polycrystalline aggregates of purely viscoplastic crystals, and simulates quasi-static deformation histories with a hybrid finite element method implemented for parallel computation. The hardening response of the individual crystals is considered to be isotropic, but modified to include a physically motivated measure of lattice incompatibility which is supposed to model, in the continuum setting, the resistance to plastic flow provided by lattice defects. The length-scale in constitutive response that is required on dimensional grounds appears naturally from physical considerations. The grain-size effect in FCC polycrystals and development of Stage IV hardening in a BCC material are examined. Though the grain-size does not enter explicitly into the constitutive model, an inverse relationship between the macroscopic flow stress and grain-size is predicted, in agreement with experimental results for deformation of FCC polycrystals having grain-sizes below 100 microns and at strains beyond the initial yield (>2%). The development of lattice incompatibility is further shown to predict a transition to Stage IV (linear) hardening upon saturation of Stage III (parabolic) hardening.

A hybrid finite element formulation for polycrystal plasticity with consideration of macrostructural and microstructural linking

A hybrid finite element formulation for the plastic deformation of FCC metals with anisotropy is outlined. Polycrystal plasticity theory is used to develop the constitutive response. The hybrid approach facilitates introduction of the microscale stress in the macroscopic statement of equilibrium. Convergence of the hybrid formulation is contrasted with that of a velocity-pressure formulation. It is demonstrated that the hybrid formulation is well suited for studies where significant spatial variations in constitutive response result from having only one, or a very few, crystal orientations represented in each finite element. A simulation of channel die compression is made with one crystal per finite element. The resulting texture evolution is compared with other texture evolution models and experimental data for cold rolled aluminum. It is demonstrated that the brass texture component, observed in the experimental data, is developed through shear deformations arising from grain-to-grain interactions.

Application of polycrystal plasticity to sheet forming

Abstract A methodology for including anisotropy in metal forming analyses is presented. A finite element formulation is developed for the analysis of the inhomogeneous macroscopic deformations. Anisotropic material properties are derived from a microscopic description based on polycrystal plasticity theory. Efficient computation of the microscopic variables is achieved through massive data parallel computations. A procedure is set forth for initialization of the microscopic state variables from experimental measurement of the metal texture. The feasibility of initializing (from experimental data) and evolving (through massive computations) a detailed microscopic description for a complex deformation process is demonstrated through a predictive simulation. The predicted location and height of ears in the hydroforming of aluminium sheets are in good agreement with experiment.

Three-dimensional deformation process simulation with explicit use of polycrystal plasticity models

Abstract The combination of massive parallel processing and polycrystal plasticity theory offers the potential for applying detailed microstructural models to macroscopic deformation processes. In this work the finite element method is used to solve for the three-dimensional deformation of a plastic workpiece. The elemental constitutive response is derived from the microstructural response of a polycrystal aggregate situated in the element. Crystal orientations and their respective weighted contributions to the aggregate response are selected to approximate the orientation distribution derived from experimental pole figure measurements. The interaction of the material symmetry adopted in analysis of pole figures and the boundary conditions posed in the plasticity boundary value problem are examined. Through the introduction of distinct aggregates with decreasing crystal to aggregate ratio, an inhomogenous material response is developed where: (1) the orientation distribution becomes well approximated only by a collection of spatially distinct aggregates, and (2) these aggregates experience deformation paths of increasing variation. It is shown that the use of spatially distinct aggregates in a material experiencing local kinematic inhomogeneities throughout its deformation history leads to texture predictions that compare favorably with experimental measurements.

Consideration of grain-size effect and kinetics in the plastic deformation of metal polycrystals

Abstract This work extends the constitutive model for the prediction of grain-size dependent hardening in f.c.c. polycrystalline metals proposed by Acharya and Beaudoin [1] (Grain-size effect in fcc viscoplastic polycrystals at moderate strains, 1999, in press) to include effects of temperature and strain rate dependence. A comparison is made between model predictions and compression data, taken at varying temperature and strain rate, for pure Ag having two different grain sizes. It is shown that an initial increase in yield stress and concomitant decrease in hardening rate for a fine-grained material, relative to a coarse-grained counterpart, can be captured through initialization of a state variable serving to describe stress response at prescribed reference conditions of temperature and strain rate. A grain-size dependence of hardening rate during parabolic (stage III) hardening is characterized by the evolution of net dislocation density in a finite element model of a polycrystal aggregate. Finally, observations from simulations of deformation of the polycrystal aggregate are introduced into an existing macroscopic constitutive model for metal plasticity based on the mechanical threshold.

Spatial coupling in jerky flow using polycrystal plasticity

A multiscale approach including a finite element framework for polycrystal plasticity is used to model jerky flow, also known as the Portevin-Le Chatelier effect. The local constitutive behavior comprises the standard description of the negative strain rate sensitivity of the flow stress in the domain of instability. Due to stress gradients inherent to the polycrystal formulation, the spatial coupling involved in the spatio-temporal dynamics of jerky flow is naturally accounted for in the model, without using any ad hoc gradient constitutive formulation. For the first time, the static, hopping and propagating band types are recovered in constant strain-rate tests, as well as the temporal properties of the stress serrations. The associated dynamic regimes are characterized and found consistent with recent experimental evidence of both chaos and self-organized criticality in Al-Mg polycrystals.

A polycrystal plasticity model based on the mechanical threshold

Abstract A temperature and rate-dependent viscoplastic polycrystalmodel is presented.It uses a single crystal constitutive response that is based on the isotropic Mechanical Threshold Stress continuum model. This combination gives us theability to relate the constitutive model parameters between the polycrystaland continuum models. The individual crystal response is used to obtain themacroscopic response through the extended Taylor hypothesis. A Newton-Raphsonalgorithm is used to solve the set of fully implicit nonlinear equations for each crystal. The analysis also uses a novel state variable integration method which renders the analysis time step size independent for constant strain rate simulations. Material parameter estimates are obtained through an identification study, where the error between experimental and computed stress response is minimized. The BFGS method, which is used to solve theidentification problem, requires first-order gradients. These gradients arecomputed efficiently via the direct method of design sensitivity analysis.Texture augmentation is performed in a second identification study by changing crystal weights (volume fractions).

Development of localized orientation gradients in fcc polycrystals

Abstract A finite-element formulation which derives constitutive response from crystal plasticity theory is used to examine localized deformation in fcc polycrystals. The polycrystals are (simple) idealized three-dimensional arrangements of grains, and many elements per grain. Non-uniform deformations within individual grains lead to the development of domains that are separated by boundaries of high misorientation. Also, localized shearing is seen to occur on a microscopic scale of grain dimensions. The important consequence. of these simulations is that the predicted local inhomogeneities are meeting various requirements that make them possible nucleation sites for recrystallization.

Finite-element modelling of femoral shaft fracture fixation techniques post total hip arthroplasty

The presence of a femoral prosthesis superior to a shaft fracture severely complicates fixation and treatment. This study uses two-dimensional, multithickness, plane stress finite-element models of a femur with prosthesis to investigate the stresses developed with the application of three popular fixation techniques: revision to a long stem prosthesis, lateral plating with a cortical bone allograft strut and cerclage wires, and custom plate application with proximal Parham band fixation with distal cortical screws (Ogden plate). The plate and bone contact as well as the fracture site contact were modelled by using orthotropic elements with custom-fit moduli so that only the normal stress to the interface was significant. A thermal analogy was used to model the cerclage and Parham band preloads so that representative preloads in the proximal fixation of the two types of plate treatments could be modelled. A parametric study was performed with the long-prosthesis model to show variations in stem lengths of one, two and three femoral diameters distal to the fracture site. The Ogden plate model showed a transfer of tensile stress near the proximal-most band, with the highest tensile stress being at the fracture site with evidence of stress shielding of the proximal lateral cortex. The cortical bone strut model showed a transfer of tensile stress to the bone strut but showed less shielding of the proximal cortex. The cerclage wires at the base of the bone strut showed the highest changes in load with the distalmost wire increasing to almost four times its original preload.(ABSTRACT TRUNCATED AT 250 WORDS)

Effect of Isolated Talocalcaneal Fusion on Contact in the Ankle and Talonavicular Joints

A cadaveric model was developed to establish the articular contact area and load distribution in the ankle joint, posterior facet of the talocalcaneal joint, and talonavicular joint using pressure sensitive film. Positions of dorsiflexion, neutral, and plantarflexion were evaluated. This model was further used to determine the effect of talocalcaneal fusion on the articular contact area in the talonavicular and ankle joints. Alteration of articular contact was most pronounced in the talonavicular joint. There, a statistically significant reduction in contact area postfusion was noted when the foot was in the plantarflexed position. Reductions in ankle joint articular contact area were observed in the dorsiflexed and plantarflexed positions in the majority of specimens. Lateral displacement of the region of articular contact was noted in some specimens. A pressure-weighted centroid calculation was performed to provide a quantitative measure of the shift of the contact region.