David M. Parks

Large inelastic deformation of glassy polymers. part I: rate dependent constitutive model

Abstract Glassy polymers constitute a large class of engineering solids. In order to successfully analyze the warm (near the glass transition temperature) mechanical processes by which many glassy polymeric products are manufactured, as well as to ascertain the response of the resulting part to service life loading conditions, a constitutive law that properly accounts for the large, inelastic deformation behavior of these materials is required. Such behavior is known to exhibit strain rate, temperature, and pressure dependent yield, as well as true strain softening and hardening after yield. This paper develops a three-dimensional constitutive model based on the macromolecular structure of these materials and the micromechanism of plastic flow which encompasses these above dependencies. The experiments necessary to determine the material properties used in the model are also identified. The model predictions for the true stress-strain behavior of PMMA are then compared with experimental data reported in the literature.

A constitutive model for transformation plasticity accompanying strain-induced martensitic transformations in metastable austenitic steels

Abstract We propose a constitutive model which describes the transformation plasticity accompanying strain-induced martensitic transformation in nonthermoelastic alloys. The model consists of two parts: a transformation kinetics law describing the evolution of the volume fraction of martensite and a constitutive law defining the flow strength of the evolving two-phase composite. The Olson-Cohen model for martensite volume fraction evolution is recast in a generalized rate form so that the extent of martensite nucleation is not only a function of plastic strain and temperature, but also of the stress state. A selfconsistent method is then used for predicting the resultant stress-strain behavior. The model describes both the hardening influence of the transformation product, and the softening influence of the transformation itself, as represented by a spontaneous transformation strain. The model is then implemented in a finite element program suitable for analysis of boundary value problems. Model predictions are compared with existing experimental data for austenitic steels. We present results from a few simple analyses, including tensile necking, illustrating the critical importance of stress state sensitivity in the evolution model.

On Criteria for J -Dominance of Crack-Tip Fields In Large-Scale Yielding

Very detailed finite-strain/finite-element analyses of deeply cracked plane-strain center-notch panel and single-edge crack bend specimens were generated using nonhardening and power-law-hardening constitutive laws. The deformation was followed from small-scale yielding into the fully plastic range. The objective was to provide insight as to the minimum specimen size limitations, relative to the characteristic crack-tip opening dimension J/σ o , necessary to assure a J-based dominance of the crack-tip region. The criterion used to judge the degree of dominance was the extent of agreement of the present stress and deformation fields at the blunted crack tips with those calculated by McMeeking for small-scale yielding. For deeply cracked bend specimens, we find very close agreement of the near-tip fields with those of small-scale yielding up to J values of σ o L/25, where L represents the remaining uncracked ligament (and in the deeply cracked case, the only pertinent specimen dimension). This value is consistent with previously proposed J testing size limitations. However, we find that quite detectable deviation from the small-scale yielding fields occurs in both hardening and nonhardening center-crack specimens at considerably smaller J values relative to ligament dimension. This suggests that minimum specimen size requirements necessary to ensure a J-based characterization of the crack tip region may well be more stringent for center-crack or other low plastic constraint configurations than in bend-type specimens. A perhaps overly conservative value of 200 is proposed as the minimum ligament-to-J/σ o ratio which ensures a sensible J-based characterization of the crack-tip region in center-crack specimens of materials exhibiting moderate to low strain hardening.

Modeling the evolution of crystallographic dislocation density in crystal plasticity

Dislocations are the most important material defects in crystal plasticity, and although dislocation mechanics has long been understood as the underlying physical basis for continuum crystal plasticity formulations, explicit consideration of crystallographic dislocation mechanics has been largely absent in working constitutive models. Here, dislocation density state variables evolve from initial conditions according to equations based on fundamental concepts in dislocation mechanics such as the conservation of Burgers vector in multiplication and annihilation processes. The model is implemented to investigate the polyslip behavior of single-crystal aluminum. The results not only capture the mechanical stress/strain response, but also detail the development of underlying dislocation structure responsible for the plastic behavior.

Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation

Abstract A strain gradient dependent crystal plasticity approach is used to model the constitutive behaviour of polycrystal FCC metals under large plastic deformation. Material points are considered as aggregates of grains, subdivided into several fictitious grain fractions: a single crystal volume element stands for the grain interior whereas grain boundaries are represented by bi-crystal volume elements, each having the crystallographic lattice orientations of its adjacent crystals. A relaxed Taylor-like interaction law is used for the transition from the local to the global scale. It is relaxed with respect to the bi-crystals, providing compatibility and stress equilibrium at their internal interface. During loading, the bi-crystal boundaries deform dissimilar to the associated grain interior. Arising from this heterogeneity, a geometrically necessary dislocation (GND) density can be computed, which is required to restore compatibility of the crystallographic lattice. This effect provides a physically based method to account for the additional hardening as introduced by the GNDs, the magnitude of which is related to the grain size. Hence, a scale-dependent response is obtained, for which the numerical simulations predict a mechanical behaviour corresponding to the Hall–Petch effect. Compared to a full-scale finite element model reported in the literature, the present polycrystalline crystal plasticity model is of equal quality yet much more efficient from a computational point of view for simulating uniaxial tension experiments with various grain sizes.

Micromechanical modeling of the elasto-viscoplastic behavior of semi-crystalline polymers

Abstract A micromechanically based constitutive model for the elasto-viscoplastic deformation and texture evolution of semi-crystalline polymers is developed. The model idealizes the microstructure to consist of an aggregate of two-phase layered composite inclusions. A new framework for the composite inclusion model is formulated to facilitate the use of finite deformation elasto-viscoplastic constitutive models for each constituent phase. The crystalline lamellae are modeled as anisotropic elastic with plastic flow occurring via crystallographic slip. The amorphous phase is modeled as isotropic elastic with plastic flow being a rate-dependent process with strain hardening resulting from molecular orientation. The volume-averaged deformation and stress within the inclusions are related to the macroscopic fields by a hybrid interaction model. The uniaxial compression of initially isotropic high density polyethylene (HDPE) is taken as a case study. The ability of the model to capture the elasto-plastic stress–strain behavior of HDPE during monotonic and cyclic loading, the evolution of anisotropy, and the effect of crystallinity on initial modulus, yield stress, post-yield behavior and unloading–reloading cycles are presented.

Determination of elastic T-stress along three-dimensional crack fronts using an interaction integral

Abstract We introduce an effective computational method, based on an interaction integral, to evaluate elastic T -stress along three-dimensional crack fronts. Using this technique, T -stress distributions of various three-dimensional geometries are determined from finite element calculations. The computed results show that the through-thickness variation of T -stress along the crack front of edge-cracked plates is relatively small under both tension and bending load conditions. The deviation from the corresponding two-dimensional results increases with increasing relative crack length and with decreasing relative plate thickness. The increase in T -stress with decreasing thickness results from the inherent positive biaxiality of thin elastic plates. Furthermore, the value of three-dimensionally computed T -stress in these through-crack geometries increases with increasing Poissons ratio. The T -stress distribution is also calculated along the curved crack front of a surface-flawed plate. For the particular geometry considered, the maximum T -stress along the crack front is located at the mid-point of the crack front, and there is a greater variation of T -stress along the crack front under bending loads than in tension.

Numerical determination of the elastic driving force for directional coarsening in Ni-superalloys

Abstract We have developed a general methodology, in the framework of the finite element method, for locally evaluating the generalized force acting on a material interface which is work-conjugate with the normal displacement of the interface itself. This methodology has been applied to the study of directional coarsening of γ′ precipitates in Ni-superalloys. The flexibility of the proposed method has allowed us to closely model the actual microstructural morphology of the alloys and to account for the effects of applied boundary conditions, lattice misfit, elastic anisotropy and inelastic behavior of the crystals. We have positively compared the indications of our model with available experimental data for a few alloys, and a circumscribed parametric study has lead us to formulate a more general interpretation of the rafting phenomenon, which appears to give a satisfactory explanation for all the available experimental observations.

On the kinematics of finite strain plasticity

Abstract In this paper, the representation of the kinematics of inelastic flow problems involving finite strains and rotations is discussed. The concept of multiplicatively decomposing of the deformation gradient into elastic and plastic components is utilized, where the plastic deformation gradient represents a stress-free, relaxed configuration. Here, it is demonstrated that the choice of relaxed configuration is not essential in the problem solution. Therefore, the kinematic decomposition of elastic-plastic deformation may be chosen to best analyse the specific material model of concern. This is demonstrated by analysing two specific materials, the planar single crystal and the glassy polymer, using various kinematic representations.

Simulation of large strain plastic deformation and texture evolution in high density polyethylene

Abstract A micromechanically based composite model which we have recently proposed is employed to study large plastic deformation and texture evolution in initially isotropic high density polyethylene (HDPE) under different modes of straining. Attention is focused on the macroscopic stress-strain response and the evolution of crystallographic, morphological and macromolecular textures in HDPE subject to uniaxial tension and compression, simple shear and plane strain compression. Comparison of the predicted results with experimental observations (e.g. stress-strain measurements, wide-angle X-ray scattering and small-angle X-ray scattering studies of deformed material) shows excellent agreement in nearly all respects.