A micromorphic continuum formulation for finite strain inelasticity

This work proposes a generalized theory of deformation which can capture scale effects also in a homogenously deforming body. Scale effects are relevant for small structures but also when it comes to high strain concentrations as in the case of localised shear bands or at crack tips, etc. In this context, so-called generalized continuum formulations have been proven to provide remedy as they allow for the incorporation of internal length-scale parameters which reflect the micro-structural influence on the macroscopic material response. Here, we want to adopt a generalized continuum framework which is based on the mathematical description of a combined macro- and micro-space [8]. The approach introduces additional degrees of freedom which constitute a so-called micromorphic deformation. First the treatment presented is general in nature but will be specified for the sake of an example and the number of extra degrees of freedom will be reduced to four. Based on the generalized deformation description new strain and stress measures are defined which lead to the formulation of a corresponding generalized variational principle. Of great advantage is the fact that the constitutive law is defined in the generalized space but can be classical otherwise. This limits the number of the extra material parameters necessary to those needed for the specification of the micro-space, in the example presented to only one

Multiscale characterization of DP980 steels for automotive applications

Development has been organized as a ÒpipelineÓ that links the separate disciplinary efforts of groups housed in seven institutions spread across the United States. The main research steps are: high resolution three-dimensional (3D) imaging of the microstructure, statistical characterization of the microstructure, formulation of a probabilistic generator for creating virtual specimens that replicate the measured statistics, creation of a computational model for a virtual specimen that allows general representation of discrete damage events, calibration of the model using room and high temperature tests, simulation of failure, and model validation. Key new experiments include digital surface image correlation and ¼-m resolution 3D computed tomography imaging of the microstructure and evolving damage, both executed at temperatures exceeding 1500°C. Conceptual advances include using both geometry and topology to characterize stochastic microstructures. Computational methods include new probabilistic algorithms for generating stochastic virtual specimens and a new Augmented Finite Element Method that yields extreme efficiency in dealing with arbitrary cracking in heterogeneous materials. The challenge of relating variance in engineering properties to stochastic microstructure in a computationally tractable manner, while retaining necessary physical details in models, will be discussed

Void-induced cross slip of screw dislocations in fcc copper

Pinning interaction between a screw dislocation and a void in fcc copper is investigated by means of molecular dynamics simulation. A screw dislocation bows out to undergo depinning on the original glide plane at low temperatures, where the behavior of the depinning stress is consistent with that obtained by a continuum model. If the temperature is higher than 300 K, the motion of a screw dislocation is no longer restricted to a single glide plane due to cross slip on the void surface. Several depinning mechanisms that involve multiple glide planes are found. In particular, a depinning mechanism that produces an intrinsic prismatic loop is found. We show that these complex depinning mechanisms significantly increase the depinning stress

Shear Modulus of an Elastic Solid under External Pressure as a function of Temperature: The case of Helium

The energy of a dislocation loop in a continuum elastic solid under pressure is considered within the framework of classical mechanics. For a circular loop, this is a function with a maximum at pressures that are well within reach of experimental conditions for solid helium suggesting, in this case, that dislocation loops can be generated by a pressure-assisted thermally activated process. It is also pointed out that pinned dislocations segments can alter the shear response of solid helium, by an amount consistent with current measurements, without any unpinning.Comment: 5 pages, 3 figure

Investigation of finite deformations and shear banding: Theory and experiment

An experimental method using a digital image processing technique is developed for the purpose of characterizing material behavior at large elastoplastic deformations and the associated phenomenon of localization of plastic flow into shear bands. This allows for a detailed description of the evolution of the nonuniform deformation pattern in the postlocalization regime. The experimental results are utilized to calibrate a recently developed gradient-dependent constitutive equation which takes into account the effect of heterogeneous plastic flow, anisotropy and large deformations. The measured values of the gradient coefficients are of small magnitude suggesting that higher order gradients are important only in the highly inhomogeneous region as expected. Moreover, it is found that anisotropic effects become significant in the post-localization regime where the anisotropy ratio changes considerably

On the role of strain gradients in adiabatic shear banding

The effect of higher order strain gradients on adiabatic shear banding is investigated by considering the simple shearing of a heat conducting thermoviscoplastic material with a gradient-dependent flow stress. The competition between the gradient-dependent plastic flow and heat conduction and their influence on the shear band width and structure are examined. Two internal length scales, i.e., the deformation internal length and the thermal internal length, are incorporated into the linear stability analysis, which shows that the band width size scales either with the square root of the strain gradient coefficient (in the absence of heat conduction) or the thermal conductivity (in the absence of strain gradients), respectively. The numerical computation for the nonlinear problem reveals that the diffusive effect of the strain gradient is much stronger than that of the heat conduction and dictates the constitutive response of the material in the postlocalization regime, and shows that the deformation length scale is much larger than the termal length scale. The band width predicted by the gradient theory agrees reasonably well with the experimental observations found in the literature