An extended multiscale principle of virtual velocities approach for evolving microstructure

AbstractA hierarchical multiscale approach is presented for modeling microstructure evolution in heterogeneous materials. Preservation of momentum across each scale transition is incorporated through the application of the principle of virtual velocities at the fine scale giving rise to the appropriate continuum momentum balance equations at the coarse scale. In addition to satisfying momentum balance and invariance of momentum among scales, invariance of elastic free energy, stored free energy, and dissipation between two scales of observation is regarded as crucial to the physics of each scale transition. The preservation of this energy partitioning scheme is obtained through construction of constitutive relations within the framework of internal state variable theory. Internal state variables that are directly computed from the fine scale response are introduced to augment the state equations and describe the inelastic energy storage and dissipation within the fine scale. By virtue of a second gradient kinematic decomposition, the framework naturally gives rise to couple stresses

Mesoscale cyclic crystal plasticity with dislocation substructures

Constitutive formulations have increasingly focused on physically-based approaches that are less phenomenological and incorporate information from multiple scales. Most dislocation-based plasticity approaches reflect many-body dislocation physics without considering the length scales introduced by the self-organization of dislocations into mesoscale structures. These structures promote internal stresses or back stresses that are heterogeneous and long-range in nature and play a critical intermediary role in distinguishing the stress at micro- and nano-scales under cyclic loading. We present a framework that explicitly incorporates length-scales and evolution laws associated with mesoscale dislocation substructures such as cells and persistent slip bands (PSBs) in metallic materials under cyclic loading. A physically-based formulation for the back stress based on the Eshelby inclusion formalism is introduced that explicitly depends on morphology of mesoscale dislocation structures. The approach employs material parameters that can be measured or computed at lower length scales to contrast the response of models and experiments for multiple single crystals orientation and polycrystals for a wide range of strains

The Learning Community Experience: Cultivating a Residual Worldview

In this essay, we conceptualize first-year learning communities as worldviews that, during the first year and residually in subsequent years, allow students to recognize and engage difference and acknowledge and articulate their biases. Students who take part in a learning community have an opportunity to develop the biases and presuppositions of the community, as well as a position that is present throughout life. Using the first-year learning communities at Duquesne University as an example, we contend that inclusion in a learning community upholds a given worldview – as narrative, philosophical or theological system, or shaper of individuals. This, in turn, fosters the biases and presuppositions of the community’s members, a residual outcome that stays with students for the rest of their lives. Christina L. McDowell Marinchak is an Assistant Professor of Business Communication at University of Alaska, Anchorage. David DeIuliis is a Ph.D. candidate in the Department of Communication & Rhetorical Studies at Duquesne University in Pittsburgh, PA

Sensitivity of polycrystal plasticity to slip system kinematic hardening laws for Al 7075-T6

The prediction of formation and early growth of microstructurally small fatigue cracks requires use of constitutive models that accurately estimate local states of stress, strain, and cyclic plastic strain. However, few research efforts have attempted to systematically consider the sensitivity of overall cyclic stress-strain hysteresis and higher order mean stress relaxation and plastic strain ratcheting responses introduced by the slip system back-stress formulation in crystal plasticity, even for face centered cubic (FCC) crystal systems. This paper explores the performance of two slip system level kinematic hardening models using a finite element crystal plasticity implementation as a User Material Subroutine (UMAT) within ABAQUS (Abaqus unified FEA, 2016) [1], with fully implicit numerical integration. The two kinematic hardening formulations aim to reproduce the cyclic deformation of polycrystalline Al 7075-T6 in terms of both macroscopic cyclic stress-strain hysteresis loop shape, as well as ratcheting and mean stress relaxation under strain- or stress-controlled loading with mean strain or stress, respectively. The first formulation is an Armstrong-Frederick type hardening-dynamic recovery law for evolution of the back stress [2]. This approach is capable of reproducing observed deformation under completely reversed uniaxial loading conditions, but overpredicts the rate of cyclic ratcheting and associated mean stress relaxation. The second formulation corresponds to a multiple back stress Ohno-Wang type hardening law [3] with nonlinear dynamic recovery. The adoption of this back stress evolution law greatly improves the capability to model experimental results for polycrystalline specimens subjected to cycling with mean stress or strain. The relation of such nonlinear dynamic recovery effects are related to slip system interactions with dislocation substructures

A rationale for modeling hydrogen effects on plastic deformation across scales in FCC metals

Although there have been many investigations on the effects of hydrogen on the plastic deformation of metals, an intense debate continues about the physical mechanisms responsible. Most puzzling is the fact that hydrogen appears to be able to both harden and soften FCC metals, depending on the loading conditions. In addition, experiments have shown that hydrogen affects slip system activity differentially, resulting in shear localization of plastic deformation. The work reported in this paper employs a physics-based crystal plasticity model to reproduce the macroscopic response of hydrogen-charged FCC metals through the hydrogen effects on dislocation interactions proposed herein. Different micro-scale mechanisms by which hydrogen may affect plastic deformation are considered, and their resulting macroscopic stress-strain responses under monotonic and cyclic loading are compared. The results support the conclusion that hydrogen screening of dislocations alone cannot explain all the observed macroscopic responses. Instead, it is argued that hydrogen can promote hardening or softening through an increase in glide activation energy and a reduction in dislocation line tension

ρ\rho-CP: Open Source Dislocation Density Based Crystal Plasticity Framework for Simulating Temperature- and Strain Rate-Dependent Deformation

This work presents an open source, dislocation density based crystal plasticity modeling framework, $\rho$-CP. A Kocks-type thermally activated flow is used for accounting for the temperature and strain rate effects on the crystallographic shearing rate. Slip system-level mobile and immobile dislocation densities, as well slip system-level backstress, are used as internal state variables for representing the substructure evolution during plastic deformation. A fully implicit numerical integration scheme is presented for the time integration of the finite deformation plasticity model. The framework is implemented and integrated with the open source finite element solver, Multiphysics Object-Oriented Simulation Environment (MOOSE). Example applications of the model are demonstrated for predicting the anisotropic mechanical response of single and polycrystalline hcp magnesium, strain rate effects and cyclic deformation of polycrystalline fcc OFHC copper, and temperature and strain rate effects on the thermo-mechanical deformation of polycrystalline bcc tantanlum. Simulations of realistic Voronoi-tessellated microstructures as well as Electron Back Scatter Diffraction (EBSD) microstructures are demonstrated to highlight the model's ability to predict large deformation and misorientation development during plastic deformation.Comment: 30 pages, 19 figures, 5 tables, v

Ballistic-diffusive phonon heat transport across grain boundaries

The propagation of a heat pulse in a single crystal and across grain boundaries (GBs) is simulated using a concurrent atomistic-continuum method furnished with a coherent phonon pulse model. With a heat pulse constructed based on a Bose-Einstein distribution of phonons, this work has reproduced the phenomenon of phonon focusing in single and polycrystalline materials. Simulation results provide visual evidence that the propagation of a heat pulse in crystalline solids with or without GBs is partially ballistic and partially diffusive, i.e., there is a co-existence of ballistic and diffusive thermal transport, with the long-wavelength phonons traveling ballistically while the short-wavelength phonons scatter with each other and travel diffusively. To gain a quantitative understanding of GB thermal resistance, the kinetic energy transmitted across GBs is monitored on the fly and the time-dependent energy transmission for each specimen is measured; the contributions of coherent and incoherent phonon transport to the energy transmission are estimated. Simulation results reveal that the presence of GBs modifies the nature of thermal transport, with the coherent long-wavelength phonons dominating the heat conduction in materials with GBs. In addition, it is found that phonon-GB interactions can result in reconstruction of GBs