September 30 – October 1, 2009
On Rethinking Plasticity Theory for Crystalline Solids: A Study in Multiscale Modeling
J. L. Bassani (University of Pennsylvania)
Abstract
The structure of classical plasticity theory, whether applied to single crystals or to the effective behavior of polycrystals, is generally assumed to be associative in the sense that the flow potential is taken to be the yield function. As Hill noted in 1950, to a large extent this choice is a matter of convenience, particularly as it gives rise to certain variational principles and uniqueness theorems, and perhaps at that time justified by a lack of contradictory evidence. But not quite, as G. I. Taylor recognized as early as 1926 that BCC iron and brass behave quite differently than FCC aluminum and copper. The root of these differences also arises in granular materials, which also do not follow an associative flow rule. Ample experimental evidence now exists, but not until atomistic simulations became sufficiently refined have we been in a position to rigorously address the issue of non-associated flow in crystals undergoing plastic deformation by the mechanism of dislocation glide. In 1985 A. Cottrell remarked: “… for too long we have taken the FCC dislocation as the paradigm of all dislocation behaviour; but, as the studies of BCC screw dislocations have shown, the FCC structures and properties are the exception rather than the norm.” Issues that arise at various scales are discussed in this lecture. Atomistic simulations are used to construct multislip models of plastic flow in single crystals, and then polycrystal behavior is estimated using simple homogenization techniques. Even for random polycrystals, the effective behavior is generally of the non-associated flow type, and this is shown to significantly affect macroscopic deformations and failure mechanisms including cavitation instabilities and sheet necking. In addition, we discovered that intermittent bursts of strain can arise as a consequence of non-associated flow, and there is experimental evidence for such behavior. For power-law hardening crack tip fields retain the HRR structure although path-independence of the J-integral that can be argued on theoretical grounds, but it appears to be a reasonable approximation.
On Matching of Discrete and Continuum Models
Gregory J. Rodin (The University of Texas at Austin)
Abstract
Matching discrete and continuum models is central to multi-scale modeling methods in which these models represent the microscopic and macroscopic responses, respectively. Accordingly, the purpose of the discrete model is to resolve details at the microscopic scale, whereas the purpose of the continuum model is to filter out unnecessary microscopic details.
It will be shown that straightforward local-to-global matching is generally inadequate for resolving forces at the microscopic scale. We present an alternative local-to-global matching scheme that allows us to correct this deficiency.
On A New Compatibility Constraint at Solid Interfaces, Oxidation and Interfacial Fracture
John C. Slattery (Texas A&M University)
Abstract
A new compatibility constraint for solid-solid and solid-fluid interfaces and a new approach to the interfacial critical energy release rate are reviewed. Applications to the residual stress distribution developed during oxidation and to interfacial fracture are discussed.
Nanoscale Piezoelectricity
Pradeep Sharma (University of Houston)
Abstract
Crystalline piezoelectric dielectrics electrically polarize upon application of uniform mechanical strain. Inhomogeneous strain, however, locally breaks inversion symmetry and can potentially polarize even non-piezoelectric (centrosymmetric) dielectrics. Flexoelectricty–the coupling of strain gradient to polarization– is expected to show a strong size-dependency due to the scaling of stain gradients with structural feature size. The existence and importance of flexoelectricity has been experimentally confirmed in several materials especially ferroelectrics. In this presentation, I present a semi-tutorial introduction to flexoelectricity and discuss its ramifications for the design of multifunctional materials, size-dependent piezoelectricity and energy storage. Specifically, I present results (based on a combination of atomistic and theoretical approaches) that provide insights into the “effective” size-dependent piezoelectric and elastic behavior of inhomogeneously strained non-piezoelectric and piezoelectric nanostructures. I will argue, through computational examples, the tantalizing possibility of creating “apparently piezoelectric” nano-composites without piezoelectric constituents. I will also present experimental evidence based upon nanoindentation of ferroelectrics. Finally, I propose that flexoelectricity is an important and essential contributor to the intrinsic dead-layer effect in high permittivity ferroelectric based nanocapacitors used for energy storage.
On Numerical Modelling of the Shape Memory Alloys Behavior – Application to Precipitation Effect in SMAs –
Etienne Patoor (Arts et Métiers ParisTech, Metz, France)
Abstract
The NiTi shape memory alloys behavior is dependant to features like cold-work ratio or annealing time and temperature. The presence of precipitates associated to alloy composition or thermal treatments strongly affect the thermomechanical response of this alloy. We propose to investigate the influence of the nature of these precipitates on the overall response. Two cases will be addressed: elastic precipitate and elasto-plastic one. The resulting material is considered as a composite material having a SMA matrix and elastic or elastoplastic inclusions. In the first part of the presentation, the phenomenological model used to describe the SMA behavior will be presented. The second part of this talk will deal with the inclusion problem for NiTiNb alloy and Ni4Ti3 precipitates in NiTi SMA.
On A Hybrid Multiscale Approach to Deformation and Fracture in Structural and Multi-functional Materials
Amine Benzerga (Texas A&M University)
Abstract
Deformation and fracture are cross-cutting phenomena in a host of engineering structures subject to severe environmental conditions of temperature, stress and sometimes irradiation. Examples include airframe and hot engine parts, first-wall and blankets in nuclear reactors, automotive body frames and high-temperature multi-functional materials. Top-down approaches to plasticity and fracture have been and remain popular.
With the advent of more fundamental dislocation-scale frameworks, concurrent with the development of nanomechanical experimental techniques, it has become possible to adopt a bottom-up approach to material deformation from the atomic to the macroscopic. However, effective modeling of ductile fracture in structural metallic materials still requires a top-down approach.
In this talk, a hybrid approach will be advocated in which the general structure of coupled plasticity-damage constitutive equations fits into a classical top-down approach with strength and hardening properties inferred from a bottom-up approach. Central to the latter is a suite of dislocation dynamics simulation techniques whereas homogenization and micromechanics determine the structure of macroscopic potentials. Recent developments of this hybrid approach will be highlighted, including anisotropy effects at the macroscale and size effects at the microscale. Mathematical, computational and physical challenges facing its development will be discussed.
Future Materials and Computational Strategies in the Development of Photovoltaic Cells
Bryan Hardin (Stanford University)
Abstract
Brief introduction on the topic of Photovoltaic (PV) cells including an analysis of current technologies. The main focus will be on emerging PV technologies such organic bulk heterojunctions, dye-sensitized solar cells, and nanostructured PV. Materials design rules, computational needs, and basic failure mechanisms, will be discussed highlighting current research from the Center for Advanced Molecular Photovoltaics (CAMP) at Stanford.
Ab Initio Investigation of Shape Memory Alloys
Raymundo Arroyave (Texas A& M University)
Abstract
In this talk, I will discuss the latest progress on the investigation of the underlying physical basis, at the electronic structure level, for the shape memory behavior of a recently discovered High Temperature Shape Memory Alloy System (HTSMA). I will describe how we have elucidated the nature of the martensitic transformation responsible for the SM effect in this system by studying the material’s structural stability, vibrational behavior and, more importantly, its electronic structure. In the talk I will also compare what we have learned about this system as it compares with the most widely investigated SMA to date, namely, Ni2MnGa. Finally, I will conclude by describing how we can use ab initio calculations to inform the development of phenomenological models that can assist the computer-aided design of SMA alloys.
On Dynamic strain localization and failure in ductile materials
K. Ravi-Chandar (University of Texas, Austin)
Abstract
In ductile materials, under uniform imposed dynamic loading, the deformation localizes into narrow regions (necks or shear bands) prior to the emergence of cracks; cracks nucleate within these bands. We focus on experiments specially designed to generate high-strain-rate loading in tubes of materials with high electrical conductivity; Al 6061-O is the primary material considered in this work. From the experiments, it is demonstrated that as the strain in the specimen evolves, the specimen deforms plastically, initially uniformly over the entire cylinder. Beyond a critical strain level, the strain localizes in narrow bands, with the entire surface of the cylindrical specimen decorated with such localization bands. Eventually, cracks are nucleated at intersections of these bands. Both macroscopic strain measurements and microscopic observations of deformation mechanisms that result in localization will be described in the presentation. Numerical simulations of the dynamic response of ductile materials and comparison to experiments will also be described.
On Multi-scale and Multi-physics Modeling of Self-healing Materials
Philippe H. Geubelle (University of Illinois)
Abstract
Self-healing composites are a new class of biomimetic polymeric materials that present the unique ability to heal slowly propagating cracks in an autonomic fashion. Over the past decade, two generations of self-healing materials have been introduced. The first one consists of an encapsulated healing agent (such as dicyclopentadiene or DCPD) embedded in a polymeric matrix (typically epoxy) together with a living catalyst. As a crack approaches a micro-capsule, the stress concentration present in the vicinity of its tip breaks the capsule wall, releasing the healing agent that polymerizes in contact with the catalyst and heals the crack. The second form of self-healing polymer involves a network of microchannels containing the healing agent, which is released onto the crack surfaces when an internal damage interacts with one of the microchannels.
The heterogeneous nature of this class of multifunctional materials presents a set of interesting challenges not only in the modeling of the triggering step of the autonomic healing process, i.e., the interaction of the crack with the microcapsule or microchannel, but especially in the capture of the impact of the ensuing chemical processes that lead to the retardation and/or arrest of the crack. This complexity is especially evident in the case of autonomic healing of internal damage under cyclic loading, characterized by a competition between fatigue crack propagation and healing kinetics.
This presentation will summarize some examples illustrating the key challenges involved in the multiphysics and multidisciplinary modeling of self-healing materials, from the capture of the basic interaction between a crack and a microcapsule to the computational design and multi-objective optimization of microvascular networks.
The Effect of Surface Tension in Modeling Fracture
Tsvetanka Sendova (University of Minnesota)
Abstract
The talk will focus on the analysis of a class of fracture models based on a new approach to modeling brittle fracture. Integral transform methods are used to reduce the problem to a Cauchy singular, linear integrodifferential equation. We show that ascribing constant surface tension to the fracture surfaces and using the appropriate crack surface boundary condition, given by the jump momentum balance, leads to a sharp crack opening profile at the crack tip, in contrast to the classical theory of brittle fracture. However, such a model still predicts singular crack tip stress.
For this reason we study a modified model, where the surface excess property is responsive to the curvature of the fracture surfaces. We show that curvature-dependent surface tension, together with boundary conditions in the form of the jump momentum balance, leads to bounded stresses and a cusp-like opening profile at the crack tip. Further, the problem of interface fracture will be discussed briey. Within the studied modeling approach, it leads to a system of four coupled singular integral equations, with a Cauchy-type singularity, which can be reduced to a four by four system of Fredholm integral equations of the second kind. We will discuss the implications of ascribing surface excess properties to the bimaterial interfaces.
Subsonic Propagation of a Semi-infinite Interfacial Crack with a Friction Zone Ahead
Yuri Antipov (Louisiana State University)
Abstract
Propagation of a semi-infinite crack along the interface between an elastic half-plane and a rigid half-plane is analyzed. The crack advances at constant subsonic speed. Ahead of the crack, there is a finite segment where the conditions of Coulomb friction law are satisfied. The contact zone of unknown a priori length propagates with the same speed as the crack. The problem reduces to a vector Riemann-Hilbert problem with a piece-wise constant matrix coefficient discontinuous at three points, 0, 1, and $\infty$. The problem is solved exactly in terms of Kummer’s solutions of the associated hypergeometric differential equation. Numerical results are reported.
Characterizing the Chemical Degradation of Polymer Composite Materials
R. B. Hall (Air Force Research Laboratory)
Abstract
Pochiraju, Stevens Institute of Technology Polymer composites are finding increasing applications in engines and hot structures, often as lower-weight replacements for titanium, for sustained operating temperatures up to 650F. Data and modeling indicating the directional growth of oxidation and accompanying damage in PMR-15 composites will be shown, as well as aspects of an emerging mixture theory approach addressing the general problem of directional chemical degradation in a finitely deforming elastic composite in the presence of a diffusing fluid.