An internal variable constitutive model for the large deformation of metals at high temperatures

The advent of large deformation finite element methodologies is beginning to permit the numerical simulation of hot working processes whose design until recently has been based on prior industrial experience. Proper application of such finite element techniques requires realistic constitutive equations which more accurately model material behavior during hot working. A simple constitutive model for hot working is the single scalar internal variable model for isotropic thermal elastoplasticity proposed by Anand. The model is recalled and the specific scalar functions, for the equivalent plastic strain rate and the evolution equation for the internal variable, presented are slight modifications of those proposed by Anand. The modified functions are better able to represent high temperature material behavior. The monotonic constant true strain rate and strain rate jump compression experiments on a 2 percent silicon iron is briefly described. The model is implemented in the general purpose finite element program ABAQUS

A thermo-mechanically-coupled theory accounting for hydrogen diffusion and large elastic–viscoplastic deformations of metals

In this paper we develop a thermodynamically-consistent coupled-theory which accounts for diffusion of hydrogen, diffusion of heat, and large elastic–viscoplastic deformations of metals. The theory should be of utility in the analysis of hydrogen diffusion in elastic–plastically-deforming solids, an analysis which is an essential prerequisite for theoretical and numerical efforts aimed at modeling the integrity of structural components used for hydrogen gas storage and distribution.King Fahd University of Petroleum and Mineral

Oxidation of high-temperature alloys. Application to failure of thermal barrier coatings

Oxidation of high-temperature alloys represents complex, strongly-coupled, nonlinear phenomena which include: (i) diffusion of oxygen in the alloy; (ii) an oxidation reaction in which the reaction product causes substantial permanent, anisotropic volumetric swelling; (iii) high-temperature elastic–viscoplastic deformation of the base alloy and the oxide; and (iv) transient heat conduction. We have formulated a continuum-level chemo-thermo--mechanically coupled theory which integrates these various nonlinear phenomena. We have numerically implemented our coupled theory in a finite-element program, and we have also calibrated the material parameters in our theory for an Fe-22Cr-4.8Al-0.3Y heat-resistant alloy experimentally studied by Tolpygo et al. (1998). Using our theory we simulate the high-temperature oxidation of thin sheets of FeCrAlY and show that our theory is capable of reproducing the oxide thickness evolution with time at different temperatures, the permanent extensional changes in dimensions of the base material being oxidized, as well as the development of large compressive residual stresses in the protective surface oxide which forms. As an application of our numerical simulation capability, we also consider the oxidation of an FeCrAlY sheet with an initial groove-like surface undulation, a geometry which has been experimentally studied by Davis and Evans (2006). Our numerical simulations reproduce (with reasonable accuracy) the shape-distortion of the groove upon oxidation, measured by these authors. The ramifications for delamination failure of a ceramic topcoat on a thermally grown-oxide layer in thermal barrier coatings are discussed

A continuum theory of amorphous solids undergoing large deformations, with application to polymeric glasses

This paper summarizes a recently developed continuum theory for the elastic-viscoplastic deformation of amorphous solids such as polymeric and metallic glasses. Introducing an internal-state variable that represents the local free-volume associated with certain metastable states, we are able to capture the highly non-linear stress-strain behavior that precedes the yield-peak and gives rise to post-yield strain-softening. Our theory explicitly accounts for the dependence of the Helmholtz free energy on the plastic deformation in a thermodynamically consistent manner. This dependence leads directly to a backstress in the underlying flow rule, and allows us to model the rapid strain-hardening response after the initial yield-drop in monotonic deformations, as well as the Bauschinger-type reverse-yielding phenomena typically observed in amorphous polymeric solids upon unloading after large plastic deformations. We have implemented a special set of constitutive equations resulting from the general theory in a finite-element computer program. Using this finite-element program, we apply the specialized equations to model the large-deformation response of the amorphous polymeric solid polycarbonate, at ambient temperature and pressure. We show numerical results to some representative problems, and compare them against corresponding results from physical experiments.Singapore-MIT Alliance (SMA

2014 Drucker Medal Paper: A Derivation of the Theory of Linear Poroelasticity From Chemoelasticity

The purpose of this brief paper is to present a new derivation of Biot's theory of linear poroelasticity (Biot, M., 1935, “Le Probleḿe de la Consolidation des Matiéres Argileuses Sous une Charge,” Ann. Soc. Sci. Bruxelles,B55, pp. 110–113; Biot, M., 1941, “General Theory of Three-Dimensional Consolidation,” J. Appl. Phys., 12, pp. 155–164; and Biot, M., and Willis, D., 1957, “The Elastic Coefficients of the Theory of Consolidation,” J. Appl. Mech., 24, pp. 594–601) in a modern thermodynamically consistent fashion, and show that it may be deduced as a special case of a more general theory of chemoelasticity.National Institutes of Health (U.S.). Civil, Mechanical and Manufacturing Innovation (Award 1063626)Center for Clean Water and Clean Energy at MIT and KFUP

Cahn–Hilliard-type phase-field theory for species diffusion coupled with large elastic deformations: application to phase-separating Li-ion electrode materials

We formulate a unified framework of balance laws and thermodynamically consistent constitutive equations which couple Cahn–Hilliard-type species diffusion with large elastic deformations of a body. The traditional Cahn–Hilliard theory, which is based on the species concentration and its spatial gradient leads to a partial differential equation for the concentration which involves fourth-order spatial derivatives in the concentration; this necessitates use of basis functions in finite-element solution procedures that are piecewise smooth and globally C1-continuous. In order to use standard C0-continuous finite-elements to implement our phase-field model, we use a split method to reduce the fourth-order equation into two second-order partial differential equations (PDES). Specifically, we introduce an additional variable – as in the micromorphic theories of continua – and formulate a theory which depends on actual concentration, the micromorphic concentration, and the gradient of the micromorphic concentration. These two PDES, when taken together with the PDE representing the balance of forces, represent the three governing pdes for chemomechanically coupled problems. These equations are amenable to finite-element solution methods which employ standard C0-continuous finite-element basis functions. We have numerically implemented our theory by writing a user-element subroutine for the widely used finite-element program Abaqus/Standard. We use this numerically implemented theory to first study the diffusion-only problem of spinodal decomposition in the absence of any mechanical deformation. Next, we use our fully-coupled theory and numerical-implementation to study the combined effects of diffusion and stress on the lithiation of a representative spheroidal-shaped particle of a phase-separating electrode material

A Novel Testing Apparatus for Tribological Studies at the Small Scale

A novel flexure-based biaxial compression/shear apparatus has been designed, built, and utilized to conduct tribological studies of interfaces relevant to MEMS. Aspects of our new apparatus are detailed and its capabilities are demonstrated by an investigation of two interfaces for MEMS applications. Tribological tests may be performed with normal and tangential forces in the µN to N range and relative sliding displacements in the nm to mm range. In this testing range, the new experimental apparatus represents an improvement over existing techniques for tribological studies at the small scale.Singapore-MIT Alliance (SMA

A theory of amorphous polymeric solids undergoing large deformations: application to micro-indentation of poly(methyl methacrylate)

Although existing continuum models for the elasto-viscoplastic response of amorphous polymeric materials phenomenologically capture the large deformation response of these materials in a reasonably acceptable manner, they do not adequately account for the creep response of these materials at stress levels below those causing “macro-yield”, as well as the Bauschinger-type reverse yielding phenomena at strain levels less than ≈ 30% associated with the macro-yield transient. Anand [1] has recently generalized the model of Anand and Gurtin [2] to begin to capture these important aspects of the mechanical response of such materials. In this work, we summarize Anand’s constitutive model and apply it to the amorphous polymeric solid poly(methyl methacrylate) (PMMA), at ambient temperature and compressive stress states under which this material does not exhibit crazing. We describe our compression-tension and creep experiments on this material from which the material parameters in the model were determined. We have implemented the constitutive model in the finite-element computer program ABAQUS/Explicit [3], and using this finite-element program, we show numerical results for some representative problems in micro-indentation of PMMA, and compare them against corresponding results from physical experiments. The overall predictions of the details of the load, P, versus depth of indentaion, h, curves are very encouraging.Singapore-MIT Alliance (SMA

A coupled theory of fluid permeation and large deformations for elastomeric materials

An elastomeric gel is a cross-linked polymer network swollen with a solvent (fluid). A continuum-mechanical theory to describe the various coupled aspects of fluid permeation and large deformations (e.g., swelling and squeezing) of elastomeric gels is formulated. The basic mechanical force balance laws and the balance law for the fluid content are reviewed, and the constitutive theory that we develop is consistent with modern treatments of continuum thermodynamics, and material frame-indifference. In discussing special constitutive equations we limit our attention to isotropic materials, and consider a model for the free energy based on a Flory-Huggins model for the free energy change due to mixing of the fluid with the polymer network, coupled with a non-Gaussian statistical-mechanical model for the change in configurational entropy — a model which accounts for the limited extensibility of polymer chains. As representative examples of application of the theory, we study (a) three-dimensional swelling-equilibrium of an elastomeric gel in an unconstrained, stress-free state; and (b) the following one-dimensional transient problems: (i) free-swelling of a gel; (ii) consolidation of an already swollen gel; and (iii) pressure-difference-driven diffusion of organic solvents across elastomeric membranes.National Science Foundation (U.S.) (grant DMI-0517966)Singapore-MIT Allianc