An infrared image processing to analyse the calorific effects accompanying strain localisation

A theoretical model for the dynamics of a simple two-phase mixture is presented. A classical averaging approach combined with symmetry arguments is used to derive the mass, momentum, and energy equations for the mixture. The theory accounts for surficial energy at the interface and employs a nonequilibrium equation to relate the rate of work done by surface tension to the rates of both pressure work and viscous deformational work. The resulting equations provide a basic model for compaction with and without surface tension. Moreover, use of the full nonequilibrium surface energy relation allows for isotropic damage, i.e., creation of surface energy through void generation and growth (e.g., microcracking), and thus a continuum description of weakening and shear localization. Applications to compaction, damage, and shear localization are investigated in two companion papers.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000JB900430

A two‐phase model for compaction and damage: 1. General Theory

SUMMARY An always increasing knowledge on material properties as well as a progressively more sophisticated production technology make shape memory alloys (SMA) extremely interesting for the industrial world. At the same time, SMA devices are typically characterized by complex multi-axial stress states as well as non-homogeneous and non-isothermal conditions both in space and time. This aspect suggests the finite element method as a useful tool to help and improve application design and realization. With this aim, we focus on a three-dimensional macroscopic thermo-mechanical model able to reproduce the most significant SMA features (Int. J. Numer. Methods Eng. 2002; 55:1255– 1264), proposing a simple modification of such a model. However, the suggested modification allows the development of a time-discrete solution algorithm, which is more effective and robust than the one previously discussed in the literature. We verify the computational tool ability to simulate realistic mechanical boundary value problems with prescribed temperature dependence, studying three SMA applications: a spring actuator, a selfexpanding stent, a coupling device for vacuum tightness. The effectiveness of the model to solve thermo-mechanical coupled problems will be discussed in a forthcoming work. Copyright 2004 John Wiley & Sons, Ltd.

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A three-dimensional model describing stress-temperature induced solid phase transformations: solution algorithm and boundary value problems

A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented. The coupled thermo-mechanical boundary-value problem under consideration consists of the equilibrium problem for a deformable, inelastic and dissipative solid with the heat conduction problem appended in addition. The variational formulation allows for general dissipative solids, including finite elastic and plastic deformations, non-Newtonian viscosity, rate sensitivity, arbitrary flow and hardening rules, as well as heat conduction. We show that a joint potential function exists such that both the conservation of energy and the balance of linear momentum equations follow as Euler–Lagrange equations. The identification of the joint potential requires a careful distinction between equilibrium and external temperatures, which are equal at equilibrium. The variational framework predicts the fraction of dissipated energy that is converted to heat. A comparison of this prediction and experimental data suggests that α-titanium and Al2024-T conform to the variational framework.

https://hal.archives-ouvertes.fr/hal-01004967/document

A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids

SUMMARY The two-phase theory for compaction and damage proposed by Bercovici et al. (2001a, J. Geophys. Res.,106, 8887‐8906) employs a nonequilibrium relation between interfacial surface energy, pressure and viscous deformation, thereby providing a model for damage (void generation and microcracking) and a continuum description of weakening, failure and shear localization. Here we examine further variations of the model which consider (1) how interfacial surface energy, when averaged over the mixture, appears to be partitioned between phases; (2) how variability in deformational-work partitioning greatly facilitates localization; and (3) how damage and localization are manifested in heat output and bulk energy exchange. Microphysical considerations of molecular bonding and activation energy suggest that the apparent partitioning of surface energy between phases goes as the viscosity of the phases. When such partitioning is used in the two-phase theory, it captures the melt-compaction theory of McKenzie (1984, J. Petrol., 25, 713‐765) exactly, as well as the void-damage theory proposed in a companion paper (Ricard & Bercovici, submitted). Calculations of 1-D shear localization with this variation of the theory still show at least three possible regimes of damage and localization: at low stress is weak localization with diffuse slowly evolving shear bands; at higher stress strong localization with narrow rapidly growing bands exists; and at yet higher shear stress it is possible for the system to undergo broadly distributed damage and no localization. However, the intensity of localization is strongly controlled by the variability of the deformational-work partitioning with dilation rate, represented by the parameter γ .F orγ � 1, extreme localization is allowed, with sharp profiles in porosity (weak zones), nearly discontinuous separation velocities and effectively singular dilation rates. Finally, the bulk heat output is examined for the 1-D system to discern how much deformational work is effectively stored as surface energy. In the high-stress, distributed-damage cases, heat output is reduced as more interfacial surface energy is created. Yet, in either the weak or strong localizing cases, the system always releases surface energy, regardless of the presence of damage or not, and thus slightly more heat is in fact released than energy is input through external work. Moreover, increased levels of damage (represented by the maximum work-partitioning f ∗ ) make the localizing system release surface energy faster as damage enhances phase separation and focusing of the porosity field, thus yielding more rapid loss of net interfacial surface area. However, when cases with different levels of damage are compared at similar stages of development (say, the peak porosity of the localization) it is apparent that increased damage causes smaller relative heat release and retards loss of net interfacial surface energy. The energetics and energy partitioning of this damage and shear-localization model are applied to estimating the energy costs of forming plate boundaries and generating plates from mantle convection.

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Energetics of a two-phase model of lithospheric damage, shear localization and plate-boundary formation

https://hal.archives-ouvertes.fr/hal-03338960/document

O. Maisonneuve

Papers

Plastic and dissipated work and stored energy

Energy balance of thermoelastic martensite transformation under stress

Dissipative and non dissipative phenomena during an elastoplastic deformation process