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

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.

/pdf/energetics-of-a-two-phase-model-of-lithospheric-damage-shear-2stuaw4876.pdf

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

An improved calibration method for infrared radiometers is developed that has been shown to increase the accuracy of temperature measurement. To validate this new calibration technique, high strain rate compression tests are performed on the aluminum alloy BS 2011 and high strain rate torsion tests are performed on the titanium alloy 90% Ti-6%Al-4%V. The adiabatic temperature rise that occurs during these tests is measured using an infrared radiometer and validated, in the case of the compression tests, using fast response thermocouples. The proportion of plastic work converted to heat, β, is found to increase with plastic strain for both materials, which is similar to previous research. These results challenge the classical assumption that β has a constant value of approximately 0.95.

Determination of the plastic work converted to heat using radiometry

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

Plastic and dissipated work and stored energy

La connaissance des phenomenes dissipatifs et non dissipatifs associes aux processus quasi-statiques de deformation, represente un atout supplementaire important pour l'elaboration de loi thermomecanique de comportement. On decrit, ici, un dispositif experimental, utilisant les techniques de thermographie infrarouge, et permettant d'observer les phenomenes thermiques et energetiques durant la deformation d'un echantillon en traction simple. Apres avoir rappele la definition du bilan energatique, dans le cas de materiaux elasto-plastiques, on relie la dissipation et l'energie interne bloquee durant l'ecrouissage, aux variables d'etat. La puissance mecanique dissipee est evaluee continument durant l'essai. On utilise pour cela, les images thermiques fournies par la camera infra-rouge. On presente le dispositif experimental, puis successivement, on decrit le modele physique permettant de relier l'energie dissipee aux cartes de temperature de surface ainsi que le protocole d'etalonnage. En fin d'article, on presente quelques resultats obtenus avec plusieurs materiaux et on evoque rapidement leur incidence sur la forme des lois de comportement.

https://hal.archives-ouvertes.fr/jpa-00246044/document

J.-C. Chezeaux

Papers

Plastic and dissipated work and stored energy

Analyse thermomécanique des lois de comportement par thermographie infrarouge