Thermodynamical Modeling of Elastic-Plastic Damage and Experimental Validation of Damage Potential

Abstract

Formulation of constitutive and damage evolution equations of elastic-plastic damage materials are first discussed. In order to facilitate the description of the experimental damage surface in axialtorsional stress space, Gibbs thermodynamic potential is employed. The damage surface is expressed as a function of the damage conjugate force which is easily related to stress tensor. Then, the resulting equations are applied to the experimental results of the spheroidized graphite cast iron. The change in elastic moduli due to damage development and the initial and the subsequent damage surface expressed in stress space are described well by the proposed theory. Finally, experimental verification of the existence of a damage potential and the corresponding normality law is performed. By noting that the normality law must be discussed in the space of damage conjugate, the direction of the damage rate vector on each loading path is identified from the change in the elastic modulus due to damage. The resulting direction of the damage rate at each loading path coincides sufficiently well with the normal of the damage surface, and hence, the proposed damage surface is certified to be identical to the damage potential.

Implementation of a Model of Coupled Elastic-Plastic Unilateral Damage Material to Finite Element Code

“…It is usually assumed that the negative components of the strain or stress tensors remain inactive as long as the loading conditions again render them active. A more realistic description of damage deactivation allows for an influence of negative principal components of strain and stress tensors for damage evolution, as observed in brittle materials (Hayakawa and Murakami, 1997;Murakami and Kamiya, 1997). These concepts reduce to introduction of the generalized projection operators (Ganczarski et al, 2003) and the modified strain or stress tensors as follows:…”

“…A slightly different approach was proposed by Hayakawa and Murakami (1997), who introduced the Gibbs thermodynamic potential, instead of the usually applied Helmholtz free energy, À , r, D,…”

“…In general, the assumption of existence of damage potential, related to the similar concept of plastic potential, should be validated. Hence Hayakawa and Murakami (1997) performed an experimental verification of the existence of a damage potential and the corresponding normality rule for the spheroidized graphite cast iron. Experiments proved that both existence and normality hold in the space of damage conjugate forces, which are easily related to stresses F d ½YðÞ:…”

“…The basic set of state and evolution equations for elastic-plastic damage material of a moderate ductility is accepted after Hayakawa and Murakami (1997). It is usually assumed that the Helmholtz free energy is used as the state potential.…”

Analysis of Interfacial Damage and Debonding Life Estimation of Cold Forging Tool Coated with Hard Film

“…Next, after introducing a nonlinear interfacial spring model and defining the interfacial damage variable, the constitutive and damage evolution equations at the interface between the hard film and the tool material are formulated under the framework of the irreversible thermodynamic constitutive theory. 8,9,11) To apply the above equations to the numerical analysis of the interface by FEM, the concept of the nonlinear interfacial spring model is employed. 7) On the basis of the calculated results on the deformation behavior of the interface, the probable debonding mechanisms of the present forging tool coated with the hard film are discussed.…”