Engineering Transactions, 54, 4, pp. 289–321, 2006

Investigation of macrocrack propagation along a bimaterial interface in adiabatic dynamic processes as a problem of mesomechanics

W. Dornowski
Polish Academy of Sciences
Poland

P. Perzyna
Polish Academy of Sciences
Poland

The main objective of the present paper is the investigation of macrocrack propagation along a bimaterial interface in adiabatic dynamic processes. The investigation has been generated by very recent experimental observation (cf. Rosakis, Samudrala and Coker [34], Guduru, Rosakis and Ravichandran [13], Guduru, Zehnder, Rosakis and Ravichandran [14]).
A general constitutive model of elastic-viscoplastic damaged polycrystalline solids has been developed within the thermodynamic framework of the rate-type covariance material structure with a finite set of internal state variables. This set of internal state variables will be assumed and interpreted so that the theory developed has been taken into account the effects as follows: (i) plastic non-normality; (ii) softening generated by microdamage mechanisms; (iii) thermomechanical coupling (thermal plastic softening and thermal expansion); (iv) strain-rate sensitivity. It is noteworthy to stress that viscosity introduces implicitly a length-scale parameter into the dynamical initial boundary value problem.
In order to describe in a constitutive model all the previously mentioned properties and incorporate their respective effects, it is intended to introduce a particular set of internal state variables, which consists of the equivalent inelastic deformation and volume fraction porosity. The equivalent inelastic deformation can describe the dissipation effects generated by viscoplastic flow phenomena and the volume fraction porosity takes into account the microdamage evolution effects. The kinetics of microdamage plays a very important role in this constitutive model. Fracture criterion based on the evolution of microdamage is assumed. The relaxation time is viewed either as a microstructural parameter to be determined from experimental observations, or as a mathematical regularization parameter. By assuming that the relaxation time tends to zero, the rate-independent elastic-plastic response can be obtained. The identification procedure is developed basing on the experimental observa¬tions.
We consider isothermal and adiabatic processes in the thin flat specimen made of two identical elements (material A) and the cohesive band (material B). The width of the cohesive band is 1 Rm, so it is a mesoscale size range. In this cohesive band the initial notch is localized symmetrically. It is assumed that the boundary conditions are modelled by the speed of the upper edge of the specimen, while the lower edge is clamped. The initial conditions of the problem are homogeneous. Both materials of the specimen are modelled as elastic-viscoplastic.
A two-dimensional, plane stress, finite-difference model of the entire specimen is applied. The numerical algorithm satisfies the material objectivity, i.e. is invariant with respect to any diffeomorphism (any motion).
Particular attention is focused on the investigation of interaction of stress waves on the propagation of macrocrack within the interface band. The macrocrack-tip speed history and the evolution of the transient macrocrack-tip temperature fields are obtained.
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