Investigation of macrocrack propagation along a bimaterial interface in adiabatic dynamic processes as a problem of mesomechanics
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.
R. ABRAHAM, J.E. MARSDEN, T. RATIU, Manifolds, tensor analysis and applications, Springer, Berlin 1988.
A.K. CHAKRABARTI, J.W. SPRETNAK, Instability of plastic flow in the direction of pure shear, Metallurgical Transactions, 6A, 733–747, 1975.
B.D. COLEMAN, W. NOLL, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal., 13, 167–178, 1963.
D.R. CURRAN, L. SEAMAN, D.A. SHOCKEY, Dynamic failure of solids, Physics Reports, 147, 253–388, 1987.
W. DORNOWSKI, Influence of finite deformation on the growth mechanism of microvoids contained in structural metals, Arch. Mechanics, 51, 71–86, 1999.
W. DORNOWSKI, A new integration procedure for thermo-elasto-viscoplasticity, Arch. Mechanics, 54, 389–410, 2002.
W. DORNOWSKI, P. PERZYNA, Constitutive modelling of inelastic solids for plastic flow processes under cyclic dynamic loadings, Transaction of the ASME, J. Eng. Materials and Technology, 121, 210–220, 1999.
W. DORNOWSKI, P. PERZYNA, Localization phenomena in thermo-viscoplastic flow processes under cyclic dynamic loadings, Computer Assisted Mechanics and Engineering Sciences, 7, 117–160, 2000.
W. DORNOWSKI, P. PERZYNA, Localized fracture phenomena in thermo-viscoplastic flow processes under cyclic dynamic loadings, Acta Mechanica, 30, 1–23, 2001.
W. DORNOWSKI, P. PERZYNA, Numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes, Int. J. Solids and Structures, 39, 4949–4977, 2002.
M.K. DUSZEK, P. PERZYNA, The localization of plastic deformation in thermoplastic solids, Int. J. Solids Structures, 27, 1419–1443, 1991.
M.K. DUSZEK-PERZYNA, P. PERZYNA, Analysis of the influence of different effects on criteria for adiabatic shear band localization in inelastic solids, [in:] Material Instabilities: Theory and Applications, ASME Congress, Chicago, 9–11 November 1994, R.C. BATRA and H.M. ZBIB [Eds.], pp. 59–85, AMD–Vol. 183/MD–Vo1.50, ASME, New York, 1994.
P.R. GUDURU, A.J. ROSAKIS, G. RAVICHANDRAN, Dynamic shear bands: an investigation using high speed optical and infrared diagnostic, Mechanics of Materials, 33, 371–402, 2001.
P.R. GUDURU, A.T. ZEHNDER, A.J. ROSAKIS, G. RAVICHANDRAN, Dynamic full field measurements of crack tip temperatures, Engineering Fracture Mechanics, 68, 1535–1556, 2001.
J.N. JOHNSON, Dynamic fracture and spallation in ductile solids, J. Appl. Phys., 52, 2812–2825, 1981.
J. LAMBROS, A. ROSAKIS, Dynamic decohesion of bimaterials: Experimental observations and failure criteria, Int. J. Solids Structures, 32, 2677–2702, 1995.
J. LAMBROS, A. ROSAKIS, Shear dominated transonic interfacial crack growth in a bimaterial — I. Experimental observations, J. Mech. Phys. Solids, 43, 169–188, 1995.
J. LAMBROS, A. ROSAKIS, Shear dominated transonic interfacial crack growth in a bimaterial — II. Asymptotic fields and favorable velocity regimes, J. Mech. Phys. Solids, 43, 189–206, 1995.
T. LODYGOWSK[, P. PERZYNA, Localized fracture of inelastic polycrystalline solids under dynamic loading processes, Int. J. Damage Mechanics, 6, 364–407, 1997.
J.E. MARSDEN, T.J.R. HUGHES, Mathematical Foundations of Elasticity, Prentice—Hall, Englewood Cliffs, New York 1983.
A. NEEDLEMAN, A.J. ROSAKIS, The effect of bound strength and loading rate on the conditions governing the attainment of intersonic crack growth along interfaces, J. Mech. Phys. Solids, 47, 2411–2449, 1999.
J.A. NEMES, J. EFTIS, Constitutive modelling of the dynamic fracture of smooth tensile bars, Int. J. Plasticity, 9, 243–270, 1993.
J. OLDROYD, On the formulation of theological equations of state, Proc. R. Soc. Lond., A200, 523–541, 1950.
P. PERZYNA, The constitutive equations for rate sensitive plastic materials, Quart. Appl. Math., 20, 321–332, 1963.
P. PERZYNA, Fundamental problems in viscoplasticity, Advances in Applied Mechanics, 9, 343–377, 1966.
P. PERZYNA, Thermodynamic theory of viscoplasticity, Advances in Applied Mechanics, 11, 313–354, 1971.
P. PERZYNA, Constitutive modelling of dissipative solids for post-critical behaviour and fracture, ASME J. Eng. Materials and Technology, 106, 410–419, 1984.
P. PERZYNA, Internal state variable description of dynamic fracture of ductile solids, Int. J. Solids Structures, 22, 797–818, 1986.
P. PERZYNA, Constitutive modelling for brittle dynamic fracture in dissipative solids, Arch. Mechanics, 38, 725–738, 1986.
P. PERZYNA, Interactions of elastic-viscoplastic waves and localization phenomena in solids, IUTAM Symposium on Nonlinear Waves in Solids, August 15–20, 1993, Victoria, Canada; J.L. WEGNER and F.R. NORWOOD [Eds.], pp. 114–121, ASME 1995.
P. PERZYNA, A. DRABIK, Description of micro-damage process by porosity parameter for nonlinear viscoplasticity, Arch. Mechanics, 41, 895–908, 1989.
A.J. ROSAKIS, G. RAVICHANDRAN, Dynamic failure mechanics, Int. J. Solids Structures, 37, 331–348, 2000.
A.J. ROSAKIS, 0. SAMUDRALA, D. COKER, Cracks faster than the shear wave speed, California Institute of Technology, SM Report 98–17, December 1998, 1998.
A.J. ROSAKIS, 0. SAMUDRALA, D. COKER, Cracks faster than the shear wave speed, Science, 284, 1337–1340, 1999.
S. SHIMA, M. OYANE, Plasticity for porous solids, Int. J. Mech. Sci., 18, 285–291, 1976.
D.A. SHOCKEY, L. SEAMAN, D.R. CURRAN, The microstatistical fracture mechanics approach to dynamic fracture problem, Int. J. Fracture, 27, 145–157, 1985.
D. SIDEY, L.F. COFFIN, Low-cycle fatigue damage mechanisms at high temperature, [in:] Fatigue Mechanisms, Proc. ASTM STP 675 Symposium, Kansas City, Mo., May 1978, J.T. Fong [Ed.], pp. 528–568, Baltimore 1979.
C. TRUESDELL, W. NOLL, The Non-linear field theories of mechanics, [in:] Handbuch der Physik 111/3, S. FIXJGGE [Ed.], Springer-Verlag, Berlin 1965.
Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland