An analytical model is presented to predict the temperature field induced in a fractured solid by mechanical loadings. The heat conduction equation used to compute the temperature field consists of three separate terms that account for the coupling effects. These are the thermoelastic, thermoplastic and thermofracture coupling terms. Finite element formulations were used for the numerical solutions of a case study. This case study involved experimental assessments of temperature rises near the tip of a stationary crack when subjected to an impact load that attempted to open the crack surfaces. Good correlations of analytical and experimental results were obtained. The measurable temperature rises in a fractured solid suggested that the coupling effect may be significant enough to influence the fracture characteristics of a solid; in particular, if the bulk temperature of the solid is close to the transition temperature from the brittle to ductile fracture mode or vice versa. Nomenclature a = thermal diffusivity bi = the ith component of body force B,, = partial differential operator matrix = crack growth rate C = the generalized damping matrix C~ = elasticity matrix Cep = elasto-plasticity matrix Cp = plasticity matrix CTT = the heat capacity matrix CTu = the thermomechanics coupling matrix Cv = specific heat at constant strain d = the generalized displacement vector D = plastic dissipation term, = (1 -A)a~j ~j D = the plastic dissipation matrix f = the generalized force vector G = the Irwin strain energy release rate, or shear modulus in Eqn. (a26) H' = material stiffness that is defined to be the slope of the flow curve of a material in the plastic region J = the Rice path-independent contour integral k = thermal conductivity k = thermal conductivity matrix K = the generalized damping matrix K~,u = the mechanical stiffness matrix KuT = the thermal coefficient matrix KTT = the conductivity matrix L~, = the mechanical load matrix M = the generalized mass matrix 68 N.S. Sun and T.R. Hsu Muu --the mass matrix Q : the thermal load matrix q = the surface heat flux matrix Qf : the crack growth dissipation matrix QT = the generalized force vector t = time T = temperature vector % = reference temperature u = x-displacement vector v = y-displacement vector Greek characters c~ = thermal expansion coefficient in (a23,a28), or the integral parameter in (a29) to (a39) flij = the thermal modulus tensor = the generalized thermal modulus matrix '7 = the reversible separation work of fracture surfaces in (3) "7 = the generalized thermal modulus matrix 5' = the thermal capacity created by coupling effect = the Dirac function in (3), or the integral parameter algorithm in (a29) to (a39) 0 = the parameter of collocation scheme of time integration algorithm in (a29) to (a39) A = the plastic dissipation parameter ~ij = the strain tensor O'ij = the stress tensor
