Thermomechanics of brittle fracture

Abstract

On the basis of the thermodynamics of thermoelastic deformation we propose an energy condition of the Griffith type for brittle fracture of solids under single loading. An analysis is given of the proposed condition under the plane stressed (strained) state for the two known models of an isolated defect. In the first model, stresses on the external (distant) surface of a solid with a defect are prescribed the same as in a similar solid without a defect. In the second model, displacements are prescribed on the external surface of a solid with a defect, which correspond to the load applied to the solid, but before the defect or crack was formed. Stresses on the surface of the defect in both models are equal to zero. It is shown that the first model in the isothermal case of deformation leads to the Griffith condition. The second model meets the energy condition of the Griffith type from which, under additional assumptions concerning the shape of the defect, and from conditions of isotropy and convexity, we obtain a curve of fracture (macroscopic criterion of fracture) in an ellipse form in the space of principal stresses. The orientation of the crack was determined. Coefficients of the curve of fracture obviously depend upon elastic constants, temperature, linear coefficient of thermal expansion and crack dimensions.