Finding the J-integral for a Crack-Like Defect of a Solid in the Form of a Physical Section in Finite Element Representation

A crack-like defect in the form of a physical section with a characteristic thickness in a linearly elastic medium is studied. The thickness of the physical section is considered as a linear parameter. For an external load, the stress-strain state of the neighborhood of the physical section is determined by the finite element method, allowing stress vectors on the free surface to be different from zero. On the basis of the thermomechanical relation, the energy characteristic of the J-integral type, including stress vectors on the free surface in the vicinity of the crack-like defect, is determined in the form of three additive integral summands. The part of the energy characteristic on the end surface of the physical section and the summands on the shores contiguous to the end are isolated. We solved the loading problems of applying normal rupture and transverse shear to the physical section based on the solution in the finite element complex ANSYS for the physical section and the model of representation of the medium on the continuation of the physical section as a layer, which is homogeneous in the thickness distribution of the stress-strain state. We compared the energy response, when the linear parameter tends to zero value, and the values of the J-integral for the crack representation in the form of a mathematical section. The correspondence of the J-integral value for the mathematical section to the considered energy characteristic at a relatively small value of the linear parameter is obtained. At the same time, its part on the end surface, depending on the model under consideration, is more than sixty per cent. For the physical section using the layer model, the closeness of the investigated characteristic to the value of the J-integral for the mathematical section is shown at a significantly lower value of the elastic modulus of the layer material with respect to the basic medium. At the same time, the influence of non-face summands of the energy characteristic is found to decrease.