Some Characteristics of a Propagating Brittle Tensile Crack

A numerical technique was used to formulate the two-dimensional equations of motion for an elastic continuum. A brittle tensile crack was simulated to form and propagate in the continuum. The stress field in front of the fracture tip was found to become increasingly hydrostatic with increasing fracture velocity. A fracture criterion in terms of the values of the principal stresses near the fracture tip indicated a terminal velocity for a straight running fracture of approximately 0.39 of the dilatational wave speed. Part of the elastic energy residing initially in the continuum accumulated at the fracture tip. A quantitative fit of the excess elastic energy as a function of crack half length and velocity showed that excess energy at the fracture tip increases as the square of fracture length and decreases with fracture velocity.