ANALYSIS of the deformation field consistent with a Prandtl stress distribution travelling with an advancing plane-strain crack reveals the functional form of the near tip crack profile in an elastic-plastic solid. The crack opening 6 is shown to have the form 6 N r In (const./r) at a distance r from the tip. This observation coupled with data generated from finite element investigations of growing cracks in small-scale yielding permits the construction of a relation characterizing the deformation at an extending crack tip. A ductile crack-growth criterion consisting of the attainment of a critical opening at a small characteristic material distance from the tip is adopted. Predictions of the stability of a growing crack for both small-scale yielding specimens and those subject to general yielding are discussed.

The paper reviews recent work on fundamentals of elastic-plastic finite-element analysis and its applications to the mechanics of crack opening and growth in ductile solids. The presentation begins with a precise formu~tion of incremental equilibrium equations and their finite-element forms in a marines valid for deformations of arbitrary magnitude. Special features of computational procedures are outlined for accuracy in view of the near-incompressibility of elastic-plastic response. Applications to crack mechanics include the analysis of large plastic deformations at a progressively opening crack tip, the determination of J integral values and of limitations to I characterizations of the intensity of the crack tip field, and the determination of crack tip fields in stable crack growth.

Although the anti-plane strain case is of minor practical value in engineering applications, such an idealization facilitates mathematical investigations of strain and displacement fields accompanying extending cracks. This paper presents finite element solutions to anti-plane strain crack propagation problems and contrasts the numerical results with available analytic solutions in an effort to assess the accuracy of the numerical procedures. The nature of dominant strain singularities for stationary and moving cracks, the question of stable versus unstable or catastrophic crack growth and the implications of various proposed fracture criteria are discussed.