ELASTIC/PLASTIC SEPARATION ENERGY RATE FOR CRACK ADVANCE IN FINITE GROWTH STEPS

A Griffith-type energy balance for crack growth leads to paradoxical results for solids that are modelled as elastic/plastic continua, since such solids provide no energy surplus in continuous crack advance to equate to a work of separation [1]. An alternative proposed recently is that the finite size of the fracture process zone be taken into account, and a simple way of doing this is to define a crack tip energy release rate Gδ based on the work of quasi-static removal of stresses from the prospective crack surfaces over a finite crack growth step δa [2]. Recent finite element results for energy releases during crack growth are reviewed in this way and an analytical solution, based on the Dugdale-Bilby-Cottrell-Swinden (DBCS) crack model, is developed for Gδ when δ a is small compared to plastic zone size. This solution and the finite element results are in remarkably good agreement and, based on the analytical solution, we develop the asymptotic formula for the value of the J integral required for crack growth, J = .70 ζ exp(.43/ζ) Gδ, with ζ = (1-v2)σy 2δa/EGδ, and this formula is valid whenever ζ is smaller than, approximatley, 0.15; σy is the yield stress. A defect of the DBCS model, however, is that unlike the finite element results, it makes no distinction between the criterion for onset of growth and that for continuing growth in the case of highly ductile solids.