For some time now the elastic T-term has been proposed as a secondary "biaxiality" parameter, to be used in conjunction with the stress intensity factor, K1, or the path independent integral J, as the primary parameter for the characterization of crack tip fracture states. At a recent conference a theorem due to Eshelby was presented [1]. The theorem provides a convenient method of calculating the T-term, obtained by evaluating appropriate J contour integrals. Examples of analytical, semi-analytical and numerical applications were included. Here, some additional finite element applications, using a fairly simple idealization, are presented in greater detail and comparisons of the results of the different independent analyses available so far are made, giving further evidence of the practical utility of Eshelby's method. New results on double-edge notched specimens are also included.

SYNOPSIS The application of Griffith energy concepts to Elastic-Plastic Fracture Mechanics (EPFM) is investigated. An elastic-plastic finite element program is used to calculate the values of the Crack Separation Energy Rate, GΔ, corresponding to a variety of biaxial stress-strain states. The effect of the size of the crack tip plastic zone on the fracture stress is investigated and a relation is established between two non-dimensional parameters φ and ψ . The first parameter φ gives a measure of the ductility of the material while the second parameter ψ is related to the applied stress when brittle fracture occurs. The character of the φ, ψ dependence suggests that when a certain value of the ductility parameter φ is exceeded, brittle crack growth is no longer possible and the mode of crack extension must change to one of a ductile nature. The theoretical predictions of fracture toughness are favourably compared with the results of experiments. Calculated values of GΔ, the stress intensity factor, K, and Rice's path independent integral J are also compared and the applicability of these parameters to brittle, quasi-brittle and ductile fracture is critically discussed.

No abstract

A square plate containing a central crack and subjected to biaxial stresses has been studied by a finite element analysis. An elastic analysis shows that the crack opening displacement and stress of separation ahead of the crack tip are not affected by the mode of biaxial loading and therefore the stress intensity factor adequately describes the crack tip states in an elastic continuum.An elastic-plastic analysis involving more than localized yielding at the crack tip provides different solutions of crack tip stress fields and crack face displacements for the different modes of biaxial loading.The equi-biaxial loading mode causes the greatest separation stress but the smallest plastic shear ear and crack displacement. The shear loading system induces the maximum size of shear ear and crack displacement but the smallest value of crack tip separation stress.

No abstract