The mechanics of transformation toughening

Abstract

Two basic problems in the theory of transformation toughening are discussed, by using a continuous distribution of strain centres to represent the inelastic strain due to stress-induced transformation. First, it is shown that the two approaches which can be used to account for transformation toughening, based on energy and on residual stress considerations, do not in general lead to equivalent measures of toughness. An expression for the crack-extension force is derived that distinguishes the contribution dependent on the external load from that due to the change in the configuration of strain centres representing the transformed zone. This distinction has direct implications for correlating the theoretical crack-extension force with the specific work of fracture which is measured experimentally. Secondly, an estimate is derived for the steady-state zone size, which takes into account the image stress associated with the transformed zone due to the proximity of traction-free crack faces. This shows that the zone size, and hence the steady-state toughness, should reach a maximum when the critical stress has a definite non-zero value, rather than when this critical stress tends to zero, as it had been implicitly assumed previously. An expression is derived that indicates qualitatively the effect of finite specimen dimensions, when the only relevant dimension is the unbroken ligament ahead of the crack. It is noted that the highest toughness which has been obtained in practice falls far below the theoretical limit. A possible explanation for this discrepancy is proposed that suggests a microstructural influence on the fracture process and thereby on the maximum toughening which can be derived from stress-induced transformation.