P.M. Kelly, L.R. Francis Rose/ Progress in Materials Science 47(2002)463-557 effective or Von mises stress critical mean stress- criterion for stress-induced transformation longitudinal strain in uniaxial test-see Eq (4.13b) 1. Introduction I.I. What is transformation toughening? In simple terms, transformation toughening is the increase in fracture toughness of a material that is the direct result of a phase transformation occurring at the tip of an advancing crack. There are a number of essential requirements for successful transformation toughening [1-3]. First, there must be a metastable phase present in the material and the transformation of this phase to a more stable state must be capable of being stress-induced in the crack-tip stress field. Second, the transforma- tion must be virtually instantaneous and not require time-dependent processes such as long-range diffusion. Third, it must be associated with a change of shape and/ volume. It is this latter feature the deviatoric character of the transformation that allows it to be stress-induced. It also provides the source of the toughening because the work done by the interaction of the crack-tip stresses and the transfor mation strains dissipates a portion of the energy that would normally be available for crack extension. An alternative, but essentially equivalent, way of regarding the toughening process is as a form of crack shielding, where the transformation strains generate local stresses that oppose further crack opening. Finally, to ensure that there is a net increase in toughness of the material, the transformed product must not be significantly more brittle than the parent phase from which it forms. This was a problem in early work on TRIP(transformation induced plasticity) steels, because the initial material was relatively tough and the stress-induced transformation pro- duced a more brittle phase around the advancing crack [4]. The benefit of transfor mation toughening was effectively compensated by the intrinsic brittleness of the product phase and in some steels there was little net toughening. In transformation toughened ceramics, which emerged nearly a decade later, the starting material was just as brittle as the transformed product phase. So, in this case, a positive, net transformation toughening was observed The essence of transformation toughening can be illustrated in Fig. 1. Under an applied load stress-induced transformation occurs at the crack tip and produces a transformation zone of height 2h. In most of the mechanistic models of transfor- mation toughening this initial process zone at the tip of a stationary crack [Fig. 1(a) has no net effect on the toughness of the material. However, as the crack grows, a wake'of transformed material is left behind [Fig. I(b). It is the strains remaining in this wake of transformed material that lead to an increase in toughness note that the primarily deviatoric strain responsible for 'triggering ' the transformation in the     <-<- 9        = , $                            $          $     
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