Transformation toughening

Two approaches are taken to determine the contribution of a stress-induced phase transformation to the fracture toughness of a brittle material. Both approaches result in an expression for the critical stress intensity factor,K_c, of whereK₀ is the critical stress intensity for the material without the transformation phenomenon, (¦ΔG^c¦−U_sef) is the work done per unit volume by the stress field to induce the transformation,E_c andν_c are the elastic properties,V_i is the volume-fraction of retained, high-temperature phase andR is the size of the transformation zone associated with the crack. It is assumed that only those inclusions (or grains) close to the free surface of the crack will contribute to the fracture toughness; thus,R the inclusion size. The chemical free-energy change associated with the transformation, ¦ΔG^c¦, will govern the temperature and alloying dependence of the fracture toughness.