Crack Growth Resistance Toughening

The crack growth resistance, as a function of crack extension, may be expressed as follows  

Solving these relationships, however, is challenging and requires an iterative process. 

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Transformation toughening increases the crack-growth resistance by producing compressive residual stresses in the material during crack propagation. These are caused by stress-induced phase transformations, described in section 7.2.4. To achieve this, particles are added to the matrix that perform a phase transformation that results in a larger volume of the particles when a sufficient tensile stress is applied. 

De Aza, A. H., Chevalier, J., Fantozzi, G., Schehl, M. Tomecillas, R. (2002). Crack growth resistance of alumina, zirconia and zirconia toughened alnmina ceramics for joint prostheses. Biomaterials 23, 937-945. 

Chapters 8 and 9 consider the mechanical properties of rubber- and ceramic-particle toughened-epoxy materials. The importance of rubber cavitation is highlighted in Chapter 8. It is well known that this mechanism can relieve the high degree of triaxiality at a crack tip in the material and enable subsequent plastic hole growth of the epoxy resin, which is a major toughening mechanism. We return to rigid particles in Chapter 9, which examines their use to increase the thermal shock resistance of epoxy resins. 

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