Effective dilatational transformation toughening in brittle materials

Abstract

The toughness of brittle materials can be increased significantly by martensitic phase transformation in which the transformable particles near the crack tip region undergo a stress-indueed transformation with a positive volume change. The mechanics of transformation toughening has been the subject of numerous studies. Earliest models of transformation toughening were based upon energy changes associated with transforation. McMeeking and Evans pointed out that there were difficulties with these earlier models when compared with experimental results and in some cases the models provided conflicting predictions of the role of microstructure, temperature, etc. on the toughness. An alternative approach, based upon the reduction in the crack-tip stress intensity factor, was first devised with the objective to provide an unequivocal basis for comparison with experimental results. The steady state dilatational transformation toughening is given in terms of the reduction in the mode I crack tip stress intensity factor: Δ K = - 0.66 Ω V_p √h (E/[2(1-ν^2)] (1) where Ω is the plane strain transformation area dilatation, V_p is the volume fraction of the transformed particles in the transformation zone, h is the transformation zone height, E and ν are the Young's modulus and Poisson's ratio. This result was derived assuming a zone shape of a hydrostatic contour. The effective transformation toughening also depends the relative elastic moduli of the transforming particle and nontransforming matrix phases. For a matrix phase of a given elastic modulus, rigid transforming particles are more effective in toughening than compliant panicles. The effect of elastic mismatch may not be important in pure zirconia ceramics containing precipitates of tetragonal ZrO_2 where the mismatch is low. However, the effect can be substantial in ZrO_2-containing composites. Therefore, the intent of the present work is to extend McMeeking and Evans' model for transformation toughening to include the effect of elastic mismatch between the particle and matrix phases. Elastic mismatch can also affect the stress intensity due to the elastic interaction between near tip stress field and the particles, but this component will not be considered here. Instead, we shall concentrate on the effect which results from the dependence of effective transformation strain on elastic mismatch.

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