Abstract
The present investigation concerns the effect of various possible laws that control transformation of certain multiphase ceramics based on the solution of axisymmetrically deforming thick ring configurations. Stress induced transformation plays a dominant role in toughening, and hence in the strength and fatigue properties of transforming ceramics. The particular transformation law, assumed to hold for multi-axial deformation, affects directly the toughening via the different extent and properties of the process zone developed around macro crack-tips. Phase transformation varies considerably in different microstructures, leading to differences in the macroscopic inelasticity of their stress-strain behavior. It is therefore necessary to develop well controlled multi-axial tests, independently of fracture tests, in order to investigate various propositions for the multi-axial transformation of ceramics. The thick ring configuration under axisymmetric load offers great advantages in experimental, analytical, and numerical assessment of different theories on stress induced transformation. In the present work, some non-linear ring problems were solved exactly accounting for a wide range of transformation laws, and especially for those mostly used in transformation toughening analysis. The exact formulae produced here show that the stress and strain fields in the ring differ considerably with each model. The validity of the various assumptions used in the present analysis stems from well documented micromechanisms reported in experimental papers. The analytic character of the solutions, if combined with experiments, may enable also quantitative predictions of the essential material parameters involved in the modelling of transforming ceramics.
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