Transformation, microcrack,and thermal residual stress as interactive processes in ZrO 2 -Toughened Al 2 O 3 , Simulated
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I.
INTRODUCTION
IMPROVEMENT of fracture toughness in ceramic materials with ZrO2 as the second phase has been studied extensively in the past. L'-~3t The stress concentration around the tip of a crack induces an allotropic transformation of the ZrO2 particles from their tetragonal to their monoclinic crystal structure. This transformation results in a shear strain of about 16 pct and a dilatation of 3 to 5 pct when the particle is unconstrained. However, for a particle embedded in an elastic matrix, the shear in successive twin bands alternates in direction, resulting in a significant reduction of the shear strain, and hence, it has only short range effect. On the other hand, the dilatant strain is still 3 to 5 pct on the average over the particle. Budiansky e t a l . t'4~ neglected any shear effect and considered the case in which the transforming particles were allowed to undergo only a volumetric strain. Their results are independent of particle shape, and they further showed that for a stationary crack under monotonically increasing loading, there is no toughness enhancement. The same conclusion (under a more restrictive assumption) was reached by McMeeking and Evans.t~sl Lambropulous[,6] analyzed the effects of shear, shape, and orientation of the transforming particles and showed that consideration of shear effects brings predicted values of toughness increment in good agreement with experimental results when ZrO2 particles are spherical. The agreement is not as good when oblate spheroidal particles are considered. Transformation in ceramics is frequently accompanied by microcracking. The associated microcrack-induced LI ZHONGHUA, Professor, and ZHAO YONG, Graduate Student, are with the Department of Engineering Mechanics, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China. S. SCHMAUDER, Doctor, is with the Max-Planck-lnstitut FiJr Metallforschung, D-70174, Stuttgart, Germany. Manuscript submitted June 29, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS A
strain can enhance the effect of the transformation dilatation and hence can be an alternative source of toughness. tl~ Furthermore, the reduction in the elastic modulus due to microcracking, t~9,z~ deflection of the main crack by the transformed particles, and presence of microcracks may also contribute to the toughness. It is apparent that these toughening mechanisms are not independent of each other. The dilatation induced by the transformation and microcracking is the principle source of toughening. The continuum mechanics model treated the transformed zone around a crack as a continuum dilatant particle in an infinitely large matrix. This model was later extended by Evans and Faber t221 to microcracking materials. For steady state supercritical condition, t23,24'25j the toughening increments due to transformation and microcracking dilatation both predict relationships of the form A K = rlEe~,h 1/2
[1]
where e~ is the overall irreversible volume strain due to transformation or microcracking, h the size of the transformation or microc
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