Model analysis of boundary residual stress and its effect on toughness in thin boundary layered yttria-stabilized tetrag
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The average thermal residual stress in a continuous boundary phase in polycrystalline ceramic composites was calculated with a simple thin boundary layer model, and a criterion for the self-cracking of the boundary phase was derived under a certain assumption. From the proposed model, the toughness of the materials can be increased by both tensile and compressive stress at boundaries when the crack propagates transgranularly. The toughness will be increased when the stress at boundary is compressive for intergranular fracture mode. The maximum increase is predicted to be achieved at boundary phase contents below 33%. The experimental results for yttria-stabilized tetragonal zirconia polycrystalline ceramics doped with different kinds of grain-boundary phase is in a qualitative agreement with the prediction by the model, but the toughness increase is largely dependent on the distribution feature of glass phases.
I. INTRODUCTION
During cooling of ceramics from the temperature at which they were sintered, the grain size decreases at a rate according to its expansion (or more accurately, shrinkage) coefficients. However, as recognized widely by materials researchers, there will be residual stress at grain boundaries and between different phases if there is a difference in the shrinkage rates between grains and/or between phases. Residual stress for the different shrinkage rates has been calculated by a very simplified model, e.g., one particle in infinite uniform matrix model.1 Recently the residual stress distribution for some more complicated systems was calculated on the basis of particulate composites, which were developed from the ideal particle-in-infinite matrix model; however, the calculation is very complicated.2 The estimation of stress and the effect of residual stress on the toughness of the composites has been made for particulate composites in which particulate is dispersed homogeneously in the matrix. Toughness increase of the various composite materials, including particulate,3–6 whisker7,9 and fiber10,11reinforced material systems, has been observed extensively. The toughness increase has been attributed to several mechanisms such as crack bowing,12 crack deflections,9,13,14 bridging and pull-out9,11 of whiskers, fibers, or elongated grains behind the crack tip, and so on. Estimations of the contribution of various mechaJ. Mater. Res., Vol. 15, No. 3, Mar 2000
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nisms to the toughening effect of the composites were attempted.5,9,11 Most of these effects are associated with boundary stress.2 For example, crack deflection is caused by the stress field around second-phase particles for particulate composites, the toughening effect is partially caused by friction force acting on fibers or whiskers for fiber- and/or whisker-reinforced composites, which is also a result of residual stress. In spite of this, the contributions of these mechanisms, like crack deflection, to the toughness increase do not account for the total increase in the toughness of par
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