The effect of crack growth stability induced by residual compressive stresses on strength variability
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Rising T- (or R-) curve behavior is increasingly being used in order to improve the mechanical reliability of ceramic materials. In this study, the possibility of inducing such behavior using residual compressive stresses is analyzed. The T-curves obtained for certain residual stress profiles induce crack stability when the stress minima (compressive stress maxima) lie away from the surface of the sample. The consequences of this stabilization on the strength characteristics are a significant reduction in the strength variability and strength insensitivity to the initial flaw size. In addition to these desirable features, considerable strengthening is also obtained. Hence, suitably engineered compressive stress profiles are shown to be a novel and alternative means of enhancing mechanical reliability. I. INTRODUCTION A state of strain in a body that persists in the absence of an externally applied force gives rise to residual stresses. Macroscopic residual stresses may arise when two dissimilar bodies are bonded to each other at elevated temperature (as in the case of a film to a substrate with different thermal properties), or when the molar volume of a certain section of the material is altered by physical or chemical processes. Tempering1 and ion-implantation2 serve as examples of physical processes, and ion-exchange3 as that for a chemical process for inducing residual stresses in glasses and ceramics. In some cases, the presence of residual stresses has a deleterious effect on the performance of the material. Residual stresses may lead to film-substrate decohesion4 and static fatigue failures.5 However, since most glasses and ceramics fail from surface flaws, the introduction of residual surface compression has served as a useful means of strengthening. Indeed, tempering and ionexchange (or ion-implantation) treatments for glasses and ceramics1'3'6'7 have been extensively studied. The introduction of surface compression is currently regarded not only as a means of strengthening but as also having potential to improve the wear7 and contact damage resistance characteristics.8 The brittle fracture behavior of glasses and ceramics at low temperatures makes the strength of these materials strongly dependent on the size and location of stress concentrating flaws. In ceramics, pores, agglomerates, and second phase inclusions often act as fracture initiating volume flaws. In glasses, surface flaws formed during contact damage invariably cause failure. Large variations in the size of such flaws may lead to wide strength distributions, thereby necessitating the use of J. Mater. Res., Vol. 7, No. 3, Mar 1992 http://journals.cambridge.org
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statistical procedures in the design process. The potential of surface compression as a strengthening mechanism has led to studies that have examined its effect on strength variability.9"11 Some of the results from Ref. 10 are shown in Fig. 1 where the failure probability as a function of failure stress is plotted for a set of ionexchanged glass rods. The ion-ex
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