Theory of Thermal Shock Resistance of Brittle Materials Based on Weibull's Statistical Theory of Strength
Authors: MANSON S. S. , SMITH R. W. 
Published: June 2006

Present theories predicting the resistance of brittle materials to thermal shock are based on the premise that failure occurs on the attainment of a definite critical stress. However, the failure of many brittle materials has been shown to be dependent upon stress distribution within the body rather than upon the maximum stress criteria. Weibull's statistical theory of strength which accounts for this behavior is adapted to predict the strength of the circular disks of brittle materials subjected to peripheral thermal shock. This analysis shows, for those materials in which tensile strength differs appreciably from the bending strength, that considerable error can be introduced by the use of the conventional maximum stress theory of fracture when predicting thermal shock resistance over a wide range of quenching severities. Experimental thermal shock data for steatite are analyzed to show procedures for applying the theory.

In most analyses of the behavior of brittle materials under conditions of thermal shock, use is made of the maximum stress criterion of fracture. It has been demonstrated, however, that many brittle materials do not obey this criterion, and that stress distribution frequently affects the stress at which fracture occurs. For this reason the bending strength of many brittle materials is frequently twice as high as the tensile strength. Weibull has developed a statistical theory of strength to account for this behavior. In the present report use is made of the concepts of Weibull to predict the behavior of circular disks of brittle materials subjected to peripheral thermal shock.

It is found that fracture most probably occurs not at the time when the surface stress is a maximum, but at a later time when the surface stress has fallen somewhat, but a greater volume of material in the interior of the disk has been brought up to moderate stress level. Utilizing the “risk of rupture” concept introduced by Weibull, a general relation is established for relating the conditions of fracture under varying degrees of quenching severity.

The analysis indicates that for materials having low material homogeneity factors, m (or materials in which the tensile strength differs appreciably from the bending strength) considerable error can be introduced by the use of the conventional maximum stress theory of fracture to relate the fracture conditions under mild and severe quenchings. Errors as high as 30% can be expected in some practical cases. It is also suggested how thermal shock data can be used to evaluate the material constant m.

Analysis of limited data on the thermal shock characteristics of steatite disks indicated that for this material the experimentally determined value of m was high enough to obscure possible small discrepancies arising from the use of the maximum stress theory of fracture. The value of m as deduced from the thermal shock tests was in very good agreement with the value determined from a statistical study of the bending strengths of twelve small specimens. More data on a variety of materials would, however, be desirable for a full evaluation of the proposed theory, particularly for cases involving low values of m for which the largest discrepancies arise.