Question

1. How would you expect a flaw to affect the mechanical properties of brittle materials?

Answer 1

Let’s take as our flaw a crack of length a (or 2a depending on the scenario) in a brittle material. The resulting fracture stress in tension, σf, is

where KIc is the fracture toughness of the material and W is a characteristic dimension of the test specimen, often its width. The factor f(a/W) is thus some function of the crack size relative to specimen size and changes with crack shape. As an example, consider the figure below depicting a sample of width W with an edge crack of length a subjected to a farfield stress σ. For this case f(a/W) is

From Eq. (3) it’s evident the fracture stress depends intimately on the dimensions of the crack. Furthermore, Eq. (3) pertains just to the specific instance of uniaxial tensile stress for the particular crack type shown. For if the loading were shear rather than tensile or the crack located in the middle of the sample instead of at its edge, the f(a/W) factor would be different. In fact, there are handbooks[3][4] tabulating such f(a/W) factors for many different crack geometries, specimen dimensions, and loading configurations. Hence, to answer the question, the sizes and shapes of defects exert a profound influence upon fracture of brittle materials with fracture strengths reducing for larger cracks. Moreover, as a concession to the inevitability of cracks, in many situations versions of Eq. (3) are used to specify for structures maximum allowable crack sizes that still maintain tensile strengths exceeding expected environmental loads.