Flaw sensitivity of stochastic elastic materials

A material-specific length, called the flaw sensitivity length or fractocohesive length, is determined by measuring the strength of samples that contain cracks of various lengths. When the crack length is small compared with the fractocohesive length, the strength is unaffected by the crack. When the crack length is large compared with the fractocohesive length, the strength reduces as the crack length increases. Here we study how the fractocohesive length is affected by the stochastics of the constituents of a material. We simulate a model system, a truss in which the constituents are linearly elastic members forming a geometrically periodic lattice. The stochastics are represented by the scatter of strength among the members. The fractocohesive length scales with the length of each individual member, but the prefactor increases with the degree of scatter in member strength. The fractocohesive length can be much larger than the constituents of a material when the constituents have pronounced statistical variation.