Yuping Wang (yxw43@po.cwru.edu)

and

Roberto Ballarini (rxb7@pop.cwru.edu)

Department of Civil Engineering

Case Western Reserve University

Cleveland, Ohio 44106-7201

The mechanical behavior of polycrystalline films depends on the properties of the grain boundaries. In the case of cracked films with relatively compliant grain boundaries, such as S1 freshwater ice (typically composed of large grains with predominantly vertical c-axes), it’s been experimentally observed that the effective fracture toughness depends strongly on specimen size. Qualitative and quantitative understanding of this size effect is necessary if one is to predict, using laboratory size specimens, maximum forces acting on a structure subjected to an ice flow.

Previous theoretical results have shown that the size effect in cracked polycrystalline films with comprised of grains that are perfectly bonded (no interfacial region) is weak. The present work is aimed at determining, as functions of the relative stiffness of the grain boundary, the number of grains required to produce stationary stress fields ahead of the crack. It is expected that this number is within the range of 100-1000.

A Poisson-Voronoi tessellation is used to construct the microstructure within a unit two-dimensional region containing a crack. For simplicity, but without loss of generality, the grains are assumed isotropic. The grain boundaries are constructed by shrinking the grains. Two cases are considered; (1) grain boundaries with much smaller shear modulus than the grain (to simulate sliding along the interfaces); b) grain boundaries with much smaller bulk modulus than that of the grain (to simulate void growth along the interfaces). The region is next discretized using finite elements, and the program ABAQUS is used to solve the elasticity boundary value problem. Results are presented for the stress fields ahead of the crack, as functions of grain boundary stiffness. These are compared with references distributions associated with the homogenized cracked continuum.