Breakdown of disordered media by surface loads.
We model an interface layer connecting two parts of a solid body by N parallel elastic springs connecting two rigid blocks. We load the system by a shear force acting on the top side. The springs have equal stiffness but are ruptured randomly when the load reaches a critical value. For the considered system, we calculate the shear modulus G as a function of the order parameter phi describing the state of damage, and also the "spalled"; material (burst) size distribution. In particular, we evaluate the relation between the damage parameter and the applied force and explore the behavior in the vicinity of material breakdown. Using this simple model for material breakdown, we show that damage, caused by applied shear forces, is analogous to a first-order phase transition. The scaling behavior of G with phi is explored analytically and numerically, close to phi=0 and phi=1 and in the vicinity of phi(c), when the shear load is close to but below the threshold force that causes material breakdown. Our model calculation represents a first approximation of a system subject to wear induced loads.
Knudsen
Jakob
J
Materials Science, Malmö University, SE 205 06 Malmö, Sweden and Solid Mechanics, Lund University, SE 221 00 Lund, Sweden.
Massih
A R
AR