  We study the relation between a threshold-force based model at the
microscopic scale and mode I fracture at the macroscopic scale in a system of
discrete interacting springs. Specifically, we idealize the contact between two
surfaces as that between a rigid surface and a collection of springs with
long-range interaction and a constant tensile threshold force. We show that a
particular scaling similar to that of crack-tip stress in Linear Elastic
Fracture Mechanics leads to a macroscopic limit behavior. The model also
reproduces the scaling behaviors of the JKR model of adhesive contact. We
determine how the threshold force depends on the fracture energy and elastic
properties of the material. The model can be used to study rough-surface
adhesion.
