Four idealised assemblies of equally sized spherical particles are subjected to a range of macroscopic compressive principal stresses and the contact forces on individual particles are determined. For each set of contact forces the stress fields within individual particles are studied. A failure criterion for brittle materials is imposed and indicates that crushing (or rupture) occurs when the maximum contact force reaches a threshold particle strength value, irrespective of the presence and magnitude of other lesser contact forces acting on the particle and the material properties of the particle. Combining the crushing mechanism with an assembly instability mechanism enables failure surfaces to be drawn in the three-dimensional stress space. A simple spatial averaging technique has been applied to the failure surfaces to remove the effects of assembly anisotropies. Sections of the failure surfaces on p planes have similarities to those commonly used in sand modelling.