Theoretical fracture analysis of double cantilever microbeam using two-phase local/nonlocal integral models with discontinuity

Abstract

A mathematical approach is proposed to apply strain-driven (εD) and stress-driven (σD) two-phase local/nonlocal integral models (TPNIMs) with discontinuity of variable fields. The equivalently differential form together with constitutive boundary conditions and constitutive continuity conditions is derived explicitly. Compare to constitutive boundary conditions, constitutive continuity conditions have one more integral item, and the discontinuity plays no role on differential constitutive relation and constitutive boundary conditions. εD- and σD-TPNIMs are applied to formulate the Mode I and II fracture problem of double cantilever Euler-Bernoulli microbeams subjected symmetric and anti-symmetrical end moment and force loads. It is found that constitutive continuity conditions play no role on Mode I fracture problem since that the flexible deformation disappears for intact microbeam under symmetry loads. The bending deflections under different loads are solved analytically, and the energy release rate (ERR) and stress intensity factor (SIF) are derived explicitly. On the basis of the superposition principle, SIF for edge-cracked Euler-Bernoulli microbeams subjected generally end moment and force can be calculated. The influence of nonlocal parameters and the intact microbeam length on the size-dependent fracture behavior is investigated numerically. The obtained results can explain the superior fracture performance of nanomaterials.