ESTIMATION OF STRENGTH AND FRACTURE TOUGHNESS FOR NANOMATERIALS

A molecular-continuum model proposed in our previous study for the estimation of elastic stiffness of nanomaterials is modified in this paper for the estimation of strength and fracture toughness. To predictyield strength and ultimate strength, a uniformly tensile strain state is assumed. As to the prediction of fracture toughness, the crack near tip deformation obtained from the linear elastic fracture mechanics is assumed. After setting the proper deformation field, the changes of bond distance and bond angle between atoms can be obtained. With this information and the proper potential energy function of molecular mechanics, the potential energy which is treated as strain energy in the deformed solids can be calculated. Similar process can be done when a small advance is added on the crack, and then the strain energy release rate can be obtained. With the above calculation procedure and the known relation between strain energy release rate and stress intensity factor, the estimation of strength and fracture toughness becomes possible for the nanomaterials. To illustrate the proposed method, the strength and fracture toughness of a graphene sheet is estimated. The numerical results fall in the reasonable range obtained by the other methods.