Applicability of continuum fracture mechanics in atomistic systems

Shao-Huan Cheng, Purdue University


By quantitating the amplitude of the unbounded stress, the continuum fracture mechanics defines the stress intensity factor K to characterize the stress and displacement fields in the vicinity of the crack tip, thereby developing the relation between the stress singularity and surface energy (energy release rate G). This G-K relation, assigning physical meaning to the stress intensity factor, makes these two fracture parameters widely used in predicting the onset of crack propagation. However, due to the discrete nature of the atomistic structures without stress singularity, there might be discrepancy between the failure prediction and the reality of nanostructured materials. Defining the local atomistic stress with convergence within one lattice ensures the near-tip stress in the discrete systems displays the detailed stress concentration. Through comparison to the equivalent continuum finite element models, although these atomistic near-tip stress distributions preserve the trend of inverse square root singularity, the corresponding fracture toughness in terms of critical stress intensity factor (or energy release rate) is size dependent (i.e., varying with the size of the singular stress zone, K-dominance zone). Consequently, the failure load predicted by constant fracture toughness deviates from what a nanostructure can sustain if the singular stress is not dominant. The two-parameter model, including the contributions from both singular and non-singular terms, is utilized to improve the inadequacy of continuum fracture mechanics. On the other hand, since the magnitude of the atomistic near-tip stress is finite, the maximum stress criterion is valid in atomistic systems, proven by the close match between the peak stress and the theoretic strength under the failure condition. Furthermore, the surface energy determined by the overall energy balance over the crack growth within several sizes of lattice constant is shown to be size-independent, in contrast to the size-dependent results obtained by the G-K relation




Sun, Purdue University.

Subject Area

Atoms & subatomic particles|Materials science

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