Thermal activation of rupture and slow crack growth in a model of homogenous brittle materials

– Slow crack growth in a model of homogenous brittle elastic material is described as a thermal activation process where stress fluctuations allow to overcome a breaking threshold through a series of irreversible steps. We study the case of a single crack in a flat sheet for which analytical predictions can be made, and compare them with results from the equivalent problem of a 2D spring network. Good statistical agreement is obtained for the crack growth profile and final rupture time. The specific scaling of the energy barrier with stress intensity factor appears as a consequence of irreversibility. In addition, the model brings out a characteristic growth length whose physical meaning could be tested experimentally. Introduction. – Although tensile rupture of atomic bonds requires a stress comparable to the Young’s modulus, brittle solids commonly rupture at a much lower applied stress (typically 3 orders of magnitude lower). Griffith’s pioneering work [1] has clarified the origin of this apparent weakening, postulating that small cracks usually preexist in real solids, with stress concentration at the crack tip strongly enhancing rupture. A somewhat similar and quite striking effect is the occurrence of failure even though the solid is stressed below its experimental breaking threshold (i.e., even if stress concentration due to flaws is taken into account). The physical process, sometimes referred to as subcritical rupture, leads to a delay in the time for complete macroscopic failure of the solid, with a strong dependence on the amplitude of the applied stress. A possible driving mechanism for subcritical damaging processes is thermal activation as supported by the early experimental work of Brenner and Zhurkov [2,3]. Zhurkov introduced a kinetic concept of strength of solids, where time to rupture follows an Arrhenius law with an energy barrier decreasing with increasing stress [3]. Interestingly, there is still debate about whether temperature fluctuations might be sufficient or not to nucleate microcracks and trigger crack growth. Recent theoretical works [4, 5, 6, 7] have emphasized the effect of disorder in decreasing the effective energy barrier (conversely increasing the ”effective temperature”). Other authors [8, 9] have used equilibrium statistical thermodynamics to study how cracks might naturally appear from thermal fluctuations in an otherwise homogenous material which