论文标题
裂纹前部内隐藏的3D结构如何揭示能量平衡
How hidden 3D structure within crack fronts reveals energy balance
论文作者
论文摘要
格里菲斯(Griffith)的充满活力的标准(或“能量平衡”)已在一个世纪中构成了断裂力学的基础。流入裂纹前部的能量通过前部的耗散(断裂能)精确平衡。如果未正确考虑裂纹前端结构,能量平衡似乎会失败或导致不切实际的结果。在这里,我们研究了在拉伸载荷条件下水凝胶中低速裂纹传播的二级结构的影响。我们首先表明这些裂缝是可行的。在相同的加载条件下,可以生成简单的(没有二级结构的裂纹)或面裂纹状态(通过沿裂纹前部传播的步骤形成)。任一裂纹状态的选择取决于初始“种子”裂纹的形式;完美的种子裂缝会产生简单的裂缝,而小型的本地模式〜III组件会产生具有多个步骤的裂纹前部。台阶粗化最终导致单步,沿裂纹前部传播。随着它们的发展,步骤在局部改变裂纹前部的瞬时结构和运动,从而破坏了横向翻译不变性。因此,与简单的裂纹相反,因此不再将面裂纹视为准2D系统中。对于简单和面的裂纹,我们同时测量沿这些裂缝沿这些裂纹前沿的能量通量和局部耗散,$ v $,跨越$ 0 <v <0.2C_R $($ C_R $是瑞利波浪速度)。我们发现,在裂纹方面存在二级结构的情况下,必须将能量平衡的实施推广到3D系统。面积的裂缝揭示了能量平衡,只有当我们考虑沿裂纹前部每个点的局部动态耗散时。
Griffith's energetic criterion, or `energy balance', has for a century formed the basis for fracture mechanics; the energy flowing into a crack front is precisely balanced by the dissipation (fracture energy) at the front. If the crack front structure is not properly accounted for, energy balance will either appear to fail or lead to unrealistic results. Here, we study the influence of the secondary structure of low-speed crack propagation in hydrogels under tensile loading conditions. We first show that these cracks are bistable; either simple (cracks having no secondary structure) or faceted crack states (formed by steps propagating along crack fronts) can be generated under identical loading conditions. The selection of either crack state is determined by the form of the initial `seed' crack; perfect seed cracks generate simple cracks while a small local mode~III component generates crack fronts having multiple steps. Step coarsening eventually leads to single steps that propagate along crack fronts. As they evolve, steps locally change the instantaneous structure and motion of the crack front, breaking transverse translational invariance. In contrast to simple cracks, faceted cracks can, therefore, no longer be considered as existing in a quasi-2D system. For both simple and faceted cracks we simultaneously measure the energy flux and local dissipation along these crack fronts over velocities, $v$, spanning $0<v<0.2c_R$ ($c_R$ is the Rayleigh wave speed). We find that, in the presence of secondary structure within the crack front, the implementation of energy balance must be generalized for 3D systems; faceted cracks reveal energy balance, only when we account for the local dynamic dissipation at each point along the crack front.