无序度对干燥诱导裂纹时间涨落的影响
Effect of disorder on temporal fluctuations in drying induced cracking
摘要：
我们调查通过计算机模拟的结构无序的均匀和各向同性干燥下的材料的薄层开裂的统计上的效果。该层被离散成一个三角形网格的弹簧。干燥过程通过以相同因子减小所有弹簧的自然长度来捕获，并且淬火无序的量通过改变弹簧的随机断裂阈值的分布的宽度来控制。一旦弹簧断裂，负载的重新分布可能会引发雪崩式的断裂。我们的模拟结果表明，该系统表现出相变的无序量作为控制参数：在低的无序度，破碎过程中占主导地位的宏观裂纹在开始时，和随后的破碎雪崩的大小分布呈指数形式。在高度紊乱时，破裂以指数分布的小规模雪崩进行，产生大量的微裂纹，这些微裂纹最终合并并破坏该层。在这两个阶段之间，在临界无序量ε_c = 0.40 \pm 0.01处发生急剧转变，其中雪崩尺寸分布变为指数τ = 2.6 \pm 0.08的幂律，与纤维束模型的平均场值τ = 5/2一致。从有限尺寸标度分析得到的高质量数据的崩塌表明，最大爆发的平均值<Δ_max>可以确定为序参量，β/v = 1.4，1/v = 1.0，并且崩塌尺寸分布的二阶矩m2和一阶矩m1的平均比值<m2 /m1>显示出与连续跃迁敏感性相似的行为，当γ/ν = 1时，1/ν = 0.9。这表明，无序诱导的薄层破裂的转变类似于连续的相变。
英文摘要：
We investigate by means of computer simulations the effect of structural disorder on the statistics of cracking for a thin layer of material under uniform and isotropic drying. The layer is discretized into a triangular lattice of springs. The drying process is captured by reducing the natural length of all springs by the same factor, and the amount of quenched disorder is controlled by varying the width ξ of the distribution of the random breaking thresholds for the springs. Once a spring breaks, redistribution of the load may trigger an avalanche of breaks. Our simulations revealed that the system exhibits a phase transition with the amount of disorder as control parameter: at low disorders, the breaking process is dominated by a macroscopic crack at the beginning, and the size distribution of the subsequent breaking avalanches shows an exponential form. At high disorders, the fracturing proceeds in small-sized avalanches with an exponential distribution, generating a large number of micro-cracks which eventually merge and break the layer. Between both phases a sharp transition occurs at a critical amount of disorder ξ_c = 0.40 \pm 0.01, where the avalanche size distribution becomes a power law with exponent τ = 2.6 \pm 0.08, in agreement with the mean-field value τ = 5/2 of the fiber bundle model. Good quality data collapses from the finite-size scaling analysis show that the average value of the largest burst <Δ_max> can be identified as the order parameter, with β/ν = 1.4 and 1/ν = 1.0, and that the average ratio <m2 /m1> of the second m2 and first moments m1 of the avalanche size distribution shows similar behaviour to the susceptibility of a continuous transition, with γ/ν = 1., 1/ν = 0.9. These suggest that the disorder induced transition of the breakup of thin layers is analogous to a continuous phase transition.
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