应变梯度纤维束的损伤过程
Damage process of a fiber bundle with a strain gradient
摘要：
我们研究了楔形几何结构中纤维束的损伤过程，该结构保证了恒定的应变梯度。为了得到楔形几何形状，我们考虑三点弯曲的酒吧，这是仿照两个刚性块粘在一起的薄弹性界面。界面离散为具有随机失效阈值的平行纤维，当杆弯曲时，纤维被拉长。分析了系统的渐进损伤，我们表明，应变梯度的结果在一个丰富的频谱的新颖行为的纤维束。我们发现，弱无序的界面裂纹是作为一个连续的区域失败的纤维。在裂纹前方形成了一个加工区，随着变形的增加，加工区收缩，使裂纹尖端随着裂纹的发展而变得更尖锐。对于强无序，系统的失效表现为空间随机的断裂序列。纤维束的损伤在猝发中进行，其尺寸分布显示出幂律行为，随着无序的减弱，指数从2.5到2.0。最大的突发的大小增加的指数为2/3的无序强度的幂律和饱和的强无序束。
英文摘要：
We study the damage process of fiber bundles in a wedge-shape geometry which ensures a constant strain gradient. To obtain the wedge geometry we consider the three-point bending of a bar, which is modelled as two rigid blocks glued together by a thin elastic interface. The interface is discretized by parallel fibers with random failure thresholds, which get elongated when the bar is bent. Analyzing the progressive damage of the system we show that the strain gradient results in a rich spectrum of novel behavior of fiber bundles. We find that for weak disorder an interface crack is formed as a continuous region of failed fibers. Ahead the crack a process zone develops which proved to shrink with increasing deformation making the crack tip sharper as the crack advances. For strong disorder, failure of the system occurs as a spatially random sequence of breakings. Damage of the fiber bundle proceeds in bursts whose size distribution shows a power law behavior with a crossover from an exponent 2.5 to 2.0 as the disorder is weakened. The size of the largest burst increases as a power law of the strength of disorder with an exponent 2/3 and saturates for strongly disordered bundles.
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