Ubiquitiform Crack of Quasi-Brittle Materials under Dynamic Loading
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摘要: 为建立动态拉伸载荷作用下准脆性材料裂纹扩展路径的泛形表征，提出了一种非均匀准脆性材料动态裂纹扩展的泛形模型，计算得到的泛形裂面复杂度与已有实验数据吻合较好。结果表明：动态拉伸载荷作用下的裂纹扩展路径是泛形的，其复杂度随加载应变率的增大而减小，并与材料动态拉伸承载能力的空间随机分布无关，且随Weibull分布形状参数m的增加而减小。研究结果为分析动态拉伸载荷作用下准脆性材料的裂纹扩展机理即泛形表征提供了依据。Abstract: To investigate the ubiquitiformal characteristic of the crack extension path in a heterogeneous quasi-brittle material under the dynamic tensile loadings, a ubiquitiformal model is developed in this paper, and the calculated numerical results for the ubiquitiform complexity are in agreement with the previous experiments. It is found that such a crack extension path is indeed of a ubiquitiform, and its complexity decreases with the increase of the loading strain-rate. Moreover, it is also found that the complexity is independent of the randomness of the spatial distribution of the dynamic tensile load-carrying capacity of the material under consideration, and the complexity decreases with increasing shape parameter m of the Weibull distribution. Thus, this work can be taken as a basis for analyzing further the mechanism as well as the ubiquitiformal characteristic of the crack profile in a quasi-brittle material under the dynamic tensile loadings.
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Key words:
- quasi-brittle materials /
- ubiquitiform crack /
- strain-rate /
- complexity
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图 1 由Weibull分布表征的强度分布直方图
Figure 1. Histogram of the strength distribution characterized by Weibull distribution
图 2 动态拉伸承载能力分布
Figure 2. Typical distribution of the dynamic tensile load-carrying capacity
图 5 计盒维数法计算泛形复杂度
Figure 5. Box-counting dimension method is used to compute the ubiquitiformal complexity
图 6 局部应变率为103 s–1的泛形裂纹轮廓线
Figure 6. Profile of ubiquitiform cracks under the local strain rate of 103 s–1
表 1 复杂度的数值计算结果
Table 1. Numerical results of the complexity C
Strain rate/s−1 C S1 S2 S3 S4 S5 Avg. 10–6 1.381 1.382 1.379 1.381 1.383 1.381 10 1.215 1.213 1.210 1.212 1.208 1.212 102 1.182 1.182 1.180 1.178 1.179 1.180 103 1.127 1.132 1.134 1.131 1.142 1.133 
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表 2 不同形状参数下的泛形复杂度
Table 2. Ubiquitiform complexity under different shape parameters
m C m C 5 1.142 8 1.086 6 1.126 9 1.057 7 1.108 10 1.033
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