发表机构
Nagoya University（名古屋大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文重新评估热塑性复合材料纤维长度分布的双指数形式，引入有限初始长度并分析断裂机理，表明该形式为有用的双参数拟合模型而非精确生成分布。
AI 中文摘要
在先前的工作[Masubuchi等人，Compos. Sci. Technol. 134, 43 (2016)]中，基于断裂和相邻断裂阻断这两个独立泊松过程，提出了纤维长度分布函数为双指数（即厄兰型）两个指数等待长度的卷积形式。本文通过引入有限初始长度L_{0}，并分析屈曲诱导纤维断裂过程的机理基础，进一步评估了这一双指数形式。将所得的有限L_{0}闭式解与玻璃纤维数据集进行比较，以追溯性证明早期工作中对此类系统采用无限长度理想化的合理性，同时为碎片尺寸与L_{0}相当的过程提供完整形式。关于纤维断裂力学，对断裂方程的梅林变换分析表明，尺度不变的级联产生幂律分布，因此无法生成特征长度；这些长度必须来源于尺度破缺因素，特别是截止区域和受阻的加工历史。对现象学有限机会级联的蒙特卡洛模拟表明，双指数形式无法再现生成分布的峰值，但能捕捉其类指数尾部，这意味着它作为一个有用的双参数拟合模型，而非精确的生成分布。
英文摘要
In a previous work [Masubuchi et al., Compos. Sci. Technol. 134, 43 (2016)], a fiber-length distribution function was proposed as the hypoexponential, or Erlang-type, convolution of two exponential waiting lengths, motivated by two independent Poisson processes for breakage and for blocking of adjacent breaks. The present paper further evaluates this hypoexponential form by introducing a finite initial length L_{0}, and by analyzing the mechanistic basis of the buckling-induced fiber breakage process. The obtained finite-L_{0} closed-form solution was compared to a glass fiber dataset to retroactively justify the infinite-length idealization in the earlier work for such systems while providing the complete form for processes in which fragments remain comparable to L_{0}. Concerning the mechanics of fiber fragmentation, a Mellin transform analysis of the fragmentation equation showed that scale-invariant cascades yield power laws and therefore cannot generate characteristic lengths; those lengths must instead arise from scale-breaking ingredients, particularly the cutoff region and the arrested processing history. Monte Carlo simulations of a phenomenological finite-opportunity cascade showed that the hypoexponential form does not reproduce the peak of the generated distribution but captures its exponential-like tail, implying that it serves as a useful two-parameter fitting model, although not an exact generative distribution.
Comments22 pages, 3 figures
