Abstract Plant fiber properties, such as morphological and mechanical, are characterized by a large dispersion. Thereby, a statistical analysis is needed to obtain consistent results. An experimental study, conducted on 50 flax yarns, shows that the flax yarn properties (Young's modulus, tensile strength and diameter) follow Gaussian distributions. This approach is obviously reliable, however time-consuming, to get relevant information. An alternative could be the identification of the yarn mechanical properties using an inverse approach, based on tensile tests conducted on flax fabric reinforcement. The aim of this study is to develop a numerical method that allows to identify the statistical distributions of flax yarn properties based on tensile tests conducted on fabric specimens. The proposed strategy relies on two assumptions. On the one hand, fabric is constituted of several yarns acting like springs in parallel. On the other hand, yarns are considered as brittle-elastic materials. Hence, a yarn breaks when the load reaches its failure strength, leading to a loading redistribution to the intact yarns. A comparison of the numerical and experimental results of flax fabric tensile behavior, and of the flax property statistical distributions allows to confirm the performance of this strategy. The results show that the flax fabric tensile behavior is correctly described by the proposed modeling strategy. The average and the standard deviation of the Young's modulus, the tensile strength and the diameter of flax yarns identified from fabric tensile tests via inverse approach are close to those obtained experimentally on individual yarns. Indeed, the measured average diameter of unitary yarns are 244.4 ± 19.2 μm and the fitted one is 2474.8 ± 17.4 μm , the fitting failure strength 292.3 ± 33.4 MPa are close to the experimental 271.2 ± 47.5 MPa . The identified Young's modulus is 9.4 ± 0.9 GPa is lower than the experimental 10.8 ± 1.3 GPa .

中文翻译：

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从织物的统计力学特征识别亚麻纱线力学性能的逆方法

摘要 植物纤维的形态学和力学性能等特性具有较大的色散性。因此，需要进行统计分析以获得一致的结果。对 50 根亚麻纱进行的一项实验研究表明，亚麻纱的特性（杨氏模量、拉伸强度和直径）服从高斯分布。这种方法显然是可靠的，但要获取相关信息很耗时。另一种方法是根据对亚麻织物增强材料进行的拉伸测试，使用逆向方法识别纱线机械性能。本研究的目的是开发一种数值方法，可以根据对织物试样进行的拉伸试验来确定亚麻纱线性能的统计分布。提议的策略依赖于两个假设。一方面，织物由几根纱线组成，就像平行的弹簧一样。另一方面，纱线被认为是脆性弹性材料。因此，当负载达到其破坏强度时，纱线会断裂，导致负载重新分配到完整的纱线。亚麻织物拉伸行为的数值和实验结果以及亚麻性能统计分布的比较可以确认该策略的性能。结果表明，所提出的建模策略正确地描述了亚麻织物的拉伸行为。通过逆向方法从织物拉伸试验中确定的杨氏模量、拉伸强度和亚麻纱直径的平均值和标准偏差与在单根纱线上实验获得的值接近。确实，实测单一纱线平均直径为244.4±19.2μm，拟合平均直径为2474.8±17.4μm，拟合破坏强度292.3±33.4MPa，接近实验值271.2±47.5MPa。确定的杨氏模量为 9.4 ± 0.9 GPa，低于实验值 10.8 ± 1.3 GPa。