To understand the mechanical property of silkworm silk fibers, it is indispensable to know the so-called crystallite modulus or the ultimate Young’s modulus of the crystalline phase along the chain axis. In many papers, the crystallite modulus of silk fiber was evaluated by using an X-ray diffraction method in which the shift of the X-ray diffraction peak induced by an externally applied force is estimated as the crystalline strain (ε_c). The external tensile stress of the bulk sample (σ_b) is assumed to work on the crystalline phase at an equal value (σ_c = σ_b). The Young’s modulus obtained under this assumption (or the homogeneous stress distribution model) is called the apparent crystallite modulus (E_c^app = σ_b/ε_c). Not only for the various kinds of synthetic polymers as reported in the previous paper (Macromolecules, 2021, 54, 6449) but also for the silk fibers targeted in the present report, the E_c^app changed remarkably depending on the annealing temperature. The thus-observed behavior of E_c^app (and the bulk Young’s modulus, E_bulk) was reproduced well by building up a mechanical series–parallel model with the heterogeneous stress distribution taken into account. As a result, the E_c^true, or the true crystallite modulus, was estimated to be 65 ± 5 GPa, which was common to both the native and regenerated silk fibers. Besides, the thus-estimated E_c^true was in good agreement with the theoretical value of 66 GPa calculated for one typical crystal structural model. The successful reproduction of the observed E_c^app and E_bulk allowed us to speculate that the existence of so-called taut tie chain segments plays an important role in the generation of heterogeneous stress distribution in these silk fibers. We are apt to imagine that the natural fibers should behave ideally with a homogeneous deformation behavior, but the actual silk fibers are not very ideal against our expectation. The difference in the mechanical property (E_c^app and E_bulk) between the native and regenerated silk samples was discussed from the viewpoint of a higher-order structure. The effect of absorbed water on the E_c^app value was also investigated experimentally.

中文翻译：

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根据 X 射线分析的表观微晶模量与异质应力分布之间的关系估计丝纤维的真晶粒模量


要了解蚕丝纤维的机械性能，必须了解所谓的晶粒模量或沿链轴的晶相的极限杨氏模量。在许多论文中，使用 X 射线衍射方法评估了丝纤维的微晶模量，其中由外部施加的力引起的 X 射线衍射峰偏移被估计为结晶应变 （ε_c）。假设本体样品的外部拉伸应力 （σ_b） 以相等的值 （σ_c = σ_b） 作用于结晶相。在此假设（或均匀应力分布模型）下获得的杨氏模量称为表观晶粒模量 （E_c^app = σ_b/ε_c）。不仅对于上篇论文 （Macromolecules， 2021， 54， 6449） 中报道的各种合成聚合物，而且对于本报告中针对的丝纤维，EC^应用程序根据退火温度发生了显着变化。通过构建一个考虑了异质应力分布的机械串-并联模型，很好地再现了 E_c^app（以及体本体杨氏模量、E_体积）的观察到的行为。结果，E_c^true 或真正的晶粒模量估计为 65 ± 5 GPa，这在天然和再生丝纤维中都是通用的。此外，由此估计的 E_c^true 与一个典型晶体结构模型计算的 66 GPa 的理论值吻合较好。 观察到的 E_c^app 和 E_bulk 的成功复制使我们能够推测，所谓的绷紧领带链段的存在在这些丝纤维中产生异质应力分布中起着重要作用。我们很容易想象天然纤维应该具有均匀变形行为的理想表现，但实际的丝纤维与我们的预期并不完全相反。从高阶结构的角度讨论了天然和再生丝样品之间机械性能 （EC^app 和 E_bulk） 的差异。还通过实验研究了吸收的水对 EC^应用程序值的影响。