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An analytic traction-displacement model for a reinforcing ligament bridging a crack at an arbitrary angle, including elastic, frictional, snubbing, yielding, creep, and fatigue phenomena
Journal of the Mechanics and Physics of Solids ( IF 5.0 ) Pub Date : 2024-09-23 , DOI: 10.1016/j.jmps.2024.105879
B.N. Cox, N. Sridhar, Q.D. Yang

A micromechanical model is developed that generates analytic expressions for the crack displacement vector u given an arbitrary far-field stress state σa for a crack that is bridged by an array of ligaments oriented at an arbitrary angle with respect to the crack plane. The model is applicable to various materials, e.g., fibrous ceramic composites, or polymer composites reinforced by stitches or z-pins or woven tows, and deals with interfacial friction, enhanced friction due to increased contact pressure (“snubbing”), and the possibility of ligament deflection enabled by yield or damage. The model also conveniently incorporates ligament failure and rate dependent phenomena (fatigue or creep). Adaptability of the model is enabled by the definition of a standard Reference Model, which generates analytic expressions for the crack displacement for given possible yield, ligament deflection, and friction and snubbing effects and is invariant for all geometrical and material choices. The switching on or off and the strengths of all phenomena are governed by assigning values to a handful of material parameters. The material parameters will generally be calibrated against data in a top-down strategy, the model thereby mapping material selection onto engineering fracture via the predicted bridging relationship u[σa]. The relationship u[σa] can depend strongly on bi-angular ligament orientation. Yield and deflection can change u[σa] qualitatively, e.g., by creating fracture surface contact even when σa includes substantial opening tension. Snubbing has significant effects, including possible stabilization of the pullout of a finite ligament. Since model output is computed via analytic expressions, its speed will support the model's use in large-scale material simulations or as constraining physical information in machine learning algorithms.

中文翻译:


用于以任意角度桥接裂缝的加强韧带的牵引-位移解析模型,包括弹性、摩擦、缓冲、屈服、蠕变和疲劳现象



开发了一个微机械模型,该模型为裂纹位移矢量 u 生成解析表达式,给定一个裂纹的任意远场应力状态 σa,该裂纹由相对于裂纹平面以任意角度定向的韧带阵列桥接。该模型适用于各种材料,例如纤维陶瓷复合材料,或通过缝合或 z 形销或编织丝束增强的聚合物复合材料,并处理界面摩擦、由于接触压力增加(“缓冲”)而增强的摩擦,以及由于屈服或损伤而导致韧带偏转的可能性。该模型还方便地结合了韧带失效和速率相关现象(疲劳或蠕变)。通过定义标准参考模型,可以生成给定可能的屈服、韧带挠度以及摩擦和缓冲效应的裂纹位移解析表达式,并且对于所有几何和材料选择都是不变的。所有现象的开启或关闭以及强度都是通过为少数材料参数分配值来控制的。材料参数通常会根据自上而下的策略中的数据进行校准,从而通过预测的桥接关系 u[σa] 将材料选择映射到工程裂缝上。关系 u[σa] 在很大程度上取决于双角韧带方向。屈服和挠度可以定性地改变 u[σa],例如,即使 σa 包含相当大的张开张力,也会产生断裂表面接触。缓冲具有显着效果,包括可能稳定有限韧带的拉出。 由于模型输出是通过解析表达式计算的,因此其速度将支持模型在大规模材料仿真中的使用,或作为机器学习算法中的约束物理信息。
更新日期:2024-09-23
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