修正内聚区长度计算公式在冰Ⅰ型裂纹扩展中的应用

Application of improved cohesive zone length formula in ice mode Ⅰ crack propagation

[目的]内聚区长度是处于破坏边缘的内聚力单元长度与其连接的其他内聚力单元长度之和,决定了网格的最大尺寸。精确估算内聚区长度并合理划分网格是影响计算精度的重要因素。[方法]为此,基于J积分的部分假设和已有的研究成果,在原有的内聚区长度计算公式中增加关于长厚比的修正函数,然后将修正后的内聚区长度计算公式应用于冰力学模型,再基于有限元法建立双悬臂梁数值模型进行模拟,并与试验结果进行对比,以验证修正后内聚区长度计算公式的精确性。[结果]研究表明,在一个内聚区长度内至少存在4个内聚力单元才能较精确地描述断裂过程。相关结果应用于三点弯曲试验模型模拟的结果显示,断裂点的极限载荷误差为2.9%且在合理范围内。[结论]修正后的内聚区长度公式更适用于冰材料。

[Objectives]The cohesive zone length is the sum of the cohesive element length at the failure edge and the lengths of the other cohesive elements connected to it. The cohesive zone length determines the maximum size of the mesh. Therefore, the accurate estimation of cohesive zone length and reasonable mesh division are important factors affecting calculation accuracy. [Methods]Based on several J-integral assumptions and existing research results, a modified function on length thickness ratio value is added to the original formula. The modified formula is then applied to an ice mechanics model. Based on the finite element method,a model of a double cantilever beam is established to verify the accuracy of the formula through comparison with the experimental results.[Results]The results show that there must be at least four cohesive elements in a cohesive zone length to describe the fracture process accurately. This conclusion is also applied to the numerical simulation of a three-point bending experiment. The error of the limit load is 2.9%, and that of the fracture point is within a reasonable range.[Conclusion] It is concluded that the modified cohesive zone length formula is more suitable for ice materials.