幂硬化材料裂纹尖端应力场特征参数近似解
1. 三江学院, 土木工程学院, 江苏南京 210012
2. 河海大学, 港口海岸与近海工程学院, 江苏南京 210024
| 摘 要： | 针对I型裂纹尖端场的渐进解析解提出的J-A双参数法可有效地表征幂硬化材料裂尖应力场分布及其裂尖拘束度。本文较系统地梳理了常用的裂纹尖端应力场表征方法，以单边缺口试样为例，阐明了J-A双参数法表征I型裂纹裂尖拘束的优越性。J-A双参数法中存在三类重要参数，包括特征指数、无量纲积分常数及应力分布角函数。基于幂硬化材料现有的裂尖渐近场高阶解析解，编制了计算程序计算这三类重要参数，基于程序的计算结果采用非线性拟合方法给出了从低硬化到高硬化水平下各类参数的高精度经验公式，拟合决定系数R2均达到0.999以上。最后给出了拘束参数A的两种计算方法，采用拟合的方法确定断裂控制区域内的拘束参数A更为合理，给出了直接计算参数A的公式，结合三类参数的拟合公式计算了单边缺口拉伸试样的裂尖拘束度，结果表明本文提出的各类重要参数的计算公式可获得高精度的裂尖拘束参数A，从而可方便J-A双参数法的广泛应用。 |
| 关 键 词： | 裂尖应力场; J-A三项解; 特征参数; 非线性拟合 |
| DOI： | 10.57237/j.se.2023.05.002 |
View:
Downloads:
收稿日期: 2023-08-10
接受日期: 2023-09-25
在线出版日期: 2023-10-09
Approximate Solutions of Characteristic Parameters of Stress Field at Crack Tip in Power Hardening Materials
1. College of Civil Engineering, Sanjiang University, Nanjing 210012, China
2. College of Harbour, Coastal and Offshore Engineering, Nanjing 210024, China
| Abstract: | The J-A two-parameter method proposed for the asymptotic analytical solution of type-I crack-tip field can effectively characterize the crack-tip stress field distribution and its constraint for power-hardening materials. This paper systematically summarizes commonly used methods for characterizing stress fields at crack tips. Taking the single-edged notched tension specimen as an example, the superiority of the J-A two-parameter method in characterizing the crack tip constraint of type I cracks is demonstrated. The J-A two-parameter method consists of three important parameters, including characteristic index, dimensionless integration constant and stress distribution angle function. Based on the existing high-order analytical solutions for the crack tip asymptotic field of power-hardening materials, a calculation program is compiled to compute these important parameters. High-precision empirical formulas for various parameters, ranging from low to high hardening levels, are obtained using the nonlinear fitting method with the determination coefficient R2 reaching above 0.999. Finally, two methods for calculating the constraint parameter A are presented. It is found that using the fitting method to determine the constraint parameter A in the fracture control zone is more reasonable. A formula for directly calculating parameter A is also provided. Combined with the fitting formulas for the three parameters, the crack tip constraint of the single-edged notched tension specimen is calculated. Results show that the proposed calculation formulas can obtain crack tip constraint parameter A with high precision, facilitating the wide application of the J-A two-parameter method. |
| Keywords: | Crack-tip Stress Field; J-A Three-term Solution; Characteristic Parameters; Nonlinear Fitting |
参考文献
| [1] | Betegon C, Hancock J W. Two-parameter characterization of elastic-plastic crack-tip fields [J]. International Journal of Applied Mechanics, 1991, 58: 104-110. |
| [2] | O'Dowd N P. Application of two parameter approaches in elastic-plastic fracture mechanics [J]. Engineering Fracture Mechanics, 1995, 52: 445-465. |
| [3] | Wang X. Two-parameter characterization of elastic-plastic crack front fields surface cracked lates under tensile loading [J]. Engineering Fracture Mechanics, 2009, 76: 958-982. |
| [4] | Yang S. Higher order asymptotic crack tip fields in a power-law hardening material [D]. USA: University of South Carolina, 1993. |
| [5] | Ding P, Wang X. Solutions of the second elastic–plastic fracture mechanics parameter in test specimens [J]. Engineering Fracture Mechanics, 2010, 77: 3462-3480. |
| [6] | Ding P, Wang X. Solutions of the second elastic-plastic fracture mechanics parameter in test specimens under biaxial loading [J]. International Journal of Pressure Vessels and Piping, 2013, 111-112: 279-294. |
| [7] | Nikishkov G P, Matvienko Y G. Elastic-plastic constraint parameter A for test specimens with thickness variation [J]. Fatigue & Fracture of Engineering Materials & Structures, 2016, 39: 939-949. |
| [8] | Huang Y. Numerical Assessments of Cracks in Elastic-Plastic Materials [M]. Heidelberg: Springer Berlin, 2002. |
| [9] | 王自强, 陈少华. 高等断裂力学 [M]. 北京: 科学出版社, 2009. |
| [10] | Nestor P. Fracture Mechanics (second edition) [M]. Switzerland: Springer Cham, 2017. |
| [11] | Duan C J, Zhang S H. Two-parameter J-A estimation for weld centerline cracks of welded SE (T) specimen under tensile loading. Theoretical and Applied Fracture Mechanics, 2020, 107(7): 102435. |
| [12] | Hutchinson J W. Singular behavior at the end of a tensile crack in a hardening material [J]. Journal of the Mechanics and Physics of Solids, 1968, 16: 13-31. |
| [13] | Rice J R, Rosengren G F. Plane Strain deformation near a crack tip in a power law hardening material [J]. Journal of the Mechanics and Physics of Solids, 1968, 16: 1-12. |
| [14] | 郦正能. 应用断裂力学 [M]. 北京: 北京航空航天大学出版社, 2012. |
| [15] | Li Y C, Wang T C. Higher-order asymptotic field of tensile plane-strain nonlinear crack problem [J]. Science in China (Ser. A), 1986, 29: 941-955. |
| [16] | Chao Y J, Yang S, Sutton M A. On the fracture of solids characterized by one or two parameters: theory and practice [J]. Journal of Mechanics and Physics of Solids, 1994, 42: 629-647. |
| [17] | Nyhus B, Polanco M L, Orjasether O. SENT specimens an alternative to SENB specimens for fracture mechanics testing of pipelines [C]. In: Proceedings of ASME 22nd International Conference on Offshore Mechanics and Arctic Engineering, Cancun, Mexico, 2003: 259-266. |
