Improvement of the Calculation Method for Stress Intensity Factors at the Free Surface of Typical Cracks in Ultra-High-Pressure Vessel
-
摘要: 自由表面处应力强度因子是超高压容器典型裂纹扩展及寿命预测过程中的核心计算参数，在分段线性插值方法的基础之上加以改进，提出了一种基于高阶多项式拟合计算的方法. 以盲底裂纹为例，采用不同次数的多项式拟合了不同采集数据量下的应力数据；按该方法进行了不同裂纹下自由表面处应力强度因子的计算，并围绕多项式次数和采集数据量展开研究，探究了二者对计算结果的影响规律；在不同的裂纹深长比下，对比分析了该方法与文献中推荐的线性插值方法及有限元法的差异. 结果表明，计算结果随着多项式次数的增加，表现出逐渐逼近且收敛的趋势，常规三次与高阶多项式拟合的计算结果最小相对误差约为-30%；采集数据量不断增多时，计算结果逐渐向稳定值收敛，对比数据量偏少与偏多场景下的计算结果，其最大相对误差约为11%；该方法与文献中的线性插值方法及有限元法的计算结果均基本一致，吻合度较高，且适用于裂纹动态扩展及寿命预测过程中.Abstract: The stress intensity factor at the free surface is a core calculation parameter in the typical crack propagation and life prediction process of ultra-high-pressure vessels. Based on the segmented linear interpolation method, an improved method based on high-order polynomial fitting calculation was proposed. With blind bottom cracks as an example, stress data under different collected data volumes were fitted by means of polynomials of different orders; The stress intensity factors at the free surface of different cracks was calculated with this method, and the effects of polynomial orders and data amounts on the calculation results were explored; At different crack depth to length ratios, the differences between this method and the recommended linear interpolation method in previous literatures and the finite element method, were compared and analyzed. The results indicate that, as the polynomial order increases, the calculation results show a gradually approaching and converging trend. The minimum relative error of the calculation results for conventional cubic and high-order polynomial fitting is about -30%; As the collected data amount continues to increase, the calculation results gradually converge towards a stable value. Comparison of calculation results between the cases with less and more data shows that, the maximum relative error can reach about 11%. This method, with its calculation results, is basically consistent with the linear interpolation method in the previous literatures and the finite element method, and is suitable for dynamic crack propagation and life prediction processes.
-
图 2 G4，G5，G6和G7的计算结果
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 2. Calculation results of G4, G5, G6 and G7
图 4 弹性应力分析及裂纹扩展路径
Figure 4. The elastic stress analysis and the crack propagation path
图 7 不同采集数据量下的计算结果
Figure 7. Calculation results under different amounts of collected data
图 8 高阶多项式拟合与线性插值的计算结果
Figure 8. Calculation results of high order polynomial fitting and linear interpolation
图 9 含裂纹盲底结构网格划分
Figure 9. The mesh division of the blind bottom structure with a crack
-
[1] 张海, 欧阳瑞洁, 张永红, 等. 钛合金气瓶疲劳试验壳体开裂失效分析[J]. 压力容器, 2021, 38(7): 77-80.ZHANG Hai, OUYANG Ruijie, ZHANG Yonghong, et al. Cracking failure analysis of a titanium alloy pressure vessel in hydraulic fatigue test[J]. Pressure Vessel Technology, 2021, 38(7): 77-80. (in Chinese) [2] 赵广洲, 鲍文杰, 陈凡, 等. 高压气瓶4130X钢低周疲劳特性及疲劳设计曲线探讨[J]. 压力容器, 2023, 40(8): 37-43.ZHAO Guangzhou, BAO Wenjie, CHEN Fan, et al. Discussion on low cycle fatigue characteristics and fatigue design curve of 4130X steel for high pressure gas cylinder[J]. Pressure Vessel Technology, 2023, 40(8): 37-43. (in Chinese) [3] 全国锅炉压力容器标准化技术委员会. 超高压容器: GB/T 34019—2017[S]. 2017.National Boiler and Pressure Vessel Standardization Technical Committee. Ultra-high pressure vessels: GB/T 34019—2017[S]. 2017. (in Chinese) [4] ASME BPVC. Ⅷ. 3, Alternative rules for construction of high-pressure vessels[S]. New York: American Society of Mechanical Engineers, 2023. [5] 国家质检总局特种设备安全监察局. 固定式压力容器安全技术监察规程: TSG 21—2016[S]. 北京: 新华出版社, 2016.General Administration of Quality Supervision, Inspection and Quarantine of China. Safety technical supervision regulations for stationary pressure vessels: TSG 21—2016[S]. Beijing: Xinhua Publishing House, 2016. (in Chinese) [6] 谢芳, 刘德俊, 杨正伟. 压力容器内外壁轴向双裂纹相互作用[J]. 油气储运, 2019, 38(2): 130-136.XIE Fang, LIU Dejun, YANG Zhengwei. The interaction between axial double cracks in the inner and outer walls of pressure vessels[J]. Oil & Gas Storage and Transportation, 2019, 38(2): 130-136. (in Chinese) [7] 王宁, 王永娟, 徐诚, 等. 硬化层力学参数对身管内表面径向裂纹Ⅰ型应力强度因子的影响[J]. 兵器装备工程学报, 2025, 46(4): 1-8.WANG Ning, WANG Yongjuan, XU Cheng, et al. Effect of mechanical parameters of hardened layer on model Ⅰ SIF of crack on inner surface of barrel[J]. Journal of Ordnance Equipment Engineering, 2025, 46(4): 1-8. (in Chinese) [8] 宋顺成, 黄建文, 许湘. 具有内表面裂纹高压厚壁圆管的疲劳寿命分析[J]. 核动力工程, 2007, 28(1): 26-31.SONG Shuncheng, HUANG Jianwen, XU Xiang. Analysis of fatigue life of thick-wall cylinder with inner surface crack subjected to high pressure[J]. Nuclear Power Engineering, 2007, 28(1): 26-31. (in Chinese) [9] 李戎, 杨萌, 梁斌, 等. 基于裂纹尖端应力比值的含裂纹功能梯度材料圆筒应力强度因子计算方法[J]. 工程力学, 2020, 37(4): 22-29.LI Rong, YANG Meng, LIANG Bin, et al. Calculation method of stress intensity factor for cracked functionally graded hollow cylinder based on the ratio of stresses at crack tip[J]. Engineering Mechanics, 2020, 37(4): 22-29. (in Chinese) [10] 张瑞凯, 刘攀, 谈建平, 等. 核电蒸汽发生器接管嘴外表面裂纹应力强度因子计算[J]. 核动力工程, 2022, 43(5): 138-146.ZHANG Ruikai, LIU Pan, TAN Jianping, et al. Calculation of stress intensity factor of external surface crack on the nozzle of steam generator in nuclear power plant[J]. Nuclear Power Engineering, 2022, 43(5): 138-146. (in Chinese) [11] 何家胜, 朱卫卫, 李书容, 等. 压力容器开孔接管处表面斜裂纹应力强度因子数值分析[J]. 核动力工程, 2010, 31(5): 1-4.HE Jiasheng, ZHU Weiwei, LI Shurong, et al. Numerical analysis of stress intensity factor of surface inclined cracks at intersection of cylindrical vessels and nozzles[J]. Nuclear Power Engineering, 2010, 31(5): 1-4. (in Chinese) [12] 汪志福, 秦宗川, 牛铮, 等. 应力集中部位裂纹自由表面处应力强度因子的计算与分析[J]. 压力容器, 2023, 40(12): 41-49.WANG Zhifu, QIN Zongchuan, NIU Zheng, et al. Calculation and analysis of stress intensity factor at the free surface of crack at the stress concentration position[J]. Pressure Vessel Technology, 2023, 40(12): 41-49. (in Chinese) [13] BUECKNER H F. A novel principle of the computation of stress intensity factors[J]. Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 1970, 50(9): 529-546. [14] RICE J R. Some remarks on elastic crack-tip stress fields[J]. International Journal of Solids and Structures, 1972, 8(6): 751-758. doi: 10.1016/0020-7683(72)90040-6 [15] GLINKA G, SHEN G. Universal features of weight functions for cracks in mode Ⅰ[J]. Engineering Fracture Mechanics, 1991, 40(6): 1135-1146. doi: 10.1016/0013-7944(91)90177-3 [16] ZHENG X J, KICIAK A, GLINKA G. Weight functions and stress intensity factors for internal surface semi-elliptical crack in thick-walled cylinder[J]. Engineering Fracture Mechanics, 1997, 58(3): 207-221. doi: 10.1016/S0013-7944(97)00083-0 [17] RAJU I S, NEWMAN J C. Stress-intensity factors for internal and external surface cracks in cylindrical vessels[J]. Journal of Pressure Vessel Technology, 1982, 104(4): 293-298. doi: 10.1115/1.3264220 [18] JONES I S, ROTHWELL G. Reference stress intensity factors with application to weight functions for internal circumferential cracks in cylinders[J]. Engineering Fracture Mechanics, 2001, 68(4): 435-454. doi: 10.1016/S0013-7944(00)00111-9 [19] SHEN G, GLINKA G. Determination of weight functions from reference stress intensity factors[J]. Theoretical and Applied Fracture Mechanics, 1991, 15(3): 237-245. doi: 10.1016/0167-8442(91)90022-C [20] CIPOLLA R C. Technical basis for the revised stress intensity factor equation for surface flaws in ASME section XI appendix A[C]//International Pressure Vessels and Piping Codes and Standards: the 1995 Joint ASME/JSME Pressure Vessels and Piping Conference. Honolulu, Hawaii: ASME, 1995, 1: 105-122. [21] CIPOLLA R C, LEE D R. Technical basis for equations for stress intensity factor coefficients in ASME section XI appendix A[C]//Pressure Vessel and Piping Codes and Standards. San Diego, California, USA, 2004: 301-312. -
下载:
图(12)
计量
- 文章访问数: 18
- HTML全文浏览量: 11
- PDF下载量: 4
- 被引次数: 0
渝公网安备50010802005915号