超高压容器开孔处裂纹最深点处应力强度因子的计算方法  

Calculation method of stress intensity factor at deepest point of crack at opening of ultra-high-pressure vessel

作　　者：汪志福 秦宗川 张羽 牛铮 范海俊 戴兴旺 WANG Zhifu;QIN Zongchuan;ZHANG Yu;NIU Zheng;FAN Haijun;DAI Xingwang(National Technology Research Center on Pressure Vessel and Pipeline Safety Engineering,Hefei General Machinery Research Institute Co.,Ltd.,Hefei 230031,China;Henan Zhongyuan Special Steel Equipment Manufacturing Co.,Ltd.,Jiyuan 459000,China)

机构地区：[1]合肥通用机械研究院有限公司国家压力容器与管道安全工程技术研究中心,安徽合肥230031 [2]河南中原特钢装备制造有限公司,河南济源459000

出　　处：《机电工程》2024年第6期1109-1115,共7页Journal of Mechanical & Electrical Engineering

基　　金：国家重点研发计划项目(2022YFB3306401,2022YFB4003003);国家工信部高质量发展专项(TC220A04W-3、188)。

摘　　要：由于超高压容器开孔处的应力梯度变化很大,通常由最小二乘法拟合的三次多项式往往与实际的应力分布之间存在较大偏差。针对这一问题,提出了一种分段插值求解的计算方法。首先,基于应力强度因子及通用权函数的理论,推导出了常数插值、线性插值、二次插值求解的计算公式;其次,结合工程实例,基于无裂纹体的弹性应力分析,对比分析了常规最小二乘法与常数插值、线性插值、二次插值的应力分布表征精度及应力强度因子计算结果,确定了线性插值和二次插值方法的可靠性;然后,分析了数据采集量对线性插值和二次插值计算结果的影响,确定了线性插值方法的实用性;最后,对线性插值与有限元分析的计算结果进行了分析验证。研究结果表明:应力分布表征精度为“最小二乘法<常数插值<线性插值<二次插值”,计算结果相对误差约为15%;随着采集数据量的增加,采用线性插值方法的计算结果能较快收敛,更适合于工程计算;线性插值与有限元法的计算结果高度一致,证明了线性插值计算的可靠性。Due to the significant variation of the stress gradient at the opening of ultra-high-pressure vessel,the cubic polynomial usually fitted by the least square method often has a large deviation from the actual stress distribution.To solve this problem,a calculation method based on piecewise interpolation was proposed.Firstly,based on the theory of stress intensity factor and general weight function,the calculation formulas were derived by constant interpolation,linear interpolation and quadratic interpolation.Secondly,combining with an engineering example,based on the elastic stress analysis of a crack free body,the calculation results of the stress distribution characterization accuracy and stress intensity factor of the conventional least square method,constant interpolation,linear interpolation and quadratic interpolation were compared and analyzed,and the reliability of the linear interpolation and quadratic interpolation methods was determined.Then,the influence of data collection on the results of linear interpolation and quadratic interpolation was analyzed,and the practicability of linear interpolation method was determined.Finally,the results of linear interpolation and finite element analysis were analyzed and verified.The results show that the representation accuracy of stress distribution is “the least square method < constant interpolation < linear interpolation < quadratic interpolation”,and the relative error of calculation results is about 15%.With the increase of the amount of collected data,the calculation results using linear interpolation method can converge faster,which is more suitable for engineering calculation.The results of linear interpolation and finite element method are highly consistent,which proves the reliability of linear interpolation calculation.

关 键 词：超高压容器开孔处 应力强度因子 通用权函数 分段插值求解计算方法 裂纹最深点处 线性插值计算方法 

分 类 号：TH49[机械工程—机械制造及自动化]