摘要
为了准确地计算出高压容器裂纹扩展过程中最深点处的应力强度因子,本文提出了将应力数据进行高阶多项式拟合,进而计算应力强度因子的方法。文中以高压容器开孔处裂纹为例,基于不同采集数据量下的应力数据,使用不同次数的多项式拟合,计算了各个裂纹深度下的最深点处应力强度因子,分析了多项式次数及采集数据量对计算结果的影响,对比验证了本方法与文献中线性插值方法的计算结果。对比研究结果表明,随着多项式次数的增加,拟合曲线的表征精度越高,计算结果逐渐逼近并趋于稳定,低阶(三次)与高阶多项式拟合的计算结果相对误差呈现出“倒S”型趋势,最小相对误差约为-20%;随着数据量的增加,计算结果逐渐收敛,较低与较高数据量下的计算结果相对误差呈现出震荡衰减的趋势,最大相对误差约为7.1%;基于高阶多项式拟合与分段线性插值的计算结果基本重合,表明本方法具有一定的可靠性,并适用于裂纹扩展过程中最深点处应力强度因子的计算。
In order to accurately calculate the stress intensity factor at the deepest point during the crack propagation process of high-pressure vessels,a method was proposed for fitting the stress data with highorder polynomials and then calculating the stress intensity factor.Taking the crack at the opening of a highpressure vessel as an example,based on stress data collected with varying data volumes,polynomial fitting of varying degrees was employed to calculate the stress intensity factor at the deepest point of each crack depth.The influence of polynomial degree and data collection volume on the calculation results was analyzed,and the calculation results of this method were compared and validated against the linear interpolation method in the literature.The research results indicate that as the increase of polynomial degree,the characterization accuracy of the fitted curve improves,and the calculation results gradually converge and stablize.The relative error between the calculation results using low-order(third-order)and high-order polynomial fitting shows an"inverted S"trend,with a minimum relative error of about−20%;As the amount of data increases,the calculation results gradually converge,and the relative error of the calculation results under lower and higher data volumes shows a trend of oscillation attenuation,with a maximum relative error of about 7.1%;The calculation results based on high-order polynomial fitting and piecewise linear interpolation are basically consistent,indicating that this method has certain reliability and is suitable for calculating the stress intensity factor at the deepest point during crack propagation.
作者
汪志福
范志超
秦宗川
牛铮
范海俊
戴兴旺
WANG Zhi−fu;FAN Zhi−chao;QIN Zong−chuan;NIU Zheng;FAN Hai−jun;DAI Xing−wang(National Technology Research Center on Pressure Vessel and Pipeline Safety Engineering,Hefei General Machinery Research Institute,Hefei 230031,China)
出处
《船舶力学》
北大核心
2025年第8期1277-1287,共11页
Journal of Ship Mechanics
基金
国家重点研发计划项目(2022YFB4003003)
工信部高质量发展专项项目(TC220A04W-3、188)。
关键词
高阶多项式拟合
高压容器
裂纹最深点处
应力强度因子
计算方法
high-order polynomial fitting
high pressure vessel
the deepest point of crack
stress intensity factor
computing method
