粘弹性应变能释放率的虚拟网格计算方法  

Virtual grid method for evaluation of the viscoelastic strain energy release rate

作　　者：崔辉如 姜强强 沈栋 吕轩 任孝宇 CUI Huiru;JIANG Qiangqiang;SHEN Dong;LYU Xuan;REN Xiaoyu(College of Defense Engineering,Army Engineering University of PLA,Nanjing210007,China;Postdoctoral Station of Civil Engineering,Army Engineering University of PLA,Nanjing210007,China;91112 Army of the PLA,Ningbo315046,China;Hubei Key Laboratory of Advanced Aerospace Propulsion Technology,Wuhan430040,China)

机构地区：[1]陆军工程大学国防工程学院,南京210007 [2]陆军工程大学土木工程博士后科研流动站,南京210007 [3]中国人民解放军91112部队,宁波315046 [4]航天动力先进技术湖北省重点实验室,武汉430040

出　　处：《固体火箭技术》2023年第6期915-922,共8页Journal of Solid Rocket Technology

基　　金：香江学者计划(XJ2023015);国家自然科学基金(12202496);中国博士后科学基金资助项目(2022M723866);江苏省青年基金(BK20210435)。

摘　　要：应变能释放率是粘弹性裂纹扩展判断的重要依据。为了解决低质量网格条件下的高精度粘弹性应变能释放率的数值计算问题,提出了裂纹尖端虚拟网格方法。在原始网格位移场基础上通过插值手段获得虚拟网格位移场、应力及应变场分布;基于虚拟网格信息并结合虚拟裂纹闭合方法,开展应变能释放率的数值计算。虚拟网格方法在应对裂纹扩展过程中任意复杂网格形式的同时,不再需要对原始裂纹尖端进行精细网格划分。两种典型断裂模式下的算例仿真结果表明,全积分形式的虚拟网格方法可以实现低泊松比条件下应变能释放率的高精度数值计算,相对误差均在5%以内。为了应对高泊松比下的断裂问题,设计了虚拟网格方法的缩减积分方案;缩减积分方案下的应变能释放率相对误差在1%左右,计算精度较全积分方案大幅提高。The strain energy release rate is an important basis for the judgment of viscoelastic crack propagation.In order to solve the problem of numerical calculation of high-precision viscoelastic strain energy release rate under the condition of low-precision mesh,a virtual grid method for crack tip was proposed.Based on the original mesh displacement field,the virtual grid displacement field,stress and strain field distribution were obtained by interpolation.Based on the virtual grid information and the virtual crack closure method,the strain energy release rate was calculated.The virtual grid method can deal with any complex mesh form in the process of crack propagation,and at the same time,fine meshing of the original crack tip was no longer required.The simulation results show that the fully integrated virtual grid method can realize the high-precision numerical calculation of strain energy release rate under low Pois-son's ratio,and the relative error is less than 5%.To deal with the fracture problem at high Poisson's ratio,the reduced integration scheme of the virtual grid method was designed.Examples show that the relative error of strain energy release rate in the reduced inte-gration scheme is about 1%,the calculation accuracy is greatly improved compared with the full integration scheme.

关 键 词：粘弹性 裂纹扩展 应变能释放率 虚拟网格方法 

分 类 号：V435[航空宇航科学与技术—航空宇航推进理论与工程]