基于能量释放率的Ⅱ型裂纹分叉研究
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摘要
裂纹尖端存在奇异应力场,该类奇异应力场所具有的高度应力集中将导致裂纹开裂.本文应用典型的J积分理论来划分裂纹尖端的积分路径,基于能量释放率理论对Ⅱ型裂纹尖端的复杂分叉情况进行研究.通过所建立的断裂模型求解出Ⅱ型裂纹多种分叉形式的能量释放率的解析解;导出了各种分叉构型的能量驱动力;提出了各种分叉构型的K-型开裂准则;给出了裂纹分叉的临界开裂角;确定了裂纹的分叉韧性与断裂韧性之间的关系.通过本文研究方法得出的裂纹分叉形式及裂纹分叉临界开裂角与已有实验结果十分吻合.
An energy-based fracture model for multiple crack-branching has been proposed and formulized for the Mode-Ⅱ crack-tip conditions. An analytical solution of the energy release rate for multiple crack-branching from a Mode-Ⅱ crack tip has been established, and the cracking angles have been analytically derived. The multiple crack-branching mechanism for quasi-static Mode-Ⅱ crack has been theoretically investigated, the relationship between the stress intensity factor K-based criterions and the fracture toughness for crack branching has been defined. The multiple crack-branching phenomena and the critical cracking angle obtained by this paper agree well with the experimental results.
An energy-based fracture model for multiple crack-branching has been proposed and formulized for the Mode-Ⅱ crack-tip conditions. An analytical solution of the energy release rate for multiple crack-branching from a Mode-Ⅱ crack tip has been established, and the cracking angles have been analytically derived. The multiple crack-branching mechanism for quasi-static Mode-Ⅱ crack has been theoretically investigated, the relationship between the stress intensity factor K-based criterions and the fracture toughness for crack branching has been defined. The multiple crack-branching phenomena and the critical cracking angle obtained by this paper agree well with the experimental results.
引文
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[16]BUDIANSKY B,RICE J R.Conservation laws and energy-release rates[J].Journal of Applied Mechanics,1973,40(1):201-203.
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[2]韩世昌,黄亚宇,胡斌.通过裂纹开口位移(CMOD)对J积分预测的方法研究[J].力学季刊,2015,36(2):232-238.
[3]FENG G,KANG Y,MENG T,et al.The influence of temperature on Mode I fracture toughness and fracture characteristics of sandstone[J].Rock Mechanics&Rock Engineering,2017,50(8):2007-2019.
[4]ZHU Z M,XU W T,FENG R Q.A new method for measuring mode-I dynamic fracture toughness of rock under blasting loads[J].Experimental Techniques,2016,40(3):899-905.
[5]宋鹍,王路生,刘泊,等.基于位移连接的单晶银板I型边裂纹扩展过程跨连续介质/原子尺度数值模拟研究[J].机械强度,2018,40(2):319-324.
[6]谷新保,周小平,徐潇.高速运动裂纹扩展和分叉现象的近场动力学数值模拟[J].应用数学和力学,2016,37(7):729-739.
[7]TENG Z H,SUN F,WU S C,et al.An adaptively refined XFEM with virtual node polygonal elements for dynamic crack problems[J].Computational Mechanics,2018,1-3:1-20.
[8]赵雪芬,李星.一维六方准晶中星形静态裂纹和运动裂纹的解析解[J].力学季刊,2015,36(4):645-654.
[9]BOBARU F,ZHANG G F.Why do cracks branch?A peridynamic investigation of dynamic brittle fracture[J].International Journal of Fracture,2015,196(1-2):59-98.
[10]XIE Y J,LI J,HU X Z,et al.Modelling of multiple crack-branching from mode-I crack-tip in isotropic solids[J].Engineering Fracture Mechanics,2013,109(3):105-116.
[11]XIE Y J,HU X Z,WANG X H,et al.A theoretical note on mode I crack branching and kinking[J].Engineering Fracture Mechanics,2011,78(6):919-929.
[12]陈特,杨凤鹏,兰天.恒扭对汽车薄板I型疲劳裂纹扩展的影响[J].力学季刊,2017,38(4):772-779.
[13]AYATOLLAHI M R,BERTO F.Evolution of crack tip constraint in mode II elastic-plastic crack problem[J].Physical Mesomechanics,2018,21(2):173-177.
[14]MOGHADDAM M R,AYATOLLAHI M R,RAZAVI S M J,et al.Mode II brittle fracture assessment using an energy based criterion[J].Physical Mesomechanics,2017,20(2):142-148.
[15]RICE J R.A path independent integral and the approximate analysis of strain concentration by notches and cracks[J].Journal of Applied Mechanics,1967,35(2):379-386.
[16]BUDIANSKY B,RICE J R.Conservation laws and energy-release rates[J].Journal of Applied Mechanics,1973,40(1):201-203.
[17]SIH G C.Dynamic aspects of crack aspects of crack propagation[J].Inelastic Behavior of Solid,1969,20:607-639.
[18]GRIFFITH A A.The phenomena of rupture and flow in solids[J].Philosophical Transactions of the Royal Society of London,1921,221(2):163-198.
[19]CHUN J H,GURUSWAMI R,KAUSHIK B.Investigating the effective fracture toughness of heterogeneous materials[J].Conference Proceeding of the Society for Experimental Mechanics Series,2016,8:15-20.
[20]SULLIVAN A M.Stress corrosion crack velocity in 4340 steel[J].Engineering Fracture Mechanics,1972,4:65-76.
[21]BELCHER J L,BROWN H R.Crack branching and arrest in environmental cracking of polyethylene[J].Journal of Materials Science,1986,21:717-714.