含共线裂纹功能梯度材料断裂问题分析
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摘要
应用分层原理分析了具有不同弹性模量含共线双裂纹的功能梯度材料断裂问题。通过积分变换得到嵌入功能梯度材料裂纹的应力场和位移场,结合边界条件、连续条件及单个裂纹的应力场和位移场,将求解该裂纹问题转化为求解奇异积分方程组。通过求解奇异积分方程组得到裂纹的应力强度因子。最后针对材料弹性模量和裂纹几何参数对应力强度因子的影响进行了探讨。结果表明材料弹性模量分布形式对裂纹的应力强度因子影响显著,该结果可为功能梯度材料制备及材料设计等提供理论依据。
The fracture problem of the functionally graded material with collinear cracks under the condition of different elasticity moduli. The stress fields and displacement fields of cracks in the functionally graded strip can be obtained by means of the method of integral transform. And solving the problem of cracks is equivalent to solving the problem of singular integral equations combined with boundary conditions and continuity conditions after solving the stress fields and displacement fields of each crack. The stress intensity factors can be obtained after solving the singular integral equations. The effects of elasticity moduli of materials and geometric parameters of cracks on SIFs are discussed. The results show that the distribution of elasticity moduli may affect SIFs significantly. And this study can provide scientific basis for forming FGMs and designing the property distribution in FGMs.
The fracture problem of the functionally graded material with collinear cracks under the condition of different elasticity moduli. The stress fields and displacement fields of cracks in the functionally graded strip can be obtained by means of the method of integral transform. And solving the problem of cracks is equivalent to solving the problem of singular integral equations combined with boundary conditions and continuity conditions after solving the stress fields and displacement fields of each crack. The stress intensity factors can be obtained after solving the singular integral equations. The effects of elasticity moduli of materials and geometric parameters of cracks on SIFs are discussed. The results show that the distribution of elasticity moduli may affect SIFs significantly. And this study can provide scientific basis for forming FGMs and designing the property distribution in FGMs.
引文
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[2] 仲政,吴林志,陈伟球.功能梯度材料与结构的若干力学问题研究进展[J].力学进展,2010,40(5):528-541.ZHONG Zheng,WU LinZhi,CHEN WeiQiu.Progress in the study on mechanics problems of functionally graded materials and structures[J].Advances in Mechanics,2010,40(5):528-541(In Chinese).
[3] Ding Sheng-Hu,Li Xing.Mode-I crack problem for functionally graded layered structures[J].Int J Fract,2011(168):209-226.
[4] Monfared MM,Ayatollahi M.Multiple crack problems in nonhomogeneous orthotropic planes under mixed mode loading conditions[J].Engineering Fracture Mechanics,2016(155):1-17.
[5] Monfared MM,Bagheri R.Multiple interacting arbitrary shaped cracks in an FGM plane[J].Theoretical and Applied Fracture mechanics,2016(86):161-170.
[6] Jamia N,El-Borgi S,Usman S.Non-local behavior of two collinear mixed-mode limited-permeable cracks in a functionally graded piezoelectric medium[J].Applied Mathematical Modeling,2016(40):5988-6005.
[7] Huang Gan-Yun,Wang Yue-Sheng,Yu Shou-Wen.Fracture analysis of a functionally graded interfacial zone under plane deformation[J].International Journal of Solids and Structures,2004(41):731-743.
[8] Huang Gan-Yun,Wang Yue-Sheng,Yu Shou-Wen.A model for fracture analysis of functionally graded coatings under plane deformation[J].Mechanics and Materials,2005(37):507-516.
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[10] Shbeeb NI,Binienda WK,Kreider KL.Analysis of the driving forces for multiple cracks in an infinite nonhomogeneous plat,Part Ⅱ:numerical solutions[J].J Appl Mech,1999(66):501-506.
[11] Guo Li-Cheng,Wang Zhi-Hai,Zhang Li.A fracture mechanics problem of a functionally graded layered structure with an arbitrarily oriented crack crossing the interface[J].Mechanics of Materials,2012(46):69-82.
[2] 仲政,吴林志,陈伟球.功能梯度材料与结构的若干力学问题研究进展[J].力学进展,2010,40(5):528-541.ZHONG Zheng,WU LinZhi,CHEN WeiQiu.Progress in the study on mechanics problems of functionally graded materials and structures[J].Advances in Mechanics,2010,40(5):528-541(In Chinese).
[3] Ding Sheng-Hu,Li Xing.Mode-I crack problem for functionally graded layered structures[J].Int J Fract,2011(168):209-226.
[4] Monfared MM,Ayatollahi M.Multiple crack problems in nonhomogeneous orthotropic planes under mixed mode loading conditions[J].Engineering Fracture Mechanics,2016(155):1-17.
[5] Monfared MM,Bagheri R.Multiple interacting arbitrary shaped cracks in an FGM plane[J].Theoretical and Applied Fracture mechanics,2016(86):161-170.
[6] Jamia N,El-Borgi S,Usman S.Non-local behavior of two collinear mixed-mode limited-permeable cracks in a functionally graded piezoelectric medium[J].Applied Mathematical Modeling,2016(40):5988-6005.
[7] Huang Gan-Yun,Wang Yue-Sheng,Yu Shou-Wen.Fracture analysis of a functionally graded interfacial zone under plane deformation[J].International Journal of Solids and Structures,2004(41):731-743.
[8] Huang Gan-Yun,Wang Yue-Sheng,Yu Shou-Wen.A model for fracture analysis of functionally graded coatings under plane deformation[J].Mechanics and Materials,2005(37):507-516.
[9] Guo Li-Cheng,Noda N.Modeling method for a crack problem of functionally graded materials with arbitrary properties—piecewise-exponential model[J].Int J Solids Struct,2007(44):6768-6790.
[10] Shbeeb NI,Binienda WK,Kreider KL.Analysis of the driving forces for multiple cracks in an infinite nonhomogeneous plat,Part Ⅱ:numerical solutions[J].J Appl Mech,1999(66):501-506.
[11] Guo Li-Cheng,Wang Zhi-Hai,Zhang Li.A fracture mechanics problem of a functionally graded layered structure with an arbitrarily oriented crack crossing the interface[J].Mechanics of Materials,2012(46):69-82.