有限尺寸下双材料界面附近裂纹位置对裂纹尖端的影响
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摘要
随着复合材料的应用和发展,不同材料组成的界面结构越来越受到人们的重视.界面层两侧材料的性能相异会引起材料界面端奇异性,同时界面和界面附近存在裂纹会引起裂尖处的应力奇异性.因此双材料界面附近的力学分析是比较复杂的.论文建立双材料直角界面模型,在材料界面附近预设初始裂纹,计算了有限材料尺寸对界面应力场及其附近裂纹应力强度因子的影响.运用弹性力学中的Goursat公式求得直角界面端在有限尺寸下的应力场以及其应力强度系数.通过叠加原理和格林函数法进一步得到在直角界面端附近的裂纹尖端应力强度因子.计算结果表明,在适当范围内改变材料内裂纹与界面之间的距离,界面附近裂纹尖端的应力强度因子随着裂纹与界面距离的增加而减少,并且逐渐趋于稳定.分析结果可以为预测双材料结构复合材料界面失效位置提供参考.
With the application and development of composite materials,the interface structure of different materials has been paid more and more attention.The dissimilarity of material properties on two sides of the interfacial layer can cause singularity of the interface.The interface and the cracks around it can lead to stress singularity at crack tips.The mechanical analysis near the bimaterial interface is thus complicated.In this paper,the rectangular interface model of bimaterial was established,and the initial crack was designed near the interface of the material.The influence of finite material size on stress field and stress intensity factor was calculated.The Goursat formula in elasticity was used to obtain the stress field and the stress intensity factor of the rectangular interface of finite size.The stress intensity factor at the crack tip near the rectangular interface was further obtained by the superposition principle and the Green function method.The results show that the stress intensity factor at the crack tip near the interface decreases with the increase of the distance between the crack and the interface,and gradually becomes stable.The results can provide a reference for predicting the failure position of bimaterial interface.
With the application and development of composite materials,the interface structure of different materials has been paid more and more attention.The dissimilarity of material properties on two sides of the interfacial layer can cause singularity of the interface.The interface and the cracks around it can lead to stress singularity at crack tips.The mechanical analysis near the bimaterial interface is thus complicated.In this paper,the rectangular interface model of bimaterial was established,and the initial crack was designed near the interface of the material.The influence of finite material size on stress field and stress intensity factor was calculated.The Goursat formula in elasticity was used to obtain the stress field and the stress intensity factor of the rectangular interface of finite size.The stress intensity factor at the crack tip near the rectangular interface was further obtained by the superposition principle and the Green function method.The results show that the stress intensity factor at the crack tip near the interface decreases with the increase of the distance between the crack and the interface,and gradually becomes stable.The results can provide a reference for predicting the failure position of bimaterial interface.
引文
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[14]Li X F,Tang G J.Shen Z B.Stress intensify factors for an external circular crack at the interface of a biomaterial in shear-compression[J].Mechanics of Materials,2015,85:80-93.
[15]Guo J X,Luo J,Xiao Z M.On the opening profile and near tip fields of an interface crack between a polymeric hydrogel and a rigid substrate[J].Engineering Fracture Mechanics,2016,153:91-102.
[16]Hideo Koguchi,Koki Yoko Yama,Chonlada Luangarpa.Variation of stress intensity factor along a small interface crack front in singular stress fields[J].International Journal of Solids and Structures,2015,71:156-168.
[17]FettT,Tilscher M,Munz D.Weight functions for cracks near the interface of a biomaterial joint and application to thermal stresses[J].Engineering Fracture Mechanics,1997,56:400-402.
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[19]Hatori T.A stress-singularity-parameter approach for evaluating adhesive strength of single-lap joints[J].Transactions of the Japan Society of Mechanical Engineers,1990,56:618-623.
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[21]Wang Q Z.Some simple mode-I SIF expressions of finite width strip with a center crack derived by using an approximate weight function[J].Eng.Fract.Mech,1998,60(1):37-45.
[22]米红林,方如华.金瓷修复体双材料界面断裂有限元分析[J].同济大学学报,2005,33(1):100-103.(Mi H L,Fang R H.Finite element analysis of bimaterial interfacial facture intensity in porcelain-fused-to-metal restoration[J].Journal of Tongji Univesity(Natural Scienced),2005,33(1):100-103.(in Chinese))
[23]Guo J X,Luo J,Xiao Z M.On the opening profile and near tip fields of an interface crack between a polymeric hydrogel and a rigid substrate[J].Engineering Fracture Mechanics,2016,153:91-102.
[24]Xia X Z,Zhang Q,Wang H,Yang S.The numerical simulation of interface crack propagation without remeshing[J].Technological Sciences,2011,54(7):1923-1929.
[25]Dundurs J.Discussion of edge boned dissimiliar orthogonal elastic wedges under normal and shear loading[J].J Appl Mech,1971,38:377-386.
[26]Hattori T,Sakata S,Hatsuda T,Murakami G.A stress singularity parameters approach for evaluating adhesive strength[J].Nihon Kikai Gakkai Ronbunshu A Hen/Transactions of the Japan Society of Mechanical Engineers Part A,1988,A54-499:597-603.
[27]许金泉.界面力学[M].科学出版社,2005:154-156.(Xu J Q.The Mechanics of Interface[M].Science Press,2005:154-156.(in Chinese))
[28]唐亮,许金泉.直角结合异材界面端应力强度系数的经验公式[J].力学季刊,2005,26(1):96-101.(Tang L,Xu J Q.An empirical formula for stress intensity coefficient of orthogonal bonded materials near interface end[J].Chinese Quart Erly of Mechanics,2005,26(1):96-101.(in Chinese))
[29]Xu J Q,Mutoh Y.Singular of residual stress field near the interface edge[J].Nihon Kikai Gakkai Ronbunshu A Hen/Transactions of the Japan Society of Mechanical Engineers Part A,1996,A62-597:1219-1225.
[30]许金泉,姜菊生.界面端附近裂纹的应力强度因子[J].上海力学,1998.19(3):221-227.(Xu J Q,Jiang J S.The Stress intensity factor of crack near interface end[J].Shanghai Journal of Mechanics,1998,19(3):221-227.(in Chinese))
[2]Williams M L,Calif P.Stress singularities resulting from various boundary conditions in angular corners of plates in extension[J].ASME Journal of Applied Mechanics,1952,19:526-528.
[3]Suo Z G.Singularities,interfaces and cracks in dissimilar anisotropic media[J].Matical and Physical Sciences,1990,427(A):331-358.
[4]Erdogan F.Bonded dissimilar materials containing cracks paralleling to the interface[J].Engng Fract Mech,1971,3:231-240.
[5]Hutchinson J W,Mear M,W Rice J R.Crack paralleling an interface between dissimilar materials[J].J Appl Mech,1987,54:828-834.
[6]England F.Stress distribution in bonded dissimilar materials with cracks[J].J Appl Mech,1965,32:403-411.
[7]England A H.A crack between dissimilar media[J].J Appl Mech,1965,32:400-407.
[8]Rice J R,Sih G C.Plane problems of cracks in dissimilar media[J].ASME Journal of Applied Mechanics,1965,2:418-423.
[9]Cominiou M.The interface crack in a combined tension-compression and shear field[J].J Appl Mech,1979,6:345-352.
[10]Rice J R.Elastic fracture mechanics concepts for interfacial cracks[J].ASME Journal of Applied Mechanics,1988,5:98-103.
[11]Tafreshi A.Computation of Jk-intergrals for biomaterial interface cracks using boundary element crack shape sensitivities[J].Theoretical and Applied Fracture Mechanics,2016,82:77-87.
[12]Nao-Aki Noda,Tatsujiro Miyazaki,Li R.Debonding strength evaluation in terms of the intensity of singular stress at the interface corner with and without fictitious crack[J].International Journal of Adhesion&Adhesives,2015,61:46-64.
[13]Li X F,Tang G J,Shen Z B.Interface crack embedded in a bi-material plane under shear and compression[J].Mechanics of Materials,2015,85:80-93.
[14]Li X F,Tang G J.Shen Z B.Stress intensify factors for an external circular crack at the interface of a biomaterial in shear-compression[J].Mechanics of Materials,2015,85:80-93.
[15]Guo J X,Luo J,Xiao Z M.On the opening profile and near tip fields of an interface crack between a polymeric hydrogel and a rigid substrate[J].Engineering Fracture Mechanics,2016,153:91-102.
[16]Hideo Koguchi,Koki Yoko Yama,Chonlada Luangarpa.Variation of stress intensity factor along a small interface crack front in singular stress fields[J].International Journal of Solids and Structures,2015,71:156-168.
[17]FettT,Tilscher M,Munz D.Weight functions for cracks near the interface of a biomaterial joint and application to thermal stresses[J].Engineering Fracture Mechanics,1997,56:400-402.
[18]Fett T,Tilscher M,Munz D.Weight functions for sub-interface cracks[J].International Journal of Solids and Structures,1997,34:393-400.
[19]Hatori T.A stress-singularity-parameter approach for evaluating adhesive strength of single-lap joints[J].Transactions of the Japan Society of Mechanical Engineers,1990,56:618-623.
[20]施斌,姜洪涛.在外力作用下土体内部裂隙发育过程的CT研究[J].岩土工程学报,2000,22(5):537-541.(Shi B,Jiang H T.A study on the development of failures inside soil under the external force using CT technique[J].Chinese Journal of Geotechnical Engineering,2000,22(5):537-541.(in Chinese))
[21]Wang Q Z.Some simple mode-I SIF expressions of finite width strip with a center crack derived by using an approximate weight function[J].Eng.Fract.Mech,1998,60(1):37-45.
[22]米红林,方如华.金瓷修复体双材料界面断裂有限元分析[J].同济大学学报,2005,33(1):100-103.(Mi H L,Fang R H.Finite element analysis of bimaterial interfacial facture intensity in porcelain-fused-to-metal restoration[J].Journal of Tongji Univesity(Natural Scienced),2005,33(1):100-103.(in Chinese))
[23]Guo J X,Luo J,Xiao Z M.On the opening profile and near tip fields of an interface crack between a polymeric hydrogel and a rigid substrate[J].Engineering Fracture Mechanics,2016,153:91-102.
[24]Xia X Z,Zhang Q,Wang H,Yang S.The numerical simulation of interface crack propagation without remeshing[J].Technological Sciences,2011,54(7):1923-1929.
[25]Dundurs J.Discussion of edge boned dissimiliar orthogonal elastic wedges under normal and shear loading[J].J Appl Mech,1971,38:377-386.
[26]Hattori T,Sakata S,Hatsuda T,Murakami G.A stress singularity parameters approach for evaluating adhesive strength[J].Nihon Kikai Gakkai Ronbunshu A Hen/Transactions of the Japan Society of Mechanical Engineers Part A,1988,A54-499:597-603.
[27]许金泉.界面力学[M].科学出版社,2005:154-156.(Xu J Q.The Mechanics of Interface[M].Science Press,2005:154-156.(in Chinese))
[28]唐亮,许金泉.直角结合异材界面端应力强度系数的经验公式[J].力学季刊,2005,26(1):96-101.(Tang L,Xu J Q.An empirical formula for stress intensity coefficient of orthogonal bonded materials near interface end[J].Chinese Quart Erly of Mechanics,2005,26(1):96-101.(in Chinese))
[29]Xu J Q,Mutoh Y.Singular of residual stress field near the interface edge[J].Nihon Kikai Gakkai Ronbunshu A Hen/Transactions of the Japan Society of Mechanical Engineers Part A,1996,A62-597:1219-1225.
[30]许金泉,姜菊生.界面端附近裂纹的应力强度因子[J].上海力学,1998.19(3):221-227.(Xu J Q,Jiang J S.The Stress intensity factor of crack near interface end[J].Shanghai Journal of Mechanics,1998,19(3):221-227.(in Chinese))
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