基体中螺位错偶极子与含共焦钝裂纹椭圆夹杂的干涉效应
|
摘要
将复变函数的分区全纯理论、柯西型积分、应力函数奇性主部分析方法与Riemann边值问题相结合,研究了基体中的螺型位错偶极子与含共焦椭圆钝裂纹的椭圆夹杂的弹性干涉问题,求得了基体和夹杂区域复势函数的级数形式精确解.并由此推导出了基体和夹杂区域的应力场、椭圆钝裂纹右端点的应力强度因子以及作用在螺型位错偶极子中心的位错像力和像力偶矩的公式,同时分析了螺位错偶极子倾角、夹杂和椭圆钝裂纹的尺寸以及材料常数对它们的影响规律.结果表明:位错力和应力强度因子随螺位错偶极子倾角作周期变化,且受相对剪切模量的影响很大.
Combining sectional holomorphic function theory,Cauchy singular integral,singularity analysis of complex functions and Riemann boundary problem,the interaction between screw dipole inside matrix and confocal blunt crack in elastic elliptical inhomogeneity was investigated to obtain the complex function of matrix and inhomogeneity in series form. The singular stress field of matrix,the stress intensity factor of blunt crack tip and the image force and image torque acting on the center of screw dipole were deduced. The influences of the dip angle,the size of inhomogeneity and blunt crack,the material parameters were also analyzed. The results show that the image force and the stress intensity factor change periodically as the dip angle,and are significantly influenced by the relative shear modulus.
Combining sectional holomorphic function theory,Cauchy singular integral,singularity analysis of complex functions and Riemann boundary problem,the interaction between screw dipole inside matrix and confocal blunt crack in elastic elliptical inhomogeneity was investigated to obtain the complex function of matrix and inhomogeneity in series form. The singular stress field of matrix,the stress intensity factor of blunt crack tip and the image force and image torque acting on the center of screw dipole were deduced. The influences of the dip angle,the size of inhomogeneity and blunt crack,the material parameters were also analyzed. The results show that the image force and the stress intensity factor change periodically as the dip angle,and are significantly influenced by the relative shear modulus.
引文
[1]Smith E.The interaction between dislocations and inhomogeneities-I[J].International Journal of Engineering Science,1968,6(3):129-143.
[2]Smith E.The interaction between dislocations and inhomogeneities-II:a screw dislocation pile-up in an infinite body containing an elliptically cylindrical rigid inhomogeneity[J].International Journal of Engineering Science,1968,6(3):145-152.
[3]Fang Q H,Liu Y W,Jiang C P.Electroelastic interaction between a piezoelectric screw dislocation and an elliptical inclusion with interfacial cracks[J].Physica Status Solidi(b),2005,242(14):2775-2794.
[4]刘又文,宋豪鹏,方棋洪.螺型位错与含共焦裂纹弹性椭圆夹杂的干涉效应[J].湖南大学学报:自然科学版,2007,34(9):62-66.Liu Youwen,Song Haopeng,Fang Qihong.Interaction between a screw dislocation and a confocal crack in an elastic elliptical inhomogeneity[J].Journal of Hunan University:Natural Sciences,2007,34(9):62-66.(in Chinese)
[5]Liu Youwen,Song Haopeng,Fang Qihong,et al.Shielding effect and emission condition of a screw dislocation near a blunt crack in elliptical inhomogeneity[J].Meccanica,2010,45(4):519-530.
[6]Yu Min,Liu Youwen,Song Haopeng,et al.Electroelastic interaction between a piezoelectric screw dislocation and a confocal elliptic blunt crack with elliptical inhomogeneity[J].Theoretical and Applied Fracture Mechanics,2010,54(3):156-165.
[7]余敏,刘又文,宋豪鹏.纵向剪切下含共焦椭圆孔椭圆夹杂中压电螺位错的干涉效应[J].中南林业科技大学学报,2011,31(2):115-121.Yu Min,Liu Youwen,Song Haopeng.The interference effect between a screw dislocation and an elliptical inhomogeneity containing a confocal elliptic hole under longitudinal shear[J].Journal of Central South University of Forestry and Technology,2011,31(2):115-121.(in Chinese)
[8]Yu Min,Liu Youwen.The interaction between a screw dipole in matrix and an elliptical inhomogeneity containing a confocal crack[J].Advanced Materials Research,2011,287/288/289/290:1569-1573.
[9]Jiang Chunzhi,Xie Chao,Liu Youwen.A piezoelectric screw dislocation interacting with an elliptical piezoelectric inhomogeneity containing a confocal elliptical rigid core[J].Commun Theor Phys,2011,56(4):774-778.
[10]Jiang Chunzhi,Liu Youwen,Xie Chao.A magnetoelectric screw dislocation interacting with an elliptical inhomogeneity containing a confocal rigid line[J].Advanced Materials Research,2011,239/240/241/242:2195-2200.
[11]Sih G C,Paris P C,Erdogan F.Crack-tip,stress-intensity factors for plane extension and plane bending problem[J].J Appl Mech,1962,29(2):306-312.
[12]Juang R R,Lee S B.Elastic interaction between general parallel screw dislocations and a surface crack[J].J Appl Phys,1986,59(10):3421-3429.
[2]Smith E.The interaction between dislocations and inhomogeneities-II:a screw dislocation pile-up in an infinite body containing an elliptically cylindrical rigid inhomogeneity[J].International Journal of Engineering Science,1968,6(3):145-152.
[3]Fang Q H,Liu Y W,Jiang C P.Electroelastic interaction between a piezoelectric screw dislocation and an elliptical inclusion with interfacial cracks[J].Physica Status Solidi(b),2005,242(14):2775-2794.
[4]刘又文,宋豪鹏,方棋洪.螺型位错与含共焦裂纹弹性椭圆夹杂的干涉效应[J].湖南大学学报:自然科学版,2007,34(9):62-66.Liu Youwen,Song Haopeng,Fang Qihong.Interaction between a screw dislocation and a confocal crack in an elastic elliptical inhomogeneity[J].Journal of Hunan University:Natural Sciences,2007,34(9):62-66.(in Chinese)
[5]Liu Youwen,Song Haopeng,Fang Qihong,et al.Shielding effect and emission condition of a screw dislocation near a blunt crack in elliptical inhomogeneity[J].Meccanica,2010,45(4):519-530.
[6]Yu Min,Liu Youwen,Song Haopeng,et al.Electroelastic interaction between a piezoelectric screw dislocation and a confocal elliptic blunt crack with elliptical inhomogeneity[J].Theoretical and Applied Fracture Mechanics,2010,54(3):156-165.
[7]余敏,刘又文,宋豪鹏.纵向剪切下含共焦椭圆孔椭圆夹杂中压电螺位错的干涉效应[J].中南林业科技大学学报,2011,31(2):115-121.Yu Min,Liu Youwen,Song Haopeng.The interference effect between a screw dislocation and an elliptical inhomogeneity containing a confocal elliptic hole under longitudinal shear[J].Journal of Central South University of Forestry and Technology,2011,31(2):115-121.(in Chinese)
[8]Yu Min,Liu Youwen.The interaction between a screw dipole in matrix and an elliptical inhomogeneity containing a confocal crack[J].Advanced Materials Research,2011,287/288/289/290:1569-1573.
[9]Jiang Chunzhi,Xie Chao,Liu Youwen.A piezoelectric screw dislocation interacting with an elliptical piezoelectric inhomogeneity containing a confocal elliptical rigid core[J].Commun Theor Phys,2011,56(4):774-778.
[10]Jiang Chunzhi,Liu Youwen,Xie Chao.A magnetoelectric screw dislocation interacting with an elliptical inhomogeneity containing a confocal rigid line[J].Advanced Materials Research,2011,239/240/241/242:2195-2200.
[11]Sih G C,Paris P C,Erdogan F.Crack-tip,stress-intensity factors for plane extension and plane bending problem[J].J Appl Mech,1962,29(2):306-312.
[12]Juang R R,Lee S B.Elastic interaction between general parallel screw dislocations and a surface crack[J].J Appl Phys,1986,59(10):3421-3429.