, Volume 49, Issue 2, pp 493–502 | Cite as

Elastic interaction between edge dislocation, concentrated force, point heat source and edge crack in a semi-infinite plane

  • Jia Li
  • QiHong Fang
  • YouWen Liu


We investigate the interaction between edge crack and edge dislocation as well as concentrated force and point heat source. The stress intensity factors at the edge crack tip and the image forces acting on the edge dislocation are calculated. The influence of the concentrated force, point heat source and edge dislocation on the shielding and anti-shielding effects to edge crack as well as the glide and climb forces acting on the edge dislocation is examined in detail. The results indicate that the shielding and anti-shielding effects increase acutely with the increment of concentrated force and point heat source. In addition, the glide and climb forces increase acutely with the decrement of the distance between dislocation and crack tip.


Edge dislocation Concentrated force Point heat source Edge crack Shielding effect Image force 



The authors would like to deeply appreciate the support from the NNSFC (11172094 and 11172095) and the NCET-11-0122. This work was also supported by Hunan Provincial Natural Science Foundation for Creative Research Groups of China (Grant No. 12JJ7001).


  1. 1.
    Song HP, Gao CF (2012) The interaction between a screw dislocation and a rigid wedge inhomogeneity with an elastic circular inhomogeneity at the tip. Meccanica 47:1097–1102 CrossRefMathSciNetGoogle Scholar
  2. 2.
    Toya M (1974) A crack along the interface of a circular inclusion embedded in an infinite solid. J Mech Phys Solids 22:325–348 ADSCrossRefMATHGoogle Scholar
  3. 3.
    Song HP, Fang QH, Liu YW (2009) The interaction between a screw dislocation and a circular inhomogeneity in gradient elasticity. Meccanica 44:499–506 CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Gao H, Rice J (1986) Shear stress intensity factors for a planar crack with slightly curved front. ASME Trans J Appl Mech 53:774–778 CrossRefMATHGoogle Scholar
  5. 5.
    Li YD, Lee KY, Feng FX (2011) Interface edge crack in a multiferroic semicylinder. Meccanica 46:1393–1399 CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Ismail AE, Ariffin AK, Abdullah S, Ghazali MJ (2012) Stress intensity factors for surface cracks in round bar under single and combined loadings. Meccanica 47:1141–1156 CrossRefGoogle Scholar
  7. 7.
    Szekrényes A (2013) Interface crack between isotropic Kirchhoff plates. Meccanica 48:507–526 CrossRefMathSciNetGoogle Scholar
  8. 8.
    Shi PP, Sun S, Li X (2013) Arc-shaped interfacial crack in a non-homogeneous electro-elastic hollow cylinder with orthotropic dielectric layer. Meccanica 48:415–426 CrossRefMathSciNetGoogle Scholar
  9. 9.
    Ringdalen VI, Stukowski A, Thaulow C, Østby E, Marian J (2013) Three-dimensional crack initiation mechanisms in bcc-Fe under loading modes I, II and III. Matter Sci Eng A 560:306–314 CrossRefGoogle Scholar
  10. 10.
    Belytschko T, Gracie R, Ventura G (2009) A review of extended/generalized finite element methods for material modeling. Model Simul Mater Sci 17:043001 ADSCrossRefGoogle Scholar
  11. 11.
    Shi J, Ma W, Li N (2013) Extended meshless method based on partition of unity for solving multiple crack problems. Meccanica. doi: 10.1007/s11012-013-9743-6 Google Scholar
  12. 12.
    Gao H, Klein P (1998) Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds. J Mech Phys Solids 46:187–218 ADSCrossRefMATHGoogle Scholar
  13. 13.
    Zhou ZG, Wang B (2006) An interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness. Meccanica 41:79–99 CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Guo JH, Lu ZX, Han HT, Yang Z (2009) Exact solutions for anti-plane problem of two asymmetrical edge cracks emanating from an elliptical hole in a piezoelectric material. Int J Solids Struct 46:3799–3809 CrossRefMATHGoogle Scholar
  15. 15.
    Shen MH, Chen SN, Lin CP (2012) A piezoelectric screw dislocation interacting with a half-plane trimaterial composite. Meccanica 47:1923–1933 CrossRefGoogle Scholar
  16. 16.
    Chue CH, Hsu WH (2008) Antiplane internal crack normal to the edge of a functionally graded piezoelectric/piezomagnetic half plane. Meccanica 43:307–325 CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Chao CK, Lee JY (1996) Interaction between a crack and a circular elastic inclusion under remote uniform heat flow. Int J Solids Struct 33:3865–3880 CrossRefMATHGoogle Scholar
  18. 18.
    Pham CV, Hasebe N, Wang XF, Saito T (2005) Interaction between a cracked hole and a line crack under uniform heat flux. Int J Fract 13:367–384 Google Scholar
  19. 19.
    Hasebe N, Wang XF, Saito T, Sheng W (2007) Interaction between a rigid inclusion and a line crack under uniform heat flux. Int J Solids Struct 44:2426–2441 CrossRefMATHGoogle Scholar
  20. 20.
    Hasebe N, Bucher C, Heuer R (2010) Heat conduction and thermal stress induced by an electric current in an infinite thin plate containing an elliptical hole with an edge crack. Int J Solids Struct 47:138–147 CrossRefMATHGoogle Scholar
  21. 21.
    Zhang TY, Tong P, Ouyang H, Lee S (1992) Interaction of an edge dislocation with a wedge crack. J Appl Phys 78:4873–4880 ADSCrossRefGoogle Scholar
  22. 22.
    Fan TY (2012) A plastic crack in a smectic liquid crystal a possible model. Philos Mag Lett 92:153–159 ADSCrossRefGoogle Scholar
  23. 23.
    Rice JR (1992) Dislocation nucleation from a crack tip: an analysis based on the Peierls concept. J Mech Phys Solids 40:239–271 ADSCrossRefGoogle Scholar
  24. 24.
    Rice JR, Beltz GE (1994) The activation energy for dislocation nucleation at a crack. J Mech Phys Solids 42:333–360 ADSCrossRefMATHGoogle Scholar
  25. 25.
    Cleveringa HHM, Van der Giessen E, Needleman A (2000) A discrete dislocation analysis of mode I crack growth. J Mech Phys Solids 48:1133–1157 ADSCrossRefMATHMathSciNetGoogle Scholar
  26. 26.
    Hansson P, Melin S (2005) Dislocation-based modelling of the growth of a microstructurally short crack by single shear due to fatigue loading. Int J Fract 27:347–356 MATHGoogle Scholar
  27. 27.
    Hansson P, Melin S (2006) Influence of fatigue load range on the growth of a microstructurally short edge crack simulated by a discrete dislocation formulation. Int J Fract 28:714–721 MATHGoogle Scholar
  28. 28.
    Olarnrithinun S, Chakravarthy SS, Curtin WA (2013) Discrete dislocation modeling of fracture in plastically anisotropic metals. J Mech Phys Solids 61:1391–1406 ADSCrossRefMathSciNetGoogle Scholar
  29. 29.
    Bhandakkar TK, Chng AC, Curtin WA, Gao H (2010) Dislocation shielding of a cohesive crack. J Mech Phys Solids 58:530–541 ADSCrossRefMATHMathSciNetGoogle Scholar
  30. 30.
    Majumdar BS, Burns SJ (1981) Crack tip shielding an elastic theory of dislocations and dislocation arrays near a sharp crack. Acta Mater 29:570–588 Google Scholar
  31. 31.
    Chiao YH, Clarke DR (1989) Direct observation of dislocation emission from crack tips in silicon at high temperatures. Acta Metall 37:203–219 CrossRefGoogle Scholar
  32. 32.
    Liu YW, Song HP, Fang QH, Jin B (2010) Shielding effect and emission condition of a screw dislocation near a blunt crack in elliptical inhomogeneity. Meccanica 45:519–530 CrossRefMATHGoogle Scholar
  33. 33.
    Lung CW, Wang L (1984) The image force on the dislocation near a finite length crack tip. Philos Mag A 36:69–84 Google Scholar
  34. 34.
    Lee S (1987) The image force on the screw dislocation around a crack of finite size. Eng Fract Mech 27:539–545 CrossRefGoogle Scholar
  35. 35.
    Ovid’ko IA, Sheinerman AG (2007) Special strain hardening mechanism and nanocrack generation in nanocrystalline materials. Appl Phys Lett 90:171927 ADSCrossRefGoogle Scholar
  36. 36.
    Ovid’ko IA, Sheinerman AG (2008) Nanocrack generation at dislocation-disclination configurations in nanocrystalline metals and ceramics. Phys Rev B 77:054109 ADSCrossRefGoogle Scholar
  37. 37.
    Zhou K, Wu MS (2010) Stress field of a disclination dipole in hcp bicrystal with imperfect interface. Int J Fract 48:237–252 Google Scholar
  38. 38.
    Fang QH, Feng H, Liu YW, Lin S, Zhang N (2012) Special rotational deformation effect on the emission of dislocations from a crack tip in deformed nanocrystalline solids. Int J Solids Struct 49:1406–1412 CrossRefGoogle Scholar
  39. 39.
    Chen YZ, Hasebe N (2001) An edge crack problem in a semi-infinite plane subjected to concentrated forces. Appl Math Mech 22:1279–1290 CrossRefMATHGoogle Scholar
  40. 40.
    Shiue ST, Hu CT, Lee S (1989) Elastic interaction between screw dislocations and a welded surface crack in composite materials. Eng Fract Mech 33:697–706 CrossRefGoogle Scholar
  41. 41.
    Muskhelishvili NL (1975) Some basic problems of mathematical theory of elasticity. Leyden, Noordhoff MATHGoogle Scholar
  42. 42.
    Bai XZ, Tian ZG, Zheng J (2009) Fracture mechanics electrothermal effect. Beijing, China Google Scholar
  43. 43.
    Fang QH, Song HP, Liu YW (2010) Elastic behaviour of an edge dislocation near a sharp crack emanating from a semi-elliptical blunt crack. Chin Phys B 19:016102 ADSCrossRefGoogle Scholar
  44. 44.
    Hirth JP, Lothe J (1983) Theory of dislocations. McGraw-Hill, New York Google Scholar
  45. 45.
    Zhang TY, Tong P, Hao O, Lee S (1995) Interaction of an edge dislocation with a wedge crack. J Appl Phys 78:4873–4880 ADSCrossRefGoogle Scholar
  46. 46.
    Stagni L (1993) Edge dislocation near an elliptic inhomogeneity with either an adhering or a slipping interface a comparative study. Philos Mag A 68:49–57 ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangshaP.R. China
  2. 2.College of Mechanical and Vehicle EngineeringHunan UniversityChangshaP.R. China

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