Path Stability of a Crack with an Eigenstrain

  • Beom, Hyeon-Gyu (Department of Mechanical Engineering, Inha University) ;
  • Kim, Yu-Hwan (Department of Mechanical Engineering, Inha University) ;
  • Cho, Chong-Du (Department of Mechanical Engineering, Inha University) ;
  • Kim, Chang-Boo (Department of Mechanical Engineering, Inha University)
  • Published : 2006.09.01

Abstract

A slightly curved crack with an eigenstrain is considered. Solutions for a slightly curved crack in a linear isotropic material under asymptotic loading as well as for a slightly curved crack in a linear isotropic material with a concentrated force are obtained from perturbation analyses, which are accurate to the first order of the parameter representing the non-straightness. Stress intensity factors for a slightly curved crack with an eigenstrain are obtained from the perturbation solutions by using a body force analogy. Particular attention is given to the crack path stability under mode I loading. A new parameter of crack path stability is proposed for a crack with an eigenstrain. The path stability of a crack with steady state growth in a transforming material and a ferroelectric material is examined.

Keywords

References

  1. Budiansky, B., Hutchinson, J. W. and Lambropoulos, 1983, 'Continuum Theory of Dilatant Transformation Toughening in Ceramics,' International Journal of Solids and Structures, Vol. 19, pp. 337-355 https://doi.org/10.1016/0020-7683(83)90031-8
  2. Cotterell, B. and Rice, J. R., 1980, 'Slightly Curved or Kinked Cracks,' International Journal Fracture, Vol. 16, pp. 155-169 https://doi.org/10.1007/BF00012619
  3. Huchinson, J. W. and Suo, Z., 1992, 'Mixed Mode Cracking in Layered Materials,' Advances in Applied Mechanics, Vol. 29, pp.63-191
  4. Karihaloo, B. L., Keer, L. M., Nernat-Nasser, S. and Oranratnachai, A., 1981, 'Approximate Description of Crack Kinking and Curving,' Journal of Applied Mechanics, Vol. 48, pp. 515-519 https://doi.org/10.1115/1.3157665
  5. Muskhelishivili, N. I., 1963, Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, The Netherlands
  6. Reece, M. J. and Guiu, F., 2002, 'Toughening Produced by Crack-Tip-Stress-Induced Domain Reorientation in Ferroelectric and / or Ferroelastic Materials,' Philosophical Magazine A, Vol. 82, pp.29-38 https://doi.org/10.1080/01418610110058301
  7. Schaufele, A. B. and Hardtl, K. H., 1996, 'Ferroelastic Properties of Lead Zirconate Titanate Ceramics,' Journal of the American Ceramic Society, Vol. 79, pp. 2637-2640 https://doi.org/10.1111/j.1151-2916.1996.tb09027.x
  8. Sumi, Y., Nemat-Nasser, S. and Keer, L. M., 1985, 'On Crack Path Stability in a Finite Body,' Engineering Fracture Mechanics, Vol. 22, pp. 759-771 https://doi.org/10.1016/0013-7944(85)90106-7
  9. Suo, Z., 1989, 'Singularities Interacting with Interfaces and Cracks,' International Journal of Solids and Structures, Vol. 25, pp. 1133-1142 https://doi.org/10.1016/0020-7683(89)90072-3
  10. Tan, X. and Shang, J. K., 2000, 'Crack Deflection in Relaxor Ferroelectric PLZT under Inclined Cyclic Electric Field,' Scripta Materialia, Vol. 43, pp. 925-928 https://doi.org/10.1016/S1359-6462(00)00514-5
  11. Uchino, K. and Furuta, A., 1992, 'Destruction Mechanism of Multilayer Ceramic Actuators,' Proceedings of ISAF 1992. Greenville, South Carolina, pp. 195-198 https://doi.org/10.1109/ISAF.1992.300660