KSME Journal

, 3:103

# Finite crack propagation in a micropolar elastic solid

• Seog Young Han
• M. N. L. Narasimhan
• T. C. Kennedy
Article

## Abstract

The dynamic propagation of a finite crack under mode-1 loading in a micropolar elastic solid is investigated. By using an integral transform method, a pair of two-dimensional singular integral equations governing stress and couple stress is formulated in terms of displacement transverse to the crack, macro and micro rotations, and microinertia. These equations are solved numerically, and solutions for dynamic stress intensity and couple stress intensity factors are obtained by utilizing the values of the strengths of the square root singularities in macrorotation and the gradient of microrotation at the crack tips. The motion of the crack tips and the load on the crack surface are not prescribed in the formulation of the problem. Therefore, the method of solution is applicable to nonuniform rates of propagation of a crack under an arbitrary time-dependent load on the crack surface. As an example, the diffraction of a micropolar dilatational wave by a stationary crack is considered. The behavior of the microrotation field and the dynamic couple stress intensity factor, influenced by microinertia, in addition to the dynamic stress intensity factor, are examined. The classical elasticity solution for the corresponding problem arises as a special case when the micropolar moduli are dropped from the present solution.

## Key Words

Micropolar, Microcontinuum Stress Intensity Factor Couple Stress Couple Stress Intensity Factor Microrotation

## References

1. Achenbach, J.D. and Bazant, Z.F., 1975. “Elastodynamic Near-Tip Stress and Displacement Fields for Rapidly Propagating Cracks in Orthotropic Materials”, Journal of Applied Mechanics, Vol. 42, p. 183.
2. Baker, B.R., 1962, “Dynamic Stresses Created by a Moving Crack”, Journal of Applied Mechanics, Vol. 29, p. 449.
3. Broberg, K.B., 1960, “The Propagation of a Brittle Crack”, Arkiv For Fysik, Vol. 18, p. 159.
4. Craggs, J.W., 1960, “On the Propagation of a Crack in an Elastic Brittle Materials”, Journal of the Mechanics and physics of Solids, Vol. 8, p. 66.
5. Eringen, A.C. and Suhubi, E.S., 1964, “Nonlinear Theory of Microelastic Solids”, International Journal of Engineering Science, Vol. 2, p. 189, p. 389.
6. Eringen, A.C., 1966, “Linear Theory of Micropolar Elasticity”, Journal of Mathematics and Mechanics, Vol. 15, No. 6, p. 909.
7. Eringen, A.C., Suhubi, 1974, “Elastodynamics”, Vol. 2, Academic Press, New York.
8. Freund, L.B., 1972, “Crack Propagation in an Elastic Solid subjected to General Loading-II.”, Journal of the Mechanics and Physics of Solid, Vol. 20, p. 141.
9. Freund, L.B. and Clifton, R.J., 1974, “On the Uniqueness of Plane Elastodynamic Solutions for Running Cracks”, Journal of Elasticity, Vol. 4, p. 293.
10. Gauthier, R.D. and Jahsman, W.E., 1979, “A Quest for Micropolar Elastic Constant-II”, Second Polish-Swedish Symposium in Microelastic Solids, Stockholm.Google Scholar
11. Han, S.Y., 1989, “Elastodynamic Analysis of a Propagating Finite Crack in a Micropolar Elastic Solid”, Unpublished Ph. D. dissertation, Oregon State University, Corvallis, OR.Google Scholar
12. Kim, K.S., 1977, “Elastodynamic analysis of a propagating finite crack”, Unpublished Ph. D. dissertation, University of Illinois at Urbana-Champaign, Urbana, IL.Google Scholar
13. Muskhelishvili, N.I., 1953, “Singular Intergral Equations”, Noordhoff Publishing Co.Google Scholar
14. Sih, G.C. snd Loeber, J.F., 1969, “Wave Propagation in an Elastic Solid with a Line of Discontinuity or Finite Crack”, Quarterly of Applied Mathematics, Vol. 27, p. 193.
15. Thau, S.A. and Lu, T.H., 1971, “Transient Stress Intensity Factors for a Finite Crack in an Elastic Solid Caused by a Dilatational Wave”, International Journal of Solids and Structures, Vol. 7, p. 731.
16. Yoffe, E.H., 1951, “The Moving Griffith Crack”, Philosophical Magagine, Vol. 42, p. 739.

© The Korean Society of Mechanical Engineers (KSME) 1989

## Authors and Affiliations

• Seog Young Han
• 1
• M. N. L. Narasimhan
• 2
• T. C. Kennedy
• 2
1. 1.Rolling DepartmentResearch Institute of Industrial Science and TechnologyPohangKorea
2. 2.Oregon State Univ.USA