Acta Mechanica

, 190:115 | Cite as

The asymptotic structure of small-scale yielding interfacial free-edge joint and crack-tip fields

  • L. MarsavinaEmail author
  • A. D. Nurse


The problem of the small-scale yielding (SSY) plane-strain asymptotic fields for the interfacial free-edge joint singularity is examined in detail, and comparisons are made with the interfacial crack tip. The geometries are idealized as isotropic elasto-plastic materials with Ramberg-Osgood power-law hardening properties bonded to a rigid elastic substrate. The resulting fields are shown to be singular and are presented in terms of radial and angular distributions of stress and displacement, and as idealized plastic slip-line sectors. A fourth-order Runge-Kutta numerical method provides solutions to fundamental equations of equilibrium and compatibility that are verified with those of a highly focused finite element (FE) analysis. It is shown that, as in the case of the crack, the asymptotic singular fields are only dependent on the hardening parameter and only a small range of interfacial mode-mix ratios are permitted. The order for the stress singularity may be formulated in terms of the hardening parameter and the elastic solution for incompressible material. The rigid-slip-line field for the interfacial free-edge joint is presented, and it is shown that there is some significant similarity between the asymptotic fields of the deviatoric polar stresses for the joint and the crack-tip having an elastic wedge sector.


Asymptotic Solution Aravas Interfacial Crack Stress Singularity Singularity Order 
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  1. Williams, M. L. 1959The stresses around a fault or crack in dissimilar mediaBull. Seismol. Soc. America49199204MathSciNetGoogle Scholar
  2. Shih, C. F., Asaro, R. J. 1988Elastic-plastic analysis of cracks on bimaterial interfaces; Part I: small scale yieldingJ. Appl. Mech.55299316CrossRefGoogle Scholar
  3. Shih, C. F., Asaro, R. J. 1989Elastic-plastic analysis of cracks on bimaterial interfaces; Part II – structures of small-scale yielding fieldsJ. Appl. Mech.56763779Google Scholar
  4. Zywicz, E., Parks, D. M. 1992Small-scale yielding interfacial crack tip fieldsJ. Mech. Phys. Solids40511536CrossRefGoogle Scholar
  5. Xia, L., Wang, T. 1993Singular behavior near the tip of a sharp V-notch in a power law hardening materialInt. J. Fract.598393Google Scholar
  6. Klingbeil, N. W., Beuth, J. L. 2000On the design of debond-resistant bimaterials Part II: a comparison of the free-edge and interface crack approachesEngng. Fract. Mech.66111128CrossRefGoogle Scholar
  7. Romeo, A., Ballarini, R. 1994The influence of the elastic mismatch on the size of the plastic zone of a crack terminating at a brittle-ductile interfaceInt. J. Fract.65183196Google Scholar
  8. Yang, Y. Y, Munz, D., Sckuhr, M. A. 1997Evaluation of the plastic zone in an elastic-plastic dissimilar materials jointEngng. Fract. Mech.56691710CrossRefGoogle Scholar
  9. Law, C. W., Delale, F. 1988Interfacial stress singularities at free edge of hybrid metal matrix compositesJ. Engng. Mater. Tech.1104147CrossRefGoogle Scholar
  10. Xu, J.-Q., Fu, L.-D., Mutoh, Y. 2002A method for determining elastic-plastic stress singularity at the interface edge of bonded power law hardening materialsJSME Int. J. Series A45177183CrossRefGoogle Scholar
  11. Rudge, M. R. H., Tiernan, D. M. 1999Stress singularities in composite wedge-shaped materialsFat. Fract. Engng. Matls. Structs.221115CrossRefGoogle Scholar
  12. Sharma, S. M., Aravas, N. 1993On the development of variable-separable asymptotic elastoplastic solutions for interface cracksInt. J. Solids Struct.30695723zbMATHCrossRefGoogle Scholar
  13. Sharma, S. M., Aravas, N. 1991Determination of higher order terms in asymptotic elastoplastic crack tip solutionsJ. Mech. Phys. Solids3910431072zbMATHCrossRefGoogle Scholar
  14. Bogy, D. B. 1971Two edge-bonded elastic wedges of different materials and wedge angles under surface tractionsJ. Appl. Mech.38377386Google Scholar
  15. Dundurs, J. 1969Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loadingJ. Appl. Mech.44650652Google Scholar
  16. Akisanya, A. R. 1997On the singular stress field near the edge of bonded jointsJ. Strain Anal.32301311CrossRefGoogle Scholar
  17. Akisanya, A. R., Fleck, N. A. 1997Interfacial cracking from the free-edge of a long bi-material stripInt. J. Solids Struct.3416451665zbMATHCrossRefGoogle Scholar
  18. Suo, Z., Hutchinson, J. W. 1989Sandwich test specimens for measuring interface toughnessMaters. Sci. Engng.107135143CrossRefGoogle Scholar
  19. Rice, J. R., Rosengren, G. R. 1968Plane strain deformation near crack tip in a power law hardening materialJ. Mech. Phys. Solids16112zbMATHCrossRefGoogle Scholar
  20. Hutchinson, J. W. 1968Singular behavior at the end of tensile crack in a hardening materialJ. Mech. Phys. Solids161331zbMATHCrossRefGoogle Scholar
  21. Bose, K., Mataga, P. A., Castaneda, P. P. 1999Stable crack growth along a brittle/ductile interface-II: small scale yielding solutions and interfacial toughness predictionsInt. J. Solids Struct.36134zbMATHCrossRefGoogle Scholar
  22. Shih, C. F. 1974Small-scale yielding analysis of mixed mode plane strain crack problemsASTM STP560187210Google Scholar
  23. Ekman, M. J., Marsavina, L., Nurse, A. D. 2000Complex fracture parameters for an interface crack between two hardening materials: a photoelastic studyFat. Fract. Engng. Matls. Structs.23619630CrossRefGoogle Scholar
  24. Rice, J. R., Tracey, D. M.: In: Numerical and computer methods in structural mechanics. (Fenves, S. J. et al., eds.), pp. 585–624. New York: Academic Press.Google Scholar

Copyright information

© Springer-Verlag Wien 2006

Authors and Affiliations

  1. 1.Department Strength of MaterialsUniversity Politehnica TimisoaraTimisoaraRomania
  2. 2.Department of Mechanical EngineeringLoughborough UniversityLoughboroughU.K

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