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Analytical Solutions for Crack Tip Plastic Zone Shape Using the Von Mises and Tresca Yield Criteria: Effects of Crack Mode and Stress Condition

Published online by Cambridge University Press:  05 May 2011

P. H. Jing  and
T. Khraishi
P. H. Jing*
Affiliation:
Mechanical Engineering Department, University of New Mexico, Albuquerque, NM87131, U.S.A.
T. Khraishi*
Affiliation:
Mechanical Engineering Department, University of New Mexico, Albuquerque, NM87131, U.S.A.
*
*Research Assistant
**Assistant Professor
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Abstract

Analytical closed-form solutions for the crack tip plastic zone shape have been derived for a semi-infinite crack in an isotropic elastic-perfectly plastic solid under both plane stress and plane strain conditions. Two yield criteria have been applied: the Von Mises and Tresca yield criteria. The solutions have been developed for crack modes I and III (mode II has been published previously). The results, which favorably compare to a limited number of existing experimental and analytical findings, indicate that the Tresca zone is larger in size than the Von Mises zone. Moreover, an interesting observation is that both zones are generally much larger than the ones predicted by classical Irwin and Dugdale-Barenblatt solutions.

Keywords

Plastic zoneVon Mises and Tresca Yield CriteriaCrack modesStress condition.
Type
Articles
Information
Journal of Mechanics , Volume 20 , Issue 3 , September 2004 , pp. 199 - 210
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2004

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References

1.Lankford, J., Davidson, D. L. and Chan, K. S., “The Influence of Crack Tip Plasticity in the Growth of Small Fatigue Cracks,” Metallurgical Transactions A, 15, pp. 1579–1588 (1984).CrossRefGoogle Scholar
2.Guerra-Rosa, L., Branco, C. M. and Radon, J. C., “Monotonic and Cyclic Crack Tip Plasticity,” International Journal of Fatigue, 6(1), pp. 17–24 (1984).CrossRefGoogle Scholar
3.Birol, Y., “Analysis of Fatigue Crack Tip Plasticity in Fe-2.6Si,” Journal of Materials Science, 23(6), pp. 2079–2086 (1988).CrossRefGoogle Scholar
4.Lu, T. J. and Chow, C. L., “A Modified Dugdale Model for Crack Tip Plasticity and Its Related Problems,” Engineering Fracture Mechanics, 37(3), pp. 551–568(1990).CrossRefGoogle Scholar
5.Sahasakmontri, K. and Horii, H., “An Analytical Model of Fatigue Crack Growth Based on the Crack-Tip Plasticity,” Engineering Fracture Mechanics, 38(6), pp. 413–437 (1991).Google Scholar
6.Wang, G. S. and Blom, A. F., “A Strip Model for Fatigue Crack Growth Predictions Under General Load Conditions,” Engineering Fracture Mechanics, 40(3), pp. 507–533(1991).CrossRefGoogle Scholar
7.Mei, Z. and Morris, J. W. Jr, “The Growth of Small Fatigue Cracks in A286 Steel,” Metallurgical Transactions A, 24, pp. 689–700 (1993).CrossRefGoogle Scholar
8.Park, H.-B., Kim, K.-M., Lee, B.-W. and Rheem, K.-S., “Effects of Crack Tip Plasticity on Fatigue Crack Propagation,” Journal of Nuclear Materials, 230, pp. 12–18 (1996).CrossRefGoogle Scholar
9.Harmain, G. A. and Provan, J. W., “Fatigue Crack-Tip Plasticity Revisited - The Issue of Shape Addressed,” Theoretical and Applied Fracture Mechanics, 26, pp. 63–79 (1997).CrossRefGoogle Scholar
10.Sadananda, K. and Ramaswamy, D.-N. V., “Role of Crack Tip Plasticity in Fatigue Crack Growth,” Philosophical Magazine A, 81(5), pp. 1283–1303 (2001).CrossRefGoogle Scholar
11.Dugdale, D. S., “Yielding in Steel Sheets Containing Slits,” J. Mech. Phys. Solids, 8, pp. 100–104 (1960).CrossRefGoogle Scholar
12.Barenblatt, G. I., “The Mathematical Theory of Equilibrium Cracks in Brittle Fracture,” Advances in Applied Mechanics, Academic Press, VII, pp. 55–129 (1962).Google Scholar
13.Irwin, G. R., “Analysis of Stresses and Strains near the End of a Crack Traversing a Plate,” J. Appl. Mech., 24, pp. 361–364 (1957).CrossRefGoogle Scholar
14.Underwood, J. H., Farrara, R. A. and Audino, M. J., “Yield-Before-Break Fracture Mechanics Analysis of High-Strength Pressure Vessels,” Journal of Pressure Vessel Technology, 117, pp. 79–84 (1995).CrossRefGoogle Scholar
15.Kelly, P. A. and Nowell, D., “Three-Dimensional Cracks with Dugdale-Type Plastic Zones,” International Journal of Fracture, 106, pp. 291–309 (2000).CrossRefGoogle Scholar
16.Hult, J. A. H. and McClintock, F. A., “Elastic-Plastic Stress and Strain Distributions Around Sharp Notches Under Repeated Shear,” Proceedings of the Ninth International Congress on Applied Mechanics, University of Brussels, Belgium, 8, pp. 51–58 (1957).Google Scholar
17.Unger, D. J., “A Transition Model of Crack Tip Plasticity,” International Journal of Fracture, 44, pp. R27–R31 (1990).CrossRefGoogle Scholar
18.Banks, T. M. and Garlick, A., “The Form of Crack Tip Plastic Zones,” Engineering Fracture Mechanics, 19(3), pp. 571–581(1984).CrossRefGoogle Scholar
19.Martin, A. N., “Crack Tip Plasticity: A Different Approach to Modelling Fracture Propagation in Soft Formations,” Proceedings of the 2000 SPE Annual Technical Conference and Exhibition, Dallas, Texas, pp. 519–529(2000).Google Scholar
20.Jing, P., Khraishi, T. and Gorbatikh, L., “Closed-Form Solutions for the Mode II Crack Tip Plastic Zone Shape,” International Journal of Fracture, 122(3–4), pp. L137–L142 (2003).CrossRefGoogle Scholar
21.Mishra, S. C. and Parida, B. K., “A Study of Crack-Tip Plastic Zone by Elastoplastic Finite Element Method,” Engineering Facture Mechanics, 22(6), pp. 951–956(1985).CrossRefGoogle Scholar
22.Dodds, R. H. Jr, Anderson, T. L. and Kirk, M. T., “A Framework to Correlate a/W Effects on Elastic-Plastic Fracture Toughness (JC),” International Journal of Fracture, 48, pp. 1–22 (1991).CrossRefGoogle Scholar
23.Mishra, S. C. and Parida, B. K., “Determination of the Size of Crack-Tip Plastic Zone in a Thin Sheet Under Uniaxial Loading,” Engineering Facture Mechanics, 22(3), pp. 351–357 (1985).CrossRefGoogle Scholar
24.Sarafianos, N., Agathonikos, K. and Kyriakopolos, B., “Microplasticity Initiation of Aluminum Matrix Alloy Elastically Stressed in Pure Model III,” Materials Science and Engineering A, 197, pp. 39–48 (1995).CrossRefGoogle Scholar
25.Anderson, T. L., Fracture Mechanics: Fundamentals and Applications, CRC Press, Boca Raton, Florida (1995).Google Scholar
26.Shigley, J. E. and Mischke, C. R., Mechanical Engineering Design, McGraw-Hill Inc., New York (1989).Google Scholar
27.Dieter, G. E., Mechanical Metallurgy, McGraw-Hill, New York (1986).Google Scholar
28.Mendelson, A., Plasticity: Theory and Application, The MacMillan Company, New York (1968).Google Scholar
29.Harris, J. W. and Stocker, H., Handbook of Mathematics and Computational Science, Springer-Verlag, New York (1998).CrossRefGoogle Scholar
30.Stewart, J., Calculus, Brooks/Cole Publishing Company, Pacific Grove, California (1991).Google Scholar