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Research Papers

A Better Estimation of Plastic Zone Size at the Crack Tip Beyond Irwin's Model

[+] Author and Article Information
Y. J. Jia

AML, CNMM,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

M. X. Shi

Southwest Jiaotong University,
Chengdu 610031, China

B. Liu

e-mail: liubin@tsinghua.edu.cn
AML, CNMM,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

1Corresponding author.

Manuscript received November 20, 2012; final manuscript received January 2, 2013; accepted manuscript posted February 12, 2013; published online July 18, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(5), 051014 (Jul 18, 2013) (6 pages) Paper No: JAM-12-1525; doi: 10.1115/1.4023642 History: Received November 20, 2012; Revised January 02, 2013; Accepted February 12, 2013

Irwin's model on plastic zone at the crack tip is discussed in many fracture mechanics textbooks. However, we found in Irwin's model that the internal resultant force on the crack plane and the one applied in remote field are not strictly balanced. This imbalance leads to the error in the scenario of small scale yielding, and an improper finite plastic zone size (PZS) is predicted when the remote stress approaches the yielding strength. In this paper, an improved model is developed through surrendering some main assumptions used in Irwin's model and an infinite PZS is then predicted as the remote stress goes up close to yielding strength, which implies that this estimation can be applied to situations with large scale yielding. In small scale yielding cases, the new estimation of PZS agrees well with finite element simulation results. In addition, a more accurate quantitative relation between the PZS and the effective stress intensity factor is derived, which might help characterize fracture behaviors in engineering applications.

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References

Griffith, A. A., 1921, “The Phenomenon of Rupture and Flow in Solids,” Philos. Trans. R. Soc. London, Ser. A, 221, pp. 163–198. [CrossRef]
Irwin, G. R., 1957, “Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate,” ASME J. Appl. Mech., 24, pp. 361–364.
Wells, 1963, “Application of Fracture Mechanics At and Beyond General Yielding,” Br. Weld. J., 10, pp. 563–570.
Rice, J. R., 1968, “A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks,” ASME J. Appl. Mech., 35, pp. 379–386. [CrossRef]
Broberg, K. B., 1968, “Critical Review of Some Theories in Fracture Mechanics,” Int. J. Fract., 4(1), pp. 11–19. [CrossRef]
Cotterell, B., and Reddel, J. K., 1977, “Essential Work of Plane Stress Ductile Fracture,” Int. J. Fract., 13(3), pp. 267–277. [CrossRef]
Turner, C. E., 1990, “A Re-Assessment of the Ductile Tearing Resistance, Part I and II,” D.Firrao, ed., ECF 8—Fracture Behavior and Design of Materials and Structures: Proceedings of the 8th European Conference on Fracture, Torino, Italy, October 1–5, Vol. II, EMAS, Warrington, UK, pp. 933–949 and 951–968.
Turner, C. E., and Kolednik, O., 1994, “Micro and Macro Approach to the Energy Dissipation Rate Model of Stable Ductile Crack Growth,” Fatigue Fract. Eng. Mater. Struct., 17(9), pp. 1089–1107. [CrossRef]
Bian, L. C., and Kim, K. S., 2004, “The Minimum Plastic Zone Radius Criterion for Crack Initiation Direction Applied to Surface Cracks and Through-Cracks Under Mixed Mode Loading,” Int. J. Fatigue, 26(11), pp. 1169–1178. [CrossRef]
Golos, K., and Wasiluk, B., 2000, “Role of Plastic Zone in Crack Growth Direction Criterion Under Mixed Mode Loading,” Int. J. Fract., 102(4), pp. 341–353. [CrossRef]
Khan, S.M.A., and Khraisheh, M. K., 2000, “Analysis of Mixed Mode Crack Initiation Angles Under Various Loading Conditions,” Eng. Fract. Mech., 67(5), pp. 397–419. [CrossRef]
Khan, S.M.A. and Khraisheh, M. K., 2004, “A New Criterion for Mixed Mode Fracture Initiation Based on the Crack Tip Plastic Core Region,” Int. J. Plasticity, 20(1), pp. 55–84. [CrossRef]
Brown, M. W., de los Rios, E. R., Miller, J. K., 1988, “A Critical Comparison of Proposed Parameters for High-Strain Fatigue Crack Growth,” ASTM Spec. Tech. Publ., 924, pp. 233–259.
Du, Y., Patki, A., and Patterson, E., 2011, “Monitoring Crack Tip Plastic Zone Size During Fatigue Loading,” Proceedings of the 2010 Annual Conference on Experimental and Applied Mechanics, 17, pp. 569–573. [CrossRef]
McClung, R. C., 1991, “Crack Closure and Plastic Zone Sizes in Fatigue,” Fatigue Fract. Eng. Mater. Struct., 14(4), pp. 455–468. [CrossRef]
Wang, G. S., 1993, “The Plasticity Aspect of Fatigue Crack Growth,” Eng. Fract. Mech., 46(6), pp. 909–930. [CrossRef]
Barthelat, F., and Rabiei, R., 2011, “Toughness Amplification in Natural Composites,” J. Mech. Phys. Solids, 59(4), pp. 829–840. [CrossRef]
Budiansky, B., Hutchinson, J. W., and Lambropoulos, J. C., 1983, “Continuum Theory of Dilatant Transformation Toughening in Ceramics,” Int. J. Solids Struct., 19(4), pp. 337–355. [CrossRef]
Gao, H., Ji, B., Buehler, M. J., and Yao, H., 2004, “Flaw Tolerant Bulk and Surface Nanostructures of Biological Systems,” Mech. Chem. Biosyst., 1(1), pp. 37–52. [CrossRef]
Qin, Z., and Buehler, M. J., 2011, “Flaw Tolerance of Nuclear Intermediate Filament Lamina Under Extreme Mechanical Deformation,” ACS Nano, 5(4), pp. 3034–3042. [CrossRef]
Banks, T. M., and Garlick, A., 1984, “The Form of Crack Tip Plastic Zones,” Eng. Fract. Mech., 19(3), pp. 571–581. [CrossRef]
Benrahou, K. H., Benguediab, M., Belhouari, M., Nait-Abdelaziz, M., and Imad, A., 2007, “Estimation of the Plastic Zone by Finite Element Method Under Mixed Mode (I and II) Loading,” Comp. Mater. Sci., 38(4), pp. 595–601. [CrossRef]
Dugdale, D. S., 1960, “Yielding of Steel Sheets Containing Slits,” J. Mech. Phys. Solids, 8, pp. 100–106. [CrossRef]
Irwin, G. R., 1960, “Plastic Zone Near a Crack and Fracture Toughness,” Proceedings of the 7th Sagamore Ordnance Materials Research Conference, Racquette Lake, NY, August 16–19, pp. 63–78.
Barenblatt, G., 1962, “The Mathematical Theory of Equilibrium Cracks in Brittle Fracture,” Adv. Appl. Mech., 7, pp. 55–129. [CrossRef]
Dodds, R. H., Anderson, T. L., and Kirk, M. T., 1991, “A Framework to Correlate a/W Ratio Effects on Elastic-Plastic Fracture Toughness (JC),” Int. J. Fract., 48(1), pp. 1–22. [CrossRef]
Hui, C. Y., Jagota, A., Bennison, S. J., and Londono, J. D., 2003, “Crack Blunting and the Strength of Soft Elastic Solids,” Proc. R. Soc. London, Ser. A, 459(2034), pp. 1489–1516. [CrossRef]
McMeeking, R. M., 1977, “Finite Deformation Analysis of Crack-Tip Opening in Elastic-Plastic Materials and Implications for Fracture,” J. Mech. Phys. Solids, 25(5), pp. 357–381. [CrossRef]
Turon, A., Dávila, C. G., Camanho, P. P., and Costa, J., 2007, “An Engineering Solution for Mesh Size Effects in the Simulation of Delamination Using Cohesive Zone Models,” Eng. Fract. Mech., 74(10), pp. 1665–1682. [CrossRef]
Anderson, T. L., 1995, Fracture Mechanics: Fundamentals and Applications, 2nd ed., CRC Press, Boca Raton, FL.
Abaqus, 2005, ABAQUS Theory Manual and User's Manual, Version 6.2, Hibbit, Karlsson and Sorensen Inc., Pawtucket, RI.

Figures

Grahic Jump Location
Fig. 1

Schematics of (a) an infinite plate with a central crack subjected to remote uniform stress without plastic yielding, and (b) Irwin's estimation on plastic zone size

Grahic Jump Location
Fig. 2

Schematics of (a) an infinite plate with a central crack subjected to remote uniform stress with plastic yielding, and (b) the improved estimation on plastic zone size

Grahic Jump Location
Fig. 3

Details of simulation model

Grahic Jump Location
Fig. 4

(a) Theoretical and numerical predictions on the normalized plastic zone size versus σ∞/σys, (b) a zoom-in figure, and (c) relative error between our prediction rpnew and the Irwin's prediction rp_3Irwin

Grahic Jump Location
Fig. 5

The normalized plastic zone size versus the effective stress intensity factor

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