Abstract
The objectives of this paper are to examine the loss of crack tip constraint in dynamically loaded fracture specimens and to assess whether it can lead to enhancement in the fracture toughness at high loading rates which has been observed in several experimental studies. To this end, 2-D plane strain finite element analyses of single edge notched (tension) specimen and three point bend specimen subjected to time varying loads are performed. The material is assumed to obey the small strain J 2 flow theory of plasticity with rate independent behaviour. The results demonstrate that a valid J–Q field exists under dynamic loading irrespective of the crack length and specimen geometry. Further, the constraint parameter Q becomes strongly negative at high loading rates, particularly in deeply cracked specimens. The variation of dynamic fracture toughness K dc with stress intensity rate K for cleavage cracking is predicted using a simple critical stress criterion. It is found that inertia-driven constraint loss can substantially enhance K dc for \(\dot K > 10^5 { MPa}\sqrt {m} {/s}\).
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References
Al-Ani, A.M. and Hancock, J.W. (1991). J-dominance of short cracks in tension and bending. Journal of the Mechanics and Physics of Solids 39, 23–43.
Basu, S. and Narasimhan, R. (2000). A numerical investigation of loss of crack tip constraint in a dynamically loaded ductile specimen. Journal of the Mechanics and Physics of Solids 48, 1967–1985.
Bathe, K.J. (1997). Finite element procedures, Prentice Hall, Englewood Cliffs, New Jersey.
Belytschko, T. (1983). An overview of semidiscretization and time integration procedures. In Computational Methods for Transient analysis. (Edited by Belytschko, T., Hughes, T.J.R.), Elsevier, Amsterdam, 1–65.
Betegón, C. and Hancock, J.W. (1991). Two-parameter characterization of elastic-plastic crack-tip fields. Transactions of the ASME, Journal of Applied Mechanics 58, 104–110.
Betegón, C., Belzunce, F.J. and Rodriguez, C. (1996). A two parameter fracture criterion for high strength low carbon steel. Acta Materialia 44, 1055–1061.
Dally, J.W. and Barker, D.B. (1988). Dynamic measurements of initiation toughness at high loading rates. Experimental Mechanics 28, 298–303.
Dodds, Jr. R.H., Shih, C.F. and Anderson, T.L. (1993). Continuum and micromechanics treatment of constraint in fracture. International Journal of Fracture 64, 101–133.
Hughes, T.J.R. (1980). Generalization of selective integration procedures to anisotropic and non-linear media. International Journal of Numerical Methods in Engineering 15, 1413-1418.
Hutchinson, J.W. (1968). Singular behaviour at the end of a tensile crack in a hardening material. Journal of the Mechanics and Physics of Solids 16, 13–31.
Jayadevan, K.R. (2001). Numerical studies on the role of T-stress in dynamic fracture. Ph.D. thesis (submitted), Indian Institute of Science, Bangalore-560012, India.
Jayadevan, K.R., Narasimhan, R., Ramamurthy, T.S. and Dattaguru, B. (2001). A numerical study of T-stress in dynamically loaded fracture specimens. International Journal of Solids and Structures 38, 4987–5005.
Kalthoff, J.F. (1986). Fracture behaviour under high rates of loading. Engineering Fracture Mechanics 23, 289–298.
Kanninen, M.F. and O'Donoghue, P.E. (1995). Research challenges arising from current and potential applications of dynamic fracture mechanics to the integrity of engineering structures. International Journal of Solids and Structures 32, 2423–2445.
Koppenhoefer, K.C. and Dodds, R.H. (1996). Constraint effects on fracture toughness of impact-loaded, precracked Charpy specimens. Nuclear Engineering and Design 162, 145–158.
Liu, C., Knauss, W.G. and Rosakis, A.J. (1998). Loading rates and the dynamic initiation toughness in brittle solids. International Journal of Fracture 90, 103–118.
Nakamura, T., Shih, C.F. and Freund, L.B. (1986). Analysis of a dynamically loaded three-point-bend ductile fracture specimen. Engineering Fracture Mechanics 25, 323–339.
O'Dowd, N.P. and Shih, C.F. (1991). Family of crack-tip fields characterized by a triaxiality parameter-I. Structure of fields. Journal of the Mechanics and Physics of Solids 39, 989–1015.
O'Dowd, N.P. and Shih, C.F. (1992). Family of crack-tip fields characterized by a triaxiality parameter-II. Fracture applications. Journal of the Mechanics and Physics of Solids 40, 939–963.
O'Dowd, N.P. and Shih, C.F. (1994). Two-parameter fracture mechanics: Theory and applications. ASTM STP 1207, 21–47.
Owen, D.M., Zhuang, S., Rosakis, A.J. and Ravichandran, G. (1998a). Experimental determination of dynamic crack initiation and propagation fracture toughness in thin aluminum sheets. International Journal of Fracture 90, 153–174.
Owen, D.M., Rosakis, A.J. and Johnson, W.L. (1998b) Dynamic failure mechanisms in beryllium-bearing bulk metallic glasses. SM Report 98-22, GALCIT, California Institute of Technology, Pasadena, USA.
Ravi-Chandar, K. and Knauss, W.G. (1984). An experimental investigation into dynamic fracture: I. crack initiation and arrest. International Journal of Fracture 25, 247–262.
Rice, J.R. and Rosengren, G.F. (1968). Plane strain deformation near a crack tip in a power-law hardening material. Journal of the Mechanics and Physics of Solids 16, 1–12.
Ritchie, R.O., Knott, J.F. and Rice, J.R. (1973). On the relationship between critical tensile stress and fracture toughness in mild steel. Journal of the Mechanics and Physics of Solids 21, 395–410.
Roy, Y.A. Narasimhan, R. and Arora, P.R. (1999). An experimental investigation of constraint effects on mixed mode fracture initiation in a ductile aluminium alloy. Acta Materialia 47, 1587–1596.
Roy, Y.A. and Narasimhan, R. (1999). Constraint effects on ductile fracture processes near a notch tip under mixed-mode loading. Engineering Fracture Mechanics 62, 511–534.
Schreyer, H.L., Kulak, R.F. and Kramer, J.M. (1979). Accurate numerical solutions for elastic-plastic models. Transactions of ASME, Journal of Pressure Vessel Technology 101, 226–234.
Venkert, A., Guduru, P.R. and Ravichandran, G. (1998). Mechanisms of dynamic failure in Ni-Cr steels. SM Report 98-5, GALCIT, California Institute of Technology, Pasadena, USA.
Williams, M.L. (1957). On the stress distribution at the base of a stationary crack. Transactions of ASME, Journal of Applied Mechanics 24, 109–114.
Zehnder, A.T. and Rosakis, A.J. (1990). Dynamic fracture initiation and propagation in 4340 steel under impact loading. International Journal of Fracture 43, 271–285.
Zehnder, A.T., Rosakis, A.J. and Krishnaswamy, S. (1990). Dynamic measurement of the J integral in ductile metals: Comparison of experimental and numerical techniques. International Journal of Fracture 42, 209–230.
Zienkiewicz, O.C. and Taylor, R.L. (1989). The finite element method, Volume 2, Solid and fluid mechanics dynamics and non-linearity. 4th edn., McGraw-Hill, U.K.
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Jayadevan, K., Narasimhan, R., Ramamurthy, T. et al. Constraint Loss under Dynamic Loading in Rate Independent Plastic Solids. International Journal of Fracture 116, 141–160 (2002). https://doi.org/10.1023/A:1020150205634
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DOI: https://doi.org/10.1023/A:1020150205634