Crack tip fields in a viscoplastic solid: monotonic and cyclic loading
Source abstract
Abstract
The asymptotic stress and strain field near the tip of a plane strain Mode I stationary crack in a viscoplastic material are investigated in this work, using a unified viscoplastic model based on Chaboche (Int J Plast 5(3):247–302, 1989). Asymptotic analysis shows that the near tip stress field is governed by the Hutchinson–Rice–Rosengren (HRR) field (Hutchinson in J Mech Phys Solids 16(1):13–31, 1968; Rice and Rosengren in J Mech Phys Solids 16(1):1–12, 1968) with a time dependent amplitude that depends on the loading history. Finite element analysis is carried out for a single edge crack specimen subjected to a constant applied load and a simple class of cyclic loading history. The focus is on small scale creep where the region of inelasticity is small in comparison with typical specimen dimensions. For the case of constant load, the amplitude of the HRR field is found to vanish at long times and the elastic K field dominates. For the case of cyclic loading, we study the effect of stress ratio on inelastic strain and find that the strain accumulated per cycle decreases with stress ratio.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Fatigue and fracture mechanics · High-Velocity Impact and Material Behavior · Structural Response to Dynamic Loads
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (50)
Show source-provided references
1. ABAQUS (2009) version 6.8-3. ABAQUS, Inc
2. Adefris N, Saxena A, McDowell D (1996a) Creep fatigue crack growth behavior in 1Cr-1Mo-0.25V steels. Part I: estimation of crack tip parameters. Fatigue Fract Eng Mater Struct 19(4): 387–39810.1111/j.1460-2695.1996.tb00976.x ↗
3. Adefris N, Saxena A, McDowell D (1996b) Creep fatigue crack growth behavior in 1Cr-1Mo-0.25V steels. Part II: crack growth behavior and models. Fatigue Fract Eng Mater Struct 19(4): 401–41110.1111/j.1460-2695.1996.tb00977.x ↗
4. Atluri SN (1982) Path-independent integrals in finite elasticity and inelasticity, with body forces, inertia, and arbitrary crack-face conditions. Eng Fract Mech 16(3): 341–36410.1016/0013-7944(82)90113-8 ↗
5. Bassani J, McClintock F (1981) Creep relaxation of stress around a crack tip. Int J Solids Struct 17(5): 479–49210.1016/0020-7683(81)90055-X ↗
6. Bassani JL, Hawk DE, Saxana A (1989) Evaluation of the C t parameter for characterizing the creep crack growth rate in the transient regime. In: Saxana A, Landes JD, Bassani JL (eds) 3rd International symposium on nonlinear fracture mechanics, Knoxville. American Society for Testing and Materials, pp 7–26
7. Chaboche J (2008) A review of some plasticity and viscoplasticity constitutive theories. Int J Plast 24(10): 1642–169310.1016/j.ijplas.2008.03.009 ↗
8. Chaboche J, Nouailhas D (1989a) Constitutive modeling of ratchetting effects—part i: experimental facts and properties of the classical models. J Eng Mater Technol 111: 38410.1115/1.3226484 ↗
9. Chaboche J, Nouailhas D (1989b) Constitutive modeling of ratchetting effects—part ii: possibilities of some additional kinematic rules. J Eng Mater Technol 111: 40910.1115/1.3226488 ↗
10. Chaboche JL (1989) Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int J Plast 5(3): 247–30210.1016/0749-6419(89)90015-6 ↗
11. Chomette S, Gentzbittel JM, Viguier B (2010) Creep behaviour of as received, aged and cold worked INCONEL 617 at 850°C and 950°C. J Nucl Mater 399(2–3): 266–27410.1016/j.jnucmat.2010.01.019 ↗
12. Cook R (1984) Creep properties of Inconel-617 in air and helium at 800 to 1000°C. Nucl Technol 66(2): 283–28810.13182/NT84-A33431 ↗
13. Ehlers R, Riedel H (1981) A finite element analysis of creep deformation in a specimen containing a macroscopic crack. In: Francois D (ed) 5th International conference on fracture. Pergamon Press, London, pp 691–698
14. Floreen S, Kane R (1979) An investigation of the crack fatigue environment interaction in a Ni base superalloy. Fatigue Fract Eng Mater Struct 2(4): 401–41210.1111/j.1460-2695.1979.tb01097.x ↗
15. Fu L (1980) Creep crack growth in technical alloys at elevated temperature—a review. Eng Fract Mech 13(2): 307–33010.1016/0013-7944(80)90062-4 ↗
16. Grover P, Saxena A (1999) Modelling the effect of creep-fatigue interaction on crack growth. Fatigue Fract Eng Mater Struct 22(2): 111–12210.1046/j.1460-2695.1999.00144.x ↗
17. Gupta C, Chakravartty J, Reddy G, Banerjee S (2005) Uniaxial cyclic deformation behaviour of SA 333 Gr 6 piping steel at room temperature. Int J Press Vessels Pip 82(6): 459–46910.1016/j.ijpvp.2005.01.005 ↗
18. Hall D, McDowell D, Saxena A (1998) Crack tip parameters for creep-brittle crack growth. Fatigue Fract Eng Mater Struct 21(4): 387–40110.1046/j.1460-2695.1998.00542.x ↗
19. Hui C, Riedel H (1981) The asymptotic stress and strain field near the tip of a growing crack under creep conditions. Int J Fract 17(4): 409–42510.1007/BF00036192 ↗
20. Hutchinson J (1968) Singular behaviour at the end of a tensile crack in a hardening material. J Mech Phys Solids 16(1): 13–3110.1016/0022-5096(68)90014-8 ↗
21. Kang G, Gao Q, Cai L, Sun Y (2002) Experimental study on uniaxial and nonproportionally multiaxial ratcheting of SS304 stainless steel at room and high temperatures. Nucl Eng Des 216(1–3): 13–2610.1016/S0029-5493(02)00062-6 ↗
22. Kang G, Kan Q, Zhang J, Sun Y (2006) Time-dependent ratchetting experiments of SS304 stainless steel. Int J Plast 22(5): 858–89410.1016/j.ijplas.2005.05.006 ↗
23. Krishnan VR, Hui CY, Long R (2008) Finite strain crack tip fields in soft incompressible elastic solids. Langmuir 24(24): 14245–1425310.1021/la802795e ↗
24. Kurata Y, Nakajima H (1995) Temperature dependence of creep properties of cold-worked Hastelloy XR. J Nucl Sci Technol 32(6): 539–54610.1080/18811248.1995.9731741 ↗
25. Landes J, Begley J (1976) A fracture mechanics approach to creep crack growth. Mech Crack Growth 128–14810.1520/STP33943S ↗
26. McDowell D (1995) Stress state dependence of cyclic ratchetting behavior of two rail steels. Int J Plast 11(4): 397–42110.1016/S0749-6419(95)00005-4 ↗
27. Ohno N (1990) Recent topics in constitutive modeling of cyclic plasticity and viscoplasticity. Appl Mech Rev 43(11): 283–29510.1115/1.3119155 ↗
28. Ohno N, Wang JD (1993) Kinematic hardening rules with critical state of dynamic recovery, part I: formulation and basic features for ratchetting behavior. Int J Plast 9(3): 375–39010.1016/0749-6419(93)90042-O ↗
29. Rice J, Rosengren G (1968) Plane strain deformation near a crack tip in a power-law hardening material. J Mech Phys Solids 16(1): 1–1210.1016/0022-5096(68)90013-6 ↗
30. Riedel H (1981) Creep deformation at crack tips in elastic viscoplastic solids. J Mech Phys Solids 29(1): 35–4910.1016/0022-5096(81)90014-4 ↗
31. Riedel H (1983) Crack-tip stress fields and crack growth under creep-fatigue conditions. In: Shih CF, Gudas JP (eds) 2nd International symposium on elastic-plastic fracture mechanics. American Society for Testing and Materials, pp I505–I52010.1520/STP37312S ↗
32. Riedel H, Rice JR (1980) Tensile cracks in creeping solids. In: Paris PC (ed) Fracture mechanics: 12th conference, Philadelphia. American Society for Testing and Materials, pp 112–13010.1520/STP36967S ↗
33. Sadananda K, Shahinian P (1981) Review of the fracture mechanics approach to creep crack growth in structural alloys. Eng Fract Mech 15(3–4): 327–34210.1016/0013-7944(81)90064-3 ↗
34. Saxena A (1986) Creep crack growth under non-steady-state conditions. ASTM Spec Tech Publ 905: 185–201
35. Saxena A, Bassani JL (1984) Time-dependent fatigue crack growth behavior at elevated temperature. In: Wells JM, Landes JD (eds) Fracture: interactions of microstructure mechanisms and mechanics. The Metallurgical Society of AIME, pp 357–383
36. Schapery RA (1986) Time-dependent fracture: continuum aspects of crack growth. In: Bever M (ed) Encyclopedia of materials science and engineering. Pergamon Press, Oxford, pp 5043–5053
37. Schneider K, Hartnagel W, Iischner B, Schepp P (1984) Creep behavior of materials for high-temperature reactor application. Nucl Technol 66(2): 289–29510.13182/NT84-A33432 ↗
38. Schubert F, te Heesen E, Bruch U, Cook R, Diehl H, Ennis P, Jakobeit W, Penkalla H, Ullrich G (1984) Creep rupture behavior of candidate materials for nuclear process heat applications. Nucl Technol 66(2): 227–24010.13182/NT84-A33426 ↗
39. Stamm H, Walz G (1993) Analytical investigation of crack tip fields in viscoplastic materials. Int J Fract 64(2): 135–15510.1007/BF00016694 ↗
40. Tada H, Paris PC, Irwin GR (2000) The stress analysis of cracks handbook, 3rd edn. ASME, New York10.1115/1.801535 ↗
41. Tong J, Dalby S, Byrne J, Henderson M, Hardy M (2001) Creep, fatigue and oxidation in crack growth in advanced nickel base superalloys. Int J Fatigue 23(10): 897–90210.1016/S0142-1123(01)00049-4 ↗
42. Walz G, Stamm H (1993) Numerical investigation of crack tip fields in viscoplastic materials. Int J Fract 64(2): 157–17810.1007/BF00016695 ↗
43. Wang W, Yuan F, Takao Y (2000) A unified loading parameter for creep-crack growth. Proc R Soc Lond Ser A Math Phys Eng Sci 456(1993): 163–18310.1098/rspa.2000.0512 ↗
44. Yaguchi M, Takahashi Y (2005) Ratchetting of viscoplastic material with cyclic softening, part 1: experiments on modified 9Cr-1Mo steel. Int J Plast 21(1): 43–6510.1016/j.ijplas.2004.02.001 ↗
45. Yaguchi M, Takahashi Y (2005) Ratchetting of viscoplastic material with cyclic softening, part 2: application of constitutive models. Int J Plast 21(4): 835–86010.1016/j.ijplas.2004.05.012 ↗
46. Yoon KB, Saxena A, McDowell DL (1992) Influence of crack-tip cyclic plasticity on creep-fatigue crack growth. In: Ernst HA, Saxena A, McDowell DL (eds) Fracture Mechanics: 22nd symposium, Philadelphia. American Society for Testing and Materials, pp 367–392
47. Yoshida F (1990) Uniaxial and biaxial creep-ratcheting behavior of SUS304 stainless steel at room temperature. Int J Press Vessels Pip 44(2): 207–22310.1016/0308-0161(90)90130-A ↗
48. Zhan ZL, Tong J (2007a) A study of cyclic plasticity and viscoplasticity in a new nickel-based superalloy using unified constitutive equations. Part I: evaluation and determination of material parameters. Mech Mater 39(1): 64–7210.1016/j.mechmat.2006.01.005 ↗
49. Zhan ZL, Tong J (2007b) A study of cyclic plasticity and viscoplasticity in a new nickel-based superalloy using unified constitutive equations. Part II: simulation of cyclic stress relaxation. Mech Mater 39(1): 73–8010.1016/j.mechmat.2006.01.006 ↗
50. Zhao L, Tong J (2008) A viscoplastic study of crack-tip deformation and crack growth in a nickel-based superalloy at elevated temperature. J Mech Phys Solids 56(12): 3363–337810.1016/j.jmps.2008.09.006 ↗