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Stress analysis of cracked bodies

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High Temperature Component Life Assessment

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Abstract

In this chapter, some basic fracture mechanics parameters are introduced. Attention is restricted at this stage to a description of the various parameters and numerical and approximate methods for their estimation. The use of the results to develop models for creep crack incubation and growth is considered in Chapter 5. As the principles of elastic and elastic—plastic fracture mechanics are covered extensively in a number of books [1–4], only a brief description is given here. More extensive coverage of parameters relevant to creeping materials is given, including energy methods which play an important role in their determination. Most of this chapter is limited to the behaviour of structures containing stationary cracks. It transpires that the analysis of stationary cracks can often be extended quite simply to growing cracks and section 4.5.4 examines the conditions under which the simple extension can be made for creeping structures.

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References

  1. Knott, J.F. (1973) Fundamentals of Fracture Mechanics, Butterworth, London.

    Google Scholar 

  2. Ewalds, H.L. and Wanhill, R.J.H. (1984) Fracture Mechanics,Edward Arnold.

    Google Scholar 

  3. Chell, G.G. (1979) Developments in Fracture Mechanics — 1, Applied Science, London.

    Google Scholar 

  4. Broek, D. (1978) Elementary Engineering Fracture Mechanics, Sitjhoff and Noordholf, Alphen aan den Rijn, The Netherlands.

    Google Scholar 

  5. Bilby, B.A., Cardew, G.E., Goldthorpe, M.R. and Howard, I.C. (1986) A finite element investigation of the effect of specimen geometry on the fields of stress and strain at the tips of stationary cracks, in Size Effects in Fracture, Proc. seminar at RAE Farnborough, I Mech E, London, pp. 37 – 46.

    Google Scholar 

  6. Tada, H., Paris, P.C. and Irwin, G.R. (1985) The Stress Analysis of Cracks Handbook, 2nd edn, Del Research Corp., St Louis, Missouri, USA.

    Google Scholar 

  7. Rooke, D.P. and Cartwright, D.J. (1976) Compendium of Stress Intensity Factors,HMSO, London.

    Google Scholar 

  8. Murakami, Y. (1987) Stress Intensity Factor Handbook, Vols 1, 2, Pergamon, Oxford.

    Google Scholar 

  9. Larsson, S.G. and Carlsson, A.J. (1973) Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic—plastic materials. J. Mech. Phys. Solids, 21, 263 – 277.

    Article  Google Scholar 

  10. O’Dowd, N.P. and Shih, C.F. (1991) Family of crack-tip fields characterised by a triaxiality parameter — I. structure of fields. J. Mech. Phys. Solids, 39, 989 – 1015.

    Article  Google Scholar 

  11. Rice, J.R. (1968) A path independent integral and the approximate analysis of strain concentrations by notches and cracks, ASME, J. Appl. Mech., 35, 379 – 386.

    Article  Google Scholar 

  12. Hutchinson, J.W. (1968) Singular behaviour at the end of a tensile crack in a hardening material. J. Mech. Phys. Solids, 16, 13 – 31.

    Article  Google Scholar 

  13. Rice, J.R. and Rosengren, G.F. (1968) Plane strain deformation near a crack tip in a power law hardening material. J. Mech. Phys. Solids, 16, 1 – 12.

    Article  Google Scholar 

  14. Shih, C.F. (1983) Tables of Hutchinson-Rice-Rosengren singular field quantities, Brown University Report MRL E-147, Providence, RI.

    Google Scholar 

  15. Shih, C.F. (1981) Relationships between the J-integral and the crack opening displacement for stationary and extending cracks, J. Mech. Phys. Solids, 29, 305 – 326.

    Article  Google Scholar 

  16. Rice, J.R. (1968) Mathematical analysis in the mechanics of fracture, in Treatise on Fracture (ed. H. Liebowitz), Vol. 2, Academic Press, New York.

    Google Scholar 

  17. Neale, B.K., Haines, A.B. and Miller, A.G. (1989) The fracture behaviour of an axial crack in a pressurised pipe. Fatigue Fract. Eng. Mater. Struct., 12, 597 – 609.

    Article  Google Scholar 

  18. Hill, R. (1950) The Mathematical Theory of Plasticity,Oxford University Press, Oxford.

    Google Scholar 

  19. 19. Hodge, P.G. (1963) Limit Analysis of Rotationally Symmetric Plates and Shells,Prentice-Hall, New Jersey.

    Google Scholar 

  20. Miller, A.G. (1988) Review of limit loads of structures containing defects. Int. J. Pres. Vessels Pip., 32, 197 – 327.

    Google Scholar 

  21. Kumar, V., German, M.D. and Shih, C.F. (1981) An engineering approach for elastic-plastic fracture. EPRI Report NP 1931.

    Google Scholar 

  22. Zahoor, A. (1989) Ductile fracture handbook, volume 1, circumferential throughwall cracks, EPRI Report NP-6301-D.

    Google Scholar 

  23. McMeeking, R.M. (1984) Estimates of the I-integral for elastic-plastic specimens in large scale yielding. ASME, J. Eng. Mater. Technol., 106, 278 – 284.

    Article  Google Scholar 

  24. ASTM E813-87 (1987) Standard test method for J,, a measure of fracture toughness, ASTM 03.01, 968 – 990.

    Google Scholar 

  25. Kumar, V. and Shih, C.F. (1980) Fully plastic crack solutions, estimation scheme and stability analyses for the compact specimen, ASTM STP 700, 406 – 438.

    Google Scholar 

  26. Miller, A.G. and Ainsworth, R.A. (1989) Consistency of numerical results for power-law hardening materials and the accuracy of the reference stress approximation for J. Eng. Fract. Mech., 32, 233 – 247.

    Article  CAS  Google Scholar 

  27. Ainsworth, R.A. (1984) The assessment of defects in structures of strain hardening materials. Eng. Fract. Mech., 19, 633 – 642.

    Article  Google Scholar 

  28. Milne, I., Ainsworth, R.A., Dowling, A.R. and Stewart, A.T. (1988) Background to and validation of CEGB report R/H/R6 - revision 3. Int. J. Pres. Vessels Pip., 32, 105 – 196.

    Article  Google Scholar 

  29. Milne, I., Ainsworth, R.A., Dowling, A.R. and Stewart, A.T. (1988) Assessment of the integrity of structures containing defects. Int. J. Pres. Vessels Pip., 32, 3 – 104.

    Article  Google Scholar 

  30. Langston, D.B., Haines, N.F. and Wilson, R. (1989) Development of a leak-before-break procedure for pressurised components. SMiRT 10 Transactions, Paper G12(F)/1, Anaheim.

    Google Scholar 

  31. Wilson, R. and Ainsworth, R.A. (1991) A probabilistic fracture mechanics assessment procedure, SMiRT 11 Transactions, Paper G30(M)/1, Tokyo.

    Google Scholar 

  32. British Standards Institution (199I) Guidance on methods for assessing the acceptability of flaws in welded structures, Published Document PD6493: 1991.

    Google Scholar 

  33. Bergman, M., Brickstad, B., Dahlberg, L., Nilsson, F. and Sattari-Far, I. (1991) A procedure for safety assessment of components with cracks - handbook, SA/FOU Report 91/01, The Swedish Plant Inspectorate, Stockholm.

    Google Scholar 

  34. Taira, S., Ohtani, R. and Kitamura, T. (1979) Application of J-integral to high-temperature crack propagation, part I - creep crack propagation. ASME, J. Eng. Matl. Techn., 101, 154 – 161.

    Article  CAS  Google Scholar 

  35. Ohtani, R. and Kitamura, T. (1988) Characterisation of high temperature strength of metals based on the mechanics of crack propagation, in High Temperature Creep-Fatigue, (eds R. Ohtani, M. Ohnami and T. Inoue ), Elsevier, London, pp. 65 – 90.

    Google Scholar 

  36. Webster, G.A. (1992) Methods of estimating C. Mater. High Temp., 10, 74 – 78.

    CAS  Google Scholar 

  37. Piques, R., Molinie, E. and Pineau, A. (1991) Comparison between two assessment methods for defects in the creep range. Fatigue Fract. Eng. Mater. Struct„ 14, 871 – 885.

    Article  Google Scholar 

  38. Ainsworth, R.A., Ruggles, M.B. and Takahashi, Y. (1990) Flaw assessment guide for high temperature reactor components subject to creep-fatigue loading, ORNL-6641, Martin Marietta Energy Systems Inc., Oak Ridge National Laboratory, USA.

    Google Scholar 

  39. Ainsworth, R.A. (1989) Approximate non-linear fracture mechanics calculations using reference stress techniques. ASME/JSME PVP Conf., Honolulu, USA.

    Google Scholar 

  40. Ainsworth, R.A., Chell, G.G., Coleman, M.C., Goodall, I.W., Gooch, D.J., Haigh, J.R., Kimmins, S.T. and Neate, G.J. (1987) CEGB assessment procedure for defects in plant operating in the creep range. Fatigue Fract. Eng. Mater. Struct., 10, 115 – 127.

    Article  Google Scholar 

  41. Ainsworth, R.A. and Budden, P.J. (1992) Approximate inelastic analysis of defective components. Nucl. Eng. Des., 133, 513 – 523.

    Article  CAS  Google Scholar 

  42. Riedel, R. and Rice, J.R. (1980) Tensile cracks in creeping solids, in Fracture Mechanics 12th Conf, ASTM STP 700, pp. 112 – 130.

    Google Scholar 

  43. Ohji, K. and Kubo, S. (1988) Fracture mechanics evaluation of crack growth behaviour under creep and creep-fatigue conditions, in High Temperature Creep-Fatigue, (eds R. Ohtani, M. Ohnami and T. Inoue ), Elsevier, London, pp. 91 – 113.

    Google Scholar 

  44. Riedel, R. (1987) Fracture at High Temperatures,Springer-Verlag, Berlin.

    Google Scholar 

  45. Joch, J. and Ainsworth, R.A. (1992) The effect of geometry on the development of creep singular fields for defects under step-load controlled loading. Fatigue Tract. Eng. Mater. Struct., 15, 229 – 240.

    Article  CAS  Google Scholar 

  46. Ainsworth, R.A. and Budden, P.J. (1990) Crack tip fields under non-steady creep conditions - I. estimates of the amplitudes of the fields. Fatigue Tract. Eng. Mater. Struct., 13, 263 – 276.

    Article  Google Scholar 

  47. Joch, J. and Ainsworth, R.A. (1992) The development of creep singular fields for defects in thermally loaded structures. Fatigue Fract. Eng. Mater. Struct., 15, 685 – 693.

    Article  CAS  Google Scholar 

  48. Ainsworth, R.A. (1993) Singular fields at defects in creeping structures subjected to mechanical loading combined with thermal stresses, in Behaviour of Defects at High Temperatures ESIS 15 (Ed R.A. Ainsworth and R.P. Skelton) Mechanical Engineering Publications, London, pp. 219 – 237.

    Google Scholar 

  49. Ohji, K., Ogura, K. and Kubo, S. (1980) Stress field and modified J-integral near a crack tip under condition of confined creep deformation (in Japanese), Zairo, 29, 467 – 471.

    Google Scholar 

  50. Bassani, J.L., Hawk, D.E. and Saxena, A. (1987) Evaluation of the Cf parameter for characterising creep crack growth rates in the transient regime, ASTM STP 995, 7 – 26.

    Google Scholar 

  51. Saxena, A. (1986) Creep crack growth under non-steady-state conditions, ASTM STP 905, 185 – 201.

    Google Scholar 

  52. Saxena, A. (1992) Evaluation of crack-tip parameters for characterising creep crack growth: results of the ASTM round-robin programme. Mater. High Temp., 10, 79 – 91.

    CAS  Google Scholar 

  53. Bassani, J.L. (1992) Mechanics of crack growth under creep conditions. Mater. High Temp., 10, 69 – 73.

    CAS  Google Scholar 

  54. Hutchinson, J.W. and Paris, P.C. (1979) Stability analysis of J-controlled crack growth, ASTM STP 668, 37 – 64.

    Google Scholar 

  55. Hui, C.-Y. and Riedel, R. (1981) The asymptotic stress and strain field near the tip of a growing crack under creep conditions. Int. J. Fract., 17, 409 – 425.

    Article  Google Scholar 

  56. Ainsworth, R.A. (1982) Some observations on creep crack growth, Int. J. Tract., 20, 147 – 159.

    Google Scholar 

  57. He, M.Y. and Hutchinson, J.W. (1981) The penny shaped crack and the plane strain crack in an infinite body of power-law material. ASME, J. Appl. Mech., 48, 830 – 840.

    Article  Google Scholar 

  58. He, M.Y. and Hutchinson, J.W. (1983) Bounds for fully plastic crack problems for infinite bodies, ASTM STP 803, 1277 – 1290.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Imperial College of Science, Technology and Medicine, London, UK

    G. A. Webster (Professor of Engineering Materials)

  2. Berkeley Technology Centre, Nuclear Electric plc, USA

    R. A. Ainsworth

Authors
  1. G. A. Webster
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  2. R. A. Ainsworth
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© 1994 Springer Science+Business Media Dordrecht

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Webster, G.A., Ainsworth, R.A. (1994). Stress analysis of cracked bodies. In: High Temperature Component Life Assessment. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1771-7_4

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  • DOI: https://doi.org/10.1007/978-94-017-1771-7_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4012-1

  • Online ISBN: 978-94-017-1771-7

  • eBook Packages: Springer Book Archive

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