Skip to main content
Top

2018 | OriginalPaper | Chapter

5. Elastic-Plastic Fracture Mechanics

Author : Wolfgang Brocks

Published in: Plasticity and Fracture

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Deformation theory of plasticity is applied to generalise fracture mechanics concepts to nonlinear material behaviour. Special emphasis is put on the J-integral as energy release rate and crack-tip intensity parameter in perfect analogy to linear-elastic fracture mechanics. Its definition as path independent integral and calculation from experimental records is addressed. Requirements, extensions, applications, validity and limitations of J as “crack driving force” are discussed, in particular its application to ductile crack extension. The asymptotic J-dominated stress and strain fields at the crack tip are derived. Alternative fracture parameters like dissipation rate, crack-tip opening displacement (CTOD) and angle (CTOA) are introduced and procedures for structural integrity assessment based on these parameters are briefly introduced.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Abaqus (2014) User’s Manual, Version 6.12. Dassault Systèmes Simulia Corp, Providence, RI, USA Abaqus (2014) User’s Manual, Version 6.12. Dassault Systèmes Simulia Corp, Providence, RI, USA
2.
go back to reference Amestoy M, Bui HD, Labbens R (1981) On the definition of local path independent integrals in 3D crack problems. Mechanics Research Communications Amestoy M, Bui HD, Labbens R (1981) On the definition of local path independent integrals in 3D crack problems. Mechanics Research Communications
3.
go back to reference Arafah D (2014) Fracture assessment of cracked components under biaxial loading. PhD Thesis, Department of Mechanical Engineering, Politecnico di Milano Arafah D (2014) Fracture assessment of cracked components under biaxial loading. PhD Thesis, Department of Mechanical Engineering, Politecnico di Milano
4.
go back to reference Arafah D, Madia M, Zerbst U, Beretta S, Cristea ME (2015) Instability analysis of pressurized pipes with longitudinal surface cracks. Int J Press Vess Piping 126–127:48–57 Arafah D, Madia M, Zerbst U, Beretta S, Cristea ME (2015) Instability analysis of pressurized pipes with longitudinal surface cracks. Int J Press Vess Piping 126–127:48–57
5.
go back to reference ASTM E561 (2015) Standard test method for K–R curve determination. Annual book of ASTM standards, Vol 03.01, American Society for Testing and Materials, West Conshohocken (PA), USA ASTM E561 (2015) Standard test method for K–R curve determination. Annual book of ASTM standards, Vol 03.01, American Society for Testing and Materials, West Conshohocken (PA), USA
6.
go back to reference ASTM E1820 (2015) Standard test method for measurement of fracture toughness, Annual Book of ASTM Standards, Vol 03.01, American Society for Testing and Materials, West Conshohocken (PA), USA ASTM E1820 (2015) Standard test method for measurement of fracture toughness, Annual Book of ASTM Standards, Vol 03.01, American Society for Testing and Materials, West Conshohocken (PA), USA
7.
go back to reference ASTM E2472 (2012) Standard test method for determination of resistance to stable crack extension under low-constraint conditions, Annual Book of ASTM Standards, Vol 03.01, American Society for Testing and Materials, West Conshohocken (PA), USA ASTM E2472 (2012) Standard test method for determination of resistance to stable crack extension under low-constraint conditions, Annual Book of ASTM Standards, Vol 03.01, American Society for Testing and Materials, West Conshohocken (PA), USA
8.
go back to reference Bakker A (1984) The three-dimensional J-Integral. PhD Thesis, Delft University of Technology (The Netherlands), Report WTHD 167 Bakker A (1984) The three-dimensional J-Integral. PhD Thesis, Delft University of Technology (The Netherlands), Report WTHD 167
9.
go back to reference Begley JA, Landes JD (1972) The J-integral as a fracture criterion. Fracture Toughness, ASTM STP 514:1–23 Begley JA, Landes JD (1972) The J-integral as a fracture criterion. Fracture Toughness, ASTM STP 514:1–23
10.
go back to reference Betegón C, Hancock JW (1991) Two-parameter characterization of elastic-plastic crack tip fields. J Appl Mech 58:104–110 Betegón C, Hancock JW (1991) Two-parameter characterization of elastic-plastic crack tip fields. J Appl Mech 58:104–110
11.
go back to reference Brocks W, Anuschewski P (2004) Parametrising ductile tearing resistance by four parameters. Eng Fract Mech 71:127–146 Brocks W, Anuschewski P (2004) Parametrising ductile tearing resistance by four parameters. Eng Fract Mech 71:127–146
12.
go back to reference Brocks W, Anuschewski P (2008) Risswiderstandskurven von Blechen. Technical Note GKSS/WMS/08/06, Institute of Materials Research, GKSS Research Centre, Geesthacht Brocks W, Anuschewski P (2008) Risswiderstandskurven von Blechen. Technical Note GKSS/WMS/08/06, Institute of Materials Research, GKSS Research Centre, Geesthacht
13.
go back to reference Brocks W, Anuschewski P, Scheider I (2010) Ductile tearing resistance of metal sheets. Eng Failure Anal 17:607–616 Brocks W, Anuschewski P, Scheider I (2010) Ductile tearing resistance of metal sheets. Eng Failure Anal 17:607–616
14.
go back to reference Brocks W, Klingbeil D, Olschewski J (1990) Lösung der HRR-Feld-Gleichungen der elastisch-plastischen Bruchmechanik, Research Report 175. Bundesanstalt für Materialforschung und -prüfung, Berlin Brocks W, Klingbeil D, Olschewski J (1990) Lösung der HRR-Feld-Gleichungen der elastisch-plastischen Bruchmechanik, Research Report 175. Bundesanstalt für Materialforschung und -prüfung, Berlin
15.
go back to reference Brocks W, Krafka H, Künecke G, Wobst K (1990) Ductile crack growth of semi-elliptical surface flaws in pressure vessels. In: Coleman CE (ed) Leak-before-break in water reactor piping and vessels. Elsevier Applied Science, London, pp 301–316 Brocks W, Krafka H, Künecke G, Wobst K (1990) Ductile crack growth of semi-elliptical surface flaws in pressure vessels. In: Coleman CE (ed) Leak-before-break in water reactor piping and vessels. Elsevier Applied Science, London, pp 301–316
16.
go back to reference Brocks W, Krafka H, Künecke G, Wobst K (1990) Ductile crack growth of semi-elliptical surface flaws in pressure vessels. Int J Pres Vess Piping 43:301–316 Brocks W, Krafka H, Künecke G, Wobst K (1990) Ductile crack growth of semi-elliptical surface flaws in pressure vessels. Int J Pres Vess Piping 43:301–316
17.
go back to reference Brocks W, Künecke G, Wobst K (1989) Stable crack growth of axial surface flaws in pressure vessels. Int J Pres Ves Piping 40:77–90 Brocks W, Künecke G, Wobst K (1989) Stable crack growth of axial surface flaws in pressure vessels. Int J Pres Ves Piping 40:77–90
18.
go back to reference Brocks W, Künecke G, Noack HD, Veith H (1989) On the transferability of fracture mechanics parameters to structures using FEM. Nucl Eng Des 112:1–14 Brocks W, Künecke G, Noack HD, Veith H (1989) On the transferability of fracture mechanics parameters to structures using FEM. Nucl Eng Des 112:1–14
19.
go back to reference Brocks W, Noack HD (1988) J-integral and stresses at an inner surface flaw in a pressure vessel. Int J Pres Ves Piping 31:187–203 Brocks W, Noack HD (1988) J-integral and stresses at an inner surface flaw in a pressure vessel. Int J Pres Ves Piping 31:187–203
20.
go back to reference Brocks W, Olschewski J (1986) On J-dominance of crack-tip fields in largely yielded 3D structures. Int J Solids Structures 22:693–708 Brocks W, Olschewski J (1986) On J-dominance of crack-tip fields in largely yielded 3D structures. Int J Solids Structures 22:693–708
21.
go back to reference Brocks W, Schmitt W (1995) The second parameter in J-R curves: constraint or triaxiality? In: Kirk M, Bakker A (eds) 2nd Symp Constraint Effects, ASTM STP 1224, Philadelphia, pp 209–231 Brocks W, Schmitt W (1995) The second parameter in J-R curves: constraint or triaxiality? In: Kirk M, Bakker A (eds) 2nd Symp Constraint Effects, ASTM STP 1224, Philadelphia, pp 209–231
22.
go back to reference Brocks W, Yuan H (1989) Numerical investigations on the significance of J for large stable crack growth. Eng Fract Mech 32:459–468 Brocks W, Yuan H (1989) Numerical investigations on the significance of J for large stable crack growth. Eng Fract Mech 32:459–468
23.
go back to reference BS 5762 (1979) Methods for crack opening displacement (COD) testing. British Standards Institution BS 5762 (1979) Methods for crack opening displacement (COD) testing. British Standards Institution
24.
go back to reference Cherepanov CP (1967) Crack propagation in continuous media. Appl Math Mech 31:476–488 Cherepanov CP (1967) Crack propagation in continuous media. Appl Math Mech 31:476–488
25.
go back to reference DeLorenzi HG (1982) Energy release rate calculations by the finite element method. General Electric Technical Information Series, Report No. 82CRD205 DeLorenzi HG (1982) Energy release rate calculations by the finite element method. General Electric Technical Information Series, Report No. 82CRD205
26.
go back to reference DeLorenzi HG (1982) On the energy release rate and the J-integral for 3D crack configurations. J Fracture 19:183–193 DeLorenzi HG (1982) On the energy release rate and the J-integral for 3D crack configurations. J Fracture 19:183–193
27.
go back to reference Dowling NE (1977) Crack growth during low-cycle fatigue of smooth axial specimens. ASTM STP 637:97–121 Dowling NE (1977) Crack growth during low-cycle fatigue of smooth axial specimens. ASTM STP 637:97–121
28.
go back to reference Dowling NE, Begley JA (1976) Fatigue crack growth during gross plasticity and the J-integral. ASTM STP 590:82–103 Dowling NE, Begley JA (1976) Fatigue crack growth during gross plasticity and the J-integral. ASTM STP 590:82–103
29.
go back to reference Dowling NE, Iyyer NS (1987) Fatigue crack growth and closure at high cyclic strains. Mater Science Eng 96:99–107 Dowling NE, Iyyer NS (1987) Fatigue crack growth and closure at high cyclic strains. Mater Science Eng 96:99–107
30.
go back to reference Dowling AR, Townly CHA (1975) The effect of defects on structural failure: a two criteria approach. Int J Press Ves Piping 3:77–107 Dowling AR, Townly CHA (1975) The effect of defects on structural failure: a two criteria approach. Int J Press Ves Piping 3:77–107
31.
go back to reference Efam GTP (2002) The GKSS procedure for determining the fracture behaviour of materials. GKSS-Forschungszentrum Geesthacht, Germany Efam GTP (2002) The GKSS procedure for determining the fracture behaviour of materials. GKSS-Forschungszentrum Geesthacht, Germany
32.
go back to reference Eftis J, Liebowitz H (1972) On the modified Westergaard equation for certain plane crack problems. Int J Fract Mech 8(1972):383–392 Eftis J, Liebowitz H (1972) On the modified Westergaard equation for certain plane crack problems. Int J Fract Mech 8(1972):383–392
33.
go back to reference Eshelby JD (1965) The continuum theory of lattice defects. Prog Solid States Phys 3:79–114 Eshelby JD (1965) The continuum theory of lattice defects. Prog Solid States Phys 3:79–114
34.
go back to reference Garwood SJ (1979) Effect of specimen geometry on crack growth resistance. In: Smith CW (ed) ASTM STP 677. American Society for Testing and Materials, pp. 511–532 Garwood SJ (1979) Effect of specimen geometry on crack growth resistance. In: Smith CW (ed) ASTM STP 677. American Society for Testing and Materials, pp. 511–532
35.
go back to reference Garwood SJ, Robinson JN, Turner CE (1975) The measurement of crack growth resistance curves (R-curves) using the J integral. Int J Fracture 11:528–530 Garwood SJ, Robinson JN, Turner CE (1975) The measurement of crack growth resistance curves (R-curves) using the J integral. Int J Fracture 11:528–530
36.
go back to reference Goodier JN, Field FA (1963) Plastic energy dissipation in crack propagation. In: Drucker DC, Gilman JJ (eds) Fracture of solids. Wiley, New York, pp 103–118 Goodier JN, Field FA (1963) Plastic energy dissipation in crack propagation. In: Drucker DC, Gilman JJ (eds) Fracture of solids. Wiley, New York, pp 103–118
37.
go back to reference Harrison JD, Dawes MG, Archer GL, Kamath KD (1978) The COD approach and its application to welded structures. Research Report 55/1978/E, The Welding Institute, Cambridge Harrison JD, Dawes MG, Archer GL, Kamath KD (1978) The COD approach and its application to welded structures. Research Report 55/1978/E, The Welding Institute, Cambridge
38.
go back to reference Hellmann D, Schwalbe KH (1984) Geometry and size effects on J-R and δ-R curves under plane stress conditions. In: Sanford RJ (ed) Fracture Mechanics, 15th Symposium. ASTM STP 833, pp 577–605 Hellmann D, Schwalbe KH (1984) Geometry and size effects on J-R and δ-R curves under plane stress conditions. In: Sanford RJ (ed) Fracture Mechanics, 15th Symposium. ASTM STP 833, pp 577–605
39.
go back to reference Heerens J, Schödel M (2009) Characterization of stable crack extension in aluminium sheet material using the crack tip opening angle determined optically and by the δ5 clip gauge technique. Eng Fract Mech 76:101–113 Heerens J, Schödel M (2009) Characterization of stable crack extension in aluminium sheet material using the crack tip opening angle determined optically and by the δ5 clip gauge technique. Eng Fract Mech 76:101–113
40.
go back to reference Hutchinson JW (1968) Singular behaviour at the end of a tensile crack in a hardening material. J Mech Phys Solids 16:13–31 Hutchinson JW (1968) Singular behaviour at the end of a tensile crack in a hardening material. J Mech Phys Solids 16:13–31
41.
go back to reference Hutchinson JW (1968) Plastic stress and strain fields at a crack tip. J Mech Phys Solids 16:337–347 Hutchinson JW (1968) Plastic stress and strain fields at a crack tip. J Mech Phys Solids 16:337–347
42.
go back to reference Hutchinson, JW, Paris, PC (1979) Stability analysis of J-controlled crack growth. In: Landes JH, Begley, JA, Clarke GA (eds) Elastic-Plastic Fracture, ASTM STP 668:37–64 Hutchinson, JW, Paris, PC (1979) Stability analysis of J-controlled crack growth. In: Landes JH, Begley, JA, Clarke GA (eds) Elastic-Plastic Fracture, ASTM STP 668:37–64
43.
go back to reference ISO 12135 (2002) Metallic materials—Unified method of test for the determination of quasistatic fracture toughness. International Standards Organisation, Geneva, Switzerland ISO 12135 (2002) Metallic materials—Unified method of test for the determination of quasistatic fracture toughness. International Standards Organisation, Geneva, Switzerland
44.
go back to reference ISO 22889 (2007) Metallic materials—method of test for the determination of resistance to stable crack extension using specimens of low constraint. International Standards Organisation, Geneva, Switzerland ISO 22889 (2007) Metallic materials—method of test for the determination of resistance to stable crack extension using specimens of low constraint. International Standards Organisation, Geneva, Switzerland
45.
go back to reference Kikuchi M, Miyamoto H (1982) Evaluation of JK integrals for a crack in multiphase materials. Recent research on mechanical behavior of materials. Bull Fracture Mechanics Lab, vol 1, Science University of Tokyo Kikuchi M, Miyamoto H (1982) Evaluation of JK integrals for a crack in multiphase materials. Recent research on mechanical behavior of materials. Bull Fracture Mechanics Lab, vol 1, Science University of Tokyo
46.
go back to reference Kikuchi M, Miyamoto H, Sakaguchi, Y (1979) Evaluation of three-dimensional J integral of semi-elliptical surface crack in pressure vessel. In: Trans 5th SMiRT, paper G7/2, Berlin Kikuchi M, Miyamoto H, Sakaguchi, Y (1979) Evaluation of three-dimensional J integral of semi-elliptical surface crack in pressure vessel. In: Trans 5th SMiRT, paper G7/2, Berlin
47.
go back to reference Kolednik O (1993) A simple model to explain the geometry dependence of J-Δa-curves. Int J Fract 63:263–274 Kolednik O (1993) A simple model to explain the geometry dependence of J-Δa-curves. Int J Fract 63:263–274
48.
go back to reference Kolednik O, Predan J, Fischer FD (2010) Cracks in inhomogeneous materials: comprehensive assessment using the configurational forces concept. Eng Fract Mech 77:2698–2711 Kolednik O, Predan J, Fischer FD (2010) Cracks in inhomogeneous materials: comprehensive assessment using the configurational forces concept. Eng Fract Mech 77:2698–2711
49.
go back to reference Kumar V, German MD, Shih CF (1981) An Engineering Approach for elastic-plastic fracture analysis. EPRI-Report NP-1931, EPRI, Palo Alto, CA Kumar V, German MD, Shih CF (1981) An Engineering Approach for elastic-plastic fracture analysis. EPRI-Report NP-1931, EPRI, Palo Alto, CA
50.
go back to reference Madia M, Arafah D, Zerbst U (2014) Reference load solutions for plates with semi-elliptical surface cracks subjected to biaxial tensile loading. Int J Press Vess Piping 119:19–28 Madia M, Arafah D, Zerbst U (2014) Reference load solutions for plates with semi-elliptical surface cracks subjected to biaxial tensile loading. Int J Press Vess Piping 119:19–28
51.
go back to reference Maugin GA (1995) Material forces: concepts and applications. Appl Mech Rev 48:213–245 Maugin GA (1995) Material forces: concepts and applications. Appl Mech Rev 48:213–245
52.
go back to reference McClung RC, Chell GG, Lee YD, Russel DA, Orient DE (1999) Development of a practical methodology for elastic-plastic and fully plastic fatigue crack growth. NASA/CR-1999-209428, Marshall Space Flight Center • MSFC, Alabama 35812 McClung RC, Chell GG, Lee YD, Russel DA, Orient DE (1999) Development of a practical methodology for elastic-plastic and fully plastic fatigue crack growth. NASA/CR-1999-209428, Marshall Space Flight Center • MSFC, Alabama 35812
53.
go back to reference McMeeking RM (1977) Path dependence of the J-Integral and the role of J as a parameter characterizing the near-tip field. In Barsom JM (ed) Flaw growth and fracture, ASTM STP 631, pp 28–41 McMeeking RM (1977) Path dependence of the J-Integral and the role of J as a parameter characterizing the near-tip field. In Barsom JM (ed) Flaw growth and fracture, ASTM STP 631, pp 28–41
54.
go back to reference McMeeking RM (1977) Finite deformation analyses of crack-tip opening in elastic-plastic materials and implications for fracture. J Mech Phys Solids 25:357–381 McMeeking RM (1977) Finite deformation analyses of crack-tip opening in elastic-plastic materials and implications for fracture. J Mech Phys Solids 25:357–381
55.
go back to reference McMeeking RM, Parks DM (1979) On criteria for J-dominance of crack-tip fields in large scale yielding. In: Landes JH, Begley, JA, Clarke GA (eds) Elastic-Plastic Fracture, ASTM STP 668, pp 175–194 McMeeking RM, Parks DM (1979) On criteria for J-dominance of crack-tip fields in large scale yielding. In: Landes JH, Begley, JA, Clarke GA (eds) Elastic-Plastic Fracture, ASTM STP 668, pp 175–194
56.
go back to reference Memhard D, Brocks W, Fricke S (1993) Characterization of ductile tearing resistance by energy dissipation rate. Fatigue Fract Eng Mater Struct 16:1109–1124 Memhard D, Brocks W, Fricke S (1993) Characterization of ductile tearing resistance by energy dissipation rate. Fatigue Fract Eng Mater Struct 16:1109–1124
57.
go back to reference Mughrabi H, Bayerlein M, Christ HJ (1987) Microstructural foundation of cyclic stress-strain response and Masing behaviour. In: Anderson et al (eds) Constitutive relations and their physical basis, 8th Risø Int Symp Metallurgy and Material Science, Roskilde, Denmark Mughrabi H, Bayerlein M, Christ HJ (1987) Microstructural foundation of cyclic stress-strain response and Masing behaviour. In: Anderson et al (eds) Constitutive relations and their physical basis, 8th Risø Int Symp Metallurgy and Material Science, Roskilde, Denmark
58.
go back to reference Muscati A, Lee DJ (1984) Elastic-plastic finite element analysis of thermally loaded cracked structures. Int J Fracture 25:246–2276 Muscati A, Lee DJ (1984) Elastic-plastic finite element analysis of thermally loaded cracked structures. Int J Fracture 25:246–2276
59.
go back to reference Neimitz A, Dzioba I, Galkiewicz G, Molasy R (2004) A study of stable crack growth using experimental methods, finite elements and fractography. Eng Fract Mech 71:1325–1355 Neimitz A, Dzioba I, Galkiewicz G, Molasy R (2004) A study of stable crack growth using experimental methods, finite elements and fractography. Eng Fract Mech 71:1325–1355
60.
go back to reference Newman JC, James MA, Zerbst U (2003) A review of the CTOA/CTOD fracture criterion. Eng Fract Mech 70:85–371 Newman JC, James MA, Zerbst U (2003) A review of the CTOA/CTOD fracture criterion. Eng Fract Mech 70:85–371
61.
go back to reference O’Dowd NP, Shih CF (1991) Family of crack-tip fields characterized by a triaxiality parameter: I Structure of fields. J Mech Phys Solids 39:989–1015 O’Dowd NP, Shih CF (1991) Family of crack-tip fields characterized by a triaxiality parameter: I Structure of fields. J Mech Phys Solids 39:989–1015
62.
go back to reference O’Dowd NP, Shih CF (1992) Family of crack-tip fields characterized by a triaxiality parameter: II Fracture applications. J Mech Phys Solids 40:939–963 O’Dowd NP, Shih CF (1992) Family of crack-tip fields characterized by a triaxiality parameter: II Fracture applications. J Mech Phys Solids 40:939–963
63.
go back to reference Paris PC, Erdogan F (1963) A critical analysis of crack propagation laws. J Basic Eng Trans Am Soc Mech Eng D85:528–534 Paris PC, Erdogan F (1963) A critical analysis of crack propagation laws. J Basic Eng Trans Am Soc Mech Eng D85:528–534
64.
go back to reference Paris PC, Tada H, Zahoor A, Ernst H (1979) The theory of instability of the tearing mode of elastic-plastic crack growth. In: Landes JH, Begley JA, Clarke GA (eds) Elastic-Plastic Fracture, ASTM STP 668, pp 5–36 Paris PC, Tada H, Zahoor A, Ernst H (1979) The theory of instability of the tearing mode of elastic-plastic crack growth. In: Landes JH, Begley JA, Clarke GA (eds) Elastic-Plastic Fracture, ASTM STP 668, pp 5–36
65.
go back to reference Parks DM, Wang YY (1988) Elastic-plastic analysis of part-through surface cracks. In: Rosakis AJ, Ravi-Chandar K, Rajapakse Y (eds) Analytical, numerical and experimental aspects of three dimensional fracture processes, New York, ASME AMD-vol 91, pp 19–32 Parks DM, Wang YY (1988) Elastic-plastic analysis of part-through surface cracks. In: Rosakis AJ, Ravi-Chandar K, Rajapakse Y (eds) Analytical, numerical and experimental aspects of three dimensional fracture processes, New York, ASME AMD-vol 91, pp 19–32
66.
go back to reference R6 (2009) Assessment of the integrity of structures containing defects. Revision 4, British Energy Generation Ltd. R6 (2009) Assessment of the integrity of structures containing defects. Revision 4, British Energy Generation Ltd.
67.
go back to reference Ramberg W, Osgood WR (1945) Description of stress strain curves by three parameters. NACA Technical Note No 902 Ramberg W, Osgood WR (1945) Description of stress strain curves by three parameters. NACA Technical Note No 902
68.
go back to reference Rice JR (1968) A path independent integral and the approximate analysis of strain concentrations by notches and cracks. J Appl Mech 35:379–386 Rice JR (1968) A path independent integral and the approximate analysis of strain concentrations by notches and cracks. J Appl Mech 35:379–386
69.
go back to reference Rice JR, Drugan WJ, Sham TL (1979) Elastic Plastic analysis of growing cracks. Technical Report No. 65 of US DOE, Brown University, Providence, RI Rice JR, Drugan WJ, Sham TL (1979) Elastic Plastic analysis of growing cracks. Technical Report No. 65 of US DOE, Brown University, Providence, RI
70.
go back to reference Rice JR, Johnson MA (1970) The role of large crack tip geometry changes in plane strain fracture. In: Kanninen MF, Adler W, Rosenfield A, Jaffe R (eds) Elastic behaviour of solids. McGraw Hill, New York Rice JR, Johnson MA (1970) The role of large crack tip geometry changes in plane strain fracture. In: Kanninen MF, Adler W, Rosenfield A, Jaffe R (eds) Elastic behaviour of solids. McGraw Hill, New York
71.
go back to reference Rice JR, Paris PC, Merkle JG (1973) Some further results of J-integral analysis and estimates. In: Kaufman J, Swedlow J, Corten H, Srawley J, Heyer R, Wessel E, Irwin G (eds) Progress in flaw growth and fracture toughness testing, ASTM STP 536, pp 231–245 Rice JR, Paris PC, Merkle JG (1973) Some further results of J-integral analysis and estimates. In: Kaufman J, Swedlow J, Corten H, Srawley J, Heyer R, Wessel E, Irwin G (eds) Progress in flaw growth and fracture toughness testing, ASTM STP 536, pp 231–245
72.
go back to reference Rice JR, Rosengren GF (1968) Plane strain deformation near a crack-tip in a power-law hardening material. J Mech Phys Solids 16:1–12 Rice JR, Rosengren GF (1968) Plane strain deformation near a crack-tip in a power-law hardening material. J Mech Phys Solids 16:1–12
73.
go back to reference Scheider I, Schödel M, Brocks W, Schönfeld W (2006) Crack propagation analyses with CTOA and cohesive model: Comparison and experimental validation. Eng Fract Mech 73:252–263 Scheider I, Schödel M, Brocks W, Schönfeld W (2006) Crack propagation analyses with CTOA and cohesive model: Comparison and experimental validation. Eng Fract Mech 73:252–263
74.
go back to reference Schwalbe KH (1995) Introduction of δ5 as an operational definition of the CTOD and its practical use. In Reuter WG, Underwood JH, Newman JC (eds) Fracture mechanics: vol 26, ASTM STP 1256, American Society for Testing and Materials, pp 763–778 Schwalbe KH (1995) Introduction of δ5 as an operational definition of the CTOD and its practical use. In Reuter WG, Underwood JH, Newman JC (eds) Fracture mechanics: vol 26, ASTM STP 1256, American Society for Testing and Materials, pp 763–778
75.
go back to reference Schwalbe KH (1998) EFAM ETM 97—the ETM method for assessing the significance of crack-like defects in engineering structures, comprising the versions ETM 97/1 and ETM 97/2. GKSS Research Centre, Geesthacht, Germany Schwalbe KH (1998) EFAM ETM 97—the ETM method for assessing the significance of crack-like defects in engineering structures, comprising the versions ETM 97/1 and ETM 97/2. GKSS Research Centre, Geesthacht, Germany
76.
go back to reference Schwalbe KH (1998) The Engineering Flaw Assessment Method (EFAM). Fatigue Fract Eng Mater Struct 21:1203–1213 Schwalbe KH (1998) The Engineering Flaw Assessment Method (EFAM). Fatigue Fract Eng Mater Struct 21:1203–1213
77.
go back to reference Schwalbe KH, Kim YJ, Hao S, Cornec A, Kocak M (1997) EFAM ETM-MM 96—the ETM method for assessing the significance of crack-like defects in joints with mechanical heterogeneity (strength mismatch). GKSS Report 97/E/9, GKSS Research Centre, Geesthacht, Germany Schwalbe KH, Kim YJ, Hao S, Cornec A, Kocak M (1997) EFAM ETM-MM 96—the ETM method for assessing the significance of crack-like defects in joints with mechanical heterogeneity (strength mismatch). GKSS Report 97/E/9, GKSS Research Centre, Geesthacht, Germany
78.
go back to reference Schwalbe KH, Newman JC, Shannon J (2005) Fracture mechanics testing on specimens with low constraint—standardisation activities within ISO and ASTM. Eng Fract Mech 72:557–576 Schwalbe KH, Newman JC, Shannon J (2005) Fracture mechanics testing on specimens with low constraint—standardisation activities within ISO and ASTM. Eng Fract Mech 72:557–576
79.
go back to reference Schwalbe KH, Zerbst U, Brocks W, Cornec A, Heerens J, Amstutz H (1998) The ETM method for assessing the significance of crack-like defects in engineering structures. Fatigue Fract Eng Mater Struct 21:1215–1231 Schwalbe KH, Zerbst U, Brocks W, Cornec A, Heerens J, Amstutz H (1998) The ETM method for assessing the significance of crack-like defects in engineering structures. Fatigue Fract Eng Mater Struct 21:1215–1231
80.
go back to reference Schwalbe KH, Zerbst U (2000) The engineering treatment model. Int J Press Vess Piping 77:905–918 Schwalbe KH, Zerbst U (2000) The engineering treatment model. Int J Press Vess Piping 77:905–918
81.
go back to reference Sharma SM, Aravas N (1991) Determination of higher order terms in asymptotic elastoplastic crack tip solutions. J Mech Phys Solids 39:1043–1072 Sharma SM, Aravas N (1991) Determination of higher order terms in asymptotic elastoplastic crack tip solutions. J Mech Phys Solids 39:1043–1072
82.
go back to reference Shih CF (1981) Relationships between the J-integral and the crack opening displacement for stationary and extending cracks. J Mech Phys Solids 29:305–326 Shih CF (1981) Relationships between the J-integral and the crack opening displacement for stationary and extending cracks. J Mech Phys Solids 29:305–326
83.
go back to reference Shih CF (1983) Tables of the Hutchinson-Rice-Rosengren singular field quantities. Report MRL E-147, Brown University, Providence (RI) Shih CF (1983) Tables of the Hutchinson-Rice-Rosengren singular field quantities. Report MRL E-147, Brown University, Providence (RI)
84.
go back to reference Shih CF (1985) J-dominance under plane strain fully plastic conditions: the edge crack panel subject to combined tension and bending. Int J Fracture 29:73–84 Shih CF (1985) J-dominance under plane strain fully plastic conditions: the edge crack panel subject to combined tension and bending. Int J Fracture 29:73–84
85.
go back to reference Shih CF, Asaro RJ (1988) Elastic-plastic analysis of cracks on bimaterial interfaces: part I—small scale yielding. J Appl Mech 55:299–316 Shih CF, Asaro RJ (1988) Elastic-plastic analysis of cracks on bimaterial interfaces: part I—small scale yielding. J Appl Mech 55:299–316
86.
go back to reference Shih CF, DeLorenzi HG, Andrews WR (1979) Studies on crack initiation and stable crack growth. In: Landes JH, Begley, JA, Clarke GA (eds) Elastic-Plastic Fracture, ASTM STP 668 Shih CF, DeLorenzi HG, Andrews WR (1979) Studies on crack initiation and stable crack growth. In: Landes JH, Begley, JA, Clarke GA (eds) Elastic-Plastic Fracture, ASTM STP 668
87.
go back to reference Shih CF, German MD (1985) Requirements for a one parameter characterization of crack tip fields by the HRR-singularity. Int J Fracture 29:73–84 Shih CF, German MD (1985) Requirements for a one parameter characterization of crack tip fields by the HRR-singularity. Int J Fracture 29:73–84
88.
go back to reference Shih CF, Hutchinson JW (1976) Fully plastic solutions and large-scale yielding estimates for plane stress crack problems. J Eng Mat Tech 98:289–295 Shih CF, Hutchinson JW (1976) Fully plastic solutions and large-scale yielding estimates for plane stress crack problems. J Eng Mat Tech 98:289–295
89.
go back to reference Shih CF, Moran B, Nakamura T (1986) Energy release rate along a three-dimensional crack front in a thermally stressed body. Int J Fracture 30:79–102 Shih CF, Moran B, Nakamura T (1986) Energy release rate along a three-dimensional crack front in a thermally stressed body. Int J Fracture 30:79–102
90.
go back to reference Siegele D (1989) 3D crack propagation using ADINA. Comp Struct 32:639–645 Siegele D (1989) 3D crack propagation using ADINA. Comp Struct 32:639–645
91.
go back to reference Siegmund T, Brocks W (2000) A numerical study on the correlation between the work of separation and the dissipation rate in ductile fracture. Eng Fract Mech 6:139–154 Siegmund T, Brocks W (2000) A numerical study on the correlation between the work of separation and the dissipation rate in ductile fracture. Eng Fract Mech 6:139–154
92.
go back to reference Sumpter JDG (1999) An alternative view of R-curve testing. Eng Fract Mech 64:161–176 Sumpter JDG (1999) An alternative view of R-curve testing. Eng Fract Mech 64:161–176
94.
go back to reference Tanaka K (1983) The cyclic J-integral as a criterion for fatigue crack growth. Int J Fract 22:91–104 Tanaka K (1983) The cyclic J-integral as a criterion for fatigue crack growth. Int J Fract 22:91–104
95.
go back to reference Turner CE (1990) A re-assessment of ductile tearing resistance, Part I: The geometry dependence of J-R curves in fully plastic bending, Part II: Energy dissipation rate and associated R-curves on normalized axes. In: Firrao D (ed) Fracture behaviour and design of materials and structures, vol II, 8th European conference on fracture, Engineering Mechanics Advisory Services, Warley, pp 933–949, 951–968 Turner CE (1990) A re-assessment of ductile tearing resistance, Part I: The geometry dependence of J-R curves in fully plastic bending, Part II: Energy dissipation rate and associated R-curves on normalized axes. In: Firrao D (ed) Fracture behaviour and design of materials and structures, vol II, 8th European conference on fracture, Engineering Mechanics Advisory Services, Warley, pp 933–949, 951–968
96.
go back to reference Turner CE, Kolednik O (1994) Application of energy dissipation rate arguments to stable crack growth. Fatigue Fract Eng Mater Struct 20:1109–1127 Turner CE, Kolednik O (1994) Application of energy dissipation rate arguments to stable crack growth. Fatigue Fract Eng Mater Struct 20:1109–1127
97.
go back to reference Tvergaard V, Hutchinson JW (1994) Effect of T stress on mode I crack growth resistance in a ductile solid. Int J Solids Struct 31:823–833 Tvergaard V, Hutchinson JW (1994) Effect of T stress on mode I crack growth resistance in a ductile solid. Int J Solids Struct 31:823–833
98.
go back to reference Wells AA (1961) Unstable crack propagation in metals: cleavage and fast fracture. In: Proceedings of the crack propagation symposium, Cranfield, UK, vol 2, pp 210–230 Wells AA (1961) Unstable crack propagation in metals: cleavage and fast fracture. In: Proceedings of the crack propagation symposium, Cranfield, UK, vol 2, pp 210–230
99.
go back to reference Yuan H, Brocks W (1991) On the J-integral concept for elastic-plastic crack extension. Nucl Eng Design 131:157–173 Yuan H, Brocks W (1991) On the J-integral concept for elastic-plastic crack extension. Nucl Eng Design 131:157–173
100.
go back to reference Yuan Y, Brocks W (1998) Quantification of constraint effects in elastic-plastic crack front fields. J Mech Phys Solids 46:219–241 Yuan Y, Brocks W (1998) Quantification of constraint effects in elastic-plastic crack front fields. J Mech Phys Solids 46:219–241
101.
go back to reference Zerbst U, Ainsworth RA, Schwalbe KH (2000) Basic principles of analytical flaw assessment methods. Int J Press Vess Piping 77:855–867 Zerbst U, Ainsworth RA, Schwalbe KH (2000) Basic principles of analytical flaw assessment methods. Int J Press Vess Piping 77:855–867
102.
go back to reference Zerbst U, Schödel M, Webster S, Ainsworth R (2007) Fitness-for-service fracture assessment of structures containing cracks. Elsevier, Oxford, UK Zerbst U, Schödel M, Webster S, Ainsworth R (2007) Fitness-for-service fracture assessment of structures containing cracks. Elsevier, Oxford, UK
Metadata
Title
Elastic-Plastic Fracture Mechanics
Author
Wolfgang Brocks
Copyright Year
2018
DOI
https://doi.org/10.1007/978-3-319-62752-6_5

Premium Partners