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2018 | OriginalPaper | Chapter

2. Concepts of Fracture Mechanics

Author : Wolfgang Brocks

Published in: Plasticity and Fracture

Publisher: Springer International Publishing

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Abstract

To begin with, linear elastic behaviour is assumed to explicate the basic concepts of fracture mechanics, namely energy and stress intensity approaches. The respective terminology is introduced and the physical quantities of energy release rate and stress intensity factor are defined. Criteria for unstable “brittle” fracture based on the energy release rate and the stress intensity factor are established. Some analytical expressions for stress intensity factors of real structures are given and the problem of a cracked cylinder under internal pressure is addressed, in particular.

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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 Arafah D, Madia M, Zerbst U, Beretta S, Cristea ME (2015) Instability analysis of pressurized pipes with longitudinal surface cracks. Int J Press Vessels Pip 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 Vessels Pip 126–127:48–57
3.
go back to reference ASME BPVC (2015) Boiler and pressure vessel code. The American Society of Mechanical Engineers ASME BPVC (2015) Boiler and pressure vessel code. The American Society of Mechanical Engineers
4.
go back to reference ASTM E399 (2012) Standard test method for linear-elastic plane-strain fracture toughness KIc of metallic materials. Annual Book of ASTM Standards, vol 03.01, American Society for Testing and Materials, West Conshohocken (PA), USA ASTM E399 (2012) Standard test method for linear-elastic plane-strain fracture toughness KIc of metallic materials. Annual Book of ASTM Standards, vol 03.01, American Society for Testing and Materials, West Conshohocken (PA), USA
5.
go back to reference ASTM E1823 (2013) Standard Terminology Relating to Fatigue and Fracture Testing. Annual Book of ASTM Standards, vol 03.01, American Society for Testing and Materials, West Conshohocken (PA), USA ASTM E1823 (2013) Standard Terminology Relating to Fatigue and Fracture Testing. Annual Book of ASTM Standards, vol 03.01, American Society for Testing and Materials, West Conshohocken (PA), USA
6.
go back to reference ASTM E2899 (2015) Standard test method for measurement of initiation toughness in surface cracks under tension and bending. Annual Book of ASTM Standards, vol 03.01, American Society for Testing and Materials, West Conshohocken (PA), USA ASTM E2899 (2015) Standard test method for measurement of initiation toughness in surface cracks under tension and bending. Annual Book of ASTM Standards, vol 03.01, American Society for Testing and Materials, West Conshohocken (PA), USA
7.
go back to reference Brocks W, Schwalbe KH (2015) Experimental and numerical fracture mechanics—an individually dyed history. In: Hütter G, Zybell L (eds) Recent trends in fracture and damage mechanics. Springer, Heidelberg, pp 23–57 Brocks W, Schwalbe KH (2015) Experimental and numerical fracture mechanics—an individually dyed history. In: Hütter G, Zybell L (eds) Recent trends in fracture and damage mechanics. Springer, Heidelberg, pp 23–57
8.
go back to reference BS 7910 (2005) Guide to methods for assessing the acceptability of flaws in metallic structures, British Standards BS 7910 (2005) Guide to methods for assessing the acceptability of flaws in metallic structures, British Standards
9.
go back to reference Erdogan F, Sih GE (1963) On the crack extension in shells and plates under plane loading and transverse shear. J Basic Eng 85:527–529 Erdogan F, Sih GE (1963) On the crack extension in shells and plates under plane loading and transverse shear. J Basic Eng 85:527–529
10.
go back to reference Folias ES (1965) An axial crack in a pressurized cylindrical shell. Int J Fract Mech 1:104–113 Folias ES (1965) An axial crack in a pressurized cylindrical shell. Int J Fract Mech 1:104–113
11.
go back to reference Griffith AA (1920) The phenomena of rupture and flow in solids. Phil Trans Roy Soc London A211:163–198 Griffith AA (1920) The phenomena of rupture and flow in solids. Phil Trans Roy Soc London A211:163–198
12.
go back to reference Griffith AA (1924) Theory of rupture. In: Biezeno B, Burgers JM (eds) Proceedings 1st International Congress for Applied Mechanics. Waltman Uitgevery, Delft, pp 55–63 Griffith AA (1924) Theory of rupture. In: Biezeno B, Burgers JM (eds) Proceedings 1st International Congress for Applied Mechanics. Waltman Uitgevery, Delft, pp 55–63
13.
go back to reference Heliot J, Labbens RC, Pelissier-Tanon A (1978) Semi-elliptical cracks in a cylinder subjected to stress gradients. In: Smith CW (ed) Proceedings of 11th National Symposium on Fracture Mechanics, ASTM STP, vol 677, pp 341–364 Heliot J, Labbens RC, Pelissier-Tanon A (1978) Semi-elliptical cracks in a cylinder subjected to stress gradients. In: Smith CW (ed) Proceedings of 11th National Symposium on Fracture Mechanics, ASTM STP, vol 677, pp 341–364
14.
go back to reference Hussain MA, Pu SI, Underwood J (1974) Strain energy release rate for a crack under combined Mode I and Mode II. ASTM STP 560:2–28 Hussain MA, Pu SI, Underwood J (1974) Strain energy release rate for a crack under combined Mode I and Mode II. ASTM STP 560:2–28
15.
go back to reference Ichikawa M, Tanaka S (1982) A critical analysis of the relationship between the energy release rate and the stress intensity factors under combined mode loading. Int J Fract 18:19–28 Ichikawa M, Tanaka S (1982) A critical analysis of the relationship between the energy release rate and the stress intensity factors under combined mode loading. Int J Fract 18:19–28
16.
go back to reference Inglis CE (1913) Stresses in a plate due to the presence of cracks and sharp corners. Trans Inst Naval Arch 60:219–230 Inglis CE (1913) Stresses in a plate due to the presence of cracks and sharp corners. Trans Inst Naval Arch 60:219–230
17.
go back to reference Irwin GR (1957) Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech 24:361–364 Irwin GR (1957) Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech 24:361–364
18.
go back to reference Irwin GR (1962) Crack extension force for a part-through crack in a plate. Trans ASME, Series E, J Appl Mech 29:615–634 Irwin GR (1962) Crack extension force for a part-through crack in a plate. Trans ASME, Series E, J Appl Mech 29:615–634
19.
go back to reference Isida M, Noguchi H, Yoshida T (1984) Tension and bending of finite thickness plates with a semi-elliptical surface crack. Int J Fract 26:157–188 Isida M, Noguchi H, Yoshida T (1984) Tension and bending of finite thickness plates with a semi-elliptical surface crack. Int J Fract 26:157–188
20.
go back to reference Kiefner JF, Maxey WA, Eiber RJ, Duffy AR (1973) Failure stress levels of flaws in pressurized cylinders. In: Progress in flaw growth and fracture toughness testing. ASTM STP 536:461–481 Kiefner JF, Maxey WA, Eiber RJ, Duffy AR (1973) Failure stress levels of flaws in pressurized cylinders. In: Progress in flaw growth and fracture toughness testing. ASTM STP 536:461–481
21.
go back to reference Kuna M (2013) Finite elements in fracture mechanics. Springer, Dordrecht Kuna M (2013) Finite elements in fracture mechanics. Springer, Dordrecht
22.
go back to reference McGowan JJ, Raymund M (1978) Stress intensity factor solutions for internal longitudinal semi-elliptical surface flaws in a cylinder under arbitrary loadings. In: Smith CW (ed) Proceedings of 11th National Symposium Fracture Mechanics, ASTM STP, vol 677, pp 365–3680 McGowan JJ, Raymund M (1978) Stress intensity factor solutions for internal longitudinal semi-elliptical surface flaws in a cylinder under arbitrary loadings. In: Smith CW (ed) Proceedings of 11th National Symposium Fracture Mechanics, ASTM STP, vol 677, pp 365–3680
23.
go back to reference Muarakami Y (ed) (1987) Stress intensity factors handbook, 3rd edn. Pergamon, New York Muarakami Y (ed) (1987) Stress intensity factors handbook, 3rd edn. Pergamon, New York
24.
go back to reference Muskhelishvili NI (1977) Some basic problems of the mathematical theory of elasticity. Springer, Dordrecht Muskhelishvili NI (1977) Some basic problems of the mathematical theory of elasticity. Springer, Dordrecht
25.
go back to reference Newman JN, Raju IS (1981) An empirical stress-intensity-factor equation for the surface crack. J Eng Fract Mech 15:185–192 Newman JN, Raju IS (1981) An empirical stress-intensity-factor equation for the surface crack. J Eng Fract Mech 15:185–192
26.
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
27.
go back to reference Parks DM (1974) A stiffness derivative finite element technique for determination of crack tip stress intensity factors. Int J Fract 10:487–502 Parks DM (1974) A stiffness derivative finite element technique for determination of crack tip stress intensity factors. Int J Fract 10:487–502
28.
go back to reference Parks DM (1977) The virtual crack extension method for nonlinear material behavior. Comput Meth Appl Mech Eng 12:353–364 Parks DM (1977) The virtual crack extension method for nonlinear material behavior. Comput Meth Appl Mech Eng 12:353–364
29.
go back to reference Raju IS, Newman JN (1979) Stress-intensity-factors for a wide range of semi-elliptical surface cracks in finite thickness plates. J Eng Fract Mech 11:817–829 Raju IS, Newman JN (1979) Stress-intensity-factors for a wide range of semi-elliptical surface cracks in finite thickness plates. J Eng Fract Mech 11:817–829
30.
go back to reference Rice JR (1974) Limitations to the small scale yielding approximation for crack tip plasticity. J Mech Phys Solids 17–26 Rice JR (1974) Limitations to the small scale yielding approximation for crack tip plasticity. J Mech Phys Solids 17–26
31.
go back to reference Richard HA, Kuna M (1990) Theoretical and experimental study of superimposed fracture modes I, II, III. Eng Fract Mech 35:949–960 Richard HA, Kuna M (1990) Theoretical and experimental study of superimposed fracture modes I, II, III. Eng Fract Mech 35:949–960
32.
go back to reference Rooke DP, Cartwright DP (1976) Compendium of stress intensity factors. Stationary Office, GB Rooke DP, Cartwright DP (1976) Compendium of stress intensity factors. Stationary Office, GB
33.
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
34.
go back to reference Sih GE (1974) Strain energy density factor applied to mixed mode crack problems. Int J Fracture 10:305–321 Sih GE (1974) Strain energy density factor applied to mixed mode crack problems. Int J Fracture 10:305–321
35.
go back to reference Sneddon IN (1946) The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc Roy Soc A187:229–260 Sneddon IN (1946) The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc Roy Soc A187:229–260
36.
go back to reference Sneddon IN (1973): Integral transform methods—circular cracks. In: Shih GC (ed) Mechanics of fracture, vol 1. Methods of analysis und solution of crack problems, pp 350–363 Sneddon IN (1973): Integral transform methods—circular cracks. In: Shih GC (ed) Mechanics of fracture, vol 1. Methods of analysis und solution of crack problems, pp 350–363
38.
go back to reference Westergaard HM (1939) Bearing pressures und cracks. J Appl Mech 6:49–53 Westergaard HM (1939) Bearing pressures und cracks. J Appl Mech 6:49–53
39.
go back to reference Williams ML (1957) On the stress distribution at the base of a stationary crack. J Appl Mech 24:109–114 Williams ML (1957) On the stress distribution at the base of a stationary crack. J Appl Mech 24:109–114
Metadata
Title
Concepts of Fracture Mechanics
Author
Wolfgang Brocks
Copyright Year
2018
DOI
https://doi.org/10.1007/978-3-319-62752-6_2

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