## Elementary engineering fracture mechanicsWhen asked to start teaching a course on engineering fracture mechanics, I realized that a concise textbook, giving a general oversight of the field, did not exist. The explanation is undoubtedly that the subject is still in a stage of early development, and that the methodologies have still a very limited applicability. It is not possible to give rules for general application of fracture mechanics concepts. Yet our comprehension of cracking and fracture beha viour of materials and structures is steadily increasing. Further developments may be expected in the not too distant future, enabling useful prediction of fracture safety and fracture characteristics on the basis of advanced fracture mechanics procedures. The user of such advanced procedures m\lst have a general understanding of the elementary concepts, which are provided by this volume. Emphasis was placed on the practical application of fracture mechanics, but it was aimed to treat the subject in a way that may interest both metallurgists and engineers. For the latter, some general knowledge of fracture mechanisms and fracture criteria is indispensable for an apprecia tion of the limita tions of fracture mechanics. Therefore a general discussion is provided on fracture mechanisms, fracture criteria, and other metal lurgical aspects, without going into much detail. Numerous references are provided to enable a more detailed study of these subjects which are still in a stage of speculative treatment. |

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#### Review: Elementary Engineering Fracture Mechanics

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### Contents

Summary of basic problems and concepts | 3 |

12 A crack in a structure | 6 |

13 The stress at a crack tip | 8 |

14 The Griffith criterion | 15 |

15 The crack opening displacement criterion | 17 |

16 Crack propagation | 18 |

17 Closure | 22 |

Mechanisms of fracture and crack growth | 24 |

99 Measurement of JK and JR | 240 |

910 Closure | 245 |

Fatigue crack propagation | 250 |

103 Factors affecting crack propagation | 256 |

104 Variable amplitude service loading | 262 |

105 Retardation models | 266 |

106 Similitude | 271 |

107 Small cracks | 278 |

22 Cleavage fracture | 31 |

23 Ductile fracture | 38 |

24 Fatigue cracking | 48 |

25 Environment assisted cracking | 59 |

26 Service failure analysis | 62 |

The elastic cracktip stress field | 67 |

32 Complex stress functions | 68 |

33 Solution to crack problems | 69 |

34 The effect of finite size | 73 |

35 Special cases | 77 |

36 Elliptical cracks | 80 |

37 Some useful expressions | 86 |

The crack tip plastic zone | 91 |

42 The Dugdale approach | 94 |

43 The shape of the plastic zone | 96 |

44 Plane stress versus plane strain | 101 |

45 Plastic constraint factor | 105 |

46 The thickness effect | 107 |

The energy principle | 115 |

52 The criterion for crack growth | 119 |

53 The crack resistance R curve | 122 |

54 Compliance | 127 |

55 The J integral | 131 |

56 Tearing modulus | 136 |

57 Stability | 137 |

Dynamics and crack arrest | 142 |

62 The dynamic stress intensity and elastic energy release rate | 147 |

63 Crack branching | 150 |

64 The principles of crack arrest | 155 |

65 Crack arrest in practice | 162 |

66 Dynamic fracture toughness | 165 |

Plane strain fracture toughness | 170 |

72 Size requirements | 174 |

73 Nonlinearity | 177 |

74 Applicability | 181 |

Plane stress and transitional behaviour | 185 |

83 The R curve concept | 193 |

84 The thickness effect | 199 |

85 Plane stress testing | 208 |

86 Closure | 216 |

Elasticplastic fracture | 219 |

92 The crack tip opening displacement | 221 |

93 The possible use of the CTOD criterion | 224 |

94 Experimental determination of CTOD | 225 |

95 Parameters affecting the critical CTOD | 228 |

96 Limitations fracture at general yield | 231 |

97 Use of the J integral | 235 |

98 Limitations of the J integral | 237 |

108 Closure | 282 |

Fracture resistance of materials | 288 |

112 Fatigue cracking criteria | 295 |

113 The effect of alloying and second phase particles | 297 |

114 Effect of processing anisotropy | 304 |

115 Effect of temperature | 309 |

116 Closure | 311 |

APPLICATIONS | 315 |

Failsafety and damage tolerance | 317 |

122 Means to provide failsafety | 318 |

123 Required information for fracture mechanics approach | 323 |

124 Closure | 326 |

Determination of stress intensity factors | 328 |

133 Finite element methods | 330 |

134 Experimental methods | 338 |

Practical problems | 347 |

143 Corner cracks at holes | 352 |

144 Cracks approaching holes | 356 |

145 Combined loading | 359 |

146 Fatigue crack growth under mixed mode loading | 366 |

147 Biaxial loading | 369 |

148 Fracture toughness of weldments | 371 |

149 Service failure analysis | 374 |

Fracture of structures | 377 |

152 Pressure vessels and pipelines | 378 |

153 Leakbeforebreak criterion | 388 |

154 Material selection | 392 |

155 The use of the J integral for structural analysis | 396 |

156 Collapse analysis | 399 |

157 Accuracy of fracture calculations | 404 |

Stiffened sheet structures | 408 |

162 Analysis | 409 |

163 Fatigue crack propagation | 413 |

164 Residual strength | 415 |

165 The R curve and the residual strength of stiffened panels | 422 |

166 Other analysis methods | 425 |

167 Crack arrest | 427 |

168 Closure | 431 |

Prediction of fatigue crack growth | 434 |

172 The load spectrum | 435 |

173 Approximation of the stress spectrum | 437 |

174 Generation of a stress history | 439 |

175 Crack growth integration | 441 |

176 Accuracy of predictions | 447 |

177 Safety factors | 452 |

Author Index | 455 |

462 | |

### Common terms and phrases

Aerospace Inst aluminium alloy amplitude analysis application ASTM STP behaviour brittle Broek calculated chapter constant crack arrest crack extension crack front crack length crack resistance crack speed crack tip critical crack CTOD curve cycle da/dN depends determined diagram discussed ductile fracture effect elastic energy electron energy release rate engineering equations failure fatigue crack growth fatigue crack propagation finite element follows fracture mechanics fracture surface fracture toughness function growth rate high toughness increase integral kg/mm kinetic energy linear elastic load maximum measured Mech method non-linear notch occur parameter particles plane strain plane stress plastic deformation plastic zone correction plate predictions pressure vessels residual strength retardation shear shear stress sheet shown in figure small crack solution specimen steel stiffened panel stress concentration stress field stress intensity factor striations stringer structures surface flaw tensile test data thickness unstiffened yield strength yield stress zero

### Popular passages

Page 345 - Stress Intensity Factors for a Single-Edge-Notch Tension Specimen by Boundary Collocation of a Stress Function," NASA Technical Note D-2395, National Aeronautics and Space Administration, 1964.

Page 287 - Atanmo, P., Kumble, R. and McEvily, AJ 'Crack opening displacement and the rate of fatigue crack growth', Int.