## Elastodynamic Crack Problems |

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### Contents

Transient response of cracks to impact loads | 1 |

12 Semiinfinite cracks | 2 |

13 Plane cracks with finite dimensions | 13 |

14 Pennyshaped cracks | 23 |

15 Transient response of a bent plate with a through crack | 36 |

16 Sudden tractions applied to a strip containing a crack | 42 |

17 Interaction of a crack with suddenly displaced boundaries | 49 |

Inverse Laplace transform of stress or moment intensity factor | 55 |

310 SHwaves striking a moving crack | 202 |

Function decomposition | 209 |

References | 211 |

Dynamic crack problems in dissimilar media | 213 |

42 Antiplane strain of a semiinfinite crack in dissimilar media | 218 |

43 Crack expanding along and through interfaces between two different elastic media under antiplane strain | 226 |

44 A crack moving along an interface at a non uniform rate antiplane strain | 229 |

45 A semiinfinite crack running along an interface plane strain | 230 |

References | 57 |

Cracks moving at constant velocity and acceleration | 59 |

22 Elastodynamic equations in twodimensions | 60 |

23 Semiinfinite moving crack | 62 |

24 Finite length crack propagating at a constant velocity | 71 |

25 Semiinfinite crack motion maintained by displacement boundary conditions | 75 |

26 Finite length crack moving between clamped and free boundaries | 82 |

27 Through crack extending at both ends | 93 |

28 Pennyshaped crack propagating at uniform velocity | 101 |

29 Crack propagation with acceleration | 108 |

References | 116 |

Scattering waves about stationary and moving cracks | 119 |

32 Wave equations in the theory of elasticity | 123 |

33 Solution of dual integral equations | 126 |

34 Plane crack engulfed by P and SVwaves | 131 |

35 Diffraction of SHwaves by a plane crack | 151 |

36 Normal compression and radial shear waves impinging on a pennyshaped crack | 156 |

37 Interaction of torsional waves with a penny shaped crack | 167 |

38 Flexural wave propagation in an elastic plate with a crack | 172 |

39 Moving crack interacting with P and SV waves | 181 |

46 Expanding cracks along interfaces plane strain | 236 |

47 Cracks in media with spatially varying elastic moduli | 237 |

References | 247 |

Dynamic analysis of cracked structures using singularity finite elements | 249 |

formulation | 250 |

applications | 268 |

formulation | 278 |

application | 283 |

Stiffness matrices for displacement compatible elements | 288 |

References | 292 |

Numerical analysis of dynamic crack problems | 295 |

62 HEMP 3D A finitedifference simulation program | 297 |

63 Twodimensional crack problems | 316 |

64 Threedimensional crack problems | 325 |

65 Determination of static values by dynamic programs | 331 |

66 Effect of grid size on calculations of stress intensity factors | 334 |

67 Computer simulation of fracture | 335 |

68 Appendix | 341 |

343 | |

### Common terms and phrases

amplitude analysis anti-plane shear anti-plane strain applied boundary conditions calculated Chen computed constant velocity corresponding crack moving crack problems crack propagation crack speed crack surfaces crack tip crack velocity deﬁned denotes dual integral equations dynamic crack dynamic stress intensity elastic solid elastodynamic equations of motion ﬁeld ﬁnite ﬁnite-element ﬁrst Fracture Mechanics Fredholm integral equation frequency function G. C. Sih grid incident wave inﬁnite intensity factor versus interface Laplace transform Loeber material method modulus moving crack nodes numerical obtained P-wave penny-shaped crack plane strain plate Poisson's ratio Rayleigh wave s-plane satisﬁed scattered wave semi-infinite crack shear stress shear waves shown in Figure singularity element solution solved static value stationary crack strain energy strain energy density stress and displacement stress components stress field stress intensity factor strip SV-wave sx)ds symmetric transient variable variations vector wave equation wave number wave potentials wave speed Wiener-Hopf zero zone

### Popular passages

Page xlvi - Kipp, ME and Sih, GC, The strain energy density failure criterion applied to notched elastic solids, International Journal of Solids and Structures, 2, pp.

Page xlvi - Dynamic aspects of crack propagation: inelastic behavior of solids, edited by MF Kanninen, WF Adler, AR Rosenfield and RI Jaffee, McGraw-Hill, pp.

Page xv - Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, New York 11794-3600 Books Received for Review Askin, Ronald G., Jeffrey B.

Page xi - For example, if the time required to apply the load, ie, increase the load from zero to its maximum value, is less than half the fundamental natural period of the structure, the loading is definitely impact.

Page x - ... metals. In this chapter we shall consider only inertia effects, even if we deal with fracture-mechanics problems, confining ourselves to brittle fracture. It has long been recognized that high loading rates tend to promote brittle fracture, a phenomenon associated with the sudden creation of a macrocrack free surface. When a body is loaded quickly, there is less time for yielding or microscopic damage to take place, and hence energy is released within a short time interval by rapid macrocrack...

Page xv - School of Engineering Science and Mechanics, Georgia Institute of Technology, Atlanta, Georgia, USA Albert S.

Page xlvii - Prospects of Fracture Mechanics, edited by GC Sih, HC van Elst and D. Broek, Noordhoff International Publishing, Leyden, pp.