Mode-III Stress Intensity Factor by Williams Element with Generalized Degrees of Freedom

2012 ◽  
Vol 487 ◽  
pp. 242-246 ◽  
Author(s):  
Hua Xu ◽  
Lu Feng Yang ◽  
Zhen Ping She
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Displacement Field ◽  
Degrees Of Freedom ◽  
Crack Tip ◽  
Relative Length ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Generalized Degrees Of Freedom

Williams series are developed for mode III cracks, based on which the displacement field is defined in the singular region around the crack tip. The Williams element with generalized degrees of freedom (GDOFs) is proposed for analysis of stress intensity factor (SIF) of mode III crack. The SIF at the crack tip can be evaluated analytically by one of the undetermined constants of the Williams element. The influence of the relative length of the crack on the SIF is investigated. Three important parameters for the Williams element, including the radial scale factor, the number of subelements and the terms of the Williams series, are discussed in detail. Numerical example shows that the Williams element is of accuracy and efficiency.

Complete Crack-Tip Shielding of the Mode III Crack in a Work-Hardening Solid

1991 ◽  
Vol 58 (4) ◽  
pp. 1107-1108 ◽  
Author(s):  
J. Weertman
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Work Hardening ◽  
Crack Tip ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Extension Force ◽  
Crack Tip Shielding ◽  
Dislocation Crack

The crack-tip shielding stress intensity factor L, for the mode III crack in a work-hardening solid is equal to L = - K, where K is the applied stress intensity factor. That is, the crack tip is perfectly shielded. This result is shown two ways: from the dislocation shielding and from the dislocation crack extension force.

Mode-II Stress Intensity Factor by Triangular Williams Element with Generalized Degrees of Freedom

2012 ◽  
Vol 204-208 ◽  
pp. 4391-4395
Author(s):  
Hua Xu ◽  
Lu Feng Yang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Degrees Of Freedom ◽  
Crack Tip ◽  
High Accuracy ◽  
Mode Ii ◽  
Mode Ii Crack ◽  
Triangular Elements ◽  
Generalized Degrees Of Freedom

A new triangular Williams element with generalized degrees of freedom (GDOFs) was proposed for analysis of stress intensity factor (SIF) of mode II crack. The singular region around the crack tip was evenly divided into a series of triangular elements, which could be approximated by the improved Williams series. On the basis of the principle, the displacement of local field must be compatible with that of the global one, so that the SIF at the crack tip can be directly evaluated by one of the undetermined constants of the Williams series. Three important parameters for the triangular Williams element, including the radial scale factor, the number of subelements and the terms of the Williams series, were discussed in detail. Numerical example shows that the triangular Williams elements with GDOFs can directly calculate the mode II SIF with high accuracy and efficiency.

Effective Stress Intensity Factor in Mode III Crack Growth in Round Shafts

2003 ◽  
Author(s):  
A. Vaziri ◽  
H. Nayeb-Hashemi
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Fracture Surface ◽  
Crack Growth ◽  
Effective Stress ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Fracture Surfaces ◽  
Effective Stress Intensity Factor

Turbine-generator shafts are often subjected to a complex transient torsional loading. Such transient torques may initiate and propagate a circumferential crack in the shafts. Mode III crack growth in turbo-generator shafts often results in a fracture surface morphology resembling a factory roof. The interactions of the mutual fracture surfaces result in a pressure, and a frictional stress field between fracture surfaces when the shaft is subjected to torsion. This interaction reduces the effective Mode III stress intensity factor. The effective stress intensity factor in circumferentially cracked round shafts is evaluated for a wide range of applied torsional loadings by considering a pressure distribution in the mating fracture surfaces. The pressure between fracture surfaces results from climbing the rought surfaces respect to each other. The pressure profile not only depends on the fracture surface roughness (height and width (wavelength) of the peak and valleys), but also depends on the magnitude of the applied Mode III stress intensity factor. The results show that the asperity interactions significantly reduce the effective Mode III stress intensity factor. However, the crack surfaces interaction diminishes beyond a critical applied Mode III stress intensity factor. The critical stress intensity factor depends on the asperities height and wavelength. The results of these analyses are used to find the effective stress intensity factor in various Mode III fatigue crack growth experiments. The results show that Mode III crack growth rate is related to the effective stress intensity factor in a form of the Paris law.

The Effects of the Crack Surfaces Interaction and the Crack Tip Plasticity on the Dynamic Response of the Circumferentially Cracked Turbo Generator Shafts

2003 ◽  
Author(s):  
A. Vaziri ◽  
H. Nayeb-Hashemi ◽  
H. R. Hamidzadeh
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Dynamic Response ◽  
Energy Loss ◽  
Pressure Distribution ◽  
Crack Tip ◽  
Local Energy ◽  
Mode Iii ◽  
Turbo Generator

Turbo generator shafts are often subjected to complex dynamic torsional loadings, resulting in generation and propagation of circumferential cracks. These cracks can severely affect the vibration characteristics of the shafts. The effects of a circumferential crack, its size and location on the torsional dynamic response of a shaft is obtained, considering the local energy loss at the crack tip due to the cyclic plasticity and the crack surfaces interaction. The crack is taken to be normal to the shaft axis and the shaft is subjected to a harmonic torsional load. The shaft material is assumed to be elastic perfectly plastic. The local flexibility is calculated by evaluating the resistance of the un-cracked region of the shaft to the rotational displacement. The effective damping constant is evaluated by considering the frictional energy loss due to the crack surfaces interaction and energy loss due to the plasticity at the crack tip. The energy loss due to the crack surfaces interaction is evaluated by assuming a pressure distribution between mating fracture surfaces. The pressure distribution parameters are obtained by considering the fracture surface roughness (asperities height and width), and crack opening displacements in Modes I and III. The Energy loss due to the plasticity at the crack tip is related to the plastic zone size. The effects of the applied Mode III stress intensity factor on the energy loss due to the friction and the energy loss due to the plasticity at the crack tip are investigated. The results show that depending on the amplitude of the applied Mode III stress intensity factor, one of these energy losses may dominate the total energy loss. The results further indicate that the vibration characteristics of the shaft are significantly affected by considering these two sources of the local energy loss.

The brittle-ductile transition in silicon. II. Interpretation

1989 ◽  
Vol 421 (1860) ◽  
pp. 25-53 ◽  
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Strain Rate ◽  
Constant Strain Rate ◽  
Crack Tip ◽  
Dynamic Crack ◽  
Mode Iii ◽  
Etch Pit ◽  
Brittle Ductile Transition

A dynamic crack tip shielding model has been developed to describe the brittle-ductile transition (BDT) of precracked crystals in constant strain-rate tests. Dislocations are emitted from a discrete number of sources at or near the crack tip. At the BDT the dislocations are emitted and move sufficiently rapidly to shield the most vulnerable parts of the crack, furthest away from the sources, such that the local stress intensity factor remains below K Ic for values of the applied stress intensity factor K above K Ic . Computer simulations of the dynamics of dislocation generation from the crack tip sources, assuming mode III loading, suggest that a sharp transition as observed in silicon is predicted only if generation starts at K ≡ K 0 ≈ K Ic , but then continues at K ≡ K N ≪ K Ic . Dislocation etch pit studies reported by Samuels & Roberts ( Proc. R. Soc. Lond. A 421, 1─23 (1989)) (hereafter called I) confirm that generation begins at K 0 ≈ K Ic . It is suggested that K 0 corresponds to the value of K at which a crack tip source is nucleated by movement of an existing dislocation in the crystal to the crack tip. The model accounts quantitatively for the strain-rate dependence of the transition temperature T c reported in I, and predicts a dependence of T c on dislocation density, in qualitative agreement with (unpublished) experiments. Calcluations of the strees field around the crack tip of a semicircular precrack, suggest that the ends of the half loops emitted by crack tip sources undergo multiple cross slip to follow the crack profile. The predicted dislocation configurations agree with etch pit observations reported in I.

A new type of cracks adding to Griffith–Irwin cracks

2019 ◽  
Vol 485 (2) ◽  
pp. 162-165
Author(s):  
V. A. Babeshko ◽  
O. M. Babeshko ◽  
O. V. Evdokimova
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Tip ◽  
Stress Concentrations ◽  
New Type

The distinctions in the description of the conditions of cracking of materials are revealed. For Griffith–Irwin cracks, fracture is determined by the magnitude of the stress-intensity factor at the crack tip; in the case of the new type of cracks, fracture occurs due to an increase in the stress concentrations up to singular concentrations.

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