Interaction of a screw dislocation with a parabolic cavity and a semi-infinite crack

2020 ◽  
Vol 25 (10) ◽  
pp. 1896-1903
Author(s):  
Xu Wang ◽  
Ping Yang ◽  
Peter Schiavone
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Screw Dislocation ◽  
Analytic Solution ◽  
Image Force ◽  
Method Of Images ◽  
Mode Iii ◽  
Sharp Crack ◽  
Mapping Techniques

We derive an analytic solution to the problem of a screw dislocation interacting with a parabolic cavity and a semi-infinite sharp crack using conformal mapping techniques and the method of images. Closed-form expressions for the image force acting on the screw dislocation, the mode III stress intensity factor at the crack tip and the generalized mode III stress intensity factor for the parabolic cavity are obtained. The correctness of the solution is validated by comparison with existing solutions in the literature.

The Dynamic Stress Intensity Factor Due to Arbitrary Screw Dislocation Motion

1983 ◽  
Vol 50 (2) ◽  
pp. 383-389 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Plane Wave ◽  
Screw Dislocation ◽  
Dynamic Stress ◽  
Critical Level ◽  
Dynamic Stress Intensity Factor ◽  
Dislocation Motion ◽  
Crack Edge

The dynamic stress intensity factor for a stationary semi-infinite crack due to the motion of a screw dislocation is obtained analytically. The dislocation position, orientation, and speed are largely arbitrary. However, a dislocation traveling toward the crack surface is assumed to arrest upon arrival. It is found that discontinuities in speed and a nonsmooth path may cause discontinuities in the intensity factor and that dislocation arrest at any point causes the intensity factor to instantaneously assume a static value. Morever, explicit dependence on speed and orientation vanish when the dislocation moves directly toward or away from the crack edge. The results are applied to antiplane shear wave diffraction at the crack edge. For an incident step-stress plane wave, a stationary dislocation near the crack tip can either accelerate or delay attainment of a critical level of stress intensity, depending on the relative orientation of the crack, the dislocation, and the plane wave. However, if the incident wave also triggers dislocation motion, then the delaying effect is diminished and the acceleration is accentuated.

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.

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.

scholarly journals The Application of Fracture Mechanics to the Problem of Crevasse Penetration

1976 ◽  
Vol 17 (76) ◽  
pp. 223-228 ◽  
Author(s):  
R. A. Smith
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Fracture Mechanics ◽  
Intensity Factor ◽  
Stress Intensity Factors ◽  
Close Agreement ◽  
Elastic Stress ◽  
Intensity Factors ◽  
Wide Range ◽  
Sharp Crack

AbstractThe elastic stress intensity factor is a parameter used in fracture mechanics to describe stress conditions in the vicinity of the tip of a sharp crack. By superimposing solutions of stress intensity factors for different loading conditions, equations are derived which model crevasses in ice. Solutions are presented for the theoretical depth of isolated crevasses, free from or partially filled with water. Close agreement exists with a previous calculation by Weertman using a different technique. The effect of crevasse spacing is investigated and it is demonstrated that closer spacing always reduces crevasse depth, but over a wide range of spacing the predicted variation in depth is slight.

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