Mode III stress intensity factor ahead of a rough crack

1997 ◽  
Vol 45 (5) ◽  
pp. 853-872 ◽  
Author(s):  
Damien Vandembroucq ◽  
Stéphane Roux
1991 ◽  
Vol 58 (4) ◽  
pp. 1107-1108 ◽  
Author(s):  
J. Weertman

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.


Author(s):  
A. Vaziri ◽  
H. Nayeb-Hashemi

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.


Author(s):  
A. Vaziri ◽  
H. Nayeb-Hashemi ◽  
H. R. Hamidzadeh

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.


2020 ◽  
Vol 25 (10) ◽  
pp. 1896-1903
Author(s):  
Xu Wang ◽  
Ping Yang ◽  
Peter Schiavone

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.


1987 ◽  
Vol 54 (2) ◽  
pp. 379-387 ◽  
Author(s):  
P. Ponte Castan˜eda

The asymptotic stress and deformation fields of a crack propagating steadily and quasi-statically into an elastic-plastic material, characterized by J2-flow theory with linear strain-hardening, were first determined by Amazigo and Hutchinson (1977) for the cases of mode III and mode I (plane strain and plane stress). Their solutions were approximate in that they neglected the possibility of plastic reloading on the crack faces. This effect was taken into account by Ponte Castan˜eda (1987b), who also introduced a new formulation for the (eigenvalue) problem in terms of a system of first order O.D.E.’s in the angular variations of the stress and velocity components. The strength of the power-type singularity, serving as the eigenvalue, and the angular variations of the field were determined as functions of the hardening parameter. The above analysis, however, does not determine the amplitude factor of these near-tip asymptotic fields, or plastic stress intensity factor. In this work, a simple, approximate technique based on direct application of a variational statement of compatibility is developed under the assumption of small scale yielding. A trial function for the stress function of the problem, that makes use of the asymptotic information in the near-tip and far-field limits, is postulated. Such a trial function depends on arbitrary parameters that measure the intensity of the near-tip fields and other global properties of the solution. Application of the variational statement then yields optimal values for these parameters, and in particular determines the plastic stress intensity factor, thus completing the knowledge of the near-tip asymptotic fields. The results obtained by this novel method are compared to available finite element results.


2013 ◽  
Vol 135 (2) ◽  
Author(s):  
S. Suresh Kumar ◽  
Raghu V. Prakash

The fracture behavior of a crack in a threaded bolt depends on the stress intensity factor (SIF). Available SIF solutions have approximated the threaded bolt as a circular groove, thus, the SIF predominantly corresponds to the opening mode, mode-I. As a thread in a bolt has a helix angle, the crack propagates under mixed mode conditions (opening, sliding and tearing), esp. when the crack sizes are small. This paper presents the results of SIF solutions for a part-through crack emanating from a Metric threaded bolt. A 3D finite element model with preexisting flaws was generated to calculate the SIF values along the crack front. Crack aspect ratios in the range of (0.2 < (a/c) < 1) and crack depth ratios in the range of (0.1 < (a/d) < 0.5) (where “a” is crack length, “c” is semi major axis of ellipse and “d” is minor diameter of the bolt) were considered along the crack plane for the SIF estimation. The SIF values at the midregion decreases with an increase in aspect ratio (a/c), and SIF increases when the crack depth ratio (a/d) increases in the midregion. Close to the free edges, higher SIF values was observed for crack depth and aspect ratios ranging between 0.2 and 0.6 compared to midregion. In the crack surface region, up to a crack depth ratio of 0.25, significant influence of mode-II and mode-III fracture was noted for shallow cracks (a/c < 0.2). Significant influence of mode-II and mode-III fracture was observed for semicircular cracks (a/c = 1) beyond the crack depth ratio of 0.3.


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