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.

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-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.

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.

scholarly journals Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Bing Yang ◽  
Zhanjiang Wei ◽  
Zhen Liao ◽  
Shuwei Zhou ◽  
Shoune Xiao ◽  
...  
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Plastic Zone ◽  
Relative Error ◽  
Crack Tip ◽  
Image Correlation ◽  
Preconditioned Conjugate Gradient ◽  
Loading Process ◽  
Tip Position

AbstractIn the digital image correlation research of fatigue crack growth rate, the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor, thereby affecting the life prediction. This paper proposes a Gauss-Newton iteration method for solving the crack tip position. The conventional linear fitting method provides an iterative initial solution for this method, and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix. A noise-added artificial displacement field is used to verify the feasibility of the method, which shows that all parameters can be solved with satisfactory results. The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result, and the relative error between the two is only − 0.621%; The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip, and the maximum relative error with the test plastic zone area is − 11.29%. The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05%. The crack tip coordinates, stress intensity factors, and plastic zone contour changes in the loading and unloading phases are explored. The results show that the crack tip change during the loading process is faster than the change during the unloading process; the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process; under the same load, the theoretical plastic zone during the unloading process is higher than that during the loading process.

scholarly journals Critical value of the generalized stress intensity factor for a crack perpendicular to an interface

2015 ◽  
Vol 471 (2183) ◽  
pp. 20150571 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Crack Tip ◽  
Critical Value ◽  
Zone Model ◽  
Cohesive Stress ◽  
Generalized Stress Intensity Factor

When a crack tip impinges upon a bi-material interface, the order of the stress singularity will be equal to, less than or greater than one-half. The generalized stress intensity factors have already been determined for some such configurations, including when a finite-length crack is perpendicular to the interface. However, for these non-square-root singular stresses, the determination of the conditions for crack growth are not well established. In this investigation, the critical value of the generalized stress intensity factor for tensile loading is related to the work of adhesion by using a cohesive zone model in an asymptotic analysis of the separation near the crack tip. It is found that the critical value of the generalized stress intensity factor depends upon the maximum stress of the cohesive zone model, as well as on the Dundurs parameters ( α and β ). As expected this dependence on the cohesive stress vanishes as the material contrast is reduced, in which case the order of the singularity approaches one-half.

Plastic Stress Intensity Factors for Small Scale Yielding in Antiplane Shear by Caustics

1982 ◽  
Vol 49 (4) ◽  
pp. 754-760 ◽  
Author(s):  
P. S. Theocaris ◽  
C. I. Razem
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Tip ◽  
Antiplane Shear ◽  
Elastic Behavior ◽  
Small Scale ◽  
Small Scale Yielding ◽  
Scale Yielding ◽  
Plastic Stress

The KIII-stress intensity factor in an edge-cracked plate submitted to antiplane shear may be evaluated by the reflected caustic created around the crack tip, provided that a purely elastic behavior exists at the crack tip [1]. For a work-hardening, elastic-plastic material, when stresses at the vicinity of the crack tip exceed the yield limit of the material, the new shape of caustic differs substantially from the corresponding shape of the elastic solution. In this paper the shape and size of the caustics created at the tip of the crack, when small-scale yielding is established in the vicinity of the crack tip, were studied, based on a closed-form solution introduced by Rice [2]. The plastic stress intensity factor may be evaluated from the dimensions of the plastic caustic. Experimental evidence with cracked plates made of opaque materials, like steel, corroborated the results of the theory.

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