A First-Order Perturbation Analysis of Crack Trapping by Arrays of Obstacles

1989 ◽  
Vol 56 (4) ◽  
pp. 828-836 ◽  
Author(s):  
Huajian Gao ◽  
James R. Rice
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Perturbation Analysis ◽  
Crack Front ◽  
Limit Load ◽  
Linear Perturbation ◽  
First Order ◽  
Crack Trapping ◽  
First Order Perturbation

A first-order perturbation analysis is presented for the configuration of an initially straight crack front which is trapped against forward advance by contact with an array of obstacles (i.e., regions of higher fracture toughness than their surroundings). The problem is important to the micromechanics of crack advance in brittle, locally heterogeneous solids. The formulation is based on a linear perturbation result for the stress intensity factor distribution along the front of a half-plane crack when the location of that front differs moderately from a straight line. The trapping solutions for a periodic array of blocking rectangular obstacles are given using an analogy to the plane stress Dugdale/BCS elastic-plastic crack model. For a periodic array of obstacles with a given spacing and size in the direction parallel to the crack front, the obstacle shape may affect the limit load at which the crack breaks through the array. When such effects are examined within the range of validity of the linear perturbation theory, it is found that obstacles whose cross-sections fully envelop a critical reference area give the maximum limit load while others are broken through at lower load levels. We also formulate a numerical procedure using the FFT technique and adopting a “viscoplastic” crack growth model which, in an appropriate limit, simulates crack growth at a critical stress intensity factor. This is applied to show how a crack front begins to surround and penetrate into various arrays of round obstacles (with a toughness ratio of 2) as the applied load is gradually increased. The limitations of the first-order analysis restrict its validity to obstacles only slightly tougher than the surrounding elastic medium. Recently, Fares (1988) analyzed the crack trapping problem by a Boundary Element Method (BEM) with results indicating that the first-order linear analysis is acceptable when the fracture of toughness of the obstacles differs by a moderate amount from that of their surroundings (e.g., the toughness ratio can be as large as 2 for circular obstacles spaced by 2 diameters). However, the first-order theory is not only quantitatively inaccurate, but can make qualitatively wrong predictions when applied to very tough obstacles.

Study on the Relationship Between Interaction Factors and Stress Intensity Factor for Elliptical Flaws

2017 ◽  
Author(s):  
Kisaburo Azuma ◽  
Yinsheng Li ◽  
Kunio Hasegawa
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Front ◽  
Elastic Solid ◽  
Element Analysis ◽  
Linear Elastic ◽  
Close Proximity ◽  
Interaction Factors ◽  
The Relationship

The interaction of multiple flaws in close proximity to one another may increase the stress intensity factor of the flaw in structures and components. This interaction effect is not distributed uniformly along the crack front. For instance, the strongest interaction is generally observed at the point closest to a neighboring flaw. For this reason, the closest point could show a higher value of the stress intensity factor than all other points in some cases, even if the original value at the point of the single flaw is relatively low. To clarify the condition when the closest point shows the maximum stress intensity factor, we investigated the interaction of two similar elliptical flaws in an infinite model subjected to remote tension loading. The stress intensity factor of the elliptical flaws was obtained by performing finite element analysis of a linear elastic solid. The results indicated that the interaction factors along the crack front can be expressed by a simple empirical formula. Finally, we show the relationship between geometrical features of the flaw and the stress intensity factor at the closest point to a neighboring flaw.

3-D Elastic Analysis of a Circular Nozzle Corner Crack

1986 ◽  
Vol 108 (4) ◽  
pp. 474-478 ◽  
Author(s):  
W. W. Wilkening
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Front ◽  
Pressure Vessel ◽  
Circular Crack ◽  
Elastic Analysis ◽  
Corner Crack ◽  
Linear Elastic ◽  
Circular Nozzle

A 3-D linear elastic analysis has been performed for a circular crack located in the nozzle corner region of a nuclear pressure vessel. The stress intensity factor, K, was found to be virtually constant along the crack front for this particular nozzle corner flaw, which extends one quarter of the distance through the nozzle corner diagonal. The magnitude of K is discussed in relation to the stress intensity factor for the ASME Maximum Postulated Flaw, and is compared to the results of a number of other analyses reported in the literature.

Effects of Local Wall Thinning With Crack on Stress Intensity Factor for Pipes Subject to Combined Pressure and Bending

2019 ◽  
Author(s):  
Joy (Xiaoya) Tao ◽  
Lei Zhu
Keyword(s):  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Nuclear Power ◽  
Power Plants ◽  
Limit Load ◽  
Minimum Thickness ◽  
Element Analysis ◽  
Accelerated Corrosion

Abstract At ageing power plants, local thinning of pipework or vessel is unavoidable due to erosion/corrosion or other reasons such as flow accelerated corrosion (FAC) — one of the common degradation mechanisms in pipework of nuclear power plant. Local thinning reduces the structure strength, resulting in crack initiation from the corrosion pit or welding defect when subject to cyclic loading. General practice is to use the minimum thickness of the thinned area to calculate both limit load and stress intensity factor (SIF) in performing Engineering Critical Assessment (ECA) using Failure Assessment Diagram (FAD). Using the minimum thickness is normally overly conservative as it assumes that thinning occurs grossly instead of locally, leading to unnecessary early repair/replacement and cost. Performing cracked body finite element analysis (FEA) can provide accurate values of limit load and SIF, but it is time consuming and impractical for daily maintenance and emergent support. To minimise the conservatisms and provide a guidance for the assessment of locally thinned pipework or vessel using existing handbook solutions, a study was carried out by the authors on the effect of local thinning on limit loads. The study demonstrates that local thinning has significant effect on limit load if the thinning ratio of thinning depth to original thickness is larger than 25%. It concluded that the limit load solutions given in handbooks (such as R6 or the net section method) are overly conservative if using the minimum local thickness and non-conservative if using the nominal thickness. This paper discusses the effect of local thinning on SIFs of internal/external defects using cracked body finite element method (FEM). The results are compared with R6 weight function SIF solutions for a cylinder. A modified R6 SIF solution is proposed to count for the effect of local thinning profile. Along with the previous published paper on limit load it provides comprehensive understanding and guidance for fracture assessment of the local thinned pipework and vessel.

Structure of Near-Tip Stress Field and Variation of Stress Intensity Factor for a Crack in a Transversely Graded Material

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
Sarveshwar C. Wadgaonkar ◽  
Venkitanarayanan Parameswaran
Keyword(s):  
Stress Intensity Factor ◽  
Elastic Modulus ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Elastic Properties ◽  
Crack Front ◽  
Homogeneous Material ◽  
Graded Materials ◽  
Crack Problems

The existing studies on the behavior of cracks in continuously graded materials assume the elastic properties to vary in the plane of the crack. In the case of a plate graded along the thickness and having a crack in its plane, the elastic properties will vary along the crack front. The present study aims at investigating the effect of elastic gradients along the crack front on the structure of the near-tip stress fields in such transversely graded materials. The first four terms in the expansion of the stress field are obtained by the eigenfunction expansion approach (Hartranft and Sih, 1969, “The Use of Eigen Function Expansion in the General Solution of Three Dimensional Crack Problems,” J. Math. Mech., 19(2), pp. 123–138) assuming an exponential variation of the elastic modulus. The results of this part of the study indicated that for an opening mode crack, the angular structure of the first three terms in the stress field expansion corresponding to r(−1∕2), r0, and r1∕2 are identical to that given by Williams’s solution for homogeneous material (Williams, 1957, “On the Stress Distribution at the Base of a Stationary Crack,” ASME J. Appl. Mech., 24, pp. 109–114). Transversely graded plates having exponential gradation of elastic modulus were prepared, and the stress intensity factor (SIF) on the compliant and stiffer face of the material was determined using strain gauges for an edge crack subjected to pure bending. The experimental results indicated that the SIF can vary as much as two times across the thickness for the gradation and loading considered in this study.

Stress Intensity Factor of an Elliptical Crack With a Wavy Crack Front

2016 ◽  
Author(s):  
Masayuki Arai
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Front ◽  
Perturbation Technique ◽  
Three Dimensional ◽  
Elastic Field ◽  
Element Analysis ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

In this paper, the stress intensity factor KI for the crack front line a − ε(1 + cosmθ), which is slightly perturbed from a complete circular line with a radius of a, is determined. The method used in this study is based upon the perturbation technique developed by Rice for solving the elastic field of a crack whose front slightly deviates from some reference geometry. It is finally shown that the solution for the stress intensity factor matches the results of a three-dimensional finite element analysis.

Influence of Crack Front Shape on 3D Numerical Modelling of Plasticity-Induced Closure of Short and Long Fatigue Cracks

2013 ◽  
Vol 577-578 ◽  
pp. 213-216
Author(s):  
S. Fiordalisi ◽  
C. Gardin ◽  
C. Sarrazin-Baudoux ◽  
M. Arzaghi ◽  
Jean Petit
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Numerical Modelling ◽  
Crack Front ◽  
Stress Intensity Factor Range ◽  
Finite Element Software ◽  
Curved Crack ◽  
3D Numerical Modelling ◽  
Front Shape

The simultaneous effect of crack length and crack front shape on plasticity-induced crack closure (PICC) for a 304L austenitic stainless steel is simulated through 3D numerical modelling using finite element software Abaqus for through-thickness cracks with different curved crack fronts in CT specimens in comparison with bidimensional through crack with a straight front. The influence of possible loading history effect is avoided by applying constant K amplitude. The local stress intensity factor range for crack opening Kopis evaluated from the simulation of the loss of the last local contact between the crack lips near the crack tip. The pertinence of the different crack front shapes is discussed in term of the effective stress intensity factor range Keffand in comparison with the experimental crack front observations.

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