Z.X. Wang

A semi-analytic solution for multiple curved cracks emanating from circular hole using singular integral equation

This paper provides an elastic solution for an infinite plate containing multiple curved edge cracks emanating from a circular hole. A fundamental solution is suggested, which represents a particular solution for a concentrated dislocation in an infinite plate with the traction free hole. The generalized image method and the concept of the modified complex potentials are used in the derivation of the fundamental solution. After using the fundamental solution and placing the distributed dislocations at the prospective sites of cracks, a singular integral equation is formulated. The singular integral equation is solved by using the curve length method in conjunction with the semi-opening quadrature rule. By taking an additional point dislocation at the hole center, the number of the unknowns is equal to the number of the resulting algebraic equations. This is a particular advantage of the suggested method. Finally, several numerical examples are given to illustrate the efficiency of the method presented. Numerical examinations are carried out and sufficient accurate results have been found.

EFFECT OF MECHANICAL PROPERTY MISMATCH ON FAILURE ASSESSMENT CURVE FOR WELDED JOINT WITH A SEMI-ELLIPTICAL CRACK

Elastic–plastic finite element analysis was performed to study the welded joints with a semi-elliptical crack. This research includes the effects of crack depth, strength mismatch ratio, and weld width on the crack driving force J-integral and the constraint parameter A2 at the crack tip. A two-parameter J-A2 fracture criterion based on the present results of crack tip stress field in the welded joints was established. The corresponding failure assessment diagrams were investigated in detail, from which the reliability and safety margin of the welded structures were discussed.

Analysis and Simulation of Elastic-Plastic Fracture Parameters at Crack Tip under Biaxial Loading and Uniaxial Loading

Based on the J-A2 two-parameter elastic-plastic fracture theory and finite element numerical method, the elastic-plastic stress field ahead of the crack tip in a single edge cracked eccentric tensile specimen (the load-line is at a finite distance from the crack tip) was analyzed and compared with that of a center cracked large plate under biaxial loading. By using the Ritchie-Knott-Rice fracture criterion, a transformational relation between the two loading modes was obtained based on the J-A2 equivalent principle. As a result, the fracture parameter determined from a single edge cracked eccentric tensile specimen can be applied to the fracture analysis of a center cracked plate under biaxial stress.

Elastic-Plastic Fracture Assessment for the Cracks Emanating from a Circular Hole under a Biaxial Loading Condition

In this study, elastic-plastic stress and strain fields were analyzed on hole-edge cracks in an aluminum alloy plate under the biaxial load. And the effects of the load parallel to the crack face on failure parameters were discussed. By quantifying the effects of the crack size and the loading mode on the crack propagation driving force, J integral, and the plastic limit load, the corresponding failure assessment curves of the hole-edge cracked plate were established with the new R6 failure assessment diagram (FAD) method. The result shows that the transverse load has a larger effect on the failure assessment curve than crack length does, the safety zone of the failure assessment diagram gradually becomes smaller while transverse loading stress changes from tensile condition to compressed. Especially, when the transverse load acts as pressure, the Option 3 failure assessment diagram results to a smaller safety zone than the Option 1 failure assessment diagram does.

Singular integral equation method for contact problem for rigidly connected punches on elastic half-plane

In the contact problem of a rigid flat-ended punch on an elastic half-plane, the contact stress under punch is studied. The angle distribution for the stress components in the elastic medium under punch is achieved in an explicit form. From obtained singular stress distribution, the punch singular stress factor (abbreviated as PSSF) is defined. A fundamental solution for the multiple flat punch problems on the elastic half-plane is investigated where the punches are disconnected and the forces applied on the punches are arbitrary. The singular integral equation method is suggested to obtain the fundamental solution. Further, the contact problem for rigidly connected punches on an elastic half-plane is considered. The solution for this problem can be considered as a superposition of many particular fundamental solutions. The resultant forces on punches are the undetermined unknowns in the problem, which can be evaluated by the condition of relative descent between punches. Finally, the resultant forces on punches can be determined, and the PSSFs at the corner points can be evaluated. Numerical examples are given.

SINGULAR STRESS ANALYSIS IN FLAT PUNCH PROBLEM OF ELASTIC HALF-PLANE

Singular stress analysis in the flat punch problem of half-plane is carried out. The angle distribution for the stress components is also achieved in an explicit form. Followed a similar study in the punch analysis, the punch singular stress factor (abbreviated as PSSF) is defined from the singular stress distribution. For the problems of two punches or three punches, solutions in a closed form are obtained. The obtained solutions may depend on some complete elliptical integrals. Meantime, the exerting location of the resultant force for punches is also determined. Interactions between punches are also addressed. Several numerical examples with the calculated results are presented.

J-Integral and Plastic Limit Load of Hole-Edge Crack in Plate under Biaxial Loadings

Elastic-plastic J-integral and plastic limit load were described by finite element (FE) analysis for single hole-edge crack in plate under far field biaxial load. In this paper, the effect of biaxial load ratio (from -1 to 1) on elastic-plastic J-integral and plastic limit load was studied, the values of coefficient h1 for J-integral engineering estimation formulas were given and the effect of material hardening on plastic limit load was discussed. The result obtained from this work provides reference for fracture evaluation, so it can be used in engineering accurately and expediently.

Creep Analysis and Constraint Effect in a Center-Cracked Plate Under Biaxial Loading

Typical pressure vessels are subject to biaxial loading. Creep analysis was conducted with two-dimensional finite element method for a center-cracked plate under a range of biaxial loading ratios (λ = −1, 0, and 0.5). The effects of crack size and the biaxial loading ratio on the crack tip field are reported. In addition, based on a two-parameter fracture theory, C(t)−A2(t), where C is a contour integral and is path-independent when the steady state creep is reached (denoted by C*), and A2 is a time dependent crack tip constraint parameter. The crack tip stress field calculated from the C(t)−A2(t) theory is shown to be more accurate than the Hutchinson–Rice–Rosengren (HRR) singularity solution, especially in the case of λ = 0.5. The loading level appears to have little effects on the constraint parameter A2(t). As creep time increases, the creep zone (based on the equivalent creep strain) increases rapidly but the yield zone (with respect to a reference stress) decreases. Meanwhile, the crack tip constraint is increasing with creep time, particularly for the small cracks. It was also found that the normalized relationship between the contour integral C(t)/C* and the creep time t/tT (where tT is the characteristic time for transition from small-scale creep to extensive creep) is insensitive to the biaxial loading. Therefore, the relationship previously provided for uniaxial loading can be used for biaxial loading.Copyright

Elastic-Plastic Stress and Strain Analysis of a Hole-Edge Crack under Biaxial Load

In this study, the effects of biaxial load on the elastic-plastic stress concentration factor and the plastic zone size of the circular hole are investigated, and the elastic-plastic stress and strain fields of the crack emanating from the circular hole are calculated in the process of crack growth. The elastic-plastic stress concentration factors for various biaxial load ratios are obtained. In order to provide a reference for structural damage monitoring, the variation characteristic of strain at crack front ligament are analyzed in the process of the crack growth.

Reliability Assessment on Pipeline with Axial Surface Crack

Stress constraints have a significant impact on the stress-strain fields of the crack front. In this paper, the weight function method is used to calculate the stress intensity factor K and constraint parameter T-stress at the crack front of pressure pipeline with a axial semi-elliptical surface crack. Based on the R6 procedure and considering the influence of stress constraint on fracture toughness, a modified failure assessment curve(FAC) and a computational formula are proposed to predict the fracture probability. In the end, a typical numerical example is presented to illustrate the proposed methodology and analyze the influences of crack geometry and axial stress on the failure probability of pipeline,where the crack size, material property parameter and load follow certain probability distribution.