Variation of mixed modes stress intensity factors of an inclined semi-elliptical surface crack

In this paper, a singular integral equation method is applied to calculate the stress intensity factor along crack front of a 3D inclined semi-elliptical surface crack in a semi-infinite body under tension. The stress field induced by displacement discontinuities in a semi-infinite body is used as the fundamental solution. Then, the problem is formulated as a system of integral equations with singularities of the form r ^–3. In the numerical calculation, the unknown body force doublets are approximated by the product of fundamental density functions and polynomials. The results show that the present method yields smooth variations of mixed modes stress intensity factors along the crack front accurately for various geometrical conditions. The effects of inclination angle, elliptical shape, and Poisson's ratio are considered in the analysis. Crack mouth opening displacements are shown in figures to predict the crack depth and inclination angle. When the inclination angle is 60 degree, the mode I stress intensity factor F _I has negative value in the limited region near free surface. Therefore, the actual crack surface seems to contact each other near the surface.     

Dual boundary element method for three-dimensional thermoelastic crack problems

This paper describes the formulation and numerical implementation of the three-dimensional dual boundary element method (DBEM) for the thermoelastic analysis of mixed-mode crack problems in linear elastic fracture mechanics. The DBEM incorporates two pairs of independent boundary integral equations; namely the temperature and displacement, and the flux and traction equations. In this technique, one pair is applied on one of the crack faces and the other pair on the opposite one. On non-crack boundaries, the temperature and displacement equations are applied. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stress intensity factors and crack opening displacements for slanted axial through-wall cracks in pressurized pipes

This paper proposes elastic stress intensity factors and crack opening displacements (CODs) for a slanted axial through-wall cracked cylinder under an internal pressure based on detailed three-dimensional (3D) elastic finite element (FE) analyses. The FE model and analysis procedure were validated against existing solutions for both elastic stress intensity factor and COD of an idealized axial through-wall cracked cylinder. To cover a practical range, four different values of the ratio of the mean radius of cylinder to the thickness ( R _m/ t ) were selected. Furthermore, four different values of the normalized crack length and five different values of the ratio of the crack length at the inner surface to the crack length at the outer surface representing the slant angle were selected. Based on the elastic FE results, the stress intensity factors along the crack front and CODs through the thickness at the centre of the crack were provided. These values were also tabulated for three selected points, that is, the inner and outer surfaces and at the mid-thickness. The present results can be used to evaluate the crack growth rate and leak rate of a slanted axial through-wall crack due to stress corrosion cracking and fatigue. Moreover, the present results can be used to perform a detailed leak-before-break analysis considering more realistic crack shape development.     

Eddy current probe response to open and closed surface flaws

A general theory of eddy current flaw response, appropriate to both standard low frequency and ferromagnetic resonance (FMR) probes, is developed for simple two-dimensional and three-dimensional open and closed surface flaw geometries. This analysis, based on the assumption of a uniform interrogating field applied to the flaw by the probe, shows that flaw opening responses increase with the operating frequency of the probe. Experimental results using both types of probe confirm this result for realistic practical geometries, where variations of crack mouth opening displacement under load provide useful information about crack dimensions.     

Elastic stress intensity factors and crack opening displacements for circumferential through-walled cracked elbows

This paper provides tabulated solutions of elastic stress intensity factors and crack opening displacements for circumferential through-wall cracked elbows under internal pressure and under in-plane bending, based on extensive three-dimensional elastic finite element analyses covering a wide range of crack lengths and elbow/pipe geometries. The effect of crack length and elbow/pipe geometry on the results is discussed, with particular emphasis on the crack closure behaviour under in-plane bending.     

Application of fracture mechanics for weld integrity assessment

The structural integrity assessment of a weld joint by conventional techniques is inadequate, because of unavoidable defects in the weld composite. The stress situation in a component having a defect is quite different from that of a homogeneous material. The significance of fracture mechanics to deal with such integrity assessments is brought out. A brief review on the basic formulations in the application of fracture mechanics is followed by established guidelines for evaluating the integrity of engineering components containing crack-like defects.     

SOLVING TRANSIENT DYNAMIC CRACK PROBLEMS BY THE HYPERSINGULAR BOUNDARY ELEMENT METHOD

Abstract— The subject of hypersingular boundary integral equations is a rapidly developing topic due to the advantages which this kind of formulation offers compared to the standard boundary integral method. The hypersingular formulation is particularly well suited for fracture mechanics problems, where there are important gradients of the stress field and singularities. This formulation for time domain antiplane problems has been recently addressed by the authors and in the present paper, the formulation for time domain plane problems is presented and applied for the first time. A mixed Boundary Element approach based on the standard integral equation and the hypersingular integral equation is developed. The mixed formulation allows for a very simple discretization of the problem, where no subregion is needed. Conforming quadratic elements are used for the crack and the external boundaries. The hypersingular integral equation is used for collocation points within the crack elements, while the standard integral representation is used for the external boundaries. Several examples with different crack geometries are studied to illustrate the possibilities of the method. The Stress Intensity Factor (S.I.F.) is very accurately computed from the crack tip opening displacements along the crack tip element. The results show that the proposed approach for S.I.F. evaluation is simple and produces accurate solutions.     

Stress intensity factor for an embedded elliptical crack under arbitrary normal loading

In this paper we introduce the boundary value problem of three-dimensional classical elasticity for an infinite body containing an elliptical crack. Using the method of simultaneous dual integral equations, the problem is transformed to the system of linear algebraic equations. Stress intensity factor is obtained in the form of the Fourier series expansion. Several solutions for specific cases of applied polynomial stress fields are derived and compared with existing results. Eligibility of the method for more complicated stress fields is demonstrated on the example of partially loaded elliptical crack.     

An analytical method for mixed-mode propagation of pressurized fractures in remotely compressed rocks

An analytical method for mixed-mode (mode I and mode II) propagation of pressurized fractures in remotely compressed rocks is presented in this paper. Stress intensity factors for such fractured rocks subjected to two-dimensional stress system are formulated approximately. A sequential crack tip propagation algorithm is developed in conjunction with the maximum tensile stress criterion for crack extension. For updating stress intensity factors during crack tip propagation, a dynamic fictitious fracture plane is used. Based on the displacement correlation technique, which is usually used in boundary element/finite element analyses, for computing stress intensity factors in terms of nodal displacements, further simplification in the estimation of crack opening and sliding displacements is suggested. The proposed method is verified comparing results (stress intensity factors, propagation paths and crack opening and sliding displacements) with that obtained from a boundary element based program and available in literatures. Results are found in good agreements for all the verification examples, while the proposed method requires a trivial computing time.     

Prediction of crack opening stress levels for 1045 quenched and tempered steel under service loading spectra

The opening stresses of a crack emanating from an edge notch in a 1045 quenched and tempered steel specimen were measured under two different Society of Automotive Engineers (SAE) standard service load histories having different average mean stress levels. The two spectra are the Grapple Skidder history (GSH), which has a positive average mean stress, and the Log Skidder history (LSH), which has a zero average mean stress. To capture the behaviour of the crack opening stress in the material, the crack opening stress levels were measured at 900X using an optical video microscope, at frequent intervals for each set of histories scaled to two different maximum stress ranges.A crack growth analysis based on a fracture mechanics approach was used to model the fatigue behaviour of the steel specimens for the given load spectra and stress ranges. Crack growth analysis was based on an effective strain‐based intensity factor, a crack growth rate curve obtained during closure‐free loading cycles and a local notch strain calculation based on Neuber's rule.The crack opening stress (S_op) was modelled and the model was implemented in a fatigue notch model, and the fatigue lives of the specimens under the two different spectra scaled to several maximum stress levels were estimated. The average measured crack opening stresses were between 6 and 12% of the average calculated crack opening stresses. In the interest of simplifying the use of S_op in design, the average S_op was correlated with the frequency of occurrence of the cycle reducing the S_op to the average crack opening stress level. The use of an S_op level corresponding to the cycle causing a reduction in S_op to a level reached once per 10 cycles gave a conservative estimate of average crack opening stress for all the histories.     

Study on crack propagation behavior in a quenched glass plate

Crack pattern transition and crack propagation behavior in a quenched glass plate are investigated. Theoretical analysis indicates that the distance between the crack tip and the cold front is closely related to the crack pattern transition. This theoretical result is examined experimentally using instantaneous phase-stepping photoelasticity. As expected theoretically, when the crack tip remains close enough to the cold front, crack propagation remains straight. When this distance reaches a given value, the crack oscillates. These experimental results are in good agreement with the theory of crack pattern transition. Therefore, present theoretical analysis is valid in predicting the instability of crack propagation. The crack tip stress field is also examined by the present experimental method. In particular, in the oscillating regime, the mode-I stress intensity factor frequently becomes larger than the fracture toughness, and the mode-II stress intensity factor has a nonzero value during propagation. For the former result, some reasons are discussed, but the cause of this problem is still unknown. However, the latter result can be explained by the theoretical analysis of an infinitesimal kinked edge crack just after crack initiation.     

基于弥散与分离裂缝模型的混凝土开裂比较研究

裂缝扩展是影响混凝土结构非线性响应的重要因素,其扩展深度与张开位移是评价结构安全性的重要指标。基于弥散裂缝框架,该文建立了等效裂缝张开位移与损伤因子、断裂带宽度之间的函数关系。分别采用弥散、分离两类裂缝模型模拟I型断裂和I-II混合型断裂试验,二者在结构承载力、裂缝扩展和裂缝张开位移方面均获得了基本一致的结果。数值算例表明弥散裂缝模型与分离裂缝模型计算精度接近但其效率更高。     

在反平面变形下功能梯度压电板条的应力强度因子分析

利用Fourier变换技术将混合边值问题化为对偶积分方程,求解对偶积分方程得到应力强度因子以及电位移强度因子的表达式。最后通过数值计算讨论了材料参数、载荷条件以及裂纹的几何参数等对功能梯度压电材料中裂纹尖端应力强度因子的影响。     

含裂纹损伤结构强度的多源数据融合方法研究

海洋结构在服役期间,不可避免地受到复杂的环境载荷和操作载荷的作用。对于金属材料的海洋结构,断裂是其失效的主要形式,所以,及时、准确地监测裂纹的萌生和扩展是很有必要的。而应力强度因子(SIF)是判断裂纹失稳扩展的一个重要指标。该文在现有研究的基础上,将基于单应变片(SSG)和最大张口位移(CMOD)的SIF的确定方法相结合,提出了一种基于数据融合的SIF的估计方法。对该方法进行了数值模拟和实验验证,结果表明,该方法适用于多种配置的裂纹试件,且与基于单应变片和最大张口位移的方法相比,所提方法可以获得更精确的结果,相对误差(RE)不超过1.2%。     

A direct method for calculating the stress intensity factor in BEM

The proposed algorithm employs singular crack tip elements in which the stress intensity factor appears as a degree of freedom. The additional degrees of freedom are compensated by constraint conditions which originate from imposing continuity across elements and a contour integration formula. The two benchmark problems indicate the proposed algorithm can accurately predict the stress intensity factor and the distribution of the primary and secondary variables in fracture problems.