Stress intensity factors for large aspect ratio surface and corner cracks at a semi-circular notch in a tension specimen

Stress intensity factor solutions for semi-elliptic surface and quarter-elliptic corner cracks emanating from a semi-circular notch in a tension specimen are presented. A threedimensional finite-element analysis in conjunction with the equivalent domain integral was used to calculate stress intensity factors (SIF). SIF solutions for surface or corner crack (crack length to depth ratio of 2) at a notch are presented for a wide range of crack sizes and notch radii. Results showed that the SIF are larger for larger crack lengths and for larger notch radii. The SIF are nearly constant all along the crack front for deep surface cracks and for all corner cracks analysed.     

Stress intensity factors for penny and half-penny shaped cracks subjected to a stress gradient

Stress intensity factors at any point on the crack front of penny and half-penny shaped cracks subjected to stress gradients are presented. The SIF's which are exact for a penny shaped crack are based on the well known solution for a point load acting normally to such a crack. The line load solution which is derived from this is different in form to those given by previous workers and is more readily integrated to give SIF's for stress gradient loading. This is demonstrated by the derivation of a general equation for the SIF at any point on a penny-shaped crack due to polynomial stress gradients. These results are extended to produce a similarly general, albeit approximate, equation for the SIF at any point on the circumference of a half-penny crack due to polynomial loading. The usefulness of the approach developed here is further indicated by the derivation of an approximate SIF for exponential stress gradients over a half-penny crack.     

Stress intensity factors for cracks emanating from two-dimensional semicircular notches using the composition of SIF weight functions

This paper presents stress intensity factor (SIF) solutions for edge cracks emanating from semicircular notches using the composition of SIF weight functions. The method isolates and combines the geometrical influences defined by constitutive SIF weight functions to yield SIFs for semicircular notches in finite thickness bodies. Finite element analysis was employed to obtain the required stress distributions and to generate reference constitutive SIFs. Problems encountered with curve fitting high gradient stress distributions were addressed and a robust mathematical solution for these was formulated. The new SIF solutions were verified by comparison with published solutions showing a high degree of accuracy and reliability. The composition model was demonstrated to allow rapid generation of SIFs for mode I cracks in complex geometries where the relevant simple constitutive solutions are available. These new solutions expressed as SIF weight functions allow interpolation between the geometrical parameters for which they are valid and also to include the effect of complex stress distributions such as those due to residual stresses.     

Investigation of the stress intensity factor changing on the hole crack subject to laser shock processing

Laser shock processing (LSP) is a new surface modification technology. The effect of the compressive residual stresses generated due to laser shock processing (LSP) on the stress intensity factor (SIF) of a through-the-thickness radial crack at the edge of the circular hole was investigated. The residual stresses around the hole induced by LSP were measured by using X-ray method. The relationship between the SIF and the residual stress was determined on the basis of the weight function theory in fracture mechanics. Crack propagation characteristics for such cracks subjected to the combination of the applied stress and residual stress were discussed. And the results showed that the compressive residual stress could lead to the decrement of the SIF. Moreover, the number of the laser shocks had an important influence on the SIF.     

Weld magnification factors for semi-elliptical surface cracks in fillet welded T-butt joint models

The weld magnification factor method has been widely used in the determination of the stress intensity factor (SIF) for weld-toe cracks in welded structural components. Weld magnification factors M _kare normally derived from two-dimensional crack models with fillet weld profiles to take account of the effect of weld-notch stress concentration at the deepest point of the crack front. This paper presents a detailed three-dimensional analysis of weld-toe surface cracks in fillet welded T-butt joint models using the finite element method. Effects of the weld notch and the welded attachment stiffness on the SIFs of the weld-toe surface cracks have been studied quantitatively. Weld magnification factors applying to the whole surface crack fronts have been estimated. Numerical results show two contradictory effects; that the effect of weld notch increases SIF values throughout the shallow surface crack fronts which are in the region of notch stress concentration, while the effect of local structural constraint reduces the SIF values. The increase in the SIF values mainly depends upon the relative crack front depth and the decrease in the SIF values mainly depends upon the crack shape aspect ratio for a specific weld profile. Both effects on the weld magnification factors can be estimated separately. A simple approach for deriving the weld magnification factors for various weld-toe surface crack problems is proposed for engineering applications.     

Stress intensity factors of semi-elliptical surface cracks in pressure vessels by global-local finite element methodology

In the present study the problem of calculation of the stress intensity factors (SIF) of semi-elliptical cracks located in the stress concentration areas of a pressure vessel is numerically solved by advanced global-local finite element (FE) analysis. The common characteristic of the cases solved is that the stress field at the crack area varies along the axial, the circumferential, as well as, the through-the-thickness directions. SIF solutions for such problems are not available, neither analytically, nor numerically, as the currently existing solutions in the literature (numerical results, Newman-Raju empirical equations, weight function solutions, etc.) are only valid for uniform stress distribution along the axial and circumferential directions of the pressure vessel and allow variation only through-the-thickness. The crack locations considered are the intersection of the cylinder to a nozzle and the connection of the cylinder with its hemi-spherical ends. The stress intensity factors are presented in a suitable table format for various geometrical configurations of both the pressure vessel and the semi-elliptical crack, thus providing a useful tool for the fracture mechanics design of cracked pressure vessels. The modeling details of the sub-structuring methodology, employed in the analysis, are extensively discussed and the numerical approach is proven to be very efficient for the SIF calculation of pressure vessel semi-elliptical cracks.     

Determination of crack-tip stress intensity factors in complex geometries by the composition of constituent weight function solutions

Linear elastic fracture mechanics (LEFM) is the science frequently used to understand the stable and progressive fatigue crack growth that often occurs in engineering components under varying applied stress. The stress intensity factor (SIF) is its basis and describes the stress state at the crack tip. This can be used with the appropriate material properties to calculate the rate at which the crack will propagate in a linear elastic manner. Unfortunately, the SIF is difficult to compute or measure, particularly if the crack is situated in a complex three‐dimensional geometry or subjected to a non‐simple stress state. This is because the SIF is not only a function of the crack and component geometry but is also dependent on the applied stress field. In the last 20 years, the SIF weight function has gained prominence as a method for calculating and presenting SIFs independent of applied stress. This paper demonstrates that the real promise of the SIF weight Function lies in its use to rapidly generate SIF solutions for cracks in complex geometries by simple composition of geometric influences from reference constituent solutions.     

Application of the weight function method to solving multiparametric three-dimensional fracture mechanics problems

A system of equations of the weight function method is obtained for the calculation of the stress intensity factors (SIF) along the crack front under arbitrary normal loading, as well as the crack opening displacement field (CODF) for cracks of arbitrary shape. The equations, in particular, make it possible to estimate the error of the known empirical formulas for the SIF, as well as to calculate the variation of the SIF values with the crack shape. It is shown that the SIF values for the problems with the mixed boundary conditions can be calculated making use of the weight functions obtained for the problems with the boundary conditions in stresses.     

Determination of stress intensity factor for embedded elliptical crack in turbine rotor

The stress intensity factor (SIF) for an embedded elliptical crack in a turbine rotor and the thermal shock stress intensity factor for a semi-elliptical surface crack in a finite plate are determined by means of Vainshtok's weight function method. The solution for the semi-elliptical surface crack is in good agreement with the previous one. The value of the SIF for the embedded elliptical crack in the turbine rotor under centrifugal and thermal loading is larger at the crack contour near the inner radius surface and almost constant at the opposite crack contour. The SIF decreases by increasing the crack ratio, and the distance between the inner radius surface and the crack center.     

Stress intensity factor analysis for part-elliptical cracks in structures

A method based on the generalized weight function theory is used for solving three-dimensional linear elastic fracture mechanics problems. A complete system of equations of the weight function method (WFM) has been obtained for the calculation of stress intensity factors (SIF) for part-elliptical cracks subjected to arbitrary normal loading.A procedure of the WFM is described to analyze structural components containing surface (semi-elliptical), corner (quarter-elliptical) and embedded (elliptical) flaws. The efficiency of the proposed method is illustrated by solving a number of methodical problems     

Estimation of three‐dimensional stress intensity factor for structural ‘T’ details

Three‐dimensional (3D) opening mode stress intensity factors (SIFs) for structural steel‐welded ‘T’ details were investigated by the finite element method. A 3D shape‐dependent correction factor is proposed for semi‐elliptical surface cracks. The aspect ratio (a/c) of a semi‐elliptical crack plays a key role in the approximation of 3D‐SIF values, and in the present study, it was estimated for a 3D crack analysis. The estimated 3D‐SIF was determined through a correlation between the a/c ratio and the two‐dimensional SIF for semi‐elliptical cracks in the thickness direction adjacent to the web‐flange junction of a welded ‘T’. The resulting equation can be used to estimate the 3D‐SIF values from the two‐dimensional SIF without much ambiguity.     

A weight function method for mixed modes hole‐edge cracks

A weight function approach is proposed to calculate the stress intensity factor and crack opening displacement for cracks emanating from a circular hole in an infinite sheet subjected to mixed modes load. The weight function for a pure mode II hole‐edge crack is given in this paper. The stress intensity factors for a mixed modes hole‐edge crack are obtained by using the present mode II weight function and existing mode I Green (weight) function for a hole‐edge crack. Without complex derivation, the weight functions for a single hole‐edge crack and a centre crack in infinite sheets are used to study 2 unequal‐length hole‐edge cracks. The stress intensity factor and crack opening displacement obtained from the present weight function method are compared well with available results from literature and finite element analysis. Compared with the alternative methods, the present weight function approach is simple, accurate, efficient, and versatile in calculating the stress intensity factor and crack opening displacement.     

Mixed Mode Stress Intensity Factor Determination of Multiple Cracks in Hollow Circular Pipe

Failure of pressure vessels and piping due to high temperature applications occurs due to the formation of fatigue cracks caused by cyclic load. It is well known that, the consequences of collapses of pipes causing enormous disruption of daily life. Thus there is a need to design and manufacture the pipes with precision and care. The major cause of crack nucleation in pipes is due to corrosion and internal fluid pressure. The crack-tip stresses are determined using stress intensity factor (SIF). In the present work an attempt has been made to determine the SIF for multiple cracks in a circular pipe subjected to internal fluid pressure. Two surface cracks of same size were introduced at the inner wall of the tube. The crack depth ratio (a/t) ranging between 0.1 and 0.5 and crack aspect ratio (a/c) of 0.6 and 1.0 was considered. Internal fluid pressure of 100 MPa was applied at the inner surface of the pipe and the corresponding SIF was measured. SIF values were calculated with consideration of mode-II and mode-III fracture in order to predict the exact SIF. As available SIF solutions of cracked pipes are limited to mode-I fracture, present work presents the influence of additional influence of mode-II and mode-III fracture. It is observed that, as crack depth ratio increases, SIF also increases considerably for semi-circular cracks. Higher SIF values were observed at the crack surface region [S/S ₀ = ±1] compared to crack middle [S/S ₀ = 0] region. A crossover in SIF was noted at a crack depth ratio of 0.3. At higher crack depths, SIF values decrease at the crack surface region due to additional influence of mode-II and mode-III fracture. In contrast to semi-circular cracks, SIF values are higher at the crack surface region for semi-elliptic cracks irrespective of the crack depths.     

A new weight function approach using indirect boundary integral method

A new weight function approach to determine SIF (stress intensity factor) using the indirect boundary integral method has been presented. The crack opening displacement field was represented by one boundary integral in the form of a single-layer potential whose kernel was modified from the fundamental solution. The proposed method enables the calculation of SIF using only one SIF formula without any modification of the crack geometries symmetric in a two-dimensional plane, e.g. a center crack in a plate with or without an internal hole, double edge cracks, circumferential crack or radial cracks in a pipe. The application procedure for this variety of crack geometries is very simple and straghtforward with only one SIF formula. The necessary information in the analysis is two reference SIFs. The analysis results, using several examples, verified that the present closed-form solution was in good agreement with those of the literature and applicable to various crack geometries.     

裂纹面荷载作用下多裂纹应力强度因子计算

该文基于比例边界有限元法计算了裂纹面荷载作用下平面多裂纹应力强度因子.比例边界有限元法可以给出裂纹尖端位移场和应力场的解析表达式,该特点可以使应力强度因子根据定义直接计算,同时不需要对裂纹尖端进行特殊处理.联合子结构技术可以计算多裂纹问题的应力强度因子.数值算例表明该文方法是有效且高精确的,进而推广了比例边界有限元法的...     

Stress intensity factors for a wide range of long-deep semi-elliptical surface cracks, partly through-wall cracks and fully through-wall cracks in tubular members

To calculate the rate of fatigue crack growth in tubular members, one approach is to make use of the fracture mechanics based Paris law. Stress intensity factors (SIF) of the cracked tubular members are prerequisite for such calculations. In this paper, stress intensity factors for circumferential deep semi-elliptical surface crack (a/t > 0.8), semi-elliptical partly through-wall crack and fully through-wall crack cracks in tubular members subjected to axial tension are presented. The work has produced a comprehensive set of equations for stress intensity factors as a function of a/T, c/πR and R/T for deep surface cracks. For the partly through-wall cracks and fully through-wall cracks, two sets of bounding stress intensity factor equations were produced based on which all stress intensity factors within the range of parameters can be obtained by interpolation.     

Approximate weight function methods using a new condition

A method is presented to derive the approximate weight functions, by using a new condition on the crack mouth, for edge cracks in the semi-infinite or finite plate under Mode I loadings. This method requires only one information, say, the reference stress intensity factor (SIF), K_r. Numerical examples show that the present method is efficient in evaluation of the SIFs for edge cracks subjected to the polynomial loadings on the crack faces.     

新的估算表面裂纹应力强度因子经验公式

该文给出了新的估算拉伸和纯弯曲载荷下表面裂纹应力强度因子的经验公式。根据疲劳裂纹扩展的数值模拟结果确定强度因子分布函数;利用按已知应力强度因子分布函数求裂纹形状及相应应力强度因子的方法计算给定尺寸的表面裂纹的应力强度因子;通过对数值结果的曲线回归得到估算表面裂纹应力强度因子经验公式。利用该公式对有限厚度和宽度平板内表面裂纹的应力强度因子进行了估算,并与已知的半椭圆形表面裂纹的应力强度因子解进行了比较。该文结果为估算表面裂纹应力强度因子提供了一种新的途径。     

Thermal striping fatigue damage in multiple edge-cracked geometries

Thermal fatigue striping damage may be caused when incompletely mixed hot and cold fluid streams pass over the surface of a component or structure containing a defect. Stress intensity factor (SIF) fluctuations are developed in response to the surface temperature fluctuations. An existing methodology for the analysis of striping damage in geometries containing a single edge‐crack geometry is extended to such an analysis of multiple edge cracks. SIFs are calculated as functions of crack depth, when an edge‐cracked plate and semi‐infinite solid, each containing multiple cracks, are subjected to thermal striping. The effect of various restraint conditions and striping frequencies on the SIF values for a stainless steel plate is examined. The degree of conservatism is shown when an assessment of thermal fatigue striping damage is based on a single, rather than multiple, crack analysis. Accurate curve fits are developed resulting in practical weight functions for an edge‐cracked plate and semi‐infinite solid.     

Irreversible growth of a spherical cavity in rubber-like material: A fracture mechanics description

A procedure is presented for determining stress intensity factors for single and double edge cracks in simply supported undamped Bernoulli–Euler beams under a moving load. The approach is based on using modal analysis to determine the equivalent load on the beam, then linear elastic fracture mechanics is used to calculate stress intensity factors (SIF). The results show that SIF is a function of time, speed of the moving load and crack size and location.