An engineering formula for the stress concentration factor of orthotropic composite plates

An engineering formula for the theoretical stress concentration factor of orthotropic notched plates under tension is provided, as a function of the material elastic constants and the K_t of the corresponding isotropic case. The accuracy and limits of applicability of the new solution are discussed by comparison to data from the literature and results from FE analyses on notched geometries of practical interests. The proposed solution represents a very useful tool to estimate the stress concentration factor of notched orthotropic plates, composite orthotropic laminae, orthotropic unidirectional laminates and homogenised orthotropic composite laminates.     

The performance of isoparametric finite elements in stress intensity factor determination

Analysis of a compact compression specimen used for fracture toughness evaluation of cementitious materials is carried out by the finite element method using isoparametric elements. Both triangular and rectangular elements were used with those surrounding the crack tip being of the quarter point type. Solutions were obtained for different mesh subdivisions and convergenece curves for the stress intensity factor were obtained by several methods based on extrapolation and energy techniques. It is found that monotonic convergence was obtained for all cases considered. Employing uniformly graded rectangular element representations converged solutions for the stress intensity factor (assuming a 1 percent convergence criterion) were obtained by the energy methods using a total of 720 degrees of freedom for solving half the structure.Tests on modified 100 mm cubes with symmetrical notches were conducted to determine the fracture toughness. The fracture toughness was calculated from the stress intensity factor and the maximum load obtained from the tests which were conducted in a stiff Instron testing machine. The fracture toughness is found to be independent of the size of the notch.     

3-D finite element analysis of stress concentration factor in spot-welded joints of steel: The effect of process-induced porosity

The work presented in this paper utilises a numerical analysis for the computation of stress concentration factor generated by the presence in the weld nugget of a pore formed during the welding process. Welded structure containing porosity is subjected to uniaxial tensile stress. The effects of geometrical parameters of the pore and the interaction pore-defect on the stress concentration factor variation have been analyzed.     

On the use of quarter-point boundary elements for stress intensity factor computations

This communication studies a procedure for stress intensity factor computations using traction singular quarter-point boundary elements. Opening mode stress intensity factors are computed from the tractions' nodal values at the crack tip. A comparison is made between the factors calculated using this procedure and those obtained by previously recommended methods which made use of the nodal values of the displacements. The proposed procedure was seen to be less discretization sensitive than any other of the considered methods. Accurate results were obtained even in the case of coarse meshes.     

A discussion on various estimations of elastic stress distributions and stress concentration factors for sharp edge notches

The elastic stress distributions in some edge-notched geometries have been estimated from Creager and Paris's and Neuber's expressions. Close to the notch root, these approximate solutions agree well with the finite element results. Further away from the notch, the approximate methods give overestimations. A simple formula derived from Creager and Paris's expression provided accurate stress concentration factor solutions for some edge-notched geometries.     

A method for stress intensity factor calculation of infinite plate containing multiple hole-edge cracks

Multiple site damage is the occurrence of small fatigue cracks at several sites within aging aircraft structures. Focusing on this typical structure, an analytical method for calculating the stress intensity factor of an infinite plate containing multiple hole-edge cracks was introduced in this paper. The properties of complex variable functions are used to evaluate the stress function. The approximate superposition method is applied to solve stress intensity factor problems on multiple holes. The equivalent crack is introduced to modify the method. Some numerical examples of an infinite plate containing two hole-edge cracks are examined by the method. By comparing the analytical and finite element analysis results it was realized that the analytical results are accurate and reliable. This modified analytical method is easier to apply than some traditional analytical methods and can provide stress intensity factor solutions for an infinite plate containing a random distribution of multiple hole-edge cracks.     

Analysis of the stress intensity factor dependence with the crack velocity using a lattice model

In this work, the influence of crack propagation velocity in the stress intensity factor has been studied. The analysis is performed with a lattice method and a linear elastic constitutive model. Numerous researchers determined the relationship between the dynamic stress intensity factor and crack propagation velocity with experimental and analytical results. They showed that toughness increases asymptotically when the crack tip velocity is near to a critical. However, these methods are very complex and computationally expensive; furthermore, the model requires the use of several parameters that are not easily obtained. Moreover, its practical implementation is not always feasible. Hence, it is usually omitted. This paper aims to capture the physics of this complex problem with a simple fracture criterion. The selected criterion is based on the maximum principal strain implemented in a lattice model. The method used to calculate the stress intensity factor is validated with other numerical methods. The selected example is a finite 2D notched under mode I fracture and different loads rates. Results show that the proposed model captures the asymptotic behaviour of the SIF in function of crack speed, as reported in the aforementioned models.     

Time domain boundary element method for dynamic stress intensity factor computations

This paper presents a procedure for transient dynamic stress intensity factor computations using traction singular quarter-point boundary elements in combination with the direct time domain formulation of the Boundary Element Method. The stress intensity factors are computed directly from the traction nodal values at the crack tip. Several examples of finite cracks in finite domains under mode-I and mixed mode dynamic loading conditions are presented. The computed stress intensity factors are represented versus time and compared with those obtained by other authors using different methods. The agreement is very good. The results are reliable and little mesh dependent. These facts allow for the analysis of dynamic crack problems with simple boundary discretizations. The versatile procedure presented can be easily applied to problems with complex geometry which include one or several cracks.     

Dynamic stress intensity factor (Mode I) of a penny-shaped crack in an infinite poroelastic solid

This paper considers the transient stress intensity factor (Mode I) of a penny-shaped crack in an infinite poroelastic solid. The crack surfaces are impermeable. By virtue of the integral transform methods, the poroelastodynamic mixed boundary value problems is formulated as a set of dual integral equations, which, in turn, are reduced to a Fredholm integral equation of the second kind in the Laplace transform domain. Time domain solutions are obtained by inverting Laplace domain solutions using a numerical scheme. A parametric study is presented to illustrate the influence of poroelastic material parameters on the transient stress intensity. The results obtained reveal that the dynamic stress intensity factor of poroelastic medium is smaller than that of elastic medium and the poroelastic medium with a small value of the potential of diffusivity shows higher value of the dynamic stress intensity factor.     

Pulse shape effects on the dynamic stress intensity factor

The interaction of a transient stress pulse with a penny-shaped crack embedded in an infinite elastic solid is investigated. The front of the incident stress pulse is assumed to be planar and parallel to the crack surfaces. A time-domain boundary integral equation method is applied for computing the time history of the crack opening displacement, from which the time dependence of the dynamic stress intensity factor is subsequently calculated. Numerical calculations are carried out for several stress pulses of different shape and time dependence, to explore the effects of the shape, duration, rise and descent time of a transient stress pulse, or the period and the mean stress of a cyclic stress pulse on the dynamic stress intensity factor. Implications regarding crack surface penetrations or crack surface interactions caused by certain stress pulses are also discussed.     

Measuring residual stress and the resulting stress intensity factor in compact tension specimens

The measurement of residual stress through the remaining ligament of a compact tension specimen was studied. In the crack compliance method, a slot or notch is successively extended through the part, and the resulting strain is measured at an appropriate location. By using a finite element simulation of a specimen preloaded beyond yield, three techniques for determining the original residual stress from the measured strains were compared for accuracy and sensitivity to measurement errors. A common beam-bending approximation was substantially inaccurate. The series expansion method proved to be very versatile and accurate. The fracture mechanics approach could determine the stress intensity factor caused by the residual stresses with a very simple calculation. This approach offers the exciting possibility of determining the stress intensity factor prior to a fatigue or fracture test by measuring strains during the specimen preparation.     

The stress intensity factor for a crack perpendicular to the welding bead

An analysis of the stress intensity factor due to the residual stress is made for a crack perpendicular to the welding joint in a large plate. The residual stress distribution is represented by a simple function which is chosen to satisfy the physical requirements for the residual stress and to simulate the commonly observed distribution. The stress intensity factor is obtained using customary method based on the superposition principle. The function chosen for the residual stress distribution leads to an exact expression of the stress intensity factor in a simple closed form. The solution yields somewhat conservative values of the stress intensity factor for large cracks and it may be conveniently used for practical applications.     

Evaluation of stress intensity factor under pure shear stress in orthotropic material

Various types of composite materials are currently being developed and used for automobiles, airplanes, ships and other structures in response to required service conditions which are getting increasingly more severe. Of growing importance under such circumstances is the study of stress analysis and fracture mechanics for these composite material structures. Particularly, the primary concern in design of structures and machines should be the initiation of cracks due to excessive deformation, delamination in material or other material defects. In evaluating safety, it is indispensable from the structural design point of view that K value should be known by an analysis conducted in advance. In this study, stress intensity factor (mode II) under a pure shear stress was obtained using the photoelastic method and caustic method and applying an isotropic material and orthotropic material (copper fibre epoxy composite (CFEC) developed by the authors), each containing the crack. Results were compared with theoretical values. As a result, this method was found useful and the effect of the direction of the primary axis of this material on the stress intensity factor was clarified.     

基于拉弯比的焊缝名义应力的提取

为了获得任意拉弯组合载荷下焊缝的名义应力,利用纯弯和纯拉压载荷下的应力集中系数,引入拉弯组合名义应力换算系数,将基于纯拉压名义应力的焊缝疲劳性能数据,转换为疲劳损伤一致的、基于拉弯组合名义应力的焊缝疲劳性能数据．为了消除有限元建模导致的计算误差,引入单元尺寸影响因子,将拉弯组合的计算应力转换为拉弯组合的名义应力．通过上面2个转换,引入拉弯组合计算名义应力换算系数,将有限元中的拉弯组合计算应力转换为基于拉压载荷疲劳试验的名义应力,从而在具体的焊缝结构疲劳强度评估时可以直接使用拉压载荷下的疲劳试验数据．计算结果表明：拉弯组合计算名义应力换算系数与拉弯比、拉弯应力集中因子比和有限元模型中拉弯单元尺寸影响因子有关．通过选择合适的单元尺寸,使得拉压单元尺寸影响因子等于拉弯应力集中因子比,且弯曲单元尺寸影响因子等于1,可使得拉弯组合计算名义应力换算系数恒等于拉压单元尺寸影响因子,而与拉弯比无关．     

Closed-form structural stress and stress intensity factor solutions for spot welds in commonly used specimens

Closed-form new structural stress and stress intensity factor solutions for spot welds in lap-shear, square-cup, U-shape, cross-tension and coach-peel specimens are obtained based on elasticity theories and fracture mechanics. The loading conditions for spot welds in the central parts of the five types of specimens are first examined. The resultant loads on the weld nugget and the self-balanced resultant loads on the lateral surface of the central parts of the specimens are then decomposed into various types of symmetric and anti-symmetric parts. Closed-form structural stress and stress intensity factor solutions for spot welds under various types of loading conditions are then adopted from the recent work of Lin and Pan to derive new closed-form structural stress and stress intensity factor solutions for spot welds in the five types of specimens. The selection of a geometric factor for square-cup specimens and the decompositions of the loads on the central parts of the U-shape, cross-tension and coach-peel specimens are based on the corresponding three-dimensional finite element analyses of these specimens. The new closed-form solutions are expressed as functions of the spot weld diameter, the sheet thickness, the width and the length of the five types of specimens. The closed-form solutions are also expressed as functions of the angular location along the nugget circumference of spot welds in the five types of specimens in contrast to the limited available solutions at the critical locations in the literature. The new closed-form solutions at the critical locations of spot welds in the five types of specimens are listed or can be easily obtained from the general closed-form solutions for fatigue life predictions.     

Analytical stress intensity factor solutions for resistance and friction stir spot welds in lap-shear specimens of different materials and thicknesses

In this paper, analytical stress intensity factor and J integral solutions for resistance and friction stir spot welds without and with gap and bend in lap-shear specimens of different materials and thicknesses are developed. The J integral and stress intensity factor solutions for spot welds are first presented in terms of the structural stresses for a strip model. Analytical structural stress solutions for spot welds without and with gap and bend in lap-shear specimens are then developed based on the closed-form structural stress solutions for a rigid inclusion in a finite thin plate subjected to various loading conditions. With the available structural stress solutions, the analytical J integral and stress intensity factor solutions can be obtained as functions of the applied load, the elastic material property parameters, and the geometric parameters of the weld and specimen. The analytical stress intensity factor solutions are selectively validated by the results of three-dimensional finite element analyses for a spot weld with ideal geometry and for a friction stir spot weld with complex geometry, gap and bend. The stress intensity factor and J integral solutions at the critical locations of spot welds in lap-shear specimens of dissimilar magnesium, aluminum and steel sheets with equal and different thicknesses are then presented in the normalized forms as functions of the ratio of the specimen width to the weld diameter. Finally, general trends and simple estimation methods of the stress intensity factor and J integral solutions at the critical locations of spot welds in lap-shear specimens of different materials and thicknesses are given for convenient engineering applications.     

Simple formula for dynamic stress intensity factor of pre-cracked Charpy specimen

It has been reported that consideration of inertia effect is important to estimate the stress intensity factor for impact loading. In the present paper a simple expression for the dynamic stress intensity factor of a pre-cracked Charpy specimen is derived by making use of an approximate solution for one-dimensional beam equations. The time variation of the dynamic stress intensity factor obtained retaining only the fundamental mode of bending vibration is in good agreement with the two-dimensional finite element solutions for step-loading and also for final-peak-sawtooth-pulse loading.     

基于应力强度因子评估WCP形状对WCP/Fe复合材料热疲劳裂纹扩展行为的影响

应力强度因子在断裂力学中广泛应用于预测由远程载荷或残余应力引起的裂缝尖端附近应力状态。本文基于平面应力条件下应力强度因子建立WC_P形状与其尖端应力之间的规律,利用有限元分析软件对含不同形状WC_P的WC_P/Fe复合材料的热应力进行模拟仿真,研究WC_P形状对WC_P/Fe复合材料热疲劳裂纹扩展行为的影响。研究结果表明,WC_P的形状显著影响应力强度因子,进一步影响WC_P/Fe复合材料的热疲劳裂纹扩展行为。含球状和不规则状WC_P的WC_P/Fe复合材料的极限抗压强度分别约为460 MPa和370 MPa。含不规则状WC_P的WC_P/Fe复合材料因应力集中而容易产生脆性开裂现象。通过热震实验进行验证,发现实验结果与模拟仿真结果相近,说明有限元法的准确性,同时为WC_P/Fe复合材料的热疲劳裂纹扩展行为研究提供科学依据和理论基础。      

Explicit calculation of the crack tip stress intensity factor for the double slip plane model crack

A more rigorous analysis is presented for the stationary double slip plane (DSP) crack loaded in mode III with constant friction stress on the slip planes. This analysis gives the dislocation distributions on the slip and crack planes. More important, the analysis leads to an explicit calculation of the crack tip stress intensity factor K_t without resort to use of the J-integral or the Rice-Thompson expression for dislocation crack tip shielding/antishielding factor. It is shown that K_t ≈ K for the stationary crack. With the results of this paper there are now essentially three independent methods of obtaining K_t for a DSP crack.     

Three-dimensional stress intensity factor calibration for a stiffened cracked plate

Three-dimensional finite element analyses are used in this paper to calibrate the stress intensity factor in a cracked stiffened plate subjected to remote uniform traction. An accurate numerical determination of the stress field and stress intensity variation through the thickness of a central cracked plate was first carried out in order to evaluate three-dimensional effects. A stiffened cracked plate was then analysed, taking into account the results and the conclusions obtained in the previous study. Such a structure was chosen due to the growing interest for large integral metallic structures for aircraft applications, following the continuous need for low cost and the emergence of new technologies. The J-Integral technique was used to calculate the values of the stress intensity factor along the plate thickness. The plane strain behaviour near the crack front and the variation of the opening stress are discussed.