Analysis of short and long crack behavior and single overload effect by crack opening stress

The study analyzed the behaviors of short and long crack as well as the effect of single tensile overload on the crack behaviors by using fatigue crack opening behavior. Crack opening stress is measured by an elastic compliance method which may precisely and continuously provide many data using strain gages during experiment. The unusual growth behaviors of short crack and crack after the single tensile overload applied, was explained by the variations of crack opening stress. In addition, fatigue crack growth rate was expressed as a linear form for short crack as for long crack by using effective stress intensity factor range as fracture mechanical parameter, which is based on crack closure concept. And investigation is performed with respect to the relation between plastic zone size formed at the crack tip and crack retardation, crack length and the number of cycles promoted or retarded, and the overload effect on the fatigue life.     

Analysis of a radial crack in cross-ply laminates under uniaxial tension

The problem of a radial crack in cross-ply laminates under uniaxial tension is investigated in this paper. The normalized stress intensity factors are obtained by the modified mapping collocation method which is based on analytic complex function theory of complex variables. The present results for an isotropic infinite plate show good agreement with existing solutions. In the range of small crack length, the stress intensity factor for a radial crack in cross-ply laminates under uniaxial tension becomes larger as the percentage of 0° plies increases. However in the range of large crack length, it is insensitive to the percentage of 0° plies.     

Analysis of a crack approaching a circular hole in cross-ply laminates under biaxial loading

The problem of a crack approaching a circular hole in cross-ply laminates under uniaxial and biaxial loading is investigated in this paper. The effects of material orthotropy, geometry [R/d and a/d], and loading conditions on crack tip singularity are investigated. The stress intensity factors are obtained by the modified mapping collocation method. The present results for an isotropic infinite plate show good agreement with existing solutions. The results for cross-ply laminates show that the stress intensity factors strongly depend on material orthotropy, geometry, and loading condition. The stress intensity factors for cross-ply laminates exist between those for θ=0° and those for θ=90° in the whole range of crack length and decrease as the percentage of 0° plies increases. In the range of small crack length the stress intensity factors for biaxial tension are higher than those for uniaxial tension. In the range of large crack length the stress intensity factors for uniaxial tension are higher than those for biaxial tension.     

Prediction of fatigue regimes in notched components

Fatigue crack growth from notches is described as a two-stage process. Cracks are assumed to initiate in, and their early growth controlled by, the plastic zone due to the notch. Later growth is controlled by the developing crack tip plastic zone which can be described by the elastic stress intensity factor. A simple model is proposed which qualitatively accounts for all observed notch phenomena including non-propagating cracks and size effects. The equation: is shown to quantitatively predict the experimental fatigue failure limit of sharply notched specimens.     

A study on the determination of closing level for finite element analysis of fatigue crack closure

An elastic-plastic finite element analysis is performed to investigate detailed closure behavior of fatigue cracks and the numerical results are compared with experimental results. The finite element analysis performed under plane stress using 4-node isoparametric elements can predict fatigue crack closure behavior. The mesh of constant element size along crack surface can not predict the opening level of fatigue crack. The crack opening level for the constant mesh size increases linearly from initial crack growth. The crack opening level for variable mesh size, is almost flat after crack tip has passed the monotonic plastic zone. The prediction of crack opening level using the variable mesh size proportioning the reversed plastic zone size with the opening stress intensity factors presents a good agreement with the experimental data regardless of stress ratios.     

Quarter elliptical crack growth using three dimensional finite element method and crack closure technique

Shape evolution of a quarter-elliptical crack emanating from a hole is studied. Three dimensional elastic-plastic finite element analysis of the fatigue crack closure was considered and the stress intensity factor was calculated based on the duplicated elastic model at each crack tip node. The crack front node was advanced proportional to the imposed effective stress intensity factor. Remeshing was applied at each step of the crack growth and solution mapping algorithm was considered. Crack growth retardation at free surfaces was successfully observed. A MATLAB-ABAQUS interference code was developed for the first time to perform crack growth on the basis of crack closure. Simulation results indicated that crack shape is sensitive to the remeshing strategy. Predictions based on the proposed models were in good agreement with Carlson’s experiments results.     

Numerical analysis for prediction of fatigue crack opening level

Finite element analysis (FEA) is the most popular numerical method to simulate plasticity-induced fatigue crack closure and can predict fatigue crack closure behavior. Finite element analysis under plane stress state using 4-node isoparametric elements is performed to investigate the detailed closure behavior of fatigue cracks and the numerical results are compared with experimental results. The mesh of constant size elements on the crack surface can not correctly predict the opening level for fatigue crack as shown in the previous works. The crack opening behavior for the size mesh with a linear change shows almost flat stress level after a crack tip has passed by the monotonic plastic zone. The prediction of crack opening level presents a good agreement with published experimental data regardless of stress ratios, which are using the mesh of the elements that are in proportion to the reversed plastic zone size considering the opening stress intensity factors. Numerical interpolation results of finite element analysis can precisely predict the crack opening level. This method shows a good agreement with the experimental data regardless of the stress ratios and kinds of materials.     

Subsurface crack mechanisms under indentation loading

A linear elastic fracture mechanics analysis of plane-strain indentation of a homogeneous half-space with a subsurface horizontal crack was performed using the finite element method. Stress intensity factor results obtained for an infinite plate with a central crack subjected to far-field tension and a half-space with a frictionless subsurface horizontal crack under a moving surface point load are shown to be in good agreement with corresponding analytical results. Crack mechanism maps illustrating the occurrence of separation, forward and backward slip, stick, and separation at the crack interface are presented for different indentation load positions and crack face friction coefficients. Results for the stresses in the vicinity of the crack tips and the mode I and mode II stress intensity factors are given for different indentation positions, crack face friction coefficients, and both concentrated and distributed surface normal tractions. Although indentation produces a predominantly shear and compressive stress field, mode I loading conditions are shown to occur for certain indentation positions. However, the magnitude of the mode I stress intensity factor is significantly smaller than that of mode II, suggesting that in-plane shear mode crack growth is most likely to occur in the absence of microstructural defects. The significance of crack face friction and sharpness of the indenter on the subsurface shear mode crack propagation rate is interpreted in terms of the mode II stress intensity factor range and material behavior.     

Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

In the digital image correlation research of fatigue crack growth rate,the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor,thereby affecting the life prediction.This paper proposes a Gauss-Newton iteration method for solving the crack tip position.The conventional linear fitting method provides an iterative initial solution for this method,and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix.A noise-added artificial displacement field is used to verify the feasibility of the method,which shows that all parameters can be solved with satisfactory results.The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result,and the relative error between the two is only-0.621％;The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip,and the maximum relative error with the test plastic zone area is-11.29％.The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05％.The crack tip coordinates,stress intensity factors,and plastic zone contour changes in the loading and unloading phases are explored.The results show that the crack tip change during the loading process is faster than the change during the unloading process;the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process;under the same load,the theoretical plastic zone during the unloading process is higher than that during the loading process.     

对2024铝合金疲劳裂纹扩展寿命进行预测

通过二维弹塑性有限元计算得到Ⅰ型静态裂纹在常幅疲劳载荷下裂纹尖端塑性应变能,进而获得裂纹尖端塑性应变能和应力强度因子幅值的非线性关系;根据能量平衡概念,建立了裂纹扩展速率与裂纹尖端塑性应变能的关系。由此得到一种基于裂纹尖端塑性应变能的疲劳裂纹扩展寿命预测模型,利用该模型预测了中心裂纹平板的疲劳裂纹扩展寿命,预测结果与试验值吻合得很好。     

Experimental and numerical determination of critical stress intensity factor of aluminum curved thin sheets under tensile stress

We determined the fracture toughness of aluminum curved thin sheets using tensile stress tests and finite element method. We applied Linear elastic fracture mechanics (LEFM) and Feddersen procedure to evaluate stress intensity factor of the samples with central wire-cut cracks and fatigue cracks with different lengths to investigate the notch radius effect. Special fixture design was utilized to establish uniform stress distribution at the crack zone. Less than 9 % difference was found between the wire-cut and the fatigue cracked samples. Since generating central fatigue crack with different lengths required so much effort, wire-cut cracked samples were used to determine critical stress intensity factor. Finite element analysis was also performed on one-quarter of the specimen using both the singular Borsum elements and the regular isoparametric elements to further investigate fracture toughness of the samples. It was observed that the singular elements presented better results than the isoparametric ones. A slight difference was also found between the results obtained from finite element method using singular elements and the experimental results.     

Static and dynamic fracture analysis for the interface crack of isotropic-orthotropic bimaterial

In the present study, interfacial cracks between an isotropic and orthotropic material, subjected to static far field tensile loading are analyzed using the technique of photoelasticity. The fracture parameters are extracted from the full-field isochromatic data and the same are compared with that obtained using boundary collocation method. Dynamic photoelasticity combined with high-speed digital photography is employed for capturing the isochromatics in the case of propagating interfacial cracks. The normalized stress intensity factors for static cracks are greater when α=90° (fibers perpendicular to the interface) than when α=0° (fibers parallel to the interface), and those when α=90° are similar to ones of isotropic material. The dynamic stress intensity factors for interfacial propagating cracks are greater when α=0° than α=90°. For the velocity ranges (0.1<c/c _s1 <0.7) observed in this study, the complex dynamic stress intensity factor |K _D |, I increases with crack speedc, however, the rate of increase of |K _D | with crack speed is not as drastic as that reported for homogeneous materials.     

疲劳近门槛值区裂纹扩展模式变化的试验研究

利用扫描电镜观察疲劳门槛值区试样的裂纹表面形貌,研究了疲劳门槛值区裂纹扩展模式的分布,分析了裂纹扩展模式的变化对疲劳裂纹扩展速率da／dN的影响。结果表明,断口形貌存在面型断裂（沿晶或穿晶）（Faceted Fracture,FF）,面型断裂分数（Percentageof Faceted Fracture,PFF）最大值出现在循环塑性区尺寸接近原始奥氏体晶粒直径时。通过比较循环塑性区尺寸与晶粒尺寸,随着应力强度因子幅值AK的降低,裂纹先以辉纹型模式扩展,在PFF达到最大值后,裂纹以晶体学模式扩展。辉纹型模式扩展时,PFF的变化对da／dN影响不大;晶体学模式扩展时,由于FF诱发裂纹闭合,从而降低da／dN。     

Statistical aspects of fatigue crack growth life of base metal,weld metal and heat affected zone in FSWed 7075-T651 aluminum alloy

The statistical aspects of fatigue crack growth life of base metal (BM), weld metal (WM) and heat affected zone (HAZ) in friction stir welded (FSWed) 7075-T651 aluminum alloy has been studied by Weibull statistical analysis. The fatigue crack growth tests were performed at room temperature on ASTM standard CT specimens under three different constant stress intensity factor range controls. The main objective of this paper is to investigate the effects of statistical aspects of fatigue crack growth life on stress intensity factor ranges and material properties, namely BM, WM and HAZ specimens. In this work, the Weibull distribution was employed to estimate the statistical aspects of fatigue crack growth life. The shape parameter of Weibull distribution for fatigue crack growth life was significantly affected by material properties and the stress intensity factor range. The scale parameter of WM specimen exhibited the lowest value at all stress intensity factor ranges.     

Anti-plane shear behavior of an arbitrarily oriented crack in bonded materials with a nonhomogeneous interfacial zone

The anti-plane shear problem of bonded elastic materials containing a crack at an arbitrary angle to the graded interfacial zone is investigated in this paper. The interfacial zone is modeled as a nonhomogeneous interlayer of finite thickness with the continuously varying shear modulus between the two dissimilar, homogeneous half-planes. Formulation of the crack problem is based upon the use of the Fourier integral transform method and the coordinate transformations of basic field variables. The resulting Cauchy-type singular integral equation is solved numerically to provide the values of modeIII stress intensity factors. A comprehensive parametric study is then presented of the influence of crack obliquity on the stress intensity factors for different crack size and locations and for different material combinations, in conjunction with the material nonhomogeneity within the graded interfacial zone.     

Characterization of the Q* parameter for evaluating creep crack growth rate for type 316LN stainless steel

In this study, the Q* parameter was characterized to evaluate the Creep crack growth rate (CCGR) of type 316LN stainless steel. Creep crack growth (CCG) data were obtained by CCG tests under different applied loads at 600°C. An additional CCG test was conducted at 550°C to investigate the possible temperature dependence of the stress intensity factor. An equation using the Q* parameter for evaluating CCGR was proposed, and this parameter was characterized and compared with the typical C* fracture parameter, which is commonly used. The Q* parameter exhibited good linearity of the data, exhibiting no nonlinearity-induced dual value at the early stage. The Q* parameter was suitable for characterizing the CCGR regardless of different applied loads and types of steels. In addition, fracture microstructures near the crack revealed a typical intergranular fracture mode, and this fracture was dominantly propagated along the grain boundary. The cracks were developed by the growth and interlinking of cavities, which were attributed to the precipitates forming along the grain boundary.

     

Modified boundary layer analysis for a mode III crack problem

A modified boundary layer problem of a semi-infinite crack in an elastic-perfectly plastic material under a Mode III load is analyzed. The analytic solution of elastic fields is derived by using complex function theory. It is found that the size and the shape of the plastic zone near the crack tip depend on the elastic T-stress given on the remote boundary. A method for determining higher order singular solutions of elastic fields is also proposed. In order to determine the higher order singular solutions of the elastic fields, Williams expansion of the solution is used. Higher order terms in the Williams expansion are obtained through simple mathematical manipulation. The coefficients of each term in the Williams expansion are also calculated numerically with the J-based mutual integral     

Numerical studies on crack growth in a steel tubular T-joint

The results of a numerical investigation on fatigue crack growth of an offshore tubular T-joint under the action of axial, in-plane and out-of-plane bending loads are presented in this paper. Extensive stress analysis has been carried out to determine the location of the hot spot stress along the brace—chord intersection for each load case. Semi-elliptical cracks with varying crack lengths and crack depths were introduced at the hot spot location by means of line spring elements for stress intensity factor evaluation. The line springs were properly constrained to prevent the problem of crack surface penetration. The stress intensity factors obtained are then used in a crack growth law for life estimation.     

The effect of bridging on fatigue crack growth behavior in Aramid Patched Aluminum Alloy(APAL)

A new hybrid composite (APAL: Aramid Patched Aluminum Alloy), consisting of a 2024-T3 aluminum alloy plate sandwiched between two aramid/epoxy laminate (HK 285/RS 1222), was developed. Fatigue crack growth behavior was examined at stress ratios of R=0.2, 0.5 using the aluminum alloy and two kinds of the APAL with different fiber orientation (0°/90° and 45° for crack direction). The APAL showed superior fatigue crack growth resistance, which may be attributed to the crack bridging effect imposed by the intact fibers in the crack wake. The magnitude of crack bridging was estimated quantitatively and determined by a new technique on basis of compliances of the 2024-T3 aluminum alloy and the APAL specimens. The crack growth rates of the APAL specimens were reduced significantly as comparison to the monolithic aluminum alloy and were not adequately correlated with the conventional stress intensity factor range(ΔK). It was found that the crack growth rate was successfully correlated with the effective stress intensity factor range (ΔK _eff =K _br -K _ct ) allowing for the crack closure and the crack bridging. The relation between da/dN and theΔK _eff was plotted within a narrow scatter band regardless of kind of stress ratio (R=0.2, 0.5) and material (2024-T3 aluminum alloy, APAL 0°/90° and APAL±45°). The result equation was as follow:da/dN=6.45×10⁻⁷(ΔK _eff )^2.4.     

小范围屈服条件下复合材料裂纹尖端塑性区分析

基于复合材料力学,推导Tsai-Hill强度准则在平面应力和平面应变条件下的一般表达式,得到了小范围屈服条件下,含中心裂纹无限大板Ⅰ型裂纹、Ⅱ型裂纹和Ⅰ/Ⅱ复合型裂纹尖端塑性区的解析解。针对不同裂纹倾角及泊松比 和,对裂尖塑性区进行了计算和分析。结果表明平面应变条件下塑性区范围小于平面应力条件下塑性区范围,参数、和 对复合材料裂尖塑性区范围和形状有明显的影响,不同的参数值得到的塑性区结果差别很大。另外,该解既适用于各向异性复合材料,也适用于各向同性材料。