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.     

Application of modified mapping-collocation method to cracks emanating from a circular hole in an orthotropic finite plate

A modified mapping-collocation method is applied to the analysis of cracks emanating from a circular hole in an orthotropic finite plate under uniform stress. To check the effectiveness of this procedure, we present the various results for comparison with references. Then, the stress intensity factors are presented for several plate configurations of [0 _n /90 _m ] _s laminates. The results show that the modified mapping-collocation method is effectively applicable to analyzing such cracks in an orthotropic finite plate. The results also show that the stress intensity factors depend on the material orthotropy and geometry.     

Effect of fiber volume fraction on the stress intensity factors for multi layered composites under arbitrary anti-plane shear loading

A multi-layered orthotropic material with a center crack is subjected to an anti-plane shear loading. The problem is formulated as a mixed boundary value problem by using the Fourier integral transform method. This gives a Fredholm integral equation of the second kind. The integral equation is solved numerically and anti-plane shear stress intensity factors are analyzed in terms of the material orthotropy for each layer, number of layers, crack length to layer thickness and the order of the loading polynomial. Also, the case of monolithic and hybrid composites are investigated in terms of the local fiber volume fraction and the global fiber volume fraction.     

Influences of equal biaxial tensile loads on the stress fields near the mixed mode crack

A hybrid method for photoelasticity is introduced and applied to the plane problems of isotropic polycarbonate plates with a central crack under uniaxial and equal biaxial tensile loads. Also, the influences of equal biaxial tensile loads on the isochromatic fringes, stress fields and stress intensity factors near the mixed mode crack-tip have been investigated. The results show that, when an equal lateral tensile load is added to the specimen under uniaxial tensile load, the asymmetric isochromatic fringes about the line of crack gradually become symmetric, and the slope of the isochromatic fringe loop near the crack-tip is inclined towards the crack surface according to the increasing of the inclined angle of crack. Furthermore, the shapes of distribution of all stress components are changed from asymmetric to symmetric. In the equal biaxial tensile load condition against the uniaxial tensile load condition, the values of stress intensity factors are changed little, and only the region of compressive stress of σ _x /σ _O is changed when β = 0°, but the values of K _I /K ₀ are increased and those of K _II /K ₀ become almost zero, namely, we have the mode I condition when β = 15°∼45°. This paper was recommended for publication in revised form by Associate Editor Chongdu Cho Dong-Chul Shin received the B.S., M.S. and Ph.D. degrees in Mechanical Engineering from Yeungnam University in 1995, 1997 and 2001, respectively. Dr. Shin studied at the University of Tokyo, Japan, for three years (from April, 2005 to January, 2008) as a Post-Doctoral fellow (supported by Korea Research Foundation (KRF) and Japan Society for the Promotion of Science (JSPS)). Dr. Shin is currently a Research Professor at the School of Mechanical Engineering at Pusan National University, Korea. His research interests include the static and dynamic fracture mechanics, stress analysis, and fracture criteria of piezoelectric ceramics, etc. Jai-Sug Hawong received a B.S. in Mechanical Engineering from Yeungnam University in 1974. Then he received his M.S. and Ph.D. degrees from Yeungnam University in Korea in 1976 and from Kanto Gakuin University in Japan in 1990, respectively. Prof. Hawong is currently a professor at the School of Mechanical Engineering at Yeungnam University, in Gyeongsan city, Korea. He is currently serving as vise-president of Korea Society Mechanical Engineering. His research interests are in the areas of static and dynamic fracture mechanics, stress analysis, experimental mechanics for stress analysis and composite material etc.     

A study on residual fatigue bending strength and damage behavior of CFRP composites subjected to impact loadings

This paper evaluates the static and fatigue bending strengths of CFRP (carbon-fiber reinforced plastic) laminates having impact damages, e.g., foreign object damages (FOD). Composite laminates used in this experiment are CF/EPOXY and CF/PEEK orthotropy laminated plates with two-interfaces [0°₄/90°₄]_s A steel ball launched by an air gun collides against the CFRP laminates to generate impact damages. The damage growth during a bending fatigue test is observed by a scanning acoustic microscope (SAM). When the impacted side is compressed, the residual fatigue bending strength of CF/PEEK specimen P is greater than that of CF/EPOXY specimen B. On the other hand, when the impacted side is in tension, the residual fatigue bending strength of CF/PEEK specimen P is smaller than that of CF/EPOXY specimen B. In the case of impacted-side compression, the fracture is propagated from the transverse crack generated near the impact point. In the case of impacted-side tension, however, the fracture develops toward the impact point from the edge of interface-B delamination.     

Experimental investigation of material deformation and failure regularities in a flat stressed state

Some problems of how to use modern experimental facilities—an Inston 8850 biaxial servohydraulic test system and Vic 3D Limess digital optical system—for analyzing the fields of deformation and displacements in order to investigate the regularities of material inelastic deformation and failure in a complicated stressed-deformed state are examined. Proportional loading with different ratios between the axial deformation and the shear angle is implemented. Diagrams of the material deformation for different stress states are generated. The diagrams of material deformation with a drop-down branch are obtained under uniaxial tension for samples with different ratios between the length and diameter. Information about the deformation fields taking place in the plates with stress concentrators determined by means of the correlation of digital images are presented.     

Fatigue crack propagation behavior in STS304 under mixed-mode loading

The use of fracture mechanics has traditionally concentrated on crack growth under an opening mechanism. However, many service failures occur from cracks subjected to mixed-mode loading. Hence, it is necessary to evaluate the fatigue behavior under mixed-mode loading. Under mixed-mode loading, not only the fatigue crack propagation rate is of importance, but also the crack propagation direction. In modified range 0.3≤a/W≤0.5, the stress intensity factors (SIFs) of mode I and mode II for the compact tension shear (CTS) specimen were calculated by using elastic finite element analysis. The propagation behavior of the fatigue cracks of cold rolled stainless steels (STS304) under mixed-mode conditions was evaluated by using K_I and K_II(SIFs of mode I and mode II). The maximum tangential stress (MTS) criterion and stress intensity factor were applied to predict the crack propagation direction and the propagation behavior of fatigue cracks.     

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.     

Regularities of the change in the coercive force under biaxial asymmetric deformation of steel 3

The change in the coercive force under biaxial asymmetric (tension and compression in mutually perpendicular directions) cyclic deformation of cross-shaped steel 3 specimens in the elastic region of deformations was studied. Specimens were deformed beforehand under biaxial asymmetric loading to various degrees of plastic deformation. It was demonstrated that the elastic-deformation dependences of the coercive force measured along the tension and compression directions are qualitatively similar to those under uniaxial tension or compression. It was also shown that, under cyclic elastic loading, these dependences are reversible for well-annealed steel and have a hysteresis that expands with increasing degree of plastic deformation for plastically deformed steel. The possible causes of the hysteresis in the dependence of the coercive force on the elastic cyclic deformations under biaxial loading are discussed. It was supposed that the hysteresis of the coercive force was caused by the appearance of free (not bound in carbide phases) carbon atoms playing the role of interstitial impurity atoms for the α-iron lattice in plastically deformed carbon steels. The possibility of estimating the stressed-strained state of steel under biaxial loading using a magnetic method was discussed.     

Approximation method for the calculation of stress intensity factors for the semi-elliptical surface flaws on thin-walled cylinder

A simple approximation method for the stress intensity factor at the tip of the axial semi-elliptical cracks on the cylindrical vessel is developed. The approximation methods, incorporated in VINTIN (Vessel INTegrity analysis-INner flaws), utilizes the influence coefficients to calculate the stress intensity factor at the crack tip. This method has been compared with other solution methods including 3-D finite element analysis for internal pressure, cooldown, and pressurized thermal shock loading conditions. For these, 3-D finite-element analyses are performed to obtain the stress intensity factors for various surface cracks witht/R=0.1. The approximation solutions are within ±2.5% of the those of finite element analysis using symmetric model of one-forth of a vessel under pressure loading, and 1–3% higher under pressurized thermal shock condition. The analysis results confirm that the approximation method provides sufficiently accurate stress intensity factor values for the axial semi-elliptical flaws on the surface of the reactor pressure vessel.     

三轴应力状态下复合型裂纹尖端前缘的塑性区分布

利用Ｍｉｓｅｓ屈服准则从理论上分析了Ⅰ－Ⅱ复合型裂纹尖端前缘的塑性区分布。推导出了由三轴应力约束参数Ｔｚ参与表征的裂纹尖端前缘塑性区尺寸ｒｐ的表达式，并绘制出了Ⅰ－Ⅱ复合型裂纹在单轴、双轴载荷作用下裂纹尖端塑性区的分布图。     

Stress singularities in dissimilar orthotropic composites containing an interlaminar crack

The problem of an interlaminar crack in dissimilar orthotropic composite materials under in-plane and anti-plane loading conditions is investigated. In the analytical model, orthotropic half-spaces are assumed to be bound together by a matrix interlayer which represents the matrix-rich interlaminar region in the fiber-reinforced composite laminate. The crack is embedded within the interlayer. With the utilization of the stiffness matrix approach, a system of singular integral equations of the first kind is derived for the current mixed boundary value problem. Numerical results are obtained for the interlaminar crack in a [0°/90°] fibrous composite laminate subjected to three basic loadings in fracture mechanics. Under each applied loading, variations of major and coupling stress intensity factors with respect to relative crack size, crack location, and fiber volume fraction are illustrated.     

Stress Intensity Factors Evaluation for Rolling Contact Fatigue Cracks in Rails

The stress intensity factors (SIFs) for multiple rolling contact fatigue cracks of a network in the Iran railway under vehicle dynamic load are evaluated in this article. Stress intensity factor evaluation under dynamic loading is simulated in three dimensions using a linear elastic boundary element code. For this purpose, a UIC60 rail with accurate geometry using a boundary element method is studied. A three-dimensional model in Franc3D is provided. Finally, the influence of the friction coefficient between the wheel and rail, crack surface friction, trapped fluid, and initial crack length on SIFs are investigated in detail.     

Error analysis of FLC experimental data at warm/hot stamping conditions

Forming limit curves（FLCs） are commonly used for evaluating the formability of sheet metals. However, it is difficult to obtain the FLCs with desirable accuracy by experiments due to that the friction effects are non-negligible under warm/hot stamping conditions. To investigate the experimental errors, experiments for obtaining the FLCs of the AA5754 are conducted at 250℃. Then, FE models are created and validated on the basis of experimental results. A number of FE simulations are carried out for FLC test-pieces and punches with different geometry configurations and varying friction coefficients between the test-piece and the punch. The errors for all the test conditions are predicted and analyzed. Particular attention of error analysis is paid to two special cases, namely, the biaxial FLC test and the uniaxial FLC test. The failure location and the variation of the error with respect to the friction coefficient are studied as well. The results obtained from the FLC tests and the above analyses show that, for the biaxial tension state, the friction coefficient should be controlled within 0.15 to avoid significant shifting of the necking location away from the center of the punch; for the uniaxial tension state, the friction coefficient should be controlled within 0.1 to guarantee the validity of the data collected from FLC tests. The conclusions summarized are beneficial for obtaining accurate FLCs under warm/hot stamping conditions.     

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.     

High-temperature rupture of 5083-Al alloy under multiaxial stress states

High-temperature rupture behavior of 5083-A1 alloy was tested for failure at 548K under multiaxial stress conditions : uniaxial tension using smooth bar specimens, biaxial shearing using double shear bar specimens, and triaxial tension using notched bar specimens. Rupture times were compared for uniaxial, biaxial, and triaxial stress conditions with respect to the maximum principal stress, the von Mises effective stress, and the principal facet stress. The results indicate that the von Mises effective and principal facet stresses give good correlation for the material investigated, and these parameters can predict creep life data under the multiaxial stress states with the rupture data obtained from specimens under the uniaxial stress. The results suggest that the creep rupture of this alloy under the testing condition is controlled by cavitation coupled with highly localized deformation process, such as grain boundary sliding. It is also conceivable that strain softening controls the highly localized deformation modes which result in cavitation damage in controlling rupture time of this alloy.     

Prediction of crack tip plasticity induced due to variation in solidification rate of weld pool and its effect on fatigue crack propagation rate (FCPR)

Effect of solidification rate on crack tip plastic zone size at various crack lengths was calculated analytically and numerically by simplified Sih’s and Irwin’s models, respectively. Influence of plastic zone size is explained in terms of COD and elastic stress intensity factor within valid range of small scale yielding approximation. Up to plastic zone size range of 4–5 mm, a good agreement between numerical and analytical plastic zone size and elastic stress intensity factor for all weldments was observed. For high loads and greater crack lengths, experimentally obtained COD values were found 15–19 % more than simulation ones due to rapidly induced plasticity at high crack dimensions. Solidification rate showed a significant influence on FCPR, for solidification rates 13.75 °C/s, 6.97 °C/s and 4.32 °C/s the obtained fatigue strength was 35.29 MPa, 36.26 MPa and 41.32 MPa, respectively.     

Ⅰ、Ⅱ型及复合型裂纹动态应力强度因子的有限元分析

对含有预制裂纹的中心穿透裂纹板和三点弯曲试样在动态载荷作用下进行了有限元模拟。前者裂纹面与载荷作用方向的夹角取15°~90°之间的6种情况,后者按纯Ⅰ型和纯Ⅱ型两种方式进行加载。得到了Ⅰ型和Ⅱ型动态应力强度因子的时间历程,并研究不同裂纹角对动态复合比的影响。结果表明:中心穿透裂纹板试样在15°和90°两种情况下KⅡ(t)和KⅠ(t)分别占主导成分;45°时KⅠ(t)和KⅡ(t)基本相同;随着裂纹面与载荷夹角的增加KⅠ(t)呈增加趋势而KⅡ(t)呈先增加后减小趋势。三点弯曲试样按纯Ⅰ型加载时KⅡ(t)基本为零,按纯Ⅱ型加载时KⅠ(t)幅值随时间而增加。     

对塑性诱导裂纹闭合几种影响因素的计算研究

基于塑性诱导裂纹闭合原理,通过弹塑性有限元方法的大规模数值计算分析,考察几何构形(带中心裂纹矩形板和中心孔双边裂纹矩形板)、材料强化模型(线性随动强化和非线性随动强化)、加载方式(等幅循环加载和等应力强度因子K循环加载)和应力比R等因素对疲劳裂纹张开、闭合规律的影响。结果表明,等幅加载中裂纹张开、闭合应力水平随裂纹长度变化且无明确规律可循。而在等K(给定应力比下保持最大应力强度因子不变)加载中,无论是使用不同材料强化模型,还是对应不同几何构形,用瞬时最大应力正则化的裂纹张开、闭合应力水平与裂纹长度无关。相同等K加载条件下,两种几何构形的裂纹张开应力强度因子均保持恒定且大小相近。两种随动强化模型对应的裂尖局部循环特性有差异,所获得的裂纹张开应力水平大小不同,但变化规律相似。文中结果可为更深入地理解疲劳裂纹扩展的驱动力机理提供帮助。