Fatigue fracture in plates in tension and out-of-plane shear

Straight cracks near a stiffening element, or curved cracks, in a pressurized shell can be subjected to out-of-plane tearing stresses in addition to normal tensile stresses due to the membrane stresses in the shell. To predict the rate of fatigue crack growth in such situations a theory and a crack growth rate correlation are needed. Such loadings are modelled as a superposition of plane stress tensile fracture (mode I) and Kirchhoff plate theory shearing fracture (mode 2). Finite element analyses using shell elements are used to compute the energy release rate and stress intensity factors associated with the loading. Three fatigue crack growth rate experiments were carried out on sheets of 2024-T3 aluminium alloy loaded in tension and torsion. The first set of experiments is constant amplitude fatigue crack growth tests. The second consists of experiments where crack closure is artificially eliminated to determine the rate of crack growth in the absence of crack face contact. The third is a set of constant stress intensity factor amplitude tests. The results all show that as the crack grows extensive crack face contact occurs, retarding crack growth. In the absence of crack face contact, however, the addition of out-of-plane shear loading increases the crack growth rate substantially.     

Fatigue life prediction of cracked attachment lugs using XFEM

In the present paper, a three dimensional finite element method (FEM) is used to compute the stress intensity factor (SIF) in straight lugs of Aluminum 7075-T6. Extended finite element method (XFEM) capability available in ABAQUS is used to calculate the stress intensity factor. Crack growth and fatigue life of single through-thickness and single quarter elliptical corner cracks in attachment lug are estimated and then compared with the available experimental data for two different load ratios equal to 0.1 and 0.5. The SIF calculated from XFEM shows that the introduction of different loading boundary conditions significantly affect the estimated fatigue life.     

Analysis of fatigue crack growth in an attachment lug based on the weight function technique and the UniGrow fatigue crack growth model

A generalised step-by-step procedure for fatigue crack growth analysis of structural components subjected to variable amplitude loading spectra has been presented. The method has been illustrated by analysing fatigue growth of planar corner crack in an attachment lug made of Al7050-T7451 alloy.Stress intensity factors required for the fatigue crack growth analysis were calculated using the weight function method. In addition, so-called “load-shedding” effect was accounted for in order to determine appropriate magnitudes of the applied stress intensity factors. The rate of the load shedding was determined with the help of the finite element (FE) method by finding the amount of the load transferred through the cracked ligament. The UniGrow fatigue crack growth model, based on the material stress–strain behaviour near the crack tip, has been used to simulate the fatigue crack growth under two variable amplitude loading spectra. The comparison between theoretical predictions and experimental data proved the ability of the UniGrow model to correctly predict fatigue crack growth behaviour of two-dimensional planar cracks under complex stress field and subjected to arbitrary variable amplitude loading.     

Stress intensity factors for fatigue cracking of round bars

The stress intensity factor for a single edge crack of either straight or circular front in a round bar has been determined using both the degenerated quarter-point isoparametric finite element and experimental fatigue crack growth data, and compared with values found by earlier investigators.The results of this study confirm that the stress intensity factors for straight edged surface cracks are lower in round bars than in square bars and a comparison of finite element and experimental results indicates that the effective stress intensity factor at the centre of the fatigue crack front in a round bar is 17% greater than its theoretical value.A correction function is proposed to account for the effect on the stress intensity factor of the circular boundary of a round bar.     

SMALL CRACK GROWTH AND FATIGUE LIFE PREDICTIONS FOR HIGH-STRENGTH ALUMINIUM ALLOYS: PART I—EXPERIMENTAL AND FRACTURE MECHANICS ANALYSIS

The small crack effect was investigated in two high-strength aluminium alloys: 7075-T6 bare and LC9cs clad alloy. Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks. In the experimental program, fatigue tests, small crack and large crack tests were conducted under constant amplitude and Mini-TWIST spectrum loading conditions. A pronounced small crack effect was observed in both materials, especially for the negative stress ratios. For all loading conditions, most of the fatigue life of the SENT specimens was shown to be crack propagation from initial material defects or from the cladding layer. In the analysis program, three-dimensional finite element and weight function methods were used to determine stress intensity factors and to develop SIF equations for surface and corner cracks at the notch in the SENT specimens. A plasticity-induced crack-closure model was used to correlate small and large crack data, and to make fatigue life predictions. Predicted crack-growth rates and fatigue lives agreed well with experiments. A total fatigue life prediction method for the aluminium alloys was developed and demonstrated using the crack-closure model.     

含单侧预制裂纹梁的冲击动态断裂过程试验研究

利用动焦散线试验方法研究了冲击下预制裂纹梁的动态断裂行为,对比分析了冲击荷载作用下单裂纹与双裂纹试件的应力强度因子、扩展轨迹以及速度、加速度等参数的变化规律。试验结果表明:冲击荷载作用下,含双裂纹且主裂纹在冲击点正下方的试件起裂时间最早,裂纹扩展后期朝向次裂纹方向发生较小的偏移;含Ⅰ型单裂纹的试件起裂时间次之,裂纹扩展路径呈直线;含双裂纹且两条裂纹均偏置于冲击点的试件起裂时间最晚,扩展过程中发生明显的曲裂现象。同时,裂纹扩展过程中曲裂现象越严重,裂纹扩展的最大速度就越小。在落锤冲击试件到试件断裂的整个阶段,应力强度因子一直表现出振荡变化。含双裂纹的试件,在主裂纹扩展中期,次裂纹上的应力强度因子有一个快速下降的过程。     

FATIGUE CRACK GROWTH UNDER MIXED-MODE I AND II LOADING

Abstract— Mixed-mode fatigue crack growth has been studied using four point bend specimens under asymmetric loads. A detailed finite element analysis provides the stress intensity factors for curved cracks under different mixed-mode load conditions. Both fatigue crack growth direction and crack growth rate are studied. The maximum tangential stress and the minimum strain energy density criteria were found to provide satisfactory predictions of the crack growth directions. An effective stress intensity factor was used to correlate the fatigue crack growth rates successfully. It is found that the use of mode I fatigue crack growth rate properties results in a conservative crack growth rate prediction for mixed-mode load conditions.     

Fatigue crack growth analyses of offshore structural tubular joints

This study investigated various aspects of a fatigue crack growth analysis, ranging from the stress intensity factor solutions to the simulation of a fatigue crack coalescence process of a tubular joint weld toe surface flaw. Fracture mechanics fatigue crack growth analyses for offshore structural tubular joints are not simple, because of the difficulty to calculate the stress intensity factors due to their geometric complexity. The fully mixed-mode stress intensity factors of nine weld toe surface cracks of an X-shaped tubular joint under tension loading were calculated by detailed three-dimensional finite element analyses. Using these stress intensity factor solutions, a fatigue crack growth study was performed for the X-joint until (the crack surface length grew to two times the tube thickness. Through this study, the crack shape change during the fatigue crack propagation was investigated in detail. Fatigue life calculations were also performed for a range of crack geometries using the stress intensity factor solutions of the nine flaws. These calculations indicate that the natural fatigue crack growing path for a crack is its quickest growing path. The study demonstrated that detailed fracture mechanics fatigue analyses of tubular joints can be practical using the finite element method.     

Strength of sandwich beams with mid-plane debondings in the core

Sandwich beams containing cracks in the mid-plane of the core are investigated. The cracked part is subjected to a constant remote shear stress field. Beams with different cross-section geometries and materials were analyzed by the finite element method (FEM) in order to compute the stress intensity factors at the crack tips. An analytical approach for estimation of the energy release rate, based on a potential energy calculation, is presented that agrees well with results from the FE analyses. Results from four-point bending tests with cracked beams show that the fracture load can be accurately predicted. The simplicity of the analytical model makes it possible to compute critical crack lengths and safety factors for various types of sandwich beams.     

Closure-free biaxial fatigue crack growth rate and life prediction under various biaxiality ratios in SAE 1045 steel

Biaxial fatigue tests were performed on thin-walled tubular 1045 steel specimens in a test fixture that applied internal and external pressure and axial load. There were two test series, one in which constant amplitude fully reversed strains (CAS) were applied and another in which large periodic compressive overstrain (PCO) cycles causing strains normal to the crack plane were inserted in a constant amplitude history of smaller strain cycles. Ratios of hoop strain to axial strain of λ = ?1, ?0.625, ?ν and +1 were used in each test series. Fatigue crack growth behaviours under CAS and PCO histories were compared, and revealed that the morphology of the fracture surface near the crack tip and the crack growth rate changed dramatically with the application of the compressive overstrains. When the magnitude of the compressive overstrains was increased, the height of the fracture surface irregularities was reduced as the increasing overstrain progressively flattened the fracture surface asperities near the crack tip. The reduced asperity height was accompanied by drastic increases in crack growth rate and decreases in fatigue life. Using a pressurizing device attached to the confocal scanning laser microscope (CSLM), crack opening measurements were obtained. Crack opening measurements showed that the biaxial cracks were fully open at zero internal pressure for block strain histories containing in-phase PCO cycles of yield stress magnitude. Therefore, for the shear-strained samples, there was no crack face interference and the strain intensity range was fully effective. For PCO tests (with biaxial strain ratios of ?0.625 and +1), effective strain intensity data were obtained from tests with positive stress ratios for which cracks did not close. A number of strain intensity parameters derived from well-known fatigue life parameters were used to correlate fatigue crack growth rates for the various strain ratios investigated. Predicted fatigue lifetimes based on a fatigue crack growth rate prediction program using critical shear plane parameters showed good agreement with the experimental fatigue life data.     

Extended Isogeometric Analysis (XIGA) of Fatigue Life in Attachment Lug

In the present paper, extended isogeometric analysis (XIGA) is used to compute the stress intensity factor (SIF) in straight lugs of Aluminum 7075-T6. XIGA uses the non-uniform rational B-spline (NURBS) functions and enrichment functions through the partition of unity. The Heaviside function is enriched to capture jump at the crack faces, while the analytical asymptotic solutions are incorporate with NURBS to perform the crack tip singularity. The XIGA-based SIF of edge-cracked plate and straight attachment lug are compared with analytical solution and extended finite element method capability available in ABAQUS. Also, crack growth and fatigue life of single crack in attachment lug are estimated and then compared with the available experimental data for two different load ratios equal to 0.1 and 0.5. The SIF calculated from XIGA are in reasonable agreement with the available data.     

Sustained Mode I and Mode II fatigue crack growth in flat plates

This study was conducted to contribute to the understanding of fatigue crack growth under mixed mode loading. This was accomplished by developing and analyzing a flat plate specimen capable of maintaining crack growth on a plane oblique to the direction of the applied load. Several specimens were built and exposed to controlled fatigue loading in the laboratory. These specimens were then modeled using finite elements to determine the stress intensity factors (SIF). For the “Mode I/Mode II” specimens developed, the crack was forced to grow in a direction other than perpendicular to the load. The resulting crack front did not remain straight and flat, but stabilized into a curved or warped shape. Based on finite element analyses of these curved specimen cracks, it is concluded that the SIR were predominantly Mode I, with the Mode II and III SIR being negligible.     

Influence of overloads and block loading sequences on Mode III fatigue crack propagation in A469 rotor steel

A study has been made of the influence of variable amplitude loading on Mode III (anti-plane shear) fatigue crack propagation in circumferentially-notched cylindrical specimens of ASTM A469 rotor steel (yield strength 621 MN/m²), subjected to cyclic torsional loading. Specifically, transient crack growth behavior has been examined following spike and fully-reversed single overloads and for low-high and high-low block loading sequences, and the results compared to equivalent tests for Mode I (tensile opening) fatigue crack growth. It is found that the transient growth rate response following such loading histories is markedly different for the Mode III and Mode I cracks. Whereas Mode I cracks show a pronounced transient retardation following single overloads (in excess of 50% of the baseline stress intensity), Mode III cracks show a corresponding acceleration. Furthermore, following high-low block loading sequences, the transient velocity of Mode I cracks is found to be less than the steady-state velocity corresponding to the lower (current) load level, whereas for Mode III cracks this transient velocity is higher. Such differences are attributed to the fact that during variable amplitude loading histories. Mode III cracks are not subjected to mechanisms such as crack tip blunting/branching and fatigue crack closure, which markedly influence the behavior of Mode I cracks. The effect of arbitrary loading sequences on anti-plane shear crack extension can thus be analyzed simply in terms of the damage accumulated within the reversed plastic zones for each individual load reversal. Based on a micro-mechanical model for cyclic Mode III crack advance, where the crack is considered to propagate via a mechanism of Mode II shear (along the main crack front) of voids initiated at inclusion close to the crack tip, models relying on Coffin-Manson damage accumulation are developed which permit estimation of the cumulative damage, and hence the crack growth rates, for arbitrary loading histories. Such models are found to closely predict the experimental post-overload behavior of Mode III cracks, provided that the damage is confined to the immediate vicinity of the crack tip, a notion which is consistent with fractographic analysis of Mode III fracture surfaces.     

Debonding and crack kinking in foam core sandwich beams—I. Analysis of fracture specimens

Sandwich beam specimens, recently developed for the study of facing/core debond fracture, were analyzed using the finite element method. Peel fracture was approached using a modified double cantilever beam (DCB) sandwich specimen with a precrack between the facing and core, while shear fracture employed a modification of the ASTM block shear test to include a facing/core precrack. Complex and conventional stress intensity factors were calculated for bimaterial cracks located between facing and bondlayer and bondlayer and core over a large range of core moduli. Overall, much larger stress intensity factors were observed for an interfacial crack between the facing and bondlayer than for a crack between the bondlayer and core for both types of specimens. Crack kinking analysis of the DCB specimen revealed that the debond tends to remain interfacial for stiff core materials, but may deflect into the core for compliant core materials. In shear loading of a debonded sandwich beam it was demonstrated that crack kinking is possible for any core material.     

FRACTURE MECHANICS ASSESSMENT OF PLANAR BRANCHED CRACKS IN AN EQUIBIAXIAL STRESS FIELD

Abstract A simplified fracture mechanics assessment is presented of branched planar cracks in an equibiaxial stress state. In linear-elastic fracture mechanics the stress intensity factors which characterize the load at the crack tips depend, for a given external load, only on the crack geometry. The stress intensity factors of a large number of branched cracks were evaluated using the Boundary Element method, and correlations between the stress intensity factors and the crack geometry were investigated. Formulae are presented which assign an individual effective crack length to each crack tip of a branched crack and hence allow approximate stress intensity factors to be determined for very complicated crack geometries. An algorithm is used for the stochastic simulation of an irregular crack pattern formation in thermal fatigue.     

Modelling considerations for stress intensity factor solutions at pin‐loaded holes

This work summarizes investigations into stress intensity factor solutions for straight, through cracks at pin‐loaded holes in thin sheets. As shown in this work, several assumptions contribute to the fidelity of a stress intensity factor solution that includes the distribution of contact pressure on the pin‐hole interface, the friction coefficient at the pin‐hole interface, the crack initiation angle, and stiffness mismatch. These assumptions lead to higher or lower stress intensity factor solutions as demonstrated by results generated from advanced finite element analyses of the relevant geometries. Results shown here contribute to the development of a realistic and conservative set of assumptions for stress intensity factor solutions. Conclusions drawn from this work are applicable to cracks originating at pin‐loaded holes in plates and lugs.     

Stress intensity factor solutions for estimation of fatigue lives of laser welds in lap-shear specimens

Fatigue behavior of laser welds in lap-shear specimens of high strength low alloy (HSLA) steel is investigated based on experimental observations and two fatigue life estimation models. Fatigue experiments of laser welded lap-shear specimens are first reviewed. Analytical stress intensity factor solutions for laser welded lap-shear specimens based on the beam bending theory are derived and compared with the analytical solutions for two semi-infinite solids with connection. Finite element analyses of laser welded lap-shear specimens with different weld widths were also conducted to obtain the stress intensity factor solutions. Approximate closed-form stress intensity factor solutions based on the results of the finite element analyses in combination with the analytical solutions based on the beam bending theory and Westergaard stress function for a full range of the normalized weld widths are developed for future engineering applications. Next, finite element analyses for laser welded lap-shear specimens with three weld widths were conducted to obtain the local stress intensity factor solutions for kinked cracks as functions of the kink length. The computational results indicate that the kinked cracks are under dominant mode I loading conditions and the normalized local stress intensity factor solutions can be used in combination with the global stress intensity factor solutions to estimate fatigue lives of laser welds with the weld width as small as the sheet thickness. The global stress intensity factor solutions and the local stress intensity factor solutions for vanishing and finite kinked cracks are then adopted in a fatigue crack growth model to estimate the fatigue lives of the laser welds. Also, a structural stress model based on the beam bending theory is adopted to estimate the fatigue lives of the welds. The fatigue life estimations based on the kinked fatigue crack growth model agree well with the experimental results whereas the fatigue life estimations based on the structural stress model agree with the experimental results under larger load ranges but are higher than the experimental results under smaller load ranges.     

Fatigue damage of low amplitude cycles in low carbon steel

The influences of low load cycles on fatigue damage in 0.15% C steel (C15E, No. 1.1141) are investigated in the very high cycle fatigue regime using ultrasonic fatigue testing equipment. Constant amplitude (CA) endurance limits at limiting lifetime of 10⁹ cycles are determined in cyclic tension–compression and cyclic torsion tests. Non-propagating fatigue cracks are found in specimens subjected to cyclic torsion loading at the endurance limit. The endurance limit is considered as maximum stress amplitude where possibly initiated fatigue cracks do not propagate to failure. Two-step variable amplitude (VA) tension–compression endurance tests are performed with repeat sequences consisting of high stress amplitudes above the endurance limit and far greater number of cycles below. The measured lifetimes are compared with linear damage accumulation calculations (Miner calculations). If the high stress amplitude is more than approximately 13% above the CA endurance limit, detrimental influences of low load cycles and failures at low damage sums are found. If the high stress is less than 13% above the CA endurance limit, numerous low load cycles cause prolonged fatigue lifetimes and specimens can sustain large damage sums without failure. Two-step VA fatigue crack growth investigations show that load cycles below the threshold stress intensity accelerate crack growth, if the high stress intensity is 18% or more above the CA threshold stress intensity. In repeat sequences with high stress intensities 14% above threshold stress intensity, low load cycles decelerated and stopped fatigue crack growth. Low load cycles can reduce or prolong fatigue lifetimes of low carbon steel and one reason is the accelerated or retarded fatigue crack growth due to numerous low amplitudes, and the maximum load amplitude of a VA load sequence determines whether detrimental or beneficial effects prevail.     

Crack initiation and crack propagation under thermal cyclic loading

Theoretical and experimental investigations of crack initiation and crack propagation under thermal cyclic loading are presented. For the experimental investigation a special thermal fatigue test rig has been constructed in which a small circular cylindrical specimen is heated up to a homogeneous temperature and cyclically cooled down under well defined thermal and mechanical boundary conditions by a jet of cold water. At the end of the cooling phase the specimen is reheated to the initial temperature and the following cycle begins. The experiments are performed with uncracked and mechanically precracked specimens of the German austenitic stainless steel X6CrNi 1811.

In the crack initiation part of the investigation the number of load cycles to initiate cracks under thermal cyclic load is compared to the number of load cycles to initiate cracks under uniaxial mechanical fatigue loading at the same strain range as in the cyclic thermal experiment. The development of initiated cracks under thermal cyclic load is compared with the development of cracks under uniaxial mechanical cyclic load.

In the crack propagation part of the investigation crack growth rates of semi-elliptical surface cracks under thermal cyclic loading are determined and compared to suitable mechanical fatigue tests made on compact-tension and four-point bending specimens with semi-elliptical surface cracks. The effect of environment, frequency, load shape and temperature on the crack growth rate is determined for the material in mechanical fatigue tests.

The theoretical investigations are based on the temperature distribution in the specimen, which is calculated using finite element programs and compared to experimental results. From the temperature distribution, elastic and elastic-plastic stress distributions are determined taking into account the temperature dependence of the material properties. The prediction of crack propagation relies on linear-elastic fracture mechanics. Stress intensity factors are calculated with the weight function method and crack propagation is determined using the Paris relation.

To demonstrate the quality of the crack growth analysis the experimental results are compared to the prediction of crack propagation under thermal cyclic load.     

基于失效评定图(FAD)研究含疲劳裂纹T型圆钢管节点的安全性

失效评定曲线(FAD)常用来评价焊接结构在出现裂纹后的安全性,为了验证这种曲线在评价焊接管结构在节点部位出现疲劳裂纹后安全性的适用性,采用实验测试和有限元分析的方法研究了3个含疲劳裂纹的T型管节点试件在静力作用下的极限承载能力及破坏过程。3个T型管节点试件首先进行疲劳实验在焊趾处产生表面裂纹,然后通过在支管端部施加轴向拉力作用检测节点的破坏过程。基于自行开发的含表面裂纹T型管节点的有限元网格自动产生程序以及ABAQUS分析软件,研究了在管节点破坏过程中表面裂纹最深点的应力强度因子大小,并通过实验的荷载-位移曲线确定了T节点试件的塑性极限承载力。在这些结果的基础上,验证了FAD在评价含疲劳裂纹的焊接管节点安全性方面的适用性。研究结果标明:FAD在评价含疲劳裂纹管节点的安全性方面是安全可靠的,但偏于保守。