Probabilistic fatigue crack growth analysis of spot‐welded joints

This paper presents a probabilistic fatigue crack growth life prediction methodology for spot‐welded joints under variable amplitude loading history. The loading is multi‐axial and is obtained from transient response analysis of a vehicle model using finite‐element analysis. A three‐dimensional (3D) finite element model of a simplified joint with four spot welds is developed, and the static stress analysis of this joint is performed. Then the fatigue crack inside the base material sheet is modelled as a surface crack. Probabilistic crack growth model is combined with the stress analysis result to develop a probabilistic fatigue crack growth life prediction methodology for spot welds. This new method is implemented with MSC/NASTRAN and MSC/FATIGUE and is useful for the reliability assessment of spot‐welded joints against fatigue crack growth.     

FATIGUE LIFE ESTIMATION IN RESISTANCE SPOT WELDS: INITIATION AND EARLY GROWTH PHASE

Abstract— The main objective of this research is to develop a model of fatigue crack initiation and early crack growth in resistance spot welds that is specimen independent. This objective is achieved by examining the stress state around a resistance spot weld. A general expression for the structural stress around the weld is formulated that is dependent only on the loading immediately surrounding the weld. As such, it is specimen independent.
An additional objective is to explore the feasibility of applying this fatigue crack initiation model of life estimation using structural response data from finite element analysis (FEA). This numerical technique is often used for evaluating structural integrity of assemblies. Limited verification examples show that the structural stress range as calculated from FEA reaction load data is capable of describing fatigue crack initiation and early crack growth in cyclically loaded resistance spot welds.     

Fatigue of spot-welded lap joints

The fatigue properties of spot-welded lap joints under a constant mean load made from 1.2 and 3 mm sheet thickness stainless steel with one, two or three-spot welds in series are reported. A log plot of cyclic load range versus fatigue life shows that for given sheet thickness and fixed load range, fatigue life increases with the number of spot welds. Oil has a beneficial effect by increasing the fatigue life of the welded joints. A fracture mechanics analysis is carried out on the data by treating the spot weld as a crack. A log plot of initial stress intensity factor range versus fatigue life is a straight line which is independent of the number of spot welds. However, increasing the sheet thickness shifts the straight line upwards in the log plot, thus indicating a longer fatigue life for the same applied initial stress intensity factor range.     

Weld arrangement effects on the fatigue behavior of multi friction stir spot welded joints

In this study, the effects of friction stir spot weld arrangements as multi type on fatigue behavior of friction stir spot welded joints is investigated. The joints that are considered with five different styles for friction stir spot welded joints: one-row four joints parallel to loading direction, two-row four-joint specimen, one-row four joints perpendicular to the loading axis, three-row as diamond shape with four joints in each edge and five friction stir spot welded specimen in three rows that middle row consist three joints. The correlation between micro hardness, cyclic material constants and mechanical strength of different zones around the friction stir spot welds are assumed to be proportional to base material hardness. A non-linear finite element analysis was carried out for simulating tensile shear multi friction stir spot welded joints with ANSYS software by considering gap effects. Using the local stress and strain calculated with finite element analysis, fatigue lives of specimens were predicted with Morrow, modified Morrow and Smith–Watson–Topper (SWT) damage equations. Experimental fatigue tests of welded specimens have been carried out using constant amplitude load control servo-hydraulic fatigue testing machine. The results reveal that there is relatively good agreement between fatigue life predictions and experimental data in reasonable fatigue life regime.     

Vibration fatigue analysis for multi-point spot-welded joints based on frequency response changes due to fatigue damage accumulation

This study conducted a vibration fatigue analysis that considered changes in frequency response resulting from the cumulative fatigue damage to multi-point spot-welded joints in an automotive body. The S–N curve was obtained using a fatigue test for tensile-shear spot-welded (single-point) joint under constant amplitude load and a finite element analysis based on the Rupp/LBF model. In addition, a vibration fatigue analysis that considered changes in the frequency response due to the fatigue damage was conducted on multi-point spot-welded joints. The fatigue life of the spot-welded joints was computed by combining the transfer function, the S–N curve of the tensile-shear spot-welded joint and the input PSD. Furthermore, a vibration fatigue test using an electronic dynamic shaker was conducted to verify the results of the analysis. The fatigue life by the proposed method was in conformance with the test results.     

Local stress–strain field intensity approach to fatigue life prediction under random cyclic loading

According to the characteristic of the local behavior of fatigue damage, on the basis of stress field intensity approach, a theory of local stress–strain field intensity for fatigue damage at the notch is developed in this paper, which can take account of the effects of the local stress–strain gradient on fatigue damage at the notch. In order to calculate the local stress–strain field intensity parameters, an incremental elastic-plastic finite element analysis under random cyclic loading is used to determine the local stress–strain response. A local stress–strain field intensity approach to fatigue life prediction is proposed by means of elastic-plastic finite element method for notched specimens. This approach is used to predict fatigue crack initiation life, and good correlation was observed with U-shape notched specimens for normalized 45 steel.     

Fatigue life estimation of coach peel riveted joints using multi-axial fatigue criteria

This study investigates fatigue behaviour of riveted joints in a coach peel configuration under various load ranges and load ratios. Three well-known multi-axial fatigue criteria of Smith–Watson–Topper, Glinka and Fatemi–Socie are used to predict the fatigue life of the joint based on the stress and strain components obtained from a finite element analysis. A three-dimensional finite element model was developed with considering elastic–plastic behaviour of aluminium alloy 2024-T3 for the joint plates as well as frictional contact between all the contacting parts. Fatigue life estimation results agreed well with existing experimental data for the same joint. This verifies the finite element results and shows how well the multi-axial fatigue equations can predict fatigue life of the riveted joints. The finite element modelling approach may be then used with confidence for fatigue life estimations of different configurations of riveted joints.     

The Prediction of Fatigue Crack Initiation Life in Spot Welds

Abstract: In this paper, strain‐based fatigue life prediction method has been used to estimate the fatigue crack initiation life of spot‐welded joints of Mild Steel JSC270D and Ultra‐High Strength Steel JSC980Y. To do so, the joints were simulated using three‐dimensional finite‐element (FE) models, and then nonlinear FE analysis was performed to obtain the local stress and strain ranges and finally, the Morrow equation was applied to estimate the crack initiation lives. The results have been compared with those obtained from experimental crack growth morphology. In addition, the difference between fatigue limits for smooth specimens and spot‐welded joints for mentioned materials has been briefly discussed. It has been shown that mean stress values in the Ultra‐High Strength Steel can significantly decrease the fatigue limit of spot‐welded joint because even at very low load level the stresses exceed the yield point at the root of nugget of spot‐welded joint, while the amount of mean stress in the Mild Steel for the same load level is much less than that of Ultra‐High Strength Steel. The comparison between numerical results of fatigue crack initiation lives and experimental data provided good agreement between numerical predictions and crack growth morphology observations. The results also shows that in some cases, depending on the joint type, the life spent in the nucleation phase can be an important part of the final failure lifetime.     

Effects of mean stress and crack closure on fatigue life of spot welds

The effects of mean stress and crack closure on fatigue life of spot welds were investigated. A review showed that several of the previously proposed mean stress corrections give similar results. Fatigue tests on shear and peel loaded specimens were carried out, and the results agreed with the corrections reviewed. The present study shows that crack closure explains the mean stress effects observed. The crack opening force for spot welds was obtained, both experimentally from F–N curves with different load ratios and analytically from the available mean stress corrections. This was verified with detailed finite element simulations. Finally, the experiments and simulations indicate that the use of linear damage accumulation in fatigue life prediction of spot welds can be non‐conservative.     

Variable amplitude fatigue of spot welds

A new method for fatigue life prediction of spot welds subjected to variable amplitude loads is proposed. The method is based on the concept of crack closure and is experimentally verified with three different specimens and four different load signals with variable amplitude. Experimental fatigue lives were found to be within a factor of three from the predicted lives. To start with, the stress intensity factor history at the spot weld is calculated with a finite element analysis. Then, crack closure is taken into account: the crack opening stress intensity factor, which is assumed to be constant, is determined from the maximum and minimum in the history. All stress intensities lower than the crack opening level are filtered from the calculated history. The filtered history is then analysed with rain flow count. Finally, fatigue life is predicted with the Palmgren–Miner cumulative damage rule together with an effective (closure‐free) curve for spot welds. In addition, single overload tests were carried out to investigate the assumption of a constant crack opening stress.     

Fatigue life estimation of ultrasonic spot welded Mg alloy joints

Lightweight magnesium alloys are increasingly used in automotive and other transportation industries for weight reduction and fuel efficiency improvement. The structural application of magnesium components requires proper welding and fatigue resistance to guarantee their durability and safety. The objective of this investigation was to identify failure mode and estimate fatigue life of ultrasonic spot welded (USWed) lap joints of an AZ31B-H24 magnesium alloy. It was observed that the solid-state USWed joints exhibited a superior fatigue life compared with other welding processes. Fatigue failure mode changed from interfacial failure to transverse-through-thickness crack growth with decreasing cyclic load level, depending on the welding energy. Fatigue crack initiation and propagation occurred from both the notch tip inside the faying surface and the edge of sonotrode indentation-footprints due to the presence of stress concentration. A life prediction model for the spot welded lap joints developed by Newman and Dowling was adopted to estimate the fatigue lives of the USWed magnesium alloy joints. The fatigue life estimation, based on the fatigue crack growth model with the global and local stress intensity factors as a function of kink length and the experimentally determined kink angle, agreed fairly well with the obtained experimental results.     

Stress Intensity Factors for Spot Welds Joining Sheets of Unequal Thickness

Determination of stress intensity factor (SIF) at spot welds is one of the main problems in fatigue assessment of spot-welded structures using fracture mechanics methods. After a brief overview of the issue, we suggest an improvement in determination of SIFs at spot welds between sheets of unequal thickness, by adding the contributions of transverse shear stresses on the spot weld edge. T-stress at the spot weld is also discussed. A simplified finite element model in conjunction with application of the results obtained is illustrated as well.     

Microstructure and fatigue properties of Mg-to-steel dissimilar resistance spot welds

The structural application of lightweight magnesium alloys in the automotive industry inevitably involves dissimilar welding with steels and the related durability issues. This study was aimed at evaluating the microstructural change and fatigue resistance of Mg/steel resistance spot welds, in comparison with Mg/Mg welds. The microstructure of Mg/Mg spot welds can be divided into: base metal, heat affected zone and fusion zone (nugget). However, the microstructure of Mg/steel dissimilar spot welds had three different regions along the joined interface: weld brazing, solid-state joining and soldering. The horizontal and vertical Mg hardness profiles of Mg/steel and Mg/Mg welds were similar. Both Mg/steel and Mg/Mg welds were observed to have an equivalent fatigue resistance due to similar crack propagation characteristics and failure mode. Both Mg/steel and Mg/Mg welds failed through thickness in the magnesium sheet under stress-controlled cyclic loading, but fatigue crack initiation of the two types of welds was different. The crack initiation of Mg/Mg welds was occurred due to a combined effect of stress concentration, grain growth in the heat affected zone (HAZ), and the presence of Al-rich phases at HAZ grain boundaries, while the penetration of small amounts of Zn coating into the Mg base metal stemming from the liquid metal induced embrittlement led to crack initiation in the Mg/steel welds.     

Low-cycle fatigue life prediction of spot welds based on hardness distribution and finite element analysis

Elasto-plastic finite element analysis was carried out for single spot tensile shear spot welds with software ANSYS. According to the relationship between micro-hardness and strength, cyclic material constants of different zones in the periphery of spot welds were determined in accordance with hardness distribution, as well as base material fatigue parameters. Using the local stress and strain obtained from finite element analysis, fatigue lives of spot welds were predicted with Morrow’s modified Manson–Coffin equation and Smith–Watson–Topper damage equation. Life prediction results showed that both equations gave good agreement with experimental data within low-cycle fatigue life regime.     

Fatigue life prediction based on natural frequency changes for spot welds under random loading

Fatigue tests were carried out on tensile-shear spot-welded specimens under random loading; at the same time, natural frequencies at different life stages were measured. Test results were compared with that under constant amplitude loading. The relationship between damage and natural frequency change ratio established under constant amplitude loading is here modified. The nonlinear damage evolution equation was established using the damage represented by frequency change for spot welds. The fatigue life of spot welds under random loading was predicted with this damage evolution relationship using the rainflow counting method results, as well as other life prediction methods with different counting methods. Comparison of life prediction results showed that the method using changes of natural frequency can be an on-line approach and the predicted lives have a good agreement with the experimental data.     

Cyclic stress–strain response and crystal plasticity finite element analysis of AISI 9310 steel in biaxial fatigue loading

There are still many gaps in the research on the multiaxial fatigue failure mechanism of the gear shaft. In this paper, cyclic stress–strain response and biaxial fatigue damage characteristics of gear steel AISI 9310 were investigated. The specimens showed obvious cyclic softening characteristics at all phase angles, and the softening rate was directly associated with the initiation and propagation of cracks. The fractographies at different phase angles revealed that the specimens under out-of-phase loading suffered fatigue failure caused by a single crack source on the surface, while the fatigue crack under in-phase loading was gathered together by the propagation of different crack sources. Finally, the established crystal plastic finite element model showed a good prediction of the plastic strain energy density at different phase angles, and the maximum error was 13.03%. Furthermore, a biaxial fatigue life prediction method was proposed, with a maximum error of 39.5%.     

Fracture mechanics solutions to spot welds

Notch stress, stress intensity factors and J-integral at a spot weld are generally expressed by structural stresses around the spot weld. The determination of these parameters are then simplified as determining the structural stresses that can be calculated by a spoke pattern in finite element analysis. Approximate stress formulas for structural stress, notch stress and equivalent stress intensity factor are given for common spot-welded specimens. With the aid of the formulas, test data in terms of the original load can be easily transformed into the data in terms of the structural stress, notch stress or equivalent stress intensity factor at the spot weld. The formulas also facilitate the transfer of test data across different specimens. A measuring method is given for lap joints. The strain gauge technique developed for the tensile-shear specimen shows that all the structural stress, notch stress, stress intensity factors and J-integral at the spot weld can be determined by two strain gauges attached only to the outer surface of one sheet. The results presented here should be helpful for the analysis and testing of spot welds and for developing measuring methods for spot welds.     

矩形钢管K型节点复合型应力强度因子计算方法研究

相比圆形钢管桁架,矩形钢管桁架在施工方面具有一定的技术经济优势,并已广泛应用于桥梁工程中,鉴于断裂力学法评估该类结构疲劳性能的需要,该文探讨矩形钢管K型节点在支管拉压平衡荷载作用下的应力强度因子计算方法。提出带表面裂纹矩形钢管K型节点有限元建模方法,并与试验进行验证;通过参数分析,研究节点和裂纹几何参数对节点几何修正系数Y的影响;多元回归分析拟合得到矩形钢管K型节点应力强度因子计算公式及其修正后的设计计算公式,并通过算例分析给出基于断裂力学的钢管节点剩余疲劳寿命评估方法。结果表明：有限元结果与试验结果比值均值为1.012,变异系数为0.034,两者最大差值仅为5.5%,表明有限元计算结果可靠;节点几何参数2γ、τ与Y呈正相关,θ与Y呈负相关,其原因主要在于节点相贯线处刚度和受拉荷载变化,改变了裂纹尖端应力场,从而影响了裂纹扩展速率,裂纹几何参数c/a与Y呈正相关,但影响不明显,a/t₀与Y呈负相关;提出的应力强度因子计算公式与有限元计算结果吻合良好,且修正后用于设计的计算公式具有95%的可靠度;圆形钢管节点应力强度因子高于矩形钢管节点,平均提高24.9%,说明在相...     

Analysis of fatigue crack behaviour based on dynamic response simulations and experiments for tensile-shear spot-welded joints

Fatigue crack initiation and propagation behaviours were studied based on the dynamic response simulation by the three‐dimensional finite‐element analysis (FEA) and dynamic response experiments for tensile‐shear spot‐welded joints. The entire fatigue propagation behaviour from the surface elliptical cracks at the initiation stage to the through thickness cracks at the final stage was taken into consideration during the three‐dimensional FEA dynamic response simulations. The results of the simulations and experiments found that the fatigue cracks of spot‐welded joint from initial detectable crack sizes to crack propagation behaviour could be described by three stages. Approximately one‐half of the total fatigue life was taken in stage I, which includes micro‐crack nucleation and the small crack growth process; 20% of the total fatigue life in stage II, in which the existing surface crack propagates through the thickness of sheet and 30% of the total fatigue life in stage III, during which the through thickness crack propagates along the direction of plate width to the final failure. According to the relationship between the crack length and depth and the dynamic response frequency during the simulated fatigue damage process, the definition of fatigue crack initiation and propagation stages was proposed. The analysis will provide some information for the fatigue life prediction of the spot‐welded structures.     

Biaxial fatigue for proportional and non‐proportional loading paths

In order to study the use of a local approach to predict crack‐initiation life on notches in mechanical components under multiaxial fatigue conditions, the study of the local cyclic elasto‐plastic behaviour and the selection of an appropriate multiaxial fatigue model are essential steps in fatigue‐life prediction. The evolution of stress–strain fields from the initial state to the stabilized state depends on the material type, loading amplitude and loading paths. A series of biaxial tension–compression tests with static or cyclic torsion were carried out on a biaxial servo‐hydraulic testing machine. Specimens were made of an alloy steel 42CrMo4 quenched and tempered. The shear stress relaxations of the cyclic tension–compression with a steady torsion angle were observed for various loading levels. Finite element analyses were used to simulate the cyclic behaviour and good agreement was found. Based on the local stabilized cyclic elastic–plastic stress–strain responses, the strain‐based multiaxial fatigue damage parameters were applied and correlated with the experimentally obtained lives. As a comparison, a stress‐invariant‐based approach with the minimum circumscribed ellipse (MCE) approach for evaluating the effective shear stress amplitude was also applied for fatigue life prediction. The comparison showed that both the equivalent strain range and the stress‐invariant parameter with non‐proportional factors correlated well with the experimental results obtained in this study.