FRACTURE MECHANICS ANALYSIS OF FATIGUE RESISTANCE OF SPOT WELDED COACH-PEEL JOINTS

Resistance spot welding is the most widely used joining method in automobile manufacture. The number, location, and quality of welds are some of the factors that influence the performance of welded subassemblies, and body panel structures. Therefore, design optimization requires knowledge of not only sheet metal behavior, but also weld behavior under service loadings. A linear elastic fracture mechanics approach was employed in this study to estimate the fatigue lives of spot welds subjected to tearing loads in a coach-peel specimen. Using a finite element method (FEM), the initial J-integral values for five coach-peel joints, each with different geometries, were calculated. Fatigue tests conducted on the same weld geometries provided life data. The experimental data were used to derive a relationship between the initial elastic J-integral values (ΔJ_e) and the fatigue life. It was found that the total fatigue life (N_f) of a weld at one applied stress range is related to its range of J-integral value such that a ΔJ_e vs N_f log-log plot gives a straight line relationship. This relationship can be used to evaluate the effects of geometrical variables on the fatigue life of coach-peel joints. The results show that, within the dimension range studied here, the effects of geometrical variables on the fatigue resistance can be ranked in the following decreasing order: weld eccentricity, sheet thickness and weld nugget diameter.     

Fatigue strength assessment of laser stake‐welded web‐core steel sandwich panels

This paper investigates the fatigue strength assessment of web‐core steel sandwich panels. The production of these structures is made possible by laser stake welding. The investigation in this study considered two series of panels, one being an empty steel structure and the other filled with in situ polyurethane foam in order to increase the panel stiffness. Both series were tested under cyclic bending loading condition (R = 0) until one of the panel joints failed completely. A 3D panel bending response was analysed using finite element method. The J‐integral values at the panel joints were obtained by means of plane strain finite element analysis and by using displacements from 3D panel response. The influence of the weld geometry on the J‐integral value was investigated. It was found that the J‐integral value is similar in the cases of the average and critical geometry. The contact between the joint plates is possible in some cases, but its influence proved to be insignificant for the fatigue strength assessment. The study further shows that by using the average geometry, the J‐integral approach was able to identify the critical panel joints and present the fatigue strength results from both panel series in a narrow scatterband. The fatigue strength at two million cycles obtained for the panels within this study was in agreement with the laser stake welds and other steel joint types from previous studies. However, the slope of the panels fatigue resistance curve was found to be shallower than in the case of joints.     

Modellierung des Ermüdungsrisswachstums in Schweißverbindungen unter Berücksichtigung von Schweißeigenspannungen

The present paper contains research results determined within the framework of a project called IBESS (?Integrale Bruchmechanische Ermittlung der Schwingfestigkeit von Schweißverbindungen“) by the Materials Mechanics Group of the Technische Universität Darmstadt [1]. Aim is to calculate the fatigue life of welded joints by taking into account the effect of residual stresses and the influence of the weld toe geometry. Here, the fatigue life is regarded as period of short fatigue crack growth. Two and three dimensional finite element models, with cracks as initial defects, are constructed for this purpose. Fatigue crack growth analyses are performed by using the node release technique together with the finite element program ABAQUS. The welding residual stresses as well as the plasticity induced crack closure effects are considered. Structural calculations are performed in order to introduce residual stress fields in finite element models. The calculated compressive residual stress field matches the measured one especially in the weld notch area. The effective cyclic J‐integral (ΔJ_eff) is used as crack tip parameter in a relation similar to the Paris equation for the calculation of the fatigue life. For this purpose, a Python code was written for the determination of ΔJ_eff at every crack length phase. The calculated fatigue lives were compared with experimental data and a good accordance between both results was achieved. The impact of welding residual stresses on ΔJ_eff as well as on the fatigue life during short crack growth was investigated. As expected, results revealed that at lower stress amplitude, a compressive residual stress field is favorable to the fatigue life, whilst a tensile residual stress field is unfavorable. The influence of residual stresses can be neglected only for large load amplitudes.     

J-integral analysis of cord-rubber serpentine belt using neural-network-based material modelling

A known factor that limits the performance of automotive front‐end accessory serpentine belt drive is cracking of the elastomer located in the rib tip. In this paper, fracture experiments were conducted using single‐edge notched tension (SENT) specimens to study the fracture behaviour of a belt rib compound. A finite‐element modelling method utilizing singular elements for crack in rubber solid was proposed and implemented in both plane‐stress and 3D solid models using ABAQUS. A newly developed neural‐network‐based model was used to represent a nonlinear elastic belt rib rubber compound. The crack finite‐element model, along with the neural‐network‐based material model, was verified with analytical and experimental results. A global–local finite‐element procedure was developed to evaluate the J‐integral for mode‐I through‐the‐thickness crack in V‐ribbed belt rib. Effects of pre‐crack length, pulley pre‐load and backside pulley displacement were investigated.     

Plastic collapse load prediction and failure assessment diagram analysis of cracked circular hollow section T‐joint and Y‐joint

This paper concerns the validation of standard safety assessment procedure given in BS 7910 for cracked circular hollow section T‐joint and Y‐joint, using the finite element (FE) results. A robust and efficient FE mesh generator is developed to produce the 3D models of the cracked joints and to calculate the elastic J‐integral (J_e) and elastic–plastic J‐integral (J_ep) values of the crack respectively. In order to verify its accuracy and convergence, the plastic collapse loads (P_c) obtained from experimental tests and FE predictions are compared; they agree very well with each other. It is also found from experimental tests that the plastic collapse loads (P_c) predicted using the BS 7910 reduction factor (F_AR) are safe and conservative. Subsequently, the failure assessment diagrams (FADs) of five cracked T‐joints and three cracked Y‐joints are constructed using the FE results, following the J‐integral method, which is classified as Level 3C in BS 7910. Thereafter, a comparison between the constructed FAD curves and the standard Level 2A curve is carried out, and it is observed that the safety assessment results using the standard Level 2A curve might be unsafe because some parts of the constructed FAD curves fall inside of the standard one. A penalty factor of 1.15 working on both the elastic–plastic J‐integral and plastic collapse load (P_c) is proposed to move all the constructed FAD curves just outside of the standard Level 2A curve.     

Fatigue life prediction and failure analysis of a gas turbine disc using the finite-element method

A numerical prediction of the life of a gas turbine model disc by means of the finite‐element technique is presented and the solution is compared with an experimental rim‐spinning test. The finite‐element method was used to obtain the K solution for a disc with two types of cracks, both at the notch root of the blade insert and located in the corner and in the centre. A crack aspect ratio of (a/c) = 1 was assumed. The fracture mechanics parameters J‐integral and K were used in the assessment, which were computed with linear elastic and elastic–plastic material behaviour. Using a crack propagation program with appropriate fatigue‐creep crack growth‐rate data, previously obtained in specimens for the nickel‐based superalloy IN718 at 600 °C, fatigue life predictions were made. The predicted life results were checked against experimental data obtained in real model discs. The numerical method, based on experimental fatigue data obtained in small laboratory specimens, shows great potential for development, and may be able to reduce the enormous costs involved in the testing of model and full‐size components.     

Driving forces for localized corrosion‐to‐fatigue crack transition in Al–Zn–Mg–Cu

Research on fatigue crack formation from a corroded 7075‐T651 surface provides insight into the governing mechanical driving forces at microstructure‐scale lengths that are intermediate between safe life and damage tolerant feature sizes. Crack surface marker‐bands accurately quantify cycles (N_i) to form a 10–20 μm fatigue crack emanating from both an isolated pit perimeter and EXCO corroded surface. The N_i decreases with increasing‐applied stress. Fatigue crack formation involves a complex interaction of elastic stress concentration due to three‐dimensional pit macro‐topography coupled with local micro‐topographic plastic strain concentration, further enhanced by microstructure (particularly sub‐surface constituents). These driving force interactions lead to high variability in cycles to form a fatigue crack, but from an engineering perspective, a broadly corroded surface should contain an extreme group of features that are likely to drive the portion of life to form a crack to near 0. At low‐applied stresses, crack formation can constitute a significant portion of life, which is predicted by coupling macro‐pit and micro‐feature elastic–plastic stress/strain concentrations from finite element analysis with empirical low‐cycle fatigue life models. The presented experimental results provide a foundation to validate next‐generation crack formation models and prognosis methods.     

Effect of crack front non-linearity on results from compact tension tests

As a consequence of a fracture toughness testing program where several of the compact tension specimens were subsequently found to have fatigue pre-crack profiles invalidated by the criteria of British Standards BS5447, computations have been made of the stress intensity factor K _I and the contour integral J for a sample of four invalid specimens to establish the error involved. A finite element analysis was carried out on models of the specimens, and the results were compared to those obtained for similar, but valid pre-crack profiles. A further comparison was also made of the K _I values obtained by the finite element modelling and the analytical approach of BS5447.     

Fatigue assessment of refill friction stir spot weld in AA 2024‐T3 similar joints

Refill friction stir spot welding is a solid‐state process technology that is suitable for welding lightweight materials in similar or dissimilar overlapped configuration. In this study, the fatigue behaviour of single overlapped spot joints of AA2024‐T3 was studied. To statistically analyse the fatigue data, a 2‐parameter Weibull distribution was deployed, considering several reliabilities (R_e = 0.99, R_e = 0.90, R_e = 0.5, R_e = 0.10). To obtain an optimized weld parameter according to the fatigue behaviour, 2 different weld conditions were studied, taking into account the effect of the hook formation. The microstructure analyses and microhardness profiles showed great similarity in both weld conditions. However, these conditions presented distinct interfacial hook profiles, in which the interfacial hook downward represented better fatigue life and infinite fatigue life at 15% of the maximum strength load. The fracture surfaces obtained from 3 different fracture modes were investigated by using scanning electron microscopy; the crack was tracked and described according to its fracture mechanisms from its initiation until the final failures. It was observed that the crack is initiated at hook profile.     

Fatigue crack propagation behavior of RC beams strengthened with CFRP under cyclic bending loads

A fatigue crack propagation equation of reinforced concrete (RC) beams strengthened with a new type carbon fiber reinforced polymer was proposed in this paper on the basis of experimental and numerical methods. Fatigue crack propagation tests were performed to obtain the crack propagation rate of the strengthened RC beams. Digital image correlation method was used to capture the fatigue crack pattern. Finite element model of RC beam strengthened with carbon fiber reinforced polymer was established to determinate J‐integral of a main crack considering material nonlinearities and degradation of material properties under cyclic loading. Paris law with a parameter of J‐integral was developed on the basis of the fatigue tests and finite element analysis. This law was preliminarily verified, which can be applied for prediction of fatigue lives of the strengthened RC beams.     

超声载荷下TC4钛合金的疲劳寿命分析

通过计算裂纹尖端应力强度因子及疲劳裂纹扩展速率da/d N,由C.Paris模型推导出安全寿命Nf,由Bathias公式计算"哑铃"状钛合金试样的裂纹扩展寿命。通过理论计算和有限元分析超声疲劳"哑铃"状试样,得出应力最大位置。利用有限元仿真和实验数据分析TC4钛合金疲劳寿命。在20 k Hz的超声疲劳试验中,试样的断口位置表明:TC4钛合金材料内部缺陷是试样萌生裂纹使断裂位置偏离最大应力处的主要原因。并得出疲劳裂纹萌生阶段寿命决定"哑铃"状试样的疲劳寿命。     

Investigation of fatigue and fracture behaviour of sensitized marine grade aluminium alloy AA 5754

In the present study, fatigue and fracture characteristics of sensitized marine grade Al‐Mg (AA 5754) alloy are experimentally evaluated. Received alloy is sensitized at temperatures of 150°C (SENS50) and 175°C (SENS75) for 100 hours. Fracture parameters, K_Ic and J_Ic, are experimentally evaluated. Slow strain rate tensile tests at a crosshead speed of 0.004, 0.006, and 0.01 mm/min; fatigue crack growth tests at load ratios (R = P_min/P_max) of 0.1, 0.2, and 0.5; and low cycle fatigue tests at four strain amplitudes of (0.3‐0.6)% are performed for SENS50 and SENS75 alloys. Relatively lower magnitude of fracture toughness values are observed for SENS75 specimen. Severe degradation in tensile properties, fatigue crack growth characteristics, and low cycle fatigue lives are observed for SENS75 samples. Extended finite element method is adopted to simulate the elasto‐plastic crack growth during fracture toughness evaluation. Scanning electron microscopy (SEM) is used to understand the failure mechanism of sensitized alloys.     

Fatigue strength assessment of laser stake‐welded T‐joints subjected to reversed bending

The paper investigates the fatigue strength of laser stake‐welded T‐joints subjected to reversed bending. The fatigue tests are carried out with the load ratio, R ≈ ?0.8. The experimental data is firstly analysed using the nominal stress approach and then by the J‐integral as the local fatigue strength parameter in the finite element (FE) assessment. The nominal stress approach demonstrated that the fatigue strength of the investigated T‐joints is lower than encountered for any other steel joint under reversed tensile loading. The results also showed that the fatigue strength of this joint under the load ratio R ≈ ?0.8 increases with respect to R = 0 bending by 22.6% in the case of the nominal stress approach and 13% in the case of the J‐integral approach. However, the slopes of the fatigue resistance curves for different load ratios appear very similar, suggesting that the load ratio has an insignificant influence to the slope. In contrast to the similar slopes, the scatter indexes were different. The nominal stress approach shows that the scatter index is 3.4 times larger for R ≈ ?0.8 than R = 0 bending. The J‐integral approach showed that the scatter index for R ≈ ?0.8 is only 67% larger than in the R = 0 case because the weld geometry is modelled in the FE analysis.     

Robust and direct evaluation of J2 in linear elastic fracture mechanics with the X‐FEM

The aim of the present paper is to study the accuracy and the robustness of the evaluation of J_k‐integrals in linear elastic fracture mechanics using the extended finite element method (X‐FEM) approach. X‐FEM is a numerical method based on the partition of unity framework that allows the representation of discontinuity surfaces such as cracks, material inclusions or holes without meshing them explicitly. The main focus in this contribution is to compare various approaches for the numerical evaluation of the J₂‐integral. These approaches have been proposed in the context of both classical and enriched finite elements. However, their convergence and the robustness have not yet been studied, which are the goals of this contribution. It is shown that the approaches that were used previously within the enriched finite element context do not converge numerically and that this convergence can be recovered with an improved strategy that is proposed in this paper. Copyright © 2008 John Wiley & Sons, Ltd.     

Low‐cycle fatigue life behaviour of BS 460B and BS B500B steel reinforcing bars

This paper investigates the low‐cycle fatigue resistance of BS 460B and BS B500B steel reinforcing bars and proposes models for predicting their fatigue life based on plastic‐strain (?_ap) and total‐strain (?_a) amplitudes. Constant‐amplitude, strain‐controlled low‐cycle fatigue tests were carried out on these bars under cyclic load with a frequency of 0.05 Hz. The maximum applied axial strain amplitude (?_s,max) ranges from 3 to 10% with zero and non‐zero mean strains. The strain ratios (R = ?_s,min/?_s,max) used are R =?1, ?0.5 and 0. Hysteresis loops were recorded and plastic and total strain amplitudes were related to the number of reversals (2N_f) to fatigue failure and models for predicting the number of reversals to fatigue failure were proposed. It is concluded that the predicted fatigue life of these bars is very accurate when compared with the measured experimental fatigue life results for wide range of values of strain ratios. It is also observed that based on plastic‐strain amplitude, BS B500B consistently has a longer life (higher number of cycles to failure) than those of BS 460B for all R values; however, at low plastic‐strain amplitudes they tend to behave similarly, irrespective of R value. Other observations and conclusions were also drawn.     

Fatigue crack growth law of API X80 pipeline steel under various stress ratios based on J‐integral

Load‐controlled three‐point bending fatigue tests were conducted on API X80 pipeline steel to investigate the effects of stress ratio and specimen orientation on the fatigue crack growth behaviour. Because of the high strength and toughness of X80 steel, crack growth rate was measured and plotted versus ΔJ with stress ratio. The fatigue crack length is longer in the transverse direction, whereas the fatigue crack growth rates are nearly the same in different orientations. Finally, a new fatigue crack growth model was proposed. The effective J‐integral range was modified by ΔJ_p in order to correlate crack closure effect due to large‐scale yield of crack tip. The model was proved to fit well for fatigue crack growth rate of API X80 at various stress ratios of R > 0.     

Comparison of methods for fracture toughness testing of thin low carbon steel plates

Abstract

The fracture toughness of double edge notched tension (DENT) specimens of a low carbon steel sheet was evaluated using experimental and numerical methods. The concepts of critical J integral J_c critical crack tip opening displacement δ_c, essential work of fracture We_e, and essential work of fracture and initiation we^init were compared. The numerical methods were based on finite strain, three-dimensional finite element simulations of the tensile straining of the DENT specimens. Good agreement was found between numerical and experimental J_c values. Fair agreement was also found between J_c and we^init. The essential work of fracture W_e was ～20% lower than J_c. This discrepancy is attributed to inaccuracy in the detection of cracking initiation. The Shih factor derived from the measured J_c and δ_c values closely corresponds with the plane stress prediction.     

Ermüdungsrißwachstum in Kerben

Fatigue Crack Growth in Notches Nowadays it is wellknown that an important part of the fatigue life time, usually differenciated in crack initiation and crack growth, is often controlled by fatigue crack growth of cracks in notches. An elastic-plastic on the J-integral based crack growth model considering the crack opening and closure phenomenon will be described to determine crack growth of cracks in notches between crack initiation and failure. Experimental results and finite element analysis were used to verify the developed model.     

Crack growth behavior and fatigue-life prediction based on worst-case near-threshold data of a large crack for 9310 steel

ABSTRACT Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks, near‐threshold growth behavior of large cracks at constant R‐ratio/decreasing ΔK and constant K_max/decreasing ΔK, respectively, for 9310 steel. The results showed that a pronounced small‐crack effect was not observed even at R = ?1, small cracks initiated by a slip mechanism at strong slip sites. Worst‐case near‐threshold testing results for large cracks under several K_max values showed that an effect of K_max on the near‐threshold behavior does not exist in the present investigation. A worst‐case near‐threshold test for a large crack, i.e. constant K_max/decreasing ΔK test, can give a conservative prediction of growth behavior of naturally initiated small cracks. Using the worst‐case near‐threshold data for a large crack and crack‐tip constraint factor equations defined in the paper, Newman's total fatigue‐life prediction method was improved. The fatigue lives predicted by the improved method were in reasonable agreement with the experiments. A three‐dimensional (3D) weight function method was used to calculate stress‐intensity factors for a surface crack at a notch of the present SENT specimen (with r/w = 1/8) by using a finite‐element reference solution. The results were verified by limited finite‐element solutions, and agreed well with those calculated by Newman's stress‐intensity factor equations when the stress concentration factor of the present specimen was used in the equations.     

Finite element evaluation of mixed mode stress intensity factors in functionally graded materials

This paper is directed towards finite element computation of fracture parameters in functionally graded material (FGM) assemblages of arbitrary geometry with stationary cracks. Graded finite elements are developed where the elastic moduli are smooth functions of spatial co‐ordinates which are integrated into the element stiffness matrix. In particular, stress intensity factors for mode I and mixed‐mode two‐dimensional problems are evaluated and compared through three different approaches tailored for FGMs: path‐independent J^*_k‐integral, modified crack‐closure integral method, and displacement correlation technique. The accuracy of these methods is discussed based on comparison with available theoretical, experimental or numerical solutions. Copyright © 2001 John Wiley & Sons, Ltd.