Fatigue life prediction for butt‐welded joints considering weld‐induced residual stresses and initial damage,relaxation of residual stress,and elasto‐plastic fatigue damage

Fatigue damage of butt‐welded joints is investigated by a damage mechanics method. First, the weld‐induced residual stresses are determined by using a sequentially coupled thermo‐mechanical finite element analysis. The plastic damage of material is then calculated with the use of Lemaitre's plastic damage model. Second, during the subsequent fatigue damage analysis, the residual stresses are superimposed on the fatigue loading, and the weld‐induced plastic damage is considered as the initial damage via an elasto‐plastic fatigue damage model. Finally, the fatigue damage evolution, the relaxation of residual stress, and the fatigue lives of the joints are evaluated using a numerical implementation. The predicted results agree well with the experimental data.     

Overload effect on the fatigue crack propagation in large‐scale tubular joints

This paper examines the overloading effect on the fatigue crack propagations monitored in a large‐scale tubular X‐joint specimen under two separate cyclic tests. The first cyclic test applies a constant‐amplitude brace in‐plane bending to the joint, with a single cycle of 150% overload before the crack depth reaches the mid‐thickness of the chord. The second fatigue test applies two batches of cyclic loads, with the amplitude of the second batch at 66% of the former. The X‐joint specimen experiences a 150% overload cycle during the first batch of loading, followed by the second batch after it has recovered from the overload effect. The experimental results reveal that deep surface cracks experience more significant overload retardation than does a shallow fatigue crack. The Paris law estimation indicates that the single overload cycle applied in the first specimen leads to a 7% increase in the fatigue life of the X‐joint.     

Low cycle thermo‐mechanical fatigue: damage operator approach

The strain‐life approach is standardized and widely accepted for determining fatigue damage under strain‐controlled low cycle fatigue (LCF) loading. It was first extended to non‐isothermal cases by introducing an equivalent temperature approach (ETA). The paper presents its extension that is the damage operator approach (DOA) enabling online continuous damage calculation for isothermal and non‐isothermal loading with mean stress correction. The cycle closure point, cycle equivalent temperature, threshold temperature and separate rainflow counting obligatory for the ETA are not necessary for the DOA any more. Both approaches are equivalent for the second and subsequent runs of block loading if temperature is constant. However, for non‐isothermal cases, the DOA is within the worst and the best case scenarios of the ETA. The approaches are compared to the simple stress histories and several thermo‐mechanical fatigue (TMF) cycle types.     

A fatigue damage indicator parameter for P91 chromium‐molybdenum alloy steel and fatigue pre‐damaged P54T carbon steel

Two grades of structural steel were subjected to fully reversible, constant stress amplitude cyclic loading. The local strain response of the material was measured and recorded during the test, with the applied testing technique enabling the monitoring of hysteresis loop variation for the narrowest cross‐section of the hourglass specimen. Changes in hysteresis loop width, representing the local inelastic response of the material, were recorded in order to monitor the density of structural imperfections. Material ratcheting behaviour was observed as changes in the mean strain for selected load cycles. Ratcheting was attributed to local deformation of the material in the vicinity of imperfections such as voids or inclusions, as well as deformation induced by the propagation of microcracks. Definitions of a damage indicator parameter and damage parameter were proposed. The fatigue behaviour of the two investigated grades of steel was finally illustrated in the form of damage curves for different stress amplitudes and for undamaged and fatigue pre‐damaged material.     

Effect of initial damage level and patch configuration on the fatigue behaviour of reinforced steel plates

The application of carbon fibre reinforced polymer composites externally bonded on cracked steel plates is an effective system in extending the fatigue life of these structural elements. In particular, composite patches bonded on the crack tip region reduce the stress concentration and the crack opening displacement, leading to an extension of the fatigue life. In order to additionally show the effectiveness of this kind of reinforcing technique, experimental tests were performed at the laboratories of the Politecnico di Milano. Fatigue tests were executed on single edge notched tension specimens reinforced by pultruded strips bonded to a single side (non‐symmetric reinforcement). Different patch configurations (reinforcement stiffness and patch location) and initial damage levels were considered as parameters influencing the repair effectiveness in extending the fatigue life. The results showed that the use of carbon fibre reinforced polymer materials bonded around the tip region allows extending the fatigue life for different amount of initial damage level. Finally, this work provides some useful information for the more efficient repair configuration.     

Effect of fatigue damage on static and dynamic tensile behaviour of electro‐discharge machined Ti‐6Al‐4V

The fatigue performance of electro‐discharge machined Ti‐6Al‐4V and, more specifically, the effect of cyclic damage on the static and dynamic tensile properties of the material have been investigated. In a first step, fatigue failure was studied. Afterwards, tensile tests were performed on specimens that had been previously subjected to cyclic loading during predefined fractions of the fatigue life. In addition to conventional experiments at quasi‐static strain rate, dynamic tests were performed using a split Hopkinson tensile bar setup. The edges of some of the specimens were removed after cyclic loading to discriminate between the effects of damage at the edges and in the bulk of the material. Results revealed that early fatigue failure is due to the growth of cracks on the machined edges of the specimens. Edge cracks can randomly reduce fracture strain and energy absorbing capacity. However, cyclic damage does not affect the tensile properties of the bulk material.     

Multi‐scale modeling of surface effect via the boundary Cauchy–Born method

In this paper, a novel multi‐scale approach is developed for modeling of the surface effect in crystalline nano‐structures. The technique is based on the Cauchy–Born hypothesis in which the strain energy density of the equivalent continua is calculated by means of inter‐atomic potentials. The notion of introducing the surface effect in the finite element method is based on the intrinsic function of quadratures, called as an indicator of material behavior. The information of quadratures is derived by interpolating the data from probable representative atoms in their proximity. The technique is implemented by the definition of reference boundary CB elements, which enable to capture not only the surface but also the edge and corner effects. As the surface effect is important in small‐scale simulation, the relative number of boundary CB elements increases which leads to predomination of boundary effects in the model. In order to implement the equivalent continua in boundary value problems, the updated‐Lagrangian formulation of nonlinear finite element is derived. The numerical simulation of the proposed model together with the direct comparison with fully atomistic model indicates that the technique provides promising results for facile modeling of boundary effects and investigating its effect on the mechanical response of metallic nano‐scale devices. Copyright © 2010 John Wiley & Sons, Ltd.     

Study on the fatigue life and damage accumulation of a compressor blade based on a modified nonlinear damage model

Comparing with the fatigue test results of Ti‐6Al‐4V, the widely used Chaboche damage model shows considerable differences in fatigue life prediction under asymmetric load, which is potentially caused by the local plastic deformation. In this paper, a modified nonlinear damage accumulation model is developed to improve the prediction accuracy for asymmetric loading condition. To account for the elastic and plastic strains, an elastoplastic fatigue factor is developed with 2 weighting factors based on the Ramberg‐Osgood equation and introduced into the stress term of the damage model. The validation of the proposed damage model is verified against the experimental data of Ti‐6Al‐4V titanium alloy and 2024‐T3 aluminium alloy with various stress ratios. Comparing with the original Chaboche model, the predicted life of the proposed model shows much better agreement with the experimental results. Then, the proposed model is used to estimate the fatigue life of a compressor blade of aero‐engine. Considering the variable amplitude loads and the loading sequence, the damage accumulation and the fatigue life of the blade are calculated, and the results indicate a longer fatigue life with slower damage accumulation rate in the early life stage.     

A cumulative damage model for fatigue life estimation of high‐strength steels in high‐cycle and very‐high‐cycle fatigue regimes

A cumulative fatigue damage model is presented to estimate fatigue life for high‐strength steels in high‐cycle and very‐high‐cycle fatigue regimes with fish‐eye mode failure, and a simple formula is obtained. The model takes into account the inclusion size, fine granular area (FGA) size, and tensile strength of materials. Then, the ‘equivalent crack growth rate’ of FGA is proposed. The model is used to estimate the fatigue life and equivalent crack growth rate for a bearing steel (GCr15) of present investigation and four high‐strength steels in the literature. The equivalent crack growth rate of FGA is calculated to be of the order of magnitude of 10^?14–10^?11 m/cycle. The estimated results accord well with the present experimental results and prior predictions and experimental results in the literature. Moreover, the effect of inclusion size on fatigue life is discussed. It is indicated that the inclusion size has an important influence on the fatigue life, and the effect is related to the relative size of inclusion for FGA. For the inclusion size close to the FGA size, the former has a substantial effect on the fatigue life. While for the relatively large value of FGA size to inclusion size, it has little effect on the fatigue life.     

Non‐destructive evaluation of fatigue damage and fatigue crack initiation in type 316 stainless steel by positron annihilation line‐shape and lifetime analyses

Rotating bending fatigue tests were conducted using type 316 stainless steel. The fatigue tests were periodically terminated, and fatigue damage and fatigue crack initiation were non‐destructively and sequentially evaluated by positron annihilation line‐shape and lifetime analyses. The counter‐jig and anticoincidence methods were used for positron annihilation line‐shape and lifetime analyses, respectively, to enhance the analytical precision. The fatigue crack lengths were monitored by a plastic replication technique, and related to the parameters in both analyses. S‐parameter obtained in the line‐shape analysis increased with increasing fatigue damage, while it was difficult to detect fatigue crack initiation and subsequent small fatigue crack growth. That was because the precision of line‐shape analysis was limited. On the other hand, both fatigue damage and fatigue crack initiation were successfully detected by lifetime analysis. Positron annihilation lifetime also increased with increasing fatigue damage, and lifetime was longer at the notch root with fatigue crack than at the smooth section without crack. It was considered that the precision of lifetime analysis was high enough to detect high dislocation density areas at the fatigue crack tips.     

A new continuum damage mechanics–based two‐scale model for high‐cycle fatigue life prediction considering the two‐segment characteristic in S‐N curves

In this study, we propose a new two‐scale fatigue model based on continuum damage mechanics. A representative volume element (RVE) consisting of microinclusions and a matrix is constructed. Further, damage‐coupled constitutive equations are derived. The degradation in the mechanical properties of the RVE is determined by the damaged inclusions and matrix using the Mori‐Tanaka scheme. A numerical calculation of the fatigue lives of notched specimens is executed. This new model predicts high‐cycle fatigue (HCF) life more effectively, considering the two‐segment characteristic of S‐N curves of smooth specimens. This study provides novel insights into the evolution mechanism of HCF damage.     

A nonlinear continuous damage model based on short‐crack concept under variable amplitude loading

In this paper, a modified nonlinear damage accumulation model is proposed by using intrinsic crack size as the damage variable in the stress‐control condition. The model's development is based on the Chaboche nonlinear damage law and the short‐crack theory. The validations are confirmed by using the experimental data of Ti–6Al–4V and 2024‐T3 collected from tests and literature. The model capabilities of predicting damage accumulation and crack growth rate in the multi‐level loading condition as well as the variable amplitude loading condition with single and multiple over‐load are investigated and discussed in detail. Comparison results show that the proposed model is able to consider the loading ratio, the loading sequence and the over‐load effect on damage accumulation correctly. Meanwhile, the damage accumulation in the last stage of fatigue life can be described more clearly by the proposed model attributed to the use of crack size as the damage variable.     

Robust structural damage identification based on multi‐objective optimization

Inverse analysis for structural damage identification often involves an optimization process that minimizes the discrepancies between the computed responses and the measured responses. Conventional single‐objective optimization approach defines the objective function by combining multiple error terms into a single one, which leads to a weaker constraint in solving the identification problem. A multi‐objective approach is proposed, which minimizes multiple error terms simultaneously. Its non‐domination‐based convergence provides a stronger constraint that enables robust identification of damages with lower false‐negative detection rate. Another merit of the proposed approach is quantified confidence in damage detection through processing Pareto‐optimal solutions. Numerical examples that simulate static testing are provided to compare the proposed approach with conventional formulation based on single‐objective optimization. Copyright © 2009 John Wiley & Sons, Ltd.     

The effect of fatigue pre‐cracking forces on fracture toughness

Testing procedures for the determination of the fracture toughness of a material by monotonic loading of fatigue pre‐cracked specimens are well established in standards such as BS 7448, BS EN ISO 15653, ISO 12135, ASTM E1820 and ASTM E1921. However, a review of these standards indicates a wide range of permitted fatigue pre‐cracking forces, whilst the underlying assumption in each standard is that the pre‐cracking conditions do not affect the fracture toughness determined. In order to establish the influence of different fatigue pre‐cracking forces on the fracture toughness, tests were carried out on specimens from an API 5L X70 pipeline steel. Single‐edge notch bend specimens of Bx2B geometry were notched through thickness and tested at temperatures of +20 °C, ?80 °C and ?140 °C to show the fracture behaviour in different regions of the fracture toughness ductile‐to‐brittle transition curve. Fatigue pre‐cracking was conducted on a high‐frequency resonance fatigue test machine over a range of pre‐cracking forces permissible within the various standards and beyond. The results showed that an excessively high pre‐cracking force can result in a significant overestimation of the value of fracture toughness for material exhibiting brittle behaviour, whilst very low fatigue pre‐cracking forces appeared to result in an increase in scatter of fracture toughness. A review of standards indicated that there was a possibility to misinterpret the intention of the ISO 12135 standard and potentially use excessively high pre‐cracking forces. Suggested clarifications to this standard have therefore been proposed to avoid the risk of overestimating fracture toughness.     

Multi‐scale analysis and FE computation for the structure of composite materials with small periodic configuration under condition of coupled thermoelasticity

The two‐scale asymptotic (TSA) expressions of the increment of temperature and the displacement for the structure of composite materials with small periodic configuration under coupled thermoelasticity condition are derived formally in this paper, especially, the two‐scale coupled relation between the increment of temperature and the displacements are set up. Then the approximate solutions and their error estimations are presented, and the multi‐scale finite element algorithm corresponding to TSA is described. Finally, simple numerical results evaluated by multi‐scale FE computation are shown. They demonstrate that the basic configuration and the increment of temperature strongly influence upon local strains and local stresses inside basic cell. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical and experimental validation of residual stresses of laser‐welded joints and their influence on the fatigue behaviour

In this work laser‐welded tube‐tube specimens made of aluminium alloys AlMg3.5Mn and AlSi1MgMn T6 were experimentally tested under constant and variable amplitude loading, under pure axial and pure torsion loading. In order to evaluate the influence on fatigue behaviour of the residual stresses, because of the welding process, some specimens were subjected to postweld heat treatment and then were tested. The numerical analyses, using finite element (FE), were carried out to obtain a reliable estimation of the residual stress in the specimen. The numerical results were in a good agreement with experimental ones obtained by means of hole‐drilling method. Finally, the residual stress distribution was superimposed to stress distribution because of fatigue loads obtained by FE analyses applying local concept, to calculate the stresses in the crack initiation zone and to understand the different types of failure that occurred in as‐welded and relieved specimens.     

Numerical modelling and experimental investigation on welding residual stresses in large‐scale tubular K‐joints

This paper is devoted to the experimental and numerical assessment of residual stresses created by welding in the region surrounding the weld toe of tubular K‐shaped joints (i.e. region most sensitive to fatigue cracking). Neutron‐diffraction measurements were carried out on K‐joints cut from large‐scale truss beams previously subjected to high cycle fatigue. Tri‐axial residual stresses in the transverse, longitudinal and radial direction were obtained from the weld toe as a function of the depth in the thickness of the tube wall. In addition, thermomechanical analyses were performed in three‐dimensional using ABAQUS and MORFEO finite element codes. Experimental and numerical results show that, at and near the weld‐toe surface, the highest residual stresses are critically oriented perpendicularly to the weld direction, and combined with the highest externally applied stresses. Based on a systematic study on geometric parameters, analytical residual stress distribution equations with depth are proposed.     

The effect of frequency on the giga‐cycle fatigue properties of a Ti–6Al–4V alloy

The effect of frequency on giga‐cycle fatigue properties was investigated in smooth and 0.3 mm‐hole‐notched specimens at three heats (Heats A, B, and C) for a 900 MPa‐class Ti‐6Al‐4V alloy. Fatigue tests were performed at frequencies of 120 Hz, 600 Hz, and 20 kHz using electromagnetic resonance, high‐speed servohydraulic, and ultrasonic fatigue testing machines, respectively. Heats A and B developed internal fractures, and in these cases, frequency effects were negligible. On the other hand, Heat C developed only surface fractures. In this case, high‐frequency tests showed a higher fatigue strength, indicating frequency effects were not negligible. The tests using the notched specimens showed almost no frequency effects regardless of the heat. The frequency effects observed in the cases of surface fracture were believed to be related to a delay in local plastic deformation in response to high‐frequency loading, since temperature increases in these specimens were successfully suppressed. The delay in the plastic deformation was observed to be reduced in the notched specimens because of stress concentration and limitation in the plastic deformation zone. In turn, the significant conclusion of this research is that high‐frequency tests can be applied not only to internal fractures but also to notch problems, but are not applicable to surface fractures of smooth specimens.