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.     

Effective strain–fatigue life data for variable amplitude fatigue

The usual analysis procedure for variable amplitude fatigue calculates fatigue damage based on constant amplitude strain controlled fatigue tests of smooth specimens. The resulting predictions are typically nonconservative due to a load interaction effect in variable amplitude fatigue. This paper reviews recent work which shows that large loads in a service load history decrease the crack opening stress and as a result increase the effective strain range for subsequent small cycles. A new strain–life fatigue test is introduced in which periodic large strain cycles reduce the crack opening stress for subsequent smaller cycles. The overloads are applied frequently enough that closure free fully open crack growth is achieved for the small cycles in the long life regime. An effective strain–life curve is derived and a crack opening stress equation calibrated by comparison of constant amplitude and effective strain ranges at given fatigue lives. The use of the effective strain–life curve in predicting fatigue lives is illustrated for service strain histories and for a variable amplitude load sequence applied to notched specimens. The predictions are good but somewhat conservative.     

Numerical simulation of plasticity induced fatigue crack opening and closure for autofrettaged intersecting holes

The autofrettage of intersecting holes leads to extremely high compressive residual stress fields. These stresses in combination with the plastic deformations decelerate fatigue cracks initiated at the hole intersection notch. Simulations of plasticity induced crack closure of such cracks are presented based on the strip yield and a finite element model. The strip yield model has been extended to allow for an input of residual stresses coming from elsewhere, e.g. from a finite element calculation or measurements. The calculations are applied for constant as well as variable amplitude loading. The numerical expense of the finite element based modelling for variable amplitude loading is still too high if millions of cycles have to be considered. Therefore, a new approximation method is proposed introducing compensatory load sequences. Simulation results are compared to experimentally determined results showing good agreement. However, the accuracy of crack initiation life estimates has turned out to provide a high potential for further improvement.     

Effect on fatigue crack growth of interactions between overloads

ABSTRACT Various types of interactions between overloads were studied in a 0.38% C low carbon steel. The retarding effect due to consecutive overloads is found to increase with the number of overloads, until it reaches a maximum. Similarly, it is found that a critical distance between overloads ensures the highest retarding effect, while shorter or longer spacing are less efficient for retarding crack growth. These effects are successfully explained using FEM calculations of the effective stress intensity factor. The kinematic hardening of the alloy, which is very efficient in ferritic–pearlitic steels, is shown to be mostly responsible for those effects. Taking into account the amplitude of kinematic hardening allows qualitative explanation of the observed effects. The order of application of the cycles during variable amplitude fatigue is thus important and should be taken into account for predicting fatigue lives.     

Fatigue crack growth of filled rubber under constant and variable amplitude loading conditions

Service conditions experienced by rubber components often involve cyclic loads which are more complex than a constant amplitude loading history. Consequently, a model is needed for relating the results of constant amplitude characterization of fatigue behaviour to the effects of variable amplitude loading signals. The issue is explored here via fatigue crack growth experiments on pure shear specimens conducted in order to evaluate the applicability of a linear crack growth model equivalent to Miner's linear damage rule. This model equates the crack growth rate for a variable amplitude signal to the sum of the constant amplitude crack growth rates associated with each individual cycle. The variable amplitude signals were selected to show the effects of R-ratio (ratio of minimum to maximum energy release rate), load level, load sequence, and dwell periods on crack growth rates. In order to distinguish the effects of strain crystallization on crack growth behaviour, two filled rubber compounds were included: one that strain crystallizes, natural rubber, and one that does not, styrene-butadiene rubber. The linear crack growth model was found to be applicable in most cases, but a dwell effect was observed that is not accounted for by the model.     

Load interaction effects during fatigue crack growth under variable amplitude loading—a literature review. Part II: qualitative interpretation

The current understanding of the underlying reasons behind the load interaction effects in fatigue crack growth under variable amplitude loading is presented. Mechanistic arguments proposed to control the load interaction phenomena are reviewed and evaluated based on their capability to qualitatively explain empirical trends in variable amplitude fatigue crack growth summarized in Part I [ Fatigue Fract. Engng Mater. Struct. 1998, 21 (8), 987–1006] of the present paper. Mechanisms linked to plastic straining at the crack tip enable an interpretation of the majority of the experimental results. Some observations, however, which cannot be understood in terms of plasticity-induced crack closure, or which are even in contradiction with the crack closure approach, indicate a possible role of other factors. A general conclusion is that conditions under which various phenomena can affect variable amplitude fatigue crack growth and interactions between them are insufficiently recognized.     

Fatigue strength of small-notched specimens under variable amplitude loading within the fatigue limit diagram

Although the fatigue limit diagram is defined in principle for constant stress amplitude, it is often considered that fatigue failure would not occur, even in varying loading, if applied stresses were kept within the fatigue limit diagram. However, it was shown in the case of small‐notched specimens that fatigue failure occurred in some special cases of variable amplitude loading, even when all stress amplitudes were kept within the fatigue limit diagram. The cause of this phenomenon was examined using two‐step stress and repeated two‐step stress patterns in which the first step stress was chosen to be equal to the fatigue limit with zero mean stress and a mean stress was superposed on the second step stress. A non‐propagating crack was formed by the first step stress. This crack functioned as a pre‐crack for the second step stress with high mean stress. Consequently, fatigue failure occurred even when all stress amplitudes were kept within the fatigue limit diagram. It was an unexpected fracture caused by the interference effect of a non‐propagating crack and a mean stress change.     

The influence of hammer peening on fatigue in high-strength steel

An investigation of the influence of hammer peening on fatigue crack initiation and propagation in high-strength steel has been performed using edge notch specimens. The crack initiation time was found to decrease after peening; however, the fatigue crack growth stage remained unchanged or decreased depending upon the peening parameters. The results have been used to develop an analytical model to predict the fatigue crack growth rate in peened materials, based upon the compressive residual stress effect.     

Fretting fatigue under variable loading below fretting fatigue limit

The fatigue limit diagram provides the critical condition of non‐failure against fatigue under constant amplitude loading. The fatigue limit diagram is usually considered to give the allowable stress if every stress component is kept within the fatigue limit diagram. In the case of variable amplitude fretting fatigue, however, this study showed that fatigue failure could occur even when all stresses were within the fatigue limit diagram. An example of such a condition is a repeated two‐step loading such as when the first step stress is R=?1 and the second step stress has a high mean value. The reason why such a phenomenon occurs was investigated. A non‐propagating crack was formed by the first step stress even when well below the fatigue limit. The resultant non‐propagating crack functioned as a pre‐crack for the second step stress with a high mean value. Consequently, fatigue failure occurred even when every stress was within the fatigue limit diagram of constant amplitude loading. The fatigue limit diagram obtained in constant amplitude fatigue test does not necessarily guarantee safety in the case of variable amplitude loading in fretting fatigue.     

Time-derivative equations for fatigue crack growth in metals

Predicting fatigue crack growth in metals remains a difficult task because available models are based on cycle-derivative equations, such as the Paris law, while service loads are often far from being cyclic. The main objective of this paper is therefore to propose a set of time-derivative equations for fatigue crack growth. The model is based on the thermodynamics of dissipative processes. For this purpose, three global state variables are introduced in order to characterize the state of the crackthe crack length a, the plastic blunting at crack tip and the intensity of crack opening C. Thermodynamics counterparts are introduced for each variable. Special attention is paid to the elastic energy stored inside the crack tip plastic zone, because, in practice, residual stresses at crack tip are known to considerably influence fatigue crack growth. The stored energy is included in the energy balance equation, and this leads to the appearance of a kinematics hardening term in the yield criterion for the cracked structure. No dissipation is associated with crack opening, but to crack growth and to crack tip blunting. Finally, the model consists in two laws: a crack propagation law, which is a relationship between d dt and da/dt and which observes the inequality stemmed from the second principle, and an elastic-plastic constitutive behaviour for the cracked structure, which provides d dt versus applied-load. The model was implemented and tested. It reproduces successfully the main features of fatigue crack growth as reported in the literature, such as the Paris law, the stress-ratio effect and the overload retardation effect.     

Unique fatigue threshold and growth properties of welded joints in a tensile residual stress field

The fatigue threshold and high growth rate region properties were investigated on several kinds of welded joints. These properties became unique in spite of the variation of steels (ferrite-pearite, martensite, austenite), welding method, heat input and stress ratio. It was revealed that the unique properties occurred from the fully opened fatigue crack due to the tensile residual stresses. Based on these results, the equation of the fatigue crack growth curve for the design and inspection of welded structures was proposed. It is also suggested that the inducement of compressive residual stress at the fatigue critical zone is effective in improving the fatigue properties of welded structures.     

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.     

Fatigue life prediction of engineering structures subjected to variable amplitude loading using the improved crack growth rate model

It is a difficult task to predict fatigue crack growth in engineering structures, because they are mostly subjected to variable amplitude loading histories in service. Many prediction models have been proposed, but no agreed model on fatigue life prediction adequately considering loading sequence effects exists. In our previous research, an improved crack growth rate model has been proposed under constant amplitude loading and its good applicability has been demonstrated in comparison with various experimental data. In this paper, the applicability of the improved crack growth rate model will be extended to variable amplitude loading by modifying crack closure level based on the concept of partial crack closure due to crack‐tip plasticity. It is assumed in this model that the crack closure level can instantly go to the peak/valley due to a larger compression/tensile plastic zone resulted from the overload/underload effect, and gradually recovers to the level of constant amplitude loading with crack propagation. To denote the variation in the affected zone of overload/underload, a modified coefficient based on Wheeler model is introduced. The improved crack growth rate model can explain the phenomena of the retardation due to overload and the tiny acceleration due to underload, even the minor retardation due to overload followed by underload. The quantitative analysis will be executed to show the capability of the model, and the comparison between the prediction results and the experimental data under different types of loading history will be used to validate the model. The good agreement indicates that the proposed model is able to explain the load interaction effect under variable amplitude loading.     

Variable amplitude fatigue of high-strength cast iron alloys for automotive applications

In the automotive sector, the cumulative damage calculation method generally applied is the Palmgren–Miner-Hypothesis with its modification according to Haibach (steeper slope of the SN-line after the knee-point) as a means of also including the damage by stress amplitudes below the knee-point. This approach results in the total damage sum of the spectrum D_spec. However, the resulting question is the value of the allowable damage sum D_al for the evaluation of D_spec ⩽ D_al. The only design code that considers the assessment of cast iron components under spectrum loading is the FKM-Guideline of the Cooperative Research Association for Mechanical Engineering (FKM, Frankfurt/Germany) for designing machine components. Here, the theoretical Palmgren–Miner-damage sum D_th = 1.0 is still suggested as the allowable damage sum D_al despite the fact that this damage sum renders unsafe calculated fatigue lives in about 90% of all published results.The results obtained with component-like notched specimens of modern high-strength cast iron alloys (R_m = 650–800 MPa) such as EN-GJS-500-7, SiboDur 700-10 and MADI (Machinable Austempered Ductile Iron), which were investigated under a standard Gaussian spectrum for chassis applications and also for a fuller injection pump spectrum, suggest the allowable damage sum D_al = 0.3 for fatigue life estimations of components manufactured with these materials can be proposed; i.e. the allowable fatigue life is about one third compared to calculations with the theoretical damage sum D_th = 1.0 that is still used.     

Examination of fatigue crack driving force parameter

Most of the previous parameters that utilized as a crack driving force were established in modifying the parameter K_op in Elber's effective SIF range ΔK_eff(=K_max?K_op). However, the parameters that replaced the traditional parameter K_op were based on different measurements or theoretical calculations, so it is difficult to distinguish their differences. This paper focuses on the physical meaning of compliance changes caused by plastic deformation at the crack tip; the tests were carried out under different amplitude loading for structural steel. Based on these test results, differences of several parameter ΔK_eff in literature are analysed and an improved two‐parameter driving force ΔK_drive(=(K_max)ⁿ(ΔK^∧)^1‐n) has been proposed. Experimental data for several different types of materials taken from literature were used in the analyses. Presented results indicate that the ΔK_drive parameter was equally effective or better than ΔK(=K_max?K_min), ΔK_eff(=K_max?K_op) and ΔK*(= (K_max)^α(ΔK⁺)^1?α) in correlating and predicting the R‐ratio effects on fatigue crack growth rate.     

Fatigue life prediction based on equivalent stresses for laser beam welded 6156 Al‐alloy joints under variable amplitude loading

In the present work, a simple fatigue life prediction approach is proposed using fracture mechanics for laser beam welded Al‐alloy joints under variable amplitude loading. In the proposed approach, variable amplitude loading sequence is transformed into an equivalent constant amplitude loading using the root mean square model. The crack growth driving force K^* is chosen to describe the fatigue crack growth rate. The influences of residual stress and its relaxation on fatigue life are taken into account in the proposed approach. The fatigue lives are also predicted using the traditional approach based on the S‐N curves and the rainflow counting method. The predicted results show that the proposed approach is better than the traditional approach.     

Effects of different indentation methods on fatigue life extension of cracked specimens

In this paper, 3 different indentation methods have been investigated for crack arresting and fatigue life enhancement of cracked components. The influence of residual stresses induced by indentation on fatigue crack growth (FCG) rate was explored by experiments and numerical simulations. Fatigue tests were conducted on a group of specimens which were indented on the crack tip by various indentation load magnitudes. For another group of specimens, the double indentation and triple indentation methods were applied on the cracked specimens with the aim of obtaining proper residual stress fields that contribute to higher crack growth retardations. Both the numerical and experimental results revealed that the higher indentation loads led to larger domain of compressive residual stress around the crack tip and consequently to higher fatigue life extension. In addition, the triple indentation method resulted in more FCG retardation compared with single and double indentation methods. Furthermore, for the specimens repaired by double and triple indentation methods, indenting ahead of the crack tip led to retardation in more crack growth compared with the other horizontal positions of indentation.     

Multiscale fatigue crack growth modelling for welded stiffened panels

The influence of welding residual stresses in stiffened panels on effective stress intensity factor (SIF) values and fatigue crack growth rate is studied in this paper. Interpretation of relevant effects on different length scales such as dislocation appearance and microstructural crack nucleation and propagation is taken into account using molecular dynamics simulations as well as a Tanaka–Mura approach for the analysis of the problem. Mode I SIFs, K_I, were calculated by the finite element method using shell elements and the crack tip displacement extrapolation technique. The total SIF value, K_tot, is derived by a part due to the applied load, K_appl, and by a part due to welding residual stresses, K_res. Fatigue crack propagation simulations based on power law models showed that high tensile residual stresses in the vicinity of a stiffener significantly increase the crack growth rate, which is in good agreement with experimental results.     

Short-crack-growth-based fatigue assessment of notched components under multiaxial variable amplitude loading

A short crack model originally proposed for multiaxial constant amplitude loading is extended and applied to multiaxial variable amplitude loading. Load sequences have a significant influence on variable amplitude life; they are taken into account using algorithms originally proposed only for uniaxial loading. The estimated fatigue lives of unnotched tubular specimens and notched shafts under different in- and out-of-phase multiaxial constant and variable amplitude load histories are compared with the experimental results. The comparison reveals that the proposed short crack approach enables sufficiently accurate estimation. Moreover, the estimated critical planes, i.e., the planes of maximum crack growth rate or minimum life, are in good agreement with the experimental observations.