Variable Amplitude Loading Spectra Research Articles

A Constitutive Model for Asymmetric Cyclic Hysteresis of Wrought Magnesium Alloys under Variable Amplitude Loading

A cyclic plasticity constitutive model was developed for materials with asymmetric cyclic behavior to explain the stabilized stress–strain response under variable amplitude loading. The proposed constitutive model incorporated the von Mises yield function with an adjustment to accommodate asymmetric yielding under tension and compression. A combined isotropic–kinematic hardening model was proposed to describe the evolution of the yield surface in the reference uniaxial frame and the actual frame. The history of plastic deformation is memorized by introducing internal variables, accumulated slip, and residual twins, which govern the cyclic flow behavior in the subsequent reversal. The additional conditions required to predict the stabilized hysteresis response of a material under variable amplitude loading were set out and incorporated into the constitutive model. The model was numerically implemented and programmed into a user material (UMAT) subroutine to run with the commercial finite element program, Abaqus/Standard 2019. The model was calibrated using the stabilized hysteresis response of ZEK100 and AZ31B sheets under constant amplitude strain-controlled cyclic loading for different strain amplitudes. To verify the model, constant amplitude and four different variable amplitude load spectra tests were performed and the stabilized stress–strain hysteresis response predicted by the model was compared with test results. It was demonstrated that the results are in very good agreement.

Experimental investigation of crack opening loads in an aircraft load spectrum

The concept of plasticity-induced fatigue crack closure is indispensable in explaining many fatigue crack growth phenomena; and it is now widely applied in advanced fatigue life evaluation procedures. This concept has been extensively investigated experimentally over the past sixty years using different methods. However, most of these investigations are related to constant amplitude loading or simple load cases such as single or multiple overloads or block loading. In contrast, there are currently no experimental studies investigating crack closure under variable amplitude loading or load spectra, which are more realistic scenarios. This can be attributed to the many difficulties associated with the evaluation of crack opening loads for large numbers of fatigue cycles, including sensor sensitivity, signal noise, data limits, etc. Recently, the authors proposed an advanced piezoelectric sensor for cycle-by-cycle crack opening load measurements, which addresses the above limitations. In this work, the piezoelectric sensor is utilised to investigate crack closure under a typical transport aircraft load spectrum. In particular, it is demonstrated that crack opening load levels can change significantly from cycle-to-cycle, and these levels are typically larger than for constant amplitude loading at the same R-ratio. The relative density plot of crack opening load levels reveals three distinct regions, which can be associated with certain load sequences. The outcomes of this research are important for the development and validation of spectrum compression algorithms as well as advanced fatigue life evaluation procedures.

Development of Combined Load Spectra for Offshore Structures Subjected to Wind, Wave, and Ice Loading

Fixed offshore wind turbines continue to be developed for high latitude areas where not only wind and wave loads need to be considered but also moving sea ice. Current rules and regulations for the design of fixed offshore structures in ice-covered waters do not adequately consider the effects of ice loading and its stochastic nature on the fatigue life of the structure. Ice crushing on such structures results in ice-induced vibrations, which can be represented by loading the structure using a variable-amplitude loading (VAL) sequence. Typical offshore load spectra are developed for wave and wind loading. Thus, a combined VAL spectrum is developed for wind, wave, and ice action. To this goal, numerical models are used to simulate the dynamic ice-, wind-, and wave-structure interaction. The stress time-history at an exemplarily selected critical point in an offshore wind energy monopile support structure is extracted from the model and translated into a VAL sequence, which can then be used as a loading sequence for the fatigue assessment or fatigue testing of welded joints of offshore wind turbine support structures. This study presents the approach to determine combined load spectra and standardized time series for wind, wave, and ice action.

Effect of Shear/Axial Stress Ratio on Multiaxial Non-Proportional Loading Fatigue Damage on AISI 303 Steel

In this paper, we investigate the cyclic response of AISI 303 stainless steel subjected to non-proportional loads with different amplitude ratios between shear stresses and normal stresses. Based on the experiments, a relationship between the proportional reference load and a varied range of non-proportional loads was established. To achieve this objective, an experimental program was implemented to evaluate the non-proportional parameter Y. Then, the evolution of this parameter was analyzed with the number of cycles to failure and with the ratio between shear and normal stresses, finally, the evolution of the non-proportional parameter Y was mapped by two functions. The results show that the non-proportional response of the AISI 303 can be estimated using the two functions obtained. This allows the estimation of the relationship between non-proportional and proportional stresses as a function of the number of cycles to failure together with the relationship between shear and normal stresses. The results obtained have direct application in the evaluation of accumulated damage, assessed in real-time, resulting from variable amplitude loading spectra. This is of particular interest for the evaluation of structural health monitoring of structures and mechanical components.

Modelling and identification of fatigue load spectra: Application in the automotive industry

This paper is focused on variable amplitude loading spectra applied in the automotive industry, more specifically for the chassis system parts with respect to high cycle fatigue design. A first analytical model referred to as Heuler’s model is considered. It is of the simplest use, with one parameter to be identified. A whole identification process, based on road measurement realized on carmaker’s proving ground with instrumented vehicles, is developed and discussed. Once the model is identified, the cycles influence on damage production is also investigated. In the light of the obtained results with this model, a second one, noted modified Heuler’s model, is introduced and investigated. This model, similar to the first, requires the identification of two parameters. Once again, the whole model identification process is applied, and the lifetime accuracy is assessed. A new tool is presented, enabling the visualisation on the loading spectrum representation of the most and less damaging cycles. Hence, a methodology is set to legitimize a gate implementation when studying a variable amplitude loading spectrum.

Fatigue life prediction under variable amplitude loading using a microplasticity-based constitutive model

We predict the fatigue life of a P355NL1 steel alloy under variable amplitude loading conditions using a newly-developed small-strain-based implicit plasticity model. The core idea behind the fatigue model is its capability to capture the inelastic work dissipation due to microplasticity whose critical value determines the fatigue life. Fatigue tests under different variable amplitude load spectra are simulated numerically and the results are compared with experimental data as well as other models for fatigue. It is shown that the model is able to describe the experimental data better than current empirical approaches, using only a few measured, physically motivated parameters.

Fatigue behaviour of maraging steel samples produced by SLM under constant and variable amplitude loading

This paper addresses the fatigue behaviour of AISI 18Ni300 samples manufactured by selective laser melting under both constant- and variable-amplitude loading. The fatigue campaign encompasses a series of low-cycle strain-controlled fatigue tests performed under fully-reversed conditions at various strain amplitudes, and a series of high-cycle stress-controlled fatigue tests performed under pulsating conditions at various stress ranges considering both constant- and variable-amplitude loading spectra. Fatigue life predictions are performed on the basis of the SWT parameter along with the Miner’s law. This approach has demonstrated to be sufficiently reliable to predict the lifetime expectancy in maraging steel samples produced by selective laser melting.

Study on Damage Accumulation and Life Prediction with Loads below Fatigue Limit Based on a Modified Nonlinear Model.

Most fatigue theories neglect the loads below fatigue limit in damage accumulation, which leads to inconsistency between the predicted and the actual fatigue lives. In this study, a novel damage model is proposed to take into account the loads below fatigue limit from two aspects: the strengthening effect and the cumulative damage. The strengthening effect is introduced by an exponential function and the cumulative damage is calculated by fuzzy method with membership functions (MFs). The proposed model is verified against the experimental data under variable amplitude loading conditions. It is found the modified model with Cauchy MF significantly reduces the relative error of predicted life from 35.18% (linear model) and 16.09% (original Chaboche model) to 8.38% (proposed model). As a case study, the proposed damage model is implemented to evaluate the service life of a compressor blade under variable amplitude loading spectrum containing small loads below the fatigue limit.

On the need to adopt strain-based probabilistic approach in predicting fatigue life

This paper presents a comparison of fatigue life prediction capabilities among three deterministic and one probabilistic strain–life models. Most existing life prediction models are deterministic even though the fatigue process is stochastic in nature. Therefore, variability in experimental fatigue life data is not statistically justified when the deterministic approach is adopted. In this study, the Coffin–Manson, Smith–Watson–Topper, Morrow, and Weibull regression models through the use of Miner’s rule for damage accumulation process are each compared with the experimental data. Both available in the literature, two sets of experimental data for variable amplitude loading and random loading spectrum were used to explore the prediction accuracies of the models. Simulations were based on models to obtain additional results for different levels of maximum strain. They were conducted to investigate the maximum strain–life behaviour under random loading. Fatigue life comparisons were then performed, and the scatter band for type of load, level of strain amplitude, and each model separately were used for evaluations. The results show that the difference percentage in comparison with experimental data varies, but all the predictions are within the acceptable limit, that is, 50% when the factor of 2 was used. Weibull regression model has the lowest normalized-root-mean square error value (0.07) and thus has highest prediction capability among the models. Therefore, the probabilistic model is a better alternative for strain–life prediction compared with deterministic models.

Certain Issues in Variable Amplitude Fatigue

Fatigue crack growth behavior of a series of aluminum alloy under single overload tests, repeated overload tests and a variable amplitude loading spectrum are analyzed. It is shown that the material behavior is governed by micro-mechanisms. For crack initiation at a notch, a short crack model presented here gives acceptable results.

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.

Elastic–plastic fatigue crack growth analysis under variable amplitude loading spectra

Most fatigue loaded components or structures experience a variety of stress histories under typical operating loading conditions. In the case of constant amplitude loading the fatigue crack growth depends only on the component geometry, applied loading and material properties. In the case of variable amplitude loading the fatigue crack growth depends also on the preceding cyclic loading history. Various load sequences may induce different load-interaction effects which can cause either acceleration or deceleration of fatigue crack growth. The recently modified two-parameter fatigue crack growth model based on the local stress–strain material behaviour at the crack tip [1,2] was used to account for the variable amplitude loading effects. The experimental verification of the proposed model was performed using 7075-T6 aluminum alloy, Ti-17 titanium alloy, and 350WT steel. The good agreement between theoretical and experimental data shows the ability of the model to predict the fatigue life under different types of variable amplitude loading spectra.

Assessing relative spectra severity using single fatigue test coupons

A common requirement of airframe fatigue analysis is to know the relative fatigue severity of two variable amplitude load spectra when they are applied to the same components or structures. For example, when the predicted service spectrum used in a full-scale airframe fatigue test is later found to be unrepresentative of the average fleet usage, it is necessary to determine the extent to which the service spectrum is more or less severe than the test spectrum. In such cases, methods are required to allow the spectra to be compared so that the results of the test may be used to represent in-service usage. Whilst conventional fatigue prediction tools/models are available for this task, these methods usually contain uncertainties which are difficult to assess without resorting to extensive coupon test programs. In this paper, a very small coupon test program is used to asses the relative severity of two spectra for crack growth from small natural cracks to failure. The two spectra were applied sequentially to fatigue coupons and the crack growth data was assessed using quantitative fractography. This allowed direct comparison of the crack growth rate from the two spectra at different times in the crack growth life.

Fatigue life predictions using fracture mechanics methods

In the present work, a simple engineering approach which is based on a relatively solid background and which is checked against fatigue test data for various test conditions was developed: it may provide a practical and reliable basis for the analysis of structures under in-service loading conditions, in the presence of previous corrosion attack, or in the presence of a residual stress field, by using widespread fracture mechanics software. In particular, the approach was checked against an experimental program which consists of the following fatigue tests: base and friction stir welded (FSW) material under constant amplitude loading at different loading ratios ( R = 0.1, 0.5, −1); pre-corroded base and FSW material under constant amplitude loading at load ratio R = 0.1; centre hole FSW specimens under the standardised variable amplitude loading spectrum FALSTAFF. Moreover, from the literature fatigue experiments under FALSTAFF of cold expanded as well as not cold expended holes were also used to validate the approach. The predictions were performed with the last version of AFGROW and NASGRO 3.0 software.

Investigation of fatigue damage to welded joints under variable amplitude loading spectra

The paper presents the results of the investigation on the effect of loading spectra with different mean stresses on the validity of Miner’s rule, and the effect of stresses below the constant amplitude fatigue limit (CAFL) on the fatigue performance of two types of weld joint. In support of understanding the mechanism for any deficiency to Miner’s rule, fracture mechanics analysis was carried out by measuring and predicting the crack growth in specimens tested under both constant amplitude and variable amplitude loading. The experimental results showed that, although Miner’s rule would predict the same fatigue life for each type of specimens tested under the same spectrum, in fact the actual value of Σ( n/ N) at failure strongly depended on the sequence applied. The influence of the loading sequence on Σ( n/ N) was in agreement with that on crack growth rates. The deficiency in Miner’s rule was attributed primarily to the stress interaction effects resulting from the type of loading sequence used. The experimental results also showed that, under certain circumstances, stress ranges well below the fatigue limit were found to be as damaging as implied by the S– N curve extrapolated beyond the CAFL without changing the slope. The value of the minimum fully damaging stress range was found to depend on the basic fatigue strength of the weld joint.

Artificial neural networks in spectrum fatigue life prediction of composite materials

An artificial neural network has been proved to be a sufficient tool for modelling fatigue life of multidirectional composite laminates made of GFRP composite materials and tested under constant amplitude loading patterns. Modelling efficiency of the network was satisfactory for both on- and off-axis coupons’ life, irrespective of the test conditions, i.e., R-ratio that defines the developed stress state on the coupon. Tension–Tension, Compression–Compression and even Tension–Compression loading patterns were investigated and modelling accuracy of the proposed ANN model was validated. The main benefit of this new modelling tool is that only a small portion, in the range of 40–50%, of the experimental data is needed for the whole analysis. Thus, expensive and time consuming tests required by the conventional way for the establishment of S– N curves could be significantly reduced without significant loss of accuracy. We applied the neural network method using experimental data from two different (in nature) material systems and proved that constant life diagrams (CLDs), which are very useful for the design of structures loaded under variable amplitude loading spectra, can be efficiently modelled using a much smaller set of experimental data compared to that needed for the development of CLDs by the conventional way.

Fatigue damage analysis and life assessment under variable amplitude loading conditions

An earlier developed critical plane-energy based damage parameter has been further developed to assess the life of engineering components subjected to variable service loading conditions. In damage analysis, the effects of materials memory, small cycles and loading sequence on the hysteresis stress–strain loops of materials have been included. The parameter successfully correlated fatigue lives of a low carbon steel and two aluminum alloys of 7075-T651 and 2024-T3 subjected to variable amplitude loading spectra.

Fatigue load sequence effect ranked by critical available energy density

The ways with which variable amplitude load spectra are simplified by taking only a portion of the load history as a block and applying it repeatedly make the prediction of fatigue life a nonunique procedure. This is because the process of damage cumulation is sensitive to alteration in load sequence. Variations in load amplitude affect the proportion of energy dissipated and that used to initiate and/or propagate cracks. A weighted wavelength index is defined that can reflect the complex load sequence effect on crack growth rate. Certain combinations of load sequence are shown to enhance crack growth while others tend to retard crack growth. This is demonstrated from a five-cycle load block where the amplitude and frequency are varied. Crack growth is modelled as the coalescence of a series of crack initiation sites, the loci of which are assumed to coincide with the cumulated volume energy density reaching a critical state, which is characteristic of the material in accordance with the strain energy density criterion. Results are based on the incremental theory of plasticity.

Mechanisms for the retardation of fatigue cracks following single tensile overloads: behavior in aluminum-lithium alloys

Mechanisms for the transient crack growth retardation of fatigue cracks following single tensile overloads are examined in a high-strength aluminium-lithium alloy 2090-T8E41, with specific emphasis on the role of fatigue crack closure. Mechanically, it is found that following the application of the overload, an immediate acceleration in fatigue crack growth is observed, which results from a reduction in (far-field) crack closure levels due to crack tip blunting. Subsequent crack growth retardation, as the crack penetrates the overload plastic zone, is associated with enhanced crack tip shielding prompted by compressive residual stresses ahead of the crack tip, crack deflection and consequent (near-tip) crack closure induced by asperity wedging in the immediate crack wake. Aluminum-lithium alloys, by virtue of their marked anisotropy and planar slip characteristics which promote meandering crack paths and hence high levels of shielding, are found to show large load interaction effects, and thus rank superior to other high strength aluminum alloys under tension-dominated variable amplitude loading spectra. However, under conditions where specimen surface layers are removed, or where cycling is performed at high (positive) load ratios, or involves compressive overload cycles (all processes which tend to limit the development of crack closure), the superior performance of aluminum-lithium alloys under variable amplitude fatigue loading may be compromised.

On the influence of single and multiple peak overloads on fatigue crack propagation in 7075-T6511 aluminum

The phenomenon of fatigue crack retardation due to variable amplitude loading spectra was studied in 7075-T6511 aluminum alloy. Selected precracked compact tension specimens were subjected to single and multiple peak applications of overload stress intensity values and subsequently cycled at lower stress intensities. Detailed characteristics of the fatigue crack propagation process were measured directly on the fracture surfaces using electron microscopy replicating techniques. The degree of retardation was shown to depend strongly on: 1. A. The relative amplitudes of the peak stress intensity ( ΔK 2 ΔK 1 ) 2. B. The number of stress applications N 2 at the peak stress intensity ( ΔK 2) 3. C. The magnitude of the constant amplitude crack growth rate at the lower stress intensity range ( da dn ) ΔK1 4. D. The number of fatigue cycles N 3 at the lower stress intensity level after the last peak stress is applied. A comparison was made between the experimentally observed magnitude of retardation and that predicted using: (1) a model where the retardation is proportional to the ratio of peak stress plastic zone size to secondary stress plastic zone size and (2) an effective stress intensity model. It appears that no present model can accurately predict many of the complex features of the cycle by cycle crack growth behavior experimentally observed. For example, immediately following the last application of the high stress, the crack growth rate at the lower stress levels was accelerated over the value normally observed at constant amplitude cycling (at that same lower stress level). After a period of several cycles, the retardation increased. This is the previously reported delayed retardation effect. After further cycling the crack growth rate slowly increased to what would normally be observed had the peak stress not been applied.