Variable amplitude cyclic deformation and fatigue behaviour of stainless steel 304L including step,periodic, and random loadings

This paper discusses cyclic deformation and fatigue behaviours of stainless steel 304L and aluminium 7075‐T6 under variable amplitude loading using strain‐controlled as well as load‐controlled tests. Load sequence effects were investigated in step tests with high‐low and low‐high sequences. For stainless steel 304L, strong hardening induced by the first step of the H‐L sequence significantly affects the fatigue behaviour, depending on the test control mode used. For periodic overload tests of stainless steel 304L, hardening due to the overloads was progressive throughout life and more significant than in H‐L step tests. For aluminium 7075‐T6, no effect on deformation behaviour was observed due to periodic overloads. However, the direction of the overloads was found to affect fatigue life, as tensile overloads led to longer lives, while compressive overloads led to shorter lives. Deformation and fatigue behaviours under random loading were also studied for the two materials. To correlate a broad range of fatigue life data for a material with strong deformation history effect, such as stainless steel, it is shown that a damage parameter with both stress and strain is required. The Smith‐Watson‐Topper parameter as such a parameter is shown to correlate the data reasonably well under different control modes and loading conditions.     

Fatigue damage of medium carbon steel under sequential application of axial and torsional loading

Fatigue tests were conducted on S45C steel under fully reversed strain control conditions with axial/torsional ( at ) and torsional/axial ( ta ) loading sequences. The linear damage value (n₁/N₁+n₂/N₂) was found to depend on the sequence of loading mode ( at or ta ), sequence of strain amplitude (low/high or high/low) and life fraction spent in the first loading. In general, at loading yields larger damage values than ta loading and the low–high sequence of equivalent strain leads to larger damage values than the high–low sequence. The material exhibits cyclic softening under axial cyclic strain. Cyclic hardening occurs in the torsion part of ta loading, which elevates the axial stress in the subsequent loading, causing more damage than in pure axial fatigue at the same strain amplitude. Fatigue life is predicted based on the linear damage rule, the double linear damage rule, the damage curve approach and the plastic work model of Morrow. Results show that overly conservative lives are obtained by these models for at loading while overestimation of life is more likely for ta loading. A modified damage curve method is proposed to account for the load sequence effect, for which predicted lives are found to lie in the factor‐2 scatter band from experimental lives.     

Interior micro-defect induced cracking mechanism and life prediction of carburized Cr−Ni steel based on double nonlinear damage under variable amplitude loading

The constant/variable amplitude loading fatigue test with interior inclusion-fine granular area-fisheye induced failure under R=0 were carried out on carburized Cr−Ni steel. The results showed that the fatigue life under variable amplitude loading is longer than that under constant amplitude loading in very-high-cycle fatigue regime under same maximum stress level, and the surface morphology of fine granular area under variable amplitude loading is coarser than that under constant amplitude loading under same order of magnitude of fatigue life. Simultaneously, it can be determined that the formation micro-mechanism of fine granular area is caused by the continuous deboning due to stress concentration around interior micro-defects. Furthermore, the life prediction model based on double nonlinear fatigue damage, which considers the coupling effect of local equivalent stress (surface residual stress and local stress concentration effect), loading sequence, failure mechanism and nonlinear characteristics of fatigue damage under constant/variable amplitude loading is established, and predicted life has good accuracy within the factor-of-three lines.     

Modelling of load interaction and overload effect on fatigue damage of steel bridges

This paper studies the effects of load sequence and interaction, and overloading effect on the fatigue damage of bridges on the basis of a non-linear fatigue damage model. The model is derived from the theory of continuum damage mechanics for high-cycle fatigue. Fatigue behaviour at two levels of constant stress range is first discussed in detail. The formulation for the effective fatigue strength of the predamaged members is then derived, and the results predicted by the model are compared with the experimental data for two stress level tests and other results obtained from linear and double linear fatigue damage models. The variation of cycle ratio and fatigue life due to overloading is secondly investigated; the equations for evaluating the effect of overloading on fatigue damage accumulation on bridges at normal traffic loading are then derived. It has been demonstrated that the developed model can well describe the effect of load sequence and interaction and has also been verified by comparing the predicted results obtained by the model with the experimental data based on two levels of stress tests. The effect of accidental overloading on the fatigue damage of existing bridges can also be evaluated using the model. The model is applied to evaluate the fatigue damage and service life of the Tsing Ma Bridge, an essential portion of the transport network for the Hong Kong airport, under normal traffic loading and possible accidental overloading.     

An experimental approach to estimate damage and remaining life of metals under uniaxial fatigue loading

An experimental procedure to estimate damage evolution and remaining fatigue life of metals associated with fatigue loading is presented. Experimental phase involves uniaxial tension–compression fatigue tests performed with solid API 5L X52 and tubular carbon steel 1018 specimens subjected to both constant and variable amplitude loading. A correlation between the so-called damage parameter and the thermal response of a material at different damage levels is proposed. Results demonstrate that the correlation can estimate damage evolution with reasonable accuracy in both constant and variable amplitude fatigue processes. It is shown that under the conditions tested the evolution of damage parameter with respect to the normalized fatigue life is independent of the load amplitude, load ratio, loading sequence, material properties, and specimen geometry. The proposed correlation and the relationship between the damage parameter and the normalized fatigue life are employed to develop a non-destructive method to predict the remaining fatigue life of metallic specimens with prior fatigue damage. The method is applied to both constant and variable amplitude loading and the predicted results are found to be in good agreement with those obtained from the experiments.     

变幅载荷下纤维金属层板的疲劳与寿命预测

文章建立了纤维金属层板等幅疲劳载荷下的疲劳裂纹扩展速率与寿命预测模型。在此基础上对玻璃纤维-铝合金层板（GLARE）的疲劳裂纹扩展与分层扩展行为进行了试验研究,探讨了层板过载疲劳行为的机理,提出了纤维金属层板变幅载荷下疲劳寿命预测的等效裂纹闭合模型,并在GLARE层板上得到了验证。     

Foreword – Materialwissenschaft und Werkstofftechnik 10/2011

Load controlled fatigue tests were performed up to 10⁷ cycles on flat notched specimens (K_t = 2.5) under constant amplitude and variable amplitude loadings with and without periodical overloads. Two materials are studied: a ferritic‐bainitic steel and a cast aluminium alloy. These materials have a very different cyclic behaviour: the steel exhibits cyclic strain softening whereas the Al alloy shows cyclic strain hardening. The fatigue tests show that, for the steel, periodical overload applications reduce significantly the fatigue life for fully reversed load ratio (R_σ = –1), while they have no influence under pulsating loading (R_σ = 0). For the Al alloy overloads have an effect (fatigue life decreasing) only for variable amplitude loadings. The detrimental effect of overloads on the steel is due to ratcheting at the notch root which evolution is overload's dependent.     

The effect of overloading sequences on landing gear fatigue damage

In service, landing gear can be subject to unexpected hard landing load, which is beyond the design domain. The consequences due to overload can affect the design life of a landing gear to some extent. In this paper, the effect of overload and different loading sequences in random spectra on fatigue damage are investigated, using strain–life based fatigue analysis methods. The discussions are emphasised on the effect of loading sequences on residual stress and mean stress, especially the effect of overload on the fatigue damage of subsequent cycles. In addition, different fatigue analysis techniques in commercial fatigue analysis packages are reviewed and compared. The analysis indicates that the overload effect is stress state dependent and dominated by local residual and mean stress. A ‘Begin’ overload in a load spectrum would cause more damage in the local compressive yield area and an ‘End’ overload within a spectrum will worsen the tensile yielding area. It is suggested that the load sequence effect should be considered in common fatigue analysis if local yielding would exist before or after overloading.     

Non-destructive fatigue damage characterization of laminated thermosetting fibrous composites

The fatigue behaviour of the laminated thermosetting Fiberdux 6376-HTA composite material is studied experimentally for both constant and variable amplitude stress reversal loading. The fatigue-induced material degradation is correlated to non-destructive evaluation data obtained from C-scan graphs through the concept of the damage severity factor ( DSF ). The DSF is able to account for the varying severity of damage at the different specimen locations and is used to quantify the fatigue-induced damage. The concept of the DSF , introduced earlier by the authors for constant amplitude fatigue loading of thermoplastic fibrous composites, is applied to characterize fatigue damage of thermosetting fibrous composites and is extended to account for variable amplitude loading. Constant amplitude fatigue tests at various stress levels were performed to correlate fatigue damage to the change of mechanical properties, such as axial stiffness, residual tensile strength and interlaminar shear strength, and to develop expressions to relate DSF to the degradation of the mechanical properties with increasing fatigue damage. Correlation between DSF evolution and consumed fatigue life is made and fatigue damage functions involving stress amplitude dependency are formulated. These expressions together with a modified rainflow method are then used to assess fatigue life under variable amplitude fatigue loading; computed fatigue lives are compared against experimental results.     

变幅荷载作用下沥青混合料的疲劳损伤试验

为了深入研究沥青混合料的疲劳性能,解决现有疲劳性能研究中没有考虑实际路面所受荷载是变幅、重复的加卸载过程这一关键问题,本文通过加载顺序和加载幅值对沥青混合料粘弹性指标的影响进行试验研究,分析了变幅荷载作用下沥青混合料劲度模量、相位角的变化,并选取耗散能作为损伤变量分析了变幅荷载下沥青混合料的疲劳损伤。试验结果表明:劲度模量与应变加载顺序有关;在低高加载顺序中,相位角在两阶段都表现为随着荷载作用次数的增加而增大,在高低加载顺序中,相位角的变化与高低应变的幅值相关;应变在高低顺序加载下累积耗散能要高于低高顺序下的累积耗散能;当采用的前后加载幅值较大时,这种现象更加明显。     

Fatigue behaviour and life prediction of fibre reinforced metal laminates under constant and variable amplitude loading

ABSTRACT Fatigue crack growth of fibre reinforced metal laminates (FRMLs) under constant and variable amplitude loading was studied through analysis and experiments. The distribution of the bridging stress along the crackline in centre‐cracked tension (CCT) specimen of FRMLs was modelled numerically, and the main factors affecting the bridging stress were identified. A test method for determining the delamination growth rates in a modified double cracked lap shear (DCLS) specimen was presented. Two models, one being fatigue‐mechanism‐based and the other phenomenological, were developed for predicting the fatigue life under constant amplitude loading. The fatigue behaviour, including crack growth and delamination growth, of glass fibre reinforced aluminium laminates (GLARE) under constant amplitude loading following a single overload was investigated experimentally, and the mechanisms for the effect of a single overload on the crack growth rates and the delamination growth rates were identified. An equivalent closure model for predicting crack‐growth in FRMLs under variable amplitude loading and spectrum loading was presented. All the models presented in this paper were verified by applying to GLARE under constant amplitude loading and Mini‐transport aircraft wing structures (TWIST) load sequence. The predicted crack growth rates are in good agreement with test results.     

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.     

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.     

Experimental investigation and numerical prediction of fatigue crack growth of 2024-T4 aluminum alloy

Compact specimens were employed to study fatigue crack growth of 2024-T4 aluminum alloy under constant/variable amplitude loading. Apparent R-ratio effect under constant amplitude loading was identified with the nominal stress intensity factor range. Fatigue crack growth rates predicted by a unified model agreed with the experimental data well. Single tensile overload resulted in significant retardation of crack growth which was fully recovered after propagating out of overload-affected zone. Retarded crack growth induced by three-step sequence loading was heavily dependent on two sequence loading parameters. The influence of variable amplitude loading on crack growth was reasonably characterized by Wheeler’s model.     

Fatigue life prediction of woven composite laminates with initial delamination

An engineering approach for fatigue life prediction of fibre‐reinforced polymer composite materials is highly desirable for industries due to the complexity in damage mechanisms and their interactions. This paper presents a fatigue‐driven residual strength model considering the effect of initial delamination size and stress ratio. Static and constant amplitude fatigue tests of woven composite specimens with delamination diameters of 0, 4 and 6 mm were carried out to determine the model parameters. Good agreement with experimental results has been achieved when the modified residual strength model has been applied for fatigue life prediction of the woven composite laminate with an initial delamination diameter of 8 mm under constant amplitude load and block fatigue load. It has been demonstrated that the residual strength degradation‐based model can effectively reflect the load sequence effect on fatigue damage and hence provide more accurate fatigue life prediction than the traditional linear damage accumulation models.     

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

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

Stochastic modelling of low-cycle fatigue damage in 316L stainless steel under variable multiaxial loading

In the present study, a stochastic model is developed for the low-cycle fatigue life prediction and reliability assessment of 316L stainless steel under variable multiaxial loading. In the proposed model, fatigue phenomenon is considered as a Markov process, and damage vector and reliability are defined on every plane. Any low-cycle fatigue damage evaluating method can be included in the proposed model. The model enables calculation of statistical reliability and crack initiation direction under variable multiaxial loading, which are generally not available. In the present study, a critical plane method proposed by Kandil et al . ( Metals Soc., London 280, 203–210, 1982) maximum tensile strain range, and von Mises equivalent strain range are used to calculate fatigue damage. When the critical plane method is chosen, the effect of multiple critical planes is also included in the proposed model. Maximum tensile strain and von Mises strain methods are used for the demonstration of the generality of the proposed model. The material properties and the stochastic model parameters are obtained from uniaxial tests only. The stochastic model made of the parameters obtained from the uniaxial tests is applied to the life prediction and reliability assessment of 316L stainless steel under variable multiaxial loading. The predicted results show good aggreement with experimental results.     

Nondestructive Evaluation of Fiberglass Reinforced Plastic Subjected to Combined Localized Heat Damage and Fatigue Damage Using Acoustic Emission

The effect of fatigue damage to unidirectional fiberglass composite specimens with prior contact heat damage was investigated. After damaging the specimens by contacting them to a hot tip at 360°C, the specimens were subjected to fatigue loading at cyclic stress amplitude corresponding to 65% of the specimens' ultimate tensile strength. The fatigue experiments was halted after 3,000 cycles. The specimens were then subjected to tensile tests while monitoring their acoustic emission (AE) activity. In addition, acoustic emission activities of undamaged and contact heat-damaged specimens were monitored during tensile tests for comparison with specimens with combined fatigue and heat damage. AE activities of all specimens can be categorized into three regions: an early rise in activity, a relatively dormant period in activity, and a high exponential activity before failure. The early rise in activity did not appear on the specimens with combined contact heat and fatigue damage. For undamaged and contact heat-damaged specimens, the period of the dormant activity was independent of the contact heat duration of less than 15 minutes. However, the period was a function of the contact heat duration for combined contact heat and fatigue damaged specimens. Analyzing event duration distribution identified micro-mechanisms of the damage growth upon tensile loading. AE-stress delay concept was used to predict the state of the damage in the composite. A correlation between stress delay parameter and damage parameter was obtained for all of the specimens. Fatigue life of contact heat damaged specimen was also studied. It was found that localized heat damage reduced the fatigue life significantly. Loss of matrix to transfer the load to the fibers uniformly was believed to be responsible for the reduction in the fatigue life.     

Fatigue damage modelling of adhesively bonded joints under variable amplitude loading using a cohesive zone model

In this paper, the fatigue response of adhesively bonded joints under variable amplitude (VA) cyclic loading was predicted using a numerical model. The adhesive layer was modelled using the cohesive zone model with a bi-linear traction-separation response. A damage model, incorporating fatigue load ratio effects, was utilised in conjunction with the cohesive zone model to simulate the detrimental influence of VA fatigue loading. This model was validated against published experimental results obtained from fatigue tests of adhesively bonded single lap joints subjected to various types of VA fatigue loading spectra. This model successfully predicted the damaging effect of VA fatigue loading on the adhesively bonded joints and was generally found to be a significant improvement on the other damage models considered.     

Cumulative fatigue damage of stress below the fatigue limit in weldment steel under block loading

To investigate the cumulative fatigue damage below the fatigue limit of multipass weldment martensitic stainless steel, and to clarify the effect of cycle ratios and high‐stress level in the statement, fatigue tests were conducted under constant and combined high‐ and low‐stress amplitude relative to stress above and below the fatigue limit. The outcomes indicate that neither modified Miner's nor Haibach's approach provided accurate evaluation under repeated two‐step amplitude loading. Moreover, effect of cycle ratios has been determined. Additionally, the cumulative fatigue damage saturated model is established and validated. Cumulative fatigue damage contributed by low‐stress below the fatigue limit in high stress of 700 MPa is higher than that with 650 MPa at identical conditions (fatigue limit 575 MPa). Thus, high stress affects fatigue damage behaviour below the fatigue limit. A new predicted approach has been proposed based on Corten‐Dolan law, whose accuracy and applicability have been proven.