Damage Accumulation Rule Research Articles

Damage evaluation under complex fatigue loading conditions

Fatigue damage and life assessment of multiaxial loadings is still an issue yet to resolve. Many methods have been proposed with promising agreements with the experimental results. However, the performance of such methods is, more than often, purely based on fatigue tests with simple loading conditions. In this work the stress scale factor (SSF) criterion and the virtual cycle counting (vcc) method are used to estimate fatigue life and damage accumulation with two damage accumulation rules. Fatigue tests were carried out with three different variable amplitude random loadings, applied to several specimens made from a 42CrMo4 high-strength steel. Fatigue crack plane measurements were compared with predictions from several critical plane models. The applied methods provided very acceptable results making the SSF package (SSF equivalent stress and virtual cycle counting method) a good method to estimate fatigue life and assessment of the damage accumulation in random fatigue loadings.

A unified frequency domain fatigue damage modeling approach for random-on-random spectrum

Current frequency domain damage models only deal with stationary random loadings (stationary Power Spectral Density), but many machine components, such as jet engines, rotating machines, and tracked vehicles are subjected to evolutionary i.e. time-dependent PSD conditions under real service loadings. An innovative fatigue damage modeling approach is proposed to predict fatigue damage of structures under complex evolutionary PSD loading conditions where the topology of PSD function changes with time. This new approach is based on a novel modeling framework that the evolutionary PSD response of a structure can be decomposed into a finite number of discrete PSD functions. Each PSD function can be split into narrow frequency bands so that each of narrowbands can be associated with Rayleigh distribution of stress cycles. Fatigue damage can then be predicted by summing up damages for each individual band and each discrete PSD function on the basis of a damage accumulation rule. The proposed modeling approach is numerically and experimentally validated by a finite element method and experiments. The proposed modeling approach provides a more efficient and accurate modeling technique for fatigue damage assessment of engineering structural components under very complex random loadings.

Fatigue Strength and Life Prediction of a MAR-M247 Nickel-Base Superalloy Gas Turbine Blade with Multiple Carbide Inclusions

Casting of a gas turbine blade from MAR-M247 nickel-base superalloy is followed by multiple carbide precipitates as a result of solidification. The microstructure of carbide was established with scanning electron microscopy and energy spectrum analysis. A finite element model simulating the blade with a random carbide precipitate is constructed using ANSYS software, and stress-strain evaluation is performed. The blade operation conditions are realized in a vibratory-tensile combined test setup with stress measurements using strain gauges arranged on different parts of the blade. The respective von Mises equivalent stresses obtained in simulation and test measurements are found to be comparable and can be used to assess the blade fatigue life based on the available fatigue curves and Palmgren–Miner rule of damage accumulation. Simulation and experimental results are the basis for plotting the relationship between the volumetric ratio of precipitates in the blade and its fatigue life. The results obtained at room temperature can; be extrapolated to the elevated ones to provide more reliable prediction of the superalloy blade fatigue and creep-fatigue life values.

Nonlinear Damage Accumulation Rule for Solder Life Prediction Under Combined Temperature Profile With Varying Amplitude

Due to a mismatch of the coefficient of thermal expansion, electronic solder joints experience cyclic shear strain, which ultimately leads to fatigue failure. Traditional predictions of solder joint thermal fatigue life that use the experimental data or the physics-of-failure model often assume a regular profile. For complex temperature profiles, the linear accumulation rule is typically used to integrate the superposition effect. However, the linear rule was proved not applicable to most of the complex loading or temperature conditions. Based on the damage curve theory and the fatigue crack propagation theory, a novel nonlinear accumulation rule has been deduced for solder joint life predictions under irregular profiles, which were composed of two standard temperature cycles and may be experienced by phased-mission system. Four groups of experiments were conducted for ball grid array package solder joints with different dimensions and materials to determine parameters of the proposed nonlinear accumulation rule. The finite-element simulation method was used to extend this rule to more general cases for application. Compared to Miner’s linear accumulation rule, prediction of solder joint thermal fatigue life via the proposed nonlinear accumulation rule is closer to the accelerated life test results of real-world electronic solder joints under a combined temperature profile.

A new modeling framework for fatigue damage of structural components under complex random spectrum

Time and frequency domains-based fatigue damage prediction approaches have been developed over past decades to predict fatigue performance of mechanical structures subjected to random loads. Frequency domain approaches are increasingly being adapted to provide fatigue assessment of mechanical components subjected to random loads due to computational efficiency and cost savings. Current frequency domain damage models only deal with stationary random loadings where Power Spectral Density (PSD) of random loadings does not change in time. However, many machine components, such as jet engines and tracked vehicles are subjected to evolutionary PSD i.e. random-on-random loadings under real service loads. A new fatigue damage modeling framework is proposed to predict fatigue damage of structures under complex evolutionary PSD where the topology of PSD function changes with time. The proposed modeling approach is based on the underlying concept that the evolutionary PSD response of a structure can be decomposed into a finite number of discrete PSDs. Each PSD can be split into narrow frequency bands so that each of narrowbands can be associated with Rayleigh distribution of stress cycles. Fatigue damage can then be predicted by summing up damages for each individual band and each discrete PSD function on the basis of a damage accumulation rule. The proposed modeling approach is numerically and experimentally validated by a finite element method and experiments using three simplified structures made of 5052-H32 aluminum alloy. The proposed approach provides a more efficient and accurate modeling technique, and account for complex random loadings of structural components.

The origins of white etching cracks and their significance to rolling bearing failures

Presence of white etching cracks has been widely associated with early failures of rolling bearings in a number of applications, with wind turbine gearbox bearings being the most frequently cited and practically significant example. Despite the recent research efforts, there is yet no universal agreement on the mechanisms of formation of these cracks and little direct evidence of their significance to bearing reliability. In an attempt to address this, this paper proposes a new theory on the origins and significance of white etching cracks. The paper provides systematic experimental evidence in support of this theory through rolling contact fatigue tests performed with AISI 52100 bearing steel specimens on a triple-disc machine over a wide range of contact conditions. The test results show that white etching cracks can be formed with base oils as well as commercially formulated transmission and engine oils. WECs were generated under slide-roll-ratios ranging from 0.05 to 0.3, under positive and negative sliding, different contact pressures and specific film thicknesses ranging from 0.1 to 0.7. No white etching areas were ever observed without the associate crack being present, and it was also shown that white etching areas themselves can be produced in a pure rubbing contact of bearing steels under both lubricated and unlubricated conditions. These results provide direct evidence that the steel transformations that exhibit themselves as white etching areas are formed through rubbing of the existing crack faces, and that the chemical composition of the lubricant and the magnitude and direction of sliding are not the primary driver of WEC formation, in contrast to literature. Instead, the results presented here show that WECs are formed through the action of a specific stress history in time via the following mechanism: (i) Short-lived high contact stresses, which can be caused by a number of factors, act in the initial stages of the component life to initiate early fatigue cracks, (ii) These high stresses cease and the contact subsequently operates under a relatively moderate nominal stress so that the early-formed cracks propagate relatively slowly and their faces rub and beat together for a prolonged period, (iii) White etching areas are formed around the existing cracks through this crack-face rubbing, (iv) Eventual contact failure occurs through pitting which can be caused by a white etching or a non-white etching crack depending on its location and propagation rate. Standard contact fatigue life models are unable to account for the adverse effects of this specific stress sequence owing to their use of linear damage accumulation rules, which leads to such failures being termed as ‘premature’. The proposed theory asserts that the white etching cracks are not the cause of ‘premature’ bearing failures, but that both the WECs and the earlier-than-predicted bearing failures are caused simultaneously by a third factor: a specific time history of applied contact stress.

Lifetime extension through Tj equalisation by use of intelligent gate driver with multi-chip power module

Typical high-current power modules used in traction and wind generation contain several dies in parallel. Non-ideal geometries and electrical parameter variations cause an unequal aging of each die which limits the effectiveness of using parallel devices. This paper presents an intelligent power module with a TSEP-based junction temperature measurement and internal temperature equalisation for extending its operational lifetime. As the magnitude and number of junction temperature cycles strongly dictate the power module lifetime, this paper focuses on the quantification of the lifetime gain via the application of common automotive drive cycles. Thus, a general thermal model is first deduced from the experimental results. The lifetime is then estimated using a stress-counting rainflow algorithm, a pre-determined damage law and a linear damage accumulation rule. Finally, in order to illustrate the lifetime extension, 160 drive cycles, including the legislatives drive cycles, are simulated. A lifetime gain of up to two times can be expected with the temperature equalisation method. Therefore, the initial investment on the developed intelligent power module is justified by the benefit of the large gain in lifetime and of the end-of life indication functions.

Neural Networks Applied to the Wave-Induced Fatigue Analysis of Steel Risers

Time domain stochastic wave dynamic analyses of offshore structures are computationally expensive. Considering the wave-induced fatigue assessment for such structures, the combination of many environmental loading cases and the need of long time-series responses make the computational cost even more critical. In order to reduce the computational burden related to the wave-induced fatigue analysis of Steel Catenary Risers (SCRs), this work presents the application of a recently developed hybrid methodology that combines dynamic Finite Element Analysis (FEA) and Artificial Neural Networks (ANN). The methodology is named hybrid once it requires short time series of structure responses (obtained by FEA) and imposed motions (evaluated analytically) to train an ANN. Subsequently, the ANN is employed to predict the remaining response time series using the prescribed motions imposed at the top of the structure by the floater unit. In this particular work, the methodology is applied aiming to predict the tension and bending moments’ time series at structural elements located at the top region and at the touchdown zone (TDZ) of a metallic riser. With the predicted responses (tensions and moments), the stress time series are determined for eight points along the pipe cross sections, and stress cycles are identified using a Rainflow algorithm. Fatigue damage is then evaluated using SN curves and the Miner-Palmgren damage accumulation rule. The methodology is applied to a SCR connected to a semisubmersible platform in a water depth of 910 m. The obtained results are compared to those from a full FEA in order to evaluate the accuracy and computer efficiency of the hybrid methodology.

Fatigue life assessment of welded joints made of the stainless steel X6CrNiNb18‐10 for thermomechanical and variable amplitude loading

AbstractThe aim of the presented work is to develop improved concepts for the prediction of fatigue lifetime under variable amplitude loading including plastic deformation and thermomechanical fatigue of welded joints made of the austenitic stainless steel 1.4550. Local strain amplitudes are located in the regime of low cycle fatigue, which is dominated by short crack growth. This can best be described by nonlinear fracture mechanics. To develop a fracture mechanics based lifetime model, different experiment types are carried out to estimate the influence of loading history, thermal cycling, and mean stresses. For the evaluation, different estimation concepts based on Palmgren‐Miner's classic linear damage accumulation rule are used: solely calculated by strain ranges, damage parameter established by Smith, Watson and Topper, and a damage parameter based on the cyclic effective J‐integral. The differences in the concepts are highlighted and used for further considerations on how to improve the lifetime prediction models.

Effects of Amplitude Variations on Deformation and Damage Evolution in SnAgCu Solder in Isothermal Cycling

Although apparently simpler than in thermal cycling, the behavior of SnAgCu (SAC) solder joints in cyclic bending or vibration is not currently well understood. The rate of damage has been shown to scale with the inelastic work per cycle, and excursions to higher amplitudes lead to an apparent softening, some of which remains so that damage accumulation is faster in subsequent cycling at lower amplitudes. This frequently leads to a dramatic breakdown of current damage accumulation rules. An empirical damage accumulation rule has been proposed to account for this, but any applicability to the extrapolation of accelerated test results to life under realistic long-term service conditions remains to be validated. This will require a better understanding of the underlying mechanisms. The present work provides experimental evidence to support recent suggestions that the observed behavior is a result of cycling-induced dislocation structures providing for increased diffusion creep. It is argued that this means that the measured work is an indicator of the instantaneous dislocation density, rather than necessarily reflecting the actual work involved in the creation of the damage.

On the applicability of Miner’s rule for multiaxial fatigue life calculations under non-proportional load histories

Fatigue design routines and computer codes must use some damage accumulation rule to deal with variable amplitude loadings (VAL), usually Palmgren-Miner (or Miner’s) linear rule for lack of a clearly better option. Nevertheless, fatigue lives are intrinsically sensitive to the order of VAL events, which may e.g. induce residual stresses and thus change the critical point stress state, much affecting its subsequent residual life. On the other hand, in general, non-linear damage accumulation rules are not robust, resulting in better predictions than Miner’s rule only for some specific load orders, requiring a case-by-case analysis. Therefore, Miner’s linear damage rule still is the usual choice in practical fatigue calculations and assessments, giving reasonable predictions at least when properly combined with approaches that sequentially consider plasticity-induced effects, following the critical point stress/strain history in a cycle-by-cycle basis. In this work, Miner’s rule is evaluated for non-proportional tension-torsion loadings on annealed tubular 316L stainless steel specimens. Normal-shear strain histories following either cross, diamond, circular or square paths are applied, and their fatigue lives are measured. Then, more complex VAL paths consisting of combinations of these individual path shapes are applied in other specimens, whose associated fatigue lives are predicted based on Miner’s rule.

Creep damage and life assessment of thick-walled spherical reactor using Larson–Miller parameter

Creep damage and remnant life assessment of a thick-walled spherical reactor made of 316LN austenitic stainless steel (316LN SS) have been investigated. The Robinson's linear damage accumulation rule has been used to obtain damage and remnant life assessment in which time to rupture is determined by Larson-Miller Parameter (LMP). Due to high temperature, creep is the most significant damage mechanism exhausting the lifetime of the reactor. The material properties, except Poisson's ratio, are assumed to depend on the temperature. An analytical solution employed to calculate the stress rates followed by an iterative method using initial thermoelastic stresses at zero time to obtain effective stress histories and then using LMP to calculate the damage and remnant life assessment. It is concluded that the temperature gradient has a significant effect on the effective stress histories so that effective stresses are decreasing with time in a uniform temperature field while they are increasing in the presence of a thermal gradient.

Numerical prediction of failure in single point incremental forming using a phenomenological ductile fracture criterion

Besides the high simplicity and flexibility, excessive thinning of the sheet metal is one of the limitations of single point incremental forming (SPIF). To overcome this drawback, a finite element (FE) simulation can be implemented for determination of an appropriate deformation strategy. Since the formability in SPIF is often limited by fracture failure, the prediction of ductile fracture using a FE simulation is of the significant importance. In this paper, by implementing the phenomenological modified Mohr-Coulomb (MMC3) model through an appropriate user subroutine within the commercial FE code Abaqus/Explicit, the ductile fracture in SPIF is investigated. Based on the designed tensile tests, the MMC3 criterion is calibrated for AA6061-T6 aluminum alloy sheet using an inverse approach. The stress and strain states of the localized deformation field in SPIF are comprehensively analyzed. With the aid of stress triaxiality and normalized Lode angle parameter, it is shown that the loading path in SPIF is highly nonlinear. Accordingly, a nonlinear damage accumulation rule is utilized to predict the onset of fracture. The comparison of predicted fracture depths of SPIF parts with experimental ones demonstrates an average discrepancy of 10% for utilizing the MMC3 criterion. A good agreement of the fracture location can also be found between experiments and FE simulations. Numerically computed fracture strains show that the fracture forming limit diagram (FFLD) under a proportional loading, like a tensile test, differs in shape and value from the one obtained under a non-proportional loading like SPIF in which the FFLD is higher.

High cycle fatigue micromechanical behavior of dual phase steel: Damage initiation, propagation and final failure

Micromechanical analyses of various materials under high cycle fatigue (HCF) loading have been investigated previously. Experimental findings have shown that failure due to HCF occurred with different pattern comparing to the other loading conditions. The current work tries to carry out both experiments and simulations at micro scale. In this research, scanning electron microscopy (SEM) and metallography images of the specimens are taken to investigate the failure and deformation patterns in dual phase (DP) steel under high cycle fatigue loading. Failure mechanisms of DP steels are also predicted using a real representative volume element (RVE) and microstructural finite element (FE) modeling. The linear damage accumulation rule (Miner's damage rule) is used to determine the material degradation due to fatigue loading. The cyclic loading is implemented in the FE model of the microstructure by developing ANSYS parametric design language (APDL) code to obtain the damage, failure pattern and fatigue life of the RVE. It is also shown that the finite element modeling of the real RVE considering both plasticity and fatigue damage leads to acceptable compatibility between the obtained cracking patterns from SEM images (experiments) and finite element predictions.

Compatibility of S-N and crack growth curves in the fatigue reliability assessment of a welded steel joint

Reliability analysis is a crucial phase in assessing the safety status of new and existing structures. One of its applications is to predict the fatigue life of fatigue prone details. Two models are used to formulate the fatigue limit state: S-N curves in combination with Palmgren-Miner damage accumulation rule and linear elastic fracture mechanics using fatigue crack growth rate curves. Within each model, choices must be made on the values of the variables and these choices are sometimes different in different standards. This study investigates the consistency between the standards by determining the failure probability of the different models and values for a transverse butt weld joint under Variable Amplitude Loading. Partial factors required for the design are then derived as a function of the required reliability for each model and associated values. The influence of the uncertainties related to each involved variable is evaluated by performing a sensitivity analysis.

Estimation of fatigue S-N curves of welded joints using advanced probabilistic approach

This paper provides a new advanced probabilistic approach for reliable estimation of the fatigue characteristic S-N curves of welded joints both for constant amplitude (CA) and variable amplitude (VA) loading conditions. The presented approach, which is referred to as the ML-MCS approach, combines Maximum Likelihood method (ML) and Monte-Carlo Simulations (MCS) method to estimate true p-quantiles of CA and VA S-N curves by using complete experimental data-sets. The ML-MCS approach includes a linearization method for use of S-N curves in combination with linear damage accumulation rule as well as for direct comparison with current standards. Application of the ML-MCS approach on two study cases and comparison with current standards shows that the use of the ML-MCS approach may have a significant impact in re-definition of CA and VA S-N curves of current standards and in particular of the CAFL, of the S-N curve second slope and of the critical value of accumulated damage at failure. The last section of the paper provides accurate guidelines for future experimental tests needed for re-definition of current standards.

A Model of BGA Thermal Fatigue Life Prediction Considering Load Sequence Effects.

Accurate testing history data is necessary for all fatigue life prediction approaches, but such data is always deficient especially for the microelectronic devices. Additionally, the sequence of the individual load cycle plays an important role in physical fatigue damage. However, most of the existing models based on the linear damage accumulation rule ignore the sequence effects. This paper proposes a thermal fatigue life prediction model for ball grid array (BGA) packages to take into consideration the load sequence effects. For the purpose of improving the availability and accessibility of testing data, a new failure criterion is discussed and verified by simulation and experimentation. The consequences for the fatigue underlying sequence load conditions are shown.

A statistically self-consistent fatigue damage accumulation model including load sequence effects under spectrum loading

A probabilistic methodology is proposed to evaluate fatigue damage accumulation and fatigue lives of specimens under variable amplitude loading. With probabilistic modifications in the present model, the calculative consistency is achieved between fatigue damage and fatigue life. The load sequence effects on fatigue damage accumulation are properly accounted for variable amplitude loading. The developed damage model overcomes the inherent deficiencies in the linear damage accumulation rule, but still preserves its simplicity for engineering application. Based on the Monte Carlo sampling method, numerical verification of this model is conducted under two kinds of spectrum loading. The predicted probabilistic distributions of fatigue lives are validated by fatigue tests on Al-alloy straight lugs. KEYWORDS. Fatigue damage; Fatigue life; Probabilistic statistical model; Load sequence effect; Statistical self-consistency.

Study of in-plane Fatigue Failure and Life Prediction of Weave Composites under Constant and Variable Amplitude Loading

The fatigue behaviour of two-dimensional weave composites under constant and variable amplitude loading was discussed in this article. The theories of life prediction methods were represented, including cycle counting, S–N formulation, constant life diagrams (CLD), damage accumulation rule and stress analysis. Special focuses on CLDs were studied through the interpolation method known as the kriging model. Fatigue tests under constant amplitude loading were carried out utilising the servo-hydraulic Shimadzu testing machine. Tension–tension, tension–compression and compression–compression loading patterns were investigated in fatigue testing. The macro-failure mode was obviously different between tensile and compressive loading. Micro-failure surfaces were observed in micro-mechanism with scanning electron microscopy (SEM). The Basquin equation and the linear Palmgren–Miner (P–M) rule were employed to characterize the fatigue properties under random loading conditions. A new constitutive relation was introduced which took into account the tensile-compressive asymmetry of composites. Finally, the benchmarking for the stochastic loading case was executed using proposed methodology and variable amplitude fatigue experiments. Through the contrast between prediction and the experimental data, it was inferred that the proposed prediction method under any loading conditions (stress ratios and ranges) gave an accurate life prediction.

Fatigue Damage Accumulation Under Quasi-Random Loading of Composite Airframe Elements

To perform engineering estimations of the fatigue life of quasi-randomly loaded layered composites, with geometric concentrators, representing the longitudinal elements of composite wing of a transport airplane, a special rule of fatigue damage accumulation is suggested. The main propositions of the method for calculating the fatigue life of these elements by using this rule are formulated. The examples of estimations presented show a good agreement between analytical results and experimental data. A number of important conclusions about the effect of different levels of cyclic loading and “GAG” cycles of different flight types of the quasi-random “TWIST” program on the total fatigue life are made.