Linear Damage Summation Research Articles

English

The main goal of this study is to investigate the creep fatigue behavior of 316 stainless steel materials. In the low cycle thermal fatigue life model, Manson’s universal slopes equation was used as an empirical correlation which relates fatigue endurance to tensile properties. Fatigue test data were used in conjunction with different modes to establish the relationship between temperature and other parameters. Statistical creep models were created for 316 stainless steel materials. In order to correlate the results of shout-time elevated temperature tests with long-term service performance at more moderate temperatures, different creep prediction models, namely Basquin model, Sherby-Dorn model and Manson-Haferd model, were studied. Comparison between the different creep prediction models were carried out for a range of stresses and temperatures. A linear damage summation method was used to establish life prediction model of 316 stainless steels materials under fatigue creep interaction. Key words: Stainless steel materials, low cycle thermal fatigue, statistical creep model.

Creep failure simulations of 316H at 550 °C: Part I – A method and validation

This paper proposes a method to simulate creep failure using finite element damage analysis. The creep damage model is based on the creep ductility exhaustion concept, and incremental damage is defined by the ratio of incremental creep strain and multi-axial creep ductility. A simple linear damage summation rule is applied and, when accumulated damage becomes unity, element stresses are reduced to zero to simulate progressive crack growth. For validation, simulated results are compared with experimental data for a compact tension specimen of 316H at 550 °C. Effects of the mesh size and scatter in uniaxial ductility are also investigated.

Experimental and Numerical Crack Initiation Analysis of the Compressor Blades Working in Resonance Conditions

Experimental and Numerical Crack Initiation Analysis of the Compressor Blades Working in Resonance ConditionsThis paper presents the results of a complex experimental and numerical crack initiation analysis of the helicopter turbo-engine compressor blades subjected to vibrations. A nonlinear finite element method was utilized to determine the stress state of the blade during the first mode of transverse vibration. In this analysis, the numerical models without defects as well as those with V-notches were defined. The quality of the numerical solution was checked by the convergence analysis. The obtained results were next used as an input data into crack initiation (ε-N) analyses performed for the load time history equivalent to one cycle of the transverse vibration. In the fatigue analysis, the different methods such as: Neuber elastic-plastic strain correction, linear damage summation and Palmgreen-Miner rule were utilized. As a result of ε-N analysis, the number of load cycles to the first fatigue crack appearing in the compressor blades was obtained. Moreover, the influence of the blade vibration amplitude on the number of cycles to the crack initiation was analyzed. Values of the fatigue properties of the blade material were calculated using the Baumel-Seeger and Muralidharan methods. The influence of both the notch radius and values of the UTS of the blade material on the fatigue behavior of the structure was also considered. In the last part of the work, the finite element results were compared with the results of experimental vibration HCF tests performed for the compressor blades.

Numerical stress and crack initiation analysis of the compressor blades after foreign object damage subjected to high-cycle fatigue

This paper presents results of the complex stress and crack initiation analysis of the PZL-10 W turbo-engine compressor blade subjected to high cycle fatigue (HCF). A nonlinear finite element method was utilized to determine the stress state of the blade during the first mode of transverse vibration. In this analysis, the numerical models without defects and also with V-notches were defined. The quality of the numerical solution was checked by the convergence analysis. Obtained results were next used as an input data into crack initiation ( ε– N) analyzes performed for the load time history equivalent to one cycle of the transverse vibration. In the fatigue analysis the different methods such as: Neuber elastic–plastic strain correction, linear damage summation and Palmgreen–Miner rule were utilized. As a result of ε– N analysis, the number of load cycles to the first fatigue crack appearing in the compressor blades was obtained. Moreover, the influence of the blade vibration amplitude on the number of cycles to the crack initiation was analyzed. Values of the fatigue properties of the blade material according to Baumel–Seeger and Muralidharan methods were calculated. The influence of both the notch radius and values of the UTS of the blade material on the fatigue behavior of the structure was also considered. In the last part of work, the finite element results were compared with the results of an experimental vibration HCF tests performed for the compressor blades.

Fatigue modeling of a notched geometry under spectrum block loading supported on elastoplastic FEA

Despite intensive research has been carried out to understand the fatigue behaviour of steel notched geometries, under variable amplitude loading, no definite and general robust models have been derived so far. Therefore, any effort to increment the knowledge in the topic is welcome. Within this premise, it is proposed an assessment of existing variable amplitude data (spectrum block loading), which has been derived by authors for a notched geometry, made from a low carbon pressure vessel steel (P355NL1), within the local approaches and linear damage summation framework, and supported by elastoplastic finite element analyses. Several blocks are analyzed using elastoplastic finite element analysis with Mises plasticity theory and Chaboche's nonlinear kinematic hardening. The predictions are assessed using available experimental fatigue data as well as with predictions made with simplified elastoplastic analyses. This paper highlights the difficulties on performing the elastoplastic analysis and compares the obtained results with those obtained using simplified classical tools for elastoplastic analysis. Fatigue predictions based on elastoplastic analysis made using the Chaboche's model with four parameters were more accurate than predictions based on simplified elastoplastic analysis.

On thermo-mechanical fatigue in single crystal Ni-base superalloys

Thermo-mechanical fatigue (TMF) is a critical damage process in gas turbine jet engines. Reliable life prediction methodologies are required both for design and life management. Current life estimation approaches are computationally burdensome and/or semi-empirical, significantly limiting their application. Complexity comes about from the multiplicity of damage processes which occur during the simultaneously changing temperatures and loads, characteristic of TMF. Furthermore, these processes interact in ways that are not observed for isothermal LCF. These interactions usually accelerate damage processes and result in significantly reduced TMF life, when compared to other fatigue scenarios. The results of a multiphased approach to life prediction will be presented. In phase I the Neu-Sehitoglu (N-S) cumulative damage model was used to: a) provide initial life predictions and b) identify processes and interactions which most significantly control the life under TMF loading. The N-S model is based on a linear damage summation rule which both explicitly and implicitly includes damage interactions. In phase II a sensitivity analysis incorporating statistical concepts was performed on the N-S model parameters. Specifically a nonlinear optimization was performed to determine optimal parameter values in order to maximize agreement with experimental results (well within 2X). In phase III, informed by phases I and II, a physics-based fatigue/oxidation (also recognizing creep effects) model was developed which correctly predicts effects of frequency, hold-time, temperature, and strain range and oxidation kinetics.

Probabilistic analysis of processes of accumulation of damages at the action of the static and cyclic loadings

Difficult character of cooperation of constructive elements with environment, and also among themselves, the casual nature of durability of materials and service conditions of engines demand in calculations on durability of application of probabilistic methods of the analysis and use of indicators of the theory of reliability. In-process created and grounded probabilistic approach to the durability’s reliability of elements of constructions of GTE analysis. The methods of probabilistic description of characteristics of durability of materials of details and probabilistic estimation of static and cyclic damaged of the controlled details are developed for a flight cycle. The probabilistic approachs are explored to the calculation of long-statical, high- and low-cyclic tireless damaged of details of engines and accumulated damaged on the basis of methods of the linear and nonlinear summation of damages as sums of independent and dependent casual sizes, casual sequences and casual processes. As a result, it is possible to estimate basic probabilistic characteristics of accumulated damageability and numbers of cycles for which accumulated damageability exceeds a critical level. The methodology for estimation of resource and other indicators of operability of CE AC (GTE) according to known probabilistic characteristics of accumulated damageability is developed.

Life Prediction of Stainless Steels under Creep-Fatigue

The aim of this study is to investigate the creep-fatigue behavior of stainless steel materials. Based on the elevated-temperature tensile, creep and rupture test data, thermal creep-fatigue modelling was conducted to predict the failure life of stainless steels. In the low cycle thermal fatigue life model, Manson’s Universal Slopes equation was used as an empirical correlation which relates fatigue endurance to tensile properties. Fatigue test data were used in conjunction with different modes to establish the relationship between temperature and other parameters. Then creep models were created for stainless steel materials. In order to correlate the results of short-time elevated temperature tests with long-term service performance at more moderate temperatures, different creep prediction models, namely Basquin model, Sherby-Dorn model and Manson-Haferd model, were studied. Comparison between the different creep prediction models were carried out for a range of stresses and temperatures. A linear damage summation method was used to establish life prediction model of stainless steel materials under creep-fatigue.

Fatigue Damage Behavior of a Structural Component Made of P355NL1 Steel Under Block Loading

The common design practice of pressure vessels subjected to variable amplitude loading is based on the application of a linear damage summation rule, also known as the Palmgren–Miner’s rule. Even though damage induced by small stress cycles, below the fatigue limit, are often taken into account in design codes of practice by two-slope stress-life curves, the sequential effects of the load history have been neglected. Several studies have shown that linear damage summation rules can predict conservative as well as nonconservative lives depending on the loading sequence. This paper presents experimental results about the fatigue damage accumulation behavior of a structural component made of P355NL1 steel, which is a material usually applied for pressure vessel purposes. The structural component is a rectangular double notched plate, which was subjected to block loading. Each block is characterized by constant remote stress amplitude. Two-block sequences were applied for various combinations of remote stress ranges. Three stress ratios were considered, namely, R=0, R=0.15, and R=0.3. Also, constant amplitude fatigue data are generated for the investigated structural component. In general, the block loading illustrates that the fatigue damage evolves nonlinearly with the number of load cycles and is a function of the load sequence, stress levels, and stress ratios. In particular, a clear load sequence effect is verified for the two-block loading, with null stress ratio. For the other (higher) stress ratios, the load sequence effect is almost negligible; however the damage evolution still is nonlinear. This suggests an important effect of the stress ratio on fatigue damage accumulation.

랜덤 진동 조건에서의 압축기 연결 파이프에 대한 가속 수명 팩터 선정 및 진동 피로 해석

According to the delivery condition, the breakage of a product occurs when it is delivered to the customers. Therefore product's makers evaluate the durability under the delivery process by accelerated life testing. In order to conduct this accelerated life testing accurately, it is very important to identify the acceleration-factor exactly between on-road and accelerated life test condition. In this paper, the acceleration-factor is identified by applying linear damage summation law, rain-flow cycle counting and Dirlik theory under the conditions of the random vibration. And approximated FEM model of the connecting-pipe to the compressor is developed for fatigue analysis. This model is finally verified by comparing the experiment results to the numerical analysis results.

Variable amplitude fatigue of bonded aluminum joints

The effect of variable amplitude loading on the fatigue life and failure mode of adhesively bonded double strap (DS) joints made from clad and bare 2024-T3 aluminum was investigated. Under constant amplitude loading, the clad specimens failed through the adhesive or the substrate at high and low stress levels, respectively. The presence of overload cycles shifted the failure mode towards adhesive failure. The specimens made from bare aluminum failed only in the adhesive. Effective stress range vs. failure life curves developed for the bare and clad specimens were used in conjunction with a linear damage summation to predict the failure lives of double strap specimens subjected to two variable amplitude aircraft load spectra with reasonable accuracy.

Power-exponent function model for low-cycle fatigue life prediction and its applications – Part II: Life prediction of turbine blades under creep–fatigue interaction

This paper is concerned with the applications of the proposed models, namely the modified linear damage summation (MLDS) method and the modified strain range partitioning (MSRP) method described in Part I of the series papers, to life prediction of turbine blades under creep–fatigue interaction. To begin with, a detailed FEM analysis is conducted considering peak loading of thermal load, centrifugal force and airflow force to determine life assessment positions. Secondly, according to the blades rig testing load, a stress–strain response analysis is performed for pure low-cycle fatigue (LCF) and creep–fatigue interaction, in which steady-state temperature field, plastic kinematic hardening and contact between the blade body and hoop segment are taken into consideration to achieve accordance with practical conditions. Finally, based on FEM simulation results, the life of turbine blades is predicted using the five different models for creep–fatigue loading. A minimum safe and conservative life of 1293 h is given by the MLDS method based on power-exponent function model. The predicted lives by the MLDS and MSRP methods show reasonable agreement with the rig testing life, which further illustrates the validity of power-exponent function model and its applications.

Power-exponent function model for low-cycle fatigue life prediction and its applications – Part I: Models and validations

Based on power transformation method, this paper advances a power-exponent function model for low-cycle fatigue (LCF) life prediction and then introduces it to creep–fatigue life prediction methods – the strain range partitioning (SRP) method and the linear damage summation (LDS) method for comprehensive assessment of power-exponent function model. Power transformation exponents ( p) are given for some typical materials. Through LCF and creep–fatigue life predictions for these materials, we illustrate the validity of power-exponent function model and its applications. The comparisons between different models show that the power-exponent function model has better performances for LCF life prediction. In nature, Manson–Coffin law is the first order Taylor expansion approximation of power-exponent function model in log–log scale coordinates, corresponding to p = 1. The enhancement of nonlinearity makes the power-exponent function model and its applications to creep–fatigue life prediction methods more precise than the corresponding unmodified methods, whereas these models still use linear parameter regression method and remain simple for engineering applications. An example of these models’ applications to life prediction of turbine blades under creep–fatigue interaction is given in the accompanying paper.

Effect of LCF on HCF crack growth of Ti-17

An improved understanding of fatigue crack growth phenomena applicable to titanium engine disks was developed through complimentary experimental and analytical investigations of Ti-17. The effect of low cycle fatigue (LCF) on the high cycle fatigue (HCF) threshold and rate of crack propagation was studied. A simplified variable-amplitude spectrum, consisting of high- R cycles, corresponding to HCF loading, and periodic R=0.1 cycles, corresponding to LCF loading, was used to demonstrate a load-interaction effect. When the ratio of HCF to LCF cycles was 100 or more the fatigue crack growth lifetimes were significantly lower than predicted using linear damage summation methods assuming no load-interaction effect. Thus, it was concluded that the LCF cycle accelerated the fatigue crack growth rate of subsequent HCF cycles, even when closure was concluded to be negligible. A phenomenological model was formulated based on hypothesized changes in the propagation resistance, K PR, and fit to the test data. The model confirmed that the periodic LCF cycles increased fatigue crack growth rates of subsequent HCF cycles.

A Critical Analysis of the Six-Nines Reliability Methodology

The current certification requirements of helicopter dynamic components demand that the probability of failure at the retirement life does not exceed one in a million, i.e. a reliability level of 0.999999 (six-nines reliability). It is therefore imperative that the component retirement time for fatigue-critical rotorcraft dynamic components be determined using probabilistic rather than deterministic methodologies. In the helicopter industry a method known as `Top of Scatter-mean minus three standard deviation (TOS/(µ - 3)) reliability method is commonly used for determining the component retirement time over which the probability of failure is 10-6. In this paper, the results of the TOS/(µ - 3) reliability method for an example of constant amplitude loading have been compared with those of an exact analytical solution, Monte Carlo simulation and Second-Moment methods. Examples using Monte Carlo simulation and a numerical approximation are evaluated for variable amplitude loading, where Miner's linear damage summation rule is assumed. Finally, this paper shows that the TOS/(µ - 3) reliability method is non-conservative for both constant and variable amplitude loading.

Acoustic-Emission Analysis of the Accumulation of Bulk Damage to Solid Bodies

Using the proposed concept, we developed a model for quantitative evaluation of the bulk damage to solid bodies in a plastically deformed volume by acoustic-emission signals. This model takes into account the principle of linear summation of damages and the solution in displacements of the dynamic problem of the formation of an isolated normal tensile microcrack in the zone of intense plastic strains. The main scientific propositions of the model are corroborated by the results of experimental investigations and published data.

Fatigue and fatigue crack growth of aluminium alloys at very high numbers of cycles

The application of ultrasonic frequency (20 kHz) loading to test fatigue and fracture mechanical properties of materials is briefly reviewed and recent investigations on high strength aluminium alloys are reported. Very high cycle endurance tests and near threshold crack growth experiments were performed with the 2024-T351 aluminium alloy. Lifetimes are approximately 10–100 times lower, if cycled in distilled water instead of ambient air. Fatigue experiments under randomly varying loads showed that linear damage summation calculations overestimated lifetimes by approximately a factor 2. Fracture mechanics studies in ambient air, dry air and in vacuum served to investigate the role of air humidity on near threshold fatigue crack growth at ultrasonic frequency. The threshold value was 2.1 MPa√m in ambient air and 3.3 MPa√m in vacuum. The aluminium alloy AlZnMgCu1.5-T66 and the aluminiumoxyde particle reinforced alloy 6061-T6 were tested at 100 Hz and 20 kHz to investigate frequency influences on high cycle fatigue properties, and similar lifetimes were found at both frequencies.

An assessment of three creep–fatigue life prediction methods for nickel‐based superalloy GH4049

High‐temperature low‐cycle fatigue tests with and without a 10‐s strain hold period in a cycle were performed on a nickel base superalloy GH4049 under a fully reversed axial total strain control mode. Three creep–fatigue life prediction methods are chosen to analyse the experimental data. These methods are the linear damage summation method (LDS), the strain range partitioning method (SRP) and the strain energy partitioning method (SEP). Their ability to predict creep‐fatigue lives of GH4049 at 700, 800 and 850 °C has been evaluated. It is found that the SEP method shows an advantage over the SRP method for all the tests under consideration. At 850 °C, the LDS and SEP methods give a more satisfactory prediction for creep–fatigue lives. At the temperatures of 700 and 800 °C, the SRP and SEP methods can correlate the life data better than the LDS method. In addition, the differences in predictive ability of these methods have also been analysed. The scanning electron microscopy (SEM) examination of fracture surfaces reveals that under creep–fatigue test conditions crack initiation mode is transgranular, while crack propagation mode is either intergranular plus transgranular or entirely intergranular, dependent on test temperature.

High temperature fatigue behavior of wrought nickel-base superailoy GH4049

Push-pull total strain-controlled fatigue tests without and with a hold period were carried at elevated temperatures for wrought nickel base superailoy GH4049. The influence of the testing temperature and strain hold period on fatigue behavior was determined. The alloy would exhibit either cyclic strain hardening, softening or stability during cyclic straining. Fatigue life depends strongly on the testing temperature and the introduction of the strain hold period. Observations on fatigue specimens using transmission electron microscopy (TEM) showed that the dislocations were distributed mostly in the γ matrix. It was observed by scanning electron microscopy (SEM) that cracks initiated always in a transgranular mode, but their propagation mode was closely related to the testing temperature. In addition, the fatigue life was predicted by linear damage summation (LDS), strain range partitioning (SRP) and the strain energy partitioning (SEP) method. The results of life prediction indicated that the SRP and SEP methods were in a good agreement as to the measured and predicted life at lower temperatures, while the LDS method showed better predictability at higher temperature as compared to the SRP and SEP methods.

Investigation of variable amplitude loading on fretting fatigue behavior of Ti–6Al–4V

The fretting fatigue behavior of Ti–6Al–4V under both constant amplitude and variable amplitude loadings was investigated. Constant amplitude fretting fatigue tests were conducted at a frequency of 200 Hz as well as at 1 Hz, while the variable amplitude loading combined the interaction of these two frequencies. The axial load ratios ranged from nominal values of 0.1 to nominal values of 0.8. Fretting fatigue lives at the higher frequency were found to be less than those from tests conducted at the lower frequency with a larger difference being noted at higher axial load ratios. In general, fretting fatigue resistance for the variable amplitude loading conditions fell within the scatter band of the 200 Hz constant amplitude fretting fatigue tests. Miner's linear damage summation model provided a reasonable, yet slightly unconservative, prediction of the variable amplitude loading tests.