Fraction Rule Research Articles

Creep-fatigue life and damage evaluation under various strain waveforms for Ni-based Alloy 740H

This paper presents creep-fatigue life evaluation of a nickel-based Alloy 740H, for evaluating its performance as a material of advanced ultra-supercritical power plants. Strain controlled creep-fatigue tests were performed under six strain waveforms using solid bar specimens at 700 °C, and the effect of strain waveform on creep-fatigue life was discussed. Creep-fatigue lives were shorter than pure fatigue life depending on the strain waveform. The failure life in symmetrical waveform was reduced to about half as the strain rate decreased by one order of magnitude. The failure lives in the unsymmetrical waveforms were smaller than that in the symmetrical waveform and tensile slow straining was more detrimental to fatigue life than compressive slow straining. The creep-fatigue life decreased significantly due to strain hold, and tensile peak strain hold had more enhanced effect on fatigue life than compressive strain hold. Applicability of five existing approaches based on linear damage summation rule were discussed. In addition, a new approach based on modified ductility exhaustion model with several modifications was proposed in order to improve the life predictability of the classical approach. Time fraction rule with ASME failure envelope and new approach satisfactorily predicted the creep-fatigue lives almost within a scatter band of 2.

Grain boundary sliding model for assessing creep-fatigue life of Sn37Pb eutectic solder

This study discusses the creep-fatigue life prediction of eutectic Sn37Pb solder. Creep-fatigue lives were experimentally obtained at 313 K using fast-fast, slow-slow, slow-fast, fast-slow, and strain-hold waveforms. Conventional four creep-fatigue life prediction rules, time fraction rule, strain range partitioning method, frequency modified fatigue life, and ductility exhaustion model was used to predict the creep-fatigue lives. However, not all the rules were able to properly estimate them. Since the grain boundary sliding rates were closely related to creep-fatigue lives, a new life prediction method based on grain boundary sliding rates was proposed.

An efficient fatigue and creep‐fatigue life prediction method by using the hysteresis energy density rate concept

AbstractFatigue damage, time‐dependent creep damage and their interaction are considered as the main failure mechanisms for many high temperature structural components. A generalized methodology for predicting both the high temperature low cycle fatigue (HTLCF) and creep‐fatigue lives by using the hysteresis energy density rate (HEDR) and fatigue damage stress concepts was proposed. Experimental data for HTLCF and creep‐fatigue in Alloy 617, Haynes 230 and P92 steel were respectively collected to validate the method. A better prediction capacity and most of the data points that fall within a 1.5 scatter band were obtained compared with the traditional energy‐based method, time fraction rule and ductility exhaustion model. Moreover, a creep‐fatigue damage diagram was also constructed by using the proposed approach.

A complete Galerkin’s type approach of finite element for the solution of a problem on modified Green–Lindsay thermoelasticity for a functionally graded hollow disk

The present work is concerned with the modified Green–Lindsay thermoelasticity theory involving strain-rate. This theory has been proposed very recently to modify the Green–Lindsay (GL) model of thermoelasticity by introducing both temperature and strain-rate in the constitutive relations of coupled thermo-mechanics. We consider a problem involving coupled thermo-mechanical interactions inside a functionally graded hollow disk due to thermal shock applied at its stress-free inner and outer boundaries. The material properties of the disk are assumed to be non-homogeneous and changing along the radial direction according to a volume fraction rule with a power of non-homogeneity index term. We formulate the problem by considering the basic governing equations of GL and modified GL thermoelasticity theories in a unified form and derive a linear system of coupled partial differential equations with variable coefficients. The major aim of this work is to apply a complete finite element method to obtain the solution of the problem. We solve the system of equations by applying a Galerkin’s approach of FEM for the space domain and derive the time differential system of equations. To solve this time differential system of equations, we use two different approaches: (1) a Galerkin’s type FE approach and (2) the Newmark time integration scheme. We compare the results obtained from these two different approaches and find that the solution obtained by complete Galerkin’s approach of FEM perfectly matches with the corresponding solution obtained from Newmark time integration scheme. We further compare the CPU time taken by these two methods with the CPU time taken by the trans-finite element method and reveal the efficiency of the present method over trans-FE method. The variation of different physical field variables with space and time is discussed for various values of the non-homogeneity index by highlighting the difference in the results under the GL model and modified GL model.

Fatigue–oxidation–creep damage model under axial-torsional thermo-mechanical loading

A fatigue–oxidation–creep damage model that can take into account the effect of multiaxial cyclic feature on the damage mechanism is proposed under axial-torsional thermo-mechanical fatigue loading. In the proposed model, the effects of non-proportional additional hardening on fatigue, oxidation, and creep damages are considered, and the variation of oxidation damage under different high temperature loading conditions is also described. Moreover, the intergranular creep damage needs to be equivalent to the transgranular damage before accumulating with the fatigue and oxidation damages. The fatigue, oxidation, and creep damages can be expressed as the fractions of fatigue life, critical crack length, and creep rupture time, respectively, which allows the linear accumulation of different types of damages on the basis of life fraction rule. In addition, the proposed model is validated by various fatigue experimental results, including uniaxial thermo-mechanical fatigue, axial-torsional thermo-mechanical fatigue, and isothermal axial-torsional fatigue under proportional and non-proportional loadings. The results showed that the errors are within a factor of 2.

Comparative Study of Nonlinear Cumulative Creep Damage Model and Time Fraction Rule to Predict Residual Creep Life of Pressure Vessels - A Review

Comparative Study of Nonlinear Cumulative Creep Damage Model and Time Fraction Rule to Predict Residual Creep Life of Pressure Vessels - A Review

Ultra-high temperature creep rupture and transient burst strength of ODS steel claddings

9Cr-ODS steel claddings consisting of tempered martensitic matrix, showed prominent creep rupture strength at 1000 °C, which surpassed that of heat-resistant austenitic steels although creep rupture strength of tempered martensitic steels is generally lower than that of austenitic steels at high temperatures. The measured creep rupture strength of 9Cr-ODS steel claddings at 1000 °C was higher than that from extrapolated creep rupture trend curves formulated using data at temperatures from 650 to 850 °C. This superior strength seemed to be owing to transformation of the matrix from the α-phase to the γ-phase. The transient burst strengths for 9Cr-ODS steel were much higher than those for 11Cr-ferritic/martensitic steel (PNC-FMS). Cumulative damage fraction analyses suggested that the life fraction rule can be used for the rupture life prediction of 9Cr-ODS steel and PNC-FMS claddings in the transient and accidental events with a certain accuracy.

Creep life assessment method for online monitoring of steam turbine rotors

ABSTRACTThe principal objective of work was to develop fast and accurate method for online creep life monitoring of steam turbine rotors. For this purpose, a characteristic strain model of creep was investigated and validated using test data of 2%CrMoV rotor steel. The model was then used to determine creep damage functions which are introduced to compute creep damage at a constant temperature based on the Robinson time fraction rule. Finite element (FE) creep calculations of a turbine rotor were performed using the same creep model to obtain reference damage results for validating the proposed method. Comparisons of the results obtained using both methods showed a very good accuracy of the online creep damage predictions.

Creep-ratcheting-fatigue life prediction of bainitic 2.25Cr1MoV steel

Ratcheting fatigue behavior of bainitic 2.25Cr1MoV forged steel was investigated at 455 oC with various hold periods at peak and valley stress. The incorporation of peak stress holding widened stress-strain hysteresis loop, and this enlargement was more significant under peak/valley hold due to the created creep strain. Fatigue life was greatly shortened with the increase of mean stress or stress amplitude, and this reduction was accelerated when stress holding was involved. The extension of stress holding resulted in shorter fatigue life, but the fatigue lives were quite close when the sum of holding period was equal, regardless of the holding direction. Fatigue damage and creep damage in creep-ratcheting fatigue tests were estimated by the time fraction rule, and creep damage became dominant at long hold period, which was closely related to shortened fatigue lives with stress holding. The linear damage summation rule was used for fatigue life prediction, and it gave satisfactory predictions for peak holding mode. A new model was proposed by introducing stress ratio to consider the influence of asymmetric cycling, and estimates for peak/valley holding were greatly improved.

Clay Mineral Suites in Submarine Mud Volcanoes in the Kumano Forearc Basin, Nankai Trough: Constraints on the Origin of Mud Volcano Sediments

Clay mineralogy is an important characteristic of mud volcano sediments. This study determined the clay mineral compositions of sediment from two submarine mud volcanoes in the Kumano forearc basin, Nankai Trough, by X-ray diffraction analysis. Similar compositions dominated by smectite in the two mud volcanoes indicate that the mud volcanoes in the basin are rooted in the same source sequence. These clay mineral compositions differed from those in Pleistocene basin sediment, suggesting that the mud volcano sediment originated beneath the Pleistocene sediment. The illite content in the illite–smectite mixed layer averaged 32% in the mud volcano sediment, which implies that the sediment experienced temperatures above 60 °C that promoted the smectite-to-illite transformation. However, porewater extracted from the mud volcano sediment had Cl‒ concentrations roughly half that of seawater and proportional enrichment in 18O and depletion in D, indicating that dehydration reactions of clay minerals had previously occurred in a deeply buried sedimentary layer. The smectite and illite contents (<60%) in the clay-size fraction rule out in situ smectite dewatering as the cause of the dilution of Cl‒ in porewater. Thus, fluids derived from clay dewatering must have originated from deeper than the source of the mud volcano sediment.

Thermal buckling analysis of functionally graded cylindrical shells

Thermal buckling behavior of cylindrical shell made of functionally graded material (FGM) is studied. The material constituents are composed of ceramic and metal. The material properties across the shell thickness are assumed to be graded according to a simple power law distribution in terms of the volume fraction rule of mixtures. Based on the Donnell shell theory, a system of dimensionless partial differential equations of buckling in terms of displacement components is derived. The method of separation of variables is used to transform the governing equations to ordinary differential equations (ODEs). A shooting method is used to search for the numerical solutions of the differential equations under two types of boundary conditions. Effects of the power law index, the dimensionless geometrical parameters, and the temperature ratio on the critical buckling temperature are discussed in detail.

Mechanical Behaviour of Materials during Creep with Changing Loads

A component in service experiences stress conditions that change continuously with time. Since service conditions are usually difficult and expensive to reproduce in laboratory, the creep behaviour of alloys in service has to be extrapolated from a limited number of creep tests at constant loads and temperatures. Empirical rules have been proposed to forecast the effects of variable load and temperature both on the time to rupture, as the life fraction rule (LFR), and on the accumulation of creep strain with time, as the strain hardening rule (SHR). Two directionally solidified (DS) nickel based superalloys have been investigated with creep tests at constant and variable loads and constant temperature. Nickel based superalloys, for the typical stresses experienced in service, are often characterised by a small negligible primary, a minimum of strain rate with no secondary state, and a dominant accelerating creep caused by dislocation multiplication. The damage mechanisms causing the final rupture appear only in the very last percentage of life. In the present work, simulation results are reported to show that the physical-sounded model used to describe the accelerating creep due to dislocation multiplication can be employed to better predict the times to rupture and the creep curves of the two DS nickel based super-alloys with step-like variable stress than the empirical LF and SH rules.

多軸応力条件下におけるGRADE 92鋼のクリープ寿命評価

Creep tests on two kinds of circumferentially notched round bar specimens as well as plain bar specimen of ASME grade 92 steels were performed to obtain the multiaxial and uniaxial creep data. Then creep damage models according to strain fraction rule and energy fraction rule were developed based on the results of these uniaxial and multiaxial creep tests. Additionally, creep damage analyses using a finite element software, MSC Marc, were carried out on notched specimens and creep failure lives were predicted using the classical time fraction rule, as well as the two approaches developed here. Experimental failure lives of all the conditions of notched specimens were compared with analytical results. As a result, creep failure lives obtained by time fraction rule with von Mises equivalent stress were underestimated in the short term region and overestimated in the long term region. On the other hands, the majority of creep failure lives obtained by strain and energy fraction rule showed an agreement within a factor of two with experimental lives.

予クリープ変形を受けたフェライト系ステンレス鋼のスモールパンチクリープ試験による累積クリープ損傷評価

Small Punch (SP) Creep test has been recognized as a practical procedure to examine creep lives only sampling a very small volume. The SP creep test enables assessment of local points that conventional uniaxial creep test cannot evaluate. In order to assess the applicability of cumulative damage rule using the time fraction rule, a series of SP creep tests were carried out in air at 700°C employing ferritic stainless steel. Experimental test results show that the time fraction rule could be applied for the residual life of slighter pre-damaged specimens. However it would overestimate the severely damaged specimens.

Determination of Remaining Useful Life of Gas Turbine Blade

The aim of this research is to determine the remaining useful life of gas turbine blade, using service-exposed turbine blades. This task is performed using Stress Rupture Test (SRT) under accelerated test conditions where the applied stresses to the specimen is between 400 MPa to 600 MPa and the test temperature is 850°C. The study will focus on the creep behaviour of the 52000 hours service-exposed blades, complemented with creep-rupture modelling using JMatPro software and microstructure examination using optical microscope. The test specimens, made up of Ni-based superalloy of the first stage turbine blades, are machined based on International Standard (ISO) 24. The results from the SRT will be analyzed using these two main equations – Larson-Miller Parameter and Life Fraction Rule. Based on the results of the remaining useful life analysis, the 52000h service-exposed blade has the condition to operate in the range of another 4751 hr to 18362 hr. The microstructure examinations shows traces of carbide precipitation that deteriorate the grain boundaries that occurs during creep process. Creep-rupture life modelling using JMatPro software has shown good agreement with the accelerated creep rupture test with minimal error.

Development of Creep–Fatigue Evaluation Method for 316FR Stainless Steel

In the design of fast reactor plants, the most important failure mode to be prevented is creep–fatigue damage at elevated temperatures. 316FR stainless steel is a candidate material for the reactor vessel and internal structures of such plants. The development of a procedure for evaluating creep–fatigue life is essential. The method for evaluating creep–fatigue life implemented in the Japan Society of Mechanical Engineers code is based on the time fraction rule for evaluating creep damage. Equations such as the fatigue curve, dynamic stress–strain curve, creep rupture curve, and creep strain curve are necessary for calculating creep–fatigue life. These equations are provided in this paper and the predicted creep–fatigue life for 316FR stainless steel is compared with experimental data. For the evaluation of creep–fatigue life, the longest time to failure is about 100,000 h. The creep–fatigue life is predicted to an accuracy that is within a factor of 2 even in the case with the longest time to failure. Furthermore, the proposed method is compared with the ductility exhaustion method to investigate whether the proposed method gives conservative predictions. Finally, a procedure based on the time fraction rule for the evaluation of creep–fatigue life is proposed for 316FR stainless steel.

Suboptimal antimicrobial drug exposure in patients with renal impairment.

Recommendations on drug dose adjustment in patients with renal impairment may vary between the references. It is often unknown which approach the dosing schemes were based on and what drug exposure is likely to be achieved. To develop a simple method to evaluate recommended dosing schemes for patients with renal impairment, to apply this method to selected antibacterial drugs in order to evaluate expected drug concentrations using dosing schemes recommended for patients with severe infections, and to evaluate the expected consequences. This was a theoretical study, which was based on data from published clinical trials. Clinically established dosing schemes for 46 antibacterial drugs, as recommended for patients with renal impairment in the Summary of Product Characteristics, were analysed using a newly developed graphical method. Consistency of the dosing schemes with two general dose adjustment rules, the proportional rule and the eliminated fraction rule, was determined and drug exposure was predicted. Predicted drug exposure. Consistency of recommended dosing schemes with the general dose adjustment rules. Only 30% of the recommended dosing schemes were associated with similar average concentrations as expected in patients with normal renal function (44 % were associated with higher and 26% with lower concentrations). The highest median exposure was found in beta-lactams (170%, range 58-443%, for creatinine clearance of <15 ml/min, and 155%, range 54-232%, for creatinine clearance of 15 to <30 ml/min), where the medians were significantly different from 100% (P < 0.02). Consistency with a dosing rule was found in 59% of the dosing schemes (proportional rule 46%, eliminated fraction rule 50%, both rules 4%). Relative low exposure was found for several drugs, including ceftazidime, cefotaxime, imipenem, erythromycin, ciprofloxacin, levofloxacin, and teicoplanin, where dosing schemes should be reconsidered or used only in clinical situations where a lower than maximum exposure appears adequate. General application of the proportional rule for calculating drug dose adjustments would lead to lower than clinically established dose practice for 44% of drugs.

Pharmacokinetic and pharmacodynamic considerations of antimicrobial drug therapy in cancer patients with kidney dysfunction.

Patients with cancer have a high inherent risk of infectious complications. In addition, the incidence of acute and chronic kidney dysfunction rises in this population. Anti-infective drugs often require dosing modifications based on an estimate of kidney function, usually the glomerular filtration rate (GFR). However, there is still no preferential GFR formula to be used, and in acute kidney injury there is always a considerable time delay between true kidney function and estimated GFR. In most cases, the anti-infective therapy should start with an immediate and high loading dose. Pharmacokinetic as well as pharmacodynamic principles must be applied for further dose adjustment. Anti-infective drugs with time-dependent action should be given with the target of high trough concentrations (e.g., beta lactam antibiotics, penems, vancomycin, antiviral drugs). Anti-infective drugs with concentration-dependent action should be given with the target of high peak concentrations (e.g., aminoglycosides, daptomycin, colistin, quinolones). Our group created a pharmacokinetic database, called NEPharm, hat serves as a reference to obtain reliable dosing regimens of anti-infective drugs in kidney dysfunction as well as renal replacement therapy. To avoid the risk of either too low or too infrequent peak concentrations, we prefer the eliminated fraction rule for dose adjustment calculations.

Accurate buckling analysis for shear deformable FGM cylindrical shells under axial compression and thermal loads

Based on the Reddy’s high-order shear deformation theory, buckling behaviors of the FGM cylindrical shells subjected to an axial compression in thermal environment are investigated analytically. Considering the temperature-dependent FGMs properties, the constituent distribution across the shell thickness is assumed to follow the volume fraction rule of mixture. Through the variational principle, basic equations are derived for shear deformable FGM cylindrical shell with the initial geometric imperfection. Method of separation of variables and Galerkin’s solving process are employed in dealing with the stability governing equations of perfect and imperfect shells, respectively. By changing the boundary conditions, material types, composition distributions, thermal load and temperature fields, the effect of the transverse shear deformation is evaluated by comparing with the results of the classical Donnell’s theory. Meanwhile, imperfection sensitivity for buckling of the shear deformable FGM cylindrical shell is discussed in detail.

A generalized hysteresis energy method for fatigue and creep-fatigue life prediction of 316L(N)

Abstract Creep-fatigue interaction is extremely important for the life prediction of structural components subjected to high temperature conditions. The widely used life prediction methods such as time fraction rule and ductility exhaustion method are found to be insufficient in long time regimes and cannot give a clear physical explanation for the material failure. In this paper, a generalized life prediction model is proposed on the basis of the hysteresis energy and law of energy conservation. The influence of hold time on the cyclic stress–strain behavior is described based on isochronous stress–strain curves and stress relaxation during hold time is evaluated with the time hardening rule. An analytical approach is set up to calculate the hysteresis energy for the creep-fatigue tests. The generalized hysteresis energy is used as a model parameter to predict the fatigue and creep-fatigue life of 316L(N) and it is found to have a power law relationship with the number of cycles to failure. The fatigue and creep-fatigue life predicted with the new energy-based method shows a good correlation with the experimental results from different researchers.