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This study proposes cyclic yield strength as a potential characteristic of safe design for structures operating under fatigue and creep conditions. Cyclic yield strength is defined on a cyclic stress-strain curve, while monotonic yield strength is defined on a monotonic curve. Both values of strengths are identified using a two-step procedure of the experimental stress-strain curves fitting with application of Ramberg-Osgood and Chaboche material models. A typical S-N curve in stress-life approach for fatigue analysis has a distinctive minimum stress lower bound, the fatigue endurance limit. Comparison of cyclic strength and fatigue limit reveals that they are approximately equal. Thus, safe fatigue design is guaranteed in the purely elastic domain defined by the cyclic yielding. A typical long-term strength curve in time-to-failure approach for creep analysis has two inflections corresponding to the cyclic and monotonic strengths. These inflections separate three domains on the long-term strength curve, which are characterised by different creep fracture modes and creep deformation mechanisms. Therefore, safe creep design is guaranteed in the linear creep domain with brittle failure mode defined by the cyclic yielding. These assumptions are confirmed using three structural steels for normal and high-temperature applications. The advantage of using cyclic yield strength for characterisation of fatigue and creep strength is a relatively quick experimental identification. The total duration of cyclic tests for a cyclic stress-strain curve identification is much less than the typical durations of fatigue and creep rupture tests at the stress levels around the cyclic yield strength.

This paper is devoted to parametric study on creep-fatigue endurance of the steel type 316N(L) weldments at 550◦C identified as type 3 according to R5 Vol. 2/3 procedure classification. The study is implemented using a direct method known as the Linear Matching Method (LMM) and based upon the creep-fatigue evaluation procedure considering time fraction rule for creep-damage assessment. Seven configurations of the weldment, characterised by particular values of a geometrical parameter ρ, are proposed. Parameter ρ, which represents different grades of TIG dressing, is a ratio between the radius of the fillet of the remelted metal on a weld toe and the thickness of welded plates. For each configuration, the total number of cycles to failure N⋆ in creep-fatigue conditions is assessed numerically for different loading cases defined by normalised bending moment ˜M and dwell period t. The obtained set of N⋆ is extrapolated by the analytic function dependent on ˜M, t and parameter ρ. Proposed function for N⋆ shows good agreement with numerical results obtained by the LMM. Therefore, it is used for the identification of Fatigue Strength Reduction Factors (FSRFs) effected by creep, which are intended for design purposes, and dependent on t and ρ.

This paper presents a comparative study between conventional hydraulic and elevated temperature autofrettage. For modelling of both methods advanced plasticity and creep material models are used. The main governing equations for the models are presented as well. A beneficial influence of compressive residual stresses induced by both methods is demonstrated on a benchmark problem of cross bored block. The effectiveness and applicability of the two methods are estimated by conduction of compressive residual stress analysis and crack arrest modeling. Numerical simulation of the cyclic plasticity and creep problems are carried out by means of FEM in ANSYS Workbench with FORTRAN user-programmable subroutines for material model incorporating custom equations.

A conventional material behaviour model can be extended to taking into account varying thermo-mechanical loading conditions in wide stress range. The motivation for developing this model is given by the well documented failure case study of high-temperature components at unit 1 of the Eddystone fossil power plant (Pennsylvania, USA), which have operated for 130,520 h in creep–fatigue interaction conditions. The developed model basis is a creep constitutive law in the form of hyperbolic sine stress response function originally proposed by Nadai (1938). The constitutive law is extended to assume the damage process by the introduction of scalar damage parameter and appropriate evolution equation according to Kachanov–Rabotnov concept. The research task is the introduction into the constitutive model of a few additional material state variables, able to reflect hardening and recovery effects under cyclic loading conditions. The first variable is represented by the relatively fast saturating back-stress [Formula: see text] describing kinematic hardening. The second variable is represented by the relatively slow saturating parameter [Formula: see text] describing isotropic hardening. Evolution equations for [Formula: see text] and [Formula: see text] are formulated in a modified form originally proposed by Chaboche and based on the Frederick–Armstrong concept. The uniaxial modelling results are compared with cyclic stress–strain diagrams and alternative experimental data in the form of creep curves, tensile stress–strain diagrams, relaxation curves, etc., for the austenitic steel AISI type 316 at 600 °C in a wide stress range.

Many materials exhibit the stress range dependent creep behavior. The power law creep observed for a certain stress range changes to the viscous type creep as the stress value decreases. Recently published experimental data for advanced heat resistant steels indicate that the high creep exponent (in the range 7–12) may decrease to the low value of approximately unity within the stress range relevant for engineering structures. The aim of this paper is to analyze the influence of the stress range dependent power-law-viscous creep transition on the behavior of structures at elevated temperature. A constitutive model for the minimum creep rate is introduced to describe both the linear and the power law creep depending upon the stress level. To demonstrate basic features of the stress range dependent creep modeling, several elementary examples from structural mechanics are presented. They include a stress relaxation problem, a beam subjected to pure bending and a pressurized thick-walled cylinder. Based on the uni-axial transition stress the transition value of the external load is estimated such that above this value the power law can be applied. For the loading levels below this value the character of the stress distribution as well as the stress values are essentially influenced by the viscous creep.

Many materials exhibit a stress range dependent creep behavior. The power-law creep observed for a certain stress range changes to the viscous type creep if the stress value decreases. Recently published experimental data for advanced heat resistant steels indicates that the high creep exponent (in the range 5-12 for the power-law behavior) may decrease to the low value of approximately 1 within the stress range relevant for engineering structures. The aim of this paper is to confirm the stress range dependence of creep behavior based on the experimental data of stress relaxation. An extended constitutive model for the minimum creep rate is introduced to consider both the linear and the power law creep ranges. To take into account the primary creep behavior a strain hardening function is introduced. The material constants are identified for published experimental data of creep and relaxation tests for a 12% Cr steel bolting material at 500°C. The data for the minimum creep rate are well-defined only for moderate and high stress levels. To reconstruct creep rates for the low stress range the data of the stress relaxation test are applied. The results show a gradual decrease of the creep exponent with the decreasing stress level. Furthermore, they illustrate that the proposed constitutive model well describes the creep rates for a wide stress range.

The classical solution of the steady-state creep problem for a pressurized thick-walled cylinder is based on the power law constitutive equation. Several heat resistant steels show, however, the linear dependence of the creep rate on the applied stress within a certain stress range. In this paper we apply an extended constitutive equation which includes both the linear and the power law stress dependencies. The material constants are identified for the 9Cr1MoVNb steel at 600 °C. We recall the boundary value problem of steady-state creep for the thick cylinder under the plane strain condition. We present an approximate solution illustrating the stress redistributions as a result of the creep process. The analysis shows that for the certain range of the internal pressure both the linear and the power law creep must be taken into account. In this case the results according to the extended constitutive model essentially differ from the classical ones. The obtained solution is also applied to verify the developed user-defined creep material subroutine inside a commercial finite element code.

This paper presents a parametric study on creep-fatigue strength of the steel AISI type 316N(L) weldments of types 1 and 2 according to R5 Vol. 2/3 Procedure classification at 550◦C. The study is implemented using the Linear Matching Method (LMM) and is based upon a latest developed creep-fatigue evaluation procedure considering time fraction rule for creep-damage assessment. Parametric models of geometry and FE-meshes for both types of weldments are developed in this way, which allows variation of parameters governing shape of the weld profile and loading conditions. Five configurations, characterised by individual sets of parameters, and presenting different fabrication cases, are proposed. For each configuration, the total number of cycles to failure N⋆ in creep-fatigue conditions is assessed numerically for different loading cases including normalised bending moment M and dwell period t. The obtained set of N⋆ is extrapolated by the analytic function, which is dependent on M, t and geometrical parameters (α and β). Proposed function for N⋆ shows good agreement with numerical results obtained by the LMM. Thus, it is used for the identification of Fatigue Strength Reduction Factors (FSRFs) intended for design purposes and dependent on t, α, β.

This paper presents parametric studies on creep-fatigue endurance of the steel AISI type 316N(L) weldments defined as types 1, 2 and 3 according to R5 Vol. 2/3 Procedure classification at 550°C. The study is implemented using the Linear Matching Method (LMM) and based upon previously developed creep-fatigue evaluation procedure considering time fraction rule. Several geometrical configurations of weldments with individual parameter sets, representing different fabrication cases, are developed. For each of configurations, the total number of cycles to failure N* in creep-fatigue conditions is assessed numerically for different loading cases. The obtained set of N* is extrapolated by the analytic function dependent on normalised bending moment M̃, dwell period Δt and geometrical parameters. Proposed function for N* shows good agreement with numerical results obtained by the LMM. Therefore, it is used for the identification of Fatigue Strength Reduction Factors (FSRFs) intended for design purposes and dependent on proposed variable parameters.

This paper presents a creep-fatigue life assessment of a cruciform weldment made of the steel AISI type 316N(L) and subjected to reversed bending and cyclic dwells at 550 °C using the Linear Matching Method (LMM) and considering different weld zones. The design limits are estimated by the shakedown analysis using the LMM and elastic-perfectly-plastic material model. The creep-fatigue analysis is implemented using the following material models: 1) Ramberg–Osgood model for plastic strains under saturated cyclic conditions; 2) power-law model in “time hardening” form for creep strains during primary creep stage. The number of cycles to failure N⋆ under creep-fatigue interaction is defined by: a) relation for cycles to fatigue failure N∗ dependent on numerical total strain range Δetot for the fatigue damage ωf; b) long-term strength relation for the time to creep rupture t∗ dependent on numerical average stress σ ¯ during dwell Δt for the creep damage ωcr; c) non-linear creep-fatigue interaction diagram for the total damage. Numerically estimated N⋆ for different Δt and Δetot shows good quantitative agreement with experiments. A parametric study of different dwell times Δt is used to formulate the functions for N⋆ and residual life L⋆ dependent on Δt and normalised bending moment M ˜ , and the corresponding contour plot intended for design applications is created.

A conventional material model is extended to taking into account of varying thermo-mechanical loading conditions in a wide stress range. The developed model basis is a creep constitutive law in the form of the hyperbolic sine stress response function originally proposed by Nadai. The extension is done by incorporation of two additional inner variables reflecting hardening and recovery effects under cyclic loading conditions. The first one is presented by the relatively fast saturating back-stress \(K\) describing the kinematic hardening. The second one is presented by the relatively slow saturating parameter \(H\) describing the isotropic hardening. Evolution equations for \(K\) and \(H\) originally proposed by Chaboche are formulated in a modified form and based on the Frederick-Armstrong concept. The uniaxial modelling results are compared with cyclic stress-strain diagrams and alternative experimental data in the form of creep curves, tensile stress-strain diagrams, relaxation curves, etc. for the austenitic steel AISI type 316 at 600\(\,^{\circ }\)C in a wide stress range.

This paper demonstrates the recent extension of the Linear Matching Method (LMM) to include cyclic creep assessment [1] in application to a creep-fatigue analysis of a cruciform weldment made of the stainless steel AISI type 316N(L). The obtained results are compared with the results of experimental studies implemented by Bretherton et al. [2] with the overall objective to identify fatigue strength reduction factors (FSRF) of austenitic weldments for further design application. These studies included a series of strain-controlled tests at 550°C with different combinations of reversed bending moment and dwell time Δt. Five levels of reversed bending moment histories corresponding to defined values of total strain range Δεtot in remote parent material (1%, 0.6%, 0.4%, 0.3%, 0.25%) were used in combination with three variants of creep-fatigue conditions: pure fatigue, 1 hour and 5 hours of dwell period Δt of hold in tension. An overview of previous works devoted to analysis and simulation of these experiments [2] and highlight of the LMM development progress could be found in [3].

This work is devoted to parametric study on creep-fatigue endurance of the steel AISI type 316N(L) weldments defined as type 3 according to R5 Vol. 2/3 procedure at 550◦C. The study is implemented using a novel direct method known as the Linear Matching Method (LMM) and based upon the creep-fatigue evaluation procedure considering time fraction rule for creep-damage assessment. Seven geometrical configurations of the weldment, which are characterised by individual values of a geometrical parameter p, are proposed. Parameter p, which represents different grades of TIG dressing, is a ratio between the radius of the fillet of the remelted metal on a weld toe and the thickness of welded plates. For each configuration, the total number of cycles to failure N⋆ in creep-fatigue conditions is assessed numerically for different loading cases including normalised bending moment ˜M and dwell period At. The obtained set of N⋆ is extrapolated by the analytic function dependent on ˜M , At and p. Proposed function for N⋆ shows good agreement with numerical results obtained by the LMM. It is used for the identification of Fatigue Strength Reduction Factors (FSRFs) effected by creep and dependent on At and p.

The purpose of this work is to extend a typical creep-damage model in order to describe material behavior under variable thermal and mechanical loading in wide stress range. The model basis is creep constitutive law in form of hyperbolic sine stress response function proposed by Nadai. The constitutive law is extended to assume the damage process under creep and fatigue by the introduction of scalar damage parameters and appropriate evolution equations according to Kachanov-Rabotnov concept. The material constants for model are identified by fitting the experimental creep and low-cycle fatigue data for the steel AISI type 316 at the range of temperatures 500°C – 750°C. The development of such model is motivated by the well described failure case study of high-temperature components at unit 1 of Eddystone power plant, which have operated during 130520 hours under creep-fatigue interaction conditions. The main steam piping (MSP) from this power plant is selected for thermo-mechanical creep-fatigue analysis applying the proposed material model. The estimated values of damage parameters comply with the real location of the component failure and a scatter of experimental data on creep-fatigue interaction diagram. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Many materials exhibit a stress range dependent creep behavior. The power–law creep observed for a certain stress range changes to the viscous type creep if the stress value decreases. Recently published experimental data for advanced heat resistant steels indicate that the high creep exponent (in the range 5–12 for power–law behaviour) may decrease to the low value of approximately 1 within the stress range relevant for engineering structures. The aim of this paper is to confirm the necessity of the assumption of the stress range dependent power–law–viscous creep transition for the solution of stress relaxation problems affected by creep behavior at elevated temperatures. A constitutive model for the minimum creep rate is introduced to describe both the linear and the power law creep depending upon the stress level. The proposed constitutive model includes a strain hardening function to describe the primary creep stage. To demonstrate the existence of the linear creep behaviour in the low stress range of application area and the influence of the primary creep behaviour on relaxation, several solutions of a uniaxial stress relaxation problem are presented for the loading values relevant to engineering applications. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Chair of Dynamics and Strength of Machines, Department of Physical Engineering, National Technical University “KhPI”,61002 Kharkiv, UkraineThe aim of creep modeling is to reflect basis features of creep in structures including the evolution of inelastic deformations,relaxation and redistribution of stresses as well as the local reduction of material strength. A model should be able to accountmaterial deterioration processes in order to predict long term structural behavior and to analyze critical zones of creep failure.In recent years general purpose finite element codes have become the widely accepted tool for the structural analysis. Toconsider both the creep and the damage processes, a specific constitutive model with selected internal state variables, specialtypes of stress and temperature functions as well as material constants identified from available experimental data should beincorporated into the commercial finite element code by writing a user defined material subroutine. To assess the reliabilityof the developed subroutine as well as the accuracy of the results with respect to the mesh density, type of finite element, thetime step, and the iteration methods, numerical benchmark problems are required. Here we present two benchmark problemsof creep-damage mechanics which can be solved by approximate numerical methods. The reference solutions are comparedwith the finite element solutions by ANSYS and ABAQUS finite element codes with user creep model subroutines.