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There is a limited data on VHCF for structural steels and their weldments for >107 cycles. Unalloyed low-carbon steel S275JR+AR (EN 10025) is a common structural material for the components made for the minerals and mining applications. The purpose of this research is an investigation of the gigacycle domain for S275JR+AR grade that is intended to work for years at normal frequencies (10-20 Hz) of loading with low stress amplitudes. The work focuses on ultrasonic fatigue testing of the steel in both as-manufactured and pre-corroded conditions. As the heating is a massive challenge for ultrasonic fatigue testing especially in the case of structural steels attributed with a pronounced frequency effect, temperature control arrangement is crucial for proper implementation of testing. The frequency effect is assessed by comparing the fatigue test data at 20kHz and conventional frequency of 15Hz. Its contribution is found to be significant because there is no overlap between the stress ranges of interest. The ultrasonic fatigue data is intended to be applied to the fatigue assessments of the equipment operating at normal frequency for 1010 cycles. Therefore, the effect of frequency sensitivity is quantified by calculating the difference in terms of stress amplitude between corresponding SN curves.

There are limited experimental data on VHCF for structural steels for >107 cycles. Unalloyed low-carbon steel S275JR+AR is a common structural material for the heavy machinery in minerals, sand and aggregate applications. The purpose of this research is to investigate the fatigue behaviour in the gigacycle domain (>109 cycles) for S275JR+AR grade steel. This is achieved using accelerated ultrasonic fatigue testing in as-manufactured, pre-corroded and non-zero mean stress conditions. As internal heat generation is a massive challenge for ultrasonic fatigue testing of structural steels which exhibit a pronounced frequency effect, effective temperature control is crucial for implementation of testing. The frequency effect is assessed by comparing the test data at 20 kHz and 15–20 Hz. Its contribution is significant, as there is no overlap between the stress ranges of interest. The obtained data are intended to be applied to the fatigue assessments of the equipment operating at the frequency for up to 1010 cycles over years of continuous service.

Two real‐domain numerical approximation methods for accurate computation of finite strain elasticity moduli are developed and their accuracy and computational efficiency investigated, with reference to hyperelastic constitutive models with known analytical solutions. The methods are higher‐order and higher floating‐point precision numerical approximation, the latter being novel in this context. A general formula for higher‐order approximation finite difference schemes is derived and a new procedure is proposed to implement increased floating‐point precision. The accuracy of the approximated elasticity moduli is investigated numerically using higher‐order approximations in standard double precision and increased quadruple precision. It is found that as the order of the approximation increases, the elasticity moduli tend towards the analytical solution. Using higher floating‐point precision, the approximated elasticity moduli for all orders of approximation are found to be more accurate than the standard double precision evaluation of the analytical moduli. Application of the techniques to a finite element problem shows that the numerically approximated methods obtain convergence equivalent to the analytical method but require greater computational effort. It is concluded that numerical approximation of elasticity moduli is a powerful and effective means of implementing advanced constitutive models in the finite element method without prior derivation of difficult analytical solutions.

Elasticity tensors for isotropic hyperelasticity in principal stretches are formulated and implemented for the Finite Element Method. Hyperelastic constitutive models defined by this strain measure are known to accurately model the response of rubber, and similar materials. These models may not be available in the library of a Finite Element Analysis software, but a numerical implementation of the constitutive model may be provided by a programmed subroutine. The implementation proposed here is robust and accurate, with straightforward user input. It is presented in multiple configurations with novel features, including efficient definition of isochoric stress and elasticity coefficients, symmetric dyadic products of the principal directions, and development of a stable and accurate algorithm for equal and similar principal stretches. The proposed implementation is validated, for unique, equal and similar principal stretches. Further validation in the Finite Element Method demonstrates the developed implementation requires lower computational effort compared with an alternative, well-known implementation.

An experimental and numerical investigation of the effect of residual compressive stress on the high cycle fatigue life of notched low carbon steel test specimens is presented. Experimentally determined cyclic stress strain curves for S355 low carbon steel are utilized in a Finite Element Analysis plasticity modelling framework incorporating a new cyclic plasticity material model representative of cyclic hardening and softening, cyclic mean stress relaxation and ratcheting behaviors. Fatigue test results are presented for standard tensile fatigue test specimens and novel double notch specimens. Double notch specimens are tested with and without compressive residual stress prior-induced through tensile overload. It is shown that cyclic plasticity phenomena have a significant influence on the induced residual stress distribution and also on material behavior when fatigue tested in the high cycle regime. It is observed that higher initial compressive residual stresses magnitude does not necessarily lead to a longer fatigue life. Finite Element Analysis using the new cyclic plasticity material model shows this behavior is due to combined residual stress redistribution under fatigue test cyclic loading and cyclic hardening effects. A fatigue life methodology based on the stress-life approach augmented by a critical distance method is proposed and shown to give good agreement with experimental results for test specimens with no induced residual stress. The results obtained for specimens with induced residual stress are more conservative but the degree of conservatism is significantly lower than that in the conventional stress life approach. The proposed methodology is therefore suitable for analysis and design assessment of components with pre-service induced compressive residual stress, such as autofrettaged pressure components.

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.

A new mathematical modelling framework for simulation of metal cyclic plasticity is proposed and experimental validation based on tension-compression cyclic testing of S355J2 low carbon structural steel presented over the two parts of this paper. The advantages and limitations of the stress-strain curve shape modelling given by “Armstrong and Frederick” type hardening rules are discussed and a new formulation for kinematic hardening is proposed for more accurate representation of the stress-strain dependence under cyclic loading conditions. The proposed model is shown to describe the shape of the stress-strain curve accurately under various different loading conditions. Transition effects occurring at loading reversals are incorporated through a new framework of Dirac delta functions. In addition to the yield surface, stress supersurfaces able to expand and instantly move to simulate a shift of stress-strain curves during loading reversals are determined. This also enables inclusion of the behaviour of monotonic stress-strain curves with yield plateau deformation in one mathematical model. The influence of the first stress invariant on the shape of a stress-strain curve in tension and compression directions observed in many metals is incorporated into the kinematic hardening rule. The ability of the model to accurately describe transition from elastic to elastic-plastic deformation at small offset strain yield points naturally accounts for nonlinearity of an unloading stress-strain curve after plastic pre-strain. Development of the model to include mixed cyclic hardening/softening, ratcheting and mean stress relaxation is presented in a companion paper (Part II), which includes experimental validation of the modelling framework.

Hyperelastic constitutive models are investigated and compared on their ability to predict the elastic, isothermal and rate-independent response of rubber. Constitutive model parameters are identified in an optimization problem by minimizing the difference between homogeneous experimental data and their analytical solutions. The results are presented for ten hyperelastic constitutive models over four case studies where varying extents of experimental data are used. The choice of constitutive model is found to determine how accurately experimental data is fitted, though this has different implications depending on the extent of available experimental data. With a complete data set, an accurate fit generally indicates an overall accurate prediction of the material’s response. However, an accurate fit to a reduced set of experimental data may not indicate an accurate prediction of the overall response. With reduced data, accurate predictions are obtained only if the constitutive model is capable of predicting unfitted deformations and the appropriate experimental data is used.

This study investigates an effect of autofrettage on the fatigue and corrosion fatigue life of high pressure parts made from low carbon structural steel. To estimate the beneficial effect of autofrettage application, an extensive experimental program and advanced theoretical modelling are conducted and analyzed in this study. Accurate calculation of compressive residual stresses is achieved by application of a cyclic plasticity model which can precisely simulate a cyclic plasticity response of material. In terms of a fatigue life prediction methodology, a non-local stress based approach with a modified critical distance theory is used for prediction of the crack initiation stage providing conservative fatigue assessment. Because of the fact that the crack propagation stage can take a considerable part of the total life for autofrettaged parts, more accurate fatigue life calculation is performed by the use of a fracture mechanics approach. The total fatigue life time of autofrettaged parts is then calculated as a sum of the crack initiation and propagation stages.

Swellable elastomeric seal is a type of specifically engineered packer that swell upon contact with wellbore fluids. Assessment of leakage tightness is a fundamental aspect in the design of swellable packers, since they should guarantee a reliable sealing under extreme pressures of the downhole fluids. Numerical capability of the leakage pressure prediction would facilitate improvement in the packer design methodology. Previous work was focused on investigation of the non-parametric optimisation capability seeking for an optimal external shape with a goal to maximise the grip of a packer with a borehole. The verification of an optimised design was done with a dynamic FE-simulation of packer’s failure by extrusion under an excessive pressure. The downside of that verification analysis was that Abaqus/Explicit solver couldn’t implement a realistic adaptive pressure application due to changing packer disposition and contact conditions. This simulation challenge is addressed in this paper by application of the Coupled Eulerian-Lagrangian (CEL) approach in Abaqus/Explicit, which provides the ability to simulate a class of problems where the fluid-structure interaction is important.

The main objective of this study is to develop a CAE-based application with a convenient GUI for identification and verification of material parameters for hyperelastic models available in the current release of the FE code ANSYS Mechanical APDL. This Windows application implements a two-step procedure: (1) fitting of experimental stress–strain curves provided by the user; (2) verification of the obtained material parameters by the solution of a modified benchmark problem. The application, which was developed using the Visual Basic.NET language, implements a two-way interaction with ANSYS as a single loop using the APDL script as input and text, graphical and video files as output. With this application, nine isotropic incompressible hyperelastic material models are compared by fitting them to the conventional Treloar’s experimental dataset (1944) for vulcanised rubber. A ranking of hyperelastic models is constructed according to model efficiency, which is estimated using fitting quality criteria. The model ranking is done based upon the complexity of their mathematical formulation and their ability to accurately reproduce the test data. Recent hyperelastic models (Extended Tube and Response Function) are found to be more efficient compared to conventional ones. The verification is done by the comparison of an analytical solution to an FEA result for the benchmark problem of a rubber cylinder under compression proposed by Lindley (1967). In the application, the classical formulation of the benchmark is improved mathematically to become valid for larger deformations. The wide applicability of the proposed two-step approach is confirmed using stress–strains curves for seven different formulations of natural rubber and seven different grades of synthetic rubber.

Swellable packers have been widely employed in various oil & gas applications. Downhole conditions are difficult to reproduce using physical testing environments, but can be simulated in a virtual environment using CAE software. A better understanding of packers’ mechanical behaviour in downhole conditions would provide a higher confidence and improvement in existing engineering design practices for the manufacturing of packers. The numerical simulation can be incorporated into optimisation procedures searching for an optimal shape of packers aiming to minimise the time to seal the borehole and maximise the contact pressure between the seal and borehole. Such an optimisation would facilitate the development of a packer with various designs optimised for different downhole conditions. The objective of this work is to develop a design tool integrated into Abaqus/CAE to implement parametric numerical studies using implicit and explicit FE-simulations. However, development of such a CAE plugin is associated with a number of technical challenges specific to this class of multiphysics problems, which are addressed in this research and discussed in the paper.

This paper presents an overview of a numerical method developed to allow one-way structure-fluid interaction of a scanned representative surface of a Pressure Relief Valve (PRV) measuring 100 μm by 100 μm to be incorporated into a coupled finite element and computational fluid dynamics model to investigate gas leak rates through micro-gaps in full size metal-to-metal contacting components. The virtual representative surface is created via a real scan using a 3D micro coordinate and surface roughness measurement system. The scan of the physical surface is converted to a CAD format and a finite element model generated which is deformed for a given loading condition. The micro-gaps of the deformed FEA model are extracted and imported into the CFD solver to find the resulting volumetric/mass flow rate for the same set of pressure conditions. This coupled approach allows the leakage rate to be found based on only the surface roughness of metal-to-metal sealing surfaces. This methodology can now be expanded to understand the behaviour and response of metal-to-metal deformable contacting surface components under pressure. Thereafter, the design objective is to minimise or eliminate component leakage.

Controlling and assessing the leak tightness of a Pressure Relief Valve (PRV) has been a challenge since the original design of the product. With more stringent demands from the nuclear power industry for leakproof PRV’s, closer to the set point, there has been a drive by both industry and academia for a better design method for many known metal-to-metal contacting seal/surface problems. This paper outlines a numerical modelling strategy drawn from industry experience and metrology measurements and investigates the effects of lapping and surface finish on leakage rate. Key influencing parameters of surface form, waviness and roughness are incorporated in the analysis. The numerical approach requires efficient coupling of a non-linear structural Finite Element Analysis (FEA) with a Computational Fluid Dynamic (CFD) solver. This allows the examination of the relationship between deformation of the contacting surfaces, based on the applied spring force, and the resulting micro-flow of gas through any available gaps and the overall leakage to be found. The API527 Seat Tightness methodology is followed to allow leakage rates to be measured and the computational model to be preliminarily validated. Using this model, engineers can adjust and optimise the design of pressure relief valves to find the minimal leakage condition for a given configuration. In addition, the numerical approach can potentially be applied to other metal-to-metal contacting surface components, such as flanges with metal gaskets, and help eliminate leakage.

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.

This paper presents a numerical study involving the deformation of contact faces in the metal-to-metal seal in a typical pressure relief valve. The valve geometry is simplified to an axisymmetric problem, which comprises a simple geometry consisting of only 3 components. A cylindrical nozzle, which has a valve seat on top, contacts with a disk, which is preloaded by a compressed linear spring. All the components are made of AISI type 316N(L) steel defined using the multilinear kinematic hardening model based on monotonic and cyclic tests at 20° C. In-service observations show that there is a limited fluid leakage through the valve seat at operational pressures about 90% of the set pressure, which is caused by the fluid penetrating into surface asperities at the microscale. Nonlinear FEA in ANSYS using the fluid pressure penetration (FPP) technique revealed that there is a limited amount of fluid penetrating into gap, which is caused by the plastic deformation of the valve seat at the macroscale. Prediction of the fluid pressure distribution over the valve seat just before the valve lift is addressed in this study considering the FPP interaction on multiscale. This is the principal scope, since it allows adjustment of the valve spring force in order to improve the leak tightness.

The motivation behind this study is to simulate high pressure gas flow through the clearance between a valve seat and disc when in a closed position using a representative model. This leakage phenomenon is common in metal-to-metal seal pressure relief valves. As a pressure relief valve reaches the set pressure, it is known for the leakage to increase. The representative model that we studied is of an ideal-gas flow through a 2D microchannel in the slip flow regime. We used a laminar continuum flow solver which solved the mass, momentum and energy equations. In addition, we applied low pressure slip boundary conditions at the wall boundaries which considered Maxwells model for slip. The channel height was varied from 1μm to 5μm while the length remained at 1.25 mm, this means the length to height ratio varied from 1250 to 250. Inlet pressure was varied from a low pressure (0.05 MPa) to a high pressure (18.6 MPa), while the outlet remained constant at atmospheric. The calculated mass flow rate is compared to an analytical solution giving very good agreement for low pressure ratios and high length to height ratios.

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 chapter is part of a research program to investigate and model the leak tightness of a Pressure Relief Valve (PRV). Presented here is: a literature review; high-temperature numerical study involving the deformation of contact faces for a metal-to-metal seal accounting for micro and macro effects; and also microscopic measurements of surface finishes and how they are modelled over a micro to nanometre scale. Currently, no review of literature exists which attempts to understand the leakage phenomenon of metal-to-metal seal contact PRV for static closed positions as they reach the set pressure point. This work attempts to do just that by drawing on inspiration from other research areas such as metal-to-metal contact and gasket seals. The key topics of interest surrounding the leakage of fluid through a gap are: fluid flow assumptions, surface characteristics and its deformation, and experimental techniques used to quantify leakage. For the numerical study, the valve geometry is simplified to an axisymmetric problem, which comprises a simple geometry consisting of only three components: a cylindrical nozzle, which is in contact with a disc (representing the valve seat on top), which is preloaded by a compressed linear spring. The nozzle-disk pair is made of the austenitic stainless steel AISI type 316N(L) steel. In a previous study, the macro–micro interaction of Fluid Pressure Penetration (FPP) was carried out in an iterative manual procedure at a temperature of 20 \(^{\circ }\)C. This procedure is now automated and implemented through an APDL script, which adjusts the spring force at a macro scale to maintain a consistent seal at elevated temperatures. Finally, using the Alicona Infinite Focus the surface form and waviness is measured, presented and modelled as 1 / 4 symmetric over a macro to nanometre scale. It is clear the surface form also needs to be accounted for, something which the literature does not focus on.

This study investigates the behaviour of the contact faces in the metal-to-metal seal of a typical pressure relief valve. The valve geometry is simplified to an axisymmetric problem. A cylindrical nozzle, which has a valve seat on top, contacts with a disk, which is preloaded by a compressed linear spring. All the components are made of the steel AISI type 316N(L) defined using the multilinear kinematic hardening material model based on monotonic and cyclic tests at 20◦C. Analysis considerations include the effects of the Fluid Pressure Penetration (FPP) across the valve seat which exists at two different scales. There is certain limited fluid leakage through the valve seat at operational pressures, which is caused by the fluid penetrating into surface asperities at the microscale. At the macroscale, non-linear FE analysis using the FPP technique available in ANSYS revealed that there is also a limited amount of fluid penetrating into gap. Accurate prediction of the fluid pressure profile over the valve seat is addressed in this study by considering the FPP interaction on both scales. The shape of this pressure profile introduces an additional component of the spring force, which needs to be considered to provide a reliable sealing. The analysis showed that the evolution of the profile, which is caused by the isotropic softening of the material, is significant during the cyclic operation of the valve.

Using a cylindrical nozzle and seat of a Pressure Relief Valve (PRV) the surface form and waviness is modelled using actual metrological data i.e. average surface form and waviness (Wa and Wsm) in a 1/4 symmetry manner. To model the surface waviness the technique used is based on the summing technique created by Tsukizoe & Hisakado (1965) for micro contact analysis. Due to the actual surface form measurements being in the micro-meter range, the model is required to incorporate micro and macro-meter dimensions. The material in question is stainless steel. The deformed finite element analysis model is then transferred into a CAD geometry allowing the void space to be meshed and solved using computational fluid dynamics.

An experimental investigation of the effect of corrosive environment on the fatigue life of circular cross section specimens made from structural low carbon steel S355 is presented in this paper. Uniaxial load controlled fatigue tests in the regime of 105 to 107cycles were performed in two different environments: at room temperature in air (without corrosion) and in-situ fresh water solution environment. Various approaches to evaluate mean stress effect on stress-life behaviour in inert environment are reviewed and used to estimate the mean stress sensitivity factors both for air and corrosive environment. Mean stress sensitivity factor is calculated based on experimental results and predicted using the different approaches. Moreover, a comparison between Haigh Diagram predicted by these models and experimental results is proposed and the Walker approach is found to be the one that best fits experimental data.

This study proposes cyclic yield strength (CYS, σ_cy) as a potential characteristic of safe design for structures operating under fatigue and creep conditions. CYS is defined on a cyclic stress-strain curve (SSC), while monotonic yield strength (MYS, σ_my) is defined on a monotonic SSC. Both values of σ_cy and σ_my are identified using a 2-step fitting procedure of the experimental SSCs using 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 (FEL, σ_f-lim). Comparison of σ_cy and σ_f-lim reveals that they are approximately equal. Thus, safe fatigue design is guaranteed in the purely elastic domain defined by the σ_cy. A typical long-term strength (LTS) curve in time-to-failure approach for creep analysis has 2 inflections corresponding to the σ_cy and σ_my. These inflections separate 3 sections on a LTS curve, which are characterised by different creep fracture modes and creep deformation mechanisms. Thus, safe creep design is guaranteed in the linear creep domain with brittle failure mode defined by the σ_cy. These assumptions are confirmed using 3 structural steels for normal and high-temperature applications. The advantage of using σ_cy for characterisation of fatigue and creep strength is a relatively quick experimental identification. The total duration of cyclic tests for a cyclic SSC identification is much less than the typical durations of fatigue and creep rupture tests at the stress levels around the σ_cy.

This numerical study investigates the behaviour of the contact faces in the metal-to-metal seal of a typical pressure relief valve in the commercial FE-package ANSYS. The valve geometry is simplified to an axisymmetric problem, which comprises a simple representative geometry consisting of only three components. A cylindrical nozzle, which has a valve seat on top, contacts with a disk, which is preloaded by a compressed linear spring. Analysis considerations include the effects of the Fluid Pressure Penetration (FPP) across the valve seat which exists at two different scales. In-service observations show that there is certain limited fluid leakage through the valve seat at operational pressures about 90% of the set pressure, which is caused by the fluid penetrating into surface asperities at the microscale. At the macroscale, non-linear FE-analysis using the FPP technique available in ANSYS revealed that there is also a limited amount of fluid penetrating into gap, which is caused primarily by the global plastic deformation of the valve seat. Accurate prediction of the fluid pressure profile over the valve seat is addressed in this study by considering the FPP interaction on both scales. The shape of this pressure profile introduces an additional component of the spring force, which needs to be considered to provide a reliable sealing.

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.

Currently, no review of literature exists which attempts to understand the leakage phenomenon of metal-to-metal seal contact Pressure Relief Valves (PRV) for static closed positions as they reach the set pressure point. This paper attempts to do just that by drawing on inspiration from other research areas such as: metal-to-metal contact and gasket seals. The key topics of interest surrounding the leakage of fluid through a gap are: fluid flow assumptions; surface characteristics and its deformation; and experimental techniques used to quantify leakage. The fluid flow assumptions relating to the gap height such as transmissivity and diffusivity are found to be directly linked to the surface roughness and the surfaces deformations. Traditionally the summing method has been used to represent two rough surfaces at a micro scale from which the Tsukizoe and Hisakado theory has been applied for deformation of the micro contact in a plastic manner. The path the fluid also takes through the gap is investigated with recent work using computational methods to determine that path. Current experimental leakage quantification techniques are also discussed. Finally, the future development of PRV static leakage is examined.

This paper presents experimental investigation and numerical modeling of the effect of compressive residual stress on the corrosion fatigue life of a low carbon steel. A fatigue life test methodology based on double notched tensile test specimens is proposed. A new plasticity model is proposed for accurate simulation of compressive residual stress and calibrated to experimental stress-strain curves obtained for low carbon steel. The proposed model is implemented as a user-material in the ANSYS Workbench Finite Element Analysis program and utilized in plastic analysis and fatigue assessment. Corrosion fatigue test results are discussed and compared to numerical predictions.

This paper investigates the effects of fatigue material data and finite element types on accuracy of residual life assessments under high cycle fatigue conditions. The bending of cross-beam connections is simulated in ANSYS Workbench for three different combinations of structural member shapes: RHS-RHS, RHS-angle and RHS-Channel. The weldments are made of the structural steel grades C350LO and C450LO according to the Australian Standard AS3678. The stress analysis of each weldment having specific profile dimensions under specific cyclic loading is implemented using solid and shell elements considering linear material and geometric response. The stress results are transferred to the fatigue code nCode DesignLife for the residual life prediction. For both variants of FE-mesh, the nominal stress in the weld toes is extracted by splitting the total stress into membrane and bending components and filtering out non-linear component. Considering the effects of mean stress, bending and thickness according to BS7608, failure locations and fatigue life are predicted using the Volvo method and stress integration rules from ASME Boiler & Pressure Vessel Code. Three different pairs of S-N curves (stiff for pure tension and flexible for pure bending) are considered in this work including generic seam weld curves from nCode DesignLife and FE-Fatigue and curves for the Japanese steel JIS G3106- SM490B, which is an equivalent with properties in between C350LO and C450LO. The numerical predictions are compared to the available experimental results highlighting the most preferable fatigue data input and FE-model formulation.

This paper presents a numerical study involving the deformation of contact faces for a metal-to-metal seal in a typical pressure relief valve. The valve geometry is simplified to an axisymmetric problem, which comprises a simple geometry consisting of only three components: A cylindrical nozzle; which is in contact with a disc (representing the valve seat on top); which is preloaded by a compressed linear spring. The nozzle-disk pair is made of the austenitic stainless steel AISI type 316N(L) steel, which is typically used for power plant components. In a previous study, the macro-micro interaction of Fluid Pressure Penetration (FPP) was carried out in an iterative manual procedure at a temperature of 20°C. This procedure is now automated and implemented through an APDL script, which adjusts the spring force according to the current depth of FPP at a macroscale to maintain a consistent seal at elevated temperatures. Based upon the obtained results, specific suggestions to improve the leak tightness of the metal-to-metal seals at elevated temperatures are formulated.

This paper presents a numerical modelling and experimental investigation of the cyclic plasticity behaviour of low carbon steel. In order to improve the accuracy of modelling the material response under cycling loading, a new set of internal variables is proposed. The developed plasticity model is applied to the problem of modelling compressive residual stress inducing methods which are based on a plastic overload of a material. A beneficial influence of induced compressive residual stress is demonstrated on a benchmark problem of autofrettage of a high pressure thick-walled cylinder. Numerical simulation of the cyclic plasticity problems and fatigue assessments are carried out by means of FEM in ANSYS Workbench with FORTRAN user-programmable subroutines for material model incorporating custom equations.

This paper presents a novel direct method, within the Linear Matching Method (LMM) framework, for the direct evaluation of steady state cyclic behaviour of structures subjected to high temperature – creep fatigue conditions. The LMM was originally developed for the evaluation of shakedown and ratchet limits. The latest extension of the LMM makes it capable of predicting the steady state stress strain solutions of component subjected to cyclic thermal and mechanical loads with creep effects. The proposed iterative method directly calculates the creep stress and cyclically enhanced creep strain during the dwell period for the assessment of the creep damage, and also creep enhanced total strain range for the assessment of fatigue damage of each load cycle. To demonstrate the efficiency and applicability of the method to assess the creep fatigue damage, two types of weldments subjected to reverse bending moment at elevated temperature of 550C are simulated by the proposed method considering a Ramberg-Osgood model for plastic strains under saturated cyclic conditions and a power-law model in “time hardening” form for creep strains during the dwell period. Further experimental validation shows that the proposed direct method provides a general purpose technique for the creep fatigue damage assessment with creep fatigue interaction.

The effect of weld angular distortion on fatigue test specimens cut from butt welded plates is investigated by experimental and numerical methods. The weld specimens are made of a structural steel equivalent to BS 4360 grade 50D. The SN curve obtained from experimental data is used with the fatigue post-processor nCode DesignLife for fatigue life prediction. Mean stress correction is applied using the FKM approach to address the component of bending stress induced by clamping the distorted specimen, which is constant during the fatigue test. A parameter identification procedure for the SN curve and mean stress correction is proposed. The weld SN curve evaluated using the procedure is compared to the generic weld SN curves provided in the material database of nCode DesignLife and discussed.