Konstantin Naumenko

A Combined Model for Hardening, Softening, and Damage Processes in Advanced Heat Resistant Steels at Elevated Temperature

Phenomenological constitutive equations that describe inelastic behavior of advanced steels at elevated temperature are developed. To characterize hardening, recovery, and softening processes, a composite model with creep-hard and creep-soft constituents is applied. The volume fraction of the creep-hard constituent is assumed to decrease toward a saturation value. This approach reproduces well the primary creep as a result of stress redistribution between constituents and tertiary creep as a result of softening. To describe the whole tertiary creep stage, a damage variable in the sense of continuum damage mechanics is introduced. The material parameters and the response functions in the model are calibrated against experimental creep curves for X20CrMoV12-1 steel. For the verification, simulations of the inelastic response are performed and the results compared with experimental data including creep under stress change conditions and stress-strain response under constant strain rate. Furthermore, the lifetime predictions are analyzed and compared with the published creep rupture strength data. The results show that the consideration of both softening and damage processes is necessary to characterize the long-term strength in a wide stress range. Finally, the model is generalized to the multi-axial stress state.

CREEP ANALYSIS FOR A WIDE STRESS RANGE BASED ON STRESS RELAXATION EXPERIMENTS

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.

Numerical Estimation of the Elastic Properties of Thin-Walled Structures Manufactured from Short-Fiber-Reinforced Thermoplastics

A model which allows us to estimate the elastic properties of thin-walled structures manufactured by injection molding is presented. The starting step is the numerical prediction of the microstructure of a short-fiber-reinforced composite developed during the filling stage of the manufacturing process. For this purpose, the Moldflow Plastic Insight® commercial program is used. As a result of simulating the filling process, a second-rank orientation tensor characterizing the microstructure of the material is obtained. The elastic properties of the prepared material locally depend on the orientational distribution of fibers. The constitutive equation is formulated by means of orientational averaging for a given orientation tensor. The tensor of elastic material properties is computed and translated into the format for a stress-strain analysis based on the ANSYSÒ finite-element code. The numerical procedure and the convergence of results are discussed for a thin strip, a rectangular plate, and a shell of revolution. The influence of manufacturing conditions on the stress-strain state of statically loaded thin-walled elements is illustrated.

A constitutive model for inelastic behavior of casting materials under thermo-mechanical loading

High-temperature components, for example turbochargers, are often subject to complex thermal and mechanical loading paths. Non-uniform temperature distribution and constraints by neighboring components result in complex timely varying stress and strain states during operation. The aim of this paper is to analyze inelastic behavior of a casting material Ni-resist D-5S in a wide stress, strain rate and temperature ranges. The material model including a constitutive equation for the inelastic strain rate tensor and a non-linear kinematic hardening rule is discussed. To calibrate the model, experimental databases from creep and low cycle fatigue tests are generated. They include creep curves for temperatures within the range 600–800 °C and stress levels from 10 to 150 MPa. The low cycle fatigue data collect a family of hysteresis loops for the strain rate of 10−3 1/s, the strain amplitude from 0.4% to 2% and temperature levels within the range 200–800 °C. For the verification of the model, simulations of the material behavior under uniaxial thermo-mechanical fatigue loading conditions are performed. The results for the stress response are compared with experimental data.

Robust Methods for Creep Fatigue Analysis of Power Plant Components Under Cyclic Transient Thermal Loading

The aim of this paper is to apply robust mechanisms-based material laws to the analysis of typical high-temperature power plant components during an idealized start-up, hold time and shut-down sequence under a moderate temperature gradient. Among others a robust constitutive model is discussed, which is able to reflect inelastic deformation, hardening/recovery, softening and damage processes at high temperature. The model is applied for a creep analysis of advanced 9–12%CrMoV heat resistant steels and calibrated in particular case against experimental data for 10%CrMoV steel type. For a steam temperature profile transient heat transfer analysis of an idealized steam turbine component is performed providing the temperature field. From the subsequent structural analysis with the inelastic constitutive model local stress and strain state variations are obtained. As an outcome a multi-axial thermo-mechanical fatigue (TMF) loading loop for one or several loading cycles can be generated. They serve as input for a fatigue life assessment based on the generalized damage accumulation rule, whose results come close to reality. In addition, the accuracy of a simplified method which allows a rapid estimation of notch stresses and strains using a notch assessment rule (NAR) [1] based on Neuber approach is examined.Copyright

Analysis of temperature and strain rate dependencies of softening regime for tempered martensitic steel

This article aims to analyse the influence of temperature and strain rate on the mechanical behaviour of the high-chromium martensitic steel X20CrMoV12-1. The analysis is based on two series of high-temperature uniaxial tensile tests. In a first series, the tensile tests are conducted until rupture, and temperature as well as strain rate are varied systematically. The corresponding stress–strain curves show an extended softening stage. In order to examine softening, it is crucial to distinguish between microstructural changes and strain localisation due to necking. For this reason, a tensile test at low strain rate is performed several times, while the test is terminated at different strain levels in order to examine the onset of necking. Based on the test results and surface measurements of the deformed specimens, the strain level at which necking starts is determined, and possible interactions between softening and necking are discussed. The tensile tests have been conducted in order to calibrate a mechanical model which supplies reliable predictions on the material behaviour under different loading scenarios at elevated temperatures. For this reason, a framework based on microstructural processes is presented in the second part of the article. The model applies a binary mixture approach in conjunction with an iso-strain concept. Furthermore, backstress and softening variables are introduced to consider hardening and softening effects. This procedure results in a system of three differential equations describing the mechanical behaviour.

Modeling creep damage of an aluminum–silicon eutectic alloy

Aluminum–silicon casting alloys are widely used in the automotive industry. The aim of this article is to analyze creep and creep damage of the eutectic AlSi12CuNiMg cast piston alloy and to present a constitutive model that reflect basic features of deformation, aging and damage behavior. Creep tests and force-controlled low cycle fatigue tests are carried out at several levels of temperature. Creep curves exhibit classical three stages. The tertiary creep stage is controlled by damage processes, mainly due to failure of the brittle inclusions and aging processes of the aluminum matrix. Ruptured specimens are analyzed with the help of optical and scanning electron microscopy to establish the fracture mode. A constitutive model is developed to describe the high temperature creep and ratcheting behavior. The proposed model involves three state variables including a back stress, an aging parameter and a damage variable. The model is calibrated against the creep and tensile curves and verified by numerical simulations of cyclic creep tests.

Cyclic creep damage in thin-walled structures

Thin-walled structural elements are often subjected to cyclic loadings. This paper presents a material model describing creep behaviour under high-cycle loading conditions (N ≥ 5 × 104-105). Assuming that the load can be split into two joint acting parts (a static and a superposed, rapidly varying small cyclic component), the asymptotic expansion of two time-scales has been applied to the governing equations of the initial-boundary value creep problem. The system of equations determine two problems. The first is similar to the creep problem by quasi-static loading. The second is the problem of forced vibrations. Both the problems are coupled by constitutive equations. The model is applied to the simulation of the cyclic creep damage behaviour of thin-walled structural elements. The results are discussed for two special numerical examples (a conical shell and a circular plate). The simulations show that the creep and the damage rates as well as the failure time are strongly sensitive to the redistribution of the stress state cycle asymmetry parameter As. The values of As increase during the creep process. For particular cases of the loading frequency, As can exceed the critical value. In this case the material model must be extended in order to consider the creep-fatigue damage interaction.

On the Prediction of Creep Damage by Bending of Thin-Walled Structures

Analysis of thin-walled structures operating at elevated temperaturesneeds a consideration of time-dependent creep-damage behaviour. Within theframework of the creep theory and the CDM the irreversible deformations ofthe structural elements can be described by constitutive equations withinternal state variables. The paper deals with an application ofphysically based creep-damage constitutive model with two damageparameters, proposed by Hayhurst, to the stress analysis of thin-walledplates and shallow shells. The governing equations of the shell theory areformulated by the consideration of geometrical nonlinearities associatedwith time-dependent finite deflections. Numerical examples show aninfluence of the finite deflections on the life-time predictions in platesas well as illustrate a dependence of damage evolution on the stress statemode. The results for creep damage evolution in plates are compared withresults based on the classical Kachanov–Rabotnov creep-damageconstitutive model.

Prediction of Accumulation of Technological Stresses in a Pipeline Upon its Repair by a Composite Band

The problem on the formation of stress fields in a pipeline with a repair composite band during the solidification of the polymer resin is considered. Heating of the composite material due to the heat release during the polymerization reaction is modeled. Two-dimensional pictures of location of the glass transition front during cooling are obtained. A numerical analysis of the stress state of a fragment of the pipeline and the composite band during the cooling process is performed. The effect of matrix shrinkage during its glass transition on the level of the technological stresses is analyzed.