Creep Constitutive Equation Research Articles

Creep Fatigue Life Simulation for Cylinder Head of Diesel Engine Based on the Concept of Continuum Damage Mechanics

The elasto-viscoplastic-creep constitutive equation based on the concept of continuum damage mechanics is formulated for the gray cast iron as used in diesel engine parts. It employs the viscoplastic strain given by Chaboche-Rousselier and the creep strain given by Perrin and Hayhurst. A part of the material parameters contained in the creep constitutive equation which was previously identified by Oka and Toi are assumed to be temperature-dependent in the present study. The identified model is applied to the creep fatigue life prediction of the cylinder head used in diesel engine parts which is made of gray cast iron. Although there are some points to be improved, the validity of the proposed model is illustrated by comparing the calculated results with the experimental results for the crack initiation locations and the crack propagation directions.

G031105 接触を考慮したカプセルチャックの変形解析([G031-10]材料力学部門,一般セッション : 圧力容器,円筒)

Capsule-Chuck is a support part used in order to grip the core of a continuation medium. In order to satisfy the needs to diversify, new product are expected. However, the deformation properties of Capsule-Chuck is not yet clarified. Creep deformation that is one of the characteristics of the Capsule-Chuck may affect to the winding of the roll. Therefore, to reveal the creep characteristics are required. In this study,using the formula Norton-Bailey the constitutive equation of creep, was carried out finite element analysis. And, were compared with experimental results to verify the validity of the model. As a result of comparing analysis and experiments, this model was found to be sufficient to represent the creep of the Capsule-Chuck.

Qualification of Ni-Based Alloys for Advanced Ultra Supercritical Plants

For the realization of advanced ultra-supercritical plant operating at service temperatures of up to 720 °C plants Ni-based alloys are indispensable. This paper describes the on-going investigations on the qualification of several Ni-based alloys such as Alloy 617, Alloy 263 and Alloy 740 within the framework of the German state funded R&D initiative COORETEC. For safe design and reliable operation of components the requirements of the European Pressure Equipment Directive (PED) have to be fulfilled. Experimental work was done in order to determine the relevant material characteristics, such as long-term creep strength values for the design of critical components. Also new design methods based on numerical calculation of the creep behaviour by using a constitutive creep equation including a damage parameter are required to make full use of the strength potential but also taking into account their specific stress-strain relaxation behaviour. Investigation of the microstructure by optical microscopy (OM), scanning electron microscopy (SEM) and transmission electron microscopy (TEM) of the as delivered and crept state show the changes in precipitation depending on time and temperature.

Establishment of an ANSYS-Based Constitutive Modeling for Age Forming of Aluminum Alloy

Constructing accurate constitutive equation from the optimal material constants is the basis for finite element numerical simulation. To accurately describe the creep ageing behavior of 2A12 aluminum alloy, the present work is tentatively to construct an elastic-plastic constitutive model for simulation based on the ANSYS environment. A time hardening model including two stages of primary and steady-state is physically derived firstly, and then determined by electronic creep tensile tests. The material constants within the creep constitutive equations are obtained. Furthermore, to verify the feasibility of the material model, the ANSYS based numerical scheme is established to simulate the creep tensile process by using the proposed material model. Results show that the creep constitutive equation can better describe the deformation characteristics of materials, and the numerical simulations and experimental test points are in good agreement.

Construction of constitutive equations of creep in orthotropic materials with different properties under tension and compression

Constitutive equations of steady creep are proposed for structural aluminum alloys that possess significant anisotropy at elevated temperatures in addition to different resistances to tension and compression.

A Space-Time-Dependant Design Method and the Stability of Ice Wall for Deep Shafts

The mechanical properties of artificial frozen soils are the key for application of artificial ground freezing, (AGF) especially the creep characteristics of artificial frozen clay when a deep shaft is sunk by using AGF. Many catastrophic accidents took place in clay strata in deep freezing shafts past because of freezing tube breaking and flooding through ice wall caused by large creep deformation of ice wall. A new creep constitutive equation with separated variables for artificial frozen clay, after C. C. Vialov, is presented on base of testing data of most kinds of artificial frozen clay under the condition of drained system. On base of the new equation, a space-time- dependant design method, a modified C. C. Vialov’s, is proposed and has been successfully used for ice wall of deep shafts all over China since 1996. Finally, the stability of ice wall for deep shafts can economically and efficiently be controlled by adjusting the variables of temperature T, un-supported height h and time elapsed t according to their sensitivity or influence.

An Experimental Study on Creep Characteristics of Salt Rock and Gypsum-salt Rock in Puguang Gas Field

Through the determination of mineralogical compositions of the salt rock and gypsum-salt rock in Puguang gas field and the creep experiments on these rocks, the authors analyze the impacts of mineralogical compositions, deviatoric stress, temperature, and confining pressure on creep behavior and proposes the constitutive equation of steady-state creep rate by combining with the creep curve and rock parameters obtained by the experiments. The experiment results indicate that the main mineralogical compositions of the salt rock and gypsum-salt rock in Puguang gas field are sodium chloride and calcium sulfate, where the content of sodium chloride can be up to more than 93%; the inherent mineralogical compositions are the internal factors that impact the creep characteristics of rock, along with the content of sodium chloride increasing, the rates of transient creep and steady-state creep increase accordingly; and as the deviatoric stress and temperature increase, the steady-state creep rate increases too. However, the impact of confining pressure is very small. The authors obtain the parameters of Heard's creep constitutive equation by fitting test data, working out the steady-state creep rates of salt rock and gypsum-salt rock under different deviatoric stresses and temperatures, which provides the theoretical basis of the calculation of safe mud density window and the analysis of abnormal casing deformation for the formations of salt rock and gypsum-salt rock in Puguang gas field.

Experimental Study on Creep Property of Similar Material for Jin Tan Salt Rock Gas Storage Medium

Uniaxial compression creep tests have been performed on a kind of rock salt similar material and laminated salt rock similar material on the base of salt rock gas-storage in Jintan. The creep tests show that the rheological property of the similar material is basically the same with the original rock. Under the uniaxial compression, the deformation gradually approaches to be constant after the early short stage of creep attenuation. The similar material shows stress-dependent behavior obviously under different stress stage, the greater the load the higher the creep ratio and creep deformation. A creep constitutive equation which is suitable to rock salt is used to the similar material, and it fits with the obtained creep data very well. The results show that the similar material developed in this passage has the same creep property as the original salt rock,and this material can be used to simulated the deformation and failure of underground gas storage constructed in bedded salt deposits.

Evaluation of creep properties for Sn–Ag–Cu micro solder joint by multi-temperature stress relaxation test

The creep properties of a Sn–Ag–Cu micro solder joint with a solder ball with 500μm were investigated by a multi-temperature stress relaxation test performed using a specimen at three temperatures (298, 348, and 398K). The stress exponents in Norton’s law were 8 at 398K, 8.8 at 348K, and 9 at 298K, and the activation energies were found to be 39kJ/mol in the high-stress region and 80kJ/mol in the low-stress region. The stress exponent in Norton’s law for a micro solder joint was lower than that for a large-scale specimen, which resulted in more coarsened intermetallics in the microstructure than in the large-scale specimen. The activation energies for the micro solder joint were almost equal to those for the large-scale specimen in the high- and low-stress regions. These results reflect the microstructure of the micro solder joint, and the creep constitutive equation for the Sn–Ag–Cu joint could be derived by the multi-temperature stress relaxation test proposed in this study.

Simulation and Springback Prediction of Integral Panel with High Ribs in Age Forming

Age forming is the best forming method of integral panel parts of aircrafts, which have large amount of springback and the springback’s accuracy, is hard to control, so a method which can make an accurate prediction of the springback after forming is needed. This article which is based on creep test data and CPT, fits the creep constitutive equation and obtained the material parameter. The numerical simulation is adopted to process age forming simulation on springback of T-specimen of aluminum 2124, and the simulation result is compared with the test result to do revision of the material parameter; the revised material parameter is applied into the numerical simulation of age forming of the integral panel which is of high strength. Through tests which can confirm the error ranges from -1mm to +1mm, this method’s accuracy is proved.

1408 スリット入りつば付き試験片のクリープ変形特性と変形一様性(OS15-2 諸観点からの物質・材料の特性評価II,OS15 諸観点からの物質・材料の特性評価)

Since numerical analyses under elevated temperature usually depend on a constitutive equation of creep, it is necessary to derive a high-precision equation. Creep properties on deformation can be normally obtained using constant load creep machines, but constant stress creep tests are more suitable to acquire high-precision creep data. Conventional uniaxial creep specimens have ridges attached on both sides of gauge length. However, even if the constant stress creep testing machines are used, these ridges prevent area reduction around them, and cause unequal deformation in the gauge part. Authors have proposed cutting slits into the ridge to release the specimen from the circumferential constraint by extensometer ridges. In this study, taking into account a realistic analytic condition, the authors carried out elastic-plastic creep Finite Element (FE) analyses to investigate the performance of uniform deformation. Subsequently, a series of interrupted constant stress creep, tests using SUS304 steel were conducted to examine the effect of introducing slits. The analytical and the experimental results showed that the introduction of these slits into the ridges would affect the deformation during creep, but not improve the uniformity of deformation along the gauge part.

Dependence of Creep Deformation Behavior in the Root of Notch on Creep Rupture Life

The object of the investigation was to examine the dependence of creep strain in root of notch on the creep rupture life for the round bar with the circumferential V-notch during the short-time creep at high temperature. In the long-time creep under the low stress, it is possible to estimate the stress and strain distributions of notch root only from the creep deformation. However, it is necessary to sufficiently consider the plastic deformation under the creep of the load of the relatively high stress, since elastic, plastic and creep deformation are dependent on each other. In this study, the tensile creep rupture tests of the circumferential 60° V-notched bar for a type SUS 304 stainless steel were carried out at 873K in the air, and in order to discussed the deformation at the notch root under short-time creep in the laboratory, elasticity, plasticity and creep analysis were carried out using a finite element method (FEM). The elongation of the notch groove was measured under creep test and compared with the results of FEM analysis using the plastic and creep constitutive equations which were determined from the tension test and the tensile creep testing of smooth specimen. A considerably good agreement is obtained between the numerically computed and the experimentally observed plastic and creep deformation behaviors of the notched bars under constant loading, and the conclusion was got like that the mean creep strain rate between the edges of the V-shaped notch governs creep deformation and rupture under highly constrained deformation in tri-axial states of stress.

703 配管用低合金鋼の応力緩和挙動に及ぼすクリープ構成則の影響(OS10-1 オーガナイズドセッション《発電機器の材料・構造解析と評価》)

Effect of creep constitutive equation on stress mitigation behavior during Post-Weld Heat Treatment (PWHT) was clarified. The material properties of Norton's law and Norton-Bailey law for low alloy steel pipe (STPA23) were experimentally investigated. To verify the stress mitigation behavior, five welded specimens were fabricated. One specimen was measured without PWHT. The other specimens were conducted by different PWHT conditions. The residual stress distributions of the welded specimens were measured using a sectioning method. The simulation results with two types of creep constitutive equation agreed well with the measured data. In addition, no differences in the creep constitutive equation were observed at a high PWHT temperature. Accordingly, these analyses with two types of creep constitutive equations were verified to be effective.

Experimental study of the creep behavior of parent, simulated HAZ and weld materials for cold-drawn 304L stainless steel

In this paper, the creep behavior and constitutive equations of different layers of the weldment for cold-drawn 304L stainless steel have been determined using experimental data. This alloy can be used in the “as-welded” condition, even in severe corrosive conditions due to its lower carbon, which minimizes both chromium carbide precipitation and intergranular corrosion during the welding. As a result, welded Austenitic Stainless Steel 304L joints have extensive application in power generation and petrochemical industries and it is critical to study their high temperature creep resistance. For this purpose, test samples have been obtained from cold drawn bars, simulated HAZ and weld material according to the ASTM A276-05a. The creep behavior and properties have been examined for these materials by conducting uni-axial creep tests. Constant temperatures and constant load uni-axial creep tests have been carried out at three temperatures of 680, 700 and 720°C, subjected to constant loads, which produce initial stresses ranging from 140 to 360MPa that are either below or above yield. The experimental data have been used to obtain the creep constitutive parameters using numerical optimization techniques. In addition, the temperature and stress dependency of the creep properties for Parent, HAZ and Weld materials have been investigated using Larson–Miller and Monkman–Grant parameters.

Experimental Study of the Creep Behaviour of the Cold‐Drawn 304L Stainless Steel

Abstract: In this article, the material and physical parameters for the creep constitutive equations of cold‐drawn 304L stainless steel have been determined using experimental data. Austenitic stainless steel 304L is used mostly in power generation and petrochemical industries because of its high‐temperature creep resistance even at above yield stresses. Test samples have been obtained from cold‐drawn bars, and the material conforms to ASTM A276‐05a specifications. The creep behaviour and properties have been examined for this material by conducting uni‐axial creep tests. Constant temperature and constant load uni‐axial creep tests have been carried out at three temperatures of 680,700 and 720 °C, subjected to constant loads which produce below and above yield initial stresses of 200, 250, 320, 340 and 360 MPa. The experimental data have been used to obtain the creep constitutive parameters using numerical optimisation techniques. In addition, the temperature and stress dependency of the creep properties for this alloy have been investigated using Larson–Miller and Monkman–Grant parameters.

Artificial Neural Network for Creep Behaviour Predictions of a Parallel‐lay Aramid Rope Under Varying Stresses

Abstract: An improvement of the creep behaviour prediction of parallel‐lay aramid ropes under varying stresses is the scope of the following study in which application of artificial neural networks (ANNs) for the prediction of creep under varying stresses is presented. This qualitatively different approach assumes that the ANN can be trained to simulate time‐dependent response of the rope in the given load (stress) programme and time interval. The classic rheological constitutive equations are not needed in this case, because ANN acts as a constitutive operator trained by stresses and the corresponding creep strains from experimental data. Carried numerical experiments were divided into the following three parts: (i) searching the best ANN for a creep behaviour approximation under varying stresses, (ii) investigating the best topology of the selected neural network and (iii) investigating the best results for the creep function identification. Comparison between the experimentally observed creep strains of the parallel‐lay aramid rope under varying stresses, predicted creep strains when the linear creep constitutive equation is applied and predicted creep strains when the obtained Jordan neural network with the 3‐10‐1 topology is used confirmed that the Jordan neural network developed achieved less than half mean square error beside the existing creep constitutive analytical approach.

Experimental Study of the Creep Lifetime of the 1.25Cr 0.5Mo Steel Pipes

Abstract: In this paper, physical parameters for the creep constitutive equations of the low alloy ferritic steel 1.25Cr0.5Mo have been determined using experimental data. This alloy is used mostly in power generation and petrochemical industries because of its high temperature creep resistance. Test samples have been obtained from a new super‐heater pipe wall of a steam‐generating boiler in Tabriz Petrochemical Plant according to the ASTM standards. By conducting creep rupture tests for 1.25Cr0.5Mo steel, creep behaviour and creep‐rupture properties were examined for this material. Creep rupture tests have been carried out at four temperatures of 700, 725, 750 and 800 °C, under applied uni‐axial stresses of 30, 35, 40 and 50 MPa. The experimental data have been used to obtain the constitutive parameters using numerical optimisation techniques. Also the temperature and stress dependency of the creep lifetime for this alloy has been investigated using Larson–Miller and Monkman–Grant parameters. The results show good agreement with other test data such as ASTM and API. Finally, these constitutive equations have been used to study the creep behaviour of the super‐heater pipe. The results show that the super‐heater tube has been over designed in terms of the creep lifetime and this is in accordance with the in‐plant observations.

Study on tri-axial creep experiment and constitutive relation of different rock salt

To evaluate the effect of the long-term operation of a salt cavern in a given construction on rock deformation and its stability, tri-axial creep tests to the glauberite, anhydrite, and argillaceous rock salt are conducted, from which the creep curves as well as exponential functions of strain rate during the steady creep stage and creep constitutive equations of different rock salt in the experimental process derived are obtained. The study results show that: (i) Under the same deviatoric stress, the strain rate of argillaceous rock salt is lower than the glauberite and anhydrite, and the difference becomes larger with the increase of the deviatoric stress; (ii) The creep constitutive equations of different kinds of rock salt are in good agreement with the Burgers model, besides which the respective characteristics of these two creep models are compared. The change of creep parameters also illustrates the discrepancy of rock salt. The researching results can provide some references for long-term stability analysis of gas storage in salt caverns.

Long-term creep characterization of Gr. 91 steel by modified creep constitutive equations

This paper focuses on the long-term creep characterization of Gr. 91 steel using creep constitutive equations. The models of three such equations, a combination of power-law form and omega model (CPO), a combination of exponential form and omega model (CEO), and a combination of logarithmic form and omega model (CLO), which are described as sum decaying primary creep and accelerating tertiary creep, are proposed. A series of creep rupture data was obtained through creep tests with various applied loads at 600 °C. On the basis of the creep data, a nonlinear least-square fitting (NLSF) analysis was carried out to provide the best fit with the experimental data in optimizing the parameter constants of an individual equation. The results of the NLSF analysis showed that in the lower stress regions of 160 MPa (σ/σys 0.65), the CPO model showed better agreement than the other two models. It was found that the CEO model was superior to the CPO and CLO models in the modeling of long-term creep curves. Using the CEO model, the long-term creep curves of Gr. 91 steel were numerically characterized, and its creep life was predicted accurately.

G030061 単軸クリープ試験片へのスリット導入と変形一様性([G03006]材料力学部門一般セッション(6):高温・環境)

Specific numerical analyses have been required at designing modern high temperature machines and structures. Since analytical results usually depend on a constitutive equation of creep, it is necessary to derive a high-precision equation. Creep properties on deformation can be normally obtained using constant load creep machines, but constant stress creep tests are more suitable to acquire high-precision creep data. In order to keep the true stress constant, an applied load or the lever ratio should be changed during the test duration. Conventional uniaxial creep specimens have ridges attached on both sides of gauge length to measure deformation outside an electric furnace. For ductile materials, however, even if the constant stress creep testing machine are used, these ridges constrain area reduction around them, and unequal-uniform deformation breaks the constant volume condition in the gauge portion during deformation. Authors have proposed introducing slits into the ridge to release the circumferential constraint by the extensometer ridges. In this study, taking into account a realistic analytic condition, the authors carried out elastic creep Finite Element (FE) analyses to investigate an optimum depth of the slit. Subsequently, a series of constant stress creep tests using SUS304 steel are conducted to examine the effect of introducing slits on the performance of uniform deformation. The analytical and the experimental results show that the introduction of these slits into the ridges would improve uniform deformation effectively.