Creep Constitutive Equation Research Articles

Research on creep constitutive model of steel cables

Creep and stress relaxation of steel cables caused by long-term loads will affect the mechanical behavior of tensile structures. A creep experiment of small-diameter steel cables was conducted at normal temperatures to determine the creep constitutive model of the cables using the time–creep strain data for different prestress levels. The viscoelastic Kelvin chain model was used to fit the data, and the creep constitutive equation of the cable was determined. An iterative expression suitable for ANSYS finite element analysis was derived, and the constitutive model was validated with MATLAB programs. The creep constitutive equation was used for the time-dependent analysis of a cable net structure. The results showed that creep caused stress relaxation of the cable net and caused structural element displacements.

A new extraction method of creep exponents and coefficients from an indentation creep test by multiaxial stress analysis

In this paper, we propose a method for analytically extracting creep exponents and coefficients in Norton’s law from the results of a ball indentation creep test using the finite element method. Elastic-creep finite element analyses were performed with the creep exponent and coefficient varied widely, and a simple method of obtaining three principal stresses at a point of the tested material in the vicinity of an indenter ball tip was developed. Using the three principal stresses in combination with a creep constitutive equation, we propose an analytical method to derive creep exponents and coefficients. This method is verified to determine the two material constants in Norton’s law with a satisfactory accuracy via finite element analyses. The indentation creep tests were performed using Sn-37Pb solder to demonstrate the validity of the proposed method in experiments. The proposed method successfully extracted the creep exponent and coefficient of the solder in experiments.

Data-based selection of creep constitutive models for high-Cr heat-resistant steel

ABSTRACT There are two types of creep constitutive equation, one with a steady-state term (steady-state type) and the other with no steady-state term (non-steady-state type). We applied the Bayesian inference framework in order to examine which type is supported by experimental creep curves for a Grade 91 (Gr.91) steel. The Bayesian free energy was significantly lower for the steady-state type under all the test conditions in the ranges of 50–90 MPa at 923 K, 90–160 MPa at 873 K and 170–240 MPa at 823 K, leading to the conclusion that the posterior probability was virtually 1.0. These findings mean that the experimental data supported the steady-state-type equation. The dependence of the evaluated steady-state creep rate on the applied stress indicates that there is a transition in the mechanism governing creep deformation around 120 MPa.

Study on the Porosity of Saturated Fragmentized Coals during Creep Process and Constitutive Relation

Pore abundance and deformation characteristics of saturated fragmentized coals during creep process are of significant meaning to the study on ground sediment in the mined‐out area. The law of porosity variation of saturated fragmentized coals during creep process and its creep constitutive model were studied by using the self‐developed multiphase coupling creep test device. And, results have indicated that the porosity logarithm of fragmentized coal during creep process shows a linear negative correlation with the time ln(n−a) = −ct + lnb, and the porosity decrease is evidently divided into three phases. In addition, when the stress level is relatively low, the porosity decreases slowly; when the stress level rises up, the porosity decreases quickly; when the stress level remains stable finally, the porosity is smaller. Under the equal stress, as the grain size of fragmentized coals decreases, the porosity tends to decrease, and as the grain size of fragmentized coal tends to be stable, the porosity tends to increase; the creep constitutive equation of fragmentized coals with different grain sizes was established by using the Kelvin–Voigt model, and the correlation analysis shows that the Kelvin–Voigt creep model of fragmentized coals is reasonable.

Estimation of creep constitutive equation by creep indentation test using cylindrical indenter

Estimation of creep constitutive equation by creep indentation test using cylindrical indenter

Peridynamic model for nonlinear viscoelastic creep and creep rupture of Polypropylene

This paper presents the peridynamic numerical method for nonlinear viscoelastic creep behaviour which consists of primary, secondary, tertiary creep stages and creep rupture. A nonlinear viscoelastic creep constitutive equation based on internal state variable (ISV) theory which covers four creep stages is examined. The viscoelastic equation is substituted into material parameter in the peridynamic equation to derive a new peridynamic method with two time parameters i.e. numerical time and real time. The parameters of the viscoelastic equation is analyzed and evaluated. In validating this peridynamic method, a comparison is made between numerical and experimental data. The peridynamic method for nonlinear viscoelastic creep behaviour (VE-PD) is approved by the good similarity between numerical and experimental creep strain curves with overall difference of 10.67%. The nonlinearity of experimental and numerical data is adequately similar as the error between experimental and numerical curves of secondary stage strain rate against load is 8.022%. The shapes of fractured numerical specimen show good resemblance with the experimental result as well.

Experimental Study on Creep Characteristics of Microdefect Articular Cartilages in the Damaged Early Stage.

Traumatic joint injury is known to cause cartilage deterioration and osteoarthritis. In order to study the mechanical mechanism of damage evolution on articular cartilage, taking the fresh porcine articular cartilage as the experimental samples, the creep experiments of the intact cartilages and the cartilages with different depth defect were carried out by using the noncontact digital image correlation technology. And then, the creep constitutive equations of cartilages were established. The results showed that the creep curves of different layers changed exponentially and were not coincident for the cartilage sample. The defect affected the strain values of the creep curves. The creep behavior of cartilage was dependent on defect depth. The deeper the defect was, the larger the strain value was. The built three-parameter viscoelastic constitutive equation had a good correlation with the experimental results and could predict the creep performance of the articular cartilage. The creep values of the microdefective cartilage in the damaged early stage were different from the diseased articular cartilage. These findings pointed out that defect could accelerate the damage of cartilage. It was helpful to study the mechanical mechanism of damage evolution.

Creep damage analysis of thin-walled pressure vessel based on continuum damage model under static loading

UNS N10003 alloy is wildly used as a heat-resistant material for components to be used in high temperature thorium molten salt reactor (TMSR). Because of high temperature operating environment, prediction of its creep behavior is required for safety assessment of reactors. In this study, a series of uniaxial tensile creep tests has been conducted at 650°C in an applied stress range from 220 MPa to 380 MPa. A creep damage model for UNS N10003 alloy based on Lemaitre's work has been derived as well as a creep constitutive equation for modelling creep strain. The experimental data have been used to determine parameters in the constitutive equation and the damage model. The model has been applied to structural integrity assessment of a thin-walled pressure vessel design for TMSR. The numerical results indicate that the pressure vessel design for TMSR is sound and safe in its designated 10-year design life.

Short-Term Creep of St3 Steel Under Low-Frequency Cyclic Loading

Creep constitutive equations have been derived for the materials that exhibit the properties of orthotropy (transversal isotropy) and transient creep under cyclic loading. A low-frequency case is considered. The paper provides results of experimental studies of the short-term creep of St3 steel under static and stepwise cyclic loading at room temperature. The results of calculations by the proposed constitutive equations are compared with the experimental data. A good agreement has been found for the number of cycles above 4 or 5, which demonstrates the applicability of the proposed constitutive equation to the low-frequency creep calculations for sheet materials.

Optimizing creep lifetime of friction stir welded PMMA pipes subjected to combined loadings using rheological model

Abstract The most important feature of the polymeric pipes is that they creep even at room temperature. Therefore, investigating the creep behavior of the polymers and their welded joints is a major concern in the mechanical engineering. The aim of this research is to estimate the creep lifetime of the friction stir welded Polymethyl Methacrylate (PMMA) pipes which operate under combined loading. To develop the creep constitutive equations for both weld zone and parent material, creep test samples have been cut from the weld zone and parent material of a PMMA sheet with friction stir butt welded joint. Constant load tests have been carried out at different initial stress and temperature levels. Based on the results of the tests, parameters of the modified Burgers model form of the constitutive equation have been derived. To validate the model, it is introduced to finite element software “ABAQUS” and the simulated creep behavior is compared with the experimental data. Furthermore, the developed constitutive model and the reference stress method (RSM) are used to produce a set of graphs which provide optimum creep lifetime and design conditions for the friction stir welded PMMA pipes that are subjected to combined internal pressure and rotation. The results show that despite using optimum conditions, creep life of the welded pipes is significantly lower than the non-welded pipe.

On Estimation of Creep Constitutive Equation for Welded Joint by High-Temperature Indentation Creep Testing Method

On Estimation of Creep Constitutive Equation for Welded Joint by High-Temperature Indentation Creep Testing Method

Effect of sediment thickness on the remaining creep lifetime of 9Cr1Mo refinery furnace tubes

AbstractStudying the creep behavior of mechanical engineering parts and estimating their remaining life is a major concern in the processing industry, power generation, and oil refineries. These industries widely use 9Cr1Mo alloy for manufacturing the tubes of main furnaces or heat exchangers. There is also a possibility of sediment formation that changes the temperature gradient in tube walls, leading to different creep behaviors. Hence, in this paper, the creep behavior of 9Cr1Mo (P9) tubes is investigated experimentally using both new and old materials. “Old” samples have been machined from the tubes of a main refinery furnace after operating for a period. Uniaxial creep tests are carried out at different stress and temperature levels. Based on various optimization methods and using test data, coefficients of the creep constitutive equation have been calculated for both materials. Then, these equations are introduced in a finite element model to carry out numerical analyses to study the effect of sediment thickness on the creep lifetime of the tubes. The results show that at high temperature, tubes with new material have longer creep lifetime comparing with the old ones; but at the low-temperature level, this difference in lifetime reduces. Also, it has been shown that tubes with no sediment have longer creep lifetime. With increasing the thickness of the sediment, creep lifetime of the tubes reduces significantly. In general, it is concluded that 1–2 mm sediment thickness has the same deteriorating effect as the accumulation of the creep during the 15 years of service time.

Creep constitutive equations for as-received 9Cr1Mo steel

9Cr1Mo has a wide application in petrochemical and power generation plants, prediction of its creep behavior is a major concern in these industries. In this paper, the creep behavior and creep lifetime of test samples machined from 15 years of service exposed boiler tubes in an oil refinery plant, are studied using uni-axial creep tests. Tests are carried out according to ASTM E139 at different stress and temperature levels (from 80 MPa to 190 MPa and at 550 °C, 600 °C and 650 °C). Based on the experimental data, the creep constitutive coefficients for three types of creep laws: Norton, Plrandtl and Garofalo are obtained together with Monkman-Grant and Larson Miller parameters. It has been shown that the constitutive equations in the form of Garofalo law predict the creep behavior of the material more accurately. The results show that the creep life relationships obtained based on both Garofalo and Norton power law give acceptable estimation. Also, the results are implemented in reference stress method to produce a set of loci for the optimal geometry of the tubes under combined loadings with maximum creep lifetime.

A Deformation Mechanism Map for Incoloy 800H Optimized Using the Genetic Algorithm

A total of fifty-eight Incoloy 800H samples were creep tested between temperatures of 1023 K and 1293 K, stresses of 14.1 to 105 MPa, and average grain sizes of 87.7 to 315 µm. Combined with data obtained by the National Institute for Materials Science (NIMS), a deformation mechanism map (DMM) for Incoloy 800H was produced. Optimization of the fit of the constitutive creep equations to the experimental data was performed using a global search iterative numerical optimization tool called a genetic algorithm (GA). It was found that the data were well represented by both high-temperature and low-temperature power-law creep mechanisms, but the extent of the influence of diffusion-based creep mechanisms, most specifically Coble creep, will require further investigation. A training and test method was performed to validate the solution and to test the extrapolability of the dataset. It was determined that the extrapolability of the data in all directions of the DMM was generally low.

Derivation of novel creep-integrated fatigue equations

This manuscript presents a systematic derivation of novel creep-integrated fatigue equations that possess the following unique characteristics: (i) creep damage and creep-fatigue interaction damage are embedded into the fatigue equation and requires no deliberate computation; (ii) the embedded creep damage is formulated from the constitutive equation of creep; and (iii) the integrated equation is capable of modelling the full range of creep fatigue from pure creep to pure fatigue. These characteristics ensure that these creep-integrated fatigue equations are fundamentally sound, easy to use, and applicable over a wide range of creep fatigue conditions. The creep-integrated fatigue equations based on three constitutive equations of steady-state creep: Dorn equation, Larson-Miller equation, and Manson-Haferd equation are derived and successfully validated using two metals of vastly different creep and fatigue characteristics – the SS316 stainless steel and the Sn37Pb solder.

A new creep fatigue model for solder joints

The simplicity of the Engelmaier equation is highly attractive; however, it suffers from two critical flaws: (i) it is incapable of modeling the full range of creep fatigue, from pure fatigue to pure creep; and (ii) the embedded creep function is inconsistent with the constitutive equation of creep. As such, the fitting constants in the Engelmaier equation are not material constants but have limited window of applicability. In this manuscript, three novel creep-integrated fatigue equations that are capable of modeling the full range of creep fatigue and that are embedded with the creep constitutive equations of Dorn, Larson-Miller, and Manson-Haferd are established. The equations are validated and benchmarked against the Engelmaier equation using the experimental creep fatigue data of Sn37Pb and An3.5Ag solders. The fitting constants in these creep-integrated fatigue equations are material constants and therefore can be used with confidence to accelerate creep fatigue testing. The acceleration factors for temperature cycle testing of solder joints in electronic assemblies have been established for these novel creep-integrated fatigue equations.

Complex failure analysis of a cable-roofed stadium structure based on diagnostics and tests

Results of comprehensive failure-related diagnostics, non-destructive and destructive tests, geodetic surveying, numerical modelling, time-dependent nonlinear static analysis and reliability assessment of a stadium structure with a suspension cable roof in the form of hyperbolic paraboloid cable net after fifty years of operation are presented in the paper. The main goal is the determination of the current degree of damage and resistance of the structure. Results of the metallographic analysis confirmed that the upper layers of the steel wires of carrying and stabilizing cables which were in contact with condensed moisture in the areas of the roof located above the ice surface are damaged by atmospheric corrosion. Current resistances of the diminished cable members obtained by tension tests and their creep constitutive equations are characterized. The geodetic surveying of the selected nodes of the cable net confirmed the significant change of the initial geometry of the cable structure subjected to corrosion and creep over a period of fifty years. Results obtained by time-dependent nonlinear finite element analysis considering rheological phenomena (shrinkage, creep and degradation of mechanical properties) affecting concrete arches and reliability assessment of the cable net with current properties showed that the reliability conditions are not fulfilled, preventing the cables from safely performing its function and consequently requiring the replacement of the cable net with a new cable structure exhibiting the required properties.

Creep Fibre Method of Simply-supported Composite Beams

Creep effects of composite beams can not be neglected in service-time. Creep Fiber method is used to obtain the time-depedent results, which proved to be quiet effect in both elastic and visco-elastic analysis. Only two individual centrical loading points or bars need considering, and then the system of two sumultaneous differential equations becomes simple in a clear fashion. It can be solved analyically by Rüsch constitutive equation of creep. For high and large beams of bridge structures the fibres of the two points are constant over time because the radius of inertial of steel beam is far larger than that of concrete slab, which simplifies the procedure further. The results show that under sustained loading creep of concrete produces significant negative effects. It may increase the modular ratio to 2.3 times of the initial, reduce the whole flexural stiffness by 76%, and cause the local buckling risk of the top flange and web of steel beam. These should be considered in the design of structure.

Study on the Influence of the Height of Steel Beam on Creep Effects of Composite Beams

The height of steel beam is an important parameter in the disign of structure. The effects of increasing the steel height of composite beam are quiet different from that of the pure steel beam because of composite and creep effects. To reveal the influences of this critical prarameter Rüsch constitutive equation of creep is used to obtain the exact results. With the increase of the steel height and after a limiting value is reached, the rate of the increase of the whole section stiffness becomes smaller, the rate of the increase of the compression zone of steel web becomes larger, yet the axial force and redistributed moment of concrete slab become almost constant. The deflection increases almost linearly and keeps a large slope with the increase of the steel height. Local buckling risk of the web must be considered.

Study on the Influence of Reinforcement on Creep and Shrinkage Effects of Composite Beams

To obtain time-dependent behaviours of composite beams, the system of differential equations is established by Rüsch constitutive equation of creep. Rigorous solutions of the system are obtained by computer programs of the authors. Creep and shrinkage effects involve internal force redistribution and deflection increase, and these are significantly large for composite beam. Parameter analyse of the reinforcement of concrete slab on these effects is conducted. Among them the reinforcement aggravates significantly the reduction of axial force between individual sections and alliviates slightly the increase of deflection of the beam.