Steady-state Creep Rate Research Articles

On the applicability of boundary condition based tensile creep model in predicting long-term creep strengths and lifetimes of engineering alloys

Creep behaviour of metal alloys for critical high temperature engineering applications is usually studied by uniaxial tensile creep tests. The stress and temperature dependence of steady-state or minimum creep rate observed in such tests is rationalised at present on the basis of either Norton or MBD equation. But, the stress exponent determined on such basis depend strongly and often irregularly on test temperature and the creep activation energy varies with stress or stress range. Hence, these parameters cannot be used for long-term predictions. Here, it is shown that these difficulties can be removed if a new creep model, which incorporates tensile strength, is used to rationalise the creep data. The stress exponent determined then does not depend on temperature although it depends on stress range, and the creep activation energy does not depend on stress. Thus, there is no relationship between stress exponent value and creep mechanism. Consequently, the new tensile creep model can be used in combination with Monkman-Grant relationship to predict the long-term tensile creep strengths and lifetimes at different temperatures using creep parameters determined from short-term tensile creep tests. Both the deficiencies of the Norton and MBD equations and the predictive quality of the new tensile creep model are demonstrated here using uniaxial tensile creep data and tensile strength data measured for two totally different types of creep resistant engineering alloys: 9Cr-1Mo steel and Ni base superalloy Ni-16Cr-8.5Co-3.5Al-3.5Ti-2.6W-1.8Mo-0.9Nb.

Enhanced double-mechanism creep laws for salt rocks

The double-mechanism creep law (DM model) is an empirical creep constitutive model widely employed in Brazilian salt rock mechanics. This model often presents good performance in steady-state creep prediction. However, transient creep is not accounted for, and whenever early creep estimates are important, the contribution of this phase might be meaningful. This work adds value by presenting two alternatives to account for transient creep in the DM model. The first alternative couples the transient function from Sandia’s multi-mechanism deformation model to the DM model steady-state creep rate (EDMT model). The second alternative couples the DM model response to Norton’s power law when the strain rate given by the latter remains lower than the one from the former (EDMP model). These models can be implemented in numerical simulators at small code extensions of the DM model implementations. Applications from previous works by the authors are revisited to validate the formulations based on experimental data. EDMT and EDMP models differ in the formulation of transient creep and, consequently, in the time of transition between the transient and the steady-state phases. Both methods were successful in treating transient creep and in simulating experimental results.

A modified theta projection model for the creep behaviour of creep-resistant steel

A modified theta projection model is proposed for the description of creep behaviour. The model shows very good flexibility in fitting the entire test data of the creep-resistant steel 12Cr1MoV over the three creep stages. The capability of describing the primary to secondary stage makes it easier to precisely evaluate the steady state or minimum creep rate using the model. The model is derived and modified from the original theta projection method. It also keeps the four indeterminate coefficients and can meet the convergence condition easily during regression by the least squares method. In this paper, the minimum creep rates of 12Cr1MoV are also obtained and discussed.

Experimental Investigation of Creep Properties Parameters of 10mowvnb Steel

The creep properties parameters of 10MoWVNb steel have been investigated by high temperature creep experiments. It shows that the steady-state creep rate of 10MoWVNb steel under 175 MPa (400 °C, 450 °C, 500 °C), 200 MPa (400 °C, 450 °C, 500 °C) are 3.60 × 10−5 h−1, 2.17 × 10−4 h−1, 4.57 × 10−3 h−1, 5.59 × 10−5 h−1, 3.34 × 10−4 h−1, 7.02 × 10−3 h−1, respecticely. The stress index of 10MoWVNb steel during creep is 3.2474. And the apparent activation energy of 10MoWVNb steel is 198.73 kJ/mol. The results of this study can provide some technical references for the safety management of 10MoWVNb steel.

Creep of closed-cell aluminum foams: Effects of imperfections and predictive modeling

The influence of five different types of morphological imperfection – curved cell wall, corrugation, cell shape irregularity, missing cell walls and non-uniform distribution of cell wall thickness – on steady state creep of closed-cell aluminum foams is systematically studied under uniaxial compressive loading. A refined theoretical model is developed to predict the steady state creep rate of idealized tetrakaidecahedral (TKD) closed-cell foams. Based upon the TKD model, finite element modeling is also carried out. The presence of imperfections usually leads to significant increase in steady state creep rate. The creep rate increases linearly with the degree of cell shape irregularity and the curvature of curved cell walls, while increases as a power law function of the area fraction of missing cell walls and the dispersion degree of non-uniform distributed cell wall thickness. The combined effect of three different random defects—cell shape irregularity, missing cell walls and non-uniform distribution of cell wall thickness—causes more drastic increase in creep rate than any single or dual imperfections. Interactions among the three are small and can be neglected. Finally, an empirical formula of steady state creep rate is proposed to give a good prediction for closed-cell foams with random imperfections.

Microstructure, Mechanical Properties, and Crack Propagation Behavior in High-Nb TiAl Alloys by Directional Solidification

Titanium aluminide (Ti-47Al-6Nb-0.1C) alloys were prepared using a cold crucible directional solidification technique with an input power range of 35 to 55 kW under a withdrawing velocity of 0.4 mm/min. The macro/microstructure was characterized, and the mechanical properties were evaluated. The results show that the directional solidification (DS) ingots exhibit β-solidification characteristics at an input power range of 35 to 55 kW, and a well-developed DS microstructure was acquired at an input power range of 40 and 45 kW. With the increasing input power, the lamellar spacing decreases, resulting in the increasing tendency in the average room-temperature yield strength. The steady-state creep rate strongly depends on the lamellar spacing, and the creep life depends on the DS microstructure. The well-developed DS alloy can significantly improve the creep properties but has little influence on the room-temperature tensile properties. Moreover, after testing the fracture toughness, the crack propagation showed interlamellar cracks, translamellar cracks, and intercolony boundary cracks that primarily propagated along the colony boundary after creep testing.

Historical experiment to measure irradiation-induced creep of graphite

This paper presents historical results of graphite irradiation-induced creep experiments that were performed at Oak Ridge National Laboratory from the 1950's to the 1970's. These experiments were performed at temperatures from 150°C to 1000 °C, and bend stresses ranging from 500 to 5000 psi (∼3.3–34.5 MPa). The experimental setup utilized in-situ measurement of specimen displacement, on-line applied stress control, and the ability to change stress during the experiment. The different stress conditions showed that the primary creep strain and the steady-state creep rates both have a linear stress dependence. The temperature range used in this work resulted in trends that have not be previously presented in the literature: 1) a linear dependence of primary creep strain on temperature, and 2) the shape of steady state creep rate versus temperature (see graphical abstract). The maximum dose in the specimens was 0.9 dpa, which is sufficient to achieve steady-state creep without the structural changes that alter the observed creep behavior. The results from this experiment provide evidence that dispels that the pinning-unpinning model describes the mechanism of irradiation creep in graphite. Instead these results suggest a dislocation climb mechanism is the probable mechanism for creep within the crystalline regions.

Laboratory investigation on rheological properties of greenschist considering anisotropy under multi-stage compressive creep condition

The influence of structural anisotropy on time-dependent behaviour of foliated metamorphic greenschist collected from deep underground tunnel (−1300 m) in China was investigated to acquire the fundamental knowledge of the long-term mobility of greenschist in nature. Considering the structural anisotropy, greenschist samples with different inclination of foliation/bedding planes (i.e., θ = 0°, 35°, 45°, 60° and 90°) was prepared for creep test. Multi-stage constant loading method is employed in this test with each stage equals to 10 MPa, 20 MPa, 30 MPa and 40 MPa respectively for presenting analogous situation of variable stressing of greenschist caused by over laying rocks and tectonic stresses. The test results revealed the significant effect of structural anisotropy on the creep development (i.e. instantaneous strain, transient creep, steady-state creep) and failure mode. The control of structural anisotropy on steady-state creep rate is strengthened at high stress level, compared to that is weaken on other properties (i.e. instantaneous strain, transient strain), which is mainly due to the evolution of tensile and shear crack along and cross the bedding plane at high stress level. The three types of failure models of greenschist (i.e. shear along the bedding plane, cross the bedding plane or compound) were observed which hints that the long-term mobility of greenschist rockmass is mainly dependent on characteristic of structural anisotropy and stress conditions. In addition, based on the experimental results, creep models were proposed for greenschist considering the bedding plane and their parameters were obtained using test result. We believe that these test results and the models would throw some insights and benefit practicing design engineers and numerical modellers.

Evaluation of the mechanical performance of the creep behavior of a fiberglass repair after aging in oil

The mechanical behavior of a glass fiber/epoxy matrix composite used to repair steel pipes was evaluated after its exposure to oil under temperature at atmospheric pressure and at 17 bar. The effect of pressure was found to affect on a different way short-term and long-term properties of the composite. Under atmospheric pressure, more oil was absorbed by the composite than at 17 bar. This behavior was attributed to the effect of the hydrostatic pressure upon the polymeric matrix-free volume. The set of mechanical properties evaluated by tree-point bending test (flexural strength, elastic modulus, toughness, and deformation at maximum load) was also more affected when aging was conducted under atmospheric pressure. However, the steady state creep rate of the composite aged under 17 bar was higher than that of the material aged at atmospheric pressure, reducing the expected service life of the repair joint when both temperature and pressure are applied together.

On the dimensional analysis for the creep rate prediction of ceramic fibers

A novel semi-empirical equation for the steady-state creep rate description of ceramic fibers is here proposed. Dimensional analysis was applied to identify the relationship between the variables related to the creep rate. Besides the variables known from the Arrhenius creep equation, a temperature factor that accounts for changes with the temperature was also taken into consideration. The resultant equation shows that the creep rate is proportional to the temperature, applied stress and two material constants, as well as inversely proportional to the fiber grain size. The two material constants k and C described in the equation can be easily determined by creep tests at different temperatures under the same applied stress. Therefore, this equation can be more efficiently applied to predict the creep rate of ceramic fibers under different applied stresses and initial grain sizes. To confirm this, the proposed equation was used to fit the creep rate data set of two ceramic fibers, Nextel 720 and CeraFib 75. In summary, the equation provides a good fit (adjusted R-squared up to 0.97) and prediction for the experimental data of tests with different temperatures, applied stresses and initial grain sizes.

A dissolution-diffusion sliding model for soft rock grains with hydro-mechanical effect

The deformation and failure of soft rock affected by hydro-mechanical (HM) effect are one of the most concerns in geotechnical engineering, which are basically attributed to the grain sliding of soft rock. This study tried to develop a dissolution-diffusion sliding model for the typical red bed soft rock in South China. Based on hydration film, mineral dissolution and diffusion theory, and geochemical thermodynamics, a dissolution-diffusion sliding model with the HM effect was established to account for the sliding rate. Combined with the digital image processing technology, the relationship between the grain size of soft rock and the amplitude of sliding surface was presented. An equation for the strain rate of soft rocks under steady state was also derived. The reliability of the dissolution-diffusion sliding model was verified by triaxial creep tests on the soft rock with the HM coupling effect and by the relationship between the inversion average disjoining pressure and the average thickness of the hydration film. The results showed that the sliding rate of the soft rock grains was affected significantly by the waviness of sliding surface, the shear stress, and the average thickness of hydration film. The average grain size is essential for controlling the steady-state creep rate of soft rock. This study provides a new idea for investigating the deformation and failure of soft rock with the HM effect.

Influence of multi-walled carbon nanotubes on creep behavior of adhesively bonded joints subjected to elevated temperatures

ABSTRACTPolymeric materials are prone to creep loading. This paper is aimed to study the effect of multi-walled carbon nanotubes (MWCNTs) on creep behavior of adhesively bonded joints. Neat and MWCNTs-reinforced adhesively bonded joints were manufactured and tested under creep loading at elevated temperatures. Two MWCNT weight percentages of 0.1 and 0.3 were used for reinforcing the single lap joints (SLJs) and the joints were tested at different temperature and load levels. The results showed that 0.1 wt% of MWCNTs resulted maximum improvements in creep behavior of adhesive joints. Adding 0.1 wt% of MWCNTs into the adhesive layer caused maximum reductions of 57%, 60% and 47% in the steady-state creep rates of the joints tested at 30, 40 and 50°C, respectively. Furthermore, 0.1 wt% of MWCNTs resulted maximum reductions of 29%, 33% and 37% in the creep strains corresponding to a specific creep loading time and maximum reductions of 23%, 45% and 49% in the elastic strains corresponding to the time at which creep loading started.

Indentation Creep Behavior of Nugget Zone of Friction Stir Welded 2014 Aluminum Alloy

The present study is aimed at evaluating the creep behavior of the nugget zone of friction welded 2014 Aluminum alloy by indentation creep tests. Impression creep testing was carried out at different temperatures of 300°C, 350°C and 400 °C with stress 124.77MPa, 187.16MPa, 249.55 MPa using a 1.0 mm diameter WC indenter. Experiments were conducted till the curve enters the steady state creep region. Constitutive modeling of creep behavior was carried out considering the temperature, stress and steady state creep rate. Microstructural investigation of the crept specimen at 400°C temperature and 187.16 MPa load was carried out and found that the small precipitates accumulate along the grain boundaries at the favorable conditions of the creep temperature and stress, new precipitates evolve due to the ageing. The grains are broken and deformed due to the creep phenomena.

Analysis of viscoelastic response and creep deformation mechanism of asphalt mixture

Asphalt mixture is a typical viscoelastic material. Its mechanical response and deformation behavior depend on the role of time, temperature conditions and stress levels. Three kinds of asphalt mixture (i.e. AC-13, AC-16, AC-20) were used for the static creep test in different temperature conditions and stress levels. According to the creep curve, The Burgers viscoelastic parameters including E1, η1, E2, η2 and the steady-state creep rate K were obtained. The effects of test temperature, stress level and aggregate gradation on the viscoelastic parameters of asphalt mixture were analyzed. Based on the relationship between the steady-state creep rate and the experimental temperature & load stress, the stress index and creep activation energy of asphalt mixture were proposed. By analyzing the relationship between the creep activation energy and the rutting depth, the creep mechanism of the asphalt mixture was discussed. The results show that with the increase of temperature, the four parameters of E1, η1, E2 and η2 of the three kinds of asphalt mixtures generally decrease. But at different temperatures, the viscoelastic parameters of these three kinds of mixtures are not the same. The stress level has a significant effect on the viscoelastic properties of the asphalt mixture. The four viscoelastic parameters have the largest differences when the stress level is at the intermediate load level of 0.5 MPa, but the responses of the different gradation asphalt mixture to the stress level are different. With the increase of temperature and load stress, the steady-state creep rate increases gradually, but the stress indexes of these three kinds of asphalt mixtures stress index are not different. All of them are less than 3, and belong to the diffusion creep under the control of aggregate interface dislocation mechanism. The asphalt mixture that has larger creep activation energy has better stability under high temperature. AC-16 mixture has the highest creep activation energy. Nominal particle size is not a decisive factor for the performance in high temperature.

Mechanism-based modeling of solute strengthening: Application to thermal creep in Zr alloy

In this work, a crystallographic thermal creep model is proposed for Zr alloys that accounts for the hardening contribution of solutes via their time-dependent pinning effect on dislocations. The core-diffusion model proposed by Soare and Curtin (2008a) is coupled with a recently proposed constitutive modeling framework (Wang et al., 2017, 2016) accounting for the heterogeneous distribution of internal stresses within grains. The Coble creep mechanism is also included. This model is, in turn, embedded in the effective medium crystallographic VPSC framework and used to predict creep strain evolution of polycrystals under different temperature and stress conditions. The simulation results reproduce the experimental creep data for Zircaloy-4 and the transition between the low (n∼1), intermediate (n∼4) and high (n∼9) power law creep regimes. This is achieved through the dependence on local aging time of the solute-dislocation binding energy. The anomalies in strain rate sensitivity (SRS) are discussed in terms of core-diffusion effects on dislocation junction strength.The mechanism-based model captures the primary and secondary creep regimes results reported by Kombaiah and Murty (2015a, 2015b) for a comprehensive set of testing conditions covering the 500–600 °C interval, stresses spanning 14–156 MPa, and steady state creep rates varying between 1.5·10−9s−1 to 2·10−3s−1. There are two major advantages to this model with respect to more empirical ones used as constitutive laws for describing thermal creep of cladding: 1) specific dependences on the nature of solutes and their concentrations are explicitly accounted for; 2) accident conditions in reactors, such as RIA and LOCA, usually take place in short times, and deformation takes place in the primary, not the steady-state creep stage. As a consequence, a model that accounts for the evolution with time of microstructure is more reliable for this kind of simulation.

Creep Behavior of Annealed Lead-free Solder for High-power Electronic Device

The present paper investigated the annealing effect on creep behaviour of lead-free Sn-3.0Ag-0.5Cu (w.t., SAC305) solder material. According to the previous finding by nanoindentation and uniaxial tensile experiments, the optimal annealing condition of SAC305 solder was believed as 210°C for 12h to minimize the residual stress and stabilize the mechanical property of annealed solder. In order to simulate the high-temperature environment of high-power devices, the annealing temperature at 210°C is adopted with varying duration from 12 hours to 48 hours as the creep deformation usually results from long-term working conditions. The creep deformations in the time history for different cases are compared and discussed. Steady-state creep rate is also calculated to quantitatively reflect the annealing effect on creep resistance. In general, a longer duration of annealing at 210°C will increase the specimen’s time to failure and decrease the steady-state creep rate. Besides, failure modes of annealed specimens are examined by scanning electron microscopy images. It is found that with increasing the annealing duration, the specimen intends to fracture in a more ductile way with a greater ultimate tensile strain.

Microstructural investigation of oxide dispersion strengthened alloy 617 after creep rupture at high temperature

Oxide dispersion strengthened (ODS) alloys have been widely considered as candidate structural materials for advanced nuclear reactors because of their good high temperature properties and irradiation resistance. In this study, the creep properties of oxide dispersion strengthened Alloy 617 (ODS-617) was examined at 950 °C under 25 MPa in the air. Conventional Alloy 617 tested under the same conditions was included for comparison. The ODS-617 exhibited superior creep resistance, including a much longer rupture life of 8533 h and a steady-state creep rate of 8.9 × 10−8 (1/s), which was two orders of magnitude lower than that of the conventional alloy. The lower steady-state creep rate was related to the dispersion of nano-sized Y-Al-O particles, which may impede grain boundary diffusion. It seems that cracks preferentially developed near some large rod-like AlN particles, resulting in the brittle creep fracture mode.

High-temperature strengthening mechanisms of Laves and B2 precipitates in a novel ferritic alloy

Precipitates of the Laves and B2 phases were engineered in a newly-designed advanced ferritic alloy. Under creep test at 650 °C with 120 MPa, the material showed a steady-state minimum creep rate of 1 × 10−4 h−1, about one order of magnitude lower than T91. Microstructural characterization of the ferritic alloy revealed primarily ductile and partially brittle fractures after the creep test. Coarse Laves phase (~ 1 µm) was observed associating with the brittle fracture, resulting in reduced creep ductility. However, fine Laves phase precipitates (~ 100 nm) helped the dimple-ductile fracture and strengthened the material through impeding the motion of dislocations and boundaries. Unlike the B2 precipitates remained coherent exerting the classic Orowan bypassing mechanism at the brittle location, some of the B2 precipitates at the ductile location became incoherent and can develop an attractive interaction with dislocations. This coherency change of B2 precipitates, together with the nucleation of ultrafine (~ 40 nm) Laves phase precipitates during the creep test, would compensate for the coarsening-induced loss of Orowan strengthening of coherent B2 precipitates.

Effect of Multi Directional Forging on Impression Creep Behavior of Zn-24Al-2Cu Alloy

Multi directional forging (MDF) of Zn-24Al-2Cu alloy were carried at 100°C and 200°C with total equivalent strain of 0.6 and 1.2 respectively. The average grain size was reduced from 30 to 1 µm after MDF processing. Impression creep behavior of MDF processed samples was studied at 2 kg and 2.5 kg load with temperatures 30, 50, 100 and 150°C. Microstructural characterizations were carried out using optical microscope, transmission electron microscope and X-Ray diffractometer. Steady state creep rate values were recorded in the range of 1.2x10-5 to 5.2x10-7. The four phase transformation occurred in the structure after MDF process and during the impression creep test. Initial stress exponent (n) values are in the range of 2.5 to greater than 5. High values of ‘n’ showed due to the existence of threshold stress. The true activation energy values calculated are in the range of 22-129 kJ/mol. Changes in creep properties of MDF processed samples seem to be more sensitive to change in temperature compared to microstructural differences. Lattice diffusion controlled by dislocation climb is the dominant creep mechanism.

A Unified Physical Model for Creep and Hot Working of Al-Mg Solid Solution Alloys

The description of the dependence of steady-state creep rate on applied stress and temperature is almost invariably based on the Norton equation or on derived power-law relationships. In hot working, the Norton equation does not work, and is therefore usually replaced with the Garofalo (sinh) equation. Both of these equations are phenomenological in nature and can be seldom unambiguously related to microstructural parameters, such as dislocation density, although early efforts in this sense led to the introduction of the “natural power law” with exponent 3. In an attempt to overcome this deficiency, a recent model with sound physical basis has been successfully used to describe the creep response of fcc metals, such as copper. The main advantage of this model is that it does not require any data fitting to predict the strain rate dependence on applied stress and temperature, which is a particularly attractive peculiarity when studying the hot workability of metals. Thus, the model, properly modified to take into account solid solution strengthening effects, has been here applied to the study of the creep and hot-working of simple Al-Mg single phase alloys. The model demonstrated an excellent accuracy in describing both creep and hot working regimes, still maintaining its most important feature, that is, it does not require any fitting of the experimental data.