Shape Of Creep Curves Research Articles

Changes in Monkman-Grant relation among four creep regions of modified 9Cr-1Mo steel

The relation of creep rupture life to minimum creep rate, namely Monkman-Grant (MG) relation is examined by using a creep database of modified 9Cr-1Mo steel. The database covers wide ranges of creep rupture life up to 1.2 × 105 h and of minimum creep rate down to 7.6 × 10−8 h−1. The MG plot exhibits a low overall value of MG exponent (p = 0.85) together with wide scatter of data points at long rupture life. Causes of the low p value and the wide scatter are discussed in the present study paying attention to change in creep curve shape with creep rupture life. There are four regions H, M, L1 and L2 showing different creep behavior in the steel. Regional MG relations are examined also in each region. Values of p are less than unity and change among the four regions. The p value is especially low (0.62) in long-term region L2. The regional p values less than unity result in the low overall p value of 0.85. The especially low regional value of p in the long-term region causes the wide scatter of data points in the overall MG plot. A modified Monkman-Grant equation (Eq. (29)) is proposed taking account of creep deceleration rate A (=−1/(dln ε˙/dε), where ε˙ and ε are the creep strain rate and the creep strain) in primary creep and creep acceleration rate B (=1/(dln ε˙/dε)) in tertiary creep. The rates characterize shape of a creep curve. The modified equation can explain the difference of p values among the four regions.

A modified θ projection model for constant load creep curves-II. Application of creep life prediction

To minimize the deviation of the predicted creep curves obtained under constant load conditions by the original θ projection model, a new modified version that can be expressed by ε=θ11-e-θ2t+θ3eθ4eθ5εt-1, was derived and experimentally validated in our last study. In the present study, the predictive capability of the modified θ projection model was investigated by comparing the simulated and experimentally determined creep curves of K465 and DZ125 superalloys over a range of temperatures and stresses. Furthermore, the linear relationship between creep temperature and initial stress was extended to the 5-parameter model. The results indicated that the modified model could be used as a creep life prediction method, as it described the creep curve shape and resulted in predictions that fall within a specified error interval. Meanwhile, this modified model provides a more accurate way of describing creep curves under constant load conditions. The limitations and future direction of the modified model were also discussed. In addition, this modified θ projection model shows great potential for the evaluation and assessment of the service safety of structural materials used in components governed by creep deformation.

Elevated-temperature shear creep evolution and life prediction of sintered nano-silver lap-shear joint

Nano-silver paste, as a state-of-the-art die-attach material, has great application potential on elevated temperature, high power wide-band semiconductor packaging. During operation of semiconductor devices, sintered nano-silver bond-lines have to withstand creep deformation caused by elevated operating temperature and high switch frequency. In this study, the shear creep behavior of nano-silver sintered lap-shear joint was studied over the shear stress range from 3.5 to 8 MPa and the elevated temperature range from 498 to 598 K. Four kinds of constitute equations, namely three-parameter theta projection concept, Kachanov damage evolution, Larson–Miller parameter relationship and Monkman–Grant relationship, were employed to describe the shear creep behavior and predict the shear creep rupture life of the joint. For nano-silver sintered lap-shear joint, the three-parameter theta projection could quantitatively describe the shape of individual creep curves at any specified stress and temperature. The creep damage evolution of the joint, which was investigated by Kachanov damage evolution, was temperature dependent. The prediction accuracy of creep rupture life using these four kinds of constitutive equations was also evaluated.

Extrapolation of Imaginal Minimum Creep Rate in Compression by a Concept of SATO-Index

Creep characteristics of alloys and compounds have been evaluated mainly by the minimum creep rate or the steady-state creep rate, and by its stress and temperature dependences. In some cases, however, direct comparison of the minimum creep rate or the steady-state creep rate are not practically easy due to difficulties of experiment, i.e., a long duration of primary stage of creep deformation. The minimum creep rates are not always precise representative value, which is directly evaluated from experiments. It should be valuable, if one could estimate the minimum creep rate from creep curve in primary stage. I have proposed a method of quantitative evaluation of creep curve based on the evaluation of strain rate change and its strain dependence during creep [1-3]. The value that reflects a shape of creep curve is named “Strain Acceleration and Transition Objective-Index (SATO-Index)” [4]. SATO-Index and related differential equation show a strain dependence of strain rate and lead entre creep curve by numerical integration. This concept provides quantitative information of shape of each creep curve, and information of the entire creep curve. In this paper, examples of evaluation and extrapolation of creep rate from primary stage in compression are presented. It is concluded that the extrapolation with the concept of SATO-Index reasonably provides imaginal minimum creep rate. Usability of extrapolation of creep curve by the concept is presented.

The effect of stress, temperature and loading direction on the creep behaviour of Ni-base single crystal superalloy miniature tensile specimens

In the present work, we use a miniature test procedure to investigate the tensile creep behaviour of the single crystal superalloy ERBO1. We test precisely oriented [0 0 1], [1 1 0] and [1 1 1] creep specimens and determine the stress and the temperature dependence of characteristic creep rates in limited stress and temperature regimes, where the stress and temperature dependence of characteristic creep rates can be well described by power law and Arrhenius type of relations, with stress exponents n and apparent activation energies Qapp. n-values increase with stress and decrease with temperature. Qapp-values, on the other hand, increase with increasing temperature and decrease with increasing stress. Creep curve shapes gradually evolve from the high temperature low stress to the low temperature high stress (LTHS) regime. This implies that there is a gradual change in elementary deformation and softening mechanisms, which is qualitatively confirmed using transmission electron microscopy. While at high temperatures different loading directions only have a moderate influence on creep, there is a very strong effect of loading direction at low temperatures. The [1 1 0] tests show the fastest deformation rates and the shortest rupture times. In the LTHS creep regime, we confirm the double minimum (DM) type of creep behaviour, which was previously reported but never explained. Further work is required to rationalise DM-creep. The implications of this type of creep behaviour on scatter and on extrapolation of creep data is discussed in the light of previous results published in the literature.

Characterization of Time-Dependent Behavior of Ramming Paste Used in an Aluminum Electrolysis Cell

A new methodology was proposed for the characterization of time-dependent behavior of materials in order to develop a constitutive model. The material used for the characterization was ramming paste, a porous material used in an aluminum electrolysis cell, which is baked in place under varying loads induced by the thermal expansion of other components of the cell. In order to develop a constitutive model representing the paste mechanical behavior, it was necessary to get some insight into its behavior using samples which had been baked at different temperatures ranging from 200 to 1000 °C. Creep stages, effect of testing temperature on the creep, creep-recovery, as well as nonlinear creep were observed for designing a constitutive law. Uniaxial creep-recovery tests were carried out at two temperatures on the baked paste: ambient and higher. Results showed that the shape of creep curves was similar to a typical creep; recovery happened and the creep was shown to be nonlinear. Those experimental observations and the identification of nonlinear parameters of developed constitutive model demonstrated that the baked paste experiences nonlinear viscoelastic-viscoplastic behavior at different temperatures.

Extrapolation of Creep Curve and Creep Rate by Strain Acceleration Parameter in Al-Mg Solid Solution Alloys

It has been widely accepted that the creep characteristics at high temperatures are mainly evaluated by a minimum creep rate. Although, a shape of creep curve may vary depending on deformation conditions, the apparent steady state or minimum creep rates be the same. Thus,for detailed analysis and prediction of creep behavior, other values which reflect the shape of each creep curve should be considered. For the purpose, authors have proposed Sato’s strain- acceleration-parameter (Strain Acceleration and Transition Objective index, SATO-index) which reflects strain rate change during creep deformation. Based on the concept of SATO-index, the whole creep curve can be represented by a set of small number of numerical parameters, and can be extrapolated from a part of creep curve. In this paper, application of the concept of SATO-index to the creep curves of aluminum-magnesium solid solutions that the creep behavior of the alloys are well investigated and analyzed. The creep curve can be extrapolated by the concept from transient part of creep curve, and the extrapolated creep rates at the minimum creep rate agree well with experiment. Efficiency of the concept of SATO-index to creep experiments is pronounced.

Extrapolation of Sigmoidal Creep Curve by Strain Acceleration Parameter

It has been widely accepted that the creep characteristics at high temperatures are mainly evaluated by a minimum creep rate and a time to fracture. Although, a shape of creep curve may vary depending on deformation conditions, the apparent minimum creep rates may become the same value. Thus, for detailed analysis and prediction of creep behavior, other values should be considered which reflects the shape of each creep curve. For the purpose, authors have proposed Satos Strain-Acceleration-Parameter (SAP) which reflects strain rate change during creep. Based on the concept of SAP, the whole creep curve can be represented by a set of small numbers of numerical parameters, and can be extrapolated from a part of creep curve [. It is also well accepted that the creep rates depend on microstructures, and microstructural changes cause strain rate change. The SAP would reflect stability and magnitude of microstructural change during deformation at high temperatures. In this paper, application of the concept of SAP to creep curves that show sigmoidal type primary creep is presented. The creep curve can be divided into two regime based on the SAP values. The sigmoidal creep curve is reasonably reproduced by the concept of Strain-Acceleration-Parameter, and reasonably agrees with experiment. Whole creep curve can be reasonably represented by a few numerical values which reflect shape of creep curve in each regime. The concept of SAP is applicable for quantitative evaluation of both normal and sigmoidal type of creep curves.

Creep property and microstructure evolution of a nickel-base single crystal superalloy in [011] orientation

The creep property and microstructure evolution of a single crystal superalloy with [011] orientation were investigated at the temperatures of 700°C, 900°C and 1040°C. It is shown that there exist stages of primary, steady-state, and tertiary creep under the lower temperature 700°C. As the temperature increases to high temperatures of 900°C and 1040°C, steady-state creep stage is reduced or disappears and the shape of creep curves is dominated by an extensive tertiary stage. The minimum creep strain rate exhibits power law dependence on the applied stress; the stress exponents at 700°C, 900°C and 1040°C are 28, 13 and 6.5, respectively. Microstructure observation shows that the morphologies of γ′ phase almost keep original shape at the lower temperature 700°C and high applied stress. With the increasing creep temperature, γ′ precipitates tend to link together and form lamellar structure at an angle of 45° inclined to the applied stress. Transmission electron microscopy (TEM) investigations reveal that multiple <110> {111} slip systems gliding in the matrix channels and shearing γ′ precipitates by stacking faults or bending dislocation pairs are the main deformation mechanism at the lower temperature of 700°C. At the high temperatures of 900°C and 1040°C, dislocation networks are formed at γ/γ′ interfaces and the γ′ rafts are sheared by dislocation pairs.

Creep behaviour of Waspaloy under non-constant stress and temperature

Current creep models are derived using data from constant stress (or load) creep tests and are capable of accurately predicting creep behaviour when applied conditions are constant or near constant. However, analyses of creep curve shapes for the nickel based superalloy Waspaloy, when applied stress and/or temperature vary greatly during testing, have shown that predictive methods based purely on strain, time or life fraction are insufficient and cannot predict the observed creep rates. This is important when considering stress concentration features where stress relaxation due to creep can significantly alter the distribution of stress and thus affect fatigue life. When both stress and temperature are changed during a creep test, dislocation movement must proceed through a dislocation network formed under different conditions, resulting in greater than expected creep rates. It is proposed that this is due to a reduction in effective internal stress due to changes in dislocation structure.

Phenomenological approach to precise creep life prediction by means of quantitative evaluation of strain rate acceleration in secondary creep

A method of creep life prediction by means of Strain-Acceleration-Parameter (SAP), α, is presented. The authors show that the shape of creep curve can be characterized by SAP that reflects magnitude of strain-rate change in secondary creep. The SAP-values, α are evaluated on magnesium-aluminium solution hardened alloys. Reconstruction of creep curves by combinations of SAP and minimum-creep rates are successfully performed, and the curves reasonably agree with experiments. The advantage of the proposed method is that the required parameters evaluated from individual creep curves are directly connected with the minimum creep rate. The predicted times-to-failure agree well with that obtained by experiments, and possibility of precise life time prediction by SAP is pronounced.

Assessment of creep and rupture behavior of 2.25Cr-1Mo steel — A strain based approach and its limitation

Strain based approach for reliable assessment of creep behavior is employed for creep data generated for different microstructural conditions as well as obtained from literature for 2.25Cr-1Mo steel. The influence of thermal ageing and pre-strain on the shape of creep curves has been studied. Analysis of data revealed that irrespective of initial microstructures, thermal ageing increases the tendency to soften but not the pre-strain. Softening due to carbide coarsening thus appears to be the dominant mechanism of creep. Based on this, a strain based approach for creep life assessment was developed. A fairly accurate prediction of creep life up to 5% creep is achieved using eight materials constants extracted from the creep curves of steel having similar initial microstructure. The limitation and reliability of the approach used to assess creep behavior of service-exposed steels have been discussed.

목재와 목질보드 복합적층재의 휨 크리프 성능

이 연구에서는 목재의 효율적인 이용의 일환으로 스프루스 직교형적층재의 중층을 중밀도섬유판(medium density fiberboard, MDF), 파티클보드(particle board, PB) 및 오에스비(oriented strand board, OSB)의 3종류의 시판용 목질보드를 복합적층한 3층 목질계 복합적층재(패널)를 제작하여, 중층 목질보드라미나의 구성엘리멘트가 복합적층재의 휨 크리프성능에 미치는 영향을 조사하였다. 복합적층재의 휨 크리프곡선은 우측상변이 급증하는 지수함수 그래프를 나타내었고, 각 복합적층재의 중층 목질보드라미나의 종류에 따라 다른 경향을 나타내었다. 복합적층재의 크리프변형은 표층섬유직각방향(<TEX>$C_{\perp}$</TEX> 타입)에서는 중층에 PB, MDF, OSB를 배열한 <TEX>$C_{\perp}$</TEX>(P)타입 > <TEX>$C_{\perp}$</TEX>(M)타입 > <TEX>$C_{\perp}$</TEX>(O)타입의 순으로, OSB를 중층에 배열한 타입의 크리프변형이 MDF나 PB를 중층에 배열한 것의 2배 이상 적은 것이 확인되었고, 복합적층에 의해 스프루스 섬유직각방향의 크리프변형의 현저한 감소가 나타났다. 한편, 표층섬유방향(<TEX>$C_{\parallel}$</TEX> 타입)의 크리프변형은 중층에 PB, OSB, MDF를 삽입한 <TEX>$C_{\parallel}$</TEX>(P)타입 > <TEX>$C_{\parallel}$</TEX>(O)타입 > <TEX>$C_{\parallel}$</TEX>(M)의 순이었으나, 복합적층에 의해 적층재상호간의 비는 현저히 감소하였고, 중층에 PB와 OSB를 배열한 복합적층재의 크리프변형의 차이는 매우 적은 것이 확인 되었다. 이 값은 목질보드의 크리프변형보다는 0.108~0.464배의 적은 크리프변형을 나타내어 복합적층에 의해 목질보드의 크리프변형의 현저한감소가 나타났다. 복합적층재의 표층섬유방향에 대한 표층섬유직각방향의 크리프이방성은 초기변형보다 크리프변형이 현저히 컸지만, 스프루스 평행형적층재의 크리프이방성보다는 현저히 감소하는 것이 확인되었다. In this study, to study an effective use and improve strength performances of woods and wood-based materials, three-ply hybrid laminated woods which are composed of spruce in the face and three kinds of wood-based boards (MDF, PB, OSB) in the core were manufactured, and the effect of constitution elements used for the core laminae on bending creep performances was investigated. The shape of creep curves showed exponential function plots which the upper right side was increased, and differed among the kinds of wood-based boards used for the core laminae of hybrid laminated wood. The creep deformation perpendicular to the grain of faces of hybrid laminated woods was in order <TEX>$C_{\perp}$</TEX>(P) > <TEX>$C_{\perp}$</TEX>(M) > <TEX>$C_{\perp}$</TEX>(O) with PB, MDF and OSB in the core, respectively. It was found that the creep deformation arranged with OSB in the core had 2 times smaller than those arranged with MDF and PB in the core. By hybrid laminating, the creep deformation of spruce perpendicular to the grain was markedly decreased. On the other hand, the creep deformation parallel to the grain of the faces (<TEX>$C_{\parallel}$</TEX> type) of hybrid laminated woods was in order <TEX>$C_{\parallel}$</TEX>(P) > <TEX>$C_{\parallel}$</TEX>(O) > <TEX>$C_{\parallel}$</TEX>(M) with PB, OSB and MDF in the core. The ratios among three hybrid laminated woods were considerably decreased, especially the difference between <TEX>$C_{\parallel}$</TEX>(P) and <TEX>$C_{\parallel}$</TEX>(O) hybrid laminated woods arranged with PB and OSB in the core was very small. These values showed 0.108~0.464 times smaller than creep deformation of three wood-based boards and it was found that creep deformation of three wood-based boards was considerably decreased by hybrid laminating. Creep anisotropy of hybrid laminated woods was greater in creep deformation than in initial deformation, whereas it was found that the values was much smaller than that of spruce parallel laminated woods.

Analysis of Creep Curves of Haynes 230 Superalloy

The creep behaviour of the solid solution strengthened nickel-based superalloy Haynes 230 has been investigated under constant load and temperature conditions on as received, after conventional solution treatment, and on overaged conditions. The experimental results have shown a very strong dependence of the creep curve shape with the applied stress/temperature: in the tests performed at high stresses/low temperatures, the primary/decelerating stage takes an important portion of the creep curve. At these test conditions, the accelerating creep is mainly caused by the increase of the applied stress with the strain as it happens in constant load creep tests. In the tests performed at low stresses/high temperatures, the primary stage is very small and the following accelerating creep is characterized by different accelerating creep stages. The analysis of the creep curves on the as received and overaged alloys, has shown that a large portion of the accelerating creep at low stresses/high temperatures is caused by microstructural instability.

Finding critical damage locations by Λ-filtering in finite-element modelling of a girth weld

In structures with uniform material properties, time dependent creep damage will develop in locations where the stress state is aggravated by triaxiality constraints. However, for non-uniform structures, such as welds, where several material zones (differing in microstructure and material properties) are present, the pin-pointing of the “weakest link” is even more challenging. For girth-welded pipes, the unfavourable conditions are known to be found in the vicinity of the heat-affected zone on the outer diameter. To find out how the triaxiality constraints influence accumulated “creep exhaustion”, three girth welds simulated for different steels have been studied using the Λ-filtering technique. The Λ-filtering has been developed for finite element modelling for visualising the combined effect of creep ductility, creep rate and triaxiality constraint evolution assuming rigid plastic deformation for the stress triaxiality-dependent part. In this work, the creep response of three-zone girth welds was studied. In the case of the P23 steel, data for a real (experimental) consumable was used and for the others, assumption on creep strength and creep curve shapes was made according to material property ratios. The creep strain rate formulation used for this work is the logistic creep strain prediction model and its multiaxial implementation has been run in the Comsol multiphysics software package. The results of the weld simulations predict similar behaviour for the P22 and P91 welds, with assumed weld metal behaviour closer to the base material, and differing behaviour for the P23 with an overmatching (experimental) weld metal.

Creep behavior of 2.25Cr1Mo steel—Effects of thermal ageing and pre-strain

Effects of thermal ageing and pre-strain on the shape of creep curves of 2.25Cr1Mo steel have been studied. Analysis revealed that the thermal ageing increases the tendency to soften but not the pre-strain. Softening due to carbide coarsening thus appears to be the dominant mechanism of creep. Over a range of stress and temperature, creep data were generated under different microstructural conditions and collected from literature to examine the potential of the mechanism-based model used for predicting creep behavior. A fairly accurate prediction of creep life up to 5% strain is achieved using eight materials constants extracted from the creep curves of steel having similar initial microstructure. The limitation and reliability of the model used to assess creep behavior of service-exposed steels have been discussed.

Long-term creep and creep rupture characteristics of TiAl-base intermetallics

The present study investigates creep in three TiAl-base intermetallic alloys, Ti–48Al–2Cr–2Nb–1B, Ti–46Al–7Nb–0.6Cr–0.2Ni–0.1Si and Ti–46Al–2W–0.5Si–0.7B (all at.%), in the range of rupture times up to 25 000 h. Creep behaviour of the individual alloys at 1023 K is assessed and compared and reasons for creep strength variations are discussed. Results suggest that dislocation processes contribute to the creep strain accumulation even at creep rates as low as 7 × 10 −10 s −1. Finally the applicability of Monkman–Grant-type relationships is critically analyzed. It is shown that these relationships stem from a general functional identity that is valid for any continuous creep curve. The role of the creep curve shape factor S is highlighted.

Assessment of θ-projection concept and fracture cavitation

The empirical approach to creep, termed θ-projection concept, is applied to the constant-load data of conventionally cast nickel-base superalloy IN-100 at constant temperature (900 °C). The normal creep curves, obtained at various initial stresses (σA = 200−400 MPa), could be accurately represented by this concept. The change in creep curve shape with stress from tertiary dominated to primary dominated view is presented by the change in the ratio of primary (ɛp) and tertiary strain (ɛt) components to rupture strain (ɛR). It is predicted that failure in the present creep conditions is dominated by the GB cavitation and the growth of the cavities is controlled by the coupled GB diffusion and power-law creep mechanism. In an attempt to provide a physical significance to θ-parameters, it is found that the internal structural variable theory and continuous GB cavitation account well, with suitable assumptions, for the θ description of primary and tertiary creep curves, respectively.

Creep and creep fracture of commercial aluminium alloys

Using standard power law equations, creep rate and creep life measurements at 373–463 K are analysed for a series of aluminium alloys, namely, 2419, 2124, 8090 and 7010. The seemingly complex behaviour patterns are easily rationalized through a modified power law expression, which incorporates the activation energy for lattice diffusion in the alloy matrices (145 kJ mol−1) and the value of the ultimate tensile stress at the creep temperature. By considering the changes in microstructure and creep curve shape as the test duration and temperature increase, all results are then interpreted straightforwardly in terms of the processes shown to govern strain accumulation and damage evolution. Moreover, the data rationalization procedures are also included in new relationships which superimpose the property sets onto sigmoidal ‘master curves’, allowing accurate prediction of the 100,000 h creep-rupture strengths of 2124 by extrapolation of creep lives determined from tests having a maximum duration of only around 1000 h.

Effect of section thickness on creep and stress rupture behaviour of DS CM247 nickel base superalloy

The effect of section thickness on creep and stress rupture behaviour of DS CM247 nickel base superalloy at three temperatures viz. 760, 982 and 1038°C, has been investigated in an effort to identify the factors contributing to the observed creep/stress rupture behaviour. Irrespective of section thickness, the shape of creep curves at the lowest temperature of 760°C differs from the shape of those at the higher temperatures, showing significantly higher primary creep strain (PCS). At higher temperatures the creep curves exhibit limited primary and secondary regimes, but predominant tertiary regime. Such a difference in shapes of the creep curves is related to the difference in dislocation bypass mechanisms operating at these temperatures. The variation of minimum creep rate (MCR) and time to rupture (tf) with section size indicates a progressive creep strengthening at 760 and 982°C, while a progressive creep weakening at 1038°C with decreasing specimen thickness. Such a behaviour can be explained in terms of relative extents of the surface oxide layer (contributing to creep strengthening) and γ′ depleted zone (causing creep weakening) formed at these temperatures. Further, the creep strengthening at 760 and 982°C as well as weakening at 1038°C is more pronounced for the thinner specimens.