Creep Exponent Research Articles

High-Temperature Creep Property of High-Cr Ferritic Heat-Resisting Steel Identified by Indentation Test

In this paper, the procedure which can estimate creep exponent and coefficient in Norton's law of the miniature sample from the impression size rather than the penetration depth is discussed based upon a high-temperature creep indentation test. First, an analytical solution related to the change in the impression size with dwelling time at an indentation load is solved by using a well-known problem of infinite creeping media embedding spherical cavity subjected to an inner pressure which characterizes an indentation load. The applicability of the formula to elastic–plastic-creeping model resembling an actual response is checked by conducting a nonlinear finite-element analysis combined with contact option. Finally, creep indentation tests are conducted for a high-Cr ferritic heat-resisting steel, grade 122. It is shown that the creep parameters at a lower stress level can be estimated at temperature 873 K.

Creep Properties of the As-Cast Al-A319 Alloy: T4 and T7 Heat Treatment Effects

In this work, the creep behavior of a commercial Al-A319 alloy was investigated in the temperature range of 413 K to 533 K (140 °C to 260 °C). Tensile creep specimens in the as-cast condition and after heat treating by solid solution (T4) and by aging (T7) were tested in a stress range varying from 60 to 170 MPa. It was found that steady-state creep strain rate was significantly low in the T7 condition when compared with either the T4 or as-cast alloy conditions. As a result, the time to failure behavior considerably increased. The experimentally determined creep exponents measured from the stress–strain curves were 4 for the as-cast alloy, 7.5 in the solid solution, and 9.5 after aging. In particular, after solid solution a grain substructure was found to develop which indicated that creep in a constant subgrain structure was active, thus accounting for the n exponent of 7.5. In the aged condition, a stress threshold is considered to account for the power law creep exponent n of 9.5. Moreover, It was found that the creep activation energy values were rather similar for the alloys in the as-cast (134 kJ/mol) and T4 (146 kJ/mol) conditions. These values are close to the one corresponding to pure Al self-diffusion (143 kJ/mol). In the aged alloy, the apparent creep activation energy (202 kJ/mol) exceeded that corresponding to Al self-diffusion. This deviation in activation energy is attributed to the effect of temperature on the alloy elastic modulus. Microstructural observations using transmission electron microscopy provided further support for the various dislocation-microstructure interactions exhibited by the alloy under the investigated creep conditions and implemented heat treatments.

The Interacting Effect for Collinear Cracks Near Mismatching Bimaterial Interface Under Elastic Creep

In this paper, the modified reference stress method is introduced to estimate the C* integral for collinear creep cracks near the mismatching bimaterial interface (MBI) and the process that leads to these solutions is also presented. The interacting factors for creep cracks near the MBI are defined and the influences of different creep exponents and mismatching factors (MF) on creep interacting effect are studied. Results show that if two inner creep crack tips get closer, the interacting effect of creep cracks near the MBI will become much stronger. Under the same condition, the interacting factors of the creep cracks in materials with higher creep exponent are larger than that of the creep cracks in materials with lower creep exponent. For the same crack location, C* integral decreases with the increase of MF. Two novel dimensionless parameters are proposed to characterize the rationality of combination rules of ASME, API 579, and R6 codes for the interacting effect for creep collinear cracks near the MBI. With the proposed parameter, the nonconservative ranges to use the combination rules of ASME, API 579, and R6 codes are rediscussed and presented.

A simple method to estimate elastic follow-up factors for transient creep parameter C(t) under secondary stress

In this article, a semi-analytical method to estimate elastic follow-up factor as input to estimate the transient creep C( t) parameter under secondary loading is presented and validated against finite element results for a cracked two-bar structure under constant displacement loading. Predicted values of C( t) agree well with the finite element results for both elastic-creep cases and for elastic-plastic cases with the same creep and plastic hardening exponents. For elastic-plastic-creep cases with different creep and plastic hardening exponents, the proposed method gives good predictions at long time but can under- or over-predict C( t) at short time.

Effects of creep properties of materials on creep crack-tip constraint parameter R*

Extensive finite element analyses have been conducted to investigate the effect of creep properties of materials on the creep crack-tip constraint parameter R*. The results show that the parameter R* increases with increasing power law creep stress exponent n of materials, and it is sensitive to lower n values and lower in-plane and out-of-plane constraints. In the engineering estimations of the creep constraint parameter R*, only the creep exponent effect needs to be considered for cracked components with lower exponent n and lower constraint, and the Norton’s coefficient A of power law creep materials can be ignored due to its insensitivity to the R*. The R*-n relation formulae have been established for single-edge-notched tension specimen (it has similar constraint level to pressurised pipes) with different in-plane and out-of-plane constraints, and they may be used to estimate the creep crack-tip constraint levels for cracked pipes with lower exponent n and lower constraint.

General time‐dependent C(t) and J(t) estimation equations for elastic‐plastic‐creep fracture mechanics analysis

AbstractThis paper presents equations for estimating the crack tip characterizing parameters C(t) and J(t), for general elastic‐plastic‐creep conditions where the power‐law creep and plasticity stress exponents differ, by modifying the plasticity correction term in published equations. The plasticity correction term in the newly proposed equations is given in terms of the initial elastic‐plastic and steady‐state creep stress fields. The predicted C(t) and J(t) results are validated by comparison with systematic elastic‐plastic‐creep FE results. Good agreement with the FE results is found.

Magnetic flux penetration in Nb superconducting films with lithographically defined microindentations

We present a thorough investigation by magneto-optical imaging of the magnetic flux penetration in Nb thin films with lithographically defined border indentations. We demonstrate that discontinuity lines ($d$ lines), caused by the abrupt bending of current streamlines around the indentations, depart from the expected parabolic trend close to the defect and depend on the shape and size of the indentation as well as on the temperature. These findings are backed up and compared with theoretical results obtained by numerical simulations and analytical calculations highlighting the key role played by demagnetization effects and the creep exponent $n$. In addition, we show that the presence of nearby indentations and submicrometer random roughness of the sample border can severely modify the flux front topology and dynamics. Strikingly, in contrast to what has been repeatedly predicted in the literature, we do not observe that indentations act as nucleation spots for flux avalanches, but they instead help to release the flux pressure and avoid thermomagnetic instabilities.

Microstructural evolution in creep aged of directionally solidified heat resistant HP-Nb steel alloyed with tungsten and nitrogen

The effect of tungsten and nitrogen on the as cast and the creep aged microstructures of heat resistant HP-Nb steel was studied. The steel was directionally solidified under two cooling rates of 31.2 and 7.6Ksec−1. Creep rupture tests were performed at temperatures of 1150–1255K on the specimens prepared from the cast ingots in transverse and longitudinal directions. It is shown that the addition of nitrogen significantly increases the eutectic temperature and thus refines the dendrites and alters the morphology of M7C3 eutectic carbide. Also, it is found that due to short time aging, nitrogen addition decreases the M7C3 carbide fragmentation, increases the secondary M23C6 precipitation density, and impedes the formation of Cr-rich M23C6 carbide on the primary Nb(C, N) carbide/matrix interface. These phenomena enhanced the creep resistance of the steel. The apparent activation energy and creep exponent of the steel containing both tungsten and nitrogen were determined as 210±30kJmol−1 and 5.2, respectively, indicating that the grain boundary region plays a significant role in controlling the creep deformation of the steel.

Elastic and creep properties of young cement paste, as determined from hourly repeated minute-long quasi-static tests

Cement pastes are highly creep active materials at early ages. We here characterize both the elastic stiffness and the creep properties of ordinary Portland cement pastes conditioned at 20°C. Three different compositions are investigated, defined in terms of initial water-to-cement mass ratios amounting to 0.42, 0.45, and 0.50, respectively. Implementing a new early-age creep testing protocol, we perform a series of 168 three minute long uniaxial macroscopic creep tests on the aging materials, with one such test per hour and corresponding material ages spanning from 21h to approximately eight days. In this way, it is guaranteed that the material microstructure remains virtually unaltered during each individual creep test, while subsequent creep tests refer to clearly different microstructures. In order to minimize material damage, the compressive loads are restricted to at most 15% of the uniaxial compressive strength reached at the time of testing. The loading protocol consists of quasi-instantaneous compressive loading and unloading steps as well as a three minute long holding period in between. Representing the measured compliances very precisely by means of a power-law expression including elastic and creep moduli, as well as a creep exponent, while requiring the elastic and creep strains to be compressive at all times, yields concavely increasing time evolutions of elastic and creep moduli, as well as slightly decreasing or quasi-constant evolutions of the creep exponent. Combination of these results with calorimetry-based evolutions of the degree of hydration yields linear elasticity-hydration degree and over-linear creep modulus-hydration degree relations, while the creep exponents (slightly) decrease with ongoing hydration. The herein quasi-statically determined elastic moduli agree very well with those determined ultrasonically on the same cement pastes. This impressively underlines the fundamental characteristics of elastic properties being related to an energy potential, independently of loading paths and corresponding strain rates.

Creep modelling of 316H stainless steel over a wide range of stress

Investigation of material creep behaviour in the diffusion controlled creep regime is often unfeasible because of the long duration associated with low stress levels. On the other side, extrapolation from higher creep rates usually provides inaccurate results because of the sharp change in the data trend as a result of the change in the governing deformation mechanism from dislocation to diffusion type controlled creep. Similarly, extrapolation based on creep models, which have been formulated and validated mainly for dislocation type creep (such power law creep with the creep exponent ranging from 6 to 9), underestimates the actual creep rate significantly. Recently, Bonora and Esposito (2010) developed a mechanism-based model (BE model) capable to account for deformation and damage mechanism occurring in creep. In this work the BE model was applied to AISI 316H stainless steel for which considerable creep data in both dislocation and diffusion temperature/stress controlled regime were available. Using the same data set, the predictive capabilities of several models were compared.

Contact size-independent method for estimation of creep properties with spherical indentation

Steady-state creep constitutes a major portion in the creep (strain vs. time) curve and is usually analyzed in characterizing creep behavior. In this numerical study, adopting a power-law creep material model, we propose a contact size-independent method for deriving creep properties from short-time spherical indentation test. Using finite element (FE) method with a wide range of creep properties, we investigate the characteristics of steady-state creep, while a fixed observation point beneath the indenter is employed to measure the material response to the indentation. We then establish functions that map indentation load–depth data to stress–strain rate data which provides creep properties without measuring the contact area. The proposed method provides the creep coefficients and the creep exponents with great accuracy from the indentation load–depth curves.

An efficient way of extracting creep properties from short-time spherical indentation tests

Abstract

탄성-소성-크리프 상태에서 SE(B) 시편의 천이크리프 균열 선단 응력장 평가

본 논문에서는 탄성-소성-크리프 상태에서 시간의존적 균열 선단 응력장을 평가하기 위해 Single-Edge-notched-Bend (SEB) 시편을 사용하여 유한요소 크리프 해석을 수행하였다. 천이크리프의 초기소성 영향을 조사하고자 다양한 초기하중을 대해 고려하였으며, 또한 소성물성과 크리프 물성의 영향을 조사하기 위해 소성 경화 지수(m)과 크리프 지수(n)이 같은 경우와 다른 경우를 모두 고려하였다. 결과로서, 기존 식의 수정을 통해서 천이크리프 상태에서의 균열 선단 응력장의 예측 식을 제안하였으며, 유한요소해석 결과와 비교를 통해서 제시된 수식의 타당성을 검증하였다. 그리고 m 과 n 이 같은 경우뿐만 아니라 m 과 n 이 다른 경우에도 천이크리프 상태에서 균열 선단 응력장을 예측 할 수 있는 식을 제안하였다.

탄성-소성-크리프 상태에서 SE(B) 시편의 천이크리프 C(t)-적분 평가

본 논문에서는 탄성-소성-2 차 크리프 상태에서 시간의존적 C(t) 적분에 대해 평가하였다. Single-Edge-notched-Bend (SEB) 시편에 대해 유한요소 크리프 해석을 수행하였다. 천이 크리프에 대한 초기 소성의 영향을 연구하기 위해 다양한 초기 하중에 대해 고려하였다. 또한, 소성물성과 크리프 물성의 영향을 보기 위해 소성 경화 지수(m)과 크리프 지수(n)이 같은 경우와 다른 경우를 모두 고려하였다. 본 논문에서는 기존 식의 수정을 통해서 천이 크리프 상태에서의 C(t) 적분의 새로운 예측 식을 제시하였다. 유한요소해석 결과와 비교를 통해서 제시된 수식의 타당성을 검증하였고, 소성 경화 지수(m)과 크리프지수(n)이 같은 경우에만 적용할 수 있는 기존 예측 식을 보완하여 m 과 n 이 다른 경우에도 천이 크리프 상태에서 C(t) 적분을 예측할 수 있는 식을 제시하였다.

Detailed three-dimensional analysis of side-grooved compact tension specimens under creep loading

The three-dimensional (3D) effect on the stress field near the crack tip under creep loading has been investigated via detailed finite-element analyses on side-grooved compact tension (CT) specimens with various thicknesses. The mechanical properties used in the model are typical of those for a 9%Cr steel at 550°C and a Norton creep exponent of 10 was applied. Plane strain and 3D analyses for the CT specimens without side grooves were also performed and the differences in stress distributions in the three analysis conditions are discussed in relation to the creep J-integral C*. The value of C* was found to decrease with increasing thickness and to decrease significantly because of the enhanced constraint effect of the side grooves. With increasing thickness, the stress state in the central region is close to that under plane strain conditions, irrespective of the existence of the side groove. Stress triaxiality, however, is distributed more uniformly along thickness in the side-grooved specimen than in the specimen without side grooves. The C* values of the side-grooved specimens are similar across the full range of thickness studied: no strong effect of thickness was observed.

An analytical model for porous single crystals with ellipsoidal voids

A rate-(in)dependent constitutive model for porous single crystals with arbitrary crystal anisotropy (e.g., FCC, BCC, HCP, etc.) containing general ellipsoidal voids is developed. The proposed model, denoted as modified variational model (MVAR), is based on the nonlinear variational homogenization method, which makes use of a linear comparison porous material to estimate the response of the nonlinear porous single crystal. Periodic multi-void finite element simulations are used in order to validate the MVAR for a large number of parameters including cubic (FCC, BCC) and hexagonal (HCP) crystal anisotropy, various creep exponents (i.e., nonlinearity), several stress triaxiality ratios, general void shapes and orientations and various porosity levels. The MVAR model, which involves a priori no calibration parameters, is found to be in good agreement with the finite element results for all cases considered in the rate-dependent context. The model is then used in a predictive manner to investigate the complex response of porous single crystals in several cases with strong coupling between the anisotropy of the crystal and the (morphological) anisotropy induced by the shape and orientation of the voids. Finally, a simple way of calibrating the MVAR with just two adjustable parameters is depicted in the rate-independent context so that an excellent agreement with the FE simulation results is obtained. In this last case, this proposed model can be thought as a generalization of the Gurson model in the context of porous single crystals and general ellipsoidal void shapes and orientations.

Mechanical Characterization of PM2000 Oxide‐Dispersion‐Strengthened Alloy by High Temperature Nanoindentation

AbstractNanoindentation measurements with a commercial Hysitron xSol 800 up to temperatures of 700 °C have been applied to study mechanical properties of PM2000 ODS steel. Beside the temperature dependence of hardness H and indentation modulus E, a careful analysis of time‐dependent features such as creep and stress exponent was performed. The H/E is dominated by a transition from small hardness variations at low temperatures to a strong hardness decrease starting at about 400 °C. The two different deformation regimes have been attributed to modifications in dislocation pinning at temperatures up to 400 °C and thermal activation over obstacles, when fine oxide nanoparticles of diameter 5–20 nm are present.

Precipitation evolution and creep strength modelling of 25Cr20NiNbN austenitic steel

25Cr-20Ni-Nb-N is a high strength and oxidation-resistant austenitic stainless steel intended for Ultra-Supercritical (USC) power plants. In this work, the precipitation evolution, and creep strength at 650 and 750°C for up to 100 000 h are predicted. Six precipitates are considered in the thermokinetic calculation by MatCalc: M23C6, η (Cr3Ni2SiN), σ, G, Z, Nb(C,N). For the creep strength prediction, three hardening mechanisms are taken into account: dislocation, precipitation, and solid solution hardening. Both matrix composition and precipitation evolution, calculated with MatCalc, are used for modelling the precipitation and solid solution hardening. It is found that the dislocation hardening, followed by precipitation hardening gives the largest contribution to the creep strength. The most important precipitates strengthening phases are found to be Z-Phase and Nb(C,N), which are nucleated at the dislocations. The model for the creep rate can represent how the creep exponent is raised with increasing applied stress and reduced temperature.

All Set Theory in the Fuzzy-Random Creep Fracture Model

According to the all set theory, a fuzzy-random creep fracture model was presented in this work. To deal with the function, the following steps were taken. First, the steady state creep coefficient (A) and steady state creep exponent (n) were considered in the fuzzy-random variables, then the C*-integral was considered in a fuzzy-random variable. Finally, with the interval analysis, the result of the fuzzy-random creep fracture model was given.

A model for porous single crystals with cylindrical voids of elliptical cross-section

This work presents a rate-dependent constitutive model for porous single crystals with arbitrary number of slip systems and orientations. The single crystal comprises cylindrical voids with elliptical cross-section at arbitrary orientations and is subjected to general plane-strain loadings. The proposed model, called modified variational model (MVAR), is based on the nonlinear variational homogenization method, which makes use of a linear comparison porous single crystal material to estimate the response of the nonlinear porous single crystal. The MVAR model is validated by periodic finite element simulations for a large number of parameters including general in-plane crystal anisotropy, general in-plane void shapes and orientations, various creep exponents (i.e., nonlinearity) and general plane strain loading conditions. The MVAR model, which at the present state involves no calibration parameters, is found to be in good agreement with the finite element results for all cases considered in this work. The model is then used in a predictive manner to investigate the complex response of porous single crystals in several cases with strong coupling between the anisotropy of the crystal and the (morphological) anisotropy induced by the shape and orientation of the voids.