Power-law Creep Regime Research Articles

The strength of a constrained lithium layer

A constrained compression test is developed to replicate the mechanical state of a lithium filament within a solid state battery. Lithium microspheres are compressed between parallel quartz plates into a pancake shape of thickness on the order of 15 µm. Full adhesion with no slip exists between the lithium and platens, and the attendant mechanical constraint implies that the average pressure on the pancake-shaped specimens increases with increasing aspect ratio of radius to height. In addition to mechanical constraint, a thickness-dependant size effect is observed whereby the apparent flow strength of the lithium increases from 0.7 MPa in the bulk to 2.0 MPa at a thickness of 15 µm. The lithium deforms in a power-law creeping manner at room temperature, and to simplify interpretation of the results, the relative velocity of the loading platens is adjusted to ensure that the true compressive strain rate is held fixed at 10−3 s−1. Additional measurements of lithium flow strength are obtained by subjecting the pancake-shaped specimens to simple shear. The size effect under shear loading is comparable to that in constrained compression. The observed size effect for lithium is consistent with that reported in the literature for lithium in indentation tests and in single pillar compression tests. Finally, the size effect of lithium in the power law creep regime is compared with that for rate-independent plasticity (for copper).

Characterization of creep properties and the microstructure of a service-exposed low alloy CrMoV steel steam pipe

The effect of service degradation on the microstructure and creep properties of a 0.5%Cr-0.5%Mo-0.3%V steel steam pipe after an accumulated service time of 77,900 h was investigated and analysed. For comparison purposes, additional experiments and analyses were carried out on the same pipe in the as-received (service unused) conditions. The results of the microstructural analysis and the short-term creep testing confirmed that the high creep resistance of the investigated steel is caused predominantly by the dispersion of fine vanadium carbides, providing an effective precipitation hardening of the steel matrix. However, the microstructure is not in an equilibrium state, and as the size of the vanadium carbides and the accompanying mean interparticle spacing increase during the creep, the detrimental effect of vanadium carbide coarsening leads to a significant weakening in the precipitation hardening and, consequently, a decrease in the creep resistance. No creep cavitation was observed in the service-exposed steel. The short-term creep testing of the service-exposed and unused states of the steel was carried out in the power-law (dislocation) creep regime. Analysis of the creep data did not reveal any change in the operating creep deformation mechanisms as a response to the structural processes occurring during the long-term service. Instead, changes in the kinetics of creep flow and fracture were found.

Optimized hot working parameters of Fe2.5Ni2.5CrAl multi-principal element alloys

The hot compressive deformation behavior of Co-free Fe2.5Ni2.5CrAl multi-principal element alloys (MPEAs) was investigated in the temperature and strain rate ranges of 800–1100∘C and 0.001 s−1 and 1 s−1, respectively. Microstructural observations were carried out by optical microscopy (OM) and electron backscatter diffraction (EBSD). A constitutive model based flow-stress analysis was carried out, the activation energy (Q) was obtained as 315.9 kJ/mol at steady state. The strain rate sensitivity (m), the power dissipation (η), and instability parameter (ξ) were utilized to construct the processing maps. Power-law breakdown and unstable flow occurred at the high strain rates at which strain hardening was pronounced. The optimal condition for successful hot working was determined to be at strain rates in the range of 10−2–10−3 s−1 and a temperature range of 850 ~ 1020∘C. FEM simulations revealed the strain and stress distribution during hot deformation and predicted instabilities during hot forming. The main deformation mechanism was dislocation climb with a stress exponent n > 5. The Q value for plastic flow in the power-law creep regime was calculated considering the effect of lattice diffusion of atoms and was in accordance with the measured Q value. Thus, our study revealed the hot working characteristics and the optimum processing parameters for successful hot working of Fe2.5Ni2.5CrAl MPEAs.

Thermal creep fracture of a Zr1%Nb cladding alloy in the α and (α+β) phase regions

The objective of the present study was to provide new relevant information on creep behaviour and fracture processes in a sponge-based modified Zr1%Nb cladding alloy (modified E110 alloy) in the α-Zr and (α+β)-Zr phase regions. To this end, constant load creep tests were carried out in argon at testing temperature intervals from 350°C to 950°C, and applied tensile stresses ranging from 5 MPa to 210 MPa, corresponding to the power-law breakdown creep regime and/or high testing temperatures, and thus to simulate disaster conditions. Creep tests were followed by metallographic and fractographic analyses of the specimens to explain the observed creep behaviour. It was found that in the power-law region (at 350°C) the values of the stress exponent n of the minimum creep rate ε˙m (n = ∂lnε˙m /∂lnσ)T, and the stress exponent m of the time to fracture tf (m = - ∂lntf /∂lnσ)T, were very high and near to each other, indicating a close relationship between creep deformation and fracture. Further support for the idea that creep deformation and fracture are interconnected can be observed by the validity of the empirical Monkman-Grant relationship. Creep tests in the α-Zr phase region revealed creep cavitation near to, and at, the fracture surface. The final fracture is a ductile dimple mode with the synergistic effect of creep cavitation. By contrast, the final fracture in the (α+β)-Zr phase region is caused by a local strain-induced instability of the matrix leading to a loss of an external section of specimen (necking). There is a marked difference between the values of the strain to fracture εf. In the α-Zr region, typical values of εf ~ 0.3-0.5 were found, whereas for the (α+β)-Zr region, the value εf increases with testing temperature up to 850°C. Following drop of εf at temperatures ≥ 900°C was explain by intensive oxidation of the alloy.

High Temperature Creep Behaviour of Cast Nickel-Based Superalloys INC 713 LC, B1914 and MAR-M247

Cast nickel-based superalloys INC713 LC, B1914 and MAR-M247 are widely used for high temperature components in the aerospace, automotive and power industries due to their good castability, high level of strength properties at high temperature and hot corrosion resistance. The present study is focused on the mutual comparison of the creep properties of the above-mentioned superalloys, their creep and fracture behaviour and the identification of creep deformation mechanism(s). Standard constant load uniaxial creep tests were carried out up to the rupture at applied stress ranging from 150 to 700 MPa and temperatures of 800–1000 °C. The experimentally determined values of the stress exponent of the minimum creep rate, n, were rationalized by considering the existence of the threshold stress, σ0. The corrected values of the stress exponent correspond to the power-law creep regime and suggest dislocation climb and glide as dominating creep deformation mechanisms. Fractographic observations clearly indicate that the creep fracture is a brittle mostly mixed transgranular and intergranular mode, resulting in relatively low values of fracture strain. Determined main creep parameters show that the superalloy MAR-M247 exhibits the best creep properties, followed by B1914 and then the superalloy INC713 LC. However, that each of the investigated superalloys can be successfully used for high temperature components fulfils the required service loading conditions.

Effect of powder purification by heat-treatment on the creep behaviour of dense boron carbide monoliths

High temperature compressive creep tests have been performed at 1650−1750 °C under applied stresses of 50−150 MPa on sintered boron carbide samples exhibiting high relative density and a mean grain size of 0.5 μm. The creep behaviour of two types of materials, sintered by spark plasma sintering from both raw and heat-treated powders, are characterized. For both materials, the identification of creep parameters (i.e. apparent activation energy and stress exponent values) coupled with TEM structural observations suggest a power law creep regime controlled by dislocation glide, which is limited by the presence of twins. However, the TP material exhibits lower stationary strain rates. This improved creep resistance seems to be directly correlated to the stoichiometry modification of the carbide induced by the powder pre-heat treatment, i.e. increase of structural carbon content and slight decrease of oxygen amount.

New flat-punch indentation creep testing approach for characterizing the local creep properties at high temperatures

An indentation creep testing approach has been developed which allows measuring creep properties at high temperatures. In contrast to existing indentation or impression creep experiments, the approach described here allows to achieve a quite high spatial resolution, as flat punch indenters with a diameter of only 20μm are used. First indentation creep tests have been performed on single crystalline nickel and nickel binary solid solution alloys with Re, Ta or W as alloying elements, respectively. The indentation creep tests have been carried out at a temperature of 650°C and stress levels in the range of 85 to 400MPa. Using crystal plasticity finite element modeling, the indentation creep response is converted into equivalent uniaxial creep properties. It is shown that the conversion parameters, evaluated for differently oriented single crystals, can be chosen independently of the creep rate exponent in the power law creep regime. It is found that the indentation creep results agree well with conventional uniaxial creep tests. Furthermore, the results show that Ta is the most effective solid solution strengthener of all tested solid-solution strengtheners at 650°C because of the large atomic size mismatch, followed by W and Re.

High-temperature deformation mechanisms and processing maps of equiatomic CoCrFeMnNi high-entropy alloy

The hot compressive deformation mechanism and processing maps of the equiatomic FCC CoCrFeMnNi high-entropy alloy (HEA) were studied in the temperature range between 1023 and 1323 K and in the strain rate range between 10−3 and 10 s−1. At high strain rates above 1 s-1, strain hardening was dominant even at the very high temperature of 0.84Tm, which may be attributed to the sluggish diffusion coefficient and low stacking fault energy of the CoCrFeMnNi HEA, leading to suppression of dynamic recovery. According to the processing maps, the best condition for hot working was near 10−3 s−1 at 1323 K. Power-law breakdown and unstable flow occurred at low temperatures and high strain rates where the strain hardening was pronounced. The activation energy for plastic flow measured in the power-law creep regime when considering the dependence of elastic modulus on temperature was 312.2 kJ/mol; this value is close to the activation energy for the weighted diffusion coefficient calculated by weighting the contribution of each element in the CoCrFeMnNi HEA (284 kJ/mol). The size and fraction of the dynamically recrystallized grains increased as the strain rate decreased and the temperature increased, as in conventional metals. Both discontinuous dynamic recrystallization and continuous dynamic recrystallization (CDRX) occurred. CDRX became more distinct as the temperature increased. The deformation mechanism and behavior of the CoCrFeMnNi HEA were very similar to those of FCC pure metals in terms of the stress exponent and the effect of the stacking fault energy and diffusivity on the creep rates.

Densification kinetics of boron carbide with medium entropy alloy as a sintering aid during spark plasma sintering

AbstractThe high sintering temperature of pure B4C considerably limits its widespread application, thus searching an effective sintering aid is critical. In this work, B4C‐based ceramic with 1 vol.% nonequiatomic Fe50Mn30Co10Cr10 medium entropy alloy as a sintering aid were fabricated at 1900‐2000°C by spark plasma sintering (SPS) under applied pressure, and their mechanical properties were examined and compared with pure B4C ceramic sintered at same condition. The maximal flexural strength of 255.59 MPa, microhardness of 2297.6 Hv0.2 and fracture toughness of 3.62 MPa m1/2 could be obtained at optimized SPS pressure of 50 MPa, which were all higher than those of pure B4C ceramic. To better understand the densification kinetics mechanisms, the densification ratio as a function of SPS temperature and pressure was theoretically analyzed using steady creep model. It was found that densification controlled by grain‐boundary sliding at lower pressure transferred to power law creep regime at higher pressure, which were proved by the dislocation net shown in transmission electron microscopy image.

The effect of a prior short-term ageing on mechanical and creep properties of P92 steel

We have investigated the effect of prior short-term ageing on the mechanical and creep properties of tungsten and boron modified 9%Cr ferritic steel (ASTM Grade P92 steel), to provide material data base for the estimation of material degradation due to occurrence of accidental overheating in the early stage of service loading. The steel was aged at 650°C for up to 100, 200, 500, 1000, 2000 and 5000h prior to mechanical and creep testing. Changes in the microstructure during ageing had a slight effect on the reduction of room temperature tensile properties. A sudden decrease on impact properties occurred after ageing for 2000h, but the occurred impact energy of about 70J is in accordance with the specified minimum value of 68J at room temperature for the virgin condition. The creep behaviour of P92 steel in the as-received condition and after different isothermal ageing exposures prior to creep was investigated at 600 and 650°C in the power-law creep regime. The initial applied tensile stress ranged from 90 to 200MPa. The results clearly show a detrimental influence of isothermal ageing on creep properties even after a few hundred hours. Based on microstructure analysis, which was done mostly in a qualitative way, a significant decrease in the creep life after ageing resulted from changes of the dislocation substructure and instability of Laves phase and M23C6 particles.

Creep properties of simulated heat-affected zone of HR3C austenitic steel

Tensile creep tests on austenitic stainless HR3C steel pipe in an as-received state and after heat affected zone (HAZ) thermal cycle simulation by means of the GLEEBLE 3800 physical simulator were carried out at 923 and 1023K and an applied stress range between 100 and 350MPa to evaluate the effect of welding on its creep properties and behaviour. It was found that creep testing was conducted in a power-law creep regime. The results show a clear detrimental influence of the HAZ simulation on creep properties of HR3C steel at 923K and for very short creep exposure. However, with increasing time to fracture, the effect of weld simulation becomes less significant. By contrast, no such deterioration of creep properties was detected at 1023K. The evaluated similar values of the stress exponents of the minimum creep rate and the time to fracture are explained using the assumption that both creep deformation and the fracture process are controlled by the same mechanism. The main creep fracture mode was intergranular brittle fracture due to grain boundary creep damage.

The effect of hot bending and thermal ageing on creep and microstructure evolution in thick-walled P92 steel pipe

In this work, the creep behaviour of an actual thick-walled P92 steel pipe bent (90°) using local induction heating was investigated at 600 and 650°C using uniaxial tension creep tests. Creep specimens were machined from the bend at different positions, namely at the intrados and extrados areas and neutral position and from the straight part of the pipe. Creep tests were followed by metallographic and fractographic analyses of the crept specimens to explain the observed creep behaviour. In order to accelerate the microstructural changes and thus to simulate long-term service conditions, isothermal ageing at 650°C for 10,000h was applied to selected creep specimens before creep exposures. The results of the creep tests performed on specimens extracted from the intrados and extrados of the thick-walled bent P92 steel pipe fall into the scatter band of the base P92 steel average line. No substantial differences were found at different positions of the pipe in the minimum creep rate, the time to fracture and creep fracture strain. However, significant detrimental effects on the creep resistance of the pipe were found after long-term static thermal ageing due to the microstructural instability of the material. The large Laves phase particles, which coarsened during ageing and creep testing, served as preferential sites for cavity nucleation leading to an accelerated tertiary stage of creep and/or premature creep fracture. Activation analysis of the creep data leads to the conclusions, that the creep tests were undertaken in the region of the power-law creep regime and the rate controlling creep deformation mechanism is most probably the climb of the intragranular dislocations.

A phase mixture model for anisotropic creep of forged Al–Cu–Mg–Si alloy

Abstract Aluminium wrought alloys are frequently applied to manufacture structural components of complex shape and used in a temperature range where creep phenomena take place. The aim of this paper is to analyze creep behavior of forged AA2014 alloy and to develop a constitutive model to describe inelastic response under multi-axial stress state. Experimental data show that creep rates depend essentially on the loading direction within the power law creep regime, while in the power law breakdown range creep anisotropy is not essential and can be neglected. Microstructural observations suggest that the anisotropy of creep is primarily caused by elongated grains and grain boundaries as a result of material processing. Assuming the inhomogeneous deformation in different microstructural zones including interiors of elongated grains and grain boundary regions, a phase mixture model of inelastic deformation is developed. The model includes constitutive equations for individual phases and an interaction rule to capture the direction dependent creep. Additional state variables including the normalized dislocation density and the normalized particle size as well as corresponding evolution equations are introduced to describe hardening/recovery and overageing processes. Through a change of variables the model is reduced to a set of kinetic equations such that the material parameters can be identified from families of creep curves for two loading directions. Results of identification are presented for the temperature of 150 °C and several stress levels.

Effect of sulphide exposure on mechanical properties of CuOFP

In Finland and Sweden nuclear waste disposal is planned to be executed according to the KBS-3-concept. In the concept copper canisters containing the used nuclear fuel are buried in 400–500 m deep in the bedrock. Eventually the surface of the copper canister will come in contact with bentonite pore water which contains corrosive species such as sulphide. In this paper the effect of exposure to sulphide containing bentonite pore water at room temperature on the mechanical properties of oxygen free phosphorous doped copper (CuOFP) was studied with standard ex situ tensile and creep tests. Stress corrosion cracking (SCC) susceptibility of CuOFP was studied with in situ slow strain rate testing (SSRT). Tensile tests performed at room temperature showed a slight trend of degradation in mechanical properties with increasing sulphide concentration. Creep tests were accelerated by performing them at an elevated temperature of T = 215°C, but still within the power law creep regime. In creep tests the same kind of trend as in the tensile tests could be observed but when the results were compared to the publicly available CuOFP creep data the variations between the exposed and reference samples lay within the data scatter.

Creep deformation mechanisms in modified 9Cr–1Mo steel

Modified 9Cr–1Mo (Grade 91) steel is currently considered as a candidate material for reactor pressure vessels (RPVs) and reactor internals for the Very High Temperature Reactor (VHTR). The tensile creep behavior of modified 9Cr–1Mo steel (Grade 91) was studied in the temperature range of 873–1023K and stresses between 35MPa and 350MPa. Analysis of creep results yielded stress exponents of ∼9–11 in the higher stress regime and ∼1 in the lower stress regime. The high stress exponent in the power-law creep regime was rationalized by invoking the concept of threshold stress, which represents the lattice diffusion controlled dislocation climb process. Without threshold stress compensation, the activation energy was 510±51kJ/mol, while after correcting for the threshold stress, the activation energy decreased to 225±24kJ/mol. This value is close to the activation energy for lattice self-diffusion in α-Fe. Threshold stress calculations were performed for the high stress regime at all test temperatures. The calculated threshold stress showed a strong dependence on temperature. The creep behavior of Grade 91 steel was described by the modified Bird–Mukherjee–Dorn relation. The rate controlling creep deformation mechanism in the high stress regime was identified as the edge dislocation climb with a stress exponent of n=5. On the other hand, the deformation mechanism in the Newtonian viscous creep regime (n=1) was identified as the Nabarro–Herring creep.

Onset of convection in fluids with strongly temperature-dependent, power-law viscosity: 2. Dependence on the initial perturbation

The onset of convection in the power-law creep regime on the silicate and icy planetary bodies requires a finite amplitude initial perturbation. This is a nonlinear problem and thus, both the amplitude and shape of the perturbation are important. We performed numerical simulations of the onset of convection in a two-dimensional layer with a fixed temperature contrast between the boundaries and in the stagnant lid regime of temperature-dependent viscosity convection. The optimal perturbations are located at the bottom of the layer (in the rheological sublayer) and have the wavelength of about twice the thickness of the rheological sublayer. The critical Rayleigh number for the onset of convection by optimal perturbations is calculated for a broad range of viscosity parameters. The results are summarized in terms of simple scaling relationships.

Onset of convection in fluids with strongly temperature-dependent, power-law viscosity

The onset of convection in the power-law creep regime on the terrestrial planets and icy satellites is poorly constrained. The major difficulty is that the viscosity of power-law fluids approaches infinity when the perturbation amplitudes approach zero and thus the methods of linear theory are inapplicable. Here, we determine the critical Rayleigh number for the onset of convection by starting in the convective regime and gradually decreasing the Rayleigh number in small increments until the solution collapses to the conductive state. For Newtonian viscosity, this approach constraints the subcritical branch and determines the critical Rayleigh number for the cessation of convection. For power-law viscosity, this gives a perturbation-independent critical Rayleigh number below which no steady-state convection solution can exist. The calculations are performed in the stagnant lid regime of temperature-dependent viscosity convection and for several values of the stress exponent. The results approximately agree with earlier theoretical estimates.

Confirmation of low stress creep regime in 9% chromium steel by stress change creep experiments

Abstract High sensitive helicoid spring specimen creep technique was modified to allow stress changes during the low stress, low strain rate experiments. The results obtained on the P-91 type modified martensitic 9% Cr steel support the previous observations of the change of the creep deformation mechanism at low stresses. The stress exponent derived from the stress change experiments approaches a value of about 4.5, considerably higher than that derived from the constant stress experiments. On the other hand, it is much lower than the value of 12, reported for the power-law creep regime of the same steel at stresses above 100 MPa. The creep behavior at low stresses is still not fully understood. The transient stages were observed after each stress change including back flow after the stress decrease. The relaxation periods are relatively long, notably after the stress decrease. The stress redistribution is suggested as a main source of the observed transient effects.

Deformation behaviour of Fe-3Si steel

The deformation behaviour of an Fe-3Si (wt-%) steel was studied in the temperature range 400-900°C over six orders of magnitude of strain rate. It was found that the Fe-3Si steel exhibits a threshold behaviour. A correlation between the deformation behaviour and the temperature dependence of the threshold stress was etermined. An analysis in terms of the threshold stress showed that two modes of deformation behaviour exist in the power law creep regime. At normalised strain rate ϵkT/(D1Eb) ranging from 2 × 10-6 to 10-3, the value of the true stress exponent n is equal to 7, and at lower values of ϵkT/(D1Eb) the value of n is ~ 5. The true activation energy for plastic deformation Qc increases from 250 ± 15 to 290 ± 30 kJ mol-1 with increasing temperature from 550 to 700°C, and remains virtually unchanged at high temperatures. The relationship between rate controlling mechanisms of plastic deformation and mechanisms of interaction between lattice dislocations and dispersoids is discussed.

Probing Mesoscopic Strain Evolution during Creep Deformation: An In-Situ Neutron Diffraction Study

ABSTRACTThe development of lattice strain was studied using in-situ time-of-flight neutron diffraction during constant-load tensile creep deformation of an austenitic 316FR stainless steel at 180, 240, and 300MPa at 873K (a power-law creep regime) with time resolution of 900 seconds. The macroscopic (global) and mesoscopic (lattice) strains were measured simultaneously during creep using an extensometer and neutron diffraction, respectively. The hkl-specific lattice strains were measured to gain insights into the plastic anisotropy at various stages of creep deformation (i.e., primary, secondary, and tertiary regimes). Furthermore, the creep-induced lattice strain behavior was compared to the result obtained from a quasistatic tension test at 873K. The lattice strain evolution in the axial direction (direction parallel to the tensile loading axis) during the primary and secondary creep (dislocation creep) is quite similar to the quasistatic case (slip). However, in the tertiary creep regime, the creep-induced lattice strain accumulation is smaller than the quasistatic case at a given total strain, except the (111) reflection.