Monkman-Grant Relationship Research Articles

Short-term creep and low cycle fatigue unified criterion for a hybridised composite material

The objective of this work is to determine a low cycle fatigue criterion for a thermoplastic matrix composite reinforced with both short and continuous fibres. The proposed criterion is based on the steady state creep strain rate and unifies the results for different fibre orientations, stress ratio, frequency and water content. The criterion is applicable in low cycle fatigue and creep. By means of this criterion, the Monkman–Grant relationship is verified both for creep and low cycle fatigue and offers interesting perspectives for numerical approaches.

Ductility coaxing during creep and tensile deformation of high temperature alloys

ABSTRACT Ductilities generated after four types of creep test are compared: (i) constant load, (ii) constant stress (calculated); (iii) constant stress (from direct observation of the minimum section) and (iv) constant strain rate. Supplementary information is obtained from a regularly interrupted plastic deformation test. The materials considered are 2¼Cr1Mo and 9Cr1Mo steels at 550°C, type 304 and 316 alloys at 650°C and 700°C, respectively, and 20Cr25Ni/Nb steel at 750°C. The principal parameter of interest is the ‘uniform ductility’ in the gauge section, that is, that part which has not severely necked. It is shown that uniform ductility is effectively described by the Monkman-Grant relation and this in turn can be used to sum creep damage via the ductility exhaustion method. It is further demonstrated that, assuming constant volume conditions, gauge length behaviour can be modelled by considering a truncated cone rather than a traditional cylindrical shape.

Creep behavior and failure mechanisms of CVI and PIP SiC/SiC composites at temperatures to 1650 °C in air

Creep properties of 2D woven CVI and PIP SiC/SiC composites with Sylramic™-iBN SiC fibers were measured at temperatures to 1650 °C in air and the data was compared with the literature. Batch-to-batch variations in the tensile and creep properties, and thermal treatment effects on creep, creep parameters, damage mechanisms, and failure modes for these composites were studied. Under the test conditions, the CVI SiC/SiC composites exhibited both matrix and fiber-dominated creep depending on stress, whereas the PIP SiC/SiC composites displayed only fiber-dominated creep. Creep durability in both composite systems is controlled by the most creep resistant phase as well as oxidation of the fibers via cracking matrix. Specimen-to- specimen variations in porosity and stress raisers caused significant differences in creep behavior and durability. The Larson-Miller parameter and Monkman-Grant relationship were used wherever applicable for analyzing and predicting creep durability.

An Investigation into the Correlation of Small Punch and Uniaxial Creep Data for Waspaloy

Within the aerospace sector, the understanding and prediction of creep strains for materials used in high-temperature applications, such as Nickel-based super alloys, is imperative. Small punch testing offers the potential for understanding creep behavior using much less material than conventional uniaxial testing but in contrast to uniaxial creep tests, the stress in small punch creep (SPC) tests is multiaxial. SPC testing can be a valuable tool for validating models of creep deformation, but the key to unlocking its full capability is through the accurate correlation of the creep material properties measured through both techniques. As such, the focus of this paper is to correlate the creep behavior of Waspaloy obtained through conventional uniaxial testing to that obtained via small punch creep testing. Recently, and for low chrome steels, this has been achieved through use of the ksp method, but there are good reasons for believing this technique will not work so well for Nickel-based super alloys. This paper shows this to be the case for Waspaloy and proposes some alternative methods of correlation based on combining the Monkman–Grant relation and the Wilshire equations for both uniaxial and small punch creep. It was found that this latter approach enabled the accurate conversion of SPC minimum displacement rates to equivalent uniaxial minimum creep rates which, when combined with the Wilshire equations, enabled SPC test loads to be converted into equivalent uniaxial stresses (and visa versa) with levels of accuracy that were significantly reduced when compared to using the ksp method. Further, the random error associated with these conversions were dramatically increased.

Creep behavior of nuclear grade 316LN austenitic stainless steel at 873 K and 923 K

Creep deformation and rupture behavior of nitrogen-alloyed (0.14 wt.%) nuclear grade 316LN austenitic stainless steel were investigated for the varying stress levels at 873 K and 923 K. The power-law dependency of creep properties such as steady-state creep rate and rupture life on applied stress was observed. For a given applied stress condition, a systematic increase in strain to failure was noticed with increasing temperature from 873 K to 923 K. Irrespective of test temperatures, creep rupture elongation of the steel increased with the increase in rupture lifetime ( $t_{r}$ ) for $t_{r} > 1000$ h. Analysis indicated that the interdependency between creep properties could be well described by the modified Monkman-Grant relationship. The predominance of inter-granular fracture arising from the triple point cracks and/or coalescence of cavities was observed at all the tested conditions for the steel. The enhanced tendency for wedge cracking was noticed for high stress levels at 873 K and 923 K. The evaluated damage tolerance factor $(\lambda ) < 5$ and the calculated ratio between time to reach the Monkman-Grant strain and creep rupture lifetime in the range of 0.69 to 0.80 indicated the accumulation of Monkman-Grant strain for the major fraction of lifetime during creep deformation of 316LN steel.

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.

Characterization of thermal aging effects on the creep performance of T91 using small punch creep testing

AbstractThis paper is concerned with the development and application of a small punch creep testing method for assessment of the effects of thermal aging and associated precipitate coarsening on the high temperature creep life and deformation behavior of a 9Cr ferritic–martensitic steel. The tests are conducted on P91 steel, for both aged (up to 1 year) and unaged specimens, at temperatures of 600°C. The unaged test results are shown to be consistent with previously published creep tensile test rupture life data in terms of Chakrabarty membrane stress. Aging is shown to have a significant, detrimental effect on creep life and deformation rate. The steady‐state displacement rate, time to failure, and displacement at failure data, for both aged and unaged, were successfully correlated via the modified Monkman–Grant relationship.

A practical power law creep modeling of alloy 690 SG tube materials

A new practical modeling of the Norton's power law creep is proposed and implemented to analyze the high temperature behaviors of Alloy 690 SG tube material. In the model, both the stress exponent n and the rate constant B are simply treated as the temperature dependent parameters. Based on the two-step optimization procedure, the temperature function of the rate constant B(T) was determined for the data set of each B value after fixing the stress exponent n value by using the prior optimized function at each temperature. This procedure could significantly reduce the numerical errors when using the power law creep equations. Based on the better description of the steady-state creep rates, the experimental rupture times could also be well predicted by using the Monkman-Grant relationship. Furthermore, the difference in tensile strengths at high temperatures could be very well estimated by assuming the imaginary creep stress related to the given strain rate after correcting the temperature effects on the elastic modulus.

High-Temperature Creep Behavior and Microstructural Evolution of a Cu-Nb Co-Alloyed Ferritic Heat-Resistant Stainless Steel

The creep behavior of Fe–17Cr–1.2Cu–0.5Nb–0.01C ferritic heat-resistant stainless steel was investigated at temperatures ranging from 973 to 1123 K and stresses from 15 to 90 MPa. The evolution of precipitates after creep deformation was analyzed by scanning electron microscopy, energy dispersion spectrum, and transmission electron microscopy. The minimum creep rate decreased with the decrease in the applied load and temperature, thereby extending the rupture life. Cu-rich phase and Nb-rich Laves particles were generated in dominant quantities during the creep process, and the co-growth relationship between them could be detected. Creep rupture was featured by ductile fracture with considerable necking. As increasing the temperature and decreasing the stress, the softening of the metal matrix was accelerated, showing more obvious plastic flow. The true stress exponent and activation energy were 4.9 and 375.5 kJ/mol, respectively, indicating that the creep deformation was dominated by the diffusion-controlled dislocation creep mechanism involving precipitate-dislocation interactions. Based on the creep rupture data obtained, the Monkman–Grant relation and Larson-Miller parameter were established, which described the creep rupture life for the studied steel well.

Creep behavior and modeling of high-density polyethylene (HDPE)

Creep behavior of high-density polyethylene (HDPE) was investigated. HDPE has many engineering applications in different industries such as piping systems, cable and wiring, automotive parts, storage containers, and biomedical implants. The temperatures chosen were 23, 53, and 82 °C based on the service temperature range for application in design of automotive fuel tanks. Creep strength decreased and creep strain as well as creep strain rate increased by increasing temperature. The Larson-Miller parameter widely used for metallic materials was able to correlate time to rupture, stress, and temperature data of HDPE. The Monkman-Grant relation was successfully used to correlate minimum creep rate and time to rupture. The Findley power law and time-stress superposition principle (TSS) were used to represent nonlinear viscoelastic creep curves. Some longer-term creep tests were also conducted at room temperature to evaluate the accuracy of extrapolation of the short-term creep test results to longer creep life predictions. The models used based on the data presented can be used in the design of parts and components made of HDPE where creep failure may be a concern.

Creep Life Assessment of a Super-Heater Tube

Characteristics of creep deformation for 2.25Cr -1Mo were studied using the Monkman–Grant relation. A series of creep tests were conducted on 2.25Cr -1Mo at low-stress levels and at different temperatures ranging from 655 0C to 6850C . The analysis of creep data indicates that 2.25Cr -1Mo is practically supported by Monkman-Grant relationship. Yet, this paper highlights the foremost difficulties associated with the parametric fitting techniques. The damage tolerance factor has been estimated to demonstrate its reliance on the loading conditions and to categorize the material strain concentration. It has been shown that at 55MPa and T=6850C , the tertiary creep stage is not well characterized. Also, this paper identifies a need to provide a serious consideration for an appropriate creep strength factor that would be applied to pressure vessels and to improve the criteria related to design against creep and the prevention of failure.

WITHDRAWN: Influence of processing routes on the creep deformation and damage evolution of Zr-2.5Nb alloy

Abstract Tensile creep behavior of the Zr-2.5Nb alloy tubes having outer diameters of 90 mm and 110 mm, processed by extrusion and forging, respectively has been studied in the temperature range of 350-450°C under the stress range of 82-319 MPa. The creep curves have shown that the minimum creep rate and time to rupture changes with the applied stress and temperature. The apparent activation energy of creep ( Q C ) values, have been determined by using the power law for 90 mm and 110 mm tube samples are found to be ∼ 231 kJ/mol and ∼ 264 kJ/mol respectively, which is significantly higher than that for lattice self-diffusion of Zr (113 kJ/mol). The microstructural examination of the creep-ruptured samples through transmission electron microscopy (TEM) has shown evidence for multiplication of dislocations, along with their interaction with the β-(Nb, Zr) precipitates in the α-Zr matrix, which is mainly contributed to origin of threshold stress during creep. By incorporating the threshold stress data in the modified power-law relation, the true activation energy of creep ( Q t ) values from the samples of 90 mm and 110 mm tubes are found as 118 kJ/mol and 132 kJ/mol, respectively, which are close to that for lattice self-diffusion in Zr. The obtained true stress exponent ( n t ) values of 3.6 and 4.9 and formation of dislocations sub-grains in the power-law regime of steady state creep, which suggests that the dislocation climb is the rate-controlling mechanism. Further, creep data of the alloy are validated by the Monkman-Grant and Modified Monkman-Grant relationship, and time to rupture effectively predicted using the Larson-Miller Parameter. The creep damage tolerance factors are in the range of 1.5-2.5 for the tubes suggest cavity growth mechanism. Additionally, the comparison of creep data with the Ashby-Dyson maps indicates early formation of cavities due to creep.

Long-Term Creep Behavior of a CoCrFeNiMn High-Entropy Alloy

The potential of high-entropy alloys (HEAs) to meet or exceed austenitic stainless steel performance with the additional benefit of improved hot corrosion/oxidation resistance makes FCC HEAs attractive for use in energy applications. While shorter-term creep tests have been reported in the literature on HEAs, not all methodologies utilize repeatable techniques. This manuscript reports on over 23,500 accumulated hours of tensile creep testing with adherence to ASTM standards on a melt-solidified ingot of CoCrFeNiMn HEA converted to wrought plate using conventional thermo-mechanical processing techniques. The typical standard creep analyses are reported, i.e., Larson–Miller parameter, Monkman–Grant relationship, activation energy for creep, and creep stress exponents were calculated and compared to previously reported short-term creep tests. Additionally, characteristics of creep fracture and microstructural evolution are reported with cursory dislocation mechanisms investigated.

Deformation transitions of ethylene-hexene copolymers under creep loading

Creep tests were conducted in the temperature range from 296 to 358 K, on three commercial ethylene-hexene copolymers (PE) with mass density of 0.938, 0.941 and 0.952 g/cc. PE with the highest density shows the well-known ductile-brittle (DB) transition in the relationship between applied stress and failure time, and PE with the medium density a different transition which was detected through the change in the dependence of failure time on the applied stress, but the failure mode remained ductile. Therefore, this transition is named ductile-ductile (DD). The work shows feasibility of establishing creep master curves to include the two transitions, and discusses exclusiveness between DD and DB transitions so that detection of the DD transition can be used to determine the likelihood of the DB transition to occur in the long-term service. The work also examines applicability of the Monkman-Grant relationship to PEs that involve DD or DB transition.

Creep and creep crack growth behaviors for base, weld, and heat affected zone in a grade 91 weldment

This study investigated the creep and creep crack growth (CCG) behavior of the base metal (BM), weld metal (WM), and heat affected zone (HAZ) in a Gr. 91 weldment, which was made by a shield metal arc weld process. A series of tensile, creep, and CCG tests were performed for the BM, WM, and HAZ at 550 °C. Creep behavior of the BM, WM, and HAZ was analyzed in terms of various creep laws; Norton’s power-law, Monkman-Grant relation and damage tolerance factor (λ), and their constants were determined. In addition, each CCGR law for the BM, WM, and HAZ was proposed and compared in terms of a C∗-fracture parameter. The WM and HAZ revealed faster creep rate, lower rupture ductility, and faster CCGRs than the BM, but they showed a similar behavior in the creep and CCG. The CCGRs obtained in the present study exhibited a marginal difference when compared with those of RCC-MRx of currently elevated design code in France. A creep crack path in the HAZ plane progressed towards a weak fine-grained HAZ adjacent to the BM.

Evaluation of tension and creep rupture behaviors of long-term exposed P91 steel in a supercritical plant

Tension and creep rupture behaviors of long-term exposed P91 steel, sampled from of a T-fitting part of reheat steam piping serviced for 73,716 h at 569 °C and 46.7 bars in a supercritical plant, were evaluated in comparison with those of virgin Gr. 91 steel. Tensile strength reduction factors were proposed for the exposed P91, and creep rupture behaviors were analyzed using various creep laws: Norton’s power law, the Monkman-Grant relations, and a damage tolerance factor (λ). The exposed P91 revealed a significant reduction in tensile strengths, but an increase in elongation. It was found to have a lower creep strength, faster creep strain rate, and higher rupture ductility than the virgin steel. The reduction of mechanical strengths in the exposed P91 was due to the coarsening of precipitates, dissolution of useful fine MX precipitates, and recovery of dislocation substructure during the long-term thermal exposure.

Characterization of stress-rupture behavior of nuclear-grade C26M2 FeCrAl alloy for accident-tolerant fuel cladding via burst testing

FeCrAl alloys demonstrate excellent high-temperature oxidation resistance compared to zirconium alloys used in LWRs. FeCrAl C26M2 has been down-selected as one of the candidate ATF cladding materials for Gen II LWRs. This study investigates the stress-rupture behavior of the nuclear-grade FeCrAl C26M2 tubing in the temperature range of 753-923 K. Rupture time and uniform strain at rupture were determined as a function of the temperature and applied stress using burst tests. The rupture data was found to obey the Larson-Miller Parameter and the Monkman-Grant relationship. Furthermore, the stress exponent (n) and the activation energy (QC) at lower stresses were determined as 4.4 ± 0.3 and 289 ± 25 kJ/mol, respectively, confirming power-law behavior. Above the normalized stress (σ/E) of 2 × 10−3, the power-law creep transited into the power-law breakdown regime. The steady-state deformation microstructure was examined using transmission electron microscopy (TEM) to detect the rate-controlling creep mechanism(s). Observation of sub-grains with dislocations at the boundaries in the power-law regime along with a stress exponent of 4.4 suggests dislocation climb as the rate-controlling mechanism. Two different fracture modes were observed: the tubing failed either by direct open-up or small crack and pinhole formation. The outcome of this study would provide essential data for the development of informative mesoscale deformation models paving way for discovery of new creep resistant alloys.

Tensile creep and rupture behavior along with evolution of microstructure in a Zr-2.5Nb alloy

Tensile creep behavior of the Zr-2.5Nb alloy has been studied through tests under constant load (stress range ~ 137–371 MPa) between 275 and 375 °C. The minimum creep rate of the alloy is found to vary with applied stress and temperature following a power-law relation. The values of stress exponent (n) obtained in the range of 5.3–6.8 in the temperature interval of 300–375 °C; whereas it is calculated as 1.2 and 7.0 under low and high stresses, respectively at 275 °C. The apparent activation energy of creep (QC) and stress exponent have been determined by analyzing the experimental data. The obtained QC (~198.5 ± 10.7 kJ/mol) is found to be higher than the lattice self-diffusion activation energy of pure zirconium (113 kJ/mol). Using this value, stress exponent ~5.6 ± 0.23 is obtained by the temperature-compensated power law. Microstructural characterization by transmission electron microscopy (TEM) with energy dispersive spectroscopy (EDS) analysis has confirmed coarsening of β-(Nb, Zr) precipitates with compositional changes during creep. The dislocation-precipitate interaction as evidenced by TEM observations is considered to be the origin of threshold stress, which decreases with increasing temperature. Considering the threshold stress, true activation energy of creep (Qt) and true stress exponent (nt) are found as ~160.4 ± 6.9 kJ/mol and ~4.8 ± 0.22, respectively. Analysis of creep data has confirmed the role of dislocation climb as the rate-controlling mechanism, along with validity of Monkman-Grant and modified Monkman-Grant relations. Scanning electron microscopy (SEM) of creep fracture surfaces has revealed evidence for prominent ductile fracture. Further, the obtained creep damage tolerance factor value of 1.9, indicating the predominance for cavitation during creep.

Creep behavior of an alumina-forming austenitic steel with simple alloy design

An Fe-18Ni-12Cr-based alumina-forming austenitic (AFA) steel with simple alloy design free of Nb and C was developed for potential application in advanced ultra-supercritical power plants. Creep behavior of the material was studied at the target application temperature of 700 °C. Creep properties were analyzed in terms of stress exponent (n), Monkman-Grant relationship and creep damage tolerance factor (λ). The microstructural evolution of crept samples was investigated by scanning electron microscope (SEM), electron back scatter diffraction (EBSD) and transmission electron microscope (TEM). The minimum creep rate decreased from 5.8 × 10−8 to 1.6 × 10-9 1/s with the applied stress decreasing from 140 to 80 MPa. Precipitation of B2-NiAl during the prolonged creep process contributed to improve creep resistance of the material. The related creep mechanism was found to be dislocation creep, which was supported by the value of n = 7.0 and by the crept microstructure of dislocations tangled with precipitations. Characterization results of creep fracture morphology indicate that the creep failure was resulted from microstructural degradation of precipitation coarsening.

On the Interrupted Creep Test Under Low Stress Levels for the Power Law Parameter Extraction

Abstract Low stress interrupted creep test, as an interim compromise, can provide essential data for creep deformation design. However, there are no clear guidelines on the characterization of the terminating time for interrupted low-stress creep test. To obtain a suitable terminating time in terms of economy and effectiveness, long-term creep strain data of 9%Cr steels are collected from literatures and their creep deformation characterization is analyzed. First, the variations of normalized time and strain of each creep stage with the stress level are discussed. Then, the effect of the terminating time on final fitted results of Norton–Bailey equation is estimated. Third, the relationship between demarcation points at different creep stages and minimum/steady-state creep rate is analyzed. The results indicate that when the creep rupture life is considered as an important factor for creep design, the tertiary creep stage is of greatest significance due to the largest life fraction and creep strain fraction at low stress level. However, the primary and secondary creep stages are of great significance for design due to their larger contribution to 1% limited creep strain. And the long-term secondary creep data could be extrapolated by combining the primary creep strain data obtained from interrupted creep tests with the time to onset of tertiary creep derived from a similar Monkman–Grant relationship.