Monkman-Grant Relationship Research Articles

Estimating the Monkman−Grant relation in the presence of errors in measurement of times to failure and minimum creep rates: with application to some high temperature materials

ABSTRACT The Monkman−Grant relation has the potential to reduce the development cycle for new materials, as it provides a means of lifting based on minimum creep rates that are typically observed early on. This paper outlines problems in estimating the nature of this relation using the least squares technique that stems from errors made in measuring failure times and minimum creep rates. The paper outlines some solutions to this problem that have been proposed within the scientific literature – such as reverse regression and the Deming regression. The evidence from the materials studied in this paper, suggest that the use of least squares results in overly conservative lifetime predictions when using the Monkman-Grant relation. It was found that for 2.25Cr-1Mo steel, the life expected for a minimum creep rate of 3.67E-12s−1 was 57 years when the least squares technique was used, but this increased to 78 years when using the Deming regression.

High temperature tensile and creep properties of the new cladding steel of 15-15Ti-Y

The 15-15Ti austenitic stainless steel is commonly used as a fast reactor cladding material due to its favorable comprehensive properties. To further enhance its high temperature strength, yttrium (Y) modified 15-15Ti (15-15Ti-Y) steel was developed. In this study, the tensile properties of 15-15Ti-Y were evaluated across the temperature range of 200–700 °C, and the constant load creep properties of 20 % cold worked (CW) 15-15Ti-Y were measured at temperatures of 550–700 °C under various applied stresses. The results indicated that Y addition led to enhanced intragranular precipitates and delayed intergranular precipitates, which resulted in a YS (YS) that was ∼ 100 MPa higher than that of Y-free steel at temperatures ranging from 200 to 600 °C, without compromising the plasticity and ductility. The creep fracture life of 15-15Ti-Y steel ranged from 21 to 5761 h, and the deformation and damage processes were found to adhere to the Norton power-law and Modified Monkman Grant relationship. The stress exponent revealed that the deformation was dislocation creep mechanism, while the creep damage tolerance parameter suggested that the creep fracture was caused by necking. These findings provide data and theoretical support for the application of Y-modified 15-15Ti steel as a fast reactor cladding material in high temperature environments.

High‐Temperature Creep Behavior and Damage Mechanism of an Advanced Powder Metallurgy Ni‐Based Superalloy

The creep behavior of a novel powder metallurgy (PM) Ni‐based superalloy is investigated at temperatures ranging from 760 to 815 °C and stress levels in the 480–620 MPa. The steady‐state creep rate, strain to rupture, and rupture time are analyzed based on the Monkman–Grant relation (MGR) and the modified MGR (MMGR). The creep damage factor is redefined by the analysis of Monkman–Grant ductility (MGD). A general relationship between the time reaching MGD and creep life is established. The sharply accelerated creep stage is proposed and the MMGR of the transient creep parameters in this stage is established. The nucleation, growth, and connection of grain‐boundary creep cavities dominate the creep damage of the alloy. The stress concentration caused by the accumulation of dislocations at grain boundaries and σ‐phase interfaces and the grain‐boundary slipping are the main reasons for the nucleation of grain‐boundary cavities. The coupling effect of the temperature and the stress aggravates the damage of grain boundary and the degradation of microstructure.

Creep life assessment of modified 9Cr-1Mo steel based on Monkman–Grant relationship considering temperature and stress dependences of strain required for rupture

ABSTRACT Regarding the application of the Monkman-Grant relationship to creep strength enhanced ferritic steels such as modified 9Cr-1Mo and 12Cr steels, there have been many reports showing that results tend to be an overestimation of the creep life in the long-term region. To address this issue, an author conducted a study to improve the estimation accuracy in the long-term region by the Monkman Grant relationship. Analysing the published creep test data for modified 9Cr-1Mo steel, the author found that the product of the minimum creep strain rate and rupture time (Ɛ MG ) is not constant but depends on the loading conditions, which are test temperature and stress. Then, the author proposed an extended Monkman-Grant relationship considering the dependence of Ɛ MG on the loading conditions. When this model was applied to the data for modified 9Cr-1Mo and 12Cr steels, the creep life was predicted with good accuracy from the short-term to long-term regions.

A new tensile creep model for predicting long-term creep strengths with short-term test data for creep resistant alloys

The difficulties in using the conventional Norton creep model to rationalise short-term creep data and to subsequently predict long-term creep rupture strengths for creep resistant alloys are presented and analysed. The results of this study show that these difficulties can be resolved if a new tensile creep model that integrates the tensile strength at creep temperature is applied to rationalise the short-term creep data. This is illustrated with the creep and tensile strength data measured for a grade of Ni-based superalloy. Based on this new tensile creep model, the activation energy of creep determined is independent of stress and the stress exponent is not influenced by temperature. Consequently, the model constants obtained from the short-term creep data can be applied together with the Monkman-Grant relationship to make the long-term creep rupture strength predictions at different temperatures. The factors affecting the reliability of the predictions made by this method are also analysed.

Tensile and creep properties of novel powder metallurgy Ni-based superalloy

The development of novel powder superalloys for aero-engine turbine disks holds significant implications. In this paper, the microstructure and mechanical properties of a novel powder nickel-based superalloy are evaluated, followed by a brief discussion of the relationship between tensile and creep properties. The results revealed that the new alloy exhibits good microstructural stability after long-term aging and excellent tensile strength at different temperatures. In particular, the creep properties are significantly superior compared to other alloys. In addition, it is verified that the Monkman-Grant relationship modified by tensile parameters has better validity.

Study on creep characteristics and the isochronous stress–strain curve of Ni-Cr-Mo superalloy

ABSTRACT C276 superalloy is considered as a potential structural material for advanced nuclear reactor with good mechanical properties and corrosion resistance. High-temperature creep behaviour of C276 alloy was investigated in the temperature range of 650°C–700°C and at stresses of 140–430 MPa. A linear relationship was fitted between stress and minimum creep rate in the logarithmic coordinate system. The rupture time is analysed for life prediction in terms of isotherm extrapolation method, Monkman–Grant relation, and Larson–Miller parameter method, respectively. The isochronous stress–strain curves as a means of representing stress–strain–time relations under creep conditions were established by the parameter method. The fracture surface morphology of ruptured specimens was characterised by a scanning electron microscope to elucidate the failure mechanism.

Exploring the creep and oxidation behaviors of four types of FeCrAl alloys through small punch test at 600 °C: Experiments and simulations

Four types of iron-chromium-aluminum (FeCrAl) alloys, composed of different elements, were used to investigate the creep performance and high-temperature oxidation resistance. The microstructures in the undeformed regions after the small punch creep test (SPCT) remained consistent with the as-received (AR) FeCrAl alloys, while the grain aspect ratio (GAR) decreased and grains elongated in the deformed regions. Amongst the four alloys, Q1 exhibited the worst oxidation resistance, whereas Q4 showed superior oxidation resistance due to the addition of Si. Precipitates were observed in the deformed regions after SPCT but not in undeformed regions, indicating that deformation had a positive effect on element segregation. Creep models including Norton power law, Monkman-Grant relationship, Larson-Miller Parameters, and Fracture-Time law were obtained. Calculation results from these creep models revealed that under low loads Q4 had lower minimum creep rate δm and longer creep fracture time tr compared to other alloys; however, Q3 demonstrated better performance in terms of δm and tr under high loads. This suggests a strong correlation between creep performance and loads. Additionally, finite element method (FEM) was employed to explore the effects of minor variation (±0.005 mm) in specimen thickness on SPT curves and SPCT curves. FEM results indicated that this slight variation alone did not account for discrepancies observed in load-deflection curves; deviations of ±6.1% for δm and ±6.3% for tr were found corresponding to specimens with 0.5 ± 0.005 mm thickness.

Creep behavior analysis on ruptured welds of heat-resistant steels with two different failure modes

The crept welded joints of heat-resistant steel 12Cr10Co3W2MoNIVNbNB under different creep conditions, 898–948 K and 105–250 MPa, were researched, and the fracture surface reveals two modes, ductile rupture in parent material for high level stress and intergranular type Ⅳ failure in fine grain heat affected zone for low stresses. Creep data are analyzed with Monkman-Grant relation and Larson-Miller parameter method. The extrapolating creep rupture stresses for 100,000 h satisfy the industry requirements. The calculated normalized creep life growth rate values indicate that mediate stress range (150–195 MPa) yields greater influence on creep life compared with high or low stresses. Micro-voids along with precipitates near the fracture surface are observed and analyzed, and creep cavities in fine grain heat affected zone grow and coalesce together and form cracks during creep with precipitates serving as the preferential cavity nucleation sites, leading into the eventual type Ⅳ fracture. Nanoindentation results in different welding zones demonstrate that local physical-mechanical properties do not maintain a decrease trend when creep time increases.

Creep deformation behaviour of thermomechanically treated India specific reduced activation ferritic martensitic steel

In the present work, the influence of thermomechanical treatment (TMT) on microstructural evolution and creep deformation behaviour of India specific reduced activation ferritic martensitic (INRAFM) steel was investigated. Firstly, the TMT was carried out on INRAFM steel by reducing its thickness to 25% at warm rolling temperature (973 K), followed by tempering for 90 min at 1033 K. The resultant microstructural characteristics were compared with those attained in normalized and tempered (N+T) condition. TMT treated steel shows a refinement in lath structure with an increment in population of finer M23C6 precipitates along the hierarchal PAG/packet/block boundaries and MX carbonitrides in the intralath region. After TMT, creep tests were performed on the steel over the stress range of 200–300 MPa at temperature of 823 K. The rupture time of the steel significantly increased upon TMT, due to refinement in microstructural features that enhanced the creep resistance. Dependence of minimum creep rate on applied stress obeys Norton's power law and the stress exponent values indicated the deformation mechanism as dislocation creep. Modified Monkman-Grant relation shows a good relation between rupture time/strain to failure with minimum creep rate. Thereafter, the effect of TMT on the transient, secondary and tertiary creep behaviour was also examined and presented in this work. The TMT treated steel shows lower rate of exhaustion, higher threshold stress and prolonged tertiary region.

Creep ductility and modified Monkman-Grant equation for Gr.92 by incorporating total strain

ABSTRACT A modified Monkman-Grant equation, which can provide a more accurate means of predicting creep rupture life than the standard Monkman-Grant formula, has been investigated for Gr.92 using creep data in the NIMS Creep Data Sheets at 550 to 750°C. The t r versus minimum creep rate min plot, which is called the Monkman-Grant relation, deviates downward at low stresses and long times. Better correlation of the t r with the min is obtained by the replacement of t r with (t r /ε r), where ε r is the total or rupture strain. The (t r /ε r) is inversely proportional to the min over a wide range of stress, temperature and test duration, and the magnitude of data scattering is only a little bit even at low stresses and long times. The creep life of Gr.92 can be predicted by evaluating the min, together with the ε r evaluated from the stress and or min dependence.

Creep life estimation of a service‐exposed P91 cross‐weld joint based on a primary‐secondary creep deformation model

AbstractCreep deformation and rupture behavior of welded joints from service‐exposed P91 steel were investigated by creep tests and microstructure examination. A series of miniature tensile creep tests were conducted at 569°C under applied stresses ranging from 182.5 to 286 MPa for the heat‐affected zone (HAZ), base metal, and weld metal. Creep deformation behavior was modeled using the experimentally measured creep strain data as the primary creep‐secondary creep (PC‐SC) model and fitting closely with the measured creep curves of each metal. Power‐law type creep equations were employed to describe the primary and secondary creep behavior. The creep rupture life of the cross‐weld specimen was predicted using the PC‐SC model with HAZ properties. An accurate prediction was possible if the stress in estimation was increased to 1.14 times of the actual applied stress. The creep test results with the cross‐weld specimens were used for verification. Applying the Monkman–Grant relationship and the creep damage tolerance factors to the cross‐weld joint life prediction are also discussed.

Modified version of Monkman-Grant equation for Gr.91 by incorporating “strain to minimum creep rate” parameter

A modified version of the Monkman-Grant equation, which can provide a more accurate means of predicting creep rupture life than the standard Monkman-Grant formula, has been investigated for Gr.91 using creep data in the NIMS Creep Data Sheets at 450–725 °C. The maximum time to rupture tr was 1.2 × 105 h. The tr versus minimum creep rate ε˙min plot, which is called the Monkman-Grant relation, deviates downward at low stresses and long times. The difference between the maximum and minimum tr at a same ε˙min becomes more significant with decreasing stress and increasing test duration. Better correlation of the tr with the ε˙min is not obtained by the replacement of tr with (tr/εr), where εr is the total or rupture strain. The magnitude of data scattering is larger in the (tr/εr) versus ε˙min plot than in the tr versus ε˙min plot. The (tr/εm), where εm is the strain to minimum creep rate, is inversely proportional to the ε˙min over a wide range of stress, temperature and test duration and the magnitude of data scattering is only a little bit even at low stresses and long times. The (tr/εm) versus ε˙min plot gives us more reliable relation for Gr.91 than the tr versus ε˙min and (tr/εr) versus ε˙min plots.

High-temperature creep rupture behavior of dissimilar welded joints in martensitic heat resistant steels

The creep rupture behavior and microstructure changes of dissimilar welded joints of two types of martensitic heat resistant steel F92 and Co3W2, under a creep testing of 115–200 MPa and 873–893 K, were investigated. Fracture position and mode change from transgranular ductile fracture in parent F92 to intergranular brittle fracture in the fine grain heat affected zone (type IV cracking) near F92, with the drop of applied stress. Microstructural degradation resulted from creep with respect to dislocation density decrease, precipitates coarsening, dislocation cells, microvoids, macroscopic secondary cracks, and fracture surface morphology are researched based on detailed experimental results. The creep rupture data are analyzed employing Norton’s power law, Monkman–Grant relation, creep damage tolerance, and Larson–Miller parameter. Main creep damage micromechanisms are analyzed with the aid of calculated and experimental data. The extrapolating creep rupture stress for a creep life of 100,000 h are obtained and the influence of stress change and temperature change on creep life are compared in terms of calculated normalized creep life growth rate.

Analysis of Monkman-Grant relationships and damage tolerance factor for creep of 25Cr35NiNb micro-alloyed steel

Creep behavior of high Cr austenitic stainless steel was investigated at temperatures ranging from 650 to 1050 °C and stress levels in the range 47–120 MPa. Primary, secondary and tertiary creep strains were analyzed in terms of minimum creep rate, constant true stress and temperature. Minimum creep rates, strain to rupture and rupture time were analyzed in terms of Monkman-Grant and modified Monkman-Grant relation. Good correlation between minimum creep rate and rupture time using both Monkman-Grant relationships is observed for the creep data on the steel. Validity of the relationship between time to reach Monkman-Grant ductility tMGD and rupture life tr in terms of damage tolerance factor λ was established for the steel. Effect of temperature on microstructure and carbide content of the steel is presented in this paper. Microstructural studies reveal failure mechanisms by nucleation and growth of cavities around carbide particles at grain boundary regions. Based on the critical continuum damage mechanics approach, the ratio of tMGD to tr express by constant fCDM separated safe and unsafe regimes of creep behavior of the steel.

Long-term tensile creep behavior of a family of FCC-structured multi-component equiatomic solid solution alloys

Long-term tensile creep experiments were performed at 973 K on a family of multicomponent equiatomic solid solution alloys with face-centered cubic crystal structures, including quinary CoCrFeMnNi alloy and quaternary CoCrFeNi alloy, together with our previous report on ternary CoCrNi alloy. Analyzing the steady-state and transient creep properties and characterizing the precipitate evolution, it is suggested that dislocation creep be the dominant deformation mechanism for all these alloys. Although CoCrNi shows the highest room-temperature strength and the lowest creep rate at 973 K, the creep lifetime data for all three alloys are similar and can be described by the Monkman-Grant relationship.

Creep behaviour of alloy 690 in the temperature range 800–1000 °C

The creep behaviour of Ni-base superalloy 690 has been studied in the temperature range of 800–1000 °C, and stress range of 25–105 MPa under constant load creep conditions. The alloy follows a power-law creep behaviour in the tested conditions and obeys a Monkman-Grant relationship. All the creep data points lay within a ±5% scatter band of the Larson-Miller parameter vs. log stress plot. The alloy spent more than 50% of its life in the tertiary regime and failed predominantly by cavitation. Creep parameters, like apparent activation energy and stress exponent, were relatively high (∼363–498 kJ/mol and 5.5–7, respectively). A high value of the apparent activation energy has been attributed to the resistance of fine carbide particles that form during creep. The microstructural sub-structure of creep deformed samples shows subgrains separated by low angle grain boundaries and randomly oriented dislocations suggesting dislocation climb as the rate-controlling creep mechanism.

Evaluation of rupture life and Larson Miller parameter using Monkman-Grant relationship from impression creep data of magnesium alloy ZM21

The creep behavior of various materials is being increasingly studied using impression tests. However, the impression tests can provide data for the primary and secondary stages of the creep curve but not the third stage for the specimen doesn’t fail during the test. Creep studies without rupture data leaves the analysis incomplete. Hence there is a need to correlate the minimum velocity obtained from impression tests with rupture time to make the creep analysis complete. The present paper attempts to evaluate rupture time and Larson Miller parameter (LMP) from the impression test data of ZM21 Magnesium alloy. The rupture time (trup) was calculated from the steady state impression velocity using Monkman-Grant relationship (MGR) and the trup was used to calculate LMP. Impression tests were carried out between equivalent stresses of 180 MPa and 66.67 MPa and the temperature was varied between 448 K and 523 K. Larson-Miller constant of 10 was found to describe the LMP by logarithm of applied stress.

Short-Term Creep-Rupture Behaviour of AISI 310S Austenitic Stainless Steel Sheets Manufactured in Salem Steel Plant, a Special Steels Unit of Steel Authority of India Limited, Ministry of Steel, Government of India

The creep behavior of AISI 310S stainless steel taken from SAIL’s Salem stainless steel plant has been investigated by constant load tensile creep test at the temperatures of 973, 1023, and 1073 K and loads of 66.6, 74.8, 86.6, and 94.8 MPa. It exhibits steadystate creep behavior in most test conditions. The double logarithm plot of rupture life and applied stress yielded straight lines at all the three test temperatures indicating that power-law creep due to dislocation climb is the operating mechanism of creep deformation. Linear relationship was obtained for plots of logarithm of rupture life against inverse temperature obeying Arrhenius type of temperature dependence with activation energy of 340 kJ/mol. The stress-rupture data yielded a master curve of Larson-Miller parameter. The plot of Monkman-Grant relationship is typical indicating that rupture is controlled by growth of grain boundary cavities. The metallographic examination of crept samples revealed formation of grain boundary voids and cracks leading to intergranular creep fracture. Deformation twins and carbide precipitates were also observed. Creep-rupture properties are compared with that of AISI 600 ironbased superalloy to analyze quantitatively its behavior

Creep properties, microstructural evolution, and fracture mechanism of an Al added high Cr ODS steel during creep deformation at 600 °C

The creep properties, microstructural evolution, and fracture mechanism of 16Cr-3Al oxide dispersion strengthened (ODS) steel were systematically investigated at 600 °C under different uniaxial tensile stresses in the range of 160–200 MPa. The minimum creep rate had a linear relationship with the mean creep rate, which followed the modified Monkman-Grant relationship with a slope of 0.57. The threshold stress was determined as 145.09 MPa based on the modified Bird-Mukherjee-Dorn (BMD) equation. Both Laves phase and Cr-rich phase were identified after creep deformation. The evolution of Cr-rich phase during creep deformation included the dissolution of W-rich σ phase and the precipitation of Si-rich σ phase. Cross-sectional cracks could be observed near the rupture surface, and these cracks mainly formed near the Si-rich σ phase and the boundaries between coarse and fine grains. It was considered that the formation of Si-rich σ phase in fine grains was the main fracture mechanism of 16Cr-3Al ODS steel during creep deformation.