Monkman-Grant Relationship Research Articles

Microstructural Degradation and Development of Damage During Creep in 9 % Chromium Ferritic Steels

Creep-rupture properties of grade 9 and 92 steels have been examined for wide range of stresses at 873 K. Both grade 9 and 92 steels obeyed power law in the stress dependence of rupture life and exhibited two-slope behaviour with separate values of stress exponents in the low and high stress regimes. Grade 92 steel exhibited significantly higher creep-rupture strength than grade 9 steel. Grade 9 steel displayed high creep ductility, transgranular fracture and obeyed Monkman–Grant and modified Monkman–Grant relations. On the contrary, grade 92 steel exhibited significant decrease in creep ductility at longer durations associated with secondary cracking originating from decohesion of Laves phase. Grade 92 steel followed generalized form of Monkman–Grant relation and obeyed modified Monkman–Grant relation. High values of creep damage tolerance factor obtained for grade 9 and 92 steels have been correlated with the observed microstructural degradation in terms of decrease in dislocation density and coarsening of precipitates and dislocation substructure.

A continuum damage model for creep fracture and fatigue analyses

In this paper a thermodynamically consistent formulation for creep and creep-damage modelling is given. The model is developed for isotropic solids by using proper expressions for the Helmholtz free energy and the complementary form of the dissipation potential, and can be proven to fulfill the dissipation inequality. Also the coupled energy equation is derived. Continuum damage model with scalar damage variable is used to facilitate simulations with tertiary creep phase. The complementary dissipation potential is written in terms of the thermodynamic forces dual to the dissipative variables of creep strain-rate and damage-rate. The model accounts for the multiaxial stress state and the difference in creep rupture time in shear and axial loading as well as in tensile and compressive axial stress. In addition, the model is simple and only four to eight material model parameters are required in addition to the elasticity parameters. A specific version of the proposed model is obtained when constrained to obey the Monkman-Grant relationship between the minimum creep strain-rate and the creep rupture time. The applicability of the Monkman-Grant hypothesis in the model development is discussed. The proposed 3D-model is implemented in the ANSYS finite element software by the USERMAT subroutine. Material parameters have been estimated for the 7CrMoVTiB10-10 steel (T24) for temperatures ranging from 500 to 600 degrees of celcius. Some test cases with cyclic thermal fatigue analysis are presented.

Creep behaviours of Cr25Ni35Nb and Cr35Ni45Nb alloys predicted by modified theta method

Creep behaviours of Cr25Ni35Nb and Cr35Ni45Nb alloys were investigated under 22–50MPa at 1173K, 1198K and 1223K. The stress dependence of minimum creep rate and rupture life obeyed power law, and the stress exponent values were similar for both alloys indicating similar deformation and fracture mechanism. These alloys also obeyed Monkman–Grant and Modified Monkman–Grant Relations, and Cr25Ni35Nb exhibited higher MG and MMG constants. It can be concluded that Cr35Ni45Nb has higher creep strength than Cr25Ni35Nb, whereas the creep ductility is not as good as Cr25Ni35Nb alloy. A modified theta equation was proposed to estimate the creep behaviours, where the random errors of experimental data from the fitted creep curves were smaller than traditional theta equation. The obtained theta parameters revealed good linear relations as a function of stress, and the predicted creep behaviours were in good agreement with experimental ones.

Creep deformation and rupture behavior of Alloy 617

A series of creep data was obtained from creep tests at different applied stresses at the temperatures of 850°C, 900°C, and 950°C for Alloy 617, which is a leading candidate material for high-temperature components in Gen-IV nuclear reactor systems. The creep deformation and rupture behavior were investigated in terms of Norton's power law, Monkman–Grant relation (MGR), modified Monkman–Grant relation (MMGR), creep damage tolerance factor (λ), Zener–Hollomon Parameter (Z), and fracture behavior. Alloy 617 did not exhibit textbook creep behavior and revealed somewhat differences from typical heat resistant steels. The MMGR provided improved correlation between creep rate and rupture life in Alloy 617. The Z parameter obeyed a good agreement for a function of Z=2.30×1033 (σ/E)5.87, and the same creep mechanism was operative within the ranges tested in the present study. The value of λ for Alloy 617 was found to be 2.40, and this was in agreement with materials exhibiting typical cavitation damage. The creep failure analysis revealed a dominant intergranular fracture mode, which proceeds via initiation, linking, and incorporation of the cavities.

An assessment of creep deformation and rupture behaviour of 9Cr–1.8W–0.5Mo–VNb (ASME grade 92) steel

Creep deformation and rupture behaviour of 9Cr–1.8W–0.5Mo–VNb steel have been investigated at 873K, 923K and 973K over a stress range of 80–220MPa. The absence of clear primary creep regime and prolonged secondary stage of creep deformation have been noticed under lower stress level at 973K. The variation of minimum creep rate with applied stress obeyed Norton's power law of creep. The apparent stress exponents of 15.2, 12.3 and 5.8, and apparent activation energy of 619kJ/mole have been estimated for creep deformation of the steel. The apparent stress exponents and activation energy have been rationalised on the basis of threshold stress. The threshold stress values of 137.5MPa, 83.3MPa and 29.7MPa were obtained at 873K, 923K and 973K respectively. The threshold stress compensated true stress exponent of 4 and true activation energy of 244kJ/mole, and threshold stress normalised by Orowan stress confirms that the lattice diffusion assisted localised climb of dislocation is the rate controlling of creep deformation in the steel. The steel obeyed Monkman and modified Monkman–Grant relationships. Damage tolerance factor of 6 in the steel demonstrates that the microstructural degradation such as coarsening of precipitates and subgrain structure is the dominant creep damaging mechanism in the steel.

Creep lifing methodologies applied to a single crystal superalloy by use of small scale test techniques

In recent years, advances in creep data interpretation have been achieved either by modified Monkman–Grant relationships or through the more contemporary Wilshire equations, which offer the opportunity of predicting long term behaviour extrapolated from short term results. Long term lifing techniques prove extremely useful in creep dominated applications, such as in the power generation industry and in particular nuclear where large static loads are applied, equally a reduction in lead time for new alloy implementation within the industry is critical. The latter requirement brings about the utilisation of the small punch (SP) creep test, a widely recognised approach for obtaining useful mechanical property information from limited material volumes, as is typically the case with novel alloy development and for any in-situ mechanical testing that may be required. The ability to correlate SP creep results with uniaxial data is vital when considering the benefits of the technique. As such an equation has been developed, known as the kSP method, which has been proven to be an effective tool across several material systems. The current work now explores the application of the aforementioned empirical approaches to correlate small punch creep data obtained on a single crystal superalloy over a range of elevated temperatures. Finite element modelling through ABAQUS software based on the uniaxial creep data has also been implemented to characterise the SP deformation and help corroborate the experimental results.

Numerical Study on Creep Rupture Behavior of SA533B Low-Alloy Steel

Time-dependent loads may significantly affect on structural integrity of RPV (Reactor Pressure Vessel) under severe accident conditions respecting to the core melting. Especially, creep rupture at the high-temperature should be regarded as an important phenomenon to cope with failure of the RPV lower plenum. In this paper, creep behavior of SA533B as a typical reactor material was assessed based on several creep relationships such as Bailey-Norton's power law, MGR (Monkman-Grant Relationship) and MMGR (Modified Monkman-Grant Relationship). Creep rupture test data were referred from experimental projects of OECD/NEA. Subsequently, corresponding parametric FE (Finite Element) analyses were carried out for various temperature and loading conditions, of which results were used to establish an enhanced creep rupture evaluation method combined with the well-known LMP (Larson-Miller Parameter) of the low-alloy steel.

An Extension of the Monkman-Grant Model for the Prediction of the Creep Rupture Time Using Small Punch Tests

Creep tests on a small scale have the potential to be used without significant removal of material or in areas where the available material is limited. In this paper an extension of the modified Monkman-Grant model for the prediction of the creep rupture time using Small Punch Creep Tests (SPCT) is investigated. This test basically consists of punching, under constant load, a small size specimen (10×10×0.5 mm) with the ends fixed. For this purpose an AZ31B magnesium alloy, taking a test temperature of 150 oC, has been selected. The Monkman-Grant relation is a predictive model, initially developed for uniaxial creep tests, which can be used to predict the rupture time of tests which have been interrupted once secondary stage of creep has been reached. The proposed extension of the Monkman-Grant model for SPCT is based on the definition of the Minimum Relative Punch Displacement Rate. The experimental techniques and data analysis, involving small punch testing, are explained in detail. The proposed predictive model allows the test times of small punch testing to be reduced and it can be directly applied to predict the failure time from an interrupted test at the time when the Minimum Relative Punch Displacement Rate is reached. Good correlations are obtained by comparing the failure time from the proposed Monkman-Grant extension with the experimental failure time.

Small Punch Creep Testing Technique for Remnant Life Assessment

Small punch creep (SPC) testing technique is a material non-intensive testing technique for evaluating creep behavior of materials using miniature specimens. It can be used for remnant life assessment (RLA) studies on components in service, by scooping out limited material for testing without impairing the strength of component. In order to ensure the reliability of use of SPC technique for RLA, it is necessary to establish sound database on SPC properties of the material before putting into service. In this investigation, SPC technique was used to evaluate creep properties of 316LN stainless steel using specimens of size 10 x 10 x 0.5 mm. SPC tests were conducted in load controlled mode at 923 K and at various loads. SPC curves clearly exhibited primary, secondary and tertiary creep stages. The minimum deflection rate increased and rupture life decreased with an increase in applied load. Like in conventional creep test results, the minimum deflection rate obeyed Norton’s power law and Monkman-Grant relationship. SPC test was correlated with corresponding conventional creep test. Good correlation was established between creep rupture life values evaluated from SPC tests and conventional creep tests.

Life assessment of die-cast Mg–5Al–1.7Ca alloys under creep service conditions

The creep rupture behavior of a Mg–5Al–1.7Ca alloy produced via die casting was investigated at temperatures between 423 and 498K, and the creep rupture life of the alloy was evaluated using the Larson–Miller parameter (LMP). It was demonstrated that the minimum creep rate and creep rupture life followed the phenomenological Monkman–Grant relationship. The value of the LMP was uniquely described by the logarithm of the applied stress when the Larson–Miller constant was set at 20. In addition, the applied stress and the LMP value followed a linear relationship below the yield stress. These results can be utilized to predict the long-term creep rupture life of the alloy under a given temperature condition and applied stress.

Cyclic creep behaviour under tension–tension loading cycles with hold time of modified 9Cr–1Mo steel

Cyclic creep behaviour of modified 9Cr–1Mo steel was investigated by a series of cyclic creep (CC) tests at 600°C, which were performed under controlled tension–tension loading cycles with the magnitude of stress ranges in a constant stress ratio (R = 0·1). Hold time was applied for a 10 min hold at the maximum stress (σmax) and minimum stress (σmin). The CC properties were compared with the static creep (SC) using Norton’s power law, Larson–Miller plot, and Monkman–Grant relation, and the microstructure was examined. For the test conditions employed in the present investigation, retardation in the CC behaviour in terms of a lower creep rate and longer rupture time compared to those in the SC was obtained. The retardation was ascribed to the effects associated with anelastic recovery during the 10 min hold time at the minimum load of the cyclic loading. The creep rupture ductility decreased with a general decrease in stress, and there was no difference in the creep ductility between the CC and SC. The steel displayed a transgranular fracture characterised by the presence of dimples resulting from micro-void coalescence. Carbide precipitation was more coarsened with increasing in exposure time in the CC tests.

Effect of Impurity Tin on the Creep Properties of a P91 Heat-Resistant Steel

The creep properties of P91 steel specimens undoped and doped with 0.058 wt pct tin, which was normalized from 1328 K (1055 °C) and tempered at 1033 K (760 °C), were examined under different engineering stresses (150 to 210 MPa) and temperatures [873 K to 923 K (600 °C to 650 °C)]. The creep behavior followed the temperature-compensated power law and Monkman–Grant equations. In the temperature-compensated power law equation, the apparent activation energy and stress exponent for creep were approximately 541 kJ/mol and 12 for the undoped steel and 527 kJ/mol and 11 for the Sn-doped one, respectively. In the Monkman–Grant relation, the values of constants m and C were around 1.062 and 0.0672 for the undoped steel, and 1.012 and 0.0650 for the Sn-doped one, respectively. The 100 MPa stress creep lifetime at 873 K (600 °C) was estimated as 100641 hours for the undoped steel and 35290 hours for the Sn-doped steel, respectively. These indicated that Sn substantially deteriorated the creep properties of the steel. It was found that grain or subgrain boundary segregation of Sn could promote the nucleation of cavities or microcracks, thereby leading to the deterioration of the steel creep properties.

Effect of multi-axial stress state on creep behavior and stress rupture life of a Ni-based DS superalloy

Effect of multi-axial stress state on creep behavior and stress rupture life of a Ni-based directionally solidified (DS) superalloy has been systematically investigated. Emphasis is placed on the roles of the applied net section stress level, initial theoretical stress concentration factor (Kt), notch shape, plate thickness and sample shape. The results show that creep behavior is obviously affected by all the mentioned factors, which are concretely embodied in the redistribution of stresses, accumulation of creep strains and evolution of creep damage. The indicators for describing the constraint degree are further quantitatively discussed and the tri-axiality factor I1/σMises is exhibited as a good indicator. Based on the Monkman–Grant relationship, the stress rupture lives of notched specimens are predicted, which are related to the constraint degree and agree well with the existing experimental laws.

Analysis of Creep Behavior of Alloy 617 for Use of VHTR System

Alloy 617 is the one of the leading candidate materials for intermediate heat exchangers (IHX) application of a Very High Temperature Reactor (VHTR) system for economic production of electricity and hydrogen. Creep rupture data for Alloy 617 were obtained from a series of creep tests with different applied stresses at 850oC, 900oC and 950oC. On the basis of a systematic analysis of the experimental data, creep behaviour for Alloy 617 was analyzed using various creep relationships and laws, such as Norton's power law, Monkman-Grant Relationships (MGR), Modified Monkman-Grant Relationships (MMGR), creep damage tolerance factor λ, and Zener-Hollomon Parameter (Z), and the creep constants used in each equation were reasonably determined. The creep curve of Alloy 617 was somewhat different from those of typical heat-resistance steels, and it did not exhibit a textbook creep curve. The secondary creep stage is unclear, and it appeared to exhibit a predominantly accelerated creep rate from the start of a tertiary creep stage in short time ranges. The creep deformation was dominantly developed from the formation and growth of cavity in creep damage process. The MMGR appeared to be more narrowed in data scattering than the MGR, and it followed well a straight line of m ≅ 1.0 as m=0.97. In the plot of the Z parameter vs. stress, it obeyed a straight line with a slope of n’=5.87 regardless of the three different temperatures. It would be inferred that the same creep mechanism was operative within the present stress and temperature ranges, and the creep damage tolerance factor of Alloy 617 was found to be 2.40.

Tensile and Creep Behaviour of Modified 9Cr-1Mo Steel Cladding Tube for Fast Reactor Using Metallic Fuel

Modified 9Cr- 1Mo ferritic martensitic steel has been considered as cladding tube material in metallic fuel fast reactors in view of the relatively lower operating temperatures. In this study, tensile and creep behaviour of modified 9Cr-1Mo steel cladding tube have been investigated. Microstructure of the normalized and tempered steel consisted of tempered lath martensite with precipitates at the prior austenite grain boundaries and sub-boundaries. Tensile tests on the cladding tube were carried out at a strain rate of 3x10-3 s-1 over the temperature range of 300 - 923K. The variations of 0.2% yield stress, ultimate tensile strength and elongation of the steel with temperature have been studied. Yield stress and ultimate strength of the cladding tube exhibited plateau in the intermediate temperature range of 523 - 673K, where the elongation exhibited a broad minimum. The tensile strength and ductility of the steel cladding tube were comparable with those reported for different products forms of the steel.Creep properties of modified 9Cr-1Mo steel cladding tube were studied at 823K at various stress levels. Creep curves of the steel generally consisted of primary and tertiary stages with no secondary stage of deformation. The variation of minimum creep rate with stress obeyed a power law. The stress exponent ‘n’ was around 25, which is the characteristic of precipitation hardened alloys. Rupture life was found to decrease with increase in stress. The Monkman-Grant relationship relating minimum creep rate with rupture life was found to be obeyed by the steel. Creep rupture strength of the modified 9Cr-1Mo steel cladding tube was in accordance with the reported values for other product forms.

Biaxial thermal creep of Inconel 617 and Haynes 230 at 850 and 950 °C

The biaxial thermal creep behavior of Inconel 617 and Haynes 230 at 850 and 950°C was investigated. Biaxial stresses were generated using the pressurized tube technique. The detailed creep deformation and fracture mechanism have been studied. Creep curves for both alloys showed that tertiary creep accounts for a greater portion of the materials’ life, while secondary creep only accounts for a small portion. Fractographic examinations of the two alloys indicated that nucleation, growth, and coalescence of creep voids are the dominant micro-mechanisms for creep fracture. At 850°C, alloy 230 has better creep resistance than alloy 617. When subjected to the biaxial stress state, the creep rupture life of the two alloys was considerably reduced when compared to the results obtained by uniaxial tensile creep tests. The Monkman–Grant relation proves to be a promising method for estimating the long-term creep life for alloy 617, whereas alloy 230 does not follow the relation. This might be associated with the significant changes in the microstructure of alloy 230 at high temperatures.

Application of the Monkman-Grant Relationship for Ultrafine-Grained Metallic Materials

The applicability of the Monkman-Grant relationship was analyzed and validated for ultrafine-grained metallic materials under investigation. A special attention has been given to the creep damage tolerance factor which is defined as the ratio of the strain to fracture to the Monkman-Grant ductility and which describes the coupling between creep deformation and damage based on continuum creep damage approach. It was found, that ultrafine-grained materials generally obey the Monkman-Grant relationship, however, the relationship is especially suitable for materials exhibiting short secondary creep and long tertiary creep stages when dislocation-controlled creep is dominant.

The importance of creep strain in linking together the Wilshire equations for minimum creep rates and times to various strains (including the rupture strain): an illustration using 1CrMoV rotor steel

This paper highlights the observation that the Wilshire equations for failure times and times to various strains, as reported in the original literature, may not be the most appropriate ones for all materials—including the one selected in this study. Further, such appropriateness can be determined by looking at the consistencies between the parameter estimates obtained using minimum creep rates in comparison to using failure times. It is shown, using 1CrMoV steel as an illustration, that the parameter consistency can be achieved by generalising the Monkman–Grant relation so that it contains a temperature correction. Indeed, the ability of the Wilshire equations to produce meaningful physical parameters, such as the activation energy, is shown to be highly dependent upon a valid specification for the Monkman–Grant relation. It is shown that variations in the measured values for some of the Wilshire parameters (w and k 3) with strain indicate that the causes of deformation are different at different strains and different stresses. Finally, the measured variations in the parameters of the Monkman–Grant relation with strain enable accurate interpolated and extrapolated creep curves to be calculated for any test condition.

Creep and microstructure of Nextel™ 720 fiber at elevated temperature in air and in steam

Creep of Nextel™ 720 alumina–mullite fiber tows was investigated at 1100 and 1200°C for tensile stresses of 100–400MPa in air and in steam. Fiber microstructures were characterized after creep by transmission electron microscopy. At low stresses steam increased creep rates by up to an order of magnitude and reduced creep lifetimes. At high stresses creep rates in steam and air were similar. Cavitation was prevalent in steam but not in air. The creep-rupture data obtained at 1200°C were analyzed in terms of a Monkman–Grant (MG) relationship. The MG parameters were independent of the test environment. Results reveal that the MG relationship can be used to predict creep rupture for Nextel™ 720 fibers and composites reinforced with these fibers at 1200°C in air and in steam. In steam the mullite in the Nextel™ 720 fibers decomposed to porous alumina. Decomposition kinetics were linear and had an activation energy of ∼200kJmol−1. Intergranular films were not observed on alumina grain boundaries or alumina–mullite interphase boundaries after creep in steam. Creep mechanisms are discussed.

Creep-rupturing of elliptical and circular cell honeycombs

This paper makes a theoretical analysis of the steady-state creep strain rates and creep rupturing times along the two principal directions of elliptical cell honeycombs using a unit cell model and assuming that solid cell walls follow power law creep and the Monkman–Grant relationship. Based on the results, the effects of the ellipticity of cell walls and relative density of elliptical cell honeycombs on their steady-state creep strain rates and creep-rupturing times can be evaluated. It is found that the Monkman–Grant parameters, m1∗ and m2∗, of elliptical and circular cell honeycombs are equal to that of solid cell walls, ms. In addition, the other Monkman–Grant parameters B1∗ and B2∗ decrease as the relative density increases, and B2∗ is always greater than B1∗. Moreover, the creep strain rates and creep-rupturing times of elliptical and circular cell honeycombs are compared with those of regular hexagonal honeycombs with the same relative-density to evaluate the efficiency of their microstructures.