Monkman-Grant Relationship Research Articles

Creep and Stress Rupture Behavior of an Advanced Silicon Nitride: Part III, Stress Rupture and the Monkman–Grant Relationship

The applicability of the Monkman–Grant relationship to predict the stress rupture life of NT154 silicon nitride is examined. The data show that the Monkman–Grant lines relating rupture life to minimum creep rate are stratified with respect to temperature. A modification to the current expression for the Monkman–Grant relation is proposed to accommodate this temperature dependence. A phenomenological approach based on crack growth as the failure mechanism is presented to explain this temperature dependence. The results can be interpreted as suggesting that the stress dependence of the failure process is greater than that for creep.

Creep and Creep Rupture of an Advanced Silicon Nitride Ceramic

Creep and creep rupture behavior of an advanced silicon nitride ceramic were systematically characterized in the temperature range 1150° to 1300°C using uniaxial tensile creep tests. Absence of tertiary creep and the order‐of‐magnitude breaks in both creep rate and rupture lifetime at certain threshold combinations of stress and temperature were two characteristic features of the creep behavior observed. Thermal annealing was found to have enhanced both subsequent creep resistance and creep rupture life. The stress exponent (n) and the activation energy (Q) defined in the Norton relation were found to be 12.6 and 1645 kJ/mol for the material investigated. Both values appear to fall in the general range of those reported for other but similar types of Si3N4 ceramic materials. The stress exponent, m, equivalent to the slope of the Larson–Miller equation was found to be in the range 13 to 14.4, and that defined as p in the Monkman–Grant relation to be 0.91, based on the available experimental data. The values of m, n, and p obtained above approximately support the interrelationship of the three exponents given by p=m/n.

Tensile Creep and Creep Rupture Behavior of Monolithic and SiC‐Whisker‐Reinforced Silicon Nitride Ceramics

The tensile creep and creep rupture behavior of silicon nitride was investigated at 1200° to 1350°C using hotpressed materials with and without SiC whiskers. Stable steady‐state creep was observed under low applied stresses at 1200°C. Accelerated creep regimes, which were absent below 1300°C, were identified above that temperature. The appearance of accelerated creep at the higher temperatures is attributable to formation of microcracks throughout a specimen. The whisker‐reinforced material exhibited better creep resistance than the monolith at 1200°C; however, the superiority disappeared above 1300°C. Considerably high values, 3 to 5, were obtained for the creep exponent in the overall temperature range. The exponent tended to decrease with decreasing applied stress at 1200°C. The primary creep mechanism was considered cavitationenhanced creep. Specimen lifetimes followed the Monkman–Grant relationship except for fractures with large accelerated creep regimes. The creep rupture behavior is discussed in association with cavity formation and crack coalescence.

Transient creep behaviour of hot isostatically pressed silicon nitride

Transient creep is shown to dominate the high-temperature behaviour of a grade of hot isostatically pressed silicon nitride containing only 4 wt% Y2O3 as a sintering aid. Contributing factors to transient creep are discussed and it is concluded that the most likely cause of longterm transient creep in the present study is intergranular sliding and interlocking of silicon nitride grains. In early stages of creep, devitrification of the intergranular phase, and intergranular flow of that phase may also contribute to the transient creep process. The occurrence of transient creep precluded the determination of an activation energy on the as-received material. However, after creep in the temperature range 1330–1430°C for times exceeding approximately 1100 h, an apparent activation energy of ≈ 1260 kJ mol−1 was measured. It is suggested that the apparent activation energy for creep is determined by the mobility and concentration of diffusing species in the intergranular glassy phase. The time-to-rupture was found to be a power function of the minimum strain rate, independent of applied stress or temperature. Hence, creep-rupture behaviour followed a Monkman-Grant relation. A strain rate exponent of − 1.12 was determined.

Rate-Controlling Process of Power Law Creep at High Temperatures in Powder Metallurgy Tungsten Wires

Creep tests and scanning electron microscopy (SEM) observation of grain boundary cavitation are made to decide the most likely mechanism which rate-controls the power law creep at high temperatures in powder metallurgy tungsten wires. The modified Monkman-Grant relation holds for the overall time, the strain to fracture and the minimum creep rate during creep. The activation energy for steady state creep is obtained to be about 130 kJ/mol which is much less than the energies for surface, dislocation, grain boundary and lattice diffusion of tungsten. The value does not approach the activation energy for lattice diffusion as the mechanism of dislocations climb even if the effect of grain boundary cavitation on creep rates is taken into account

Evaluation of the Strength and Creep–Fatigue Behavior of Hot Isostatically Pressed Silicon Nitride

The strength of a commericially available hot isostatically pressed silicon nitride was measured as a function of temperature. To evaluate long‐term mechanical reliability of this material, the tensile creep and fatigue behavior was measured at 1150°, 1260°, and 1370°C. The stress and temperature sensitivities of the secondary (or minimum) creep strain rate were used to estimate the stress exponent and activation energy associated with the dominant creep mechanism. The fatigue characteristics were evaluated by allowing individual creep tests to continue until specimen failure. The applicability of the four‐point load geometry to the study of strength and creep behavior was also determined by conducting a limited number of flexural creep tests. The tensile fatigue data revealed two distinct failure mechanisms. At 1150°C, failure was controlled by a slow crack growth mechanism. At 1260° and 1370°C, the accumulation of creep damage in the form of grain boundary cavities and cracks dominated the fatigue behavior. In this temperature regime, the fatigue life was controlled by the secondary (or minimum) creep strain rate in accordance with the Monkman–Grant relation.

The relationship between transient and steady state creep in AISI 304 stainless steel

The results of constant load creep tests on AISI 304 stainless steel at 873 and 973 K for different test conditions were found to obey first order reaction rate theory first proposed by Webster, Cox and Dorn. The transient creep parameters ϵ T and K were found to have different values in the two stress regimes where the variation of ϵ dot s with stress ( ϵ dot s = Aσ n ) show different values of exponents. For a given set of n, ϵ T and K, the transient and steady state creep obeying same kinetics law, could be described by unique master creep curve. A new relation between ϵ dot s, time for onset of steady state t os and limiting transient creep strain ϵ T is proposed as ( ϵ dot s α · t os )/ϵ T = constant ; this relation along with Monkman-Grant and modified Monkman-Grant relations are tested for all test conditions. Further it is postulated that the values of α and m ( m is the exponent for ϵ dot s in Monkman-Grant relation) equal to unity is a consequence of first order kinetics and that the concept of Monkman-Grant relation extends to totality of deformation and fracture.

Analysis of creep curve by constitutive equations

AbstractCreep curves of 0·5Cr–0·5Mo–0·25V steel have been analysed based on a simple power function of time. The long term creep properties, namely, the creep rate and the rupture lifetimes at low stress levels can be very well predicted by this simple power function. The Monkman–Grant relationship can also be obtained based on the predicted values.MST/1411

Material laws for inelastic analyses on elbows of 12% or 0.5% Cr-steel up to creep rupture for 30 000 hours creep tests at 550°C

Damages on elbows gave rise to a study of their creep and creep rupture behaviour comparatively by inelastic finite element analyses and 30000 hours creep tests. The procedure how the elastic-plastic and creep laws for the monotonic and constant loading have been deduced from test results gained by uniaxially loaded specimens, and the results, are outlined. The description of the creep behaviour due to uniaxial loading up to the rupture strain has been based on the concept of true strains and stresses and an extended and modified Theta-projection method. Among several functions selected for the approximation of experimental strain-time data, two expressions approach them up to rupture within an error of only a few per cent. The methods and results throw new light on the tertiary creep range, the stress dependence of the creep behaviour and the technique of creep tests. Representations showing the stress and time dependence of Norton's coefficients, evaluations of the Monkman—Grant relation and other relations based on the experimental and theoretical data, complete the insight into the creep behaviour of the ferritic steels concerned.

On the cavity-growth-model-based prediction of the stress dependence of time to creep fracture

Abstract A model describing intergranular cavity growth and cavity shape evolution during its growth is applied to the numerical study of the growth of cavities by coupled diffusion and power-law creep, and to predict the stress dependence of time to creep fracture. It is shown that at stresses at which the power-law creep represents an important component of the growth the predicted time to fracture is inversely proportional to the third power of stress independent of the values of the ratio of surface diffusion to grain boundary diffusion conductance, while the minimum creep rate varies with approximately the fifth power of stress. Even if the cavity nucleation process is taken into account, assuming that the nucleation rate is proportional to the power-law creep rate, the predicted time to fracture is not inversely proportional to the creep rate, i.e. to the fifth power of stress. This contradicts the commonly observed proportionality of the product of time to fracture and minimum creep rate to the creep strain to fracture (modified Monkman-Grant (M-G) relationship). The analysis made suggests that the experimentally observed validity of the modified M-G relationship is always associated with the constrained cavity growth which cannot proceed unless accomodated by power-law creep.

The Monkman-Grant relationship

Abstract The interrelationships between the steady creep rate e dot s , time tf to fracture and strain ef to fracture are usually characterized in terms of Monkman-Grant relationships or their modifications. The objective of the present paper is to rationalized the modified Monkman-Grant relationship ( e dot s t f /e f = constant ) on the basis of the intergranular creep fracture model. A generalized intergranular cavity growth model which allows for varying degrees of matrix constraint on cavity growth has been developed for this purpose. The variation of the modified Monkman-Grant constant CMMG with applied stress predicted by such a model corresponds extremely well with the variation of CMMG with stress observed in the literature. The model also explains why CMMG correlates the data better than the originally proposed Monkman-Grant constant.

Standzeit von ZrNbl-Brennelementhüllrohren unter Störfallbedingungen / Lifetime of ZrNb1 fuel cans under accident conditions.

The lifetime of fuel cans under accident conditions is determined on the basis of isobaric-isothermal creep rupture tests in argon and steam at fuel can temperatures of 700˚C to 1000˚C and use of a modified Monkman Grant relation. Experimental values of the parameters in this relation are given

Effect of grain and grain boundary strengths on the life of main creep crack initiation in a notched plate specimen.

Effect of grain and grain boundary strengths on the life of main creep crack initiation in a notched plate specimen was investigated, using an austenitic heat resisting steel. In a range of lower grain strength below about HV 300, the life of main crack initiation increases with an increase in grain strength, independent of grain boundary strength. In a range above HV 300, however, it decreases drastically with increasing grain strength when a specimen has a weaker grain boundary strength. On the contrary, if a specimen has a stronger grain boundary strength, it continues to increase with increasing grain strength. Further, a relationship between the main crack initiation life, ti, and the mean notch opening displacement rate, V^^·m, that is, tiV^^·nm=C (n and C are constant), was obtained which was analogous to the Monkman-Grant relationship. Finally, the effect of grain and grain boundary strengths on ti was discussed in terms of the relationship tiV^^·nm=C, considering the effect of both strengths on V^^m and a critical notch opening displacement at the time of main crack initiation.

Creep and tensile behavior of lead-rich lead-tin solder alloys

The authors report on the tensile and creep deformation of a series of high-lead solders with 0 to 10% tin, over a temperature range of 0 degrees C to 10 degrees C. In these alloys, the yield strength is strongly influenced by the precipitation of the tin phase, which depends on temperature and tin content. The creep rupture behavior follows the Monkman-Grant relationship. The results are generally consistent with a power-low creep mechanism, controlled by dislocation-core diffusion. There is a clear trend to greater creep resistance (lower creep rate at a given stress and temperature) for alloys of higher tin concentration. It is concluded that the mechanical behavior during thermal cycling tests may depend on cycle frequency and temperature range in a manner determined by the evolution of the precipitate microstructure.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Creep and Tensile Behavior of Lead-Rich Lead-Tin Solder Alloys

The authors report on the tensile and creep deformation of a series of high-lead solders with 0 to 10% tin, over a temperature range of 0 degrees C to 10 degrees C. In these alloys, the yield strength is strongly influenced by the precipitation of the tin phase, which depends on temperature and tin content. The creep rupture behavior follows the Monkman-Grant relationship. The results are generally consistent with a power-low creep mechanism, controlled by dislocation-core diffusion. There is a clear trend to greater creep resistance (lower creep rate at a given stress and temperature) for alloys of higher tin concentration. It is concluded that the mechanical behavior during thermal cycling tests may depend on cycle frequency and temperature range in a manner determined by the evolution of the precipitate microstructure.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Application of the dc potential drop technique in investigating crack initiation and propagation under sustained load in notched rupture tests

Creep specimens of IN-X750 with U and V notch geometries have been tested at 700 °C under constant load. The do potential drop technique was employed to measure local deformation, detect crack initiation, and measure crack propagation rates in the notched specimens. Rupture of the U-notched bars and crack initiation in the V-notched bars were found to be controlled by creep deformation. The time to crack initiation and the rupture time can be predicted by using the Monkman-Grant relationship, which was shown to apply to localized crack initiation and multiaxial loading conditions. Sustained load crack growth rates were measured in the V-notched specimens. The dependence of the stage II crack growth rates on the stress intensity factor, the crack initiation, and rupture behavior of IN-X750 can be unified and interpreted with the continuous nucleation and constrained cavity growth model.

Lifetime Prediction Under Constant Load Creep Conditions for a Cast Ni-Base Superalloy

Creep and stress-rupture properties of cast IN-738LC turbine blades have been analyzed to review the suitability of the Monkman-Grant relationship as a reliable life prediction method where tr ε˙sm = C and m and C are material constants. The constants m and C in the Monkman-Grant relationship are temperature dependent and the relationship predicts lives within a factor of ±4 relative to the observed values. A modified form of this relationship is derived where (−b trn1 + tr) ε˙sm1 = K and b, n, m1, and K are material constants. The modified relationship is more accurate and predicts lives within a factor of 2 relative to the observed values. The constants b, n, m, and k are independent of stress and temperature.

Influence of variations in creep curve on creep behavior of a high-temperature structure

It is one of the key issues for a high-temperature structural design guideline to evaluate the influence of variations in creep curve on the creep behavior of a high-temperature structure. In the present paper, a comparative evaluation was made to clarify such influence. The evaluation results showed that, in almost all cases of a creep behavior pattern in which creep strain accumulated during a stress cycle caused significant relaxation of the corresponding deformation-controlled stress in the following cycles, the variations in creep behavior with the creep curve were qualitatively similar to those in fundamental creep properties. On the other hand, in many cases of another creep behavior pattern in which creep strain accumulated during a cycle doesn't cause the significant stress-relaxation in the following cycles, the variations in creep behavior for earlier cycles are different from those in fundamental creep properties. Even in these cases, however, those get qualitatively similar after several cycles when their stress-time histories are stabilized. Additional consideration was given to the influence of the relationship between creep rupture life and minimum creep rate, i.e., the Monkman-Grant's relationship, on the creep damage evaluation. The consideration suggested that the Monkman-Grant's relationship be taken into account in evaluating the creep damage behavior, especially the creep damage variations. However, it was clarified that the application of the creep damage evaluation rule of ASME B.&P.V. Code Case N-47 to the “standard case”which was predicted from the average creep property would predict the creep damage on the safe side.

Creep and fracture of a vitreous-bonded aluminium oxide

Creep and creep-rupture behaviour of a commercial grade of glass-bonded, 96% aluminum oxide was characterized as a function of temperature and applied stress. The creep data were fitted to the classical empirical relation usually used to describe this phenomenon. The apparent activation enthalpy, ΔH = 926 kJ mol−1, and the stress exponent,n = 4.8, lie at the high end of the range reported for two-phase materials, primarily as a result of structural modifications that occur during creep. A stress-modified Monkman-Grant relationship was fitted to the creep-rupture data to give a stress exponent of −4.2. None of the available theories of creep rupture provided a satisfactory description of the present set of data. Analytical electron microscopy was used to characterize the composition and structure of this material. In the as-received material the intergranular phase was a glass of nearly uniform composition. During high-temperature exposure, devitrification of the glass resulted in the formation of various crystalline phases within the intergranular region of the material. Devitrification depended on both the proximity to the surface, where it was most pronounced, and on the state of stress. In this regard, flexural creep samples exhibited extensive crystallization within the tensile region of the flexural specimens, but little crystallization within the compressive cross-section. From the composition of the retained glass, estimates of the viscosity of the glass at the grain boundaries were made and used, in combination with microstructural information, to compare the creep behaviour with available theories of creep. The results of this paper are consistent with percolation and solution precipitation mechanisms of creep deformation. By contrast, cavitation did not seem to play a major role in the creep deformation process.

Comments on the Monkman-Grant and the modified Monkman-Grant relationships

The Monkman-Grant and the modified Monkman-Grant relationships are shown to be a consequence of a simple mathematical analysis of the strain rate-time curves and of a smoothing-out of the scattering in the results produced by the double-logarithmic representation. The analysis is applied to experimental data obtained in Zircaloy-4 and in stainless steel AISI 304.