Change In Stress Exponent Research Articles

Effect of Loading Rate on Creep Properties of HgCdTe Epitaxial Films

Nanoindentation creep studies were performed on Hg1-xCdxTe (x~0.29) epitaxial films using different loading rates of 0.5 mN.s-1, 1 mN.s-1, 2 mN.s-1 and 4 mN.s-1, keeping a constant peak load of 10 mN. A constant hold time of 20 sec at peak load was maintained for all experiments. The effect of loading rate on creep behaviour of material has been investigated. Creep displacement had shown increasing trend with increase of loading rates. Stress exponents were extracted using creep curve fitting with an empirical equation. A strong dependence of loading rate on stress exponent was observed. The value of stress exponent was found varying in the range 0.60-1.76, 0.96-2.23, 0.98-2,87 and 0.90-2.81 for loading rates 0.5 mN.s-1, 1 mN.s-1, 2 mN.s-1 and 4 mN.s-1, respectively. The change of stress exponent was attributed to change of creep mechanism. Hardness and elastic modulus were extracted from load-displacement curves and it was found that with the increase of the loading rate hardness increases, while elastic modulus remains constant. A correlation between variation of hardness and creep displacement has also been presented.

Creep Behavior of As-Cast Mg-10 wt.%Sn and Mg-10 wt.%Sn-3 wt.%Al-1 wt.%Zn Alloys: A Comparative Study

The present investigation highlights the creep deformation and rupture behavior of indigenously produced as-cast Mg-10 wt.%Sn-3 wt.%Al-1 wt.%Zn (TAZ1031) and Mg-10 wt.%Sn (T10) alloys. Conventional creep tests were conducted at 423 K (150 °C) in the stress range of 30-45 MPa and at 45 MPa in the temperature range of 423-453 K (150-180 °C) for both the alloys. The nature of creep curves was found to be identical for both the alloys with short primary and secondary creep regime, followed by extended tertiary creep region. The creep resistance of the TAZ1031 alloy was better than the T10 alloy. The former exhibited reduced minimum creep rate and enhanced creep rupture life under identical creep test conditions with respect to the latter. The change of minimum creep rate (έmin) followed a power-law relationship with a change in applied stress (σ) for both the alloys with a significant change in stress exponent (n) value. Activation energy for creep deformation of TAZ1031 alloy (~ 117 kJ/mol) was found to be higher than T10 alloy (~ 105 kJ/mol). Fine secondary Mg2Sn precipitates within the α-Mg matrix and primary Mg2Sn, Mg17Al12 and MgZn2 precipitates along the grain boundaries improved the creep properties of TAZ1031 alloy. On the contrary, the threshold stress required for creep deformation was found to be significantly low in TAZ1031 alloy due to the presence of Mg17Al12. Both creep damage analysis and dimpled fracture surfaces revealed necking dominated creep deformation for the alloys. SEM studies revealed the absence of creep cavities along grain/dendritic boundaries for the investigated alloys, which substantiated the formation of dimpled fracture surfaces during creep deformation.

Evolution of Microstructure and Creep Behavior in an Fe-Ni-Cr-Nb-C Alloy during Service in Hydrocarbon Cracker Tubes

Heat resistant, cast austenitic Fe-Ni-Cr-Nb-C alloy tubes are used by the petrochemical industry to transport hydrocarbons at temperatures between 850 and 1050 °C. Exposure to carbon from the process stream and nitrogen from the air causes severe carburization and nitridation in the tube walls, which influences creep resistance and degrades their ductility. A better understanding of these processes would enable their service life to be extended. To this end, we report the results of an experimental and computational study of the changes in microstructure and creep behavior in a representative alloy during service. The microstructure of the fresh material is compared to that of 8- and 10-year-old tubes. The results confirm the presence of M23C6, M7C3, and M2(CN) phases reported in prior studies, and also reveal the nucleation and growth of the carbo-nitride phase M6(CN). We show that the spatial variations of carbide and nitride particle volume fractions in aged tubes can be predicted by a simple reaction–diffusion equation. In addition, the uniaxial compressive creep response of the fresh and aged tubes was obtained as functions of temperature and strain rate. The materials deform by power-law creep, with strain rate versus stress relation as $$\dot{\varepsilon } = A\sigma^{n}$$. Aging reduces the stress exponent from n = 8 in fresh tubes to n = 5 in aged tubes, and also reduces the pre-exponential coefficient A. Tests on model alloys with composition identical to that of the matrix combined with finite element simulations of creep in model microstructures reveal that Cr depletion is responsible for the change in stress exponent, while the change in A is caused by the increase in particle volume fraction. By combining the microstructure-scale simulations of creep with the predictions of the reaction–diffusion model of microstructure evolution, the creep behavior of tubes left in service beyond 10 years is estimated.

Flow laws and fabric transitions in wet quartzite

We investigated quartzite flow laws based on data from 21 different experimental studies on samples deformed with added water at temperatures from 700 to 1200°C. Two clear trends emerge: one with a power-law stress exponent of n=4±0.3 and the other, at higher stresses and lower temperatures, with a stress exponent of n=2.7±0.3. The change in stress exponent indicates a transition in the rate-limiting process of dislocation creep. The deformation conditions where the change in n occurs also correlate with conditions where a distinctive change in the c-axis fabric is observed for samples deformed in general shear. At low stresses, quartz fabrics are defined by a Y-max (where c-axes align parallel to the Y direction of the strain ellipse), suggesting easy slip on the prism <a> system. At higher stresses quartz fabrics indicate easy slip on the basal <a> system. The correlation between the stress exponents and c-axis fabrics suggests that the flow law transition results from a concomitant switch in the dominant slip system and the slip system that rate-limits deformation. Alternatively, recent studies on both experimental and natural samples provide evidence for dislocation-accommodated grain boundary sliding (disGBS) in quartz aggregates; microstructures and mechanical data acquired on samples deformed at conditions near the transition between the n=4 and n=2.7 flows laws are indicative of this process, providing evidence for a rheological model similar to that proposed for ice and olivine. Extrapolation of these newly constrained flow laws delineates estimated deformation conditions where the Y-max and basal <a> fabrics are preserved in the crust. These results provide further support for the application of quartzite flow laws to investigate the rheology of the continental crust and motivate more analyses on the grain size dependence of creep in quartz aggregates.

On the physical models for predicting the long-term creep strengths and lifetimes of modified 9Cr-1Mo steel

The present study examines the physical models for predicting long-term creep strengths at different application temperatures using creep parameters determined from short term creep tests for the modified 9Cr-1Mo steel, which is a candidate material for design and construction of Gen-IV nuclear power plants with a specified service life of minimum 60 years. It is demonstrated that the complex stress and temperature dependence of minimum creep rate of this steel grade can be rationalised in a simple manner on the basis of the new power law creep equation that incorporates the tensile strength σTS. The activation energy of creep determined on this basis does not depend on stress and the stress exponent depends only on the stress ratio σ/σTS region but not on temperature. This allows the new power law equation to be used in combination with Monkman-Grant relationship to predict long-term (60 years) creep strengths and lifetimes at different application temperatures using creep parameters determined from creep tests lasting less than 6000 h. The reliability of these predictions is discussed and the causes for possible over-predictions are considered. It is also shown that the previously observed stress dependence of activation energy of creep is simply the consequence of the conventional method by which this parameter is determined and hence has no physical significance. The change in stress exponent in respective stress ratio σ/σTS regions is not due to the change in creep mechanism but may be attributed to microstructure changes under creep load in respective σ/σTS ranges.

Creep strength degradation of ASME P23/T23 steels

Creep behavior of ASME P23/T23 steels was investigated and analyzed, focusing on creep strength degradation in the long-term. Creep rupture strength at 898 and 923 K dropped in the long-term in both P23 and T23 steels. The stress exponent of minimum creep rate at 898 and 923 K was 7.8–13 for higher stresses and 3.9–5.3 for lower stresses in the P23/T23 steels. The change of stress exponent with stress levels was consistent with the drop in creep rupture strength in the long-term. The Monkman–Grant rule was confirmed in the range examined in P23 steel, while the data points deviated from the rule in the long-term in the case of T23 steel. The creep ductility of P23 steel was high over a wide stress and temperature range. On the other hand, in T23 steel, creep ductility at 898 and 923 K decreased as time to rupture increased, and then recovered again in the long-term. Fracture mode changed from transgranular to intergranular fracture in the long-term at 898 and 923 K. At 923 K, the rapid tertiary creep was observed under lower stresses in T23 steel, comparing with P23 steel.

Extrapolation of short-term creep rupture data—The potential risk of over-estimation

This work deals with the creep behaviour of 9–12% Cr steels in the steady-state (secondary) creep regime in order to enable a more detailed and exact description of the creep rupture strength on the basis of the Monkman–Grant relation. The stationary creep behaviour has been investigated by evaluating the creep rate and the change of stress exponent of established grades of high temperature creep resistant steels using the so-called back-stress concept. A change in creep mechanism with applied stress is clearly identified in the creep rupture curves. The impact of this change is discussed and the huge potential for over-estimation of creep strengths from extrapolated short-term creep rupture data is emphasized.

Grain Size-Sensitive Creep in Ice II

Rheological experiments on fine-grained water ice II at low strain rates reveal a creep mechanism that dominates at conditions of low stress. Using cryogenic scanning electron microscopy, we observed that a change in stress exponent from 5 to 2.5 correlates strongly with a decrease in grain size from about 40 to 6 micrometers. The grain size-sensitive creep of ice II demonstrated here plausibly dominates plastic strain at the low-stress conditions in the interior of medium- to large-sized icy moons of the outer solar system.

Analysis of steady state creep behaviour of 9–12% chromium ferritic–martensitic steels

The present work deals with the creep behaviour of 9–12% Cr steels in the steady state (secondary) creep regime in order to enable a more detailed and exact description of the creep rupture strength on the basis of the Monkman– Grant relationship. Special attention is paid to the microstructural aspects. The steady state creep behaviour has been investigated by evaluating the creep rate and the change of stress exponent of already established grades of high temperature creep resistant steels.

Deformation characteristics of polysynthetically twinned (PST) crystals during creep at 1150 K

The creep deformation characteristics of a lamellar polysynthetically twinned (PST) crystal of the composition Ti–48 mol% Al was investigated as a function of the lamellar orientation with respect to the compression axis and the applied stress. The creep resistance of hard PST orientation with the lamellar plates parallel or perpendicular to the compression axis was substantially higher than that of soft orientations with their lamellar plates oriented at intermediate angles to the compression axis. This fact could be associated with the predominant deformation of the hard orientations by deformation modes with the slip plane inclined to the lamellar interfaces in contrast to the predominant deformation of the soft orientations by deformation modes with the slip plane parallel to the lamellar plates. In the soft orientations, mainly straight ordinary dislocations with the Burgers vector b=1/2[1-10] aligned parallel to the lamellar interfaces were encountered in domains with a high resolved shear stress as well as in domains with no resolved shear stress. In the hard orientations, ordinary dislocations b=1/2[110] and superdislocations with a Burgers vector of the type b=1/2〈112] were observed. Despite a high resolved shear stress in certain oriented domains, superdislocations of the type b=〈101] were not found to play a considerable role during creep deformation under the investigated conditions. Cross twinning contributed to the deformation in favourably oriented variants, but twinning parallel to the lamellar interfaces was much more pronounced in the soft orientations leading to a substantial lamellar refinement. This microstructural hardening during creep results in the observed stress exponents of the soft orientations near unity at high stresses. A change in stress exponent from near unity at high stresses to about 9 at low stresses occurs at about 200 MPa. A critical stress of about 200 MPa for parallel twinning is proposed as a reason for the change in stress exponent.

Steady state creep behaviour of particulate-reinforced titanium matrix composites

The steady state creep behaviour of unreinforced Ti, TiTi 2C and TiTiBTi 2C composites has been examined in the temperature range 823–923 K. It is shown that the creep deformation of unreinforced Ti is governed by climb-controlled creep mechanism for which the stress exponent is between 4.1 and 4.3 and the activation energy is 236 kJ mol −1. For composites, the stress exponents are between 6 and 7 at 823 K but are similar to unreinforced Ti at 923 K. The measured steady state creep rate of composites is found to be 2–3 orders of magnitude lower than unreinforced Ti in the investigated temperature range. It is then established that the origin of creep strengthening at 823–923 K is due to the combined effects of increased modulus of composites and the refined microstructure. It is further shown that the change of stress exponent of composites at 823 K is because of the change in creep mechanism from lattice-diffusion controlled dislocation climb to pipe-diffusion controlled dislocation climb. By analyzing the creep data, a modification in the dimensionless constant, A = 3.2 × 10 5 exp(−24.2 V r) for lattice-diffusion regime and A = 9.4 × 10 5 exp(−28.1 V r) for pipe-diffusion regime, where V r is the volume fraction of reinforcements, is suggested to account for the influence of reinforcements on creep kinetics.

Impression test of 63Sn37Pb eutectic alloy

Impression creep and stress relaxation experiments on the SnPb eutectic alloy were carried out in the RSA II instrument modified to use a 0.5 mm diameter cylindrical punch under 1.5–47 MPa punching stress and within a temperature range of 25 °C to 110 °C. Based on a power law between the impression velocity and stress or between the stress rate and stress, the exponent increased with stress from 1 to 3.5 within the temperature range 80–110 °C and 2.5 to 6 within the range 25–65 °C. These exponents were generally comparable to those reported in the literature. Because of the change of stress exponent, several mechanisms have been proposed. However, the stress dependence was found to obey a hyperbolic sine function of stress for all the stresses and temperatures studied. Similarly before using the hyperbolic sine function, the activation energy was found to increase with stress, an abnormal behaviour. Fortunately, after using the hyperbolic sine function, a single activation energy, 55 kJ mol −1 was obtained. Based on the present data, a single mechanism of interfacial viscous shearing between the two eutectic phases is proposed for both creep and stress relaxation. In addition to the effect of stress and temperature, the impression velocity based on this model should be directly proportional to the punch radius and inversely proportional to the nth ( n = 1–3) power of the size of phase particles. These predictions are consistent with available information in the literature.

High temperature creep transitions in single crystalline Ni3Al(Ta, B)

The high temperature (T= 1083–1388 K, 0.65–0.84Tm) creep behavior of single crystalline Ni3Al(Ta, B) was investigated. A change in the creep characteristics as a function of applied stress was observed at the uppermost testing temperatures of 1288 and 1388 K. At low applied stress levels the Norton law stress exponent is equal to 4.3; for higher stresses the stress exponent is equal to 3.2. Different creep curves were observed, depending on the value of the stress exponent. The change in stress exponent and nature of the creep curve correspond to a change in the controlling deformation mechanism from dislocation climb to viscous dislocation glide for Ni3Al(Ta, B). The experimentally observed transition stress values between climb and viscous glide are in good agreement with values predicted from theory, assuming that the major force retarding viscous dislocation glide in Ni3Al(Ta, B) is the antiphase boundary interaction.

Superplastic creep of eutectic tinlead solder joints

This paper presents experimental evidence that as-solidified eutectic Pb-Sn solder joints can exhibit superplastic behavior in shear creep loading. Stepped load creep tests of as-solidified joints show a change in the stress exponent from a high value typical of con-ventional creep at high stress and strain rate to a superplastic value near 2 at lower stress and strain rates. In addition, the change in stress exponent is accompanied by a change in the activation energy for creep from a value near that for bulk self-diffusion (20 kcal/mol) to a value near that for grain boundary diffusion (12 kcal/mol). The total shear deformation of joints in stress-rupture tests performed at 65° C are found to ex-ceed 150%. The concomitant observation that quenched solder joints creep faster than air-cooled ones is attributed to a grain, or phase, size dependence of the strain rate. The source of superplastic behavior is a fine, equiaxed microstructure. It is not yet clear whether the superplastic microstructure is present in the as-solidified joint, or develops during the early stages of plastic deformation.

On the transition between dislocation and diffusion creep

Abstract It has become common to represent different creep mechanisms as areas on ‘maps’ with sharp boundaries delineating such areas and indicating the conditions of predominance of each mechanism. These boundaries represent transition stages and the present contribution attempts to clarify the nature of the transition between dislocation and diffusion creep. It is concluded that dislocation- and diffusion-creep mechanisms may occur simultaneously over a wide range of strain rate, but in distinct regions of each grain, and that the form and extent of their individual contributions when combined in a physically plausible manner lead to a gradual change in stress exponent. Two consequences arising from this approach are that new methods of extrapolation of creep data become apparent and that the relative contributions of dislocation and diffusion creep may conceivably be identified by the regions which become free of particles in certain materials.

The Effect of Particle Size and Spacing on Creep of Two-Phase Copper–Cobalt Alloys

The effects of variations in particle diameter and spacing on the steady creep rate (έ s ) of three copper–cobalt alloys containing 0·88, 2·48, and 4·04%Co have been studied over a range of stresses at 712 K. At constant particle size and spacing, the stress (σ) and temperature-(T) dependence of έ s for each alloy can be described as <disp-formula> <mml:math> <mml:mrow> <mml:msub> <mml:mrow> <mml:mover> <mml:mi>ɛ</mml:mi> <mml:mi>˙</mml:mi> </mml:mover> </mml:mrow> <mml:mi>S</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>A</mml:mi> <mml:msup> <mml:mi>σ</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:mtext> exp</mml:mtext> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:mi>R</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> </disp-formula>A change in stress exponent, n, and activation energy for creep, Q c , occurs at a stress comparable with the macroscopic yield stress. It is proposed that with stresses < YS, when n ≃ 4·5 and Q c ≃ 140 kJ/mol, only limited deformation of the grains takes place and creep is attributable primarily to grain-boundary sliding and accommodating deformation. In the high-stress regime, when n ≃ 12 and Qc ≃ 210 kJ/mol, deformation occurs both in the grains and in the grain-boundary regions. For each alloy tested at σ > YS, έ s decreases with increasing particle diameter until a minimum value is reached and then increases rapidly with further increase in particle size. The decrease in έ s appears to be a result of the increase in work done by the dislocations in cutting particles as their size increases, until at maximum creep-resistance the dislocations are forced to bow between the particles. The creep rate increases with further increase in particle size and spacing as dislocation bowing becomes progressively easier. Under all conditions, the effect of particles on the creep rate is shown to be largely a consequence of their effect on the rate of recovery.