Showing papers on "Stress relaxation published in 1977"

The temperature and strain rate dependence of the flow stress of tantalum

Abstract: The temperature and strain rate dependence of the flow stress of tantalum was studied between 78 to 800 K at strain rates from 10−5 to 2×104 sec−1. The effect of temperature and strain rate on the lower yield stress can be explained by a model incorporating the combined operation of the Peierls mechanism and dislocation drag processes. The general behaviour of the stress—strain curve at various strain rates and temperatures is analysed in terms of a rate—temperature parameter.

Creep of Nimonic 80A in torsion and tension

Abstract: With the object of observing the influence of stress system, the creep of Nimonic 80A has been studied in torsion and tension over the range of effective stress σ from 100 to 500 MPa and at the temperature 750°C For a given σ, tertiary creep and fracture occur sooner in tension than in torsion, while nucleation of cavities is faster The cavities evidently accelerate creep strain and, since creep strain produces cavities, the behaviour as regards both strain and cavitation is autocatalytic The results are expressed and explained in terms of (σ1/σ), where σ1 is the maximum principal stress, and a predictive law for fracture life is derived from constitutive relations connecting strain, cavity volume, and stress

Predicting the Strain Rate in the Zone of Intense Shear in which the Chip is Formed in Machining from the Dynamic Flow Stress Properties of the Work Material and the Cutting Conditions

Abstract: In previous applications of an approximate machining theory in which account is taken of the strain rate and temperature dependence of the work material flow stress properties it has been found necessary to use an empirical relation to determine the maximum value of the maximum shear strain rate in the chip formation zone. In this paper the machining theory is further developed so that this strain rate can be obtained as part of the solution. Predicted values found in this way are shown to be in excellent agreement with the rather limited number of experimental strain rate results which are available. The paper ends by showing that if the work material is allowed to approach the ideal constant flow stress material usually assumed in slip-line field theory then the predicted strain rates become extremely large. However, it is still found necessary in calculating the corresponding hydrostatic stresses to use the stress equilibrium equations for a variable flow stress material as the variable flow stress terms do not diminish as rapidly as might have been expected.

Creep-fatigue interaction in austenitic stainless steels

Abstract: Low cycle fatigue failures occur by the initiation and controlled growth of a surface crack. The development of crack propagation models, based on continuum mechanics, have enabled successful predictions of fatigue life at both room and elevated temperatures. This paper attempts to extend such models to cover the situations in which creep damage, introduced during periods of stress relaxation, influences the rate of growth of the surface fatigue crack. Equations predicting fatigue life as a function of hold period are in good agreement with experimental data, for Type 304 stainless steel, Type 316 stainless steel and Incoloy-800.

A theory of the initiation of creep crack growth

Abstract: A computer simulation of the time dependent development of the plastic zone ahead of a crack loaded in uniform tension was performed. The material was assumed to deform according to a creep law relating the local strain rate to the local stress. The plastic zone was modelled by an array of edge dislocations coplanar with the crack. For a given time the stress was found to be uniform in a region ahead of the crack. This region increased and the local stress decreased with increasing time. The distribution of dislocations in the zone at a given time was found to be almost the same as that given by the Bilby, Cottrell and Swinden model (1963) if the friction stress in that model was replaced by an apparent friction stress equal to the uniform stress ahead of the crack. This apparent friction stress is dependent on both the applied stress and time. Assuming a critical crack opening displacement (COD) or a critical value of theJ integral,J c, to be the criteria for the onset of the creep crack growth the initiation time can be calculated using the results of this study. A good agreement between the theory and experiment is obtained for two different CrMoV steels. This comparison with experiments suggests that the COD is an appropriate crack growth initiation parameter for both ductile and brittle materials whilstJ cdoes not seem to be applicable in creep fracture.

The existence of a friction stress for high-temperature creep

Abstract: Recent experimental work indicating the existence of a friction stress, σ0 during high temperature creep is reviewed. The friction stress concept has been used to alter the normal power law creep equation to the relationship e=B(σ−σ0)4. It is contended that linear treatment of the decremental unloading data used to determine ao is inadequate in view of the inherent nonlinearity of the stress/strain rate relationship. A modified analysis which accounts for the power law nature of the creep process is proposed in which these data are treated in a manner similar to stress relaxation data. On this basis, the evidence for a friction stress in a pure metal and in a precipitation-hardened alloy is shown to be inconclusive. However, the existence of a threshold is confirmed for a dispersion-strengthened alloy. In addition, further experimental results are presented for pure lead in which delay times of zero creep are not observed for small unloadings. Since these delay times are a necessary part of the de...

Experimental tests of constitutive relations for polymers undergoing uniaxial shear flows

Abstract: Stress development at the onset of steady shear flow and stress relaxation from steady state were measured in a stiffened Weissenberg Rheogoniometer over wide ranges of shear rate for three polystyrene solutions. Time dependent shear stressσ and first normal stress differenceN 1 were obtained from the torque and axial thrust. From extensive auxiliary tests we believe these data to be free of spurious effects associated with instrument compliance. The solutions have zero shear viscosities of 890, 3900 and 67 000 poise. Tests for consistency with strain rate constitutive models were made using thevan Es-Christensen relation and with relative strain models using theKearsley-Zapas relations. Substantial deviations were found in both cases. TheMarrucci model was also examined. As in theCarreau model B, the predicted start-up curves from theMarrucci model are in general qualitative accord with observations, but some systematic quantitative discrepancies remain.

Constitutive law for nonlinear creep of concrete

Abstract: Endochronic theory, previously proposed and verified for multiaxial time-independent experimental data, is extended to nonlinear long-time creep at high stress and is compared with available uniaxial creep data. The extension is based on a Maxwell chain model, each unit of which is characterized by its own intrinsic time, an independent variable whose increments depend both on time and strain increments. The dependence on the latter involves the previously determined hardening and softening functions. Aging is included and the previously established Maxwell chain model for low-stress creep with aging is obtained as a special case. The theory also describes the decrease of strength with load duration when the compression is high, gives an increase when the compression is low, and yields the additional inelastic strain accumulation due to cyclic load. An effective and numerically stable algorithm for timestep integration of structural response, permitting the time steps to be increased with the load duration, is presented.

The role of diffusion in determining the controlling creep mechanisms in Al-Zn solid-solutions: Part II

Abstract: The theoretically appropriate diffusion coefficients for creep in binary solid solutions are verified in Part I. Furthermore it is observed that the observed composition dependence of the steady-state creep rate for Al-Zn alloys may be described by these diffusion coefficients. Part II further examines the creep behavior of the Al-Zn system. Stress exponent and activation energy measurements indicate that a transition from climb-controlled to glide-controlled creep occurs as the Zn concentration increases. It is found that the observed creep behavior can be explained by a combination of climb and glide controlled creep processes. Glide creep is dependent on the chemical diffusivity which approaches zero at the miscibility gap composition and temperature. This causes a minimum in the creep rate at the miscibility gap composition. By using a sequential summation of a semiempirical climb equation and the Cottrell-Jaswon glide equation, the absolute magnitude of the observed creep rate can be rationalized for all compositions. The observed behavior of the stress exponent and activation energy is also predicted.

The stress dependence of the crack growth rate during creep

Abstract: An equation is derived for the crack growth rate under creep conditions. In the model, the propagation of a grain boundary crack is controlled by the plastic growth of cavities located in the grain boundaries ahead of the crack. It is assumed that the cavities grow by power law creep in the elastic crack tip stress field. Hence, the stress dependence of the crack velocity is provided through the elastic stress intensity factor, i.e., dC/dt=BK . The cavity spacing, λ, appears as an important factor in the coefficient,B ∝ λ−(p−2)/2. At large values of λ, corresponding to less severe creep damage in the grain boundaries, the above equation would predict very low values for the crack velocity. Under such conditions, we suggest that another mechanism, whose stress dependence is provided through the net section stress, becomes active, i.e., dC/dt=B′σ net ′ . Since λ increases with decreasing applied stress, one should observe the σnet correlation at low stresses. The results of recent creep crack growth experiments which tend to support this hypothesis are presented.

Interpretation of high-temperature creep of type 304 stainless steel

Abstract: The elevated-temperature creep behavior of Type 304 stainless steel is examined in terms of the measured effective and internal stresses. Results show that the mean effective stress is related to the applied stress by a power law of the form σ* = α(σ)β, where the constants α and β are functions of temperature. The dependence of creep rate on applied stress follows a power law, and the stress exponent is dependent on temperature. The latter behavior arises from the variation in the mean effective stress with applied stress and temperature. The creep rates are also described as a function of effective stress. The dislocation velocity-stress exponent obtained from stresschange tests is higher than the effective stress exponent evaluated from creep data. The dependence of creep rate on temperature at various values of effective stress yields a total activation energy of approximately the same magnitude as self-diffusion.

Activation energy of creep of concrete under short-term static and cyclic stresses

Abstract: Synopsis A theoretically derived relation which has previously been shown by other authors to agree well with static creep is extended and transformed so that cyclic creep can be related to static creep as a function of the range of stress and time. Experimental results for periods under load up to 160 h show excellent agreement with the theory. The time dependence of the relation between cyclic creep and static creep is unclear from the short-term data used, but long-term data should clarify the function. With the relation fully defined, it would be a useful extension to the methods of predicting creep given in a number of codes of practice.

On stretching maxwell models

Abstract: The transient response of selected Maxwell models to various modes of spatially homogeneous uniaxial elongation is studied qualitatively. New results include the effect of non-linearity on the creep curve (constant stress elongation), which leads to a delay in attaining steady flow, and the difference in recoverable strain estimates obtained from extrapolating the linear part of the creep curve back to zero time and from reducing the applied stress to zero. Constant force elongation is found to lead to mathematical difficulties (non-existence of solutions) for some models including the lower convected Maxwell model. The notion of a “limiting stretch rate” is re-examined critically and is seen to have meaning only once a mode of elongation is specified. For example, the maximum rate of strain attainable in constant force elongation of an upper convected Maxwell model is twice that attainable in constant stress elongation, and in fact any desired constant rate of strain may be obtained provided only that the stress is increased rapidly enough. The correspondence of a class of rate equations (Gordon-Schowalter-Everage) to integral equations based on non-linear strain measures due to Seth is established for elongational flow and is exploited to obtain initial values of strain and rate of strain when a load is applied suddenly. Extension of the results to more complicated models is discussed and the relative merits of some of the simple (three-parameter) models are examined.

Studies in Non‐Isothermal Rheology

Abstract: Almost all basic work in rheology, both experimental and theoretical, has dealt with isothermal flows, with the temperature being held constant during any one measurement. The present paper presents systematic studies of the nonisothermal behavior of two polystyrenes (a commercial sample and a sample of sharp molecular weight distribution). The experiments involve stress growth and stress relaxation during elongation in an Instron tensile tester, with rapid changes of temperature being imposed during the pulling and after it. Generalized non‐isothermal viscoelastic theory is proposed and tested. The generalized time‐temperature superposition involved there works well in simple stress relaxation (when the temperature changes are imposed after the pulling) but in the simultaneous type of experiments (when the temperature changes are imposed during the pulling), the accommodation to the new state seems to be more rapid than expected from theory.

Effect of stress and temperature on the creep and rupture behavior of a 1.25 Pct chromium—0.5 Pct molybdenum steel

Abstract: The creep and stress rupture behavior of a normalized 1.25 pct chromium-0.5 pct molybdenum steel has been investigated over a temperature (T) range of 510 to 620°C and a stress(σ) range of 65 to 425 MN/m2. The creep rate ( $$\dot \in $$ ) and time to rupture (t r ) data have been analyzed in terms of the general expression $$\dot \in $$ ort r -A σn exp (Q/RT), whereA is a constant,n is the power exponent of stress,Q is an empirical activation energy for the rate controlling process andR is the universal gas constant. At each temperature, the logarithmic plots of creep rate and time to rupture as functions of stress consist of two linear segments, separating the data into low stress and high stress regimes. The stress exponent has approximate values of 4 and 10 in the low stress and high stress regimes respectively in the appropriate expressions for both creep rate and for time to rupture. The activation energy has values of 367 and 420 kJ/mole in the low stress regime for time to rupture and creep rate respectively. In the high stress regime, the respective values of activation energy are 581 and 670 kJ/mole. Fractographic observations show that the changes from low stress to high stress behavior in creep rate and time to rupture approximately coincide with the transition in fracture mode from intergranular to transgranular cracking as well as with the transition in the rupture ductility from a region of linear variation with stress to one of constant ductility. These observations suggest that the transition from low stress to high stress behavior may be associated with a change in deformation mode from predominantly grain boundary sliding at low stress to transgranular matrix deformation at high stress. Analysis of the creep rate data based on this premise enables calculation of the ratio of the contributions of the grain boundary sliding mode to the total deformation (e gb /e T ) at various values of stress and temperature. Results of this analysis are consistent with numerous experimental observations reported in the literature.

Physical and chemical stress relaxation of a fluoroelastomer

Abstract: Stress relaxation measurements were made at various temperatures on V-747-7, a commercial high-temperature rubber formulation from the Parker Seal Company. The data were analyzed by separating the chemical and physical relaxation processes by a method described in an earlier publication. The chemical relaxation process was found to be Arrhenius with an activation energy of 35.7 kcal/mole. The results allow us to predict the relative useful lifetimes of this material up to approximately 320/sup 0/C.

Transient Shear and Elongational Data for Polyisobutylene Melts

Abstract: For a commercial polyisobutylene, at room temperature, stress relaxation after a sudden imposition of a shear or elongational strain has been performed in the limit of linear viscoelasticity. Transient shear and elongational stresses have been determined in the non‐linear region by using a Universal Instron Testing Machine. While for shear flow steady‐state conditions were reached in some cases, the elongational results are only transient because the experimental procedure gives a rate of stretching which decreases in time. Some steady shear results have been obtained at higher temperatures with a capillary viscometer. The results have been interpreted by means of a one‐parameter model which attributes the non‐linearities arising from the change in the spectrum of relaxation times to modification of the entangled network. The Bogue‐White model has been also considered for comparison.

Application of mechanical state relations at low and high homologous temperatures

Abstract: The rate dependent behavior of a 50 Sn-50 In alloy has been characterized by means of load relaxation experiments over a range of homologous temperatures from 0.2 to 0.88. The data can be represented over its entire range by use of a power law description of dislocation dynamics, modified to incorporate evolution of structure-dependent variables. At low homologous temperatures a macroscopic internal stress apparently exists; this stress vanishes at higher homologous temperatures. The results indicate that intermediate and high temperature load relaxation can be interpreted in terms of an evolving structure. Under this analysis the material passes through a continuous succession of mechanical states during a relaxation event.