Showing papers on "Stress relaxation published in 1979"

Characterization of the stress relaxation curves of solid foods

Abstract: Relaxation curves of Agar gel, apple, bologna sausage, bread, cheddar cheese, pear and potato specimens, at various deformation levels, were normalized and fitted to the equation: [F0 - F(t)J /F, = abt/(1 + bt) where F, is the initial force, f(t) the force after time t and a and b constants. Unlike other equations (e.g. a series of exponential terms derived from a Maxwellian model), this equation contains only two constants and these are directly related to the curve shape features. This enables simple comparison between the shape characteristics of curves of different materials. Similarly, the equation facilitates quantitative evaluation of the effects of the straining history on the shape of the stress relaxation curves of solid foods.

Relation between viscoelasticity and shear-thinning behaviour in liquids

Abstract: The shear-thinning behaviour of a liquid is represented in terms of a relaxation timeλ, defined by the ratioη 0/G0 of initial viscous and elastic constants. The relationship provides a very simple basis for the evaluation ofλ andG 0 from viscosity/shear data. Results are compared with relaxation times and moduli from primary normal-stress measurement, from stress relaxation and from direct measurement of recoverable shear strain. Good agreement is found but there is experimental evidence the recoverable shear strainγ e is related to normal stressN 1 and shear stressσ byγ e = N1/3σ, which does not agree with the theoretical prediction of eitherWeissenberg orLodge.

An experimental study of the influence of carbon black on the rheological properties of a polystyrene melt

Abstract: A broad range of experiments on carbon black filled polystyrene melts shows the reinforcing effect of the filler. This study represents one of the most extensive investigations of a series of highly filled polymer melts. Stress relaxation and dynamic experiments characterize the small strain behavior while the steady state shear viscosity, normal stresses, and elongational flow experiments describe the large strain deformation rate response. Extrudate swell and unconstrained shrinkage of extrudates are also measured. Highly filled systems exhibit yield values. This is seen in the dynamic experiments and in the shear and elongational viscosities. Viscosity does not level off at finite values with decreasing deformation rate but continues to increase in an approximately inverse manner. This corresponds to yield values of order 5 × 105 dynes/cm2. The storage modulus also does not tend to zero at low frequencies. The small strain dynamic properties and stress relaxation results suggest high memories for small strain experiments. Txtrudate swell values are however small and the systems exhibit minimal delayed recovery. The implications of this are considered. Generally it is argued that at volume loadings between 10 and 20 percent, the system takes on the characteristics of a gel and the response is similar to that of a Schwedoff body.

An experimental study of room-temperature rate-sensitivity, creep and relaxation of AISI type 304 stainless steel

Abstract: T he spuniaxial viscoplastic behavior of AISI Type 304 stainless steel was investigated by tensile tests at various strain-rates (10−8−10−2s−1), and by short-term creep and relaxation tests up to 5 h. Instantaneous large changes in strain-rate were also performed during monotoniC and cyclic loading. A servocontrolled testing machine and displacement measurement on the specimen gage length were used for all tests. The results show significant rate-sensitivity, creep and relaxation. Test histories involving loading and unloading with positive loads up to 15% strain show that the relaxation behavior in the plastic range depends only on the strain-rate preceding the relaxation test and is independent of the strain magnitude. Also, the relaxation behavior is uniquely related to the stress changes corresponding to instantaneous large changes in the strain-rate during tensile tests. Completely reversed strain-controlled loading gradually changes the stress change/strain-rate change behavior. Annealed specimens and specimens loaded to a cyclic steady-state differ not only in their work-hardening characteristics but also in their rate-dependent behavior. In the cyclic steady-state, different hysteresis loops are traced for different strain-rates with fully reversible transitions from one hysteresis loop to another under strain-rate changes. These results support the notion that the viscoplastic behavior can be represented by piecewise nonlinear viscoelasticity.

Dynamic deformation of polycrystalline alumina

Abstract: Using one‐dimensional strain conditions, the dynamic stress‐wave response of polycrystalline Al2O3 was measured with interferometry in both stress‐wave loading and unloading to about 16 GPa and with slanted resistor gauges in loading to about 50 GPa. The stress‐wave loading and unloading measurements were of high resolution and showed a 9.1‐GPa elastic precursor wave (velocity 10.9 km/s) followed by a slower dispersive permanent deformation wave. Unloading was elastic in the stress range of these experiments. Both loading and unloading wave propagation were modeled well with a Maxwellian elastic‐stress‐relaxing model with a yield stress of 5.8 GPa and a relaxation time of 70 ns. The rate‐dependent model correctly predicts both the dispersion of the permanent deformation wave and the unloading‐wave behavior. The bulk pressure‐volume behavior of alumina is given by the shock‐velocity–particle‐velocity relationship of Us=8.14 +1.28up (km/s). Thermodynamic corrections to the dynamic bulk response yielded isot...

A uniaxial viscoplastic model based on total strain and overstress

Abstract: A previously proposed, uniaxial differential constitutive equation (E.R. C ernocky and E. K rempl , 1979a, b), nonlinear in the Cauchy stress and the engineering strain but linear in the stress and strain-rates, is specialized to an overstress model. It is shown by qualitative arguments that the solutions correspond to typical room-temperature viscoplastic behavior of AISI type 304 stainless steel. Two unknown coefficient functions are determined by extrapolation of room temperature relaxation data for this steel. The stiff first-order nonlinear differential equations are then numerically integrated for a variety of test histories. These include strain control with strain-rates from 10 −6 to 800s −1 , stress control with stressrates from 1.95 kPa s −1 to 19.5 MPa s −1 , instantaneous large changes in strain-rate and stress-rate, and partial unloading and reloading in strain and stress control and tension-tension cyclic creep. The computed results show good qualitative agreement with tests. Based on these results we consider that the model is a good representation of metal deformation behavior as long as the overstress does not change sign.

Mechanisms controlling creep of single phase metals and alloys.

Abstract: The physical mechanisms that control creep of single phase metals and alloys are reviewed Attention is given to both steady state and non-steady state properties The evolution of dislocation substructure in the course of primary creep is followed for both pure metals and solid solution alloys in an effort to demonstrate its dominant role in creep It is shown that the subgrain size and dislocation density scale in a natural way with the applied stress The long range internal back stresses that are responsible for creep anelasticity are shown to be determined not only by the scale of the substructure but also by the bias of the applied stress Creep transients following load changes are also described and interpreted in terms of the nature and properties of the creep substructure In addition, the characteristics of steady state creep are described by referring to the extensive phenomenological evidence which supports the concept that steady state creep at high temperatures is controlled by lattice self diffusion It is suggested that the diffusion controlled recovery and thermally activated glide approaches to creep should be complimentary rather than competitive In general, dislocation motion can occur either as a result of thermal activation past obstacles or as a consequence of obstacle recovery We argue that the inherently inhomogeneous dislocation substructures that form during creep produce inhomogeneous stresses that enhance the rate of obstacle recovery in the “hard” regions of the creep substructure and inhibit thermally activated glide in the “soft” regions This “composite” model of creep allows us to explain both steady state and non-steady state creep properties in a semiquantitative way

A non-linear uniaxial integral constitutive equation incorporating rate effects, creep and relaxation

Abstract: A previously proposed first order non-linear differential equation for uniaxial viscoplasticity, which is non-linear in stress and strain but linear in stress and strain rates, is transformed into an equivalent integral equation. The proposed equation employs total strain only and is symmetric with respect to the origin and applies for tension and compression. The limiting behavior for large strains and large times for monotonic, creep and relaxation loading is investigated and appropriate limits are obtained. When the equation is specialized to an overstress model it is qualitatively shown to reproduce key features of viscoplastic behavior. These include: initial linear elastic or linear viscoelastic response: immediate elastic slope for a large instantaneous change in strain rate normal strain rate sensitivity and non-linear spacing of the stress-strain curves obtained at various strain rates; and primary and secondary creep and relaxation such that the creep (relaxation) curves do not cross. Isochronous creep curves are also considered. Other specializations yield wavy stress-strain curves and inverse strain rate sensitivity. For cyclic loading the model must be modified to account for history dependence in the sense of plasticity.

Alloying aluminum with magnesium for ductility at warm temperatures (25 to 250°C)

Abstract: Solute additions generally increase flow stress and decrease ductility. However, in an earlier study which compared the tensile behavior of a commercial Al-4 pct Mg alloy (5182-0) relative to pure aluminum, the commercial alloy exhibited increases in both strength and ductility at elevated temperatures (<250°C). To more fully understand this unexpected behavior, a series of high purity Al-Mg alloys (0 to 6 wt pct) were tested over the same range of temperatures (25 to 250°C) and initial strain rates (10-4 to 10-1 s-1) as in the earlier study. At ambient temperature the Mg solutes decreased elongation while increasing flow stress, but as the temperature was increased to 250°C the elongation increased with Mg content. This increase in ductility accompanied the linear increases in strain-rate sensitivity which occurred with increasing amounts of Mg. Stress relaxation tests indicated that Mg solutes increase the amount of dynamic recovery occurring at elevated temperatures. These results are explained on the basis of an increased amount of vacancies in the Al-Mg alloys relative to pure aluminum.

Piezoelectric relaxation in polyvinylidene fluoride

Abstract: The piezoelectric and related properties have been measured for stretched polyvinylidene fluoride as a function of temperature. The piezoelectric relaxation observed around the glass transition temperature Tg is discussed taking the two‐phase structure into consideration. The piezoelectric constant e31 (polarization/strain) is positive and increases with temperature. This increase is ascribed to the increase of the electrostrictive constant in noncrystalline regions which couples with the residual polarization located in crystalline and/or noncrystalline regions. The electrostrictive constant changes its sign below Tg from negative to positive with temperature. The piezoelectric activity below Tg is considered to be originated from the intrinsic piezoelectricity, i.e., the rotation of oriented molecular dipoles caused by strain. The residual polarization in the sample due to the dipoles is estimated to be 0.9×10−2 C/m2. The piezoelectric increment around Tg is accounted for by assuming the spatial distrib...

Development of strain-rate testing and its implications. Discussion

Abstract: The application of slow dynamic straining to specimens to facilitate stress corrosion cracking (SCC) now has been in use for more than a decade, and the test is beginning to emerge as one that has much more relevance thanthe rapid sorting test to which its early use was related. The importance of creep effects in constant load testing is considered, and it is shown that reasonable predictions of threshold stresses for SCC can be made from relevant creep data and that the effects of prior creep upon the incidence of cracking and of the phenomenon of non-propagating cracks below the threshold stress are all in agreement with the concept of the crack tip strain rate playing a major role, even under constant load conditions. The reasonable correlation between appropriate strain rate and constant load tests is therefore not surprising, nor is the reduction in threshold stress by dynamic straining, with or without cyclic loading, over that observed for constant loads.

Nonlinear creep of concrete adaptation and flow

Abstract: A nonlinear integral-type creep law is developed by generalizing the linear superposition integral for the creep rate rather than the total strain. At low service stress level there is a significant (though previously overlooked) nonlinearity that consists in gradual stiffening or adaptation to a sustained compressive stress. It is modeled by a stress-dependent acceleration of the age-dependence of stiffness, and by an adaptation parameter whose rate is a function of the stress and age. The high-stress nonlinearity that consists of a weakening of the stiffness, is essentially without memory and is described by an additive rate-type flow term. Its stress dependence and the flow rate decay is modeled by kinematic hardening. An extension to elevated temperatures, which agrees with recovery data, is indicated. Although uniaxial creep is of primary interest, a rational triaxial generalization involving proper stress invariants is derived.

Approximate Relaxation Function for Concrete

Abstract: Presented is an approximate algebraic formula for calculating the relaxation function for aging concrete. The formula is general; it applies to any form of the creep function. Compared to the previously used effective modulus method, the formula reduces the error from up to 37% to within 2% relative to the exact solution according to the superpositon principle. Calculation of long-time relaxation does not require knowledge of the elastic modulus and of the creep function for load duration below one day. The formula enables direct calculation of the age-adjusted effective modulus from the creep function, and thus it allows dispensing with the table of the aging coefficient. This is particularly useful in case of a more sophisticated creep model which reflects the fact that the creep functions for different humidities and sizes have different (nonproportional) shapes.

Deformation parameters in single steel wire-copper matrix composites

Abstract: By using the single carbon-steel fibre-copper matrix composites, the important parameters controlling dislocation motions in the fibre, matrix and composite, namely flow stress, internal stress, effective stress, change in flow stress due to change in strain-rate or temperature, stress exponent of strain-rate, effective stress exponent of dislocation velocity, activation volume and activation enthalpy were measured at the stage in which the mechanical interaction between the components was negligible. It was found that all the composite parameters were determined only by the properties of the components and for each parameter, a modified rule of mixtures was derived.

Viscoplasticity Based on Total Strain. The Modelling of Creep With Special Considerations of Initial Strain and Aging

Abstract: A previously proposed theory is specialized for the uniaxial state of stress and its prediction for creep and relaxation is analyzed in detail. Constant true stress and constant load creep tests are simulated in the presence and absence of thermal aging together with the constant strain relaxation test. The signs of the creep rate and its time derivative as well as the relaxation rate and its time derivative are introduced as criteria. The constant load creep test can reproduce the normal creep curves and nonclassical creep curves (epsilon-. > 0; epsilon-.. > 0 for all epsilon and for sigma/sub 0/ > 0). The capabilities of the constant true stress test are limited to primary creep if the work-hardening slope is positive. When aging is introduced almost any creep curve can be reproduced in both tests. The importance of initial strain is discussed and demonstrated by room temperature creep tests on Type 304 Stainless Steel. It is suggested that the initial strains together with the creep curves be reported in the future. Poisson's ratio in creep needs to be measured and tests are proposed which will enable a quantitative assessment of aging.

Superposition of alloy hardening, strain hardening, and dynamic recovery

Abstract: The principles and heuristics of flow stress superposition are illustrated for the case that one of the components is due to dislocation/dislocation interactions and is the only one that changes with strain. A simultaneous investigation of the flow stress and its rate sensitivity as a function of strain then allows one to confirm or refute postulated superposition laws and, in addition, to separate the effects of alloying or heat treatment on yield stress and on strain hardening. The slope of the observed stress strain curve depends on the form of the superposition law even if there is no physical influence of alloying on the dislocation storage rate; the frequently observed low initial strain hardening associated with a higher yield stress may in some cases be merely a consequence of a nonlinear superposition. At higher strains, the influence of alloying on dynamic recovery becomes the predominant effect; it also controls the high-temperature creep strength. When dynamic recovery plays an important role, it provides a further straining mechanism which, however, is not additive to the low-temperature strain rate; a form of the superposition law for long-range slip and this dynamic recovery strain is proposed. An application of these principles has demonstrated thatmore » dynamic strain aging is due to an effect of mobile solute atoms on the strain-hardening component of the flow stress, not on the friction stress.« less

Generation and relaxation of the molecular orientation during hot-stretching of amorphous thermoplastics

Abstract: Between the mechanical properties and the molecular orientation of hot-stretched amorphous polymers there exist definite and univalent relationships which are independent of the stretching conditions. It, therefore, seemed of great interest to find out whether the orientation and thereby the mechanical properties of such materials can be predicted from their thermomechanical stretching history. In order to check this conjecture stress relaxation, tensile, creep, creep recovery, and free shrinkage tests were performed on polystyrene at temperatures between 105 and 140 °C. During these experiments the stress (or the strain) and the birefringence (as a measure of the orientation) were measured simultaneously. If polystyrene aboveT g would behave like an ideal rubber the true stressσ (force per actual cross section) and the birefringenceΔn should increase proportional to (λ 2 −λ −1) (λ = draw ratio). Furthermore the stress optical coefficientΔn/σ should be strain-independent. In reality, the measuredσ- andΔn-values increase more slowly than they would do in accordance with the rubber theory. In addition, both quantities are not only strain- but also time-dependent. They relax already during the stretching process. Nevertheless, the stress optical coefficient remains constant (i. e. strain- and time-independent as well) with the exception of the values obtained at temperatures below 120 °C. At these low temperatures the stress contains a considerable energy elastic part and consequently the quotient ofΔn andσ is reduced. Furthermore it turned out thatσ andΔn as functions of the Cauchy strain (λ − 1) formally follow the theory of linear viscoelasticity over a strain range up to about 600%. That means, ifσ andΔn are presented in isochronous plots, they prove to be linear functions of (λ − 1) in this range. According to additional experiments carried out on some other amorphous polymers the mentioned findings turned out to be true not only for polystyrene but also for high impact polystyrene, PVC, and PMMA over a strain range the upper limit of which is to be found between 100 and about 600%. The formally linear viscoelastic behaviour of these polymers aboveT g leads to the following consequences: