Uniaxial stress-strain experiments

The results of uniaxial stress-strain experiments are often analyzed in terms of the reduced stress defined by... 

The shear component of the applied stress appears to be the major factor in causing yielding. The uniaxial tensile stress in a conventional stress-strain experiment can be resolved into a shear stress and a dilational (negative compressive) stress normal to the parallel sides of test specimens ofthe type shown in Fig. 11-20. Yielding occurs when the shear strain energy reaches a critical value that depends on the material, according to the von Mises yield criterion, which applies fairly well to polymers. 

As a matter of fact, stress-strain experiments on swollen networks are more frequently performed by means of the uniaxial compression technique The compres-sional stress a per unit undeformed area of swollen gel may be generally written... 

The gauge is usually calibrated in well-controlled uniaxial strain experiments by measuring the fractional change in resistance AR/Rq as a function of the shock stress. The results are empirically correlated to the stress through the relation... 

A simple bubble machine is devised and successfully applied in characterising lightly crosslinked PE resins for foam expansion. The biaxial stress-strain relationship is deduced from the air injection rate and pressure. The effects of strain rate, temperatnre and crosslinker level on the stress-strain behavionr are investigated. Uniaxial extension experiments are also performed and compared with biaxial extension data. 5 refs. 

Gas compression in closed-cell polymer foams was analysed, and the effect on the uniaxial compression stress-strain curve predicted. Results were compared with experimental data for a foams with a range of cell sizes, and the heat transfer conditions inferred from the best fit with the simulations. The lateral expansion of the foam must be considered in the simulation, so in subsidiary experiments Poisson s ratio was measured at high compressive strains. 13 refs. 

The exact laws, based on continuum analysis of the fibers and the matrix, would be very complicated. The analysis would involve equilibrium of stresses around, and in, the fibers and compatibility of matrix deformation with the fiber strains. Furthermore, end and edge effects near the free surfaces of the composite material would introduce complications. However, a simplified model can be developed for the interior of the composite material based on the notion that the fibers and the matrix interact only by having to experience the same longitudinal strain. Otherwise, the phases behave as two uniaxially stressed materials. McLean5 introduced such a model for materials with elastic fibers and he notes that McDanels et al.6 developed the model for the case where both the fibrous phase and the matrix phase are creeping. In both cases, the longitudinal parameters are the same, namely... 

FIGURE 14 Idealized stress-strain curve for uniaxial tension experiment. 

Another approach to the investigation of the intermolecular polariton coupling, as well as to the effects of strain, is piezomodulation spectroscopy. In this experiment a periodic uniaxial stress, within the elastic regime, is applied to the sample and the optical signal is detected synchronously with the stress. The measurement can yield information on the coupling, the strain dependence of the spectra, and more extensively resolved structure (12). Because of sample size and stability, PTS was studied by piezomodulation spectroscopy at low temperature. 

As an example, consider the following experiments. First, a polymer is subjected to a constant uniaxial stress cr for one hour this perturbation results in some measurable strain, say e(l hour). In a second experiment, however, an identical sample is subjected to sufficient stress to result in the same strain s (1 hour) immediately upon application of the stress. Then the stress is decreased so that the strain remains constant at s (1 hour). The value of the stress after 1 hour in the second experiment is defined as associated with the constant strain experiment being lower. However, since the strains are the same, the two "modulus" values... 

The first step in the project was to perform an extensive set of experimental tests on the actual glass-filled PTFE that was used in the gasket. Specifically, uniaxial tension and compression experiments at different strain rates and different final strain levels were performed. Both the loading and unloading behavior was examined. A few select stress relaxation experiments were also performed to directly probe the stress relaxation behavior of the material. Examples of the experimental data obtained from these tests are shown in Figs. 11.13 to 11.16. 

Stress-strain measurements at uniaxial extension are the most frequently performed experiments on stress-strain behaviour, and the typical deviations from the phantom network behaviour, which can be observed in many experiments, provided the most important motivation for the development of theories of real networks. However, it has turned out that the stress-strain relations in uniaxial deformation are unable to distinguish between different models. This can be demonstrated by comparing Eqs. (49) and (54) with precise experimental data of Kawabata et al. on uniaxially stretched natural rubber crosslinked with sulphur. The corresponding stress-strain curves and the experimental points are shown in Fig. 4. The predictions of both... 

Figure 5 demonstrates the different behaviour resulting from Eqs. (49) and (54) in the case of uniaxial compression. We also tested the elastic potential (Eq. (44)) in the two cases v = 1/2 and v = —1/4 by comparing the corresponding stress-strain relations with biaxial extension experiments which cover relatively small as well as large deformation regions for an isoprene rubber vulcanizate. In the rectan-... 

Figure 7.20(a) gives the simulation results of the plastic response of this particular structure in a tensile-flow experiment at a given constant strain rate at 0 K and 300 K. The response is given as a deviatoric shear resistance (stress) shear resistance r at 0 K, plotted as a function of the total deviatoric shear strain y, where, in a formal application of a Tresca connection between tensile and shear response, a in shear is taken as half of the tensile deviatoric plastic resistance and y is twice the total uniaxial deviatoric strain (McClintock and Argon 1966). The initial quenched-in level of tp for this alloy is... 

Figure 8.2 shows a series of stress-strain curves at different temperatures for bisphenol-A polyearbonate (PQ recorded at an effective uniaxial strain rate of 10 " s obtained from extensional deformation in pre-contoured tensile bars using the special instrumentation mentioned above that resulted in deviatoric, effective true-stress-true-strain curves (G Sell et al. 1992). In these experiments the initial state of the material was fully annealed, exhibiting strong yield phenomena and strain softening. Figure 8.3 shows the temperature dependence of the yield stress of PC in tension and compression at a strain rate of = 4.16 x 10 s . 

Figure 9.28 shows the stress train eurves of a whole eomplement of deformation modes with all flow stresses normalized with tq, giving the dependenees of e/ro, the normalized global equivalent deviatorie shear resistances, on Se, the global equivalent plastic strain. The predieted stress strain eurve for plane-strain eompression agrees well with the data points of the Gal ski et al. experiments. We note that the predicted response for uniaxial tension is also elose to the predietion for plane-strain compression and that these two, as examples of irrotational flow, differ markedly from the simple shear results and also from the experimental results and the predictions for uniaxial compression, in comparison with the experimental results of Bartczak et al. (1992b). 

Finding the material parameters for the /2-plasticity theory is straightforward and can be obtained from a simple uniaxial tension experiment. The material model, in fact, is a piecewise linear model (Figure 14.13) in which the material parameters specify the vertices of the stress-strain curve. The /2-plasticity model can be made to fit monotonic, constant strain-rate, constant temperature test data well (Figure 14.14). Two of the main limitations of the theory are... 

Rheological properties Rheology is the study of the deformation and flow of matter under the influence of an applied stress. The measurement of rheological properties is helpful to predict the physical properties of polymer nanocomposites during and after processing. Oberdisse [44] studied the rheological properties of a special nanocomposite material obtained by film formation of mixtures of colloidal silica and nanolatex solutions by means of uniaxial strain experiments. 

From equation (1), It can be seen that If the bar at time x=0 is subjected to a single step in strain, p(t), then the stress necessary to keep the bar stretched at time t is equal to H(p(t), t), where H(l,t) 0. From data obtained from single step stress-relaxation experiments carried out at different levels of strain. It is evident that one can determine the stress response for any other strain history in uniaxial extension. However, since equation (1) is nonlinear, one cannot determine the strain as a function of the stress, as for example In a creep experiment. Equation (1) applies to the type of experiment where, knowing the strain history, one can determine the stress response and the calculated values can then be compared with experimentally determined quantities. 

The technique of loading dilatometry, in which a small, controlled uniaxial stress Pj is applied to a powda- compact during sintering has been used to investigate the simultaneous occurrence of densification and creep, as well as their interaction (57,58). Parameters such as the stress intensity factor < > and the sintering stress 2 can be determined from the data. In the experiments, simultaneous measurement of the time-dependent axial and radial strains allows the determination of the... 

The challenges inherent in the measurement of stress-strain response of thin film materials by means of direct tensile testing are commonly more than offset by the distinct advantage that properties characterizing deformation resistance of the material in the plastic range can be determined under isothermal conditions for a relatively simple state of stress on the specimen. However, these techniques are not readily amenable to modifications that can accommodate uniaxial compression, simple shear stress, equi-biaxial stress or states stress on the specimen. As a result, it is difficult to draw conclusions concerning the dependence of plastic response on stress path history. It is noted that results for some cyclic tension-compression experiments were reported by Hommel et al. (1999). 

The theory appears to reproduce all of the main features of the stress-strain curve for uniaxial deformation. Only the nonlinearity of f /lph with 1/a in extension is at variance with experiment. This deficiency may reflect quantitative inaccuracy in the assumption above concerning the deformation of domains of constraints under strain. 

The onset of ductile failure in sohds is determined by the Considire construction, in which a maximum in the stress-strain curve causes an instability that manifests itself as a neck. This concept is unhkely to be apphcable to the onset of necking in polymer melts. All constitutive equations, including the Maxwell model. Equation 9.16, predict a maximum in the stress-strain curve for stretching at a constant stretch rate, and this maximum normally occurs prior to the attainment of steady state. Hence, hteral interpretation of the construction as a sufficient condition for failure would imply that uniform uniaxial extensional experiments could never be carried out past the force maximum, which often corresponds to a relatively low strain such an interpretation is clearly contrary to substantial experimental experience in extensional rheometry, and several experimental studies focusing specifically on the Considere construction have shown that it does not predict the experimental onset of necking in melts. 

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