Tensile strain instantaneous

Natural rubber exhibits unique physical and chemical properties. Rubbers stress-strain behavior exhibits the Mullins effect and the Payne effect. It strain crystallizes. Under repeated tensile strain, many filler reinforced rubbers exhibit a reduction in stress after the initial extension, and this is the so-called Mullins Effect which is technically understood as stress decay or relaxation. The phenomenon is named after the British rubber scientist Leonard Mullins, working at MBL Group in Leyland, and can be applied for many purposes as an instantaneous and irreversible softening of the stress-strain curve that occurs whenever the load increases beyond... 

Stress relaxation is the time-dependent change in stress after an instantaneous and constant deformation and constant temperature. As the shape of the specimen does not change during stress relaxation, this is a pure relaxation phenomenon in the sense defined at the beginning of this section. It is common use to call the time dependent ratio of tensile stress to strain the relaxation modulus, E, and to present the results of the experiments in the form of E as a function of time. This quantity should be distinguished, however, from the tensile modulus E as determined in elastic deformations, because stress relaxation does not occur upon deformation of an ideal rubber. 

Fig. 5.5 Effect of changing the elastic modulus ratio and constituent creep stress exponents on the total strain rate of a 1-D composite subjected to tensile creep loading.31 In both (a) and (b), the dashed lines represent the composite behavior, and the thin solid lines the constituent behavior. In the calculations, it was assumed that the creep load was applied instantaneously.

This is an important point, so let s beat it to death with an example. Imagine that we perform a simple tensile creep experiment where a stress oQ is applied to a sample and after 10 hours the strain, (10) is measured. Now let s take an identical sample and perform a stress relaxation experiment where the sample is stretched instantaneously to give... 

Storage modulus measurements. All measurements were taken at temperatures near 45 °C above the network Tg s. Representative network true stress versus strain curves from the tensile experiments are shown in Fig. 2. The ordinate axis, true stress, is normalized by 3eRT to account for the different test temperatures employed. The resultant curves are thereby directly comparable for structural differences, since the instantaneous slopes are proportional to l/M, after Eq. (2). The curves of all five networks are linear and reversible up to strains of around 10 percent. The reversibility suggests that the measurements were performed under near-equilibrium conditions and that the networks were stable at the high test temperatures employed. 

In a tensile test, for example. Eq. (11-10) relates the strain and stress in a creep experiment when the stress Tq is applied instantaneously at time zero. If this loading... 

The instantaneous tensile modulus is just the stress divided by the strain, so... 

The stress that induces 3nelding is called the yield stress tensile test—in which the clamps are moved apart at a set rate—as the stress where the rate of flow equals the imposed strain rate. Thus, in Figure S.2, the yield stress for polyetl lene is the stress at the stress maximum at this point flow takes place instantaneously at the imposed strain rate, with the stress neither increasing nor deoeasing. For some pofymers there is no maximum, the stress-strain curve merely changing firom a higher to a lower slope in this, less well-defined, case the stress at the knee is taken, somewhat arbitrarity, to be the yield stress. In our treatment we will discuss onfy the first case. 

First-Stage Deformation Elastic Response. The instantaneous axial elongation of the tensile specimen is attributed to dissipation of elastic strain that is equivalent to the ratio of the applied tensile stress and tensile modulus, that is, the amount of strain predicted by the short-term characteristics of stress-strain encountered in the measurement of tensile strength. 

Recognizing the importance of the true stress-strain test and the need for specimen diameter measurements during tests where the material deforms by a series of discontinuous yields, the Watertown Arsenal Laboratories contracted with A, D. Little, Inc. [1] to construct a tensile test cryostat capable of measuring and recording instantaneous diameter data to be compatible with an existing true-stress true-strain computer [2]. 

Thermomechanical analysis instruments are ideally suited to measure creep. In these experiments the increase in strain is measured with time following the application of a constant stress to the sample, followed by the recovery of the strain when the stress is removed. Figure 4.26 shows a typical TMA creep-recovery curve. In these experiments, an instantaneous compression or tensile stress is applied to the sample, and the time-dependent strain is measured at constant temperature. During the loading cycle, the resultant creep curve... 

Rg.2 Instantaneous strain-rate sensitivity of H-6AI-4V during tensile testing at 925 °C (1700 °F) showing decrsas-ing m with increasing strain. 

A second method in mechanical tests is the stress relaxation experiment. Here, a certain constant strain is instantaneously imposed on a sample and the stress induced by this procedure is measured as a function of time. Figure 5.2 shows schematically for an uniaxially deformed sample the possible shape of a stress relaxation curve. The tensile stress has its maximum directly after... 

O Figure 34.10 represents the typical course of a creep experiment using single lap shear specimen bonded with a viscoelastic acrylic adhesive under tensile load. The curve progression can be divided into three phases of creep. At the end of phase I, instantaneous elastic strain and delayed elastic strain are completed and the creep progress in phase II is dominated by secondary creep. At the end of phase II, creep accelerates leading to failure of the specimen at the end of phase III. 

Sometimes it is more meaningful to use a true stress-true strain scheme. True stress cTf is defined as the load F divided by the instantaneous cross-sectional area At over which deformation is occurring (i.e., the neck, past the tensile point), or... 

Many polymeric materials are susceptible to time-dependent deformation when the stress level is maintained constant such deformation is termed viscoelastic creep. This type of deformation may be significant even at room temperature and under modest stresses that lie below the yield strength of the material. For example, automobile tires may develop flat spots on their contact surfaces when the automobile is parked for prolonged time periods. Creep tests on polymers are conducted in the same manner as for metals (Chapter 8) that is, a stress (normally tensile) is applied instantaneously and is maintained at a constant level while strain is measured as a function of time. Furthermore, the tests are performed under isothermal conditions. Creep results are represented as a time-dependent creep modulus E t), defined by ... 

The effect of a change of strain rate in the course of a tensile experiment can be predicted from Figure 7.10. An instantaneous increase in strain rate is equivalent... 

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