Tensile creep stress relaxation

This is because although 0 = (10), in general, cr(10) oQ (it will usually be less). In principle, the quantities we have defined, E(t), Dit), Gif), and J(i), provide a complete description of tensile and shear properties in creep and stress relaxation (and equivalent functions can be used to describe dynamic mechanical behavior). Obviously, we could fit individual sets of data to mathematical functions of various types, but what we would really like to do is develop a universal model that not only provides a good description of individual creep, stress relaxation and DMA experiments, but also allows us to relate modulus and compliance functions. It would also be nice to be able formulate this model in terms of parameters that could be related to molecular relaxation processes, to provide a link to molecular theories. 

Fig. 4.143 Tensile-creep and relaxation modulus of polycarbonate with 30 wt.-% glass fibers at various stress and strain levels for 22 °C [98Dom].

The results from creep or relaxation compression test are evaluated and represented on the same way as for tensile creep or relaxation tests. After the applying of the weight m to the specimen accompanying load generates a uniaxial stress ffco (Eq. 4.53) in the initial cross-section area Aq. At this moment the extens-ometer monitors the increase in time-dependent compression AL (t) from which normative compression... 

Meanwhile, the mechanical properties to be considered are also many-fold (tensile, flexural, compression, shear, twist, hardness, creep, stress relaxation, impact, fatigue, friction, abrasion, tear properties, etc.). 

Some of the viscoelastic or rheological properties that can be measured using this technique include viscosity, modulus tensile compliance, creep-stress relaxation, gel time and gel temperature, tensile compliance, and stress-strain properties. 

Characterization of the viscoelastic properties of polymers are classified into two categories static and dynamic measurements. The static mechanical tests involve creep, stress relaxation, and stress-strain measurements. In a creep test, a constant stress is applied to the specimen, and its deformation is measured as a function of time. In a stress relaxation test, the specimen is deformed a fixed amount, and the change in the stress is measured as a function of time. The stress-strain measurement is carried out by stretching the sample at constant tensile speed and then recording the load and deformation simultaneously. 

Tensile Testing. The most widely used instmment for measuring the viscoelastic properties of soHds is the tensile tester or stress—strain instmment, which extends a sample at constant rate and records the stress. Creep and stress—relaxation can also be measured. Numerous commercial instmments of various sizes and capacities are available. They vary greatiy in terms of automation, from manually operated to completely computer controlled. Some have temperature chambers, which allow measurements over a range of temperatures. Manufacturers include Instron, MTS, Tinius Olsen, Apphed Test Systems, Thwing-Albert, Shimadzu, GRC Instmments, SATEC Systems, Inc., and Monsanto. 

A typical stress—strain curve generated by a tensile tester is shown in Eigure 41. Creep and stress—relaxation results are essentially the same as those described above. Regarding stress—strain diagrams and from the standpoint of measuring viscoelastic properties, the early part of the curve, ie, the region... 

Not only are the creep compliance and the stress relaxation shear modulus related but in turn the shear modulus is related to the tensile modulus which itself is related to the stress relaxation time 0. It is therefore in theory possible to predict creep-temperature relationships from WLF data although in practice these are still best determined by experiment. 

For elastomers, factorizability holds out to large strains (57,58). For glassy and crystalline polymers the data confirm what would be expected from stress relaxation—beyond the linear range the creep depends on the stress level. In some cases, factorizability holds over only limited ranges of stress or time scale. One way of describing this nonlinear behavior in uniaxial tensile creep, especially for high modulus/low creep polymers, is by a power... 

ISO 2285 2001 Rubber, vulcanized or thermoplastic - Determination of tension set under constant elongation, and of tension set, elongation and creep under constant tensile load ISO 2782 1995 Rubber, vulcanized or thermoplastic - Determination of permeability to gases ISO 3384 1999 Rubber, vulcanized or thermoplastic - Determination of stress relaxation in compression at ambient and at elevated temperatures ISO 3865 1997 Rubber, vulcanized or thermoplastic - Methods of test for staining in contact with organic material... 

Capillary pipette Falling sphere Parallel plate Falling coaxial cylinder Stress relaxation Rotating cylinder Tensile creep... 

Figure 3.1 The five most common mechanical tests (I) constant elongation for tensile strength determinations, (2) constant force for creep determinations, (3) fixed elongation for stress relaxation determinations, (4) cyclic strain for dynamic mechanical determinations, and (5) impact for impact determinations. (After J. Fried, Plastics Engineering, July 1982, with permission.)...

The next two tests falling into this category are tensile creep and stress relaxation. In tensile creep a load is applied instantaneously to the specimen at zero time and the extension monitored as a function of time. In stress relaxation an extension is imposed and the load monitored as a function of time. 

All these tests are in common use to measure the tensile stiffness of polymers. For example, tests at constant extension rate are often carried out on an Instron tensile testing machine. Tensile creep is used in many cases while stress relaxation is not so common. Dynamic testing is commonly performed using the Rheovibron or other commercial equipment32 or home made equipment33,... 

The mechanical properties of Shell Kraton 102 were determined in tensile creep and stress relaxation. Below 15°C the temperature dependence is described by a WLF equation. Here the polystyrene domains act as inert filler. Above 15°C the temperature dependence reflects added contributions from the polystyrene domains. The shift factors, after the WLF contribution, obeyed Arrhenius equations (AHa = 35 and 39 kcal/mole). From plots of the creep data shifted according to the WLF equation, the added compliance could be obtained and its temperature dependence determined independently. It obeyed an Arrhenius equation ( AHa = 37 kcal/mole). Plots of the compliances derived from the relaxation measurements after conversion to creep data gave the same activation energy. Thus, the compliances are additive in determining the mechanical behavior. 

Fig. 5.1 Idealized representation of the transient change in fiber and matrix stress that occurs during the isothermal tensile creep and creep recovery of a fiber-reinforced ceramic (the loading and unloading transients have been exaggerated for clarity). It is assumed that the fibers have a much higher creep resistance than the matrix. The matrix stress reaches a maximum at the end of the initial loading transient. After full application of the creep load, the matrix stress relaxes and the fiber stress increases. Upon specimen unloading, elastic contraction of the composite occurs, followed by a time-dependent decrease in fiber stress and increase in matrix stress. Overall, creep tends to increase the difference in stress between constituents and recovery tends to minimize the difference in stress. After Wu and Holmes.15...

We will first consider the parameters we are trying to model. Let us start with stress relaxation, where it is usual to describe properties in terms of a relaxation modulus, defined in Table 13-5 for tensile [ (r)] and shear [G(r)] experiments. The parameter used to describe the equivalent creep experiments are the tensile creep compliance [D(r)] and shear creep compliance [7(0]. It is important to realize that the modulus and the compliance are inversely related to one another for linear, tune-independent behavior, but this relationship no longer holds if the parameters depend on time. 

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... 

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