Uniaxial tension test

The first apphcation of the model is a displacement-controlled uniaxial tension test. The geometry and the loading conditions are shown in Fig. 21.2. The values of the material parameters belong to a virtual material and are hsted in Table 21.1. They are chosen in such a way that the effects become clearly visible. 

3213 DOFs 1U71 [lodes lOlKI QlPl-edmiietilii 

Note that in addition to the standard Dirichlet boundary data for the displacements, Dirichlet boundary data for the microstructural parameter also have to be prescribed. Experimentally [24, 37] the local mechanical properties in the interphase depend on both the polymer and the substrate. The possibility of prescribing additional boundary conditions for k is utilized to describe the variations of the mechanical properties in the interphase depending on the substrate. If on the one hand ic = ko is chosen as Dirichlet data for the structural parameter, no interphase is predicted by the model. If on the other hand, ic Kq or K Ko is chosen, an interphase is predicted which is either stiffer or weaker than the bulk material, respectively. The thickness of the interphase is mainly governed by the material parameters a and yS. 

The results shown in Fig. 21.3 belong to k/kq = 2. As can be seen on the left-hand side of the figure, the strain component S22 in the loading direction shows boundary layers while the stress component T22 in the direction of the applied load is constant. The strain in the boundary layers decreases compared with the inner part of the specimen, which means that the model predicts a stiff boundary layer for k/kq = 2. On the right-hand side of Fig. 21.3, the distributions of the microstructural flux S2 and of the microstructural parameter k itself are shown. It can be seen that k decreases from fc at the boundaries to Kq in the inner part of the specimen. 

If the same displacement is prescribed at the top of the specimen, but the Dirichlet data for k are changed to k/kq = 0, a weak boundary layer is obtained. This can be seen from the increasing strain component in the boundary layer as shown in Fig. 21.4. Again, the stress is constant in the specimen according to the equilibrium condition. The microstructural flux changes its direction and the parameter k now increases from the boundaries to the inner part of the specimen. 

---

In a uniaxial tension test to determine the elastic modulus of the composite material, E, the stress and strain states will be assumed to be macroscopically uniform in consonance with the basic presumption that the composite material is macroscopically Isotropic and homogene-ous. However, on a microscopic scSeTBotFTfhe sfre and strain states will be nonuniform. In the uniaxial tension test,... 

Uniaxial tension testing with superposed hydrostatic pressure has been described by Vernon (111) and Surland et al. (103). Such tests provide response and failure measurements in the triaxial compression or tension-compression-compression octants. 

Although the uniaxial tension test is the one most widely used, it has two drawbacks when it is used to provide information on the yielding of polymers. First, the tensile stress applied can lead to brittle fracture before yield takes place, and second, yield occurs in an inhomogeneous way due to the formation of a neck accompanying the tensile test. In any case, given that the section of sample decreases as the stress increases, cj cy . 

Equations (14.10) and (14.12) give the pressure-dependent von Mises criterion. Also, for any state of stresses, P is an invariant given by the expression P = (l/3)(ai-I-Q2-1-cy3). On the basis of this expression, in a uniaxial tension test 02 = a3 = 0)... 

In the uniaxial tension test (Fig. 2.8), there is usually a transverse strain, i.e., a strain perpendicular to the applied stress. This can be used to define a second elastic constant, Poisson s ratio (v), as the negative ratio of the transverse strain (e.j.) to the longitudinal strain (s ), i.e., v= -Sj/cl- For isotropic materials, it can be shown from thermodynamic arguments, that -1< u <0.5. For many ceramics and glasses, v is usually in the range 0.18-0.30. 

As an example, consider a uniaxial tension test and the resolution of the stress onto a plane with its normal inclined at an angle a to the x, (loading) direction. 

The test data overpage were gathered in a uniaxial tension test on a polycrystalline alumina specimen. The gage section of the specimen (section of specimen under uniform tension) was cylindrical with a length of 50 mm and a diameter of 3 mm. 

Uniaxial tension tests were performed on polycrystalline zirconia speei-mens (specimen volume= 10000 mm ). 

Uniaxial tension tests were performed at room temperature at a constant strain rate (50 pm/mn). The load was measured using a 500 N load cell. The minicomposite elongation was measured using two-parallel linear-variable differential transformer (LVDT) extensometers that were attached to the grips. Extensometers were located on each side of specimens, in order to control specimen alignment. 

In Sect. 1.2 above, the stress-strain relation in uniaxial tension tests was given in Eq. (1.5), indicating a Hookean behavior. This section now considers linear elastic solids, as described by Hooke, according to which (Ty is linearly proportional to the strain, y. Each stress component is expected to depend linearly on each strain component. For example, the Cn may be expressed as follows ... 

According to the maximum principal stress theory, failure occurs when one of the three principal stresses reaches a stress value of elastic limit as determined from a uniaxial tension test. This theory is meaningful for brittle fracture situations. 

According to the maximum shear stress theory, the maximum shear equals the shear stress at the elastic limit as determined from the uniaxial tension test. Here the maximum shear stress is one half the difference between the largest (say principal stresses. This is also known as the Tresca criterion, which states that pelding takes place when... 

There is much less information available in the literature on the tensile strength of rice kernels, probably because measurements under tension are more difficult to realize than measurements under compression. For uniaxial tension tests, the... 

Figure 2. (a) Effective stress versus effective remanent strain curves for the model material described in Section 2 in uniaxial compression, pure shear strain, pure shear stress and uniaxial tension tests, (b) Uniaxial stress versus remanent strain hysteresis loops for the model material illustrating the effect of the hardening parameter In both cases notice the asymmetry in the remanent strains that can be achieved in tension versus compression. 

Show that the deviatoric stored energy comprises 93% of the total stored energy in a uniaxial tension test. 

FIGURE 35.14 Comparison between experimental data (obtained from a uniaxial tension test with a grip displacement rate of 75 mm/min) for UHMWPE (GUR 1050, 30kGy t-N2> and predictions made using the J2-plasticity model. 

UHMWPE specimens subjected to very small strains, while exploration of hyperelasticity theory led to the conclusion that it is often safer to use a more sophisticated constitutive model when modeling UHMWPE. The use of linear viscoelasticity theory led to a reasonable prediction for the response of the material during a uniaxial compression test however, even small changes to the strain rate rendered the previously identified material parameters unsatisfactory. Isotropic J2-plasticity theory provided excellent predictions under monotonic, uniaxial, constant-strain rate, constant-temperature conditions, but it was unable to predict reasonable results for a cyclic test. The augmented Hybrid Model was capable of predicting the behavior of UHMWPE during a uniaxial tension test, a cyclic uniaxial fully... 

In laboratory pracixce, uniaxial tension tests are very often in use We v ill take into account two cases with cylindrical and rectangular samples. Taking the same rule of energy transference as mentioned at the beginning, and following the same way as for the brasilian test, we obtain ... 

---