Stress-strain curves uniaxial tensile loading

Even plastics with fairly linear stress-strain curves to failure, for example short-fiber reinforced TSs (RPs), usually display moduli of rupture values that are higher than the tensile strength obtained in uniaxial tests wood behaves much the same. Qualitatively, this can be explained from statistically considering flaws and fractures and the fracture energy available in flexural samples under a constant rate of deflection as compared to tensile samples under the same load conditions. These differences become less as the... 

As mentioned earlier, the Gc value required to define the CZ model is obtained from TDCB tests. The remaining parameter Gm is chosen as the UTS, and was extracted from the stress-strain curves at the corresponding rates. This was an arbitrary choice, since the level of the constraint near the crack tip is higher than that in uniaxial tensile tests used to obtain the stress-strain curves. Therefore, a sensitivity study on this parameter was performed. For illustration purposes, a numerical analysis carried out on TDCB test specimens bonded with the two adhesives under investigation is shown in this section. The value of a was varied from 20 to 80 MPa and numerical predictions of load versus time were compared against the experimental results. Fig. 5 shows a comparison of the FV and experimental results for different values for TDCB tests performed at 0.1 mm/min. The best fit G value should be able to predict correctly both the experimental force and crack history. (Note that the latter was found to be less sensitive to changes of the cohesive strength.)... 

Uniaxial tensile tests were carried out to determine the stress-strain curves and document the damage growth on a computer-controlled Instron model 8516 servo hydraulic testing machine operating at a strain rate of 5% min . The macroscopic tensile yield stress was considered equal to the maximum stress on the loading curve. The Young s modulus was determined as the plateau value of a plot of the secant modulus as a function of the strain. 

General Stress-Strain Curves under Uniaxial Tensile Loading. In... 

While the true stress-true strain response is qualitatively similar in both compression and tension, the resulting deformation states are very different. Tensile loading leads to uniaxial molecular orientation along the loading axis. Compression on the other hand results in a biaxial orientation state in a plane perpendicular to the loading direction and so it is expected that quantitatively different stress-strain curves are seen. In addition, as discussed below, the hydrostatic pressure difference between tension and compression leads to differences in yield strength because yield in polymers is pressure dependent. 

Thus far, the discussion has centered on uniaxial tension. Let us see what happens when the bar in tension is unloaded first and then loaded in compression. The typical stress-strain curve is represented in Figure A.6. The loading is initially in tension up to a stress of Si at which the unloading process starts and follows a straight line parallel to the elastic curve. Upon unloading as the strain reaches zero, a tensile strain of Sp remains. Subsequently as the material is loaded in compression, it may yield in... 

If we approximate the stress state at the notch root as uniaxial, the material state must lie on the stress-strain curve measured in tensile tests. This provides another relation between Cmax and max, which are therefore uniquely determined. Graphically, equation (4.5) corresponds to a hyperbola in the a-e space of the stress-strain diagram, since the right side is constant for a given load case. The stresses and strains at the notch root can be found as the intersection of the hyperbola and the stress-strain curve as shown in figure 4.6. 

Other less well-known types of nonlinearities include interaction and intermode . In the former, stress-strain response for a fundamental load component (e.g. shear) in a multi-axial stress state is not equivalent to the stress-strain response in simple one component load test (e.g. simple shear). For example. Fig. 10.3 shows that the stress-strain curve under pure shear loading of a composite specimen varies considerably from the shear stress-strain curve obtained from an off-axis specimen. In this type of test, a unidirectional laminate is tested in uniaxial tension where the fiber axis runs 15° to the tensile loading axis. A 90° strain gage rosette is applied to the specimen oriented to the fiber direction and normal to the fiber direction and thus obtain the strain components in the fiber coordinate system. Using simple coordinate transformations, the shear response of the unidirectional composite can be found (Daniel, 1993, Hyer, 1998). At small strains in the linear range, the shear response from the two tests coincide. 

Figure 3.5 shows this effect for an ordinary carbon steel and illustrates that the ductility of a material is affected by the type of stress system and the rate of application of this stress system. Between T2 and for example, the carbon steel displays ductile behavior in a simple uniaxial stress system (tensile test) or displays brittle characteristics at high rates of loading (impact test). Increasing either the strain rate or the complexity of the stress system moves the curve in Fig. 3.5 to the right. This amounts to an increase in the brittle transition temperature. Similar ductile or brittle behavior is observed above T4 and below Tj. 

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