Load-elongation curves yield stress

Yield stress may be regarded most simply as the minimum stress at which permanent strain is produced when the stress is subsequently removed. Although this deformation is satisfactory for metals, where there is a clear distinction between elastic recoverable definition and plastic irrecoverable deformation, in polymers the distinction is not so straightforward. In many cases, such as the tensile tests discussed above, yield coincides with the observation of a maximum load in the load-elongation curve. The yield stress then can be defined as the true stress at the maximum observed load (Figure 11.8(a)). Because this stress is achieved at a comparatively low elongation of the sample, it is often adequate to use the engineering definition of the yield stress as the maximum observed load divided by the initial cross-sectional area. 

In some cases there is no observed load drop and another definition of yield stress is required. One approach is to determine the stress where the two tangents to the initial and final parts of the load elongation curve intersect (Figure 11.8(b)). An alternative is to attempt to define an initial linear slope on the stress-strain curve and then to draw a line parallel to this that is offset by a specified straia, say 2 per cent. The interception of this line with the stress strain curve then... 

In some cases, there is no observed load drop and another definition of yield stress is required. One approach is to determine the stress where the two tangents to the initial and final parts of the load-elongation curve intersect (Figure 12.8(b)). 

Sketch a load-elongation curve of a typical material having a yield point, identifying or defining stress, strain, proportional limit, yield point, elastic limit, ultimate strength, and rupture strength. 

The maximum in the curve denotes the stress at yield av and the elongation at yield v. The end of the curve denotes the failure of the material, which is characterized by the tensile strength a and the ultimate strain or elon gation to break. These values are determined from a stress-strain curve while the actual experimental values are generally reported as load-deformation curves. Thus (he experimental curves require a transformation of scales to obtain the desired stress-strain curves. This is accomplished by the following definitions. For tensile tests ... 

The tensile modulus can be determined from the slope of the linear portion of this stress-strain curve. If the relationship between stress and strain is linear to the yield point, where deformation continues without an increased load, the modulus of elasticity can be calculated by dividing the yield strength (pascals) by the elongation to yield ... 

Studies of the tensile properties concerned true stress-true strain measurements taken by means of an INSTRON Tensile Testing Machine and video system. The course of the deformation process running at 20%/min. (2 mm/min.) rate was recorded by means of a video camera. Observations were performed on the volume elements of each sample (see Fig. 2). Changes of sample thickness were measured with a properly modified micrometer screw. Elasticity moduli E, elasticity limit eg and elongation at yield ey were determined on the basis of registered load - crosshead displacement curves. 

The effect of the CNT loading on mechanical properties of the come fibrefiber (2x drawn) was investigated and the tensile stress-strain curves are shown in Figure 5. For imdoped PANi, the addition of 2% w/w CNTs increased the yield stress by 100%, the tensile stress (Oj by 50%, the Young s Modulus (E) by more than 200% compared to the neaniline fiber. A 30% decrease in elongation at break (e ) also occurred (Table 1). 

The displacement of the point of initial load measurement along the strain axis, observed for curves 5-8 in Fig. 9b, indicates irreversible extension (or slack) resulting from previous displacement. As this was not observed for curves 2-4, this confirms that the material elongates irreversibly in extension where stress and strain levels exceed a critical value. Moreover, this demonstrates that the initial linear stress-strain region corresponds to Hookean or elastic behavior and the onset of irreversible extension is marked by the initial point of deviation from this linearity. It is therefore appropriate to calculate tensile modulus based on the slope of the initial linear stress-strain region. Additionally, yield stress and yield strain can be equated to the respective levels of stress and strain at the observed point of deviation from linearity. 

---