Stress-stain curve

Kucherskii88 has proposed a new measure to be taken from the tensile stress strain curve which he terms the knee-point strain. This is the point on the curve where the differential modulus stops decreasing and starts to increase, i.e. where the curve starts to go steeply upwards. It is difficult to find this point on the stress stain curve but it can be pinpointed by looking at where the first derivative of stress with respect to strain passes through a minimum. He relates the knee-point strain to structure and was able to normalize curves for both filled and gum rubbers. 

Elastic modulus A stress-stains curve 1 TPa Treacy et al. (1996) and Jian (1997)... 

During compression of polymeric foams, three characteristic stages of deformation are commonly observed. At low deformations, the polymer foam is in the linear elastic response regime, i.e., the stress increases linearly with deformation and the strain is recoverable. The second phase is characterized by continued deformation at relatively constant stress, known as the stress collapse plateau. And the final phase of deformation is densification where the foam begins to respond as a compacted solid. At this point the cellular structure within the material is collapsed, and further deformation requires compression of the solid foam material (Ouellet et al. 2006). As mentioned above, a specific technique is required to obtain stress-strain curves of ferroelectrets in thickness direction because the thickness in ferroelectrets is normally very thin, corresponding to very small defiections. Dansachmiiller et al. developed an experimental technique that allows obtaining the stress-strain curves in ferroelectret films (Dansachmiiller et al. 2005). This method may also be used to obtain the stress-stain curve for a polymer foam film without oriented macro-dipoles. The schematic of the experimental setup is shown in Fig. 4. 

Figure 5 shows stress-stain curve of a ceUular PP film determined by the method mentioned above. The strain of die foam displays a quasi-instantaneous elastic response with a strain 5 % (Dansachmiiller et al. 2005). 

At higher temperatures or lower strain rates, the stress-strain curve of the same material may exhibit a more gradual initial slope and a lower yield stress, as well as the drastic deviation from initial linearity and the higher failure stain characteristic of a ductile material. 

Fig. 12 Stress-strain curve of varying mineralized and unmineralized scaffolds (a). hFOB proliferation (b), ALP activity (c), and calcium deposition (d) on varying scaffolds. Alizaren Red staining of PLLA scaffold (top left), PLLA/HA scaffold (top right), PLLA/Col/HA scaffold (bottom left), TCP (bottom right) (e) [83]...

When a viscoelastic material such as tire cord or rubber Is subjected to a small amplitude sinusoidal straining, the resulting stress-strain curve Is an ellipse and the material properties are characterized by the real and Imaginary moduli E and E" or the ratio E /E ( tan[Pg.372]

Stage II The polymer chain segments start to move and orientation starts to occur. The characteristic of this stage is strain softening, i.e., the stress decreases with increase in strain. (The stain softening phenomenon disappears if true stress and true strain are used in the stress-strain curve. However, the... 

It is important to understand the creep behavior shown in Figure 16.4 is not a simple superposition of linear elastic and viscous responses. Figure 16.5 shows the typical strain-time curves of ideal elastic material, ideal viscous material, and viscoelastic polymer fibers under constant stress. The ideal elastic material deforms instantaneously as the stress is applied and the stain remains constant with time. The removal of the stress causes the ideal elastic material to return to its original dimension. For the ideal viscous material, the strain increases linearly with time as long as the stress is applied. The removal of the stress does not return the ideal viscous material to the original dimension. This is because the eneigy introduced by the woik of the external stress is dissipated in the flow, leading to a permanent deformation. Both the ideal elastic and viscous responses contribute to the creep-recovery curve of the viscoelastic polymer fibers. However, the creep-recovery curve of viscoelastic polymer fibers is not a simple superposition of these two ideal behaviors. In addition to the ideal responses, the creep-recovery curve of the polymer fibers also includes retarded elastic response, in which... 

---