Toughness stress-strain behavior

If a material exhibits linear-elastic stress-strain behavior prior to rupture (an ideal behavior approximated by many thermosets), then a simple relationship exists between the material s fracture toughness and its fracture surface energy, J (or G),... 

The load-displacement curves for C(T) tests of the neat EpoxyH were almost linear until the final unstable fracture. The fracture toughness value in 77K-LNj was 210 J/m and that in RT-air was 120 J/m. Thus the toughness increased by 1.8 times by changing the test environment from RT-air to 77K-LN. Brown and co-workers have found that amorphous polymers crazed in 77K-LNj, but not in a helium or vacuum at about 78K [20-22]. They have also reported that the stress-strain behavior of all polymers, amorphous and crystalline, is affected by at low temperatures [22]. Kneifel has reported that the fracture toughness of epoxy in 77K-LNj is higher than that in RT-air and 5K, and that the reason for this is the reduced notch effect by plastic deformation [23]. Then, the increase of the fracture toughness of the neat EpoxyH in this study is probably caused by the similar effect. 

Figure 6. The initial slope of the toughness ratio versus the relative saturation strain, a, as a function of the initial hardening Ho/f-o, for a range of Poisson s ratio and m. The insert plots hysteresis loops in order to illustrate the dependence of the stress strain behavior on m.

Ochiai S, Hojo M, Schulte K and Fiedler B (2001) Nondimenaonal nulatiou of influence of toughness of interface on tensile stress-strain behavior of unidirectional microcomposite, Composites Part A 2 749-761. 

A number of metrics can be assessed from stress-strain behavior (Dowling 2007). Properties that are often evaluated include the modulus (initial modulus, or secant modulus evaluated to some specific strain), the yield stress, the yield strain, the ultimate strength, and the strain at break, as have been discussed in O Chap. 19. The area under the curve is known as the modulus of toughness, as this area has physical units of energy per unit volume, which are equivalent to force per unit area, the units of stress and modulus. 

Figure 8.6 shows a representative set of stress-strain curves for the 12 1 melt-drawn samples at each nanotube concentration. The addition of nanotubes significantly alters the stress-strain behavior of the fibers. The ultimate stress, yield stress and modulus increase with the addition of nanotubes. In contrast, the ultimate elongation slightly decreases with the addition of nanotubes. The significant increases in ultimate and yield stress combined with a small decrease in ultimate elongation lead to the observed increases in toughness. 

Based on the stress-strain behavior, moleculariy oriented polymer fibers can be divided into three groups high modulus-high tenacity (HM-HT) fibers, tough... 

It is important to note that the behavior of polymers below the yield point is Hookean and essentially reversible for short-term service. Thus this range, which is associated with stretching and bending of covalent bonds, is called the elastic range. The area under the stress-strain curve is a measure of toughness. 

---