Master stress-strain plot

For a monolayer film, the stress-strain curve from Eqs. (103) and (106) is plotted in Fig. 15. For small shear strains (or stress) the stress-strain curve is linear (Hookean limit). At larger strains the stress-strain curve is increasingly nonlinear, eventually reaching a maximum stress at the yield point defined by = dT Id oLx x) = 0 or equivalently by c (q x4) = 0- The stress = where is the (experimentally accessible) static friction force [138]. By plotting T /Tlx versus o-x/o x shear-stress curves for various loads T x can be mapped onto a universal master curve irrespective of the number of strata [148]. Thus, for stresses (or strains) lower than those at the yield point the substrate sticks to the confined film while it can slip across the surface of the film otherwise so that the yield point separates the sticking from the slipping regime. By comparison with Eq. (106) it is also clear that at the yield point oo. 

Superposition techniques may also be used to correlate stress-strain behavior in the rubbery state. In their study of styrene-acrylonitrile copolymers filled with glass beads, Narkis and Nicolais (1971) obtained stress-strain curves at temperatures above 7. Stress-strain curves were plotted for different fractions of filler, and in terms of both the polymer and composite strain. At a given strain, the stress increased with increasing filler concentration, as expected. It was possible to shift curves of stress vs. polymer strain along the stress axis to produce a master curve (Figure 12.12). In addition to the empirical measurements, an attempt was made to calculate stress-strain curves from the strain-independent relaxation moduli (see Section 1.16 and Chapter 10) by integrating the following equation ... 

TMA, DMA Thermal expansion coefficient calculation Display of stress-strain curve Display of creep curve Display of stress-relaxation curve Arrhenius plot and associated parameters Calculation and display of master curve Heating rate control harmonized with sample deformation... 

The above interpretations of the Mullins effect of stress softening ignore the important results of Haarwood et al. [73, 74], who showed that a plot of stress in second extension vs ratio between strain and pre-strain of natural rubber filled with a variety of carbon blacks yields a single master curve [60, 73]. This demonstrates that stress softening is related to hydrodynamic strain amplification due to the presence of the filler. Based on this observation a micro-mechanical model of stress softening has been developed by referring to hydrodynamic reinforcement of the rubber matrix by rigid filler... 

The strain to break 6, may be plotted against the stress to break in the master curve to yield a failure envelope, shown schematically in Figure 1.25 (Scott, 1967). The failure envelope is independent of temperature, time to break, and strain rate. It is a universal curve independent (at least ideally) of the type of rupture test. If is further divided by the crosslink density, the resulting failure envelope is also approximately independent of both the degree of crosslinking and the chemical structure of the elastomer. The latter... 

Ward and co-workers used extensive creep data to construct master plots of log strain rate versus true stress at constant plastic strain (draw ratio) [76], One such plot for a polyethylene copolymer is shown in Figure 12.28. It was shown that slow crack propagation data were consistent with the proposition that this related to creep to failure of oriented fibrils in the craze. These fibrils then followed the computed route to failure shown in Figure 12.28. 

It was noted that the time-temperature-moisture characterization of a polyimide film during stress relaxation varied with the level of applied strain, implying a nonlinear effect. Furthermore, while plots of the time-dependent portion A (t) of the relaxation modulus E t) = e + A (t) collected at various fixed level of RH could be coalesced by horizontal shifts alone to form a master curve, this could not be achieved for (1) as a whole. It was therefore necessary to incorporate a vertical shift into the formulation and write... 

Free crystallization (i.e., no strain or stress) starts from a number of point nuclei and progresses in all directions at equal linear rates (i.e., the rate of increase of the radius of a spherulite, G, is linear with time). The rate of growth is very dependent on the temperature of crystallization. In particular, G = 0 at 7g and and passes through a maximum at some intermediate temperature, Tk. According to Gandica and Magill (1972) the crystallization process of all the normal polymers follows a master curve. This master curve is a plot of G/Gmax versus a dimensionless temperature, 6 ... 

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