Stress curves

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. 

The resulting data can then be presented as a series of curves much like the isometric stress curves in Fig. 2-27. A relaxation modulus similar to the creep modulus can also be derived from the relaxation data. It has been shown that using the creep modulus calculated from creep curves can approximate the decrease in load from stress relaxation. 

The elastic stress curve in figure perfectly follows elastic strain [2]. This constant is the elastic modulus of the material. In this idealized example, this would be equal to Young s modulus. Here at this point of maximum stretch, the viscous stress is not a maximum, it is zero. This state is called Newton s law of viscosity, which states that, viscous stress is proportional to strain rate. Rubber has some properties of a liquid. At the point when the elastic band is fully stretched and is about to return, its velocity or strain rate is zero, and therefore its viscous stress is also zero. 

Figure 28.9 shows the total stress curve (a combination of the viscous and elastic), it is called viscoelastic curve. It is following, the elastic one, by a distance, equivalent to a certain number of degrees, known as delta, 8. 

The stress curve sharply increases when the steric component appears upon compression. The initial thickness of a deformed layer is equal to be half the distance Dq obtained by extrapolating the sharpest initial increase to stress zero. The value Do is 21 1 nm, which is close the thickness of two molecular layers (19.2 nm) of the a-helix brush, calculated using the CPK model and the orientation angles obtained by FTIR analysis. We have calculated the elastic compressibility modulus Y,... 

Metal from internal friction from velocity-stress curves... 

The stress at the interface was measured as a function of temperature and sliding velocity for the resin using the equipment shown in Fig. 4.11, and the data are shown in Fig. 12.33. The stress curve had two maximums the first peak was at the Tg of the resin at 150 °C, and the second peak occurred at a temperature of about 240 °C. In order to maximize solids conveying while maintaining a viable process, the optimal forwarding forces would occur at a barrel surface temperature near 240 °C, and the retarding forces at the screw surfaces would be minimized at temperatures less than about 120 °C. In order to maintain the high rate of this line and the inside barrel wall at a temperature near 240 °C, the first zone of the extruder needed to be maintained at a temperature of 310 °C. 

Slurry Viscosities. In addition to the yield stress, the characteristic shear stress-shear rate relation of the fuel slurry should be known since the shape of the shear rate-shear stress curve (consistency curve) is an indication of the gel characteristics. Low shear rate data (102 sec."1) are useful mainly in determining batch-to-batch reproducibility, while high shear rate data (104 to 106 sec."1) are required to assess the flow characteristics in engine hardware. 

Figure 8. Shear-stress curves for native and alkylated-reduced gliadin and glutenin solutions at low shear stresses (5)...

Fig. 4.5.11. Stress curves—elastic recovery for glazes with a high modulus of elasticity (1) and with a low modulus of elasticity (2).

Similar tests of sections deformed under the action of a Vickers indenter were conducted by Lawn et al. (1980) who used transmission and interference microscopy for this purpose. Tests with Si, Ge, SiC and A1203 crystals revealed a similar, spherical pattern of stress curves for sharp cracking and sharp indenter. Chandhri -et al. (1980) confirmed the test results of... 

The sample must have reached steady state before cessation of the test or the application of a second step. Steady state in a creep test is seen as a constant slope in the strain curve. A constant slope in the stress curve may also be seen in a stress relaxation test, but often the signal is lost in the noise. A material that is liquid-like in real time will need a test period of 5 to 10 min. A stress relaxation test is likely to be somewhat shorter than a creep test since the signal inevitably decays into the noise at some point. A creep test will last indefinitely but will probably reach steady state within an hour. For a material that is a solid in real time, all experiments should be longer as molecular motion is, by definition, slower. Viscoelastic materials will lie in between these extremes. Polymer melts can take 1 hr or more to respond in a creep test, but somewhat less time in a stress relaxation test. 

A tangent line from the point (a, i n) - (0, —1) on the true stress curve hits this curve at that value of n where the engineering stress curve has its maximum value. This is called... 

The yield stress curve will be increased by crystallinity, but within certain limits the brittle strength will not be affected. Consequently the brittle temperature will increase with increasing crystallinity the material becomes more brittle. 

Samples for impact measurements are frequently provided with a notch. Such a notch will of course in principle not affect the brittle temperature, but it does affect the distribution of the applied force in the sample. Near the notch the stresses are triaxially distributed and a higher yield stress in the direction of the net force causes the "normal" yield stress in the sample near the notch. Accordingly, the yield stress curve will be increased and consequently the brittle temperature will apparently be shifted to higher values. 

The main experimental methodology used is to directly characterize the tensile properties of CNTs/polymer composites by conventional pull tests (e.g. with Instron tensile testers). Similarly, dynamic mechanical analysis (DMA) and thermal mechanical analysis (TMA) were also applied to investigate the tensile strength and tensile modulus. With these tensile tests, the ultimate tensile strength, tensile modulus and elongation to break of composites can be determined from the tensile strain-stress curve. 

Fig. 32. Comparison of the calculated [49] and measured [51, 52] yield stress. Curve I is for PPO/PS blends under uniaxial compression, and curve 2 for PPO/PS-pCIS blends under uniaxial tension...

Tihe brittle-ductile transition of metals as reported by Orowan (I) is explained on the basis that brittle fracture occurs when the yield stress exceeds a critical value. This is based on the Ludwik-Davidenkov-Orowan hypothesis that brittle fracture and plastic flow are independent processes yielding separate curves as a function of temperature and strain rate. Therefore, the operative deformation process is the one occurring at the lower stress. The intersection of the brittle stress and yield stress curves therefore defines the brittle-ductile transition. 

Steady State Measurements Fig. 1 shows the shear rate-shear stress curves at various bentonite concentrations (calculated on the basis of the continuous phase) Hysteresis in the shear rate-shear stress curves was insignificant and the correlation between the ascending and descending curves was within experimental error. The results shown in Fig. 1 were therefore, the mean value of the ascending and descending curves. In the absence of any bentonite the suspension was Newtonian, whereas all suspensions containing bentonite at concentrations > 30 g dm were all pseudoplastic. This is illustrated from a plot of viscosity versus shear rate (Figure 2) which shows an exponential reduction of h with increase in shear rate. 

Two extrapolation methods were used to obtain the yield value, Tg, from the shear rate-shear stress curves. In the first method, the data were fitted to a Bingham model, ie. 

Figure 1, Shear rate - shear stress curves at various bentonite concentrations...

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