Strain rate curves

Figure 6-1. Shear stress/strain rate curves...

The Power Law Model. The power law model proposed by Ostwald [57] and de Waale [15] is a simple model that accurately represents the shear thinning region in the viscosity versus strain rate curve but neglects the Newtonian plateau present at small strain rates. The power law model can be written as follows ... 

According to figs. 10a and 10b, the stress exponents where calculated from the slope of the creep stress vs. strain rate curves. The n value for creep of the Ti5Si3 compound is n=3.0 0.2. This predicts a power law creep behavior based on viscous glide of dislocations sustained by diffusion... 

Here K and n are constants whose values are determined by fitting experimental data. For newtonian fluids n = 1 and AT = /x. For pseudoplastic fluids n is less than 1, and for dilatant fluids it is greater than 1. The power law has little theoretical basis its virtues are that it represents a considerable amount of experimental data with reasonable accuracy and that it leads to relatively simple mathematics. Many other equations have been used to represent these stress-strain rate curves. Some of the simpler ones are those of Ellis [3]... 

Figure 5. Top Intensity arbitrary units) vSj strain rate curve for a 0.025% solution of a-PS in decahydronaphthalene. 4.4 X JO . Bottom Pressure drop arbitrary units) across the Jets vs. strain rate curves of a, 0.025% solution of Mw 4.4 X 10 a-PS-decahydronaphthalene b, decahydronaphthalene and c, the result from subtraction of curve b from curve a.

The unit strain rate curves are not fully suitable for describing the behavior of sealants, for they give little information on failure behavior because the failure points for given conditions fall at various points on them. To investigate failure properties as a function of the four basic variables a three-dimensional system has to be used an example is shown in Figure 6 for two-part polysulfide sealant. Each line represents a tensile curve, calculated from the original curves, and the failure points form the upper curved edge of the three-dimensional representation. 

It must be recognized that for silicone sealants the time-temperature superposition was not necessary because the unit strain rate curves fell on the same cumulative single line at each temperature (Figure 4). In other words, the silicone sealant was insensitive to temperature changes within the temperature region observed and within experimental error. 

A pair of stress-strain rate curves for carbon steel was investigated by Parkins [ 19]. The stress vs. strain curves are compared in an inert (hot oil) atmosphere and in boiling 4 N... 

For an elastic solid, stress linear function of the applied strain e, and there is no strain-rate dependence. Elastic modulus E is the slope of the stress versus strain curve. An elastic material can be modeled as a spring, whereas viscous materials can be modeled as a dashpot. For a fluid (viscous material), stress is proportional to strain rate (de/dt) and unrelated to strain. Viscosity 17 is the slt of the stress versus strain rate curve. Figure 11.9 shows the stress/siiain relationship for elastic solids and the stress/strain-rate relationships for viscous liquids. 

Fig. 14 Effect of test temperature on the stress-strain rate curves for super Og.

Stress-strain rate curves for extensional flow of glass fibers suspended in polybutene 0.1 to 1%, rp m 282, S86, and 1259). Adapted from Mewis and Metzner (1974). 

Flgnre 6.6 (a) Creep (time—strain) curves measured during two long-term tests at 600°C 90 MPa, 600°C, f pt = 94,000 h ( 10 years) and 70 MPa, 600°C, f p, 230,000 h (estimate, namely about 25 years) (steel grade 91) (b) stress—minimum strain rate curves and ass(x iated Norton law crrrves, at different temperatures (steel grade 91) [10]. 

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