Stress concentration curve

The apparent viscosity, defined as du/dj) drops with increased rate of strain. Dilatant fluids foUow a constitutive relation similar to that for pseudoplastics except that the viscosities increase with increased rate of strain, ie, n > 1 in equation 22. Dilatancy is observed in highly concentrated suspensions of very small particles such as titanium oxide in a sucrose solution. Bingham fluids display a linear stress—strain curve similar to Newtonian fluids, but have a nonzero intercept termed the yield stress (eq. 23) ... 

Typical S-N (stress versus number of cycles) curves for various metals and composite materials are shown in Figure 6-4 [6-3]. The boron-epoxy composite material curve is much flatter than the aluminum curve as well as being flatter than the curves for any of the metals shown. The susceptibility of composite materials to effects of stress concentrations such as those caused by notches, holes, etc., is much less than for metals. Thus, the initial advantage of higher strength of boron-epoxy... 

FIGURE 12.18 Stress-strain curves of rubber-fiber composites developed for solid rocket motor insulator A, ethylene-propylene-diene monomer (EPDM) rubber-carbon fiber composites B, EPDM mbber-melamine fiber composites C, EPDM mbber-aramid fiber composites and D, EPDM rubber-aramid pulp composites. 1 and 2 stands for unaged and aged composites respectively. Carbon fiber- and melamine fiber-reinforced composites contain resorcinol, hexamine, and silica in the concentrations 10, 6 and 15, respectively and aramid fiber- and aramid pulp-based composites contain resorcinol, hexamine, and silica in the concentrations 5, 3 and 15, respectively. (From Rajeev, R.S., Bhowmick, A.K., De, S.K., and John, B., Internal communication. Rubber Technology Center, Indian Institute of Technology, Kharagpur, India, 2002.)... 

Figure 4 Experimental stress-strain curves for UHMW polyethylene (Mw = 1.5 X 10, Mn = 2 X 10 ) crystallized from the melt and from solutions of various initial polymer concentrations 0. T = 120°C and e = 500%/min.

We [47] further studied quantitatively the strain-induced complex formation in PVA films in dilute iodine solutions whose iodine concentration is lower than the threshold required for the complex formation. We were interested in the effects of degree of hydration D.H. of PVA films and the iodine concentration of the soaking solutions on the strain-induced complex formation. PVA films were stretched in iodine-KI soaking solutions whose iodine concentration was in the range of 2 x 10 9 x 10 mol/1. No boric acid was added to the solution. No complex forms in these solutions, and therefore films remain brown in color before extension. However, when stretched in the solution the color turns to blue at the points indicated by arrows on the stress-strain curves shown in Fig. 11, which shows the beginning of the formation of the complex. The strain-induced complex formation is also shown by the visible ray absorption spectra measured before and after extension in a solution of 3x 10 mol/1 iodine concentration at 30 °C as shown in Fig. 12. A broad peak of the complex with... 

Figure 13 shows the absorbance at km of a specimen of D.H. = 0.84, soaked in 3 x 10 4 mol/1 iodine concentration, as a function of the extension at 30 °C. This absorbance is proportional to the amount of complex formed. The amount of the complex increases successively with extension after passing the point indicated by an arrow on the stress-strain curve. All the swollen PVA films used are so highly elastic that the strain is released when the extension is not more than about 100%. The complex disappears after removal of the extension force when strain is released. This reversible strain-induced complex formation is explained by the increased free energy of PVA chains due to the extension. 

It is customary when evaluating plasticizers in polyvinyl chloride to compare them at concentrations which produce a standard apparent modulus in tension, as measured at room temperature. Since the stress-strain relationship is generally nonlinear it is necessary to specify a given point on the stress-strain curve as well as the rate of loading or straining. The efficiency may be expressed as the concentration of a given plasticizer necessary to produce this standaid modulus. Other properties, e g., indentation hardness, may take the place of tensile modulus. 

Irrespective of how the abnormal stress concentration arises, it is possible that the material at the crack apex is locally stressed into the plastic deformation region of the stress-strain curve. What is the result of the yielding of the metal near the crack apex The result is that as anodic dissolution dissolves away the kinky surface, further plastic yielding creates a fresh kinky surface inside the crack, and thus the yielding helps the metal dissolution along at a rate (e.g., of millimeters per hour) that turns out to be far greater than what would be expected at the overpotential concerned from measurements on the normal surface (Hoar and West, 1976). 

Similar well fitting simulation curves for the experimental stress-strain data as those shown in Fig. 46b can also be obtained for higher filler concentrations and silica instead of carbon black. In most cases, the log-normal distribution Eq. (55) gives a better prediction for the first stretching cycle of the virgin samples than the distribution function Eq. (37). Nevertheless, adaptations of stress-strain curves of the pre-strained samples are excellent for both types of cluster size distributions, similar to Fig. 45c and Fig. 46b. The obtained material parameters of four variously filled S-SBR composites used for testing the model are summarized in Table 4, whereby both cluster... 

Figure 3. Stress-strain curves of three gradient polymers and one interpenetrating network of poly(methyl methacrylate) with 2-chloroethyl acrylate at comparable strain rates of 2-3% /sec and same temperature of 80° C. The numerals in parentheses indicate concentrations (mole percent) of chloroethyl acrylate in poly(methyl methacrylate).

Figure 2.8. Stress-strain curves of nanotube nanocomposites (a) containing 0.2 wt % of different types of functionalized CNTs and (b) containing different concentration of fFWNTs. Reproduced from reference 4 with permission from American Chemical Society.

Fig. 29. The compressive stress-strain curves of silica filled epoxy at different filler concentrations [46]...

Fig. 40. Stress-strain curves of SBS toughened PS composites prepared via the concentration emulsion pathway. SBSx (with x = 10,15,20, 25 and 30) stands for wt. parts of SBS to 100 wt. parts of styrene...

Maximum absolute stress concentration factors are shown in Figure 5, again for an ellipticity R = 0.1. As before, all orientations p give the same stress concentration for equal biaxial tension ( = 45°). In addition equal biaxial compression ( = —135°) gives the same stress concentration since absolute stress concentration is being considered. The shear stress concentration is given by Q /2. The curves shown in Figure 5 are symmetrical about the pure shear condition ( = —45°). 

---