tailieunhanh - Mechanical properties of polymers and composites-Nielsen Episode 12

Tham khảo tài liệu 'mechanical properties of polymers and composites-nielsen episode 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Creep and Stress Relaxation 103 plateau. It was first given empirically by Plazek 183 for creep and subsequently derived for stress relaxation from reptation dynamics by Curro et ai. 184 185 . A useful expression for Plazek s tabulated MOeni function is 185a log X 10 11 - X 10 1 k g flf - X 10 - log- r a - X to s log t r 59 valid over the range - 16 log i 0 where J is a shift factor which depends on the degree of cross-linking and shifts log MOi-ni along the line until it joins with the curve loglMOr E 0tl .J- Figure 17 shows the course of MO for live uncross-linked rubbers as calculated by Landel and Fedors 186 from the Marvin 187 extension of the Rouse theory to undiluted polymers which gives the time dependence of MO The Marvin theory employs the Rons parameters a the bond length and ill. the monomeric friction factor plus the ratio M Mr-The addition of a term M. .TV whose magnitude will be determined by the extent of cross-linking . the elastic chain concentration as determined by swelling would give rise to the dashed-line response shown in Figure 18 for the silicone rubber. Finally the solid line shows the expected response when the entanglement term is added. Using this approach Landel Figure 17 Calculated stress-relaxation behavior at 298 K for five uncross-linked elastomers ofM 200 000 EP cthylene-propylene 56 44 styrene-butadiene SB natural rubber N butyl and dimethyl siloxane. 104 Chapter 3 Figure 18 Calculated stress-relaxation curves for styrene-butadiene and silicone rubbers both uncross-linkcd from Figure 17 and cross-linked to V - 50 X 10 6 mol cm and for SBR additionally cross-linked lo V 100 and 200 X 10 i mol cm . The horizontal bars show the location of the equilibrium modulus for SBR. M - 200 000 T - 29 K and Fedors calculated E t for four quite different types of elastomers. They showed that can be predicted with no adjustable parameters using molecular constants evaluated a priori over at least seven decades