tailieunhanh - Engineering Materials 2E VOLUME2 Episode 11

Tham khảo tài liệu 'engineering materials 2e volume2 episode 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Mechanical behaviour of polymers 241 Fig. . The way in which the modulus of polymers changes with the fraction of covalent bonds in the loading direction. Cross-linking increases this fraction a little drawing increases it much more. Substituting this information into the last equation gives an equation for the glassy modulus as a function of the fraction of covalent bonding E f- LJ2ị GPa. This function is plotted in Fig. . The glassy modulus of random linear polymers f ị is always around 3 GPa. Heavily cross-linked polymers have a higher modulus because f is larger - as high as - giving E 8 GPa. Drawn polymers are different they are anisotropic having the chains lined up along the draw direction. Then the fraction of covalent bonds in the loading direction is increased dramatically. In extreme drawing of fibres like nylon or Kevlar this fraction reaches 98 and the modulus rises to 100 GPa about the same as that of aluminium. This orientation strengthening is a potent way of increasing the modulus of polymers. The stiffness normal to the drawing direction of course decreases because f falls towards zero in that direction. You might expect that the glassy modulus which like that of metals and ceramics is just due to bond-stretching should not depend much on temperature. At very low temperatures this is correct. But the tangled packing of polymer molecules leaves some loose sites in the structure side groups or chain segments with a little help from thermal energy readjust their positions to give a little extra strain. These secondary relaxations Fig. can lower the modulus by a factor of 2 or more so they cannot be ignored. But their effect is small compared with that of the visco-elastic or glass transition which we come to next. 242 Engineering Materials 2 Fig. . Each molecule in a linear polymer can be thought of as being contained in a tube made up by its surroundings. When the polymer is loaded at or above Tg each molecule can move .

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