By I. M. Ward
Ward and Sweeney, either affiliated with the IRC in Polymer technological know-how and know-how on the collage of Leeds, united kingdom, introduce the mechanical habit of reliable polymers, including new fabric on mechanical relaxations and anisotopy, composites modeling, nonlinear viscoelasticity, and fracture of difficult polymers to this moment variation. The obtainable procedure of the e-book has been retained for this variation, with every one bankruptcy designed to be self-contained and the idea and purposes of the topic brought the place acceptable. bankruptcy difficulties and mathematical appendices are incorporated. The e-book is for college students of fabrics, chemistry, physics, and engineering.
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An applied stress óxx will produce a strain e xx ¼ ó xx E in the x direction and strains e yy ¼ Àí ó xx E and e zz ¼ Àí ó xx E in the y and z directions, respectively. ) A shear strain e xz is related to the corresponding shear stress óxz by the relationship e xz ¼ óxz /G, where G is the shear modulus. 25 FINITE STRAIN ELASTICITY Thus we obtain the stress–strain relationships that are the starting point in many elementary textbooks of elasticity ([1], pp. 7–9): e xx ¼ 1 í ó xx À (ó yy þ ó zz ) E E e yy ¼ 1 í ó yy À (ó xx þ ó zz ) E E e zz ¼ 1 í ó zz À (ó xx þ ó yy ) E E e xz ¼ 1 ó xz G eyz ¼ 1 ó yz G exy ¼ 1 ó xy G A bulk modulus K, related to the fractional change in volume, can also be defined, but only two of the quantities E, í, G and K are independent.
Phys. Solids, 41, 427 (1993). 14. , Comput. Theor. Polym. , 9, 27 (1999). 15. Stepto, R. F. T. and Taylor, D. J. , Macromol. , 93, 261 (1995). 16. Stepto, R. F. T. and Taylor, D. J. , J. Chem. Soc. , 91, 2639 (1995) 17. Flory, P. , Crescenzi, V. and Mark, J. , J. Am. Chem. , 67, 3202 (1971). 18. Taylor, D. J. , Stepto, R. F. , Jones, R. , Macromolecules, 32, 1978 (1999). 19. Cail, J. , Taylor, D. J. , Stepto, R. F. , Macromolecules, 33, 4966 (2000). Problems for Chapters 2 and 3 1. The tensile stress ó in an ideal rubber when simply extended to a length º times its initial length is given by ó ¼ NkT (º2 À ºÀ1 ) Explain without giving any mathematical details the physical model that leads to this expression.
A sample of polyisoprene (density 1300 kg mÀ3 , monomer of relative molar mass 68) has a shear modulus of 4 3 105 Pa at room temperature. Calculate the average number of monomers between cross-links. 2. 5000 at small 52 RUBBER-LIKE ELASTICITY strains. 4900? 3. What would be the root mean square end-to-end distance of a paraffinic chain ˚ and the consisting of 1000 carbon atoms? e. without the restriction that valence angles should remain constant). 4. A non-Gaussian rubber has the strain-energy function 1:3 U ¼ C1 (º11:3 þ º1:3 2 þ º3 À 3) where º1 , º2 and º3 are the principal extension ratios and C1 ¼ 4 3 105 Pa.