File:Uniaxial extension and compression in stress-strain relations of rubber (IA jresv82n1p57).pdf

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Uniaxial extension and compression in stress-strain relations of rubber ( )
Author	Wood, Lawrence A.
Title	Uniaxial extension and compression in stress-strain relations of rubber
Volume	82
Publisher	National Bureau of Standards
Description	Journal of Research of the National Bureau of Standards Subjects: Extension and compression in rubber; Martin-Roth-Stiehler equation; modulus of rubber; Mooney-Rivlin equation; rubber; stress-strain relations; stress-strain relations in rubber; uniaxial extension and compression in rubber
Language	English
Publication date	1977 publication_date QS:P577,+1977-00-00T00:00:00Z/9
Current location	IA Collections: NISTJournalofResearch; NISTresearchlibrary; fedlink
Accession number	jresv82n1p57
Source	Internet Archive identifier: jresv82n1p57 https://archive.org/download/jresv82n1p57/jresv82n1p57_A1b.pdf
Permission (Reusing this file)	The Journal of Research of the National Institute of Standards and Technology is a publication of the U.S. Government. The papers are in the public domain and are not subject to copyright in the United States. However, please pay special attention to the

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Short title	Uniaxial extension and compression in stress-strain relations of rubber
Image title	A survey of experimental data from the literature in cases where the deformation of a specimen is varied continuously from uniaxial compression to tensile deformation shows that Young's Modulus M, defined as the limit of stress to strain in the undeformed state, is independent of the direction of approach to the limit. The normalized stress-strain relation of Martin, Roth, and Stiehler (MRS, 1956) is F/M = (L-1 - L-2) exp A (L - L-1) where F is the stress on the undeformed section, L is the extension ratio, and M and A are constants. Values of M and A are obtained from the intercept and slope of a graph of experimental observations of log F/(L-1 - L-2) against (L - L-1) including observations of uniaxial compression if available. They found the value of A to be about 0.38 for pure-gum vulcanizates of natural rubber and several synthetics. In later work several observers have now found that the equation is also valid for vulcanizates containing a filler, but A is higher, reaching a value of about 1 for large amounts of filler. In extreme cases A is not constant at low deformations. The range of applicability in many cases now is found to extend from the compressive region where L = 0.5 up to the point of tensile rupture or to a point where A increases abruptly because of crystallization. Taking A as a constant parameter in the range 0.36 to 1, graphs are presented showing calculated values of (1) F/M as a function of L and (2) the normalized Mooney-Rivlin plot of F/[2M(L - L-2)] against L-1. Each of the latter graphs has only a limited region of linearity corresponding to constant values of the Mooney-Rivlin coefficients C1 and C2. Since this region does not include the undeformed state, where L = 1, or any of the compression region, the utility of the Mooney-Rivlin equation is extremely limited, since it can not be used at low elongations. The coefficients are dramatically altered for rubbers showing different values of the MRS constant A. For rubbers showing the higher values of A, the coefficients are radically altered and the region of approximate linearity is drastically reduced.
Author	Wood
Software used	Adobe Acrobat 9.0
Conversion program	Adobe Acrobat 9.13 Paper Capture Plug-in
Encrypted	no
Page size	536.52 x 726.72 pts 536.04 x 727.2 pts 537.96 x 727.2 pts
Version of PDF format	1.4

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