STRESS-STRAIN RELATIONSHIPS FOR SOLID POLYMERS UNDER BI . C I'LL LOADINGS
I ND[T PR,AK ASH SINGE
Applied Mechanics Department
bz:i.t ted
in fulfilment of the requirements of the degree of Doctor of Philosophy
to the
Indian Institute of Technology, Delhi.
OCTOBER 1977.
Gl3 TIFICATF
This is to certify that the thesis entitled
"Stress-Strain Relationships for Solid Polymers under Biaxial Loadings" being submitted by Mr. I.P. Singh to the Indian a.
Institute of Technology, Delhi for the award of the degree of Doctor of iilosophy is a record of the bonafide research work
carried out by Mn. Mr. I.P. Singe has worked ceder zy guidance and supervision and has fulfilled the requirements for the submission of this thesis,, which to my laiowledge has reached the requisite standard.
The thesis, or any part thereof, has not been
submitted to any other TJnivergity or Institute for the award of any degree or diploma.
(Dr. R.K.Nittai) Assistant Professor Deptt. of Applied Mechanics Indian Institute of Technology, Delhi,
I 1 DMM—JL10029.
1 C ? ,- ,TTS
The author is deeply indebted to Dr. E.K.Mittal,
Deptt. of Ajpiied Tliechha Tics, for his expertguidance and constant encouragement during the course of this investigation.
The author also wishes td thank Prof. V.D.Gupta, Deptt. of Textile Engineering, for his keen interest in this
investigation and is indebted to him for hi guidance during the absence of Dr. TMittal.
Thanks are due to the faculty members of the Deptt. of Applied Mechanics, especially prof. B.Marunes, for their assistance and suggestions. The author acknowledges the help and co—operation extended by the laboratory and workshop personnel of the Applied Mechanics Deptt. He is indebted to the I.D.D.Centre for their help
in the fabrication of the experimental set-pup and the preparation of the specimens.
The author is indebted to his colleague Mrs. Jhu ur Lahiri for her assistance during experimentation and calculations.
Tho author is grateful to the C.S.I.R. for the financial assistance for this investigation.
iBiTRLCtP
In this investigation the stress-strain relationship of nylon 6, a semicrystailine polyner,and Fi'M (Perspex) an amorphous
Jassy polyner,have been studied under uniaziol (tensile and torsional) and biaxial (combined tensile and torsional) loadings. Measures of
goneralisod stress and generalized strain were dot mined. experimentally for these polymers in order to describe their deformation behaviour for all loading paths by the same functional relationship involving these measures.
For conducting the experiments a combined tension-torsion
machine was fabricated. This was of the dead weight type, v&-ere tensile and torsional loads coolci be apnlied independent of each other. Thin walled tubular speciriens were subjected to raop loading through various
loading paths, i.e., tension only,torsion only, tension and torsion simultaneously, tension followed by torsion, and torsion followed by tension. They were also subjected to step loadings of tension only, torsion only and combined toncion-torsion. The torsional and. tensile dinpcements were monitored independently.
From the experimental observations, it was found that
seriicrystaiiine nylon 6 follows a generalized stress-generalized strain behaviour litaiLively similar to that of dead. annealed notaic as put
foriard by hell and generalized. by Mittol. The stress-strain
relationship is piecewise rabolic and. the measures of generalized stress and strain for nylon 6 were found to be
a 2 generalized stress = 'G
genera_lizea strain =
where CT and r are the tensile end shear stresses, and e end '1 a-re the tensile and sheer strains resnoc vivel.y.
On the other a »:_ Ph A, , wh-ich is an a°nory ? e?3 ucy poly`Ler,
oz ibits a behaviour that can be coiiparod in a piecewise nan er to rubbers. This jas further co _f i -med by the ex minati.on of the stress- strain data of others for Corp ous ,)olyeers (Fid , PC,, unpiasticized PVC). The generalized measures of ,tress end strain for Ra-EL wore
found to be
generalized ,tress = + a '~ 2
generalized strain =3 , + Y2
The 'ortevin-le Chatelier effect and the Poynting effect were observed for both the polyners.
Theoretical models based or strain enerE - functions of 1: ttal and Mooney- .ivlirx have been discussed, to explain the stress-
strain behaviour of nylon 6 end PLEA respectively.
TABLE OF C0NT!TS
CIRT1FICLTE ...
ACTDGEiEiTTS • ii
ST1iLCT
iBLE D2 CC1JTJTS .. V
LIST UP PIUJRiS vjj
LIST CF TABLES .. xi
LIST Cr FLLTES ... Xli
cLPTI1as
I. flITIICDtCTICIT ..• I
1. ITature of 1-1,01yaers 2
2. Literature Survey ...
3. 12a±,roduction to the Problem • . 13 4. Objectives an,-1 Scope of the
Problem
•..
16I.I. OUML,iTTJL DE2fiILS
,..
201. Plan of 1TDeriiicnts
•..
202. Preparation of Specimens... 22
3. The iermental Set-Up .. 26
4. Calibration o_i the Set-Tip .•. 33
III. ThEIfPICb 11MULTS
37
1 icpresoion for Stress and Strain .•.
37
2. qorinental Thoetdt for ITylon 6 • . 38
30 &erinenta1 Reu1ts for PMA ... 54 4. Me Portevin-lo Chatelier Effect ... 72
(vi)
IV. L1TAjYSI3 OF a'T .RESULTS • .. 74 1. Analysis of the Stress-Strain
Behaviour for Nylon 6 ... 7 2. Discussion for 1Tylo a 6 ... 92 3. analysis of he Stress-Strain
Behavioir for 2i21L ... 94
!. Discussion for R ... 98
V. i~XICIJ MOD FOR a SSS—STMLIN
.L _J_TICITSH .0 SY ... 108