• No results found

Stress-strain relationships for solid polymers under biaxial loadings

N/A
N/A
Protected

Academic year: 2023

Share "Stress-strain relationships for solid polymers under biaxial loadings"

Copied!
7
0
0

Loading.... (view fulltext now)

Full text

(1)

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.

(2)

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.

(3)

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.

(4)

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

(5)

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.

(6)

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

•..

16

I.I. OUML,iTTJL DE2fiILS

,..

20

1. Plan of 1TDeriiicnts

•..

20

2. 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

(7)

(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

1. Theoretical Nodel for Nylon 6 . o . 109 2. Theoretical ilodol for F i>:k ... 110

VI, CUiTC JSIOTJ ... 116

B: LIOGI~, Z :L' ... 122

LPP+{ • DC ... 126

810-DATA • • • 134

References

Related documents

Also, the effect of Chakrabarti's modification to the Airy's linear wave theory, the effect of coupling of stiffness coefficients, the effect of consideration of current velocity

In the present work, the behaviour and performance of rectangular reinforced concrete beams strengthened with externally bonded Glass Fibre Reinforced Polymer (GFRP) fabrics

Even when the stress or strain is held constant for a duration either in tension or in compression, if the temperature is not high enough to cause creep damage or stress

Since temperature or concentration gradients can cause gradients in surface tension as well as density, buoyancy and surface-tension driven flows can occur

As wind pressure increases, tension in the ground wire and conductor increases by about 7–8% for every increase of 0.01% of dust particles, since the tension is directly dependent

The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are

The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are

Kxperimental results, whi( h show that viscosity influences the rotational “ wings " in light-scattering, necessitate a view-point of viscosity independent of