information to users

INFORMATION TO USERS This manuscript has been reproduced from the microfilm master UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order.

Bell & Howell Information and Learning 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 800-521-0600

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.


FINITE ELEMENT ANALYSIS OF COMPOSITE INDUSTRIAL GRATINGS

A Thesis Presented to The F aculty of the College of G ra d u a te Studies L am ar U niversity

In P artial Fulfillm ent of th e R equirem ents for the D egree M aster o f E ngineering Science

by S uresh Dharm araj A ugust, 2000


UMI N um ber 1401106

_ ___

(fo

UMI

UMI Microform 1401106 Copyright 2000 by Bell & Howell Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code.

Bell & Howell Information and Learning Company 300 North Z eeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346


FINITE ELEMENT ANALYSIS OF COMPOSITE INDUSTRIAL GRATINGS by Suresh D harm araj A pproved:

M alur N. Srinivasan Supervising Professor

H sing-w ei C hu C om m ittee M em ber

Jam es L. Thom as C om m ittee M em ber

Victor A. Z aloom C hair, D e p artm en t of Industrial E ngineering

vc/k R. H o p p e r 'ean, C ollege of Engineering

James W. W estgate Interim A ssociate Vice President for Research and D ean of G ra d u ate Studies


© 2000 by Suresh Dharmaraj

No part of this work can be reproduced without permission except as indicated by the "Fair Use” clause of the copyright law. Passages, images, or ideas taken from this work must be properly credited in any written or published materials.


The author respectfully dedicates this thesis to his beloved parents, Dharmaraj and Rajammal Dharmaraj


ABSTRACT Finite E lem ent Analysis of C om posite Industrial G ratings by Suresh D harm araj The objective of this study w as to p red ic t the behavior of glass fiber reinforced po ly m er m atrix com posite gratings u sin g finite elem ent analy sis an d experim ental testing. C om posite m aterials are o f g reat interest in in d u stries, used as stru c tu ra l m em bers to reduce w eight. Because of a paucity of d e sig n criteria and stru c tu ra l stability specifications as co m p a red to steel an d concrete, they are not extensively used. The basic intent of th e research w as to in vestig ate the m axim um allow able deflection and m axim um load bearing capacity o f the com posite gratin g considered for analysis. By this stu d y , the effect of in ter-sp acer distances in load bearing, deflection restriction a n d buckling of the b eam s can be analyzed.

A

finite

elem ent

m odel

is

d e v elo p ed

and

an aly zed

using

P ro /M E C H A N IC A. It w as concluded from this research s tu d y that, in the gratings stu d ie d , the m axim um deflection w as in the range of 0.75 a n d 0.85 inches irrespectiv e of the load applied. The effect of spacers used for assem bling the I-beam s w a s stu d ied . O ptim al inter-spacer distance was selected from am ong the tested m o d els an d su g gested for practical im plem entation. M icrom echanical stu d y w as done a t the

fracture zone

u n d e rstan d in g of th e cause and nature of the fracture.


for b etter

ACKNOWLEDGEMENTS The a u th o r w ould like to sincerely thank his su pervising professor Dr. M alur N . Srinivasan for the helpful insights a n d m otiv atio n rendered to him d u rin g the course of this work. Special appreciation goes to Dr. Victor A. Zaloom and com m ittee m em bers for their detailed suggestions a n d com m ents. I w ould also like to th an k Dr. Paul R. C order for his helpful suggestions du rin g the course of this research. The a u th o r is grateful to the Texas D epartm ent of T ransportation (TxDoT) for funding the project and Fibergrate C orporation Inc., for supply in g the m aterial. T he a u th o r extends his acknow ledgem ent to his colleague D evanathan K rishnan a n d lab adm inistrators R ichard M cClelland an d Bud Colville for helping him in the experim ental p a rt of the research w ork. Also, special thanks goes to P o ly h ed ro n laboratories Inc., for its tim ely deliv ery of the SEM stu d y results. Finally, I w o u ld like to thank m y parents for th eir advice a n d w onderful su p p o rt offered to me.

iii


TABLE OF CONTENTS Page

List of Tables...........................................................................................................viii List of Figures....................................................................................................... ix N om enclature....................................................................................................... xvi G lossary................................................................................................................... xviii Chapter 1. INTRODUCTION.......................................................................................................01 1.1. Objective of R esearch.......................................................................................01 1.2. T erm inology.......................................................................................................02 1.3. C losure................................................................................................................ 02 1.4. H istorical b a ck g ro u n d of FE M /F E A ...........................................................03 1.5. H istory a n d E volution of C om posites......................................................... 04 2.

LITERATURE REVIEW............................................................................................06 2.1. C o m p o site s......................................................................................................... 06 2.1.1. D efinition...................................................................................................06 2.1.2. C lassification............................................................................................ 07 2.1.3. P ro p erties................................................................................................... 07 2.1.4. A pplication ................................................................................................08 2.2. M anufacturing o f C o m p o sites......................................................................... 08 iv


2.2.1. P u ltru sio n .................................................................................................... 09 2.3. S tru ctu ral a n d Finite E lem ent stu d ie s of FRP b e am s.................................. 10 2.4. M aterials T ypes......................................................................................................13 2.4.1. Isotropic m aterial.......................................................................................13 2.4.2. T ransversely Isotropic m ateria l.............................................................13 2.4.3.

O rth o tro p ic m aterial................................................................................ 14

2.5. M aterial P ro p erties............................................................................................... 14 2.5.1.

Y oung's m o d u lu s.......................................................................................14

2.5.2.

B ulk m o d u lu s.............................................................................................14

2.5.3.

P oisson ratio ...............................................................................................15

2.5.4.

D ensity.........................................................................................................15

2.6. M aterial F ailure.....................................................................................................16 2.6.1.

Failure m odes an d T heories................................................................... 16

2.6.2.

Failure Theories for D uctile m aterials.................................................17

2.6.3.

F ailure T heories for Brittle m aterials...................................................17

3. EXPERIMENTAL W ORK........................................................................................... 18 3.1. S etup ......................................................................................................................... 18 3.2. C ontrol U n it............................................................................................................ 18 3.3. T esting U n it............................................................................................................ 19 3.4. P ro c ed u re ............................................................................................................... 19 v


4.

M O D ELIN G AND ANALYSIS................................................................................20 4.1. M odeling Procedure........................................................................................... 20 4.2. D esign M odifications......................................................................................... 21 4.3. A nalysis Procedure..............................................................................................22 4.4. In p u t D ata.............................................................................................................. 23

5.

MICROSTUCTURAL EVALUATION................................................................... 24 5.1. Possible reasons for failure................................................................................25 5.2. L im itations of M icrom echanical s tu d y .......................................................... 25 5.3. A nalytical report of SEM.................................................................................... 26

6.

RESULTS A N D DISCUSSION.................................................................................29 6.1. P resentation of Results....................................................................................... 29 6.2. D iscussion of Results.......................................................................................... 30

7.

SUMM ARY, CONCLUSIONS & SCOPE FOR FUTURE W O RK .................. 33 7.1. S u m m ary ................................................................................................................ 33 7.2. C onclusion............................................................................................................. 34 7.3. Scope for Future w ork........................................................................................ 34

REFERENCES.....................................................................................................................35 APPEND ICES A. Figures and Tables.................................................................................................39 B. M athem atical M odel using ID Bar E lem ent................................................... 126 vi


C. V alidation of P ro /M results w ith M athem atical so lu tio n ..........................133 D. M athem atical In p u t value calculations........................................................... 136 BIOGRAPHICAL N O TE................................................................................................140

vii


LIST OF TABLES Table

Page

A l.

D eflection valu es for 3" inter-spacer d istance g ra tin g ...................................109

A2.

D eflection v alu es for 6" inter-spacer d istance g ra tin g ...................................112

A3.

D eflection v alu es for 9" inter-spacer distance g ra tin g .................................. 116

A4.

D eflection v alu es for 12" inter-spacer distance g ra tin g ................................ 119

A5.

T herm al a n d M echanical properties of Glass fibers.......................................122

A6.

M atrix p ro p e rtie s.................................................................................................... 123

A 7.

M echanical p ro p erties of Resins.......................................................................... 124

AS.

C o m p ariso n o f Deflection values........................................................................125

A9.

C o m p ariso n o f F racture loads............................................................................. 125 C om parison o f Buckling...................................................................................... 125

v iii


LIST OF FIGURES Figures

Page

A l.

C lassification of C om posites................................................................................ 40

A2.

T y p es o f FEA............................................................................................................41

A3.

C ra ck p ro p ag atio n in FRP’s.................................................................................. 42

A4.

PM C M anufacturing p ro cess............................................................................... 43

A5.

M a n u factu rin g Flow D iag ram .............................................................................44

A6.

U T M - C ontrol u n it................................................................................................ 45

A7.

U T M - T esting u n it................................................................................................. 46

A8.

P u ltru sio n process.................................................................................................. 47

A9.

T op view of 3" spaced g ra tin g ......................................................................... 47

A10.

L eft view of 3" spaced g ra tin g ...........................................................................48

A l l . R ig h t view of 3" spaced g ra tin g ......................................................................... 48 A12.

T o p view of 9" spaced g ra tin g ......................................................................... 49

A13.

T o p view of 9" spaced g ra tin g ......................................................................... 49

A14. R ig h t view of 9" spaced g ra tin g ......................................................................... 50 A15.

T o p view of 12" spaced g ra tin g before fracture...........................................50

A16.

T o p view of 12" spaced g ra tin g after fracture..............................................51

A17.

D eflection of 3" spaced g ra tin g - lOOlbs/Beam............................................ 52

A18.

D eflection o f 3" spaced g ra tin g - 2001bs/Beam ............................................ 52 ix


A19.

Deflection of 3” spaced grating - 3001bs/Beam........................................ 53

A20.

D eflection of 3" spaced grating - 400lbs/B eam ............................................53

A21.

Deflection of 3" spaced grating - 500lbs/B eam .............................................54

A22.

Deflection of 3" spaced grating - 600lb s/B ea m .............................................54

A23.

Deflection of 3" spaced grating - 7001bs/Beam .............................................55

A24.

Deflection of 3" spaced grating - 800lbs/B eam .............................................55

A25.

Deflection of 3" spaced grating - 900lb s/B e a m .............................................56

A26.

D eflection of 3" spaced g rating - lOOOlbs/Beam...........................................56

A27.

Deflection of 3" spaced g rating - llO O lbs/B eam ...........................................57

A28.

Deflection of 6" spaced g rating - lOOlbs/Beam.............................................58

A29.

Deflection of 6" spaced g rating - 2001bs/Beam .............................................58

A30.


A31.


A32.


A33.


A34.

Deflection of 6" spaced grating - 7001bs/Beam ............................................ 61

A35.


A36.


A37.

Deflection of 6" spaced g rating - lOOOlbs/Beam...........................................62

A38.

Deflection of 6" spaced g rating - llO O lbs/B eam .......................................... 63 x


A39.

Deflection of 6" spaced grating - 12001bs/Beam....................................... 63

A40.

Deflection of 6" spaced grating - 13001bs/Beam...........................................64

A41.

Deflection of 6" spaced grating - 14001bs/Beam...........................................64

A42.

Deflection of 6" spaced grating - 15001bs/Beam.......................................... 65

A43.

Deflection of 9" spaced grating - lOOlbs/Beam.............................................66

A44.

D eflection o f 9" spaced grating - 2001bs/Beam .............................................66

A45.


A46.


A47.

Deflection o f 9" spaced grating - 5001bs/Beam ............................................ 68

A48.

Deflection of 9" spaced grating - 600ibs/B eam ............................................ 68

A49.

Deflection o f 9" spaced grating - 7001bs/Beam ............................................ 69

A50.


A51.


A52.

Deflection o f 9" spaced grating - 1000lb s/B eam .......................................... 70

A53.

Deflection of 12" spaced grating - lOOlbs/Beam.......................................... 71

A54.

Deflection of 12" spaced grating - 2001bs/Beam.......................................... 71

A55.

Deflection of 12" spaced grating - 3001bs/Beam ...........................................72

A56.

Deflection of 12" spaced grating - 4001bs/Beam .......................................... 72

A57.

Deflection of 12" spaced grating - 5001bs/Beam ...........................................73

A58.

Deflection of 12" spaced grating - 6001bs/Beam.......................................... 73 xi


A59.

Deflection of 12" spaced grating - 7001bs/Beam........................................ 74

A60.

D eflection of 12" spaced g ratin g - 8001bs/Beam ........................................... 74

A61.

D eflection of 12" spaced g ratin g - 9001bs/Beam ............................................75

A62.

D eflection of 12" spaced g ratin g - 1000lb s/B eam ......................................... 75

A63.

D eflection of 12" spaced g ratin g - llO O lbs/B eam ......................................... 76

A64.

D eflection of 12" spaced g ratin g - 12001bs/Beam......................................... 76

A65.

L oad-D eflection curves of 3" sp aced g rating..................................................77

A66.

Load D eflection curves of 6" sp aced g ratin g ..................................................78

A67.

L oad D eflection curves of 9" sp aced gratin g ..................................................79

A68.

L oad D eflection curves of 12" sp aced gratin g ............................................... 80

A69.

Isom etric view of the sp acer.............................................................................. 81

A70.

Isom etric view of 3" spaced

b e am ...............................................................81

A71.


b e a m ...............................................................82

A72.


b e a m ...............................................................82

A73.

Isom etric view of 12" spaced b e a m ................................................................. 83

A74.

Isom etric view of 3" spaced g ra tin g ................................................................. 83

A75.


A76.


A 77.

Isom etric view of 12" spaced g ra tin g .............................................................. 85

A78.

D etailed view of the sp acer.................................................................................85 xii


A79.

Detailed view of 3" spaced beam................................................................ 86

A80.

D etailed view of 6" sp aced beam ......................................................................86

A81.

D etailed view of 9" spaced beam ......................................................................87

A82.

D etailed view of 12" sp aced b eam ....................................................................87

A83.

D etailed view of 3" sp aced g ratin g...................................................................88

A84.

D etailed view of 6" sp aced g ratin g...................................................................88

A85.

D etailed view of 9" spaced g ratin g...................................................................89

A86. D etailed view of 12" sp aced g ratin g ..................................................................89 A87...... E lectron M icrograph 1 - Fracture surface........................................................90 A88...... E lectron M icrograph 2 - Fracture surface........................................................90 A89.

E lectron M icrograph 3 - Fracture surface........................................................91

A90...... E lectron M icrograph 4 - Fracture surface........................................................91 A91...... E lectron M icrograph 5 - Fracture surface........................................................92 A92.


A93...... E lectron M icrograph 7 - Fracture surface........................................................93 A94.


A95......E lectron M icrograph 9 - Fracture surface........................................................94 A96.

E lectron M icrograph 10 - Fracture surface....................................................... 94

A97. E lectron M icrograph 11- Fracture surface........................................................ 95 A98.

E lectron M icrograph 12 - Fracture surface..................................................... 95 xiii


A99.

E lectron M icrograph 13 - Fracture surface..................................................... 96

A100. Electron M icrograph 14 - Fracture surface..................................................... 96 A101. Electron M icrograph 15 - Fracture surface..................................................... 97 A102. Electron M icrograph 16 - Fracture surface..................................................... 97 A103. Electron M icrograph 17 - Fracture surface..................................................... 98 A104. E lectron M icrograph 18 - Fracture surface..................................................... 98 A105. E lectron M icrograph 19 - Fracture surface..................................................... 99 A106. Electron M icrograph 20 - Fracture surface..................................................... 99 A107. E lectron M icrograp h 21 - Fracture surface..................................................... 100 A108. Electron M icrograph 22 - Fracture surface......................................................100 A109. Electron M icrograph 23 - Fracture surface..................................................... 101 A110. E lectron M icrograp h 24 - Fracture surface..................................................... 101 A l l l . Electron M icrograph 25 - Fracture surface......................................................102 A112. Electron M icrograph 26 - Fracture surface......................................................102 A113. Electron M icrograph 27 - Fracture surface......................................................103 A114. Electron M icrograph 28 - Fracture surface......................................................103 A115. E lectron M icrograph 29 - Fracture surface......................................................104 A116. E lectron M icrograp h 30 - Fracture surface......................................................104 A117. Electron M icrograp h 31 - Fracture surface......................................................105 A118. Electron M icrograph 32 - Fracture surface......................................................105 xiv


A119. Electron Micrograph 33 - Fracture surface..................................................106 A120. Deflection o f cantilever beam - lOOlbs............................................................ 107 A121. Isom etric v iew o f a cantilever b e am ..................................................................108 A122. D etailed view o f a cantilever b eam .................................................................... 108

XV


NOMENCLATURE K

Bulk modulus

E

Young’s modulus

E,,

-

Longitudinal Young's modulus in direction 1

E l Icon:

“

Longitudinal Young's modulus of the core

E 1 1core

“

Longitudinal Young’s modulus of the mat

e 22 E 2 2core

Transverse Young's modulus in direction 1 “

Transverse Young's modulus of the mat

E 22mat

E 33

g

12

G ,3

Transverse Young's modulus of the core

*

Transverse Young's modulus in direction 1

-

Longitudinal Shear modulus

-

Transverse Shear modulus

V

Poisson ratio

v ,2

Longitudinal Poisson ratio in direction 1

v 2|

Transverse Poisson ratio in direction 2

V3 1

Transverse Poisson ratio in direction 3

V12corc

“

Longitudinal Poisson ratio of the core

V i 2mat

Longitudinal Poisson ratio of the mat

Vf

Volume fraction of Fiber Volume fraction of Matrix

P

Fiber constant

a

Stress


z

Strain

p

Density

Pc

Density of the Composite

pf

Density of the Fiber

pm

Density of the Matrix

Pcorc

Density of core

Pm at

Density of mat

xvii


GLOSSARY FEM

-

Finite E lem ent M ethod

FEA

-

Finite E lem ent Analysis

P ro /E

-

Pro / ENGINEER

P ro /M

-

P ro/M E C H A N IC A

PP

-

Polypropylene resin

PA

-

Polyam ide resin

PSU

-

P olysulphone resin

PES

-

Polyether su lphone resin

PAS

-

Polyaryl su lp h o n e resin

PPS

-

Polyphynylene sulphide resin

PEI

-

Polyether im ide resin

PAI

-

P olyam ide im ide resin

PEK

-

Polyether keytone resin

PEEK

-

Polyether e th e r keytone resin

GR

-

G lass Reinforced

FRP

-

Fiber Reinforced Plastic

FR

-

Fiber Reinforced

E

-

G lass fiber in general use

R S-2

A h ig h stre n g th version of E-Glass fiber -

A h ig h stre n g th version of E-Glass fiber xviii


E-CR

-

E-Glass fiber w ith enhanced chem ical resistance to corro sio n

LM

-

Low m odulus

HM

-

H igh m odulus

IMLS

-

Interm ediate m o d u lu s low stre n g th

IMHS

-

Interm ediate m o d u lu s high stre n g th

UTM

-

U niversal testing m achine

xix


Dharmaraj 1 C H A PTER 1 In tro d u ctio n 1.1 O bjective o f R esearch The m ain objective of this stu d y w as to have som e u n d e rsta n d in g of the deflectional b e h av io r of a glass fiber reinforced polym er com posite g ratin g u n d e r transverse lo ad in g conditions an d to p re d ic t its behavior in a w id e v ariety o f cases. The tw o in te n d e d w ays of stu d y w ere by: 1. E xperim ental testing 2. Finite ele m e n t analysis The effect o f

inter-spacer distances

on

the grating deflection

w as also

in vestigated for v ary in g loads. The follow ing w ere the areas exam in ed in this research w ork. a) D eflection b ehavior of the gratings. b) Effect o f th e inter-spacer distances. c) A d eta ile d investigation of the n a tu re a n d cause of the fractu re from a m icrom echanical stand point. d) F o rm u late a 1-D m athem atical m o d el o f the setup w ith sim ilar b o u n d a ry conditions. e) C loseness of P ro /M results w ith a m athem atical result o f a sim p le cantilever beam .


Dharmaraj 2 1.2 T erm inology The Composite referred to in this research w ork w as fabricated using continuous unidirectional E-Glass fibers reinforced in V inylester m atrix w ith a fiber-m atrix ratio of 60:40 respectively. Span refers to the entire len g th of the com posite b eam in the direction parallel to the fiber axis. Spacer refers to the reinforcem ent in th e grating to increase the load bearin g capacity and to m aintain a co n stan t spacing betw een the I-beam s of the grating. Support refers to the rollers on w h ich the beam is placed in the setup. Core refers to the in n er part of the I-beam , w h ich has a fiber-m atrix ratio of 60:40. M at refers to the o u te r layer of the I-beam , w h ich has a fiber-m atrix ratio of 80:20. Fiber/Filament [21] is referred to as a ro d of very sm all d iam eter an d indefinite length m ad e of organic or non-m etallic m aterials. In this case it is the E-glass. M atrix [21] is the base m aterial in w hich various reinforcem ents are em bedded. In this case it is the vinylester resin.

1.3 C losure H ere, the load environm ent an d the present construction tren d s are introduced briefly. G ratings are com m only em ployed as w alk w ay s a n d flooring in in d u stry to red u ce the load tran sm itted to the supports. The p rim a ry load to be considered is th e transverse load ap p lied d u e to the m ovem ent o f people or m aterial. H eavy w eights a n d im pacts m ight cause high deflection o r cracks


Dharmaraj 3 leading to fracture. As the loading conditions are highly unpredictable in real life, the com posite grating is designed w ith different spacer distances and analyzed to predict its behavior u n d e r various loads an d inter-spacer distances.

1.4 H istorical Background of FEM /FEA A ny n atu ral phenom enon can be described w ith the help of the law s of physics in term s of algebraic, differential a n d integral eq u atio n s relating the quantities of interest. The m ost com m only used m ethods in explaining these p h en o m en o n are Ritz and G alerkin m ethods [7]. FEA, also know n as FEM, w as probably the m ost im p o rtan t tool a d d ed to the design engineer's toolkit this century. Some key features of FEM were found in the early w orks of H em ikoff and C ourant. In 1941, H em ikoff [7], [8] in troduced the fram ew ork m ethod. In 1943, C o u ran t [7], [8] used assem blage of triangular elem ents and principle of m inim um potential en erg y to stu d y St. V enent's torsion problem . The book by A rgyris [8] in 1955 on energy theorem an d m atrix m ethods laid the foundation for further developm ents. Turner et al. in 1956 an d A rgyris an d Kelsey [7] in 1960 m ade the form al p resentation of FEM. Clough[7], [8] coined the w ord "Finite Elem ent" in 1960. Z ienkiew icz and C hang [8] publish ed a book on N onlinear C ontinua in 1970. E lem ent developm ents, convergence studies and developm ents in oth er related areas took place in the 1970's.


Dharmaraj 4 Im m ense developm ents in science and technology in the area of co m p u ters helped FEA to reach stu d e n ts a n d engineers [8]. N orm ally, FEA is categorized into tw o types [9] as follow s: 1) D ead-end FEA 2) Iterative FEA T he tw o categories of FEA are b est show n schem atically in figure A2.

1.5 H isto ry an d E volution of C om posites The first appearance o f m an m ad e polym er com posite d ates back to a b o u t 5000 B.C. in the M iddle East [6]. L am inated w ood com posite based on shelloc resin [6], w as used in Thebes since 1500 B.C., and in India for the p ast 3000 years. The g ro w th of m o d em po ly m er in d u stries in the last cen tu ry accelerated the d ev elo p m en ts in the area o f com posites. In 1847 [6], the Sw edish chem ist Berzelius p rep ared the first p olyester resin. Parkes in 1862 [6] in tro d u ced cellulose nitrate plastic to the w orld. In 1909, Phenolic com posite in the form of Bakelite w ere in the m arket. Betw een 1928 and 1958 [6], urea form aldehyde, m elam ine form aldehyde, GR polyester, epoxy resin, GR nylon, GR polystyrene, vinyl polym ers and phenolic-asbestos ablative com posites w ere develo p ed an d used . Betw een 1965 an d 1975 [6], carbon FRP, boron FRP, c a rb o n /g la ss FRP, a ra m id FRP, a ra m id /g ra p h ite fiber h y b rid com posites w ere developed.


Dharmaraj 5 The need for n e w lighter and stro n g er m aterials led to today's d riv e for m ore an d b etter p o ly m e r com posites. M o d e m in d u stry is focusing o n high stre n g th to w eig h t ratio to m inim ize m aterial h a n d lin g cost, installation cost, m oving o r relocation cost, etc. Due to this, there has been a trem endou s su rg e of interest in com posites.


Dharmaraj 6

CHAPTER 2 Literature R eview In a su p e rstru ctu re, beam s and colum ns are the vital load carrying m em bers. Beams a re the horizontal m em bers subjected to tran sv erse loading. C olum ns are the vertical m em bers subjected to axial loading. Beams an d colum ns a re also classified according to their geom etry. Some of th e different types of beam s classified according to the g eom etry are I, T, L, channel, circular, rectangular, square, shell, irregular, etc.

2.1 C om posites 2.1.1 Definition: C om posites [1] can be defined as the com bination of tw o or m ore m aterials in w hich one of the m aterials, called the reinforcing phase, is em b edded in the o th e r m aterial, called the m atrix phase, w ith a sufficient aspectratio to p rovide the req u ire d strength in one o r m ore directions [2]. Som e exam ples of reinforcing agents [3] are (i) glass fibers, (ii) carbon, (iii) boron, (iv) silicon, (v) carbon, (vi) kevlar 49, etc. Some exam ples of m atrix [3] or e m b e d d in g agents are (i) polym ers, (ii) carbon, (iii) m etal, (iv) ceram ics. H ybrid com posites are defined as the com posite that com bines tw o or m ore different types of fibers in the sam e m atrix or vice versa or co m bin atio n of both of these.


Dharmaraj 7 S uper-hybrid com posites are a generic class of com posites that com bine a p p ro p ria te proportions of Fiber-M etal-M atrix com posites, Fiber-Resin-M atrix com posites a n d /o r metallic plies in a pre-determ ined fashion in o rd e r to m eet co m p etin g an d diverse design m odifications. O ne exam ple is fan blades in high b y p ass ratio turbojet engines.

2.1.2 Classification:

The classification of fiber-reinforced com posites based on

fiber o rien ta tio n [3] is schem atically rep resen ted in figure A l. The classification of fiber-reinforced com posites based o n the kind of m atrix[3] used is schem atically rep resen ted in figure A l.

2.1.3 Properties: In a com posite, b o th fiber an d m atrix m ain tain th eir physical p ro p erties an d together contribute a d d itio n al strength to the e n d p ro d u ct, the com posite,

w hich

cannot be a tta in e d

w hen

used

in d ividually.

M odem

com posites have replaced m etals in certain applications d u e to their extrem ely good m echanical and physical properties. As a result of reinforcem ent the crack p ro p a g a tio n p attern was different from the hom ogenous m aterials. Exam ple: Steel. This is clearly ev id en t in figure A3.

2.1.4 A pplications: In the m o d em w o rld , designers prefer a h igh stre n g th to low w eig ht ratio. So com posites are p icking u p in day-to- d a y usage. In som e areas


Dharmaraj 8 th ey h a v e replaced the use o f conventional m etals. Som e com m on areas of c o m p o site application are listed below [4], [28], [29]: 1) A ircraft, aerospace, m ilitary 2) A ppliances, business e q u ip m en t 3) C onstruction 4) C o n su m e r products 5) C orrosion-resistant e q u ip m en t 6) Electrical-electronic eq u ip m en t 7) M arine equipm ent 8) S ports goods 9) T ransportation, etc.

2.2 M an u fac tu rin g of C om posites T here are m any processes for the m an u factu re of com posites. N o t all k in d s of com posites can be m an u factu red by all the m eth o d s. So, ind u stry has e v o lv e d o v er half a d ozen m an u factu rin g process a n d a n u m b er of h y b rid p rocesses. Each m ethod has its o w n advantages an d d isad v an tag es. C hoosing a m an u fa c tu rin g process w as to tally d ep en d e n t on the choice of com posite, a v ailab le facility, optim al p ro d u c tio n cost a n d ease w ith w hich it can be p ro d u c e d . Schem atic rep resen tatio n of PMC m an u factu rin g process is sh o w n in


Dharmaraj 9 figure A4. The d ifferen t w ays of m anufacturing the com posites are listed b elo w [2], [5], [27]: 1) H an d lay-up 2) Spray-up 3) Filam ent w in d in g 4) P u ltru sio n 5) Pullform ing 6) Press m o ld in g 7) Vaccum b a g m o ld in g 8) A utoclave m o ld in g 9) Resin tran sfe r m olding 10) B i-dim ensional com pression m olding

2.2.1 Pultrusion: P u ltru sio n is a non-stop m a n u fa ctu rin g process for p ro d u cin g unidirectional fibers. This process is n o t ad v isab le for the m anufacture of sh o rt fibers. The su g g ested process is pullform ing. T he p u ltru sio n setup is sh o w n in figure A8. In the process of pultrusion, the reinforcing agent, the E-glass fiber is fed from a creel. The fiber from the creel w as c o n tin u o u sly fed into a resin bath. T he fibers get com pletely coated w ith the resin. T hen, the individual fibers w ere directed to pass th ro u g h a guiding device, w h ic h b u n d le s all the fibers to g eth er.


Dharmaraj 10 The resin covering each fiber acts as an adhesive in binding the fibers. The g u iding device w as o f the shape of the req u ired end product. The final sh ap e is thus obtained, w h ich in tu rn w as m ade to pass th ro u g h a cu rin g device m aintained a t a p a rtic u la r tem perature. A p u llin g device placed just n ex t to the curing device, p u lls o u t the final product. The final p ro d u ct com ing o u t of the pulling device is re a d y for practical im plem entation. Schem atically, th e process of p u ltru sio n can b e su m m arized as show n in figure A5.

2.3 Structural and Finite Elem ent Studies of FRP Beams Qiao et al. [14] tested FRP com posite beam s subjected to tran sv erse loading. The tested m odels are the in ten d ed sections that w ere to be u sed as short-span bridges, sim ilar to the one being cu rren tly researched. The co n strain ts included in o p tim izin g the design of the com posite beam s for such app licatio n s include m axim um deflection limit, m aterial failure and buckling. T he tested results w ere used to p red ict the behavior of sim ilar structures. K yriakides a n d Ruff [15] talk about th e m ajor reasons for the fractu re of fiber com posites in com pression. The m ain fiber im perfections iden tified after extensive testing w ere im perfections caused d u rin g the m an u factu re of the prepeg an d fiber w av in ess caused d u rin g the cu rin g of the com posite. K alaprasad et al. [16] conducted extensive research on e n h an cin g the m echanical p ro p erties of com posites. This w as done by the a d d itio n of short


Dharmaraj 11 glass fibers as a m ix w ith sisal. The lo n g itu d in al tensile m odulus w as enhanced u p to 80% by a d d in g a volum e fraction of 0.03 sisal-glass m ixtures to the m atrix. The flexural stre n g th of the com posite increased by 60% by a d d in g the sam e volum e fraction of th e m ixture. K arbhari et al. [17] studied the influence of polyam ide coating on the Eglass fabric-V inylester com posite for en erg y absorption behavior. T ests w ere perform ed using low velocity im pacts on the com posite w ith o u t d estro y in g it. The thickness p lay ed a vital role in en erg y absorption. Thin coatings restricted cracking w hile thick ones allow ed g reater deflection. Raju, M antena et al. [18] stu d ied the effects of h y b rid izatio n o n the longitudinal and flexural properties of the unidirectional p u ltru d e d glassg ra p h ite /e p o x y com posite. These p ro p erties o f the com posite w ere u sed as the in p uts for FEA, to pred ict various h y b rid com binations. The d y n am ic storage m odulus an d loss factor h ad been d e term in ed using a non-destructiv e testing technique. Results clearly depicted the d ep en d en cy of flexural p ro p erties on fiber location and fiber packing geom etry an d the independency of extensional properties over the sam e. Barbero [19] developed an analytical form ula for the calculation of com pressive stre n g th in unidirectional p o ly m e r m atrix com posites. The form ula found here can be validated to a b ro ad ran g e of g la ss/ca rb o n fibers. The


Dharmaraj 12 com m on p a ra m e te rs required for the p rediction of the stre n g th w ere sh ear stiffness, co m p o site stren g th and sta n d a rd deviation of the fiber m isalignm ent. N e m at-N asse r et al. [20] stu d ied the behavior a n d d u rab ility of the Eg la s s / V inylester com posite m aterial w h e n subjected to v a rio u s env iro n m en tal effects like m o istu re, elevated tem p eratu res an d sustain ed load. It w as inferred from the e x p erim en ts that m oisture a t h ig h tem p eratu res red u c ed the tensile stre n g th a n d so d o the sustained load o n d u rab ility of the com posite. P ig g o t [24] stu d ied m icrocrack d ev elo p m en t in com posites d u e to stress co n cen tratio n s a t the ends. This w ork d eta ile d the volum e fraction o f glass-fibers n eed ed as reinforcem ent. Z h u et al. [25] developed a m athem atical p rogram to calculate the stren g th of the com posites. This m inim izes the m athem atics a n d the tim e involved in d o in g this m anually. The results had a h ig h degree of c o rre sp o n d e n ce w ith the e x p erim en tal values. Li e t al. [26] investigated the d a m a g e m echanism in lam in ated com posites w h en subjected to concentrated tran sv erse loading. T his p a p e r extensively stu d ies the in teractio n betw een m atrix cracking a n d d ela m in a tio n pro p ag atio n .


Dharmaraj 13

2.4 M aterial T ypes G enerally, all m aterials are classified into 3 types accordin g to th e v a ria tio n in m aterial p ro p erties in three different directions. The classification is as follow s: 1) Isotropic 2) T ransversely Isotropic 3) O rth o tropic

2.4.1 Isotropic M aterial: In a n isotropic m aterial, the pro p erties are u n ifo rm in all th ree directions. The least req u ire d in p u ts for conducting a stru ctu ral analysis are E,v,p.

2.4.2 T ransversely Isotropic M aterial: In a transversely isotropic m aterial the p ro p e rtie s are uniform in d irectio n one an d sam e in directions tw o & three. So, tw o a n d th ree can be interch an g ed an d m akes no difference, as p ro p erties are the sam e. A ll U nidirectional GRP com posites are theoretically o rth o tro p ic, b u t can be a ssu m e d to be transversely isotropic. The least required in p u ts for co n d u ctin g a stru c tu ra l analysis are En, E22, V12, V21 , G 12, p.


Dharmaraj 14 2.4.3 O rth o tro p ic M aterial: In an orthotropic m aterial the p roperties are different in all the three directions. The least required in p u ts for conducting a stru ctu ral analysis are En, E 2 2 , E 3 3 , V 1 2 , V 2 1 ,

V 31, G 1 2 , G 1 3 ,

p.

2.5 M aterial P roperties 2.5.1 Y oung's M od u lu s (E): is defined as the ratio of the stress to strain in a isotropic b o d y [10], [11], [12], [13]. Y oung’s m od u lu s = S tress/S train E = a /Z If the m aterial is transversely isotropic or o rth o tro p ic the value of E changes w ith different d irection o f the principle axis. E11, E22. E33 - are the different Y oung's m od u lu s o f a m aterial. The value of En u se d in this analysis is 7.56e+6. The value of E 22 u se d in this analysis is 1.61e+6.

2.5.2 Bulk M o d u lu s (K): is defined as the ratio o f norm al stress to unit volum e change in a bo d y [10], [12]. Bulk m odulus = norm al stress /

u n it volum e change

U sually, volum e change in a m aterial can be calculated in a m aterial for triaxial stresses a n d expressed in term s of bulk m o d u lu s o r the m od u lu s of volum e expansion.


Dharmaraj 15 2.5.3 Poisson Ratio (v): is defined as the ratio of lateral strain to axial strain w ith in the elastic lim it [10], [11], [12], [13]. Poisson ratio = lateral stra in / axial strain For isotropic m aterial, v is independent of the orientation. V12, V21 , V31

- are the different v's for an orthotropic material

T he value of v u used in this analysis is 0.259. The value of V21 used in this analysis is 0.06.

2.5.4 Density (p): is defined as the ratio of m ass to volum e [10], [11], [12], [13]. D ensity = m ass/v o lu m e But density o f a com posite m aterial is calculated using the rule of m ixtures. pc =

p f V f + P m Vm

w here, pc is the sum of the p ro d u c t of the volum e fraction of the fiber an d its d en sity an d volum e fraction o f the m atrix and its density. The value of p used in this analysis is 0.079.

2.6 M aterial Failure Every m aterial in the universe fails a t som e point of time. Som e m aterials give prior w arn in g before failure and som e do not. Based on this the m aterials can be classified p rim arily into tw o categories, viz..


Dharmaraj 16 A. D uctile

- T hese m aterials give p rio r w a rn in g before failure in the

form o f necking o r buck lin g o r by som e o th er m eans. Plastic deform ation w as som etim es ev id en t. Example: a lu m in u m , co p p er, steel, etc. B. Brittle

- T hese m aterials do not give p rio r w a rn in g before failure.

Plastic d efo rm atio n is n o t possible in this category o f m aterials. Example: cast iron, glass, etc.

2.6.1 Failure M odes a n d Theories: As stated above, failu re of the m aterial d ep en d s on th e ductility o r the brittleness of the m aterial. T he differen t types of failure in m aterials are: 1) D uctile 2) Brittle 3) Brittle failure in ductile m aterials The th ird case m en tio n in g "Brittle failure in ductile m ateria ls" is a special case of ductile failure. This happens in the ductile m aterials w hen it is reinforced beyond its req u ire m e n t or w hen the thickness is u n ev en w ithin the sam e system or w h en th e re is a n u m b er of w eld joints in th e system . The different theories th at are dealing w ith m aterial failu re a re stated below:


Dharmaraj 17 2.6.2 Failure T heories for D uctile M aterials: The different theories p e rta in in g to ductile m aterial failure are g iv en below: 1) M axim um N orm al Stress T heory o r R ankine Theory [10], [11], [12], [13]. 2) M axim um Shear Stress Theory [10], [12], [13]. 3) D istortion Energy T heory [10], [13].

2.6.3 Failure T heories for Brittle M aterials: The different theories p e rta in in g to brittle m aterial failure are g iv en below: 1) M axim um N orm al Stress Theory w h e n all forces are Tensile [10]. 2) C oulom b-M ohr T heory [10], [13].


Dharmaraj 18

CHAPTER 3 Experim ental W ork The research w o rk also involved the experim ental testing o f g rating sam ples. This section explains the experim ental setu p and the p ro ce d u re for p erfo rm in g the experim ental testing.

3.1 Setup A U niversal T esting M achine [UTM] w as used to test the g ratin g sam ples. The m achine setup is sh o w n in figures A6 an d A7. The m achine is m echanically driven. The m ovem ent of oil controls the load being applied. T he m achine setup consists of tw o distinct p arts, viz.. 1) C ontrol U nit 2) Testing U nit

3.2 C on tro l U nit The m ain p u rp o se of this un it is to control the oil flow thereby controlling the load that is bein g applied. This setup consists of two w heels u sed for reg ulating the oil circulation in the m achine and a large dial th at indicates the load being applied. T he control un it is show n in figure A6.


Dharmaraj 19

3.3 Testing U nit T he m ain p u rp o se of this u n it is to apply the load o n the sam p les for experim entation. It has tw o large vertical arm s, w hich are connected by a horizontal arm . T he horizontal a rm w as used in tran sm ittin g the g e n erate d load from the arm to the w ork-piece. The generated load can be eith er u sed as a tensile o r com pressive load d e p e n d in g on the w ork-piece setu p . The w ork-piece w as placed on the w orkbench, parallel to the loading arm . W hen the oil w as p u m p ed inside the p u m p in g cy lin d er the loading or the h o rizo n tal a rm starts m oving d o w n w a rd s for ap p ly in g the load an d vice versa. The testin g unit is show n in figure A 7.

3.4 Procedure The beam is set to lie parallel to the w orkbench above a certain distance so as to place a d ial-gauge to m easure the deflection of the beam . The dial-gauge is placed right below the load application point. The horizontal arm h o u ses a hole to connect a circular rod req u ired for applying load. A cen ter p o in t load was applied using a long solid p ip e a t the m id-span. In this case, com pression loading w as in the transverse direction to the grating. The loading pro ced u re sta rts from lOOlbs for the w h o le assem bly. The load w as increm ented by lOOlbs a n d the deflection readings w ere n o ted dow n. This p ro ced u re w as rep eated until fracture.


Dharmaraj 20

CHAPTER 4 M odeling and A nalysis As th is research em p h asizes FEA of the com posite g ratin g structures, m o d elin g th e beam a n d sp acer w as of p rim ary concern. A p o w erfu l param etric, feature-based solid m o d elin g tool called P ro /E by P aram etric Technology C o rp o ratio n , W altham , M A w as u sed for the m odeling p u rp o se. The m odel d esig n ed u sin g P ro /E w as d irectly interfaced w ith the finite elem ent softw are P ro /M . U sing P ro /M , the m o d el w as analyzed for deflection a n d stresses.

4.1 M o deling P rocedure M odeling is the process o f creating an accurate rep resen tatio n o f the physical object an d w as the first step o f the analysis. This w as d o n e using points, lines, arcs, a n d prim itives from the p a rt library [23]. The m o d elin g o f the stru c tu re is given step-by-step as follows: 1) "D atum Planes" w ere c re a te d to sketch the req u ired section on the screen. 2) "C o-ordinates System " w a s created an d placed

in the ap p ro p ria te

position.(D efault p o sitio n is O rigin) 3) The m e th o d of object cre atio n w as selected. In this case, it w as "Solid". 4) V olum e generation w as d o n e using "Extrude" co m m an d 5) The a p p ro p ria te "Sketching planes" w ere selected to d ra w the 2D sketch of the b e a m required for extrusion.


Dharmaraj 21 6) T he section w as "Aligned" to the references to place the section w ith respect to the planes. 7) T he sketch w as "D im ensioned" to represent the real-life structure. 8) "Regeneration" w as d o n e to finalize the sketch. 9) The "Blind depth" w as given to the required length. 10) T he necessary "Cuts" w ere m ade to fit the spacer in the beam. 11) The sam e sequence of steps w as used to m odel the spacer according to the requirem ent. 12) T he m odeled beam a n d spacer were th en "A ssem bled" to rep resen t the g ratin g assem bly u sed in the testing. 13) Isom etric view s of the spacer, different kinds of I-beam s and the g ratin g are sh o w n in figures A69 th ro u g h A77. 14) D etailed view s of the spacer, different kinds of I-beam s and the g ratin g are sh o w n in figures A78 th ro u g h A86.

4.2 D esign M odifications T here w ere several assu m p tio n s m ade w hile m odeling the com ponents[30]. They are listed as follows: 1) T he ro u n d com ers w ere om itted. 2) Spacer w as assum ed to be a single piece. 3) C o n cep t of sym m etry w as u sed to m ake the m odel sm aller and sim pler.


Dharmaraj 22 4) The spacers w ere placed uniform ly at a distance of 0.8" from the base.

4.3 A nalysis P rocedure A nalyzing the m odeled p a rt or com ponent is the second and final step. This w as follow ed b y design m odification d e p en d in g on the analysis resu lts to get a correct solution. The analysis of the m odeled structure is g iv en step-by-step as follows: 1) The P ro /E m o d el w as analyzed in P ro /M in the linked m ode [30]. 2) The surface regions w ere created at the required locations for ap p ly in g load and constraints. 3) The required load at the appropriate position w as applied. 4) The a p p ro p ria te constraints w ere applied in the point of the su p p o rts. 5) The required m aterial properties were defined. 6) The type of analysis (Static) w as defined. 7) The softw are's auto-m esh generation capability w as used to create a pelem ent m esh m ad e of solid elements. 8) The analysis w a s m ad e to non for calculating the results. 9) The results w ere view ed for deflection a n d stresses. 10) The results w ere p lo tted for records purpose.


Dharmaraj 23

4.4 Input Data T he in p u ts required for p e rfo rm in g FEA are given as follows: 1) Y oung's m odulus(E n)

= 7.56 e+6 lb f/in 2.

2) Y oung's m odulus(E 22 )

= 1.61 e+6 lb f/in 2.

3) P oisson ratio(vi 2 )

= 0.259

4) P oisson ratio(v 2i)

= 0.06

5) Shear m odulusfG n)

= 3 e+6 lb f/in 2.


Dharmaraj 24

CH A PTER 5 M icrostuctural Evaluation T he use of com posites an d related m aterials a re increasing steadily in recent d ay s. So the behavior o f the com posites before a n d after fracture sh o u ld be stu d ie d in d e tail for better u n d e rstan d in g . The stu d y w a s perfo rm ed w ith regard to the m echanics of the com posite m aterial w hen subjected to loadin g in tw o m odes, n am ely , m icrom ecahnical v iew p o in t and m acrom echanical view point. M icrom echanics is the s tu d y of com posite m aterial beh av io r w herein the in teractio n o f the constituent m aterials is exam ined o n a m icroscopic scale [33]. M acrom echanics is the stu d y of the com posite m aterial b ehavio r w herein the m ateria l is presum ed h o m ogeneous and the effects of the constituent m aterials a re detected as the a v erag e a p p aren t p ro p erties of the com posite. T he above m entioned techniques w hen used to g eth er helps us to m ake a go o d selection in the m aterial w ith o u t losing m uch of the m aterial's capability. The com plex aspects of failure th a t is not visible to n a k ed eye can be analyzed th ro u g h a m icrom echanical stu d y . The three d ifferen t kinds of failure in lam in ated com posites are: 1. Interlam inar fracture 2. Intralam inar fracture 3. T ranslam inar fracture


Dharmaraj 25

5.1 Possible reasons for failure Som e of the possible reasons for failure [32] of a com posite from a m icrom echanical v iew p o in t are stated below: 1) Possibility of a ir bubbles getting locked internally d u rin g the cu rin g process. W hen the stru ctu re is subjected to loading, this b u b b le initiates one o r m ore cracks from th at position. These m icro-cracks act to d elam in ate the structure. 2) Sub-surface cavities initiate m atrix cru sh in g subsequently lead in g to sn ap p in g of fibers due to load. 3) Local o v erlo ad in g at som e points caused m atrix crushing, en d in g -u p in delam ination. 4) M icrobuckling w as evident in alm ost all the FRP's m ade w ith low m od u lu s m atrix. 5) Fiber pu ll-o u t w as another com m on aspect of failure w hen the stru ctu re w as subjected to longitudinal tension.

5.2 Lim itations of M icrom echanical Study 1) A n exact copy o f a FR com posite m aterial c an n o t be reproduced d u e to the ran d o m o rien tatio n of fibers in a short fiber com posite. 2) In case of u nidirectional FR com posite, the fiber-packing geom etry is n ev er entirely repeatable.


Dharmaraj 26 3) D uring a FEA, the input values given are En, E22, V12, V21. G 12, p. These are no th in g b u t averaged quantities an d not for th at p articu lar structure. So, the results m ay not be exact. 4) In theory, the fiber-packing geom etry w as taken to be square, rectangle, hexagonal, etc. for the ease of calculating volum e fractions o f fiber, m atrix, voids, etc. But practically, such packing geom etry can n ever be achieved. 5) So, it can be concluded that theoretical an d FEA results will n ev er be the same. 6) M icrom echanical analysis of one stru ctu re cannot be used as a full reference for a n o th er stru ctu re of the sam e kind o r sim ilar geom etry. It can only be referred and n o t reliable.

5.3 Analytical R eport of SEM The Scanning Electron M icrographs are sh o w n in figures A87 th ro u g h v

A119. These SEM pictures clearly show the fracture surfaces an d fractured fibers and m atrix in three different levels of m agnification varying from lOOx to 1600x.

(1)

Electron M icrographs 4-6, 22-24 an d 31-33 in figures A90 - A92, A108 -

110 and A l l 7 - 119 show the fracture surface of beam s six, three a n d seven respectively in a 3" spaced grating.


Dharmaraj 27

In figures A90, A108 and A l l 7, i.

G ood fiber-m atrix bonding is visible.

ii.

N o t m an y fibers are broken.

iii.

G ood n u m b er of fiber dislocations, possibly d u e to m icrobuckling.

In figures A91, A92, A110 and A119, the fractured surface o f a single fiber is clearly show n. i. ii.

The stra ig h t fracture surface indicates radial fracture of fibers. W hen the adjacent stru ctu re d enies m ovem ent o r displacem ent, the fibers fail radially. This w as d u e to h ig h volum e fraction o f fibers in the stru c tu re or m ore reinforcem ent m ak in g the stru c tu re stiffer.

(2) E lectron M icrographs 1-3, 13-18 a n d 28-30 in figures A87 - A89, A99 A104 a n d A114 - A116 show the fracture surface of beam s six, o n e a n d five in a 9" spaced grating. i. ii.

Figures A87, A101, A102 a n d A103 show the resin b o n d in g clearly. Figure A89 an d A104 show the fracture surface of the fibers, w hich w as a b rittle failure caused by local overloading , called the sn ap p in g of fibers.

iii.

The fiber surface indicates th a t it fractured after a co n sid erab le am o u n t of b e n d in g o r buckling because fracture surface w as n o t radial.


Dharmaraj 28 iv.

In figures A115 a n d A116, fiber surface fracture is clearly visible. T his p henom enon w as n o t seen in any of the sam ples th a t w ere an aly zed . So this could be a defect from the curing process. N orm ally, Scaling in a brittle m aterial is uncom m on. (3)

Electron M icrographs 7-12,19-21 an d 25-27 in figures A93 - A98, A105 -

107 a n d A l l l - 113 show the fracture surface of beam s five, four, five a n d fo u r respectively in a 12" spaced grating. In fig u res A93, A94, A96, A97 a n d A105, i. ii.

M atrix bonding is clearly visible. G aps betw een the fibers show that there had been som e m o v em en t before fracture d u e to buckling of fibers.

iii.

Also, only flakes o f m atrix m aterial are seen an d n o t found in m asses o r layers.

In fig u re A95, A98, A107 an d A l l l , the fracture surfaces are clearly visible. F rag m en ts of fibers are also seen, w hich indicates th at th ere has been m u ltip le fractu re p o in ts due to stiffness o f neighboring filam ents o r stru ctu res. It is sim ilar to onion dom e fractu re w ith a groove in the center.


Dharmaraj 29

CHAPTER 6 Results and D iscussion

6.1 Presentation of Results The results of the experim ental w ork an d the sim ulation are p resen te d as follows: 1) The behavior of th e 3" spaced grating at the fractu re load is sh o w n in the scanned p h o to g rap h s in figures A9 th ro u g h A l l . 2) The behavior of th e 9" spaced grating at the fracture load is sh o w n in the scanned p h o to g rap h s in Figures A12 th ro u g h A14. 3) The behavior of the 12" spaced grating at the fractu re load is show n in the scanned p h o to g rap h s in Figures A15 and A16. 4) The deflection plots for 3" spaced grating a t different loads are sh o w n in Figures A17 th ro u g h A27. 5) The deflection plots for 6" spaced grating a t d ifferen t loads are sh o w n in Figures A28 th ro u g h A42. 6) The deflection plots for 9" spaced grating a t differen t loads are sh o w n in Figures A43 th ro u g h A52. 7) The deflection plots for 12" spaced grating a t different loads are sh o w n in Figures A53 th ro u g h A64. 8) SEM stu d y results are show n in figures A87 th ro u g h A119.


Dharmaraj 30 9) G raphical p lo ts of load vs deflection for the 4 types of g ratin g s are show n in figures A65 th ro u g h A69 in the follow ing sequence - 3", 6", 9" an d 12" respectively. 10) Tables A1 th ro u g h A4 tabulate the deflection values of th e four types of grating assem blies subjected to transverse loading in the follow ing sequence - 3", 6", 9" an d 12" respectively.. 11) Table A8 tabulate the experim ental and FEA results for the deflection in the different types of grating assemblies. 12) Table A9 tabulate the fracture load or the m axim um load b earin g capacity of the different types of grating assem blies. 13) Table A10 sh o w s the com parison for the buckling in the d ifferen t types of grating.

6.2 Discussion of R esults The deflection values from table A2 indicates clearly th a t 6" spaced grating deflects the m axim um com pared to all others. From table A 9, w e see that the 6" spaced grating has the m axim um load bearing capacity. The reason for h ig h load bearing capability of the 6" sp aced g ratin g was the optim um n u m b er of spacers m ounted in the assem bly a p p ro p ria te ly spaced betw een each other. As there w as a spacer lying below the load a p p lica tio n area, stress sharing in the spacer takes place, w hich increased the life o f the grating.


Dharmaraj 31 The beh av io r of this g ra tin g for different loads can be seen in figures A28 th ro u g h A42. In the case o f 3" sp aced grating, the reinforcem ents a re too close to each other. This m akes the m odel stiffest am ong the different types. As the load was ap plied, the stresses g en erated at the loading reached the holes d rilled for the spacers quickly w h e n c o m p ared to the oth er m odels. A lso th e re w e re cracks p ro p ag a tin g b etw een tw o sp a ce r holes in the m id-span o f th e assem b ly d u e to their closeness. The grating b eh av es m ore like a brittle stru c tu re lead in g to cracks a t a low er w o rk in g load. T he m ain cause for the stress c o n cen tratio n s in the spacer holes w as geom etry itself. The spacer holes contain six sh a rp co rn ers and practically sp eaking, any sh a rp c o m e r w hen subjected to lo ad in g y ield s first. There w as no buckling d u rin g fracture and low er b e n d in g w as e v id e n t w hen co m pared to o th e r types. T he b ehavior of this grating for d ifferen t loads can be seen in figures A17 th ro u g h A27. In the case of 9" spaced grating, the reinforcem ents w ere sp re a d far e n o ugh a p a rt th a t there w as no crack propagation betw een th e sp acer holes. The p rim ary reaso n for no crack p ro p ag a tio n w as the creation o f n u m e ro u s m icro cracks in the p ro p ag a tio n reg io n d iverting or sto p p in g th e crack from being evident. The reason for failure a t low er loads w as d u e to th e lack o f stress sh aring in the spacers. Buckling w as ev ident a t high loads m a k in g th e se tu p very


Dharmaraj 32 u nstable, consequently lead in g to fracture. T he b ehavior of this g ra tin g for d ifferent loads can be seen in figures A43 th ro u g h A52. In the case in 12" spaced grating, the crack p ro p ag a tio n p a tte rn w as sim ilar to th at of the 9" spaced grating. The p h en o m en o n of b u ck lin g w as very m uch e v id en t at a low er load d u e to lack of close reinforcem ent. The b e h av io r of this g ratin g for different loads can be seen in figures A53 th ro u g h A64. In all the cases, the p a tte rn of failure in the load application a re a sh o w s lo n g itu d in al cracks in the beam s along its sp an o riginating from th e lo ad in g point. The crushing o r plastic flow w as seen at the loading p o in t d u e to h ig h load co n centration at a sm aller surface area. As a result of this, the fiber starts sn a p p in g consequently lead in g to fracture. This longitu d in al fracture can be seen in figures A12, A13, A14 a n d A16.


Dharmaraj 33 CHA PTER 7 S um m ary, Conclusions a n d Scope for Future W ork This sessio n sum m arizes the w h o le research w ork follow ed b y the conclusion a n d scope for further research in the sam e w ith som e in n o v ativ e ideas.

7.1 S um m ary 1) The sam p les w ere cut to the a p p ro p ria te length required for m echanical testing, to sim ulate a real life stru c tu re o r real life loading conditions. 2) The sam p les w ere tested as p er p ro c e d u re a n d the readings w ere n o ted . 3) A sim ilar m o d el of the beam assem bly w as created using P ro /E . 4) The m o d el w as created w ith som e m odifications to m ake it sim p le for FEA. 5) The necessary inputs in the form o f m aterial properties, loads, co n strain ts and reg io n s are defined. 6) The m o d el w as analyzed for deflection an d static stresses (stresses, reactions, rotations). 7) The ex p erim en tal results and FEA results for deflection w ere com p ared . 8) From the results, it was concluded th at 6" spaced grating to be the o p tim u m design-


Dharmaraj 34 9) Sim ilar m athem atical m odel of the problem is m o d eled using 1-D b ar elem ents w ith sim ilar b o u n d a ry conditions. 10) A nalytical and FEA results o f a sim ple cantilever beam w ere com pared to h av e an idea about the closeness of results. A fter extensive investigation o f the results it is co n clu d ed as follows w ith som e ideas for future w ork.

7.2 C onclusions F rom the discussion p a rt o f results, w e conclude th a t 6" inter-spacer distance to be the optim um design. This is due to the h ig h load b earin g capacity of the b eam assem bly, m oderate buckling and com paratively low deflection at a given load.

7.3 Scope for fu tu re w ork T he m odel can be fabricated w ith different spacer sh a p es w ith few er sh arp co m ers so as to reduce stress concentration effects. By a v o id in g sh a rp edges in the sp acer geom etry, the chances for crack form ation b etw een the adjacent spacers in the 3" spaced grating m ay be reduced. A lso, the sam ples m ay be tested b y lo ad in g them uniform ly, ra th e r than at a point, to get an indication of their b e h av io r u n d e r practical conditions.


Dharmaraj 35 REFERENCES [1] Jam es P. Schaffer e t al. The Science and D esign o f E ngineering M a terials. Chicago: Richard D. Irw in , Inc., 1995. [2] T ara E. M iller. In tro d u ctio n to C om posites. N ew York: C om posites In stitu te, 1997. [3] P. K. Mailick. Fiber-R einforced C om posites. N ew Y ork: M aecel D ekker Inc., 1988. [4] G reorge Lubin. H a n d b o o k o f Fiberglass an d A d v a n ce d Plastic C o m p o sites. N ew York: Van N o stra n d R einhold C om pany, 1969. [5]

K. H. G. Ashbee. F u n d a m en tal Principles of Fiber-R einforced C o m p o sites.

Pensylvania: Technom ic p u b lish in g C om pany, Inc., 1989. [6] R. P. Sheldon. C om p o site Polym er M aterials. N e w York: Elsevier Science p u b lish in g C om pany, Inc., 1982. [7]

J. N. Reddy. A n In tro d u ctio n to the Finite E lem ent M eth o d . N ew York:

M cG raw -H ill p u b lish in g C om pany, 1984. [8] T. R. C h an d rap atla a n d A. D. Belegundu. In tro d u ctio n to Finite E lem ents in E ngineering. N ew Delhi: Prentice- H all of India, 1997. [9]

Paul K urow ski. "W hen good Engineers deliver b a d FEA." c h ttp :/ /w w w .

m ac h in e d esig n .co m /> (20 D ecem ber 1999). [10] A lexander Blake. H a n d b o o k of M echanics, M aterials a n d S tructu res. N e w York: John W iley an d Sons, Inc., 1985.


Dharmaraj 36 [11] A n d rew P ytel a n d Ferdinand L. Singer. Strength of M aterials. N ew York: H a rp e r a n d Row , Publishers, 1987. [12] Peter Black. Strength of M aterials - A course for stu d e n ts . N ew York: P ergam on P ress Inc., 1966. [13] W illiam F. Riley, Leroy D. Sturges an d Don H. M orris. M echanics of M aterials. N ew York: John W iley an d Sons Inc., 1999. [14] P izhong Q iao, Juliio F. D avalos a n d E ver J. Barbero. "Design o p tim iza tio n of Fiber R einforced Plastic C om posite Shapes." Toumal of C om posite M aterials vol 32, no 2 (1998): 177-96 [15] S. K yriakides a n d A. E. Ruff. "A spects of the Failure a n d p o st-failu re of Fibrous C om posites in Com pression." Toumal of C om posite M aterials vol 31, no 20 (1997): 2000-37 [16] G. K alaprasad, K uruvilla Joseph a n d Sabu Thom as. "Influence o f sh o rt glass fiber a d d itio n o n the M echanical p ro p erties of sisal reinforced low density p o lyethylene com posites." Toumal of C om p osite M aterials vol 31, no 5 (1997): 509-27 [17] R. W. R ydin, P. C. Varelidis, C. D. P ap o sp y rid es an d V. M. K arbhari. " Glass Fiber V inylester C om posites: T ailoring the fiber B u n d le/M atrix in te rp h ase w ith N y lon coatings to m odify energy a b so rp tio n behavior." Toumal o f C om posite M aterials vol 31, n o 2 (1997): 182-209


Dharmaraj 37 [18] C h a n d rasek ar V. N ori, P. Raju M antena and T yrus A. M cCarthy. "E xperim ental an d Finite E lem ent A nalysis of P u ltru d ed G lass G rap h ite/E p o x y h y b rid s in A xial and Flexural m odes of Vibration." Toumal o f C om posite M aterials vol 30, no 18 (1996): 1996-2018 [19] E ver J. Barbero. "Prediction of C om pression Strength of U nidirectional P olym er M atrix Com posites." Toumal of C om posite M aterials vol 32, no 5 (1998): 483-502 [20] S tephanie E. Buck D avid W. Lischer an d Sia N em at-N asser. "The Durability of E -G lass/V inylester com posite m aterial subjected to en v ironm etal conditions a n d su stain ed loading." Toumal o f C om posite M aterials vol 32, no 9(1998): 874-92 [21] E. Scala. C om posite M aterials for C om bined Fnctions. N ew Jersy: H ayden Book C om p an y , Inc., 1978. [22] N iel L. H ancox and R ayner M. M ayer. Design Data for R einforced Plastics. N ew York: C hapm an and Hall, 1994. [23] M SC /N A ST R A N for W indow s - Q uick start g u id e. California: The M acNealS chw endler C orporation, 1999. [24] D. R. C larke, S. Suresh, I. M. W ards FRS. A n In troduction to C om posite M aterials. N ew York: C am bridge U niversity Press, 1996. [25] M ichael R. Piggott. "Short Fiber Polym er C om posites: A Fracture-Based T heory of Fiber Reinforcement." Toumal of C om posite M aterials vol 28, no 7 (1994): 588-606


Dharmaraj 38 [26] Y. T. Z h u a n d G u ish en g zong. "On the A p p licatio n of Statistical S trength M odel of Fiber-Reinforced Com posites." Toumal of C o m p o site M aterials vol 27, no 9 (1993): 9 4 4 -5 9 [27] Sheng Liu, Zafer K u ttu a n d K uo C hang. "M atrix C rack in g a n d D elam ination in L am inated C om posite Beams subjected to a T ran sv erse C oncentrated Line load." Toumal of C om posite M aterials vol 27, no 5/1993: 436 - 470 [28] L eonard H ollaw ay. H an d b o o k of Polym er C o m p o sites for Engineers. C am bridge: W oodhead P ublishing Limited, 1994. [29]

B hagw an D. A garw al, Law rence J. B rontm an. A nalysis a n d Perform ance

of F ibrous C om posites. N ew York: John W iley a n d Sons, Inc., 1990. [30] R oger Toogood. P ro/M E C H A N IC A S tru ctu ral T u to rial. Kansas: SDC Publications, 1999. [31] R onald F. Gibson. Principles of C om posite M aterial M echanics. N ew York: M cG raw -H ill, Inc., 1994. [32] G. C. Shi and V.P. T am uzs. Fracture of C om posite M aterials. M assachusetts: K lvw er Boston Inc., 1982. [33] R obert M. Jones. M echanics of C om posite M aterials. N ew York: M cG raw H ill Book com pany, 1975. [34] A nthony Kelly. "An Introduction to C o m p o site

M aterials." C oncise

encyclopedia of C om posite M aterials. 1994 ed.


Dharmaraj 39

A PPE N D IX A FIGURES AND TABLES


Dharmaraj 40

Fiber R einforced C om posites

T U nidirectional

1

D iscontinuous

C o n tin u o u s

P articulate I

Flake[4]

---------- ^

3D W oven

I

i 2D W oven

L am inates

Skeletal[4]

Fiber R einforced C om posites

I Polym er

t ------------ 1------------ 1 --------------------- 1 M etal

C arbon

F ig u re A1

Classification o f C om posites


C eram ic

Dharmaraj 41 Iterative FEA

D ead-end FEA

DESIGN PROCESS

DESIGN PROCESS

R edesign

No

FEA - Does die part meet established goals?

FEA - Conduct Analysis

PROTOTYPE

PROTOTYPE

TEST

TEST

Figure A2 Types of FEA


Dharmaraj 42

Without fibers

With fibers

~~

Figure A3 Crack Propagation in FRP's


Dharmaraj 43 This figure sh o w s the schem atic o verview of the approaches em p lo y ed in fabrication of po ly m er m atrix com posites [24].

M aterials

In term ediate Stages

C o m p o n en t P ro d u ctio n

T herm oplastic p o ly m e r

C hopped fiber

T herm oset p olym er

Im p reg n atio n

M o u ld in g com pound

Injection m o u ld in g

W eaving, braiding, etc.

Resin Injection

P u ltru sio n

C om pression m o u ld in g

C o n tin u o u s fiber

Filam ent w in d in g

Figure A4 PMC M anufacturing Process


Dharmaraj 44

C ontinuous stran d roving

Resin bath

G uiding device

End p ro d u ct of required shape

Pulling device

C uring device & h eat

Figure A5 M anufacturing Flow D iagram


Dharmaraj 45

Figure A6 UTM - C ontrol unit


Dharmaraj 46

Figure A7 UTM - C ontrol unit

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission

Dharmaraj 47

P ulling Device H eat source

C o n tin u o u s stra n d R oving

Resin A pplicator Figure A8 P ultrusion Process

sagstev--

Figure A9 Top view of 3" spaced G ratin g


Dharmaraj 48

Figure A10 Left view of 3" spaced G rating

Figure A l l Right view of 3" spaced G ratin g


Figure A12

Top view of 9" spaced Grating

Figure A13 Top view of 9" spaced G rating


Reproduced with P6rmissi0n

Dharmaraj 51

Figure A16 Top v iew of 12" spaced G rating afte r fracture


Dharmaraj 52 S tress Max

-t-4 . 0 4 9 7 E + 0 4

Min

+2 . 9 3 3 3E+00

Deformed

a

( Ma xi mum)

Von M ise s

O riginal

3. 6 0 0 e * 0 « 3. l 5 0 e - 0 « 2. ? e e e * e - « 2 . 2S 0e-0 «

i .ecee*e«

Model

1 . 35Be*0*

Ma x D i s p * 1 . 1013E-01 S cale 2.7242E-01

S .0 0 2 e -0 3 * . 5B2e-03

Load: l o a d l p rin c ip a l U nits: Inch

Pound Second

(IPS)

A nalysis

of

Safe-T -Span

Beam,

lOQlbs/Beam

F ig u re A17 - Deflection of 3" spaced G rating - lOOlbs/Beam

S tress

Von M ise s

Max + 5 . 7730E»04 Min 04 4 .6 B 2 e -0 4 3 .9 0 2 e -0 4 3.

A n a ly sis

12 2 ,-0 4

2. 3 4 2 ,-0 4

Max D i s p ♦ 2 .5 3 8 S E -0 1 S c a le 1 . 1813E+01 Load: lo a d l P rin c ip a l U n its: In c h Pound S e c o n d (IP S )

1. S61e*04

7 . 009«*03

of

S afe-T -S p an

Beam ,

4 0 0 1 b s/B eam

Figure A46 - Deflection of 9" spaced Grating - 4001bs/Beam


Dharmaraj 68 S tre ss

Von M i s e s

1 . 036e*0S

(M axim um )

9 .0 6 9 * * 0 -4

M ax

+ 1 .1660E+05

7.774**0*

M in

+ 5 .5350E+00

6 . 478**04

D eform ed O r ig in a l M ax D is p S c a le L oad:

3 .887**0*

+ 3 .3 7 2 1 E -0 1

2.592**04 1.296**04

8 . 8966E+00 lo a d l

P rin c ip a l In ch

5 . 183**04

M odel

Pound

U n its: Second

(IP S )

A n a ly sis

of

S afe-T -S p an

Beam .

5 0 0 1 b s/B e am


1. 0 29**05

S t r e s s V on M i s e s (M axim um ) Max + 1 .1 5 7 9 E + 0 5 M in + 6 .2 2 2 1 E + 0 Q D eform ed O r i g i n a l M odel Max D i s p + 4 .0 5 6 4 E -0 1 S c a le 7 .3 9 5 7 E + 0 0 Load: l o a d l p rin c ip a l U n its: In ch Pound S econd

9 .00 6* *0 4 7.700**04

6.433**04 S . 147**04 3.660**04 2 .57 4* *0 4

t . 207e*04

(IP S )

A n a ly sis

of

S afe-T -S p an

Beam ,

6001 b s/B eam



Dharmaraj 69 S C ire ss

Von M is e s

M ax

+ 1 .0 7 5 2 E f0 5

M in

+7 . 0 U 5 E + 0 0

D eform ed M ax

D isp

S c a le

O rig in al

( M a x im u m )

9 . 5 5 7 e -»04

B .3 63 e-0« 7 . 16Be*04 5 . 9 7 4 e -0 4 4 .7 7 9 * * 0 4

M odel

3 .5 0 4 * * 0 4

+ 4 . 6148E -01

2 .3 9 0 * * 0 4

6 .5 0 0 8 E + 0 0

Load:

1 . 19S**04

lo ad l

P rin c ip a l In ch

U n its:

Pound Second

(IP S )

A n a ly sis

of

S afe-T -S p an

Beam ,

7 0 0 1 b s/B eam

Figure A49 - Deflection of 9" spaced Grating - 7001bs/Beam S tre ss

Von M i s e s

M ax

+1 •2288E+05

M in

+ 8 .0131E+00

D eform ed M ax D i s p S c a le

O rig in a l

l . 092*»0S

(M axim um )

9 . 557e*04

0. 192e-*-04 6 .0 2 7 * * 0 4 5 . 462e*04

M odel

4 .0 9 6 e » 0 4

+ 5 .2 7 4 1 E -0 1

2 .7 3 1 * * 0 4 1 . 366**04

5 . 6882E+00

Load: lo a d l P rin c ip a l U n its: Inch

Pound Second

(IP S )

A n a ly sis

of

S afe-T -S p an

Beam ,

8 0 0 1 b s/B eam

Figure A50 - Deflection o f 9" spaced Grating - 8001bs/Beam

Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.

Dharmaraj 70 S tre ss

Von K i s e s

Max:

+1 . 8267E+05

M in

+ 7 .6 2 2 8 E + 0 0

(M axim um )

t .

1 .01S9»0S B. U 9 »* 0
h* 3 u

o

(A £

O ^ O m *

Cl

nE tn

o

c

.2

cni

V at G ai Qt

o o o

•£ OE CD

T3

e« O ►J ■ oo v£

o o o

ai v*

o o o

CO

e am

Figure A81 - Detailed view of 9" spaced I-Beam THESIS

30 00

Au q u s t 20 00

S u r c j h Ohcrmcffl j

Beam

Figure A82 - Detailed view of 12" spaced I-Beam

Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.

Dharmaraj 88 . 50 — H

THESI S

3.00

ilBlfaTB L

Auqus t

Sureih

2000

Ohor mor oj

*83

Figure A83 - D etailed view of 3" spaced grating THESI S

3.00 I . 52 I . 50

D

73 H

12.14

Aucu11

2000

Or

N

M

S f i ft i

±

30.00 Surejh

Ohor mor oj

-

Becm

Gr a i i n g

Figure A84 - D etailed view of 6" spaced grating


*6*

Dharmaraj 89

THESI S

30.00

----- 1 50 —

9 . 0 0 ----- -

- 1 \________________ August

2000

Or

N.

Suresh

Ohcrmcrcj

SriniTOScn

\

n

a \ «ss

- Be o r a G r o t i n o

Figure A85 - D etailed view of 9" spaced grating ~~~

|

Figure A 86 - Detailed v iew of 12" spaced grating


THESI S

Dharmaraj 90

Figure A87 Electron Micrograph 1 - Fracture surface

Figure A88 Electron Micrograph 2- Fracture surface


Dharmaraj 91


Figure A90 Electron Micrograph 4- Fracture surface


Dharmaraj 92




Dharmaraj 93




Dharmaraj 94




Dharmaraj 95 ' ‘~'-^SP




Dharmaraj 96




Dharmaraj 97

OF

1 0 . 0U Figure A101 Electron Micrograph 15 - Fracture surface

16

r-t.

*- .



P

Dharmaraj 98




Dharmaraj 99


..v-

^

'. X-W



Dharmaraj 100

Figure A107 Electron M icrograph 21 - Fracture surface



Dharmaraj 101




Dharmaraj 102

Figure A l l l Electron Micrograph 25 - Fracture surface



Dharmaraj 103




Dharmaraj 104




Dharmaraj 105

r^csicfraffS*




Dharmaraj 106



Dharmaraj 107

Stress Von Mises (Maximum) Max * 2 . 1130E