Failure envelopes of paint films as related to pigmentation and snelling

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Failure envelopes of paint films as related to pigmentation and snelling

Zorll, U.; National Research Council of Canada. Division of Building

CANADA INSTITUTE

FOR

SCIENTIFIC AND TECHNICAL

INFORMATION

INSTITUT CANADIEN

DE L'INFORMATION SCIENTIFIQUE

ET TECHIVIQUE

NRC

I

CNR TT

-

178 TECHNICAL TRANSLATION TRADUCTION TECHNIQUE U.

ZORLL

FAILURE ENVELOPES

OF

PAINT FILMS

A S RELATED

TO

PIGMENTATION

AND

SWELLING

BOOK O F THE Xlth FATIPEC CONGRESS. FLORENCE 1 1

-

16 JUNE 1972. PP. 401

-

4 0 7

MILAN, EDlZlONl ARIMINUM, 1972

T R A N S L A T E D BY

I

T R A D U C T I O N DE P.

J. HYDE

AND ASSOCIATES

THIS IS THE TWO HUNDRED AND SIXTEENTH I N THE SERIES OF TRANSLATIONS

PREPARED FOR THE DIVISION OF BUILDING RESEARCH

TRADUCTION N U M ~ R O 216 DE LA S ~ R I E P R € P A R € E POUR

LA DIVISION DES RECHERCHES EN B ~ T I M E N T

OTTAWA 1975

National Research Conseil national

PREFACE

The Ruilding Materials Section of the Division of Building Research has been interested for some time in the use of failure envelopes to present the results of tensile tests. With a f:tilure envelope it is possible to take into account all of the variables associated with t h y mechanical behnviour o f t,he rn:%t,erial

.

The interest of the :kc! i n r l in t h i s t'i cl t i i s

cxorr~pli f i ec1 by t h e considerable work or1 the f'a i1ur.c. c ~ n v c l o p e s o f . ; c ~ l . ~ r ~ t s

.

Consideration has been r i v e n to extentlir~i; this work to other. orpsrlic t ~ i l i l d i rirr

materials that have viscoelastic properties, such as C O : L ~ ~ I I / T : ; arid ron l'inr

membranes. Dr. Zorllls report is considered to be of special j r i t c ~ r c : ; t , i o

paint chemists concerned with using tensile properties t,o characterize organic coatings and similar materials.

The translation was made by

P.J.

Hyde and Associates and checked for technical content by Mr.

H.E.

Ashton of the Division of Building Research.

Ot

t Rwa.

January 1975

C.

B.

Crnwford Jlirector

TECHNICAL TRANSLATION

1787

TRADUCTION TECHNIQUE

Failure envelopes of paint films as rclatcd to

pigmentation and swelling

(Bruch-Enveloppen von Anstrichfilmen in Abhaengigkeit

von Pigmentierung und Quellungszustand)

AuthorIAuteur:

U. Zorll

Reference/R&fgrence:

Book of the

XI^^

FATIPEC Congress (Federation

dlAssociations

de Techniciens des Industries des

Peintures, Vernis, Emaux et Encres dtImprimerie

de

llEurope

Continentale), Florence, 11-16 June, 1972.

pp. 401-407. Published by Edizioni Ariminum, Via

Negroli 51, Milan, Italy, ,972

Translator/Traducteur:

P.

J. Hyde and Associates

Canada Institute for

Institut canadien de

Scientific and Technical

l'information scientifique et

Information

technique

Ottawa, Canada

1:AILURE ENVELOPES OF PAINT PI1,MS AS RELATED 7'0

PIGMENTATION AND SWELLING

ABSTRACT

A s u i t a b l e p r e s e n t a t i o n of t h e t e n s i l e p r o p e r t i e s of p a i n t f i l m s i s o b t a i n e d by means of T. S m i t h ' s f a i l u r e envelope. The v i s c o e l a s t i c s t a t e s of m a t e r i a l a p p e a r d i s t i n c t l y on t h e f a i l u r e envelope. T e c h n o l o g i c a l p r o p e r t i e s , such a s s t r e n g t h , tough- n e s s and d e f o r m a b i l i t y , c a n a l s o be e v a l u a t e d i n t h i s way. Films of l i n s e e d a l k y d , pigmented w i t h Pb304, MgO and ZnO, e x h i b i t e d a s h i f t t o t h e e n e r g y - e l a s t i c s t a t e w i t h i n c r e a s i n g p i g m e n t a t i o n . I n t h e s w o l l e n s t a t e , t h i s tendency i s markedly reduced by

s w e l l i n g of t h e b i n d e r . The " a c t i v e " e f f e c t of t h e pigments a r e d i m i n i s h e d a t h i g h e r pigment volume c o n c e n t r a t i o n , s i n c e r e a c t i v e g r o u p s i n t h e b i n d e r may t h e n be l a c k i n g . For systems w i t h i n a c t i v e pigments, such a s u r e a r e s i n / F e 2 0 3 and PVC-

copolymer/Ti02, f a i l u r e e n v e l o p e s i n t h e d r y and s w o l l e n s t a t e were found which i n d i c a t e no e s s e n t i a l change i n t h e v i s c o e l a s t i c

c h a r a c t e r of t h e f i l m s . Measurements of t h e systems s t u d i e d c o u l d be e x p l a i n e d q u a l i t a t i v e l y on t h e b a s i s of t h e o r e t i c a l i d e a s d e r i v e d by T. Smith, Bueche and Halpin.

INTRODUCTION

The s t r e n g t h p r o p e r t i e s of c o a t i n g f i l m s a r e b a s i c a l l y determined by t h e v i s c o e l a s t i c c h a r a c t e r of t h e b i n d e r . An a d d i t i o n a l c o n s i d e r a t i o n i s t h e i n f l u e n c e of t h e pigment which i s c h i e f l y shown t h r o u g h t h e e x t e n t of

i n t e r a c t i o n between pigment and b i n d e r . A s a r u l e , t h e most i m p o r t a n t p a r a m e t e r s which d e t e r m i n e t h e t e n s i l e p r o p e r t i e s a r e b r e a k i n g s t r e n g t h and e l o n g a t i o n a t b r e a k . Owing t o t h e v i s c o e l a s t i c n a t u r e of c o a t i n g s , t h e s e two p a r a m e t e r s a r e s i g n i f i c a n t l y a f f e c t e d by t e m p e r a t u r e , s t r a i n r a t e and o t h e r f a c t o r s , p r i n c i p a l l y t h e s t a t e of s w e l l i n g . To b e a b l e t o r e c o g n i z e t h e i n f l u e n c e of t h e s t r u c t u r a l f e a t u r e s of t h e f i l m on t h e t e n s i l e p r o p e r t i e s , a s u i t a b l e form of p r e s e n t a t i o n must be chosen f o r t h e p a r a m e t e r s , b r e a k i n g s t r e n g t h and e l o n g a t i o n a t b r e a k . T h i s

( 1 i s a t t a i n e d by u s e of t h e f a i l u r e e n v e l o p e , o r i g i n a l l y proposed by Smith

,

which h a s a l r e a d y been proven by a p p l i c a t i o n t o t h e e v a l u a t i o n of v a r i o u s polymers. For a g i v e n m a t e r i a l a c u r v e i s o b t a i n e d by p l o t t i n g p a i r s of v a l u e s f o r b r e a k i n g s t r e n g t h and e l o n g a t i o n a t b r e a k determined a t d i f f e r e n t

t e m p e r a t u r e s and r a t e s of s t r a i n . Such a f a i l u r e e n v e l o p e makes i t p o s s i b l e t o judge c l e a r l y t h e i n t r i n s i c f i l m p r o p e r t i e s a s a f f e c t e d by t h e s t r u c t u r e . I t i s t h e r e f o r e p o s s i b l e ( a s Bueche and H a l p i n have shown(2)) f o r t h e f a i l u r e envelope under s u i t a b l e c o n d i t i o n s t o p r o v i d e a t h e o r e t i c a l b a s i s f o r c o r r e l a t i n g t h e s t r e n g t h p r o p e r t i e s of a polymer m a t e r i a l w i t h i t s c r e e p and r e l a x a t i o n b e h a v i o u r . The c h a r a c t e r i z i n g of m a t e r i a l s by f a i l u r e e n v e l o p e s r e p r e s e n t s , t h e r e f o r e , a u s e f u l complement t o t h e p o s s i b i l i t i e s of e v a l u a t i n g m a t e r i a l b e h a v i o u r which i s normally u n d e r t a k e n on t h e b a s i s of s t r e s s - s t r a i n c u r v e s . T h i s l a t t e r c o n v e n t i o n a l form of p r e s e n t a t i o n h a s a l r e a d y been widely used t o d e s c r i b e t h e behaviour of p a i n t f i l m s . I n most c a s e s t h e purpose was t o i n v e s t i g a t e t h e s p e c i f i c e f f e c t s of c e r t a i n i m p o r t a n t f a c t o r s . The e f f e c t of t h e d i f f e r e n t c h a r a c t e r i s t i c s of pigments, s u c h a s p a r t i c l e s i z e , s h a p e , a c t i v i t y and c o n c e n t r a t i o n , a s w e l l a s t h e s t r u c t u r e of t h e b i n d e r , was f i r s t d i s c u s s e d i n d e t a i l by Elm(3). Using v a r i o u s pigments i n a l k y d r e s i n f i l m s , Snoddon and ~ a r r i c k ' ~ ) have c a r r i e d o u t i n v e s t i g a t i o n s on s t r e n g t h p r o p e r t i e s i n r e l a t i o n t o pigment d i s t r i b u t i o n and have t a k e n i n t e r f a c i a l e f f e c t s i n t o c o n s i d e r a t i o n . The e f f e c t of r a t e of s t r a i n a p p l i c a t i o n was c l o s e l y examined by ~ v a n s ' ~ ) . The e v a l u a t i o n of f i l m d u r a b i l i t y was i n v e s t i g a t e d by t e n s i l e

( 6 )

measurements by S c h u r r e t a l .

.

Other a u t h o r s c a r r i e d o u t r e s e a r c h on f i l m s t r e n g t h of s p e c i f i c p a i n t systems. For a c o n s i d e r a b l e number of d i f f e r e n t systems Talen") d i s c u s s e d i n g e n e r a l terms t h e t e n s i l e p r o p e r t i e s of f i l m s i n r e l a t i o n t o t h e i r

b e h a v i o u r i n p r a c t i c e . J a f f e and ~ i c k e n s c h e r ' ~ ) s t u d i e d t h e behaviour of v i n y l r e s i n f i l m s d u r i n g w e a t h e r i n g . The t e n s i l e p r o p e r t i e s of t y p i c a l i n d u s t r i a l c o a t i n g s a p p l i e d by v a r i o u s methods of t r e a t m e n t have been i n v e s t i g a t e d by Bono and pagani('). Funke and Z o r l l ( l o ) have examined t h e i n f l u e n c e of s o l v e n t composition on t h e t e n s i l e p r o p e r t i e s of PVC-copolymer f i l m s . F i n a l l y , t h e r e l a t i o n s h i p between t h e s t r e n g t h p r o p e r t i e s and o t h e r

(11) f i l m p r o p e r t i e s has been e x h a u s t i v e l y d e a l t w i t h by J . Wright

.

S t r e s s - s t r a i n measurements have a l s o been w i d e l y u t i l i z e d f o r t h e a d d i t i o n a l c h a r a c t e r i z i n g of f i l m p r o p e r t i e s . I n a l l t h e c a s e s p r e v i o u s l y mentioned, d i s c u s s i o n h a s been l i m i t e d t o t h e r e s u l t i n g s t r e s s - s t r a i n c u r v e s . While i n p r i n c i p l e t h e l a t t e r method i s s t i l l i m p o r t a n t , t h e f a i l u r e e n v e l o p e d o e s p e r m i t a d e e p e r i n s i g h t i n t o m a t e r i a l p r o p e r t i e s , s i n c e i t p r o v i d e s a compact p r e s e n t a t i o n of t e s t r e s u l t s .

CHIEF CHARACTERISTICS OF THE FAILURE ENVELOPE

The a p p e a r a n c e of a f a i l u r e envelope i s shown s c h e m a t i c a l l y i n F i g u r e 1. The c o - o r d i n a t e s of t h e diagram a r e t h e e l o n g a t i o n a t b r e a k 6 : and t h e

B

b r e a k i n g s t r e s s a a t a g i v e n t e m p e r a t u r e To. S u i t a b l e p r e s e n t a t i o n of t h e s e B

v a l u e s , which may f r e q u e n t l y v a r y over s e v e r a l o r d e r s of magnitude, i s a c h i e v e d by means of a l o g a r i t h m i c p l o t . C o n s i d e r a t i o n of t h e measured t e m p e r a t u r e T a t t h e b r e a k i n g s t r e n g t h c o r r e s p o n d s t o p r e v i o u s l y developed i d e a s on t h e v i s c o e l a s t i c n a t u r e of t h e m a t e r i a l . The e x p e r i m e n t a l l y

v e r i f i e d b a s i s proposed by smith'') f o r t h e u s e of a kind of reduced b r e a k i n g s t r e n g t h i n t h e f a i l u r e e n v e l o p e diagram i s j u s t i f i e d by t h e a p p e a r a n c e of i n t e r n a l f o r c e s when a polymer i n a s o f t e n e d c o n d i t i o n i s s u b j e c t e d t o d e f o r m a t i o n . These f o r c e s a r e p r o p o r t i o n a l t o t h e a b s o l u t e t e m p e r a t u r e .

The measured p a i r s of v a l u e s of e l o n g a t i o n a t b r e a k and b r e a k i n g s t r e s s a r e a r r a n g e d on t h e f a i l u r e envelope depending on t h e t e m p e r a t u r e o r

measurement. Thus, i n t h e f i g u r e , t h e t e m p e r a t u r e g e n e r a l l y i n c r e a s e s a l o n g t h e e n v e l o p e i n t h e d i r e c t i o n i n d i c a t e d . I n t h e o p p o s i t e s e n s e , a r i s e of t e m p e r a t u r e m a n i f e s t s i t s e l f a s a n i n c r e a s e i n t h e d e f o r m a t i o n r a t e which, n e v e r t h e l e s s , was m a i n t a i n e d c o n s t a n t i n t h e p r e s e n t work. The b a s i c a d v a n t a g e of t h i s form of p r e s e n t a t i o n a r i s e s from t h e f a c t t h a t , w i t h v a r i a t i o n of t e m p e r a t u r e and s t r a i n r a t e , t h e p a i r s of v a l u e s p r o v i d e a u n i - form c u r v e . The t y p i c a l f i e l d o f a p p l i c a t i o n of t h e f a i l u r e e n v e l o p e i s i n a s s o c i a t i o n w i t h v i s c o e l a s t i c c o n d i t i o n s , a s a l s o i n d i c a t e d i n F i g u r e 1. It w i l l be a p p a r e n t a t a g l a n c e t o which v i s c o e l a s t i c s t r u c t u r a l c h a r a c t e r i s t i c s t h e measured v a l u e s found i n a p a r t i c u l a r t e m p e r a t u r e r e g i o n

c o r r e s p o n d . J u s t a s i m p o r t a n t a s t h e s e o b s e r v a t i o n s , which a r e drawn more from t h e s t r u c t u r e of t h e m a t e r i a l , a r e t h e c h a r a c t e r i s t i c s which c a n be l e a r n e d from t h e f a i l u r e envelope i n r e g a r d t o t h e mechanical p r o p e r t i e s of t h e f i l m . An i n c r e a s e i n s t r e n g t h , toughness and d e f o r m a b i l i t y i s i n d i c a t e d by t h e d i r e c t i o n of t h e a r r o w s . T h e r e f o r e , t h e more t h e whole f a i l u r e

e n v e l o p e , o r o n l y p a r t s of i t , a p p e a r s t o be s h i f t e d i n one of t h e named d i r e c t i o n s , t h e more pronounced i s t h e m a n i f e s t a t i o n of t h a t p a r t i c u l a r c h a r a c t e r i s t i c p r o p e r t y of t h e f i l m . T h i s p r e s e n t a t i o n i s e s p e c i a l l y advantageous when comparisons between f a i l u r e e n v e l o p e s of d i f f e r e n t f i l m s a r e u n d e r t a k e n i n which t h e f i l m s d i f f e r g r e a t l y i n composition o r method of p r e p a r a t i o n . Examples of such d i f f e r e n c e s a r e g i v e n i n t h e f o l l o w i n g .

EXPERIMENTAL PROCEDURE

The p r e s e n t i n v e s t i g a t i o n s d e a l w i t h t y p i c a l p a i n t systems i n which t h e p i g m e n t a t i o n was v a r i e d o v e r a v e r y wide range. Pigments t o which a

d i s t i n c t a c t i v i t y c o u l d be a t t r i b u t e d when used i n c o n n e c t i o n w i t h a g i v e n b i n d e r a g e n t were employed. I n o r d e r t o be a b l e t o u s e t h e p r e s e n t a t i o n of t h e f a i l u r e e n v e l o p e , measurements t a k e n covered a d e f i n i t e t e m p e r a t u r e r a n g e conforming t o t h a t found i n normal p r a c t i c e .

The primary p a r a m e t e r s , b r e a k i n g s t r e n g t h and e l o n g a t i o n a t b r e a k were determined i n a one-dimensional t e n s i l e t e s t on f r e e f i l m s t h e t h i c k n e s s of which was i n t h e u s u a l r a n g e of 20 t o 60 Dm. A t a b l e model TNSTRON t e n s i l e t e s t i n g machine was used Tor t h e s e measurements. The instrument was equipped w i t h a n a d d i t i o n a l d e v i c e by means of which t h e f i l m c o u l d always be t e s t e d a t c o n s t a n t t e m p e r a t u r e , and, i n a d d i t i o n e i t h e r i n t h e d r y o r i n t h e s w o l l e n s t a t e . T h i s a d d i t i o n a l equipment c o n s i s t e d of a double- w a l l e d t e m p e r a t u r e - c o n t r o l l e d chamber, which i n t h e l a t t e r c a s e c o u l d be f i l l e d w i t h w a t e r s o t h a t d u r i n g measurements t h e f i l m was s i t u a t e d i n t h e s w e l l i n g medium. The f i l m s on which t h e e f f e c t of w a t e r was t o be s t u d i e d had been p r e v i o u s l y immersed i n w a t e r a t room t e m p e r a t u r e f o r a t l e a s t 30 d a y s . The number of r e p l i c a t e measurements l a y between 3 and 1 0 . The a c c u r a c y of measurement a t t a i n e d was a b o u t 10%. R a t e of d e f o r m a t i o n was m a i n t a i n e d c o n s t a n t a t 0 . 5 cm p e r minute.

RESULTS OF MEASUREMENTS

Linseed Alkvd ResinIRed Lead

I n v e s t i g a t i o n of t h i s system d e a l t w i t h a t y p i c a l r e p r e s e n t a t i v e of a n a n t i c o r r o s i o n c o a t i n g . The c o r r e s p o n d i n g f a i l u r e e n v e l o p e s a r e shown i n F i g u r e 2. The change i n t h e t r e n d s of t h e c u r v e s caused by p i g m e n t a t i o n , which i n t h i s c a s e v a r i e d up t o a PVC of 30%, i s c l e a r l y d i s t i n g u i s h e d f o r d r y f i l m s i n t h e l e f t h a l f of t h e f i g u r e . Temperature v a r i e d i n t h e range between 5 and 5 0 ' ~ . While i n t h i s r a n g e t h e c l e a r r e s i n f i l m l i e s f o r t h e g r e a t e s t p a r t i n t h e e n t r o p y - e l a s t i c c o n d i t i o n and o n l y a t lower t e m p e r a t u r e s conforms t o t h e s o f t e n i n g r e g i o n , w i t h i n c r e a s e d p i g m e n t a t i o n a t r a n s i t i o n of t h e f i l m i n t o t h e e n e r g y - e l a s t i c c o n d i t i o n i s o b s e r v a b l e , c h a r a c t e r i z e d by g r e a t e r b r i t t l e n e s s . The u n i f o r m i t y i n t h e s h i f t of t h e c u r v e s up t o a PVC of 30% i s s t r i k i n g ; t h i s i s c o n s i d e r e d proof of t h e good c o m p a t a b i l i t y of t h e pigment i n t h e system under i n v e s t i g a t i o n . The v a l u e s of b r e a k i n g s t r e n g t h a t low t e m p e r a t u r e s a r e i n t h e same o r d e r of magnitude, independent of t h e PVC. I n t h e e n e r g y - e l a s t i c r e g i o n i n i t i a t i o n of m a t e r i a l f a i l u r e a p p a r e n t l y t a k e s p l a c e i n t h e b i n d e r . The good a d h e s i o n between pigment and b i n d e r i s demonstrated h e r e i n t h e a l k y d r e s i n l r e d l e a d system g e n e r a l l y c h a r a c t e r i z e d a s " a c t i v e " . T h i s r e s u l t i s i n agreement w i t h t h e work of Ronay ( I 2 ) who s t a t e s t h a t t h e a p p e a r a n c e of f a i l u r e h a s a s t r o n g l y l o c a l i z c d c h a r a c t e r which o c c u r s i n a s i m i l a r manner b o t h w i t h f i l l e d and u n f i l l e d polymeric m a t e r i a l s .

On t h e o t h e r hand, i n t h e e n t r o p y - e l a s t i c r e g i o n t h e r e i s a much g r e a t e r dependence of t h e b r e a k i n g s t r e n g t h on t h e PVC. A comparison of t h e v a l u e s of

b r e a k i n g s t r e s s a t 5 0 ' ~ shows t h a t , s t a r t i n g from c l e a r r e s i n , t h e v a l u e of b r e a k i n g s t r e n g t h r i s e s a t f i r s t w i t h i n c r e a s i n g p i g m e n t a t i o n and t h e n , a t a PVC above

l o % ,

changes t o a c o n s t a n t v a l u e . T h i s phenomenon c a n be e x p l a i n e d from i d e a s developed by ~ u e c h e ( ' ~ ) . I n a pigment-free m a t e r i a l once a

m o l e c u l a r c h a i n i s broken t h e b r e a k t e n d s t o p r o p a g a t e i t s e l f e s s e n t i a l l y w i t h o u t r e s t r a i n t , t h u s r e s u l t i n g i n a lowered b r e a k i n g s t r e n g t h . Assuming t h a t t h e c h a i n s a r e t i g h t l y bound t o t h e pigment s u r f a c e s , a s would be expected w i t h t h e pigment p a r t i c l e s under d i s c u s s i o n , t h e pigment would be a b l e t o g i v e d e f i n i t e s u p p o r t t o t h e f r e e ends of t h e c h a i n s , s o t h a t f u r t h e r

development of t h e f a i l u r e i s r e s t r i c t e d . Consequent I y , t h ~ I)rc:~kinl: strcwt:t 11

Ls i n c r e a s e d . The assumption n e c e s s a r y f o r t h i s e f f e c t is n s t r o n g e r l i n k a g e of b i n d e r molecule t o t h e p a r t i c l e s u r f a c e . Only c e r t a i n , mostly a c i d i c g r o u p s a r e i n a p o s i t i o n t o do t h i s . I f t h e number of t h e s e i s r e s t r i c t e d , t h e n w i t h t h e a d d i t i o n of f u r t h e r pigment p a r t i c l e s no f u r t h e r e f f e c t i v e r e a c t i o n o c c u r s . Hence, t h e c o n s t a n c y of b r e a k i n g s t r e n g t h a t h i g h e r PVC can be e x p l a i n e d . I n c o n t r a s t t o t h e f a i l u r e envelopesmeasured i n t h e d r y s t a t e , t h o s e i n t h e s w o l l e n c o n d i t i o n e x h i b i t a much g r e a t e r expansion of t h e s o f t e n i n g r e g i o n . I n t h i s c a s e , t h e p l a s t i c i z i n g a c t i o n of t h e w a t e r caused by s w e l l i n g a p p a r e n t l y i s r e v e a l e d . The f a c t t h a t t h e bond between pigment and b i n d e r i s s u b s t a n t i a l l y m a i n t a i n e d i n t h e e n e r g y - e l a s t i c c o n d i t i o n shows t h a t t h e r e i s a l s o a somewhat s i m i l a r magnitude of b r e a k i n g s t r e n g t h f o r water-swollen f i l m s . A t h i g h e r t e m p e r a t u r e s , however, a n a p p a r e n t r e l a x i n g of t h e bond o c c u r s which shows up a s a d e c r e a s e i n t h e b r e a k i n g s t r e n g t h v a l u e . The s p e c i a l form of t h e f a i l u r e envelope f o r t h e c l e a r r e s i n f i l m s i n t h e e n t r o p y - e l a s t i c r e g i o n must now be c o n s i d e r e d . I n t h i s r e g i o n , a c c o r d i n g t o i d e a s developed by S m i t h ( 1 4 ) , t h e f a i l u r e envelope t a k e s t h e form of a s t r a i g h t l i n e , which i s a l s o confirmed by t h e r e s u l t s d e s c r i b e d i n t h i s paper. The s l o p e of t h i s l i n e i s r e l a t e d t o t h e modulus of e l a s t i c i t y , and t h e r e f o r e t o t h e d e g r e e of c r o s s - l i n k i n g of t h e m a t e r i a l . A c o m p a r a t i v e l y s t e e p s l o p e of t h e l i n e i n d i c a t e s t h a t t h e c r o s s - l i n k i n g i s r e l a t i v e l y d e n s e . P a r a l l e l i s m of t h e l i n e s i n t h e d r y and s w o l l e n s t a t e i n d i c a t e s t h a t t h e c r o s s - l i n k d e n s i t y remains p r a c t i c a l l y t h e same when t h e f i l m s a r e exposed t o t h e a c t i o n of w a t e r . A lower s l o p e i n t h e water-soaked c o n d i t i o n i n d i c a t e s

a somewhat wider c r o s s - l i n k i n g which c o r r e s p o n d s t o t h e above mentioned i n s i g n i f i c a n t r e d u c t i o n i n b r e a k i n g s t r e n g t h of t h e c l e a r r e s i n a t h i g h e r t e m p e r a t u r e s .

Linseed Alkyd ResinIMagnesium Oxide

Although magnesium o x i d e h a s no c o l o u r i n g p r o p e r t i e s and i s r e g a r d e d a s more i n t h e n a t u r e of a f i l l e r , i t s u s e i n t h e p r e s e n t i n v e s t i g a t i o n was

i n t e r e s t i n g b e c a u s e a n undoubtedly e f f e c t i v e r e a c t i o n c a n be a t t r i b u t e d t o i t on a c c o u n t of i t s o x i d i z i n g n a t u r e . I n c o n t r a s t t o r e d l e a d , however,

t h i s s p e c i a l p r o p e r t y c a n a l s o be s t u d i e d . From t h e f a i l u r e e n v e l o p e s i n F i g u r e 3 i t w i l l be observed t h a t i n t h e t e m p e r a t u r e r a n g e i n v e s t i g a t e d 0 ( 5

-

50 C ) , t h e s o f t e n i n g r e g i o n i s determined by t h e accolnpanying c o n d i t i o n s . I n d i r e c t c o n t r a s t t o o b s e r v a t i o n s i n t h e r e d l e a d pigmented system, t h e r e i s no n o t i c e a b l e s h i f t of t h e v i s c o e l a s t i c c h a r a c t e r towards t h e e n e r g y - e l a s t i c c o n d i t i o n w i t h i n c r e a s e d PVC. Apparently t h e lowered r e a r t i v i t y of t h e magnesium o x i d e i s demonstrated h e r e ; any a c t i v i t y t o be e x p e c t e d i s r a t h e r

by r e a s o n of t h e f i n e l y d i v i d e d s t a t e of t h e m a t e r i a l . I n t h e e n t r o p y - e l a s t i c r e g i o n , i n c r e a s e of b r e a k i n g s t r e n g t h w i t h i n c r e a s e i n PVC i s p r a c t i c a l l y unobserved. E v i d e n t l y t h e r e l a t i v e l y e a s i l y moved magnesium o x i d e p a r t i c l e s do n o t c a u s e t h e same s u p p o r t i n g a c t i o n t o o c c u r a s w i t h t h e more massive l e a d p a r t i c l e s . According t o t h e c o n c e p t i o n of H a l p i n and ~ u e c h e " ~ ) , th e

r e i n f o r c i n g a c t i o n of a p a r t i c l e i s determined b a s i c a l l y by t h e r e s t r i c t i o n of i t s movement i n t h e s u r r o u n d i n g v i s c o e l a s t i c medium.

For pigmented f i l m s i n t h e s w o l l e n s t a t e , a g r e a t e r s h i f t i n t h e d i r e c t i o n of t h e e n t r o p y - e l a s t i c r e g i o n i s e s t a b l i s h e d . T h i s e f f e c t must a p p a r e n t l y be c o n s i d e r e d a s a s s o c i a t e d w i t h t h e low s o l u b i l i t y of magnesium o x i d e . Taken on t h e whole, t h e e f f e c t of t h e p i g m e n t a t i o n i n t h e f i l m i s reduced and t h e

r u b b e r y - e l a s t i c c h a r a c t e r of t h e b i n d e r i t s e l f c a n a g a i n a p p e a r more c l e a r l y , p r i m a r i l y a t h i g h e r t e m p e r a t u r e s . The g r e a t e r r e d u c t i o n of t h e b r e a k i n g s t r e n g t h of t h e pigmented f i l m s i n t h e lower t e m p e r a t u r e r e g i o n c a n be e x p l a i n e d by t h e i n c r e a s e d f o r m a t i o n of weak s p o t s i n t h e f i l m which have o r i g i n a t e d t h r o u g h t h e p a r t i a l s o l u t i o n of t h e magnesium o x i d e .

Linseed Alkyd R e s i n I Z i n c Oxide

On t h e b a s i s of t h e p o s s i b i l i t y of z i n c o x i d e r e a c t i n g w i t h c o n s t i t u e n t s of t h e b i n d e r , a c e r t a i n amount of a c t i v i t y of t h e pigment must be reckoned w i t h i n t h i s system ( F i g u r e

4 ) .

I n a manner s i m i l a r t o t h a t f o r r e d l e a d pigmented f i l m s , t h i s r e a c t i o n i n t h e d r y s t a t e shows i t s e l f a s a s h i f t of t h e c u r v e s w i t h h i g h e r PVC i n t h e d i r e c t i o n of t h e e n e r g y - e l a s t i c r e g i o n . I t i s t r u e t h a t a c e r t a i n i n c r e a s e i n s t r e n g t h i s a c h i e v e d by t h i s , b u t a t t h e same t i m e , however, b r i t t l e n e s s r e s u l t s . T h i s i s a l s o shown i n c o r r e s p o n d i n g i n v e s t i g a t i o n s by E i s s l e r and p r i n c e n ( 1 6 ) . Indeed i t a p p e a r s t h a t t h e a c t i v e r e a c t i o n a t t r i b u t e d t o t h e z i n c o x i d e o n l y e x t e n d s t o a c e r t a i n PVC. The

~ r p p r t ~ c i ; l b l y tli rTc.rent p o s i t i o n of t h e f a i l u r c pnvcJnpc~ Tor ;I T'VC o f 30T i n d icatc3s t h a t ;+ d e c l i n e i n t h e a c t i v e mechanism h a s a p p a r e n t l y n c c u r r e t l . Tlle v a l u e s of b r e a k i n g s t r e n g t h a r e d r a s t i c a l l y r e d u c e d . Because of t h c h i g h PVC, t h e e l o n g a t i o n i s s t i l l o n l y r e l a t i v e l y s m a l l . T h i s r e d u c t i o n c a n a g a i n b e e x p l a i n e d by t h e f a c t t h a t t h e r e s i d u a l c a r b o x y l g r o u p s i n t h e b i n d e r , which a r e n e c e s s a r y f o r a r e a c t i o n w i t h z i n c o x i d e , a r e a l r e a d y u s e d up i n t h e r e a c t i o n a t t h i s h i g h PVC. Thus, a d d i t i o n a l pigment p a r t i c l e s c a n no l o n g e r e x e r c i s e a n a c t i v e i n f l u e n c e . C o n s e q u e n t l y , t h i s must a l w a y s b e t a k e n i n t o c o n s i d e r a t i o n whenever t h e a c t i v e i n f l u e n c e of a pigment a t a h i g h e r PVC i s b e i n g d i s c u s s e d . The e f f e c t of w a t e r i n t h e s w o l l e n c o n d i t i o n shows i t s e l f i n t h e marked s p r e a d i n g o u t o f t h e f a i l u r e e n v e l o p e s . W i t h i n t h e t e m p e r a t u r e r a n g e u n d e r i n v e s t i g a t i o n , between 25 and 5 5 ' ~ , t h e m a t e r i a l i s n o t o n l y i n t h e s o f t e n i n g r e g i o n , b u t a l r e a d y p a r t l y i n t h e e n t r o p y - e l a s t i c c o n d i t i o n , a s i n d i c a t e d by t h e c l e a r f i l m . The d i f f e r e n c e i n t h e s l o p e s o f t h e l i n e a r s e c t i o n s of t h e f a i l u r e e n v e l o p e s f o r t l i e c l e a r r e s i n i n t h e d r v and s w o l l e n c o n d i t i o n s shows t h a t t h e c r o s s - l i n k d e n s i t y h a s been lowered i n t h e s w o l l e n s t a t e . Thus, e v e n w i t h o u t t h e i n f l u e n c e of t h e p i g m e n t , w a t e r c a u s e s a c e r t a i n amount of c h a i n c l e a v a g e t o o c c u r . T h i s e f f e c t i s l a r g e l y r e l a t e d t o t h e p r e s e n c e of t h e p i g m e n t , a s i n d i c a t e d by t h e o b s e r v e d s i m i l a r i t y a s a whole o f t h e f a i l u r e e n v e l o p e s f o r t h e pigmented f i l m s i n t h e d r y and s w o l l e n s t a t e s . Due t o t h e e f f e c t of w a t e r , t h e a c t i v e i n f l u e n c e of t h e pigment becomes c o n s i d e r a b l y l e s s o b v i o u s , s i n c e t h e l i n k a g e t o t h e i n t e r f a c e s i s l a r g e l y b r o k e n . T h i s i s a l s o c o n f i r m e d by c o r r e s p o n d i n g measurements o f p e r m e a t i o n ( 1 7 ) . Hence, t h e r e d u c t i o n i n a c t i v i t y o f t h e f i l m a t 30% PVC c a n no l o n g e r b e o b s e r v e d t o t h e same d e g r e e as i n t h e c a s e of d r y f i l m s . Common C h a r a c t e r i s t i c s of t h e F i l m s I n v e s t i g a t e d The t h r e e s y s t e m s s o f a r d i s c u s s e d h a v e c o n t a i n e d p i g m e n t s t o which a d e f i n i t e i n f l u e n c e c o u l d b e a t t r i b u t e d . The b i n d e r s u t i l i z e d

-

l o n g o i l l i n s e e d a l k y d r e s i n s

-

p r o v i d e a n a d e q u a t e h y p o t h e s i s by t h e i r s t r u c t u r e , w i t h i t s r e s i d u a l c a r b o x y l g r o u p s . The f a i l u r e e n v e l o p e s of t h e s y s t e m s b a s i c a l l y r e v e a l i n t h e t e m p e r a t u r e r a n g e between 5 t o 50°c t h a t t h e f i l m s w e r e c o m p l e t e l y l o c a t e d i n t h e e n t r o p y - e l a s t i c r e g i o n . Thus, c h i e f l y b e c a u s e of t h e i r m a r k e d l y c u r v e d r e g i o n , t h e f a i l u r e e n v e l o p e s were s h i f t e d r e l a t i v e l y

f a r towards t h e o u t s i d e . (:orrcspolid i n ? t o t h e schemnt i c p r c s c - n t n t i o n 1 1 1

F i g u r e 1, t h i s p o s i t i o n s i g n i f i e s a c o m p a r a t i v e l y h i g h toughness. T h i s mechanical p r o p e r t y i s v e r y d e s i r a b l e i n r e l a t i o n t o t h e g r e a t e s t p o s s i b l e wear r e s i s t a n c e of t h e f i l m . I n t h i s r e s p e c t t h e systems c u r r e n t l y

i n v e s t i g a t e d prove t o be t r u l y advantageous. Apart from t h e f i l m s w i t h t h e h i g h e s t

PVC,

t h e r e m a i n d e r , a c c o r d i n g t o t h e p o s i t i o n of t h e f a i l u r e e n v e l o p e s , g e n e r a l l y show a n o v e r a l l f a v o u r a b l e toughness which s u i t s t h e i r a p p l i c a t i o n i n c o r r o s i o n - p r e v e n t i o n systems. Urea ~ e s i n / I r o n Oxide The c o m p o s i t i o n of t h e b i n d e r e n s u r e d t h a t , i n t h e t e m p e r a t u r e r a n g e 0 i n v e s t i g a t e d , from 25 t o 55 C , t h e f i l m s were l o c a t e d i n t h e e n t r o p y - e l a s t i c r e g i o n . T h i s c h a r a c t e r i s t i c i s a l s o e v i d e n t from t h e p o s i t i o n of t h e l i n e a r s e c t i o n s of t h e f a i l u r e e n v e l o p e s i n F i g u r e 5 . A comparison of t h e s e

s e c t i o n s f o r t h e c l e a r r e s i n f i l m s i n t h e d r y and s w o l l e n s t a t e shows tlt;it t h e s l o p e of t h e l i n e s remains e s s e n t i a l l y c o n s t a n t , s o t h a t no g r e a t change i n t h e s t a t e of c r o s s - l i n k i n g can have o c c u r r e d due t o t h e a c t i o n of w a t e r . The i n f l u e n c e of water i s r e v e a l e d s o l e l y by t h e n o t i c e a b l e r e d u c t i o n i n t h e b r e a k i n g s t r e n g t h on changing from t h e d r y t o t h e s w o l l e n s t a t e and a s m a l l e r d e c r e a s e i n t h e e l o n g a t i o n a t b r e a k . A p p a r e n t l y t h e w a t e r i n t h e r e s i n

a c t i v a t e d v u l n e r a b l e weak p o i n t s t o a c e r t a i n d e g r e e . However, t h e s e must

o n l y have v e r y s m a l l dimensions s i n c e i t c a n be e s t a b l i s h e d by s w e l l i n g t e s t s (18) t h a t i n t h e s e p a r t i c u l a r systems w a t e r i s o n l y t a k e n up from t h e b i n d e r i n

m o l e c u l a r form.

The i n a c t i v i t y of t h e i r o n o x i d e pigment i s shown by t h e f a c t t h a t , up t o a PVC of 30%, t h e b a s i c c h a r a c t e r of t h e f i l m s remains t h e same, f o r o n l y t h e e n t r o p y - e l a s t i c s e c t i o n of t h e f a i l u r e e n v e l o p e s c a n be observed by measurement. N e v e r t h e l e s s , t h e a d h e s i o n between t h e pigment and t h e b i n d e r must be r e l a t i v e l y s t r o n g . With i n c r e a s i n g PVC, a marked i n c r e a s e i n t h e b r e a k i n g s t r e n g t h o c c u r r e d which, a c c o r d i n g t o t h e c o n c e p t i o n of Bueche ( 1 3 )

mentioned above, r e p r e s e n t s t h e r e i n f o r c i n g a c t i o n of t h e pigment opposing

t h e e f f e c t of t h e l i b e r a t e d c h a i n s e c t i o n s caused by c h a i n r u p t u r e . The n e c e s s a r y a d h e s i o n between t h e c h a i n s e c t i o n s and t h e pigment s u r f a c e f o r t h i s

i n t h e t e m p e r a t u r e r a n g e under i n v e s t i g a t i o n a r e l o c a t e d c o m p l e t c ~ l y i n the. e n t r o p y - e l a s t i c r e g i o n , i t i s e a s y t o e x p l a i n t h a t t h i s cFCect becomes e v i d e n t a t a b o u t t h e same o r d e r of magnitude a t b o t h t h e lowcst a n d h i g h e s t t e m p e r a t u r e s i n v e s t i g a t e d . I n t h e t r a n s i t i o n from lower t o h i g h e r t e m p e r a t u r e o n l y a r e d u c t i o n i n d e f o r m a b i l i t y i s g e n e r a l l y e s t a b l i s h e d . One c o n c l u s i v e e x p l a n a t i o n f o r t h i s i s t h a t i n c r e a s i n g p i g m e n t a t i o n l e a d s t o t h e e x p e c t e d g r e a t e r inhomogeneity i n t h e s t r e s s f i e l d i n t h e f i l m . Thus, t h e c r i t i c a l s t r e s s f o r a l o c a l i z e d c h a i n r u p t u r e i s more e a s i l y and more o f t e n a t t a i n e d s o t h a t , a s a whole, a reduced e l o n g a t i o n a t b r e a k r e s u l t s . Because of t h e a c t i o n of w a t e r which c a u s e s a r e d u c t i o n i n t h e s t r e n g t h of t h e p u r e b i n d e r , t h e pigmented f i l m s a r e a l s o a f f e c t e d . Of c o u r s e w i t h i n c r e a s i n g PVC, t h i s e f f e c t i s l e s s s t r o n g l y o p e r a t i v e simply b e c a u s e of t h e f a c t t h a t t h e pigment o c c u p i e s a p a r t of he f i l m volume. Tn t h e c a s e of s w o l l e n f i l m s t h e b r e a k i n g s t r e n g t h t h e r e f o r e r i s e s markedly w i t h i n c r e a s e d PVC, w h i l e a t t h e same time t h e v a l u e s of e l o n g a t i o n a t b r e a k a r e somewhat h i g h e r . A remarkable f e a t u r e , however, i s t h a t a t t h e h i g h e s t PVC of 302,

t h e v i s c o e l a s t i c c h a r a c t e r of t h e f i l m i s s i g n i f i c a n t l y changed. The

r e l a t i v e l y s m a l l s e c t i o n of t h e f a i l u r e e n v e l o p e i n d i c a t e s t h a t , i n t h i s c a s e , t h e t e m p e r a t u r e h a s s c a r c e l y any e f f e c t on t h e behaviour of t h e f i l m . The s i m u l t a n e o u s p r e s e n c e of w a t e r i n t h e b i n d e r and t h e h i g h pigment c o n c e n t r a t i . o n of t h e f i l m c a u s e t h e f i l m t o remain no l o n g e r i n t h e e n t r o p y - e l a s t i c r e g i o n b u t t o be s h i f t e d i n i t s behaviour i n t h e d i r e c t i o n of t h e e n e r g y - e l a s t i c c o n d i t i o n . Consequently, o n l y a c o m p a r a t i v e l y s m a l l s e c t i o n o u t of t h e s o f t e n i n g r e g i o n of t h e f a i l u r e envelope i s encompassed. The f o r e g o i n g r e s u l t s show t h a t i n o r d e r t o comprehend t h e complete v i s c o e l a s t i c n a t u r e of t h e s e f i l m s , i t would be n e c e s s a r y t o i n v e s t i g a t e a s u b s t a n t i a l l y g r e a t e r r a n g e of t e m p e r a t u r e . PVC-Copolymer/Titanium Dioxide A s F i g u r e 6 shows, i n b o t h t h e d r y a s w e l l a s t h e s w o l l e n s t a t e t h e m a t e r i a l i s l o c a t e d i n t h e upper r e g i o n of f a i l u r e e n v e l o p e s , which d i s t i n g u i s h e s c l e a r l y t h e e n e r g y - e l a s t i c c o n d i t i o n and i t s t r a n s i t i o n i n t o t h e s o f t e n i n g r e g i o n . Hence, h i g h v a l u e s of e l o n g a t i o n a t b r e a k a r e r e a c h e d by t h i s m a t e r i a l . Owing t o t h e l o g a r i t h m i c method of p l o t t i n g , t h e s e c a n be

c l e a r l y a p p r e c i a t e d from t h e t y p e of p r e s e n t a t i o n s e l e c t e d . F i r s t of a l l i t c a n be e s t a b l i s h e d from t h e c u r v e s shown t h a t t h e v a l u e s show a c o n s i d e r a b l e s c a t t e r around t h e middle s e c t i o n of t h e f a i l u r e envelope. T h i s phenomenon

i s g e n e r a l f o r t h e observed f a i l u r e e n v e l o p e s . Smith ( I 4 ) a t t r i b u t e s t h e s c a t t e r t o s i d e e f f e c t s which a r e p a r t i c u l a r l y a c t i v e a t low t e m p e r a t u r e s . I t i s connected w i t h l o c a l v a r i a t i o n s d u r i n g d e f o r m a t i o n (necking) of t h e t e s t p i e c e which c a n be r e l a t e d t o l o c a l i z e d d i f f e r e n c e s i n h e a t p r o d u c t i o n . A comparison of t h e f a i l u r e e n v e l o p e s f o r d i f f e r e n t v a l u e s of PVC i n d i c a t e s t h a t h e r e t h e p i g m e n t a t i o n c a n a p p a r e n t l y develop no r e i n f o r c i n g a c t i o n . Both i n t h e d r y and i n t h e s w o l l e n s t a t e s , s t r e n g t h and d e f o r m a b i l i t y d e c l i n e w i t h i n c r e a s i n g PVC. I n d e e d , a p a r t from f i l m s a t t h e h i g h e s t PVC ( 3 0 % ) , t h e v a l u e s a r e g e n e r a l l y i n a r e g i o n which p u t s t h e t e c h n o l o g i c a l a p p l i c a t i o n of t h e f i l m s o u t of q u e s t i o n . The h i g h l y pigmented f i l m i s d i s t i n g u i s h e d by a s p e c i a l b e h a v i o u r . I n t h e d r y s t a t e , i t a p p a r e n t l y remains c l e a r l y i n t h e e n e r g y - e l a s t i c r e g i o n w i t h i n t h e t e m p e r a t u r e r a n g e i n v e s t i g a t e d (10

-

50°C,). The d e s i r e d h i g h d e f o r m a b i l i t y of t h e b i n d e r i s no l o n g e r e v i d e n t i n t h i s f i l m . The s i m u l t a n e o u s a c t i o n of w a t e r d o e s , however, a l l o w t h i s d e s i r a b l e p r o p e r t y of t h e b i n d e r t o d e v e l o p t o a l i m i t e d e x t e n t , a s t h e c o r r e s p o n d i n g s l o p e of t h e f a i l u r e envelope i n t h e s w o l l e n c o n d i t i o n shows. On t h e whole, t h e r e i s l i t t l e d i f f e r e n c e i n t h e v i s c o e l a s t i c c h a r a c t e r of t h e f i l m s between t h e d r y and s w o l l e n s t a t e s . From t h e t e c h n o l o g i c a l v i e w p o i n t , t h e system i n v e s t i g a t e d i s t h e r e f o r e e q u a l l y w e l l s u i t e d t o d r y and humid c o n d i t i o n s . The r o l e of t h e t e m p e r a t u r e i s more i m p o r t a n t h e r e . A t lower t e m p e r a t u r e s , of c o u r s e , a r e l a t i v e l y h i g h s t r e n g t h i s e x h i b i t e d ; however, i t i s g e n e r a l l y o n l y t h e e x t e n s i b i l i t y which i s r e s t r i c t e d . Use of a p i g m e n t a t i o n which i s n o t t o o h i g h works o u t f a v o u r a b l y h e r e . I n t h e c a s e of t i t a n i u m d i o x i d e , t h i s i s a r e q u i r e m e n t which can e a s i l y be met. With i n c r e a s i n g t e m p e r a t u r e , t h e f a i l u r e e n v e l o p e s i n d i c a t e t h a t t h e m a t e r i a l e n t e r s more i n t o a r e g i o n which i s d i s t i n g u i s h e d by h i g h t o u g h n e s s and d e f o r m a b i l i t y . Immediately w i t h i n t h e upper p a r t of t h e t e m p e r a t u r e r a n g e s i t u a t e d n e a r room t e m p e r a t u r e , t h e m a t e r i a l c a n b e extended t o meet t h e mechanical r e q u i r e m e n t s found i n normal p r a c t i c e w i t h o u t l e a d i n g t o a

f a i l u r e e n v e l o p e s i n t h i s r e g i o n , i t w i l l be n o t e d t h a t t h e i d e a s d e v e l o p e d by Rueche ( I 3 ) have h e r e r e a c h e d t h e l i m i t s of t h e i r a p p l i c a b i l i t y . I n o r d e r t o d e s c r i b e t h e b e h a v i o u r o f t h e m a t e r i a l i n t h i s r e g i o n , which c h i e f l y encompasses t h e zone of e n e r g y - e l a s t i c b e h a v i o u r and r e g i o n of s o f t e n i n g , o t h e r c o n c e p t s must b e u s e d , e . g . , t h e t h e o r y d e v e l o p e d by Haward and

(19) Thackray

.

CONCLUSIONS The s y s t e m s i n v e s t i g a t e d i n t h i s p a p e r d e m o n s t r a t e t h a t tlie c o n c e p t i o n of t h e f a i l u r e e n v e l o p e makes p o s s i b l e a s y s t e m a t i c a r r a n g e m e n t of t h e o b s e r v e d v a l u e s of b r e a k i n g s t r e n g t h and e l o n g a t i o n a t b r e a k f o r a m a t e r i a l . The e f f e c t of v a r i a t i o n s i n p i g m e n t a t i o n and s w e l l i n g was e s p e c i a l l y a p p a r e n t b o t h q u a l i t a t i v e l y a n d q u a n t i t a t i v e l y . The p a r t i c u l a r v a l u e of t h i s p r e s e n t a t i o n l i e s i n t h e f a c t t h a t t h e f a i l u r e e n v e l o p e s r e p r e s e n t c h a r a c t e r i s t i c c u r v e s which, t o a l a r g e e x t e n t , d i s p l a y t h e b e h a v i o u r of t h e m a t e r i a l i n d e p e n d e n t l y of t h e r e m a i n i n g p a r a m e t e r s . The f a c t o r o f r a t e of s t r a i n a p p l i c a t i o n ,

which was h e r e h e l d c o n s t a n t , d o e s n o t p r o v i d e , by e x p e r i e n c e , new f a i l u r e

I

e n v e l o p e s . Only t h e p o s i t i o n o f t h e measured v a l u e s a s s o c i a t e d w i t h

I

p a r t i c u l a r t e m p e r a t u r e s i s c o r r e s p o n d i n g l y s h i f t e d a l o n g t h e e n v e l o p e .

?

C o n s e q u e n t l y , t h e f a i l u r e e n v e l o p e f r e q u e n t l y d i s p l a y s d e f o r m a t i o n p r o p e r t i e s C

i b o t h a t f a s t e r and s l o w e r r a t e s of s t r a i n a p p l i c a t i o n i n a s i m i l a r way. The

I

method of p l o t t i n g a l s o i n d i c a t e s w h e t h e r t h e s e l e c t e d t e m p e r a t u r e r a n g e was s u f f i c i e n t and

-

i f t h i s w a s n o t t h e c a s e

-

which zone of t h e v i s c o e l a s t i c I

'

1

c o n d i t i o n s s h o u l d a c c o r d i n g l y b e u t i l i z e d . Thus, i t becomes c l e a r i n which

'1

d i r e c t i o n t h e t e m p e r a t u r e r a n g e s h o u l d , i f n e c e s s a r y , b e e x t e n d e d i n o r d e r t o 1 o b t a i n t h e c o m p l e t e p i c t u r e of t h e p r o p e r t i e s . I S t i l l f u r t h e r p o s s i b i l i t i e s of t h i s form of p r e s e n t a t i o n e x i s t . B e s i d e s t h e p o s s i b i l i t i e s a l r e a d y mentioned o f d e s c r i b i n g t h e f a i l u r e e n v e l o p e s t h e o r e t i c a l l y , t h e r e a r e o t h e r a t t e m p t s t o b r i n g t h e f o r m s of f a i l u r e e n v e l o p e s I a l r e a d y d i s c o v e r e d i n t o r e l a t i o n s h i p w i t h t h e s t r u c t u r a l f e a t u r e s o f t h e I (20) m a t e r i a l , p a r t i c u l a r l y i n t h e v i c i n i t y of t h e i n t e r f a c e s

.

An e x t e n s i o n of t h e t e c h n o l o g i c a l i n t e r p r e t a t i o n of f a i l u r e e n v e l o p e s s h o u l d a l s o b e p o s s i b l e . A p p l i c a t i o n of t h e l i m i t i n g v a l u e s f o r d e f o r m a b i l i t y and s t r e n g t h

t o t h e r e s p e c t i v e a x e s s h o u l d e n a b l e one t o e s t r i b l i s l ~ im r n c d i : ~ t r l y wl~cbrl~cr, f o r a g i v e n f a i l u r e e n v e l o p e , t h e m a t e r i a l p r o p e r t i e s a t a g i v e n t e m p e r a t u r e s t i l l meet t h e s t i p u l a t e d r e q u i r e m e n t s . A t o l e r a n c e l i m i t of t h i s kind i s a l s o p o s s i b l e f o r t h e t o u g h n e s s ; by p l o t t i n g c u r v e s of c o n s t a n t toughness i t s h o u l d b e p o s s i b l e t o e s t a b l i s h whether and t o what e x t e n t t h e f a i l u r e envelope l i e s i n s i d e o r o u t s i d e t h e toughness t o l e r a n c e r e g i o n .

A more d e t a i l e d d i s c u s s i o n of t h e mechanical d e f o r m a t i o n p r o p e r t i e s i n t h e v i c i n i t y of t h e t e n s i l e s t r e n g t h b o u n d a r i e s would n a t u r a l l y have t o i n c u d e v a l u e s of s e c o n d a r y p a r a m e t e r s d e r i v e d from t h e s t r e s s - s t r a i n c u r v e s , such a s e l a s t i c l i m i t s and y i e l d v a l u e s . S i n c e c h i e f l y e l o n g a t i o n a t b r e a k and b r e a k i n g s t r e n g t h a r e determined from such d i a g r a m s , t h e form of

p r e s e n t a t i o n of t h e f a i l u r e envelope p r o v i d e s a f a v o u r a b l e p o s s i b i l i t y of c h a r a c t e r i z i n g t h e b e h a v i o u r i n a framework i n which t h e combined s i g n i f i c a n c e of b o t h p a r a m e t e r s a p p e a r s . Also, p o s s i b l e d e v i a t i o n s from t h e normal

b e h a v i o u r of a m a t e r i a l c a n be d e t e c t e d . From e x p e r i e n c e , such k i n d s of

f a i l u r e e n v e l o p e s a r e always produced by t h e common p l o t t i n g of t h e p a r a m e t e r s , b r e a k i n g s t r e n g t h and e l o n g a t i o n a t b r e a k . I f i t were once shown t h a t such a complete p r e s e n t a t i o n of t h e measurement r e s u l t s i s i m p o s s i b l e , i t would be t a k e n a s t h e f i r s t v a l u a b l e s i g n t h a t t h e f i l m b e h a v i o u r d e v i a t e d

c o n s i d e r a b l y from t h e u s u a l l y observed norm and, c o n s e q u e n t l y , s p e c i a l i n v e s t i g a t i o n s would b e n e c e s s a r y .

V e r i f i c a t i o n of whether a f i l m on t h e whole behaves a c c o r d i n g t o

e x p e c t a t i o n s when under t h e i n f l u e n c e of e x t e r n a l f a c t o r s , s o t h a t i t s g e n e r a l behaviour c a n b e t t e r be judged, i s a s a r u l e t h e d e s i r a b l e aim of m a t e r i a l t e s t i n g .

F i n a l l y , t h e p r e s e n t a t i o n of f a i l u r e e n v e l o p e s i s d i r e c t l y p o s s i b l e w i t h o u t e x t e n s i v e c a l c u l a t i o n s . Because of t h e l o g a r i t h m i c p l o t , a

c o m p a r a t i v e l y uniform s c a l e o f measurement f o r a l l m a t e r i a l s i s p o s s i b l e . The above r e a s o n s a r e a p r e r e q u i s i t e f o r a wider a p p l i c a t i o n of f a i l u r e e n v e l o p e s t o t h e e v a l u a t i o n of t h e mechanical behaviour of c o a t i n g f i l m s .

Thanks a r e due t o t h e B a v a r i a n S t a t e M i n i s t r y f o r I n d u s t r y and T r a n s p o r t which gave f i n a n c i a l s u p p o r t t o t h i s work.

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( 2 ) 1;. 13ucchc und 1.C. Flalprn, J . Appl. Phys. 35, 36 (1964)

( 3 ) A.C. Elm, Off. Dig. 25, 751 (1953)

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f l . Frckcnschcr, Off. Dig. 3 3 , 331 (1961) ( 9 ) M. Botro und D P a ~ u n r , J Paint Technol. 40, 123 (1968) (10) W lutrkc untl IJ Zorll, X . Fatipcc-Kongress, Montreux

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appl. I'hys. T T , 3142 (1963) ( 1 6 ) K L. lrssler und L.II. Prrncen. J . I'aint Technol. 40, 105

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(18) P . Wiiruwg, Disscrtation TH Stuttgart, 1964

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( 2 0 ) R . Ecker, Kautschuk u. Gurnrni-Kunststoffe 21, 304 (1968)

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log,, E~ 1%) Water swollen Fig. 3

1% 1273/1,)0, I n'/m'l I Water s w o l l e n Srcl Fig. 4 Linseed a l k y d r e s i n l z i n c o x i d e Water Dry s w o l l e n

"&*

Jd

,

4

'

r PVC Fig. 5 Urea r e s i n l i r o n o x i d e

Fig. 6