Deformation and damage processes in wood

DEFORMATION AND DAMAGE

PROCESSES IN WOOD

T.A.C.M. VAN DER PUT

TR diss

1740

DEFORMATION AND DAMAGE

PROCESSES IN WOOD

PROEFSCHRIFT ter verkrijging van de graad van

doctor aan de Technische Universiteit Delft, op gezag

van de Rector Magnificus, prof.drs. P.A. Schenck,

in het openbaar te verdedigen ten overstaan van een

commissie aangewezen door het College van Dekanen

op donderdag 15 juni 1989 te 16.00 uur door

THOMAS ADRIAAN CORNELIS MARIA VAN DER PUT

geboren te Bandung, civiel ingenieur.

Delft University Press 1989

TR diss

1740

CIP-GEGEVENS KONINKLIJKE BIBLIOTHEEK, DEN HAAG

ISBN 90-6275-548-8

NUGI 841

Copyright (C) 1989 by Section Steel and Timber Structures.

All rights reserved.

No part of this book may be reproduced in any form by print,

photoprint, microfilm or any other means without written

permission from the publisher:

PRE FACE

This work was p a r t of an i n t e r n a t i o n a l rheology program, s p o n s o r e d by the EC, and done by the Timber group of the Faculty of Civil Engineering of the Delft University of Technology.

One of the objectives of the Dutch projects was t o develop a g e n e r a l c r e e p and d a m a g e model b a s e d on d e f o r m a t i o n kinetics. The derivation of this g e n e r a l theory, t o g e t h e r with the m a t h e m a t i c a l verification t h a t this t h e o r y may explain the phenomonological laws of the time d e p e n d e n t behaviour of wood, is the subject of this t h e s i s .

The r e s u l t s of this work were published earlier in r e p o r t s , magazines and proceedings, often in a different form and a r e here extended and b r o u g h t t o g e t h e r into one c o h e r e n t a c c o u n t

P r e f a c e

1. Introduction 1

2 . S t r u c t u r e and mechanical p r o p e r t i e s of wood

2.1 S t r u c t u r e of softwoods 5 2.2 Rheology of wood

2.2.1 Phenomenologic a p p r o a c h 8 2 . 2 . 2 Viscoelastic behaviour of s t r u c t u r a l e l e m e n t s in

c o m p a r i s o n with o t h e r polymers 1 1 2.3 S t r e n g t h and time d e p e n d e n t behaviour

2.3.1 F a c t o r s affecting the s t r e n g t h 13 2 . 3 . 2 Mode of f r a c t u r e ' 16

2 . 3 . 3 Failure of the u l t r a s t r u c t u r e 17

2.4 Conclusions 21 2.5 Re fe r e n e e s 2 3

3. Discussion of t h e b a s i c principles of the t h e o r y of molecular deformation kinetics.

3.1 Introduction 2 5 3.2 Theory of r e a c t i o n r a t e s for plastic deformation in solids 2 5 3.3 Reaction o r d e r of deformation and f r a c t u r e p r o c e s s e s 28

3.4 T h e r m o d y n a m i c s 29 3.5 P a r a m e t e r s of the flow units 33

3.6 R e f e r e n c e s 34

4. Derivation of a c r e e p and damage model b a s e d on t h e theory of deformation kinetics

4.1 Introduction 3 5

4.2 Basic r e a c t i o n r a t e equations 3 5 4.3 Derivation of a g e n e r a l c r e e p - and d a m a g e - m o d e l by s e r i e s

approximation 37 4.4 Basic equations for f r a c t u r e 4 3

4.5 F r a c t u r e a t c o n s t a n t loading r a t e and for c r e e p loading 48

4.7 References 5 5

5.Solution and discussion of the derived m o d e l - e q u a t i o n s for different loading p a t h e s . 5.1 Introduction 5 7 5.2 C o n s t a n t s t r a i n r a t e t e s t 58 5.3 C o n s t a n t loading r a t e t e s t 62 5.4 C r e e p and c r e e p recovery 65 5.5 S t r e s s relaxation 74 5.6 Conclusions 81 5.7 References 83 ó . O t h e r a s p e c t s of the theory 6.1 Introduction 85 6.2 M a t h e m a t i c a l e x p l a n a t i o n of t h e A n d r a d e c r e e p e q u a t i o n o r of t h e p o w e r m o d e l f o r c r e e p 85 6.3 Derivation of the WLF-equation for the t i m e - t e m p e r a t u r e

e q u i v a l e n c e a b a v e g l a s s - r u b b e r transition 88

6.4 Relaxation and r e t a r d a t i o n s p e c t r a 94 6.5 S p e c t r u m of energy loss a t forced vibrations and f a t i g u e

b e h a v i o u r 96

6.6 R e f e r e n c e s 100

7. Explanation of the of the mechano - sorptive e f f e c t

7.1 Small c h a n g e s of moisture c o n t e n t a t low s t r e s s e s 101 7.2 Influence of high s t r e s s e s and m o i s t u r e c h a n g e s 106

7.3 Simplification of the model 109 7.4 References 1 1 6

8. E x p e r i m e n t a l r e s e a r c h

8.1 Scope of the experimental program 117

8.2 T e s t program 118 8.3 Results of the p a r a m e t e r estimation 123

8.3.1 P a r a m e t e r s for s h e a r 125 8.3.2 P a r a m e t e r s for tension in tangential direction 126

8.3.3 P a r a m e t e r s for c o m p r e s s i o n in radial direction 127 8.3.4 P a r a m e t e r s for c o m p r e s s i o n in grain direction 129 8.3.5 P a r a m e t e r s for tension in grain direction 130

9 .Conclusions 9.1 General conclusions 135 9.2 Results of the e x p e r i m e n t a l r e s e a r c h 137 S u m m a r y 139 S a m e n v a t t i n g 145 Notations 153

1 INTRODUCTION

As for o t h e r m a t e r i a l s , the time dependent behaviour of wood is non-line-ar and h a s to be d e s c r i b e d by the theory of deformation k i n e t i c s . The basic c o n c e p t of this theory is to r e g a r d plastic flow a s a m a t t e r of molecular bond breaking and bond reformation, w h a t is the s a m e as t o s t a t e t h a t flow is the r e s u l t of a chemical reaction like isomerization. Until now, the theory was mainly applied phenomenologicaly a n d in this work this is e x t e n d e d to a general theory t h a t may predict the time d e ­ pendent behaviour of materials and may explain the phenomenological laws in this field. Further, possible simplifications a r e derived, in o r d e r t o find the main determining molecular p r o c e s s e s .

The mathematical derivation of this general rheological model is solely b a s e d on the reaction equations of the bondbreaking and b o n d r e f o r m a t i o n p r o c e s s e s a t the deformation s i t e s (i.e. s p a c e s w h e r e the molecules may move into) due to the local s t r e s s e s in the elastic material a r o u n d t h e s e s i t e s . The model d o e s n ' t contain o t h e r suppositions and will show the c o n s e q u e n c e s of the s t a t e d s t a r t i n g point.

In the originai theory, the plastic s t r a i n r a t e was arbitrarily t a k e n to be proportinal to the r a t e of change of the flow unit c o n c e n t r a t i o n and the form of the p a r a m e t e r s in the r a t e equation t h a t d e t e r m i n e for i n s t a n c e the hardening and the delay time, w e r e also a r b i t r a r y phenomelogical e x -p r e s s i o n s of the s t r a i n . This is avoided in this derivation. By e x -p r e s s i n g the concentration and work t e r m s of the r a t e equation in the number and dimensions of the flow units, the e x p r e s s i o n s for the s t r a i n r a t e , f r a c t u r e , hardening and delay time are directly derived without any a s s u m p t i o n s . The derivation s h o w s t h a t time dependent behaviour is a m a t t e r of very small s t r u c t u r a l c h a n g e s and the p a r a m e t e r s of the model a r e c o n s t a n t a n d / o r linearly d e p e n d e n t on the variables according to the first, or f i r s t two, t e r m s of the polynomial expansion of t h e s e p a r a m e t e r s .

Because of t h e s e small c h a n g e s , the s t r u c t u r e of the dislocations and the o r d e r of the r e a c t i o n is not determinable. S o the r e a c t i o n can be r e g a r d e d to be of the first o r d e r or quasi f i r s t o r d e r and a l s o t h e a c t i v a -tion enthalpy, entropy and external work can be r e g a r d e d a s c o n s t a n t a n d / o r linearly d e p e n d e n t on t e m p e r a t u r e , moisture c o n t e n t and s t r e s s . The activation e n e r g y and volume will provide however information about the type of bonds t h a t is involved and the dimensions of the flow units. To obtain simplifications, a general c r e e p - and damage model for small

s t r u c t u r a l c h a n g e s is derived by s e r i e s expansion of the potential energy curve, leading to a proof of the generalized flow theory, and showing t h a t the h y p o t h e s e s , on wich this theory was based, are c o n s e q u e n c e s of the s e r i e s expansion. This model is a l s o extended for a description of larger s t r u c t u r a l c h a n g e s , giving an explanation of the existing damage models and phenomenological laws of f r a c t u r e .

The theory is able t o explain the different power models (of the s t r e s s and of the time), giving the physical meaning of the exponents and con­ s t a n t s . This applies for instance for the explanation of the Forintek mo­ del of the s t r e n g t h and the Andrade and Clouser c r e e p - e q u a t i o n s . An explanation of the WLF-equation (Williams-Landel—Ferry is WLF) for the t i m e - t e m p e r a t u r e equivalence above g l a s s - r u b b e r transition is also derived, showing t h a t the change of the c o n c e n t r a t i o n of mobile s e g m e n t s , and not n e c e s s a r i l y the change of the free volume c o n c e n t r a t i o n , is the c a u s e of the transition. The theory is extended for c r o s s - l i n k e d polymers a t t r a n s i e n t c r e e p for the component t h a t performs the transition. It fol-lows from the theory that for the special c a s e of a c o n s t a n t c o n c e n t r a ­ tion of flow units, the t e m p e r a t u r e dependence is according to the A r r h e -nius equation. For higher values of the activation enthalpy, when not the c h a n g e of entropy is dominating, t h e theory p r e d i c t s a shift factor b e t w e e n the A r r h e n i u s - and WLF-equation. The WLF- equation is further extended for the influence of the time s c a l e of the p r o c e s s .

It is further shown t h a t a single p r o c e s s may explain the m e a s u r e d , broad, nearly flat mechanical relaxation s p e c t r a of g l a s s e s and crystalline poly­ m e r s and an outline of the relaxation s p e c t r u m for wood can be explained by two p r o c e s s e s in s t e a d of the a s s u m e d infinite number of linear pro-c e s s e s t h a t is r e g a r d e d to be the basis of the relaxation s p e pro-c t r u m . Also the l o s s - s p e c t r u m by forced vibrations and the fatigue behaviour can be explained by one p r o c e s s .

The solutions of the model equations are given for t r a n s i e n t p r o c e s s e s a t d i f f e r e n t loading h i s t o r i e s and it is shown t h a t the model can explain the phenomenological laws as for i n s t a n c e the linear dependence of the stiff-n e s s ostiff-n the logarithmic value of t h e straistiff-n r a t e istiff-n a c o stiff-n s t a stiff-n t s t r a i stiff-n r a t e t e s t ; the logarithmic law for c r e e p and relaxation and the n e c e s s a r y b r e a k ­ down of the law for longer times; the shift factor along the log-time axis due t o s t r e s s and t e m p e r a t u r e and the influence on this factor of a t r a n ­ sition to a second mechanism.

3

effect is given and the behaviour a t moisture cycling is explained. The d e r i -vation t h r o w s a new light on the mechanism, being a s e p a r a t e d s o r p t i o n effect and not an interaction of c r e e p and moisture change or an i n t e r a c -tion of loading on the overall shrinkage.

The aim of the experimental r e s e a r c h was to verify the model and t o g e t a first e s t i m a t e of the o r d e r of the p a r a m e t e r s and the d e p e n d e n c e on t e m p e r a t u r e , moisture c o n t e n t and loading direction. Because data a r e available for p e r f e c t c o n s t a n t humidity conditions, it was decided to use oscillating relative air humidity conditions a s may o c c u r in p r a c t i s e . Quick and low relative humidity cycling may be e x p e c t e d t o behave like c o n s t a n t moisture c o n t e n t conditions. However the behaviour of the wood polymers is very sensitive for t r a c e s of diluent, the previous history and m o i s t u r e c h a n g e s and this may c a u s e a different behaviour in c o m p a r i s o n to p e r ­ fect c o n s t a n t moisture conditions.

2 STRUCTURE AND MECHANICAL PROPERTIES OF WOOD

2.1 S t r u c t u r e of softwoods

Timber can be defined as a low-density, cellular (tubular), polymeric fibre composite lil, C2L The m a c r o s t r u c t u r e is cellular and due t o the b r a n ­ ches of the t r e e , t h e r e are knots a s main d i s t u r b a n c e s of the s t r u c t u r e . On microscopic level, most cells a r e aligned in the vertical axis and only S to 10% a r e aligned in the radial planes (rays). T h e s e r a y s a r e the main disturbances of the alignment of the vertical cells. In softwood two types of cells a r e available. The g r e a t e r number a r e called t r a c h e i d s and have a length of 2 to 4 mm with an a s p e c t r a t i o of 100:1. T h e s e cells have a supporting and conducting role. Most cells of the s e c o n d type a r e in the rays and are block-like cells of 200 x 30 um. These a r e called p a r e n c h y m a and have a function for food s t o r a g e . The t r a c h e i d s a r e thin walled (2 um) in the early p a r t of the s e a s o n a l growth (earlywood) and a r e thick walled (up t o 10 (xm in latewood) in the l a t e r p a r t of the s e a s o n .

The cells a r e i n t e r c o n n e c t e d by pits (holes in the cell wall) to p e r m i t food

1 c r o s s - s e c t i o n 2 radial plane 3 t a n g e n t i a l plane 4 g r o w t h ring 5 earlywood 6 latewood 7 rays 7a ray with r e s i n canal 8 r e s i n c a n a l s 9 pits 10 pits of the r a y s fig. 2.1.1 S t r u c t u r e of softwood

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p a s s a g e and t h e s e holes a r e the main d i s t u r b a n c e s of the s t r u c t u r e of the cell walls.

Chemical analysis shows four c o n s t i t u e n s : cellulose, hemicellulose, lignin and e x t r a c t i v e s . The cellulose (C H O ) is formed of b e t a - g l u c o s e : (C,H O ) with removal of H O (condensation reaction).

6 12 6 2

Cellulose chains may crystallise in many ways, but one form, cellulose I, is c h a r a c t e r i s t i c of natural cellulosic materials. Adjacent chains in the c r y s t a l lie in opposite directions. The unit cell (1.03 nm) of crystalline repetition is i n t e r p r e t e d as monoclinic. The molecule is not folded and t h e r e is no evidence of primary bonding Iaterally between the chains. The laterally bonding b e t w e e n the chains is a complex mixture of fairly s t r o n g hydrogen bonds and weak van der Waals f o r c e s .

The length of the cellulosic molecules is about 5 0 0 0 nm (0.005 mm). The crystalline regions a r e only 60 nm (length) by S nm (width) and 3 nm t h i c k n e s s . S o the cellulosic molecule will p a s s through several of t h e s e

regions of high crystallinity with intermediate noncrystalline or l o w c r y s t a l -line z o n e s . The collective unit passing the c r y s t a l l i t e s is t e r m e d microfi-bril, having- an infinite length. It is clothed with chains of s u g a r units (other than glucose) wich lie parallel, but a r e not regularly s p a c e d making the microfibril to about 10 nm in breadth.

Hemicellulose and lignin a r e r e g a r d e d as c e m e n t i n g m a t e r i a l s . Hemicellulo-se is a c a r b o h y d r a t e like celluloHemicellulo-se, however the d e g r e e of c r y s t a l l i s a t i o n and polymerisation (less than 150 units) a r e low. Lignin is a complex a r o ­ matic compound c o m p o s e d of phenyl groups and is noncrystalline; 25% is in the middle lamella (the intercellular layer c o m p o s e d of lignin and pectin) and 75% is within the cell wall.

So the cell wall is a fibre composite with s l e n d e r microfibrils a s fibres in a cementing matrix of reiatively unoriented (amorphous) s h o r t - c h a i n e d or b r a n c h e d polymers (lignin and hemicellulose) containing a l s o tiny voids and second o r d e r pore s p a c e s .

The cell wall is also a laminated composite b e c a u s e of the layered s t r u c -ture of the wall. To be distinguished a r e in s u c c e s s i o n : the middle lamel­ la, a ligninpectin complex without microfibrils; the primary wall with l o o s e -ly packed random microfibrils and no lamellation and the s e c o n d a r y wall with closely packed parallel layers. The o u t e r layer or S layer of the s e

-Inner layer (S )

Primary wa

Middle layer (S ) Outer layer (S )

Middle lamella '

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condary wall is thin (4 to 6 lamellae) with 2 a l t e r n a t i n g spiral microfibrils with a pitch t o the longitudinal axis of about 60 d e g r e e . The middle layer or S layer is thick (30 to 150 lamellae) with fibrils in a right-hand spiral with a pitch of a b o u t 20 d e g r e e and the inner layer or S layer is very thin and is simular a s S with a pitch of about 80 deg., is however looser and c o n t a i n s lignin in a high proportion. Because t h e r e a r e 2 cell walls b e t w e e n the a d j a c e n t t r a c h e i d s , a microfibrillar angle deviation from the longitudinal axis in a layer is c o m p e n s a t e d by the opposite angle in the equivalent layer of the second cell wall causing the orthotropic behaviour and the s t i f f n e s s and s t r e n g t h a t an angle to the grain follow the com-mon t e n s o r t r a n s f o r m a t i o n laws. S o the behaviour of a tracheid alone is far from o r t h o t r o p i c and the r e s u l t s of t e s t s on s e p a r a t e d t r a c h e i d s as done for the p a p e r industry c a n n o t be used to p r e d i c t the behaviour of wood.

2.2 Rheology of wood

2.2.1 Phenomenological approach

Because of the complex s t r u c t u r e of wood, complete molecular models a r e not yet developed and the r e s e a r c h is b a s e d on phenomenological s t u ­ dies. A s u m m a r y of the r e s u l t s [ 3 ] will be given here.

Like o t h e r m a t e r i a l s , wood can be r e g a r d e d a s linear elastic when s t r e s s , moisture c o n t e n t and t e m p e r a t u r e are sufficiently low. At higher levels of t h e s e variables the behaviour is linear viscoelastic and at still higher le­ vels, the behaviour is nonlinear. This d e s c r i p t i o n applies for not too long t e s t i n g times. For longer times the nonlinear behaviour is evident and can be explained by the kinetic theory. However a linear approach is possible by using s p e c t r a of relaxation times. A t e s t of linearity is often done by applying a single s t e p - f u n c t i o n in s t r e s s on a specimen. Then linearity is a s s u m e d when the c r e e p compliance is independent of the applied s t r e s s . B e t t e r is to do superposition t e s t s . However b e c a u s e of the small a m o u n t of c r e e p during s h o r t times, a l s o nonlinear models may show a quasi linear behaviour. The c r e e p compliance is s e p a r a t e d into instantaneous, delayed elastic, and flow c o m p o n e n t s . The i n s t a n t a n e o u s or glassy com­ pliance is always independent of the s t r e s s . The delayed elastic and flow compliances a r e approximately independent of s t r e s s below certain s t r e s s

limits depending on moisture c o n t e n t and t e m p e r a t u r e . For tension p a r a l ­ lel to the grain e.g. limits of 35 to 80 % a r e given depending on the s p e ­ cies. Mostly the limit is taken b e t w e e n 40 t o 50 %. Of c o u r s e t h e s e limits depend on the time of testing. These limits a r e a l s o r e g a r d e d a s the

, a c c e l e r a t e d

s t a t i o n a r y "' . . ,. . __±_^---r-.rjr.r d e c e l a r a t e d

c r e e p recovery

time fig. 2.2 C r e e p and recovery

boundaries below wich t h e r e is only d e c e l e r a t e d c r e e p and above wich t h e r e is, a f t e r d e c e l e r a t e d c r e e p , s t a t i o n a r y c r e e p a n d a c c e l e r a t e d c r e e p (see fig. 2 . 2 ) . Because wood is a c r o s s - l i n k e d polymer, s t a t i o n a r y c r e e p , or c r e e p a t a c o n s t a n t s t r a i n r a t e , cannot occur. A c c e l e r a t e d c r e e p is due to a s t r u c t u r a l change p r o c e s s , a s will be shown l a t e r . Nonlinear behaviour is partly a t t r i b u t e d t o s t r u c t u r a l c h a n g e s . Another p a r t of the " i r r e c o v e r a b l e " flow can be r e c o v e r e d by an i n c r e a s e of m o i s t u r e and t e m p e r a t u r e . This indicates nonlinear behaviour providing a very stiff "dashpot" for the low internal s t r e s s e s a f t e r unloading, making r e c o v e r y very slow and t h u s showing a quasi p e r m a n e n t s t r a i n .

Repeated s t r e s s i n g may lead to stiffening shown by a d e c r e a s e in h y s t e r e -sis and an i n c r e a s e in elastic moduli (crystalization). At sufficiënt high s t r e s s , t h e r e may also be an i n c r e a s e of the g l a s s y compliance. This s t r e s s - i n d u c e d t r a n s i t i o n is a l s o found in wet cellulose films, indicating probably the p e n e t r a t i o n of w a t e r in the (normally inaccessible) more high-ly o r d e r e d regions. For green wood a t a c o n s t a n t t e m p e r a t u r e and a t a given time and s t r e s s , the deflection i n c r e a s e s exponentially with i n c r e a s -ing t e m p e r a t u r e (between 5 and 70 °C) a s can be explained by the kinetic theory a s a relative i n c r e a s e of the s t r e s s level and with t h a t a shift of a t r a n s i t i o n t o a second (irrecoverable) c r e e p mechanism to lower t i m e s . Between transition points, the c r e e p compliance i n c r e a s e s linearly with t e m p e r a t u r e . At high t e m p e r a t u r e s (100 to 180 °C) a l s o for dry wood the exponential i n c r e a s e is m e a s u r e d due t o transition t o a n o t h e r mechanism (transition point 140 °C). The transition points depend on t h e m o i s t u r e

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c o n t e n t , a s will be d i s c u s s e d later, and a r e close to the g l a s s - t r a n s i t i o n points of hemicellulose and lignin. For green wood, the first transition is a t about 50 to 60 °C, causing an i n c r e a s e in the c r e e p r a t e . For dry wood this t r a n s i t i o n t e m p e r a t u r e is higher, above a b o u t 70 to 80 °C. In an investigation it was r e p o r t e d t h a t in the range of 15 t o 60 °C, the relaxation modulus d e c r e a s e d , but the r a t e of relaxation a p p e a r e d to be hardly affected by the t e m p e r a t u r e (lower s t r e s s a t the s a m e s t r a i n and c o n s t a n t ep if u = 0, see l a t e r ) . At high initial s t r a i n s t h e r e are a l s o tem­ p e r a t u r e r a n g e s where the c r e e p r a t e s differ not much. For wet wood, the c r e e p compliance may i n c r e a s e more than linear with t e m p e r a t u r e b e c a u s e of the earlier s t a r t of the second mechanism.

Simple superposition of time and moisture c o n t e n t is not valid b e c a u s e of o t h e r s t r u c t u r a l c h a n g e s (shape and volume) a s s o c i a t e d with the c h a n ­ ge of m o i s t u r e c o n t e n t .

Absorption of w a t e r by wood c a u s e s swelling up to a moisture c o n t e n t of about 28%. The swelling is roughly proportional t o the water uptake. Although the w a t e r e n t e r s only in the amorphous z o n e s , the s t r e n g t h and s t i f f n e s s a r e reduced. The tangential shrinkage e x c e e d s the radial shrin-kage partly by the r e s t r a i n t of the r a y s . The swelling and shrinshrin-kage in longitudinal direction a r e very small compared with the other two d i r e c -tions. It is the s m a l l e s t for s t e e p micro-fibrillar helixes in the S layer a s can be e x p e c t e d in the direction of the crystalline micro-fibrills. S w e l ­ ling of the s e c o n d a r y wall is much g r e a t e r than swelling of the middle lamella. S o the l a t t e r probably r e s t r a i n s the shrinkage of the wood c a u s ­ ing high internal s t r e s s e s . The planes, wich a r e the r i c h e s t in hydroxyl g r o u p s , lie parallel to the microfibril s u r f a c e and p a r t of the n o n c r y s t a l -line m a t e r i a l is o r i e n t e d in parallel with the cellulose and this m a t e r i a l is a c c e s s i b l e to w a t e r . S o the planes b e t w e e n the lamellae of the cell wall a r e the places for bond breaking p r o c e s s e s due to w a t e r movement. In f a c t the cell wall a c t s as one layer for dry wood and the S layer is splitted in h u n d r e d s of lamellae in the s a t u r a t e d s t a g e . It is to be expec­ t e d t h a t the high r e s t r a i n t s for swelling and shrinkage will cause "flow" in the gel-like matrix. This flow is d i r e c t e d if a specimen is maintained under s t r e s s during a change in m o i s t u r e c o n t e n t . The moisture movement through the wood involves breaking of s t r e s s e d hydrogen bonds and r e f o r -mation of t h e s e bonds in an u n s t r e s s e d position causing the large c r e e p deformation a t d e s o r p t i o n when one of two adjacent layers shrinks, while the other swells. This mechanism d e t e r m i n e s the behaviour a t cycling

mois-ture c o n t e n t conditions. There is an i n c r e a s e of c r e e p during desorption and recovery during the first, or for tension a l s o possible in the second absorption period, depending on the initial m o i s t u r e c o n t e n t . At large s t r e s s e s and small moisture c o n t e n t c h a n g e s t h e r e is no r e c o v e r y but a r e d u c t i o n of the c r e e p r a t e during adsorption. The deformation is usual-ly devided in t h r e e components: overall shrinkage by m o i s t u r e change; t i m e - d e p e n d e n t s t r a i n by the s t r e s s history and an i n t e r a c t i o n effect between t h e s e two. The s a m e can be said for t e m p e r a t u r e changes. There is f u r t h e r an interaction influence of t e m p e r a t u r e and m o i s t u r e c o n t e n t if one of t h e s e cycles. As s t a t e d above t h e s e i n t e r a c t i o n e f f e c t s a r e not real i n t e r a c t i o n s but can be explained a s c o n s e q u e n c e s of the differential swelling and shrinkage of adjacent layers. This will be shown l a t e r . The sorption influence is for a single change linear with the amount of mois­ ture change, independent on the moisture c o n t e n t , t e m p e r a t u r e , r a t e of sorption and previous c r e e p - h i s t o r y a t c o n s t a n t t e m p e r a t u r e and moistu­ re content, indicating a flow p r o c e s s . The r a t e of t h e deformation is d e -pendent on t h e r a t e of change of moisture c o n t e n t . It is e x p e c t e d t h a t the moisture g r a d i ë n t is not the c a u s e of the i n c r e a s e d deformation (there is no influence of the size of the specimen). A s t e p w i s e i n c r e a s e in mois­ ture (5% in 7 days) under loading gives a maximal deflection a t the first moisture i n c r e a s e and this is the s m a l l e s t a t t h e l a s t m o i s t u r e jump (being above the s a t u r a t i o n point). The sum of t h e s e deformations is probably equal t o an equal one s t e p moisture i n c r e a s e . Above s a t u r a t i o n t h e r e is a little influence. The deformation a t changing m o i s t u r e conditions is pro­ bably independent on the loading, a t l e a s t a t not too low and not too high levels. There is no d e c r e a s e in the modulus of elasticity.

2.2.2 Viscoelastic behaviour of the s t r u c t u r a l e l e m e n t s in c o m p a r i s o n with o t h e r polymers

The cellulose molecules a r e very long and have very s h o r t side chains and are able to be packed close t o g e t h e r fprming crystalline a r e a s . Hemicel-lulosis has different forms between the linear s t r u c t u r e and the very s t r o n g b r a n c h e d s t r u c t u r e . The linear form with not r e g u l a r s p a c e d s h o r t side chains and many polar hydroxyl groups has, 'as cellulosis, good fibre forming p r o p e r t i e s and the b r a n c h e d type has good e n t a n g l e m e n t and filler p r o p e r t i e s . Lignin is c r o s s - l i n k e d in all directions and is able to form

12

s t r o n g bonds with the celluloses and has a l s o hydroxyl groups.

The cellulose is highly crystalline (~ 70 %) and the crystallinity d o e s n ' t change much on straining or drying. Because of the physicaly side bonds (hydrogen- and v a n d e r w a a l s - bonds) it is to be e x p e c t e d t h a t the binding e n e r g y will be t i m e - and t e m p e r a t u r e dependent. However the deformation of a c r y s t a l l i t e is energy elastic ( r e p r e s e n t i n g d i s p l a c e m e n t s from equili-brium positions) and time d e p e n d e n t behaviour is only noticeble in t h e a m o r p h o u s r e g i o n s . The modulus of elasticity is 1.1 10 N / m m in chain direction and a b o u t 104 N / m m perpendicular to this direction. The a m o r ­ phous r e g i o n s of the cellulose a r e highly oriented and will have many c r o s s - l i n k s (hydrogen bonds). Because t h e r e is no "coiling" s t r u c t u r e , an uncoiling p r o c e s s c a n n o t be e x p e c t e d to occur.

The b r a n c h e d hemicellulose polymers have the function as filler of the lig— nin and b e c a u s e the s t r o n g bonds with the lignin it i n c r e a s e s the c r o s s -linking, a c t i n g a s copolymer. The linear hemicellulose a c t s by hydrogen bonds a s flexible bridge between t h e microfibrils, making movements of the fibrils possible and avoiding s t r e s s peaks between fibrils on loading. Lignin is a random amorph c r o s s - l i n k e d polymer t h a t is able to form s t r o n g bonds with the polysaccharides. Real rubbery behaviour (uncoiling) is not possible.

S o the polymers in wood t h a t d e t e r m i n e the time dependent behaviour c o n -tain densely c r o s s - l i n k e d filled a m o r p h o u s polymers a s well a s highly crystalline and o r i e n t e d polymers. Although s u c h polymers don't p o s s e s s a zone of rubberlike behaviour, t h e r e is a t r a n s i t i o n possible t o a more flexible s t a t e . Crystalline polymers with the amorphous region in the flex­ ible s t a t e (above the transition t e m p e r a t u r e of these regions) show a quick s t r e s s relaxation loosing 25 t o 50 % of the s t r e s s in a few minutes. This is foliowed by a slow p r o c e s s and the remaining s t r e s s a f t e r 17 d e ­ c a d e s (the age of the universe) is above S to 10 %, as follows from t h e t i m e - t e m p e r a t u r e equivalence. So this s t r e s s reduction of about one o r d e r is much l e s s d r a s t i c than t h a t for the rubbery transition where t h e s t r e s s r e d u c e s 5 t o 6 o r d e r s . This quick mechanism is not m e a s u r e d for wood, even not a t high t e m p e r a t u r e s , s u g g e s t i n g a very high c r o s s - l i n k i n g . S o t h e slow p r o c e s s is dominating in wood ( a t low s t r e s s e s ) and has t h e s a m e p r o p e r t i e s a s for other crystalline and c r o s s - l i n k e d polymers. This m e a n s t h a t t h e c r e e p is recoverable; t h a t i n c r e a s e of s t r e s s s h o r t e n s the r e t a r d a t i o n time (crystalline materials) and t h a t the c r e e p r a t e on loga-rithmic time s c a l e is not proportional to the s t r e s s but i n c r e a s e s with a

power of the s t r e s s a t higher s t r e s s e s with the c o n s e q u e n c e t h a t the c r e e p and r e c o v e r y functions have different s h a p e s . The t e m p e r a t u r e d e -pendence of the viscoelastic p r o p e r t i e s follows the WLF- or t h e Arrhenius equation. The Arrhenius form applies for cellulose. Because the c r y s t a l -linity d o e s n ' t change much, t h e r e a r e no vertical shifts (due t o change of the p s e u d o equilibrium modulus) of the c r e e p lines along t h e log- time-axis. The c r e e p can be d e s c r i b e d by the Andrade-equation or is a .straight line on a log-time-plot. This mechanism is a t t r i b u t e d to the mobility of the s h o r t s t r a n d s in the amorphous regions, probably due to c o - o p e r a t i v e motions of g r o u p s of s t r a n d s coupled through linkage points. The thermal and mechanical history is very critical for the behaviour a s for g l a s s e s and also t r a c e s of diluent have an influence.

At room t e m p e r a t u r e the amorphous p a r t s in wood a r e probably in the glassy s t a t e , and only the s o called p - m e c h a n i s m a p p e a r s ( t h e « - m e c h a ­ nism r e p r e s e n t s the g l a s s - l e a t h e r transition due to mobility of the back-bones of the polymers). The (3- or s e c o n d a r y mechanism is due to local r e a d j u s t m e n t of side groups in glassy amorphous polymers or in t h e a m o r ­ phous s t r a n d s of crystalline polymers. These side g r o u p s can b e chemical-ly a t t a c h e d groups or hydrogen bonds wich a c t as side group on the pochemical-ly- poly-mer chain and even only polar w a t e r molecules. In this l a s t c a s e the p - m e c h a n i s m d i s a p p e a r s on removal of the w a t e r . Dielectric m e a s u r e m e n t s support this model b e c a u s e they r e f l e c t dipole orientation due to side group motions, showing the s a m e t e m p e r a t u r e dependence a s the visco­ elastic behaviour. This t e m p e r a t u r e dependence follows t h e Arrhenius equation and the activation energy lies b e t w e e n 20 and 30 k c a l / m o l e . The s t r e s s reduction in relaxation by the secondary m e c h a n i s m is smaller than by the a - m e c h a n i s m and will be smaller than a factor 0.S to 0.8, where 0.S is used as a rule of thumb for wood. The s a m e a s for the a - m e c h a n i s m the behaviour is nonlinear for high s t r e s s e s and t h e s e p r o ­ perties will be explained here by the kinetic model.

2.3 S t r e n g t h and time dependent behaviour 2.3.1 F a c t o r s affecting the s t r e n g t h

The influence on the s t r e n g t h of the native origin of the wood, d e t e r m i n e d by the c h a r a c t e r of the soil, the climate, density of t h e f o r e s t , e t c . is not

14

important, because the variability within one area is comparable with the

variability of the whole population.

The main features of the macro-structure that may determine the strength

are the density, moisture content, width of the growth rings and width of

the latewood part of those rings. Disturbances will also have an influence.

The main disturbances of the structure are the knots, deviations of the

grain angle, compression wood, resin channels, growth defects and checks.

Because timber is selected for structural use, larger disturbances by

cracks, resin heaps, growth faults, etc. are excluded and only minor dis­

turbances are allowed having a little influence on the strength.

Compression wood will cause twisting and splitting due to differential

shrinkage by seasoning and also serious grain angle deviations may cause

twisting. So by selection, this timber will not be used for structural

ap-plications and it appears that for gross wood the regression of the

strength is nearly totally determined by only the knot area, the density

and the moisture content (see e.g. the discussion in [4]).

Knots act similar like holes and the strength dependent on the KAR (knot

area ratio) can be fully explained by the stress field around a hole [SI.

An increase in moisture content in wood gives a reduction in strength by

the weakening of the interchain hydrogen bonds of the cellulosic

compo-nents in the amorphous regions. The moisture effects will be explained

later by the chemical reaction kinetics of this water binding. At a moisture

content of about 28% there is no further reduction of the strength and

also no further increase in swelling of the wood.

There is a very general correlation between strength and density even

when comparing different wood species. The amount of latewood is highly

correlated with the density. This is not so for the total ring width so the

density of earlywood varies in every ring. Because of the correlation of

the strength with the density, it can be expected that mainly the late­

wood part determines the strength. This can be true if there is early

plastic flow in the earlywood transmitting the s t r e s s e s to the latewood.

This also explains the higher magnitude of the tensile strength of the

individual fibres compared with gross wood. In gross wood early crack

formation occurs at imperfections between the layers due to s t r e s s

con-centrations. Because there is sufficiënt overlap of the adjacent fibres,

these cracks have to propagate through the clear wood layers for total

f r a c t u r e w h e r e the amount of latewood d e t e r m i n e s t h e s t r e n g t h .

M e a s u r e m e n t s in tension of w e t early wood and late wood single fibres, indicate a 1.1 to 3 times higher ultimate s t r e n g t h (at a b o u t the s a m e ul-timate s t r a i n ) and stiffness of the l a t e wood fibres (from the s a m e s p e ­ cies) C6L In [ 7 ] higher differences b e t w e e n earlywood and latewood were m e a s u r e d . Dry late wood was about 6 x s t r o n g e r than early wood, c l o s e r to the t h e o r e t i c a l e x p e c t a t i o n and w e t late wood was a b o u t 4 x s t r o n g e r , indicating m o r e influence of plasticity for w e t wood. It was a l s o found t h a t the ultimate s t r a i n for failure of latewood was higher than for early­ wood. P r e p a r a t i o n of single fibres t e s t s p e c i m e n s will always induce c r a c -ked s u r f a c e s with the possibility of c r a c k propagation, diminishing the s t r e n g t h differences b e t w e e n early and late wood. Probably this explains the differences of the m e a s u r e m e n t s of [63 and [71.

Elastic models of the mechanical behaviour of cell wall layers ( e . g . [ 8 ] ) indicate a much w o r s e r loading of springwood in c o m p a r i s o n with s u m m e r -wood. The maximum s t r e s s parallel to the microfibril is a b o u t 4 times higher and the s t r e s s perpendicular and the s h e a r s t r e s s is a b o u t 7 times higher in springwood than in summerwood. This i n d i c a t e s early plastic flow in the cell wall layers of the springwood with c o n s i d e r a b l e s t r e s s redistributions between the layer components b e c a u s e e l s e , the relatively high e x p e r i m e n t a l s t r e n g t h of this layer c a n n o t be explained.

The s u m m e r w o o d fiber has an almost ideal s t r e s s p a t t e r n in a c c o r d a n c e with the s t r e n g t h s of the different c o n s t i t u e n t s and c a n be e x p e c t e d t o behave e l a s t i c up to high s t r e s s e s making probably a d e s c r i p t i o n possible by an e l a s t i c model of the cell wall s t r e n g t h . S o w h a t e v e r the mode of failure is, the s t r e n g t h is close to the fiber s t r e n g t h .

An e l a s t i c model for the tensile s t r e n g t h of the cell wall, [9 3, indicates that f r a c t u r e first o c c u r s in the S layer by a s h e a r i n g m e c h a n i s m with a very high s h e a r s t r e s s a t failure, s u g g e s t i n g a s t r o n g bonding b e t w e e n lignin, hemicellulose and cellulose. This initial f r a c t u r e of the S layer follows al'so from the theory of maximum e n e r g y of d i s t o r s i o n .

The model further s h o w s opposite signs of the s h e a r s t r e s s e s in the S and S layers indicating also high s t r e s s e s in the i n t e r f a c e b e t w e e n the S and S l a y e r s . Microscopic studies have confirmed this interlayer f r a c ­ ture by the puiling out of the S and S layers out of t h e enclosing s h e e t of the S . - '

ï

As s e c o n d type of failure, helical b r e a k along the d i r e c t i o n of the S mi-crofibrils w a s observed leading to the ultimate r u p t u r e of this layer.

16

2 . 3 . 2 Mode of f r a c t u r e

The failure of wood is d e p e n d e n t on the type of s t r e s s . The cleavage b e -haviour of wood w a s studied by f r a c t u r e mechanics t e s t s on notched s a m ­ ples (e.g.CIO]). The s t r a i n - e n e r g y r e l e a s e r a t e depends on t e m p e r a t u r e and m o i s t u r e c o n t e n t and t h e r e is a dominating stability of c r a c k extension. The slow and s t a b l e c r a c k propagation was mainly within the cell wall of the t r a c h e i d s , e i t h e r b e t w e e n the primary and S walls, or b e t w e e n the middie lamella and the primary wall and was moving through t h e middie lamella to the adjacent cells. So the cell lumina w e r e not in g e n e r a l e x -posed. The stable c r a c k extension indicates the e x i s t a n c e of discontinuities with higher f r a c t u r e r e s i s t a n c e t h a t has to be overcome for rapid e x t e n ­ sion. In many c a s e s rapid f r a c t u r e was initiated a t a minor discontinuity in the o r i e n t a t i o n of the t r a c h e i d s such as the points w e r e the ray cells c r o s s the line of t r a c h e i d s . At higher t e m p e r a t u r e s and moisture c o n t e n t s , wood is l e s s brittle b e c a u s e t h e r e is more viscous dissipation and unstable c r a c k s a r e more infrequent and s h o r t in length.

Tension t e s t s along the grain on g r o s s wood show mostly failure within the fibre walls r a t h e r than b e t w e e n fibres (p.e. along the S microfibrils). The o v e r l a p of t h e adjacent cells w h e r e the force is t r a n s m i t t e d by s h e a r in the middie lamella is thus in g e n e r a l sufficiënt long. As mentioned before, failure is possible b e t w e e n the S and S layers.

Tensile failure perpendicular to the grain follows, as in cleavage t e s t s , the radial plane a s p r e f e r r e d plane. Both t r a n s w a l l failure, wich goes through t h e cells and the lumen, and intrawall failure, wich o c c u r s nor-mally within the zone of the primary wall and S , a r e possible. An in-c r e a s e in t e m p e r a t u r e (0 to 150 °C) r e s u l t e d in a high reduin-ction of the tensile s t r e n g t h perpendicular to the grain and a reduction of t r a n s - w a l l failures, indicating a reduction in bond s t r e n g t h b e t w e e n adjacent cells. In c o m p r e s s i o n parallel to the fibre direction, lines of buckling a p p e a r wich make an angle on the tangential face of the s p e c i m e n of a b o u t 60 d e g r e e t o t h e axial direction, which lie in the radial direction. This is a c o n s e q u e n c e of s h e a r failure b e t w e e n adjacent cells and the angle of 60 deg. in s t e a d of 4 5 deg. is due t o anisotropy. The failure t a k e s place within the cell wall and only occasionally does s e p a r a t i o n occur along the middie lamella mostly in the regions adjacent to the r a y s . The e x i s t e n c e of m i c r o s c o p i c c r a c k s is visible a s loosening of the bonding b e t w e e n mi­ crofibrils and the implication is t h a t the l a t e r a l cohesion b e t w e e n

micro-fibrils of the s e c o n d a r y wall is l e s s than b e t w e e n cells [11]. In [12] and [13] it is mentioned t h a t r u p t u r e o c c u r s at the cellulose-lignine interface (because of the preferentially staining with lignin s t a i n s ) .

Besides bond r u p t u r e (as follows from the i n c r e a s e d chemical reactivity with dilute acid) micellar distortion o c c u r s . T h e r e is a sequential develop-ment in types of dislocations (being p e r m a n e n t crinks of the fibrils) with increasing s t r e s s . T r u s t lines, being local thickenings of the cell wall by small fibril deformation, develope into slip planes which grow to bands of slip planes ( c r e a s e s ) leading to failure with considerable buckling and delamination of the cell walls. Slip planes develop a t about 25% loading level and the number i n c r e a s e s about linearly with s t r e s s level. At a level of about 50 to 65% c r e a s e s (bands of more than 2 slip lines) a r e formed increasing parabolically with s t r e s s level. At 80 to 100% g r o s s buckling of the cell walls occur containing about 40% of the t o t a l failure strain. The developement of t h e s e micro-failures is r e l a t e d t o time a t a given s t r e s s level. At relatively high moisture c o n t e n t or when d e f o r m a t i o n s develope slowly a t low s t r e s s levels, the micro deformations a r e widely distributed through the specimen. C r e e p t e s t s on wood show t h a t a f t e r long time, depending on the s t r e s s level, the deformation may i n c r e a s e at a higher r a t e indicating the development of c r e a s e s after long t i m e s . At low moisture c o n t e n t s and rapid s t r e s s i n g a t high s t r e s s levels the micro deformations a r e fewer in number and localized preferentially a t rays.

For high c o m p r e s s i o n perpendicular to the fibre direction, having a modu­ lus of elasticity of about o n e t e n t h of t h a t in longitudinal direction, s i d e -ways distortion of cells occur. The whole shape of the cell c h a n g e s . When failure does take place s e p a r a t i o n o c c u r s b e t w e e n the layers S and S of the s e c o n d a r y wall. The g r e a t e r s t r e n g t h in radial direction than in tangential direction is due to support from the rays.

2.3.3 Failure of the u l t r a s t r u c t u r e

Two c o m p o n e n t s of the fine or chemical s t r u c t u r e have a profound influen-ce on the s t r e n g t h and stiffness. The first c o n s i s t s of matrix material and especially of lignin and the second is the celulosic fibre m a t e r i a l . To investigate the failure mechanism of the cellulose chains, Ifju [ 7 ] r e -ported the effect of reducing the cellulose chain length by gamma

irradia-18

tion. The d e g r e e of polymerization of the cellulose was r e d u c e d from 5000 down to a b o u t 2 0 0 by s u c c e s s i v e higher d o s e s of radiation. If slippage of the chains is a c a u s e of failure it can be e x p e c t e d t h a t there will be a critical chain length where below failure is c a u s e d by slippage and where above failure is by primary bond breaking of the chain itself and is inde­ pendent on the chain length (or independent of the d e g r e e of polymeriza­ tion). Based on an a s s u m e d very high activation energy of breaking of the - C - O - C - linkage and a very low activation energy of breaking of the lateral hydrogen bonds it was calculated t h a t this critical length is r e a c h e d a t a d e g r e e of polymerization of about 70. The experiments however showed a d e c r e a s e of the s t r e n g t h at any reduction of the d e g r e e of pol}'merization. The conclusion t h a t slippage a t a d e g r e e of polizerization of 5000 is between micelles or fibrils through the "losely" amorphous cellulose (with very few side bonds) s e e m s not to be right, b e c a u s e this e x p e c t e d long r a n g e interaction would indicate an early o c c u r r e n c e of rubbery behaviour. The stiffness is however not proportional to the a b s o ­ lute t e m p e r a t u r e , as is n e c e s s a r y for rubbery behaviour, and a l s o the t r a n s i t i o n with t e m p e r a t u r e is different (Arrhenius equation) and the molecular models show only a very localized slip of a b o u t a cellobiosic unit.

S o the b a s i s of the c a l c u l a t e d critical chain length is more complicated t h a n a s s u m e d . This can be s e e n by the bonding model of cellulose of Giles a s e.g. d i s c u s s e d in c h a p t e r 4 of [ 8 ] where a special type of bonding is a s s u m e d in o r d e r to explain the high experimental stiffness of cellulose.

fig. 2.3 S c h e m e of a cellulose chain linked by hydrogen bonds

S t r a i g h t e n i n g of the cellulose chain c a u s e s lateral s t r e t c h i n g of the hy­ drogen bonds causing a four- to six- fold stiffness i n c r e a s e of the chain. S o if a chain is s t r e t c h e d , the hydrogen bonds may fail, reducing t h e stiff­ n e s s of the chain and s o the s t r e s s on the chain. If within the crystaline

region 4 s u c c e s s i v e hydrogen bonds have failed, the maximum r e d u c t i o n of the force is r e a c h e d . The activation energy for this will be l e s s than 4 x 6 = 24 k c a l / m o l , while for primary bond breaking the activation energy will be about 60 t o 80 k c a l / m o l . This d o e s n ' t mean that a type of dislocation propagation by cooperative bond breaking of 4 bonds is the n e c e s -sary failure mechanism. Also possible is e.g. the breaking of 1 hydrogen bond with a rotation of 4 to 5 bonds of the g l u c o s e - r i n g s (activation e n e r ­ gy l e s s than: 6 + 5x3.2 = 22 k c a l / m o l , t o releave a high chain force. Also for o t h e r polymers the flipping of the ring b e t w e e n two i s o m e r i c chair forms, is s u p p o s e d to be a deformation mechanism. T h e r e is s t e r i c possibUity for this movement [14] in cellulosis. This m e c h a n i s m , of b r e a k ­ ing of one hydrogen bond, is in a c c o r d a n c e with the m e a s u r e d first o r d e r r e a c t i o n and the m e a s u r e d activation energy and volume of the bond b r e a k ­ ing. F u r t h e r the in [ 7 ] m e a s u r e d d e p e n d e n c e of the s t r e n g t h on the loga-rithmic value of the degree of polymerization (being a m e a s u r e of the lo-garithmic value of the numbers of c u t s of the chain or the number of s o u r c e s of dislocations) is explained by the molecular model a s developed here. As shown l a t e r the f l o w - s t r e s s is:

ö = ll n( 2 l ) = il n(2fe_) = r ♦ lln(D)

where k is the the strain r a t e in a c o n s t a n t s t r a i n r a t e t e s t , A = A'p = p - v e x p ( - E / k T ) is proportional to the flow unit density p, and D is the d e g r e e of polymerization being inversely proportional to the number of c u t s , and thus inversely proportional to p. This leads to the e x p r e s s i o n :

2 2 2

By r e g r e s s i o n analysis, it can be shown t h a t l/<po is c o n s t a n t , indepen­ dent on t e m p e r a t u r e and moisture c o n t e n t and is about 0.11 for latewood and 0.17 for earlywood (coëfficiënt of variation: 0 . 4 5 ) . The values of this c o n s t a n t , 1/tpö , indicate a different failure mechanism by irradiation than o c c u r s normaly in wood (showing values of about 0 . 0 3 ) .

The c h a n g e in molecular a r r a n g e m e n t in the o r d e r e d , c r y s t a l i n e regions of the micelles by loading can be m e a s u r e d with the X-ray d i f f r a c t o m e t e r [ 1 5 ] . Truly e l a s t i c behaviour is due to chain straightening, orientation of c r y s t a l l i t e s or reorganisation of the l e s s o r d e r e d regions. C o n s t a n t loading t e s t s in tension show immediate orientation by loading and no i n c r e a s e in

20

crystallinity with time (within 24 hours). Because X-ray diffraction shows only o r d e r e d regions of molecules, t h e s e regions only show e l a s t i c beha-viour. The alignment by loading gives some i n c r e a s e of the length of the c r y s t a l l i t e s and s o of the d e g r e e of crystallinity. At unloading (indepen­ d e n t of the loading time) some alignment remains indicating also s o m e plas-ticity, increasing with increasing s t r e s s level (some of the new bonds r e c o ­ ver a t a not noticible low r a t e by the low internal s t r e s s after unloading). Time d e p e n d e n t molecular orientation activity in the amorphous regions can be observed by the infrared polarization technique. This was done in [16] for balsam fir t i s s u e s s t r a i n e d parallel t o the fiber axis. The chosen a d s o r p t i o n bands in C16] contained no crystalline band with almost immidi-a t e orientimmidi-ation r e p r e s e n t i n g the elimmidi-astic behimmidi-aviour. S o the r e c o r d e d bimmidi-ands gave the activity in the amorphous regions. In the c h o s e n bands for lignin, hemicellulose and cellulose, only quick time d e p e n d e n t p r o c e s s e s of orien­ tation w e r e r e c o r d e d . The main slow s t r e s s relaxation p r o c e s s was not given. The explanation, given in [16], of the s h o r t periodic p r o c e s s e s of loading and unloading as a r e s u l t of the ability of the lignin network to a c t a s an energy sink and to control the energy s e t up of the s t r e s s i n g is not probable. Obvious all components will be loaded on quick straining and b e c a u s e of the s h o r t e r r e t a r d a t i o n time of the lignin, the s t r e s s will be t r a n s m i t t e d from the lignin to the cellulose chains instead of in the r e v e r s e d direction. More probable is therefore t h a t a type of dynamic crystallization o c c u r s like in metals. Also in partly crystallized polymers this may occur if the d e g r e e of crystallinity i n c r e a s e s during the straining. S o a p r o c e s s of crystallization, flow and r e c r y s t a l l i z a t i o n may occur. A s t r o n g indication for this supposition is t h a t the time of the p r o c e s s is d e p e n d e n t on the kinetics of crystalization and not on the r a t e of straining or the viscoelastic p r o p e r t i e s and also that the s t r e s s of the relaxation t e s t d e c r e a s e s during the orientation b e c a u s e like in the mentioned poly­ m e r s the crystallization lowers the s t r e s s on the ends of the amorphous s t r a n d s . This mechanism is however of minor importance, and need not be described, b e c a u s e the crystallization p r o c e s s in wood is very small s o t h a t it r e s u l t s only in a small wavy form of (or around) the main s t r e s s relaxation line. It can be concluded that t h e r e is a lack of the m e a s u r e -m e n t of the -main slow overall relaxation by this -method.

The main relaxation p r o c e s s of the amorphous material and the lignin is t o be e x p e c t e d to follow the Arrhenius equation in the glassy s t a t e and the WLF-equation for the transition to the " l e a t h e r " s t a t e as will be

d i s c u s s e d l a t e r .

2.4 Conclusions

Timber c a n be defined a s a cellular polymeric fibre composite with s l e n d e r microfibrils as fibres in a cementing matrix of relatively unoriented (amorphous) s h o r t - chained or b r a n c h e d polymers (lignin and hemicellulose). The cell wall is a l s o a laminated composite b e c a u s e of the l a y e r e d s t r u c ­ ture of the wall. T h e s e layers a r e : the middle lamella, an a m o r p h o u s filled c r o s s - l i n k e d polymer without microfibrils; the primary wall with loosely packed random microfibrils and no lamellation and the s e c o n d a r y wall with closely packed parallel layers containing spiral microfibrils with various pitches t o the longitudinal axis. The microfibrils c o n s i s t of parallel cellulo-sic molecules having regions of high crystallinity with i n t e r m e d i a t e low-crystalline z o n e s .

So the s t r u c t u r e is h e t e r o g e n e o u s with d i s t u r b a n c e s of the s t r u c t u r e a t any level and many t r a n s i e n t p r o c e s s e s can be e x p e c t e d to o c c u r a t load-ing. This can be due t o plasticity a s well a s due to c r a c k p r o p a g a t i o n . Early flow has to o c c u r in the earlywood cells and in the matrix. As around t h e r e i n f o r c e m e n t bar in c o n c r e t e , it can be e x p e c t e d t h a t s t r e s s redistribution c a u s e s mainly s h e a r with c o m p r e s s i o n in the matrix, i n c r e a s -ing the tensile s t r e s s in the fibres. The m e a s u r e d negative c o n t r a c t i o n for c r e e p in tension is an indication for this mechanism. An indication of flow of t h e earlywood is the c o r r e l a t i o n of the s t r e n g t h with the amount of latewood. Also the elastic layer models indicate early flow of the e a r ­ lywood cells.

The d i s t u r b a n c e s t h a t c a u s e s t r e s s c o n c e n t r a t i o n s and t h u s t r a n s i e n t p r o c e s s e s , a r e for instance the knots, d e f e c t s , r a y - c r o s s i n g s , t r a c h e i d ends, p i t s , interlayer imperfections, voids, second o r d e r p o r e s and p r e -vious c r a c k s in the weak layers. If s t r e s s redistribution a r o u n d t h e s e d i s t u r b a n c e s is due to c r a c k propagation c a u s e d by mainly h y d r o g e n - b o n d breaking, it is t o be expected, by the h e t e r o g e n e o u s s t r u c t u r e , t h a t the delay-time p a r a m e t e r [17] of the kinetic model will be highly r a n d o m and b e c a u s e of the s t r u c t u r a l deviations and deviations of the alignment and of the s t r e s s s t a t e s also a random value of the activation volume p a r a ­ meter c a n be e x p e c t e d .

22

t o be a d a p t e d for the possibility of description of more p r o c e s s e s . This is done for wood in [17]. However different p r o c e s s e s with about the s a m e relaxation time cannot be distinguished, for i n s t a n c e f r a c t u r e due t o interlayer c r a c k propagation shows not much p r e f e r r e n c e for a special plane and may go through the middle lamella or through the interface with the primary wall and also between the P- and S layer. This indicates the s a m e type of bonding between t h e s e layers (the s a m e strength) and the r e s u l t is one a p p a r e n t determinating p r o c e s s with random p a r a m e t e r s due to the different bond d e n s i t i e s .

An explanation can be given of the s t r e n g t h behaviour of cellulose chains depending on the logarithmic value of the degree of polymerization. The c u t s in the chain, due to irradiation, reducing the d e g r e e of polymeriza­ tion, a c t a s flow units for a failure p r o c e s s .

Also a new explanation of the time d e p e n d e n t behaviour of the amorphous regions in the fibrils is given a s a dynamic crystallization p r o c e s s t h a t c a n be d e s c r i b e d by the kinetic model by a s t r u c t u r a l change p r o c e s s . However this very small influence on the c r e e p behaviour can be neglec-ted.

The rheologic behaviour of the wood-polymers is comparable with o t h e r high polymers and is only quasi linear. There a r e also specific differences a s for i n s t a n c e the special p r o p e r t i e s of the activation volumes, as will be d i s c u s s e d later and for i n s t a n c e the special behaviour a t moisture and t e m p e r a t u r e c h a n g e s . These phenomena have to be explained by the kine­ tic model for wood.

The s t r e n g t h is mainly determined by the knot area, the density and the m o i s t u r e c o n t e n t . To determine the p a r a m e t e r s of the p r o c e s s e s in the wood, t e s t s have to be done on clear wood without knots b e c a u s e the s t r e s s redistribution p r o c e s s e s around the knots will dominate and c o n -c e a l the t r a n s i e n t p r o -c e s s e s in the wood. As far a s possible, m e a s u r e d p r o p e r t i e s of wood components have to be used in the model t o be able t o distinguish the different p r o c e s s e s in wood.

The s p e c i m e n s can be taken from one plank in o r d e r to have the l e a s t influence of the variation of the s t r u c t u r e and the density. To investigate the influence of the different modes of f r a c t u r e and c r e e p on t h e activa­ tion p a r a m e t e r s , t e s t s in s h e a r , compression and tension, along the grain and perpendicular to the grain have to be done.

Also t e s t s with fluctuating relative air humidity c h a n g e s have t o be done b e c a u s e the behaviour of the wood polymers is very sensitive for t r a c e s

of water, the previous history and m o i s t u r e c h a n g e s and this will c a u s e a different behaviour in comparison to c o n s t a n t m o i s t u r e conditions.

2.5 References

[ 1] Concrete, Timber and Metals. J.M. Dinwoodie a.o. 1979, Van N o s t r a n d Rheinhold Company, New York.

[ 2 ] Principles of Wood S c i e n c e and Technology. F.F.P. Kollmann, W. A. Cote 1968, S p r i n g e r - V e r l a g , Berlin New york.

[ 3 ] Recent p r o g r e s s in the study of the rheology of wood, A.P. S c h n i e -wind, Wood S c i e n c e and Techn. Vol. 2 )1968) p. 1 8 8 - 2 0 6 .

[ 4 ] Berekeningsmodel voor horizontaal gelamineerde balken. T.A.C.M. van der Put, Rapport 4 - 8 3 - 1 6 GKH 6, 1983 Stevinlaboratorium Delft.

[ 5 ] Vingerlasverbindingen in horizontaal g e l a m i n e e r d hout, T. A.C. M. van der Put, Rapport 4 - 7 6 - 5 VL5, 1976, S t e v i n l a b o r a t o r i u m Delft.

C6] Wood fibres in tension. B.A. Jayne, F o r e s t Prod. J., 1960, 3 1 6 - 3 2 2 .

[71 Tensile s t r e n g t h behaviour as a function of cellulose in wood. G. Ifju, F o r e s t Prod. J., 14, 1964, 3 6 6 - 3 7 2 .

C81 Theory and Design of Wood and Fiber Composite Materials. B.A. Jayne Editor, pg. 8 3 - 9 5 , 1972, S y r a c u s e Wood S c i e n c e S e r i e s , 3 .

[ 9 ] Cell Wall Mechanics of T r a c h e i d s , R.E. Mark, 1967, Yale University P r e s s , New Haven.

[10] Morphology and mechanics of wood f r a c t u r e , G. R. D e b r a i s e , A. W. P o r t e r , R E . Pentoney, Mater. Res. Std., 6, 1966, 4 9 3 - 4 9 9 .

t i l ] The anatomy and fine s t r u c t u r e of wood in relation t o its mechanica! failure, A.B. Wardrop, F.W. Addo-Ashong, Proc. T e w k s b u r y Symp. Melbourne, 1964, 169- 2 0 0 .

24

[12] Failure in t i m b e r p a r t II, The angle of s h e a r through t h e cell wall during longitudinal c o m p r e s s i o n s t r e s s i n g , J.M. Dinwoodie, Wood S c i e n c e and Technology, Vol. 8, 19 74, 5 6 - 6 7.

[13] Failure in t i m b e r p a r t I, Microscopic changes in cell-wall s t r u c t u r e a s s o c i a t e d with compression failure, J.M Dinwoodie, Journal of the insti-tute of wood science 21, 1968, 37-53.

[14] Ueber die G e s t a l t und die Beweglichkeit des Molekuls der Zellulose. P.H. Hermans, Kolloid Z e i t s s c h r i f t , 102, Heft 2, 1943, 169-180.

[15] Cell-Wall Crystallinity a s a Function of Tensile S t r a i n . W. K. Murphy F o r e s t Prod. J., April 1963.

[16] Molecular Rheology of Coniferous Wood T i s s u e s , S. Chow, T r a n s -a c t i o n s of the Soc. of Rheology 17:1, 1973, 109-128.

[17] Reaction kinetics of bond exchange of deformation and damage p r o -c e s s e s in wood, T.A.C. M. van der Put, Pro-c. IUFRO--conferen-ce Firen-ce Italy, S e p t . 1986.

DISCUSSION OF THE BAS IC PRINCIPLES OF THE THEORY OF MOLE-CULAR DEFORMATION K1NETICS

3.1 Introduction

For plastic flow in a material, it is n e c e s s a r y to have "holes" into wich the m a t e r i a l may move, and a lowered energy potential (energy b a r r i e r ) by the p r e s e n c e of this hole (with a bond s t r e n g t h of about a q u a r t e r of the bond s t r e n g t h in a p e r f e c t region for all m a t e r i a l s ) . So t h e number of mobile molecules or mobile s e g m e n t s a r e determined by the n u m b e r of these holes (flow units).

i

L—j-.

fig. 3.1 Energy s u r f a c e a c r ö s s an edge dislocation Cl]

The r a t e of flow is determined simularly a s the chemical r e a c t i o n r a t e of bond breaking and some a s p e c t s of this theory will be d i s c u s s e d (fol-lowing Cl]) t o clarify the physical meaning of the c o n s t a n t s of the b a s i c equations t h a t will be used for the derivation of a e r e e p a n d d a m a g e model. The s t a r t i n g points on the r e a c t i o n order, thermodynamics of the free energy change and p a r a m e t e r s of the flow units a r e derived for use in the derivations of the next c h a p t e r .

3.2 Theory of r e a c t i o n r a t e s for plastic deformation in solids.

The basic c o n c e p t of this theory is to r e g a r d plastic flow as a s p e c i a l form of a chemical reaction (like isomerization, where the composition

26

remains c o n s t a n t but the bond s t r u c t u r e of the molecules c h a n g e s ) , b e -c a u s e flow is a m a t t e r of mole-cular bond breaking and bond reformation. A simple form of the r e a c t i o n r a t e equation is:

d P, d p

Ïï-T = " T t = ?!

f " e

b- <

-

»

w h e r e p is the c o n c e n t r a t i o n of flow units, t h a t may be kinks and holes in the polymers or v a c a n c i e s and dislocation s e g m e n t s in the crystalline regions.

C= v e x p ( - E / k T ) (where v is a frequency) with: E= the activation energy

k= Boltzmann's c o n s t a n t T= the a b s o l u t e t e m p e r a t u r e

Because t h e r e is a f o r w a r d r e a c t i o n into the p r o d u c t s t a t e and a b a c k -ward reaction into the r e a c t a n t s t a t e , t h e r e a r e two r a t e c o n s t a n t s :

Cf = v e x p ( - Ef/ k T ) , (3.2.2)

C^ = v e x p ( - Eb/ k T ) . (3.2.3)

The molecules occupy equilibrium positions and a r e vibrating about the minimum of the free energy potential. Every position of the molecules with r e s p e c t to e a c h o t h e r d e t e r m i n e s a point of the potential e n e r g y s u r f a c e . The molecules m u s t r e a c h an a c t i v a t e d s t a t e on this potential s u r f a c e in going from the r e a c t a n t to the p r o d u c t s t a t e . The t h e r m a l e n e r ­ gy is not equaly devided among the molecules and it is a m a t t e r of c h a n -ce for a molecule t o get high enough energy t o be activated and to be able to b r e a k bonds.

The explanation of the form of the r a t e c o n s t a n t s C. above is given by Bolzmann s t a t i s t i c s .

C = ( k T / h ) e x p ( - E / k T ) ,

v = k T / h can be a p p r o x i m a t e d t o the Debye frequency (about 10 ) t h a t may be r e g a r d e d as the number of a t t e m p t s per s e c o n d of a partiele t o c r o s s the b a r r i e r of height E. However, any a t t e m p t can s u c c e e d only if the e n e r g y of the partiele e x c e e d s E, and the probability of a jump p e r second is: P = v - e x p ( - E / k T ) , w h e r e kT is the mean vibrational energy of the p a r t i c l e s (in t h a t direction).

Mostly not one group of r e a c t i n g atoms is c o n s i d e r e d but a moial quantity. The molal free e n e r g y is then Em = N E and the Boltzmann c o n s t a n t k

is replaced by the g a s c o n s t a n t R, where R = N k and N is Avogadro's ° m m ° Number. So: E / ( k T ) = NmE / ( Nmk T ) = Em/ ( R T ) . k = 8.616*10 "s e V K "1 h = 4.135*10 ~1S e V s e c k/h= 2.084*10 10 s e c _ 1 K- 1 R = 1.987 cal K~l m o l "1 N = 6 . 0 2 * 1 02 3 m

1 Joule = INm = 0.618*101 9 eV = 0 . 2 3 9 cal

f pot. E' f W f energy C b

ƒ

V

— - c

fig. 3.2 Potential e n e r g y change for an e l e m e n t a r y r e a c t i o n [ 1]

The free energy of the activated complex c o n s i s t of an entha'lpy term, an entropy t e r m and a work t e r m due to the applied s t r e s s ( s e e 3 . 4 ) . When the molecules a r e displaced from their equilibrium positions by an applied s t r e s s , the potential energy is i n c r e a s e d . This means t h a t the potential energy s u r f a c e is changed, making the r e a c t i o n more probable, decreasing the b a r r i e r height with Wp in f o r w a r d direction and i n c r e a s i n g the b a r r i e r height with W, in backward direction, w h e r e W= Wf + W, is the work of the e x t e r n a l c o n s t r a i n t s . So:

k T - Ef+ Wf

c

f - T T

P l — k T ~ )■

Cb=l Te xP (

Eb -Wb x

28

3.3 Reaction o r d e r of deformation and f r a c t u r e p r o c e s s e s .

The theory is given for first o r d e r r e a c t i o n s b e c a u s e nearly all m a t e r i a l s a p p e a r to follow t h a t law. So the s l o w e s t determining bond breaking r e a c ­ tions a r e of f i r s t o r d e r or quasi first o r d e r .

A d e s c r i p t i o n by higher o r d e r r e a c t i o n s is also possible and is e.g. given in [ 2 ] w h e r e a Taylor s e r i e s expansion of the r a t e equation is given for hydrogen bonded m a t e r i a l s , leading to t e r m s with increasing r e a c t i o n order. The first t e r m of the expansion will not be z e r o , b e c a u s e it gives the f i r s t o r d e r r e a c t i o n t h a t is shown to occur in p r o c e s s e s like relaxation, f i r s t m o i s t u r e regain, e t c . in dry cellulosic material. The disadventage of this a p p r o a c h by Taylor s e r i e s is, t h a t the r a t e equation for t h e s e c a s e s r e d u c e s to a single forward reaction. This is insufficiënt to d e s c r i b e the t o t a l behaviour of relaxation and a b e t t e r a p p r o a c h is then possible by a single first o r d e r p r o c e s s (with a, for equilibrium n e c e s s a r y , b a c k w a r d process) a s done by Meredith [ 2 ] for the s a m e material. An explanation why a first o r d e r theory can be used is given below and in c h a p t e r 4, w h e r e we have shown t h a t the generalized Eyring theory can be r e g a r d e d a s an expansion into simple parallel p r o c e s s e s . Deviations from t h e first o r d e r a r e due to t h e s e parallel acting p r o c e s s e s . The s a m e a p p e a r s to be possible even for the complex r e a c t i o n s of decomposition of wood a t high t e m p e r a t u r e s t h a t can be given by p s e u d o - f i r s t order r e a c t i o n s , (W = weight loss; W = residual weight ) [ 3 J :

d W / d t = - £ . k . ( W - W ).

The determining (slowest) bond breaking p r o c e s s e s m u s t be of f i r s t o r d e r (or quasi f i r s t o r d e r ) in this c a s e , b e c a u s e the overall r e a c t i o n has an o r d e r close t o one (at the highest r a t e ) . This follows from thermogravic e x p e r i m e n t s [ 4 ] .

The possibility of a quasi first o r d e r r e a c t i o n in a c o - o p e r a t i v e bond b r e a k ­ ing p r o c e s s can be shown by the following higher o r d e r reaction:

- j £ = C pn. (3.3.1)

In the Eyring model for c r e e p , the density of the flow units p is taken t o be c o n s t a n t , a s given by the l a s t t e r m of equation (3.3.2). This can only be t r u e for p r o c e s s e s t h a t may a p p r o a c h the s t e a d y s t a t e . If p is splitted in an initial value p and a small change Ap, eq. (3.3.1) b e c o m e s :