T h e v i s c o e l a s t i c i t y o f W o o d at v a r y i n g M o i s t u r e C o n t e n t

Wood Science and Technology 9 by Springer-Verlag 1975

Vol. 9 (1975) p. 189-205

The Viscoelasticity of Wood at Varying Moisture Content By Alpo Ranta-Maunus* Structural Mechanics Laboratory, Division of Building Technology and Community Development, Technical Research Centre of Finland, Espoo, Finland

Abstract. Wood is regarded as a viscoelastic material. Creep deformations that arise from variations in the moisture content are described by a theory of hydroviscoelasticity developed by the author. Two different types of behaviour have been appazent: one, arising from a continuously increasing strain with periodic variation in the moisture content, and another with no cumulative effect. The theory has been applied to previously published experimental results concerned with beech, pine, hoop pine, klinki pine, along with birch and spruce plywood. Birch and spruce plywood have been used for experiments concerned with periodically-cycling bending moment and moisture content. The results obtained have been compared with the theory presented. Glue-laminated beams have been subjected to long-term out-door loading extending for five years. A brief discussion is given of the results obtained.

Introduction

When climatic conditions remain constant, wood behaves like a viscoelastic material. The stress level determines the question of linearity. As a role, the linearity is assumed under working stresses. The constitutive equation may then be written in the form t

eij (t) = of Jijkl (t -- r) d Old (r) , where

(1)

Jijkl is creep compliance tensor, oij %

stress tensor, strain tensor, and

t, r time-variables. As has been mentioned in a number of papers, changes in moisture content and temperature induce an additional creep deformation. The creep of pine in the longitudinal direction has been studied by Bethe [1969], Eriksson and Noren [ 1965], and Raczkowski [ 1969]. A common observation is that the first change in moisture content results in an increasing step in creep strain for both drying and wetting changes. Subsequently, after some variations of moisture content, a drying change

* The author is indebted to Professor Siimes and Mr. Saarelainen for the planning and carrying out of glue-laminated beam tests and for being kind enough to make the results available to the author for publication. The author acknowledges the valuable assistance of Mr. Kortesmaa in connection with recovery experiments, and computation of the results.

190

A. Ranta-Maunus

Viscoelasticity of wood at varying m. c.

induces an increasing step in creep strain, and a wetting change diminishes the creep strain. The total effect of consecutive variations increases the creep strain. Araucaria has been studied by Armstrong and Christensen [ 1961]. The qualitative behaviour in bending is similar to that described above for pine. Recovery is essentially dependent upon the moisture conditions after the unloading. Additional consideration is given to the observations of some authors, to the effect that the theological deformations induced by changes in moisture and temperature occur simultaneously with these climatic changes, and that the rate of climatic changes is not significant. Accordingly, mention is made of the basic conceptions necessary to establish the theory in the following chapter.

Theory of hydroviscoelastieity Several authors have observed that the variations in temperature, T, and moisture content, u, exert some influence upon the creep deformation. In the theory of thermoviscoelasticity, account is taken of the variation in temperature. It is now assumed that the effect of moisture changes can be described by a similar mathematical formulation [Ranta-Maunus t973]. Considering a non-ageing material, which is initially unloaded until the time t = 0, the constitutive equation is expanded in a Fr6chet series t

eli (t) = i J i ~ (t - r) d Okl (7-) t

j.o.lo (t -- r) d u (r) tj

+ f 0 t + f 0

jOOl (t - r) d T 0-)

t t

200 (t - 7-1, t -- 72) d Old (rl) d Omn (72) + f f Jijk/rm~ 0 0 t

t

+ f f J~ij . -- r l , t -- r2) d U ( r l ) d u ( r 2 ) (10 t

t

002 + f f Jij (t - r l , t - r2) d T ( r l ) dT(r2) 00 t t

11o + f f Jijkl (t - r l, t - r2) dola (ra) d u ( r 2 ) O0 t

t

+ff

j~

- 7"1, t - 72)

d u ( r 1) d T (7-2)

O0 t

t

101 (t -- r 1, t -- 7"2) dold (7"1) d T ( r z ) + f f Jtfkl 00

t t t

j 1 2 o [r + f f f iikl ~ - 7"1, t - 7"2, t - r 3) dokl (7-1) d u (7-2) d u ( r 3 ) O0

0

(2)

A. Ranta-Maunus

Viscoelasticity of wood at varying m.c.

191

t t t

+f f f O ~~

-

rl, t

-

r2, t

-

% ) d OM (~'1) d T ( ' r 2 ) d T ( ' r 3 )

ooo

+ . . .

The kernels jioo represent the nonlinear viscoelastic behaviour under equilibrium conditions of temperature and moisture content. The case of linear viscoelasticity (1) is involved by the first term. The expansion o f an unloaded body due to temperature and moisture content is expressed by kernels j o i o j o 0 i and j0ij. The possibility that changes in the moisture and temperature of a loaded body induce an additionaI part o f creep deformation m a y be incorporated in the integrals with kernels jij0, jioj and jiik. The terms with jijk disappear under b o t h isothermal and constant moisture conditions. Now, when no interest is attached to the moisture expansion, the isothermal constitutive relation is written in the form t eij ( t ) = f Jiiva 100 (t - r ) d Ok, (r) 0 t t +

f f ql l lmO ( t

-- r l , t - r 2 ) d akl ( r l ) d u ( r 2 )

oo

t t t

+f f f 00o

(3)

j12o/'f

tjk! v~ -- r l , t -- r 2, t - -r3) d a k t ( r l ) d u ( r 2 ) d u ( r 3 ) .

The Eq. (3) implies a linear stress-dependence. To derive a convenient "moisture m e m o r y " , we write, in accordance with Ranta-Maunus [ t 9 7 3 ] lOO

Jokl (t -- r) = Jijkt (t -- r ) , jllO/f3 ijkl t.v, t - "/'2) = O ,

~} 1110 (t -- r l , t -- r2) = ~1110 ijkl (t -- r l , t -- 72) T 1 ~ kl { K i j k l ( t - 7 ) for T l = T 2 = T rl #r2 120 Jijkl ( t -- T1, t - r2, t - r3) = Lijkl (t - r2) H (r 1 - r2) H (r 3 - r2) ,

where H (t) is Heaviside step function =

1 for t > 0 0 t ~< 0 '

By the use of these assumptions and notations, the relation (3) is reduced to t

eli (t) = f Jijkl (t -- r ) d Okl (T) 0

t

+ f (mijkl (t - r) Okl (r) + t i j k l (t - r) [a u (t) - 17kl (T)] X o

x [u (t) - u (r)] } d u ( r ) .

(4)

192

A. Ranta-Maunus

Viscoelasticity of wood at varying m. c.

It is apparent that Kiikl relates to the creep that arises from a constant stress distribution old, and that Lijkl indicates a recovery phenomenon. When an experimental study is made for determination of the kernel functions, choice may be made of the only stress-component, say akl, which is acting, and denoted by o. Measured strain, say eij , is denoted by e. Analogically, symbols J, K, L may be employed. Accordingly, t

e (t) = f J (t - T) d o (7) 0 t

+f { K ( t - r ) o ( ' O + L ( t - z ) [ o ( t ) - o ( r ) ] [ u ( t ) - u ( r ) ] } d u ( ~ ) .

(5)

0

The derivation of kernel functions is divided into two parts, according to which the behaviour is termed birch-like or spruce-like.

Birch-like behaviour All of the papers mentioned in the Introduction state that a single change in moisture content brings about a change in strain that does not depend significantly upon the instant at which the moisture variation acts. In these tests, a and e are the axial stress and strain in the same direction. Moreover, o remains unchanged. Thus in (5) it is written that K (t - T) = K is a constant, which assumes different values, depending upon whether d u (~-) is positive or negative. L (t ~-) shows the amount of K which recovers until time t. One necessary condition for the recovery is that there exists a moment ~ such that ~- ~< ~ ~< t and Io(~)l < Io(r)l, ([al means the absolute value of a). It has been observed by Armstrong and Christensen [1961] and RantaMaunus [1973] that the recovery o f an unloaded specimen occurs in particular with increase in the moisture content. Thus, it is also demanded for ~ that u (~) > u (r). Under many usual conditions, these two requirements are valid when ~ is so chosen that r ~< ~ ~< t and [Io(~)l - I o ( ~ - ) l l u ( ~ )

(6)

reaches its minimum value. When examination is made of the effect of a single change of moisture content, d u (r), at time t, the value t is thus replaced by ~, defined in (6). If the increase in moisture content is sufficiently large, the entire effect of the moisture change will disappear. This critical moisture interval is denoted in regard to the unloaded state (o (~) = 0) by Uc- Thus an impulse function for a single change of moisture content is found as follows u (~) -

u (r)

where u c (~) is the larger of two values u c or u (~) - u (T).

A. Ranta-Maunus

Viscoelasticity of wood at varying m.c.

193

When many sequent changes of moisture content occur during a period of unchanged loading, it is found reasonable to replace the comparison moisture content u (r) b y the value u (r?). The time r~ is now so chosen that r//> r and Io(r/)l < I o ( r ) l

(7)

the first time. In other words, the diminution in the load begins at m o m e n t r/. In the case of a small variation in moisture content during the loading time, the employment o f r/ does not induce any practical change in the numerical results. When the effects o f several changes in moisture content are superimposed, we write, by the application of (5) to a birch-like wood t

e ( t ) : f J ( t - r) d o ( r ) 0

'[

+fK

o

o(r)+(o(~)-o(r))u(~)-u(r/)

]

du(r)

(8)

Fig. 1 illustrates the quantities used in (8), in the case o f the stress history o

(t)

I ao for

0 < t ~< t* 0 otherwise I

The differences d u (r) are the differences in the extreme values of the moisture content: u i - ui_ 1. Thus, at the m o m e n t of unloading, t*, the last integral takes the

U

- - m -

l] I

0 Fig. 1.

--_--

t*~=q2=q3

~z tz

t~:~3

Illustration of quantities used in the theory of birch-like behaviour. To obtain a strata

of e (ti), there are needed the maximum value of the moisture content u (~i), and the value at the unloading instant u (rti), together with all the extreme values during loading u 0 . . . u4 4

value of the sum o o 2~ K ( u i - u i_~). After the unloading, recovery occurs in regard i=l

to the effect o f moisture variation when the moisture content assumes a value exceeding that at the unloading instant t* = r~. Three various moments, ti, are considered with corresponding values of ~i. Consequently, the dotted curve represents the

194

A. R a n t a - M a u n u s

V i s c o e l a s t i c i t y o f w o o d a t v a r y i n g m. c.

monotonic behaviour o f u (~) when ~ is considered as a function of t. In this case (Fig. 1), Eq. (8) is reduced to

[

e(t) = a o J ( t ) - J ( t - t*) +

(

1 - u(~) - u(t*)~ N K(ui _ ui-1 ) Uc (~) / i=1

]

,

when t > t*.

Spruce-like behaviour Creep tests of spruce veneer have shown that the difference between the initial moisture content, Uo, and the maximum moisture content during the loading time, Umax, is of the greatest significance (Fig. 3) [Ranta-Maunus, 1973]. In regard to this, the time O is so determined that [ o (O) l u (0) attains its maximum value. On the assumption that the behaviour of the memory is similar to that of the birch-like material, (5) is written in the form t

e(t)=f

J(t-r)

do(r)

0 0

- u (7) + f0 Ko [off)+ (o(~)- o(r))u (~)Uc(~

]

j du(7)

(9)

Here, K o is constant, and ~ and ~ are defined as in Eq. (8). Eq. (9) is applied to the loading case represented in Fig. 1. Eq. (9) now takes the form u (t*) U (~ e (t) = o o (J (t) - J (t - t*)) + K o (Umax - u o) a o ( 1 uc (~) ! ' when t > t*. Moreover, Umax here takes the value of u 3.

Previous works The principal directions of solid wood are so chosen that subscripts 1 indicates the longitudinal direction, 2 the tangential direction, and 3 the radial direction. When plywood is under discussion, accordingly, we define in the plane of a veneer the direction 1 as parallel to the grain, 2 as perpendicular to the grain, and the direction 3 as the normal direction to the veneer. In the design o f wooden constructions, the behaviour of wood in the longitudinal direction is of the most significance. Consequently, the nature of J~k 1 fkernels is of practical interest. The determination of kernels ~rijk 2 2 2 2 and ~lijk 3 3 3 3 ' however, has a

A. Ranta-Maunus

Viscoelasticity of wood at varying m.c.

195

solely physical meaning. The coupling compliances rijk OUmm, as well as the "shearing kernels" lijk may also be of practical importance in the discussion of certain plate Olmlm, and disk constructions. The following contains a summary of the test results obtained with eight various qualities of wood. For birch-like materials, the notations used are as follows

[a

-for du<0 K _ ~a + > 0 J(O)

(10)

[ a ++ for the first change d u > 0 .

The symbols a-, a § and a §247are thus the material constants chosen. Analogically, for a spruce-like material there is denoted Ko - b. J(O)

(11)

A brief compilation of experimental results is listed in Table 1. Araucar& The longitudinal behaviour o f hoop pine in bending has been studied by Armstrong and Kingston [ 1962], and that of klinki pine by Armstrong and Christensen [ 1961]. The results are given in Table 1. Very large deformations were induced by extreme changes in moisture. It soon became apparent that the wetting of a test specimen (after unloading) induced an almost complete recovery. The numerical values are calculated by the assumption that moisture changes exerted an effect upon the interval u = 0 . . . 0.4, with the value u c < 0.4 indicating only that complete recovery occurred when u = 0 during the unloading, and after the wetting attained a value of u = 0.4. Beech The longitudinal behaviour of small beech specimens has been studied by Hearmon and Paton [1964]. On variation in the moisture content from 0 to 0.3 (r.h. = 90%), a quick rupture occurred when the stress level exceeded 0.2. For value 0.125 of the stress level, it can be estimated that a + - a- = 1.4, o n the assumption that the whole moisture interval exerts an effect. Tangential behaviour in tension has been studied by Schniewind [ 1966]. Drying between u = 0.26 and u = 0.10 induces a very large strain with a- = 55 at a stress level of 0.30 and a temperature of 20 ~ C . - T h e effect of a single change of temperature T was also investigated. Apparently it is possible to write kernel 11~ e2222, including the factor aT, in a way similar to that for kernel t~iltl0l l ' by virtue of definitions (4) and (10). On the application of a stress level 0.3 under moist conditions (u > 0.3), a value of a~ = 0.07 1/K was derived with a change in temperature from 20 ~ C to 60 ~ C. Recovery at various temperatures has been studied by Lawniczak and Raczkowski [1961].

bending, s = 0.2

rolling shear, s = 0 . 1 2

beech

5 x 20 x 2 3 0

birch veneer, P = 0.68

7 x 50 x 9 0 0

21 x 7 x 2 5 0

Schniewind

[19661

Ranta-Maunus

[ 19731

b e n d i n g , s = 0.2

rolling shear, s = 0 . 2 6

ktinki p i n e 1 x 1 x60

pine, p = 0.44 7x7x200

pine, p = 0.52

1 0 x 1 0 x 300

pine, s a p w o o d

20x25x30

spruce veneer, p = 0.46

12x50x900

36 x 7 x 2 5 0

Armstrong, Christensen [1961]

Bethe [1969]

Raczkowski

[19691

Perkitny

[19651

Ranta-Maunus

[19731

s = 0.1 to 0.4

tangential compression,

Sma x = 0.2

longitudinal bending,

longitudinal bending, s=0.16

longitudinal bending, s ~ 0.25

s = 0.37

19 x 1 9 x 9 0 0

Kingston 119621

longitudinal bending,

h o o p pine

Armstrong,

s = 0.3

tangential tension,

longitudinal bending, s= 0.12

beech 2x2x60

Hearmon, Paton [1964]

Loading

Test specimen

Author

u = 0.05 to 0 . 3 0

T = 20-+ 60~

u = 0.11 to 0 . 2 6

0.21

T = 20 ~

T = 20~

u = 0 . 0 5 to 0 . 3 0

u = 0.05 to 0 . 3 0

u = 0 t o 0.3 (sat)

T = ?

u = s a t - + 0.1, u = 0.1 -+ sat

T = 9

T = 20~ u=0.09+-+

T = 9 u = 0 +-> sat

u = 0 . 0 5 +-+ sat

T = 25~

T = 20 ~ C, u = 0 . 0 5 to 0 . 3 0

T = 20~

u ~0.3,

T = 20~

T = ? u =0+-+0.3

Climate

a-=

-7.4,

a§ = -4.37,

2, a ++ = 5

a-=2

b = 70, u e = 0 . 1 2

b = 15, u e = 0,05

a ++ = 17

a-=

a+

a - = - 2, a + =

1, a ++ = 2.5, u c ~

a - = - 2, a + = - 1, a ++ = 2

b = 50, u c = 0 . 0 8

a-=

0.4

a + + = 12.6, u c = 0 . 0 8

(single c h a n g e )

1.4

a~ = 0 . 0 7 K - t

a-= -55

a+

Result

T a b l e 1. A c o m p i l a t i o n o f s o m e e x p e r i m e n t a l c r e e p results, p is t h e d e n s i t y o f w o o d in g / c m 3. D i m e n s i o n s o f size o f t e s t s p e c i m e n s are in m m

0~

O o

g

<

.>

O~

A. Ranta-Maunus

Viscoelasticity of wood at varying m.c.

197

Birch veneer

The behaviour of birch veneer has been studied by the author [1973].

Tests were

made in the grain direction by bending 5-ply strips of birch plywood. The temperature was 20 ~ C, and the moisture content varied within a range of 0.05 . . . 0.30. There was observed lower boundary value, u = 0 . 0 8 . . . 0.10, so that variations of u below this limit had no effect. After unloading, the recovery was found to occur with increasing moisture content. Numerical results are given in detail in Table 1. This theory and the values observed are illustrated in Fig. 2.

Illll

3

o observation theory _ _ _ . creep at constant

Z 0

b 133

U LL W 0

III

t: ~

~

humidity

L -~4

.....-4 s o

2

LU .... I

f

--3 IJA t'V

~,, 4. ~ ' e .......

0

D

< o _J

LO Z O

I

--,i

-I

el 0.3

c~ 0.2 W ct"

i--m_ 0.1 (D 0

"100

200

300

time

/~00

day s

500

Creep and recovery of birch veneer in the grain direction, the values observed being the T h e theoretical curve has been drawn in accordance with the parameters given in Table 1

Fig. 2.

a v e r a g e s o f five similar test s p e c i m e n s .

Shearing behaviour, Iijk ~2323, was studied by the bending of short (span = 200 m m ) 15-ply strips. The climate was the same as that for the axial tests. It was observed that the shear deformation assumed a spruce-like character, with b = 50, and u c = 0.08 (for stress level s = 0.12).

198

A. Ranta-iVlaunus Viscoelasticity of wood at varying m. c.

Hinoki The effect o f temperature changes has been investigated in the longitudinal direction (bending) by Kitahara and Yukawa [1964], and in radial compression by Arima [1972]. In both cases, an increasing change in temperature was observed to influence an immediate, increasing creep deformation. The decrease in temperature brings about a decreasing step in creep strain. The test specimens were placed in water. The changes within the range of 2 0 . . . 75 ~ C indicate an apparently nonlinear relationship between creep strain and temperature change d T. It may thus be ap1"102 and r103 propriate to apply theory (2) to kernels "ijkl oijkl in discussion of the variations in temperature. Takemura [1966] has presented a theory for consideration of the effect of a single change of moisture content.

Pine Bethe [1969] has studied the effect of moisture variations between 0.09 and 0.21 upon the deflection of longitudinal pine beams, when the stress level is s = 0.16 . . . 0.40, and stated that the change in deflection after six moisture periods is related to 03. The value for a + - a- denoted in Table 1 is derived by the assumption that creep behaviour can be regarded as linear as far as the lowest stress level investigated, s = 0.16. This article further illustrates the relationship between relative creep and wood density. Raczkowski [1969] has studied the effect upon the deflection o f pine beams of single wetting or drying changes. The values a- = - 2 and a §247= 5 in Table 1 are derived by the assumption o f the effective change o f moisture content in the interval beingu=0.1 ...0.4. The longitudinal tension has been studied by Eriksson and Nor6n [1965]. Perkitny [1965] has given consideration to radial and tangential compression. As had been expected, a single wetting change of moisture exercised an influence denoted by a +§ = 17; however, by reason of a drying moisture change, the deformation was found proportional to the term 03 .

Spruce veneer The author [1973] has studied the behaviour o f spruce veneer. Tests were made in the grain direction by the bending of 5-ply strips of plywood. The temperature was 20 ~ C, and the moisture content varied within the range 0.06 . . . 0.30. It was observed also here that moisture variations below u = 0 . 0 8 . . . 0.10 did not exert any effect. For numerical values, there were obtained b = 15 and ur = 0.05. Fig. 3 illustrates a comparison between theory and the results of tests. Rolling shear strain was studied by the bending o f short 15-ply strips (span = 200mm). Results of b = 70 and u c = 0.12 in regard to lijk ~2323 were obtained for s = 0.26.

A. Ranta-Maunus

Viscoelasticity of wood at varying m.c.

199

3, I I I 1%~o' Iooo~ Z 0 Ld LII Q W 2~

t.u

0 Q

0

_.J

0

I

i 0.23 O'ult

~0.3

II

Z 0

w 0.2

o~

^iA

at

~

,

CO

I

0 Fig. 3.

100

time

200

days

Creep and recovery of spruce veneer in the grain direction

Recovery tests with a non-zero stress

The kernel functions in the theory of hydroviscoelasticity are based upon tests in which variations occur in the moisture content, but the load does not change more than twice, as is illustrated in Fig. 1. However, the load of practical wooden constructions may vary in a number of ways. In many cases, the time-dependence of loading is expressible by a cyclic function, in which a given dead load acts for the whole of the time. A further series of experiments was made with a view to checking the validity of results (8) and (9) in the case of a periodically changing load. Test material and conditions

Both birch and spruce plywood were tested under conditions of pure bending. The 5-ply birch plywood strips subjected to test, and 5 0 m m x 8 5 0 m m in size, were loaded by a constant bending moment which was 7 % of the short-time ultimate strength when the full load was acting. During a period of 81 days after the first

200

A. Ranta-Maunus 3

Viscoelasticity of wood at varying m. c.

I case 1 0

~0

case 2 Ld r~

o

<

o 0

CA LU :> o 0 d

LU n-"

'

o u

0.59

case 1

0.25

case 2 '

r

I

i

l

J

j

i z

r

vAf

0.25

z 0,20 w c~

0.15

81

88

95

102

i

9

L

I

I

i

t

kJ"k]v

k/"

0,10--4,

i

109

115

123

130

137. 144 t~me

151

158

165 days

Fig. 4. Recovery experiments in the pure bending of birch plywood. Each point represents the mean of five observations. Both load and climate were unchanged during 81 first days with s = 0.07, u = 0.22 and T = 20~

loading, the moisture c o n t e n t o f birch p l y w o o d was f o u n d to be constant, 0.22 w i t h full load.

Subsequently, both load and moisture were varied, with a cycle o f

14 days as indicated in Fig. 4. tested. load.

T w o test series, each comprising 5 specimens, were

In one series, the m i n i m u m load was 50%, and in the other 2 5 % o f the full Similar tests were m a d e for spruce p l y w o o d , with a full load o f s = 0.23.

The temperature was constant at 20 ~ C.

A. Ranta-Maunus

Viscoelasticity of wood at varying m.c.

201

Results with birch plywood The three moisture cycles between t = 116 and 158 days are closely similar. Therefore, the cumulative effect of moisture variation during these three cycles is examined. In the following, two parallel values observed are given in regard to two loading cases: the recovery period with 50% and 25 % of the full load. Firstly, a discussion is given of the creep during each full-load period. The extent of elastic deformation plus creep under constant conditions in a week is assumed to be 0.59 and 0.89 of the elastic curvature induced by the full load, respectively, in the two cases of loadhag. We thus observe that the amount of creep strain arising from moisture variation on the average amounted to 0.28 and 0.33 during a full-load week (Fig. 4). These correspond to the values of a- and a§ which are about ~- of those given in Table 1. The difference can be explained by the low stress level s = 0.07. The recovery during partly4oaded periods is discussed adapting the following assumptions: 1. The recovery occurs in a linear relation to the decrease in load. 2. The moisture variation does not induce any creep when s < 0.05, i.e. there is a creep limit for stress. 3. During partly-loaded periods, the increase in moisture content is sufficiently large to induce full recovery of moisture creep strain, if a perfect unloading were carried out (u c ~< 0.05). While the moisture variation induces a creep amounting to 0.28 and 0.33 during a thll-load week, the cumulative effect of three cycles is 0.42 and 0.25, in the actual cases of loading, as derived by application of the assumptions mentioned. Corresponding values observed, the differences of the observations at the points 158 and 116 days are 0.34 and 0.20, which principally arise from the moisture variation but include also the effect of linear viscoelasticity during a varying load. The latter effect is small, but it is not simply evaluated trustworthily, because of the wide range of moisture variation and the fact that during 81 first days the average moisture content had a higher value than during the varying-load-period. In conclusion, it may be stated that the theory of hydroviscoetasticity is satisfactorily compatible with the results of the recovery tests with birch plywood, when it is completed by the adoption of the creep limit with respect to kernel function -1111" 1110 The observation that u c may be less than 0.05 is extremely positive when the cumulative effect of snow-load is discussed.

Results with spruce plywood Spruce plywood behaved as had been expected: no perceptible creep deformation arose on variation in the moisture, as the maximum moisture content was fixed at the start of each full4oad-period. The observations made, the means of five test specimens, are indicated in Fig. 5. These experiments were carried out in the same room as that for the birch plywood tests. In the test series with a minimum load, being 50% of the full load, the points of measurement deviate to some extent from the theoretical curve. The principal rea-

202

A. Ranta-Maunus Viscoelasticity of wood at varying m. c.

2.0

1.0

I

cycle : 1 0 0 % / 2 5 % of ful[-toad

o

:1 :1

0

'

e

I

0 cycle : 100 ~'o/50% of fult-toad

2.0

o

0--0

o

f

f

o

f

<2__o 81

88

95

102

[

109

116

123

o

J

]

I

130

137

144

]

f

0

1.0

o

o

l 151 time

158

days

Fig. 5. Recovery experiments in pure bending of spruce plywood. Each point represents the mean of five observations. Both load and climate were unchanged during 81 first days with s = 0.23, u = 0.195 and T = 20~ C. The curves indicated show the expected behaviour at u = 0.195 on the basis of the creep curve observed during 81 first days son for this is that one of the five specimens behaved i n an exceptional way during the changing loading. If the results of this test specimen were omitted, the compatibility between the theory and the experiments would improve. However, all the test results have been taken into account in Fig. 5, because no acceptable reason for omitting was found.

Glue-laminated beams under natural conditions Material and conditions During the period 1962 to 68, tests were made with glue-laminated beams; pine beams had dimensions of 7 0 8 0 r a m x t 7 6 m m x 9 5 m m for span, height and width respectively. A beam was glued from 8 boards. Highly classified heavy wood and unclassified light wood were utilized, so that each beam had 4 lamellae of both qualities. If the heavy lamellae were positioned as the two outermost lamellae of the tension and compression sides, the beam was called "heavy", and if the two outermost lamellae were light, it was called "light". The beams of spruce, glued from 10 boards, had dimensions of 7 6 0 0 r a m x 220ram x x 150 ram. The four heavy boards were positioned as the outermost or middle lamellae. The beams were subjected to a point-load at mid-beam, and the midpoint deflection was measured in each case. The m a x i m u m stresses, 8.2 N/mm 2 for pine, and 5.4 N/mm 2 for spruce, were largely attributable to the load, and to a lesser extent to the weight of the beam (15%).

A. Ranta-Maunus

203

Viscoelasticity of wood at varying m . c .

A heavy pine beam and a light one were kept out of doors without any cover, while two similar beams were enclosed in a plastic cover, relatively tight initially. The spruce beams were tested in the enclosed form.

Results with pine The relative deflection was calculated in relation to the elastic deflection induced by both the load and the weight of the beam itself. The values observed have been indicated in Fig. 6. No appreciable differences were discernible between heavy and light wood. However, the cover was found to be valuable: the average increase in relative deflection after the first year amounted to 0.25 per annum for the uncovered beams, and less than 0.1 for the covered ones. Thus the variation in moisture exercises a remarkable cumulative effect to deflection in the case of uncovered pine beams. The major part of the creep deflection of beams enclosed in a plastic cover apparently consists of the conventional viscoelastic strain (denoted by j,oo in Eq. (2)). This experiment did not permit any conclusion to be drawn as to a time-limit subsequent to which the moisture creep terminates, or changes.

3.2

3.0

%

2 h~

2.6

9

,.%,) ~\

C 2.4 o 9

~e32 . 2

!

> 2.0

t

~ 1.8

. . \

t-~-o~'~ 1.6 1.4

k"

l

,,

o heavy p i n e , u n c o v e r e d

s = 0.2

9 light

s = 9.4

pine,uncovered

,..-+lio

,~ heavy pine , c o v e r e d ~

s = 0.2

r

+

s = O.z,

2

ight pine,c0vered,

1.2 1.0

Fig. 6.

1963

1964

1965

1966

1967 y e a r

1968

Long-term loading of glue-laminated beams of pine, on the southern coast of Finland

204

A. Ranta-Maunus

Viscoelasticity of wood at varying m. c.

3.0 light spruc%covered heavy spruce,covered theoretical. ~t~ot~=1-~Q.66 ut ~247

2.8 2.~

theore~ieo[

2.4 r-

9s

\

?,

//

0J

u=0,20

/

_A

2.2

fo r

x

2.0 1.8

2/

1.6

" ~

~heorotieaL for u*0,15

1.z, 1.2 1.0

1963

1964

1965

1966

1967 time

1968 year

Fig. 7. Long-term loading of glue-laminated beams of spruce, in Helsinki. All the beams were plastic-enclosed. The observation points indicated are the means of two similar tests. The theoretical curves are the results the author (1972) found for spruce plywood under constant climatic conditions (T = 20 ~ C)

Results with spruce The observations made have been illustrated in Fig. 7. It is evident that, although the annual maximum value o f deflection increases during the first three years, the difference between the annual minimum values of deflection, and the creep curve for a constant moisture content of 0.15, became an almost constant value after spring 1964. The annual minimum values may accordingly be described by the theory if the effective mean moisture content is 0.15, and the increase in moisture content during the first year assumes a value o f the order of 0.01 to 0.02. Although the behaviour of the spruce beam cannot be explained in detail, one may conclude that neither the variation in temperature, nor the variation in moisture content, exercises a cumulative effect upon the creep strain o f spruce. Consequently, the linear theory of viscoelasticity describes the long-term behaviour o f spruce in its principal traits. This excludes the considerable variation in annual deflection, which is assumed to originate in the short-term effects o f temperature and moisture content.

Conclusions The theory o f hydroviscoelasticity expresses a functional relationship between strain, stress and moisture history. Wooden materials are divided into two groups, birchand spruce-like materials, depending on whether the variations in moisture content have a cumulative effect or not.

A. Ranta-Maunus

Viscoelasticity of wood at varying m.c.

205

In the planning of practical applications, the following questions arise: (i) What are the material constants in accordance with the theory of hydroviscoelasticity? (ii) What are the limits of validity of the theory in time, stress and moisture content? (iii) What is the moisture-content history in different places in the wood? (iv) What role does temperature play? In this paper, problems (i) and (ii) have been discussed as follows: -

the material constants have been determined for birch and spruce plywood in laboratory tests (Table 1) - approximate values for the material constants have also been calculated for certain qualities of tree on the basis of data published earlier (Table 1) -

in regard to the creep that arises from variation in the moisture content, it was observed that the creep limit in stress level for birch veneer is about s = 0.05, and the lower creep limit in moisture content for spruce and birch veneer is u = 0.08 to 0.10.

In future, particular interest should be attached to laboratory experiments at temperatures of - 20 ~ C to + 10~ C, along with measures of real-scale structures, with a duration of many years.

References Arima, T. 1972. J. Japan Wood Res. Soc. 18:349-353 Armstrong, L. D.; Christensen, G. 1961. Nature 191:869-870 Armstrong, L. D.; Kingston, R. S. T. 1962. Aust. J. appl. Sci. 13:257-276 Bethe, E. 1969. Holz Roh- u. Werkstoff 27:291-303 Eriksson, L.; Noren, B. 1965. Holz Roh- u. Werkstoff 23:201-209 Hearmon, R. F. S.; Paton, J. M. 1964. Forest Prod. J. 14:357-359 Kitallara, K.; Yukawa, K. 1964. J. Japan Wood Res. Soc. 10:169-175 Lawniczak, M.; Raczkowski, J. 1961. Nature 192:583-584 Perkitny, T. 1965. Holz Roh- u. Werkstoff 23:173-182 Raczkowski, J. t969. Holz Roh- u. Werkstoff 27:232-237 Ranta-Maunus, A. 1972. Building Technology and Community Development, Technical Research Centre of Finland, Helsinki. Publication 3 Ranta-Maunus, A. 1973. Publication 4. Schniewind, A. P. 1966. Holz Roh- u. Werkstoff 2 4 : 8 7 - 9 8 Takemura, T. 1966. Coll. Agric. Kyoto Univ. 88. Forestry Ser. 1 : 3 1 - 4 8

(Received August 20, 1974/April 14, 1975) Alpo Ranta-Maunus Structural Mechanics Laboratory Technical Research Centre of Finland SF-02150 Otaniemi, Finland Present address of the author: Institute of Radiation Protection BOX 268 SF-00101 Helsinki 10, Finland