MECHANICS

POLYMER

VIBROCREEP OF POLYMER MATERIALS 2. Polyethylene. I s o t h e r m a l Deformation (+20 ° C) R. D. Maksimov and Yu. S. Urzhumtsev Mekhanika Polimerov, Vol. 4, No. 2, pp. 246-254, 1968 UDC 678:539.376

The normal and vibrational creep and r e c o v e r y of low- and high-density polyethylene (LDPE and HDPE) and filled LDPE have been studied experimentally under isothermal conditions when the superposition of vibration is not accompanied by mechanohysteresis heating of the material. F r o m the relatively few studies of p o l y m e r v i b r o c r e e p [ 1 - 5 ] it m a y be concluded that the "vibration effect" in various p o l y m e r s is determined by a number of f a c t o r s . Chief among these are m e c h a n o h y s t e r e s i s heating, which causes a sharp i n c r e a s e in creep rate, usually under nonisothermal conditions, and a marked isothermal acceleration of the relaxation p r o c e s s e s . The latter is not associated with an effective t e m p e r a t u r e r i s e , although its external manifestations a r e s i m i l a r to those of a change in t e m p e r a t u r e conditions. In [4] the v i b r o c r e e p of makrolon was studied at small incremental dynamic loads (up to 10% of the s h o r t - t e r m strength), when v i b r o c r e e p is not accompanied by m e c h a n o h y s t e r e s i s heating. The static and dynamic creep curves for makrolon practically coincided. We examined the v i b r o c r e e p of polyethylene under s i m i l a r isothermal conditions (+20 ° C), when superimposing small vibrations does not cause heating of the material. Experimental material. We used specimens of HDPE (36 specimens), LDPE (72 specimens) and LDPE with filler (24 specimens). The HDPE specimens were cut f r o m a single batch of m a s s - p r o d u c e d tubes (MRTU 6-05-917-63) manufactured by the Riga Polyethylene Plant. These tubes were made from black granulated P4007 HDPE (containing 1.5% gas black) with a flow melt index of 0.6/10 min, a s h o r t - t e r m tensile strength R = 256 k g f / c m 2, Cauehy relative elongation at b r e a k e R = 400%, and density p = 0.95 g / c m s at T = +25 ° C. The LDPE specimens were also made f r o m tubes (MRTU 6-05-918-63) manufactured at the same plant. The starting m a t e r i a l was P2020 granulated LDPE containing 2% carbon black with a flow melt index of 0.7/10 min, R = 95.5 k g f / c m 2, ~R = 540%, and p = 0.92 g / c m 3 at T = +25 ° C. The specimens of LDPE with filler were made at the Institute of P o l y m e r Mechanics of the AS Latvian SSR (under the supervision of L. A. Irgen). The filler was carbonized CaSiO3 f r o m the Erevan Scientific R e s e a r c h Institute of Inorganic Chemistry (composition: SiO2 40.83%; 1~O~; 1.28%; CaO 38.50%; R20 0.56%; CO2 17.28%, and volatiles 1.55%). The filler content was 25% by volume. The composition was p r e p a r e d on L-16 r o l l s at T = +135 i 5 o C. Rolling lasted 30 rain; then the composition was granulated and molded into sheets at T = +190 ± 5 ° C and a p r e s s u r e of 50-60 k g f / c m 2. The actual specimens were obtained from these sheets by mechanical means. In all the experiments the dimensions of the paddle-shaped specimens were constant: c r o s s section 10 × 10 mm, gauge length 100 ram. Method. The tests were conducted on the electronic-mechanical equipment described in [6] in uniaxial tension with the vibrations superimposed in the direction of the constant s t r e s s c%. Thus, the vibrated specimen was subjected to a s t r e s s a=(~0-+-Cf:sin tot

(1)

The vibration frequency was 300 o r 1000 Hz, and the amplitude of the cyclic s t r e s s e s cra was selected to avoid mecha~ohysteresis heating in the material. The t e m p e r a t u r e was m e a s u r e d inside and at the surface of the specimen with an accuracy of not less than ±0.5 ° C.

180

POLYMER MECHANICS

F o r c o m p a r i s o n we conducted t e s t s under s t a t i c loads (~0) and p a r a l l e l t e s t s with the addition of c y c l i c s t r e s s e s . The effect of v i b r a t i o n was i n v e s t i g a t e d over as wide an i n t e r v a l of v a l u e s of cr0 as p o s s i b l e . Thus, for LDPE we took eight ¢0 l e v e l s on t:he i n t e r v a l 0 . 1 7 - 0 . 5 4 R, for HDPE five l e v e l s on the i n t e r v a l 0.05-0.37 R, and for LDPE with f i l l e r four l e v e l s on the i n t e r v a l 0 . 2 4 - 0 . 6 5 R . Complete loading and unloading of the s p e c i m e n and the f i r s t s t r a i n r e a d i n g s took 1 sec. The c r e e p e x p e r i m e n t s (up to unloading) l a s t e d 30 hr and the r e c o v e r y e x p e r i m e n t s (after unloading) l a s t e d 20 hr. The elongation of the specimens was measured by dial gauges and from two marks using a KIVI-6 cathetometer. In each loading regime three tests were performed on twin specimens; the results of the measurements were treated statistically and averaged. A n a l y s i s of v a r i a n c e . C r e e p t e s t s on pol)mler m a t e r i a l s a r e c h a r a c t e r i z e d by the s c a t t e r of the e x p e r i m e n t a l data. The r e p r o d u c i b i l i t y e r r o r s d e t e r m i n e d by the inhomogeneity of the t e s t m a t e r i a l s a r e a g g r a v a t e d by v a r i o u s addiltional f a c t o r s - - v a r i a t i o n of the s t r e s s level, i n s t a b i l i t y of the test equipment, and, in our c a s e , s u p e r p o s i t i o n of the v i b r a t i o n s . F o r a valid c o m p a r i s o n of s t a t i c and v i b r a t i o n c r e e p it is, above all, n e c e s s a r y to make a careful s t a t i s t i c a l a n a l y s i s of all the t e s t data. For this purpose we made an analysis of variance that enabled us to decompose t h e total variance s 2 into its individual components: reproducibility variance 52rep , "time" variance 52t due to the instability of the measurements on different time intervals, variance due to variation of the static stress 52, and, finally, that due to the vibration load 2 To obtain these variances we employed a three-step classification [7] of the test data in accordance with the scheme indicated in Fig. i.

5v.

Tests ~e position tep 1: super1of vibrations ~' step 3: readlags at differenttimes ] parallel tests {

k_. I

Fig. 1. C l a s s i f i c a t i o n of the t e s t data. The following a u x i l i a r y sums w e r e calculated. The sum of the s q u a r e s of all the d a t a included in the c a l c u l a t i o n

Sl= where

rq~j~ 2 = ~[he~{~. ~q~j~

2 2 rq,,J

(2)

q=i i~1 / = l ",'=t

100 ; ¥ is the a r i t h m e t i c mean of t h r e e t e s t s on twin s p e c i m e n s , n is the number of p a r a l l e l t e s t s ,

m is the number of r e a d i n g s at d i f f e r e n t t i m e s , k is the n u m b e r of c o n s t a n t - s t r e s s l e v e l s , and T is the number of i n c r e m e n t a l v i b r a t i o n loading r e g i m e s . The sum

of the squares

of the results for each test divided by the total number

$2

q=l i=~ j=I

n

of parallel tests

(3)

n

w h e r e R=Er~.. ¥=I

The sum of the s q u a r e s of the r e s u l t s of the t h i r d step divided by the n u m b e r of d a t a in each block of the third 181

POLYMER MECHANICS

step

q=!

'=

=

Rq~j )2

(4)

3 3~ . nrn

The sum of the r e s u l t s of the second step divided by the number of data in each block of the second step

R¢~j S4~_'

=

i=l

(5)

j~l

knrn

The square of the total r e s u l t divided by the total number of data

t~t j=l S~ . . . . . .

tkmn

Rqtj

)2

.......................... "

(6)

The r e s u l t s of the calculations are presented in the table. After finding the above-mentioned sums we determined the sample v a r i a n c e s s 2, s~, s}, and s~, which were subsequently used to estimate the components of the general variances. Before determining the components of the general variances it is n e c e s s a r y to test the statistical _2/S2 2 2 2 2 significance of the ratios of the sample variances ~2/ ~, sis2, and S4/B3. F o r this purpose we used a one-sided F i s h e r test. (This was justified since in the analysis of variance we test the hypothesis 5~ > 62 with the alternative 61 = 5]. ) In our experiments the quantity sl/s~ proved to be nonsignificant; therefore we adopted the null hypothesis (r~ = 0, and for the variance a r2 e p we used the two estimates s~ and s~ in the combined variance ~=

t k ( m - 1 ) s 2 ~ + t k r n ( n - l)sl 2 tk(rn-- l) + t k m ( n - - 1)

(7)

The quantities s i2s --2 2 and S~/S32proved to be significant at significance levels of 0.001 and 0.05, respectively, which made it possible to determine the variances 5~ and 52. The values obtained for the variance components (table) show that in the total e r r o r balance the m o s t important role is played by the e r r o r associated with repetition of the tests on twin specimens, which is chiefly attributable to the differences in the p r o p e r t i e s of the material of which the different specimens are composed. The total v a r i a n c e of the test data is obtained as the sum of the individual components 52=8~+8~ 2+8t 2+~rep ~.

(8)

F r o m the value obtained for 6 z we obtained a maximum coefficient of variation Wmax = 8.8% with a fiducial probability of 0.95. Statistical tests that confirm the applicability of analysis to material of this kind a r e presented in [8]. Discussion of experimental r e s u l t s . The most probable static c r e e p and r e c o v e r y curves f o r HDPE a r e presented in Figs. 2 and 3. In parallel with the static c r e e p tests we conducted tests with additional vibrations. The "input" amplitude of the cyclic s t r e s s e s was always the same, namely, 1.0 k g f / c m 2. At all values of the static load the vibration frequency was 300 Hz; however, additional experiments at a vibration frequency of 1000 Hz were conducted at s t r e s s e s of 25.0 and 31.25 k g f / c m 2. Under these vibration conditions, assuming that the t e m p e r a t u r e was m e a s u r e d with an a c c u r a c y of ±0.5 ° C, no vibrational heating of the material was observed. Figure 2 shows that the vibration c r e e p strains differ little f r o m the static c r e e p strains. In any event they do not lie outside the confidence interval obtained by statistical analysis.

182

co ¢,o

Between parallel determinations

Between levels of step 3

s ~ = - S s - - S)_ =7,1 tk(m-1)

s.~= t(~- 1-----~

S~- S, = 154,0

s~ = -~-~:-"-.~= 823,0

Variances

Classification

~s=6repS+~?+Ou~+~v~=19.48, with P=0.95; Wra~x=8.8%

~=--~rep ~=12.7

~z = 12.7

sa~= mn6~ + rt~t2 + 8 rep ~= 154,0

s~Z=kmnSv2+rnnScr2+nSt2+ + 6 rep 2= 823.0

~rep u-~ 12.7

6~2=0

5ff=4.25

l 8v2~=2"53

Estimate of components of general Components variances I of variances

,u

Data for a Three-Step

Sl -- $2 = 8047 tkm(n- 1) = 3 , 8 . 1 1 (3-1) =528 s z ~ tkm(n-- 1) = 15.2

Sz-Sa= 1701 tk(m-- 1) = 3 . 8 ( l l - - 1 ) =240

$ 3 - $4= 3227 t(k--l) = 3 ( 8 - 1 ) =21

Between levels of step 2

l

of t h e E x p e r i m e n t a l

Number of degrees of freedom

of V a r i a n c e

S~-$6= t646 t - - 1 = 3 - - 1 = 2

~um of squares

of an Analysis

Between levels of step 1

Variation

Results

Z

t~ f3

©

P O L Y M E R MECHANICS

A f t e r u n l o a d i n g the v i b r a t i o n s w e r e s w i t c h e d off. T h e r e c o v e r y c u r v e s d i d not depend on w h e t h e r the i n i t i a l l o a d w a s a s t a t i c l o a d o r a l o a d with s u p e r i m p o s e d v i b r a t i o n s .

0

Io

20

30

~,o

~o

F i g . 2. C r e e p and r e c o v e r y c u r v e s f o r H D P E : 1) o"0 = 12.50 kgf/cm2; 2) 18.75; 3) 25.00; 4) 31.25; o"a = 1.0 k g f / c m 2. Instantaneous-elastie strains excluded. T h e c r e e p c u r v e s shown in F i g . 2 w e r e o b t a i n e d at r e l a t i v e l y low s t r e s s e s . The m a x i m u m 3 0 - h r c r e e p s t r a i n s d i d not e x c e e d 1%. To d e t e r m i n e the e f f e c t of v i b r a t i o n at l a r g e r s t a t i c l o a d s we c o n d u c t e d e x p e r i m e n t s at a0 = 93.8 k g f / e m 2. In t h i s c a s e the 3 0 - h r c r e e p s t r a i n e x c e e d e d 5%. T h e s u p e r i m p o s e d v i b r a t i o n s h a d an "input" a m p l i t u d e of 1.0 k g f / c m 2 and a f r e q u e n c y of 300 ttz. In F i g . 3 e v e n a t an e n h a n c e d s t a t i c s t r e s s and in the p r e s e n c e of the a b o v e m e n t i o n e d v i b r a t i o n s the c r e e p and r e c o v e r y c u r v e s r e m a i n w i t h i n the c o n f i d e n c e i n t e r v a l s .

~5 ~

i

/': i

i

i

l

l

{

i

}

owi,hvibra,ion

{

]

•

j

!

/0

30

with, out vibration 1

- t~o~fi-J 50

F i g . 3. C r e e p c u r v e f o r H D P E at ~o = 93.8

k g f / e m 2 ; cra = 1.0 k g f / e m 2 ; f = 300 Hz. Instantaneous-elastic strains excluded. A f t e r 20 h r the r e c o v e r y had not s t o p p e d . A t t h i s p o i n t the r e s i d u a l s t r a i n w a s 1.4%. It i s i n t e r e s t i n g to c o n s i d e r w h e t h e r t h e s e r e s i d u a l s t r a i n s a r e r e v e r s i b l e in t i m e and w h e t h e r t h e y a r e a f f e c t e d b y the s u p e r i m p o s i t i o n of v i b r a t i o n s d u r i n g c r e e p . A c c o r d i n g l y , a f t e r 20 h r of r e c o v e r y the t e m p e r a t u r e in the c h a m b e r w a s i n c r e a s e d to +72 ° C in the c o u r s e of I h r and s u b s e q u e n t l y k e p t c o n s t a n t f o r 3 h r . A m a r k e d a c c e l e r a t i o n of r e c o v e r y w a s o b s e r v e d . T h e s t r a i n s f e l l f r o m 1.4 to 0.35% (with a l l o w a n c e f o r the c o e f f i c i e n t of l i n e a r e x p a n s i o n ) and c o r r e s p o n d e d to o n l y 5 - 6 % of the m a x i m u m s t r a i n s a f t e r unloading. T h i s i n d i c a t e s that the p r e s e n c e of r e s i d u a l r e v e r s i b l e s t r a i n s d o e s not d e p e n d on the n a t u r e of the p r e l i m i n a r y load. T h e d a t a in F i g . 4 i l l u s t r a t e the c r e e p and r e c o v e r y of L D P E u n d e r c o n s t a n t l o a d s with and without s u p e r i m p o s e d v i b r a t i o n s . T h e e x p e r i m e n t s w e r e c o n d u c t e d a t e i g h t v a l u e s of the s t a t i c s t r e s s . It i s c l e a r f r o m the f i g u r e that the c r e e p c u r v e s r e m a i n w i t h i n the c o n f i d e n c e i n t e r v a l s at all s t a t i c s t r e s s l e v e l s e v e n when v i b r a t i o n s a r e s u p e r i m p o s e d . S u p e r i m p o s i t i o n of v i b r a t i o n s d u r i n g the c r e e p p r o c e s s a l s o h a d no e f f e c t on r e c o v e r y ( F i g . 4b). To s u m m a r i z e , at s m a l l ( c o m p a r e d with a0) v i b r a t i o n a m p l i t u d e s (although a t r e l a t i v e l y high f r e q u e n c i e s , 300 and 1000 Hz) that do not c a u s e m e c h a n o h y s t e r e s i s h e a t i n g of the m a t e r i a l a v i b r a t i o n e f f e c t d o e s not d e v e l o p in the i n v e s t i g a t e d p o l y e t h y l e n e s at a t e m p e r a t u r e of +20 ° C. H o w e v e r , the v i s c o e l a s t i c i t y of t h e s e m a t e r i a l s , e s p e c i a l l y L D P E , i s n o n l i n e a r . T h i s is a p p a r e n t f r o m an e x a m i n a t i o n of the c u r v e s of F i g s . 2 and 4a in i s o e h r o n o u s c r - e c o o r d i n a t e s . T h i s r e l a t i o n s h i p i s i l l u s t r a t e d in F i g . 5. C l e a r l y , a s the s t r e s s e s and the d u r a t i o n of the e x p e r i m e n t s i n c r e a s e , the n o n l i n e a r i t y i s d i s t i n c t l y m a n i f e s t e d . H o w e v e r , this n o n l i n e a r i t y is not i m p o r t a n t within the s e l e c t e d r a n g e of Cra/Cro v a l u e s . T h e r e f o r e , the n o n l i n e a r h e r e d i t y e f f e c t l i k e w i s e d o e s not h a v e m u c h i n f l u e n c e on the n a t u r e of t h e v i b r o e r e e p c u r v e s [9]. A m o r e d e t a i l e d e x a m i n a t i o n of the c r e e p and r e c o v e r y c u r v e s r e v e a l s t h a t the d e f o r m a t i o n b e h a v e s d i f f e r e n t l y on the i n i t i a l s e c t i o n . If the u n l o a d i n g c u r v e i s i n v e r t e d and c o m p a r e d with the c r e e p c u r v e , the s i m i l a r i t y of the c o r r e s p o n d i n g c u r v e s i s d i s t u r b e d : the r e l a x a t i o n p r o c e s s e s in the t r a n s i t i o n r e g i o n p r o c e e d m o r e r a p i d l y in r e c o v e r y than in d i r e c t c r e e p . 184

POLYMER MECHANICS

20

30

~ur$

Fig. 4. Creep c u r v e s for LDPE: a) creep; b) r e c o v e r y after unloading. 1) ~0 = 16.6 kgf/cm2; 2) 21.6; 3) 24.6; 4) 30.1; 5) 34.8; 6) 39.8; 7) 45.3; 8) 51.6; ffa = 1.1 kgf/cm2; f = 300 and 1000 Hz. I n s t a n t a n e o u s - e l a s t i c strains excluded.

185

POLYMER MECHANICS

~s

o.m

b

J I ........

$2" hr~'/omin_~hr ~

~50

£z ~o

~0

ZO

~0

t -- Z rain 2 - - / 0 rain 3 ~ 3 hr #-30 hr

Fig. 5. Isochronous s t r e s s - s t r a i n d i a g r a m s : a ) H D P E , b ) L D P E .

OJ5 / .

.

.

.

/I/ O.~OP . I .JZ__.A

0,O.'

,/Y/ ! " i ,N i i

l

i 1

t

'-/

~Z

o.,,.,o.i,.!

- - t a r t e r unloading[

t.O

0.#

2.0

3,0

Fig. 6. Instantaneous strains f o r polyethylene (time base 1 sec): a) HDPE (H = 10 386 • 617 kgf/cm2), b) LDPE (H = = 2000 ± 107 kgf/cm2).

186

POLYMER MECHANICS

2.O

i

f

i /-'~ o

i

--c,

;

~

• without Vibration o with vibration

o z

I

,P "o

X ~ d a =¢8k g / c m T 0

iO

30

20

t ho~rs Z

~¢0

5O

Fig. 7. Vibrocreep of filled polyethylene: 1) o'0 = 36.4 kgf/ /cm2; 2) 63.6; 3) 80.0; 4) 100; f = 350 Hz.

.1

A

kg/cm~

~Z o

m

f5

zo

25

Fig. 8. S h o r t - t e r m s t r e s s - s t r a i n ourves f o r

LDPE with different fillers at a loading rate of t0 m m / m i n : 1) 2% gas black, 2) 10% uncarbonized CaSiO~: 3) 15% carbonized CaSiQ, 4) 15% uncarbonized CaSiO3, 5) 20% carbonized CaSiO3, 6) 25% carbonized CaSiO3.

187

POLYMER MECHANICS

In conclusion, we p r e s e n t experimental data on the instantaneous strains (time base 1 sec) for loading and unloading (Fig. 6}. Clearly, up to loading levels of 0.15 and 0.5R f o r HDPE and LDPE, respectively, the instantaneous modulus of elasticity may be assumed linear and the experimental data for loading and unloading lie within the same confidence interval. Numerical values of the instantaneous modulus of elasticity H, calculated by the method of least squares, are indicated in the caption to Fig. 6. The averaged creep curves for LDPE with filler are shown in Fig. 7. The tests were made at four values of the static s t r e s s . The figure shows that superposition of vibration on constant s t r e s s e s not exceeding 0.5R does not cause an appreciable change in the creep curves. However, at elevated loads ((r0 = 0.65R) the superposition of vibration led to a considerable acceleration of the creep, ending in failure of the specimen during the test period. Mechanoh y s t e r e s i s heating was not observed. The "vibration effect" detected in the latter case is evidently p r i m a r i l y associated with the accumulation of fatigue damage due to "embrittlement" of the polyethylene resulting from the introduction of a filler. This is indicated, in particular, by the ~ - e diagrams shown in Fig. 8 for a given r a t e of deformation of polyethylene with fillers of different composition. These curves show that as the percentage of filler i n c r e a s e s there is an appreciable increase in the instantaneous modulus of elasticity and s h o r t - t e r m strength, but the viscoplastic properties sharply deteriorate. F o r example, the maximum strain falls from 500-600% for lightly filled polyethylene (2% gas black) to 7% at a 25% (by volume} content of carbonized calcium metasilicate. CONCLUSIONS

1. We have investigated the v i b r o c r e e p of high- and tow-density polyethylene in the isothermal deformation r e g i m e (ambient t e m p e r a t u r e +20 ° C), when the superposition of vibration on the static load is not accompanied by m e c h a n o h y s t e r e s i s heating of the material. The introduct{on of vibration does not cause additional creep in the polyethylene and theoretical strain calculations can be based on the ordinary linear (at small strains) and nonlinear theories. 2. In polyethylene with a high filler content a vibration effect, accompanied by isothermal acceleration of the creep, o c c u r s at a t e m p e r a t u r e of +20 ° C, but in the region of higher static s t r e s s e s (more than 50% of the s h o r t - t e r m breaking stress}. REFERENCES 1. G. L. Slonimskii and P. I. Alekseev, DAN, 106, 1053, 1956. 2. G. I. Barenblatt, Yu. I. Kozyrev, N. I. Malinin, D. Ya. Pavlov, and S. A Shesterikov, ZhPMTF [Journal of Applied Mechanics and Technical Physics], 5, 68, 1965. 3. A. K. Malmeister, Mekh. polim. [ P o l y m e r Mechanics], 2, 197, 1966. 4. P. M. Ogibalov and V. I. Moroz-Shobolova, Mekh. polim. [ P o l y m e r Mechanics], 1, 46, 1967. 5. Yu. S. Urzhumtsev and R. D. Maksimov, Mekh. polim. [Polymer Mechanics], 1, 34, 1968. 6. R. D. Maksimov, A. A. Rutkis, V. P. Mochalov, A. P. Smala, and Yu. S. Urzhumtsev, Mekh. polim. [ P o l y m e r Mechanics], 2, 372, 1968. 7. V. V. Nalimov, Application of Mathematical Statistics to Chemical Analysis [in Russian], Moscow, 1960. 8. A. V. Putans and Yu. S. Urzhumtsev, Mekh. polim. [ P o l y m e r Mechanics], 4, 676, 1967. 9. G. I. Buyanov, V D. Kasyuk, N. I. Malinin, and B. I. Panshin, Mekh. polim. [ P o l y m e r Mechanics], 3, 330, 1966. 11 September 1967 Institute of P o l y m e r Mechanics, AS Latvian SSR, Riga

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