ON THE DURABLE STATIC STRENGTH

OF FIBER-REINFORCED PLASTICIZED POLYVINYL CHLORIDE

I~. S . U m a n s k i i

Kiev Polytechnical Institute Translated from Poroshkovaya Metal lurgiya, No. 2 (26), pp. 60-70, February, 1965

Original ar t ic le submitted May 6, 1964

Recent experiments have confirmed the hypothesis on the exclusively cr i t ica l character of the destructive pro-

cess. It has been shown that cracks and tears grow under loads which are less than the cr i t ica l loads; and moreover, the rate of growth depends on the loads, temperature and act ivi ty of the environmental atmosphere. The strength of various mater ia ls therefore depends on the t ime for which the mater ia l remains in the strained state, i . e . , a re la t ion- ship exists between t ime and strength which under constant stat ic loading sometimes produces static fatigue in the mater ia ls .

Many investigators have revealed the existence of a t ime-s t rength relationship for glass [1-4], plastics [5-16],

rubber [8, 17-20], metals [22-27], wood [28-32] and data on the durable strength of fibers and yarn are given in paper [aa].

For a range of mater ia ls S. N. Zhurkov and his col leagues [8-12] have shown that the t ime-s t rength re la t ion- ship obeys the exponent ia l rule

tE =Ce kr , (1)

where t B is the duration ( t ime from ini t ia l appl ica t ion of the load to rupture of the specimen); o is the true tensile

strain; C,~, are constants; U is the energy of ac t iva t ion of the process leading to failure; T is the absolute t empera - tare; and k is the Boltzman constant.

The same relat ionship was also obtained by Busse and coworkers [5] for cords made of cotton and viscose fibers.

At the same t ime experiments show that in some cases there are deviations from formula (1). Thus, for s i l ica te glasses [1, 3], rubbers and in general rubber - l ike polymers [8, 16-20], some meta l l i c alloys [27] the rule for change in durabil i ty does not follow Eq. (1). In these cases it can be considered that the relat ionship between the logari thm

of duration and the logari thm of strain is l inear . Thus, at a given temperature the t ime-s t rength relationship for mos t mater ia ls takes the form:

t~ = Ae - a ~ . (2)

For rubber- l ike polymers and cer ta in other mater ia ls

IB = B a - b , (3)

where the coeff ic ient b does not depend on femperature but the coefficients c~, A and B do depend on it.

The discovery of a t ime-s t rength relat ionship for mater ia ls is of great theore t ica l and prac t ica l importance. Spec ia l value is a t tached to this relat ionship for h igh-polymer mater ia ls where in view of the known features of struc- ture and nature of deformat ion mechanisms the t ime effects are very not iceable even at room temperature . As stated, for many polymer mater ia ls , including glass-plast ics, the durable resistance has been quite thoroughly invest igated. However, as far as we know, the l i terature contains no account of the durable stat ic and dynamic strength of soft composite mater ia ls made up of a combinat ion of natural or synthetic fibers and plas t ic ized polyvinyl -chlor ide f i lm (for short we shall ca l l these AVP). Cotton f leece is more often used as the fibrous base, and the impregnating poly- mer is usually p las t ic ized polyvinyl chloride (90 parts by weight of p l a s t i c i z e r - d i b u t y l phthalate, per 100 parts by weight of Igel i t -R polyvinyl -ch lor ide resin).

136

Fig. 1.

e~ze Mn tm 2 a=n Mn/m 2

~-29 Mn/m, ~ ~4~Mn/m2

/ / / V / l i " ' / /

/ "/ ,/ I /

/ 1 i7 / l:.

i , ./ I I , I

�9 / ! i , P, /~1

/ .I I / / / / I / / /

t �9

1,0 /.~ Z,~ 7,2 2.0 3.0 4, ~2 1.6 2,o 2,4 2,a a,2 ~, 40 4.* logt , sec

Integral distribmion curves for log durability of AVP based on oriented

cotton (series 2, m = 0.8) for different load levels.

Up,s p,.,~ a 99,9

99,5 99

7 97 95 9O

6 80 7O O0

5 50

3O 4 20

10

3 !

0.1

Fig. 2.

~=22Mn/m 2

@'5. ? % 6:3I Mn/rr~ ~':~0 Mn/rn 2

et~ i /'/ ' I,,,l ] ' / / 9~ / / I /

, .,l / " / �9 ,~. , , ~ / / i t

//2.- .;,,, I, / / /" F/ /~'

/

/ �9 g ;i!/ / / / ,//" ) I I

/ i i I

/ ! / I ! / ,

0.6 l0 ~.* ~,a U 26 a0 3,4 a,8 4,2 Z* Z8 12 g6 40 44 4,a log t, sec

2.0 Z4 7.8 t2 16 4,o ,,~ 40

Integral distribution curves for log durability of AVP based on oriented

cotton (series 6, m ; 0.4) for different load levels.

Impregnation is done at 170"C and the specific pressure is of the order of 4.0 Mn/m z. Anisotropic material is formed

by impregnating fibrous wraps of the or iented-f leece type, and quasi-isotropic materials are obtained by impregnating twisted warps.

This article gives experimental data on the durable strength of AVP of oriented and crossed cotton warps. The relationships between the durable strength and the change in the form and composition of the warp, the number of

fibers and films in the materials, etc.,were determined. It might be expected that the features established for the

durable strength of AVP are peculiar also to other reinforced structures, especially certain types of reinforced me ta l - loceramic materials.

The durable static strength of AVP was studied for materials with oriented and crossed cotton warp with differ- ent weight ratios of fiber and pvc film. Specimens in the form of "double-sided" vanes 3 mm wide and 30 mm long were cut out in the main direction of the fibrous fleeces. The variations over the thickness of the specimens were slight.

Tests were done by the usual method for several levels of constant strain for each of the series. For each strain level to get reliable results the durable strength was measured on from 18 to 60 specimens. All tests were done at

137

l&*~ q,%

7

6

5 / zX

//:i i 1 /

/ . I /

, ' / , 2

Fig. 8.

d.2,~ Mn/m 2

2 / , /

i ' / / / =, ~ / ( / /

/ / ~ " "~ I I "

~..i : ! ~ . / " / i . t /

L,.ils, i~ / I , , I

I / /

/ / /

V / .~,2 .o,8 "4~ o o,~ o.e ~,z ta z,o

O.22Mnlrn~=eu Mnlm 2 / " /

V i I ,#" / / " i o!I

/ 2 f / / I I /

1 .4 / #G

/ r l I I . l

/ I " ~'J / / / /

, / / / ' / I

/ / i~

1.6 gO 2,4 2.8 ~2 3,6 40 */, logt , rain

O @ 48 #,2 ~,6 2.o 2,* 2,a l z ~,6 ~,o 4,~

Integral distribution curves for log durability of AVP based on oriented cot-

ton (series 1-grind, m = 1.0, specimens ground).

8

7

6

5

i

3

(5-Z3 Mnlm ~

.99s I I / / ~ I . I �9 gl / / / / 9,~ i . , go , . / i 80 I I I / lO I ; ' / 60

30 I ' , I I / , . ' j l I I J

2~ I.I I / ",~" !1 3 # # I I

, l i ;l l / I/ O j A / ~, I / " / ! 1

@ Od/,Z #,~ 20

0 -21Mnlm 2 6--l.QMnlm z

, / / I / / "/ '

' / / / / / < t I _l J" 1 I I / " / /

/ f : . / " I / ' 1 ., J ." . / / / i,,I/.. ,, ..

, .:. / , f ; , / / i / . ' /

~:. I I i i

/ / 7 "z I . / r~ / I / I I

I " J

I ' / / I I , . I I I /

t2 ~6 ~,0 2,~ 2,8 3,2 3.6

/ F

/ 1

/

lO I,~ 1,8 ZZ Z~ 3.0 3,4 2.63.0 3.1, 3.8 42 ~.6

Fig. 4.

(~,nMnlm z

/ E / / /

/

log t, see

Integral distribution curves for log durability AVP based on crossed cot-

ton (series 12, m = 0.8) with different load levels.

18-20~ on a special frame designed for investigating the creep of viscous and elastic materials and suitable for the

simultaneous testing of 6 specimens. It should be mentioned that the mobile table incorporated in this device quite rapidly and smoothly transfers the load to the specimen. Since the cross-sectional area of the AVP specimens under strain changes slightly [8, 4] then it is possible to consider that the constant-load tests also correspond to the test schedule with constant nominal strain.

The group of materials based on oriented cotton was divided into series 2, g and 6, corresponding to the weight

ratios of the cotton and film, m = Qc0tton/Qfilm = 0.8, 0.g and 0.4. To explain the effect of gr iming the "back" side of the mater ial (the effect of cuts in the surface) data were obtained on the durable resistance of the ground specimens in series 1 (m = 1.0) and 2 (m = 0.8). The grinding was done along the direction of the fibrous f leeceset-

ting on the 8hMMK-2 machine with corundum saws No. 60. The durable strength of the AVP based on crossed cot- ton 12 (m = 0.8) and 16 (m = 0.6).

The process of pressure impregnation, which is irregular in density, predetermines the static distribution of the impregnated composition and fibers in various parts of the material when uncrossed fibrous warps are used. The free orientation and movement of the unsupported component (the reinforcing fiber) during the process leads to statistical

1.38

TABLE 1. Characteristics of Durability of AVP with an Oriented Cotton Warp

(Specimen cut "along the fibers")

Series m y-

Q c o t t o n Constant strain, Mn/m 2

Average Number log dura- iofspec- bility, imens log tB,sec

log tmin l o g t ma~

s e c

I'm,,_---- log t8

31,0

30,0

29,0

27,0

23,5

23,1}

22,0

21,0

20,0

19,0

20

25

25

20

13

34

18

10

18

20

2,596

2,877

3,323'

3,697

3,280

3,395

2,644

2,88 c

3,27(

3,866

1,176 3,314 1,845 3,744 2,230 4,272 3,086 4,082

1,996 3,948 2,111 4,484

1,000 3,709 1,929 3,921 2,086 4,378 2,816

0,589

0,4547

0,528

0,318

0,599

0;618

0,752

0,675

0,718

0,449

0,23

0,16

0,16

0,086

0,18

0,18

0,28

0,23

0,22

0,12

1o~ t sec2 i

\ \ \ k "\ \

:0 \ \ \

t.5 t,2 1.3 1,~ 1.51og5 Mn/m 2 "

Fig. 5. Relationship between the average durability of AvP based on oriented cotton and strain: 1) series 2 (m = 0.8); 2)series 6 (m : 0.4).

type of strength pattern and deformability [34, 35]. There is a par- ticularly wide scatter in the values for the time needed for the de- struction of the specimens at a certain constant strain. Therefore, without the appropriate statistical processing of the test results and determination of the rules for distribution of the durability values of the specimens at each load levels it is impossible to get reliable results for the durable strength of AVP.

The statistical treatment of the results for durable strength was done on the basis of the logarithmic normal rule for the distri- bution of durability [26, 36, 87]. The experimental points at each loading level for all the types of AVP studied were plotted on nor- mal probability paper along the axes of which were plotted the ac- cumulated frequencies of failure, and along the abcissa of which the logarithm of time prior to the failure of the specimens (Figs. 1- 4). As the diagrams show, the experimental points deviate haphaz- ardly from straight lines, which allows us to assume the normality of distribution for log of durability (log tB). Thus, the most probable value for the logarithm of durability at a given level of strain will be the mean value

.I 2 X = l o g & = -n - - ( l o g t . h ,

i = 1

(4)

and the scatter will be characterized by the mean square deviation

( ' 2 S= n--1 i = 1

[(logtB)~ - - l o g tB] 2 (5)

139

TABLE 2. Characteristics of Durability of AVP Based on Oriented Cotton (Specimen cut "along the fibers;" film ground on "back" face)

Series ~=QcottoE Qfilm

} Number ] Mean I Constant I

I log dur a - l z - - - - - - load, [ of spec- [vaIue of [log tmi n

[ bility, [ x~ tmax M n / m z I linens

I [log tB,sec I

v_____ ~ lo~t~

12

15

2~,0

22,0

21,0

20,0

19,0

17,0

20

25

18

28

20

20

19,0 20

18,0 25

16,0 17

14,0 15

1,015

1,518

2,092

2,242

2,649

3,827

0,715

1,158

2,352

3,888

0,477 1,699

_o,602 2,778

1,114 3,210 1,079 3,441 1,398 3,637 2,700 4,564

0,301 1,740

_0,301 3,380 1,380 3,923

_2,797 4,652

0,440

0}598

0,592

0,7429

0,632

0,5323

0,389

0,9172

0,6882

0,5212

0,43

0,39

0,28

0,33

0,24

0,14

0,53

0,78

0,29

0,13

log sec )j 1 so \ \

\ \

\

k\ zo \ \ \ \

\ 1.0

t2 t,3 l,t, log o, Mn/m ~

FiR. 6. Relationship between average durability of AVP based on oriented cotton and strains, for ground speci- mere: 1) series 1-grind; 2) series 2- grind.

Since the empirical values for X" and ~ are also of a random char- acter, since they vary with repeated experiment, then for greater re- liability in assessing the parameters for the logarithm of durability at each loading level we determined the confidence limits, which, with 95% probability, consist of the general values of durability a and the mean square deviation S:

- ~ - -~

x - a x + t.,k;

-S / n - l Z1~< S -~ ]// / n - - ~ z ~ .

In these formulas the coefficients tq, k, Z1 and Z z depend on the confidence probability and the number of specimens. Using the values found for log t B and S we drew the middle lines on the graphs and from the confidence limits applied the confidence regions shown in Figs. 2-6 by the thin lines. The main characteristics of the durability of AVP based on oriented and crossed cotton with different strain levels are shown in Tables 1-3.

The time-strength relationship for AVP of different types and composition was drawn in logarithmic coordinates. As Figs. 5 and 7 show, the experimental points consisting of mean values of durability, should in general follow a straight line. Thus, in me range being studied it can be considered that the relationship between mean durability and constant strain for AVP based on oriented and crossed cotton at a given temperature, as for rubber-like polymers,

is determined by formula (3).

t40

TABLE 3. cut in main direction of fleece arrangement)

Series

I grind

2grind

4 grind

Characteristics of Durability of AVP Based on Crossed Cotton ,( Specimen

Ic~ [ load,

1Qfilm I Mn/mz

Mean Number value of ~f spec- [ogdura- mens bility,

logtB,se

2,3570

3,3980

4,0853

5,0901

1,7180

2,1940

3,3360

44 4,2885

45 1,9080

37 4,9540

28,0

25,0 1,0

22,0

20,0

28,0

0,8 25,0

22,0

20,0

25,0 0,57

17,0

log tmi n log tma x

0,623 3,756 1,477 4,084 1,778 6,051 3,697 6,075

0,079 2,892 0,699 3,369 1,477 4,714 3,28_____3 5,929

0,000 3,774 2,477 6,316

0,726

0,448

1,04'I

0,538

0,814

0,727

0,673

0,550

1,035

1,022

0,307

0,132

0,~56

0,I06

0,473

0,332

0,200

0,128

0,540

0,207

log t B, sec

3.o \ \

2,0

7.0

0 tl t2

\

\

t31og~Mn/m 2

Fig. q. Relationship between mean durability of AVP based on crossed cotton and strain: 1) series 12; 2) series 15.

TABLE 4. Values of Coefficients B for Various Types of AVP with Cotton Base

Type of base

Oriented

Oriented (ground specimens)

Crossed

Series m = Qcotton Qfilm

2 0.8 6 0.4

1-grind 1.0 2-grind 0.8

12 0.8 15 0.5

B, sec (Mn/rn2) z~

2.51. 1032 2.63" 1029 1.10. 1031

3.58" 10 a~ 2.69" 1028 3.72" 1026

Straight lines expressing the relationship between the mean logarithm of durability and the logarithm of strain are practically parallel for AVP of different composition with the stated type of base (Figs. 5, 6, 7). They are also practically parallel for AVP based on oriented and crossed warps as seen from Fig. 8 where the lines 1 and 3 respectively represent the t ime re- lationship for AVP on an oriented and crossed cotton warp with the same

weight ratio of cotton and film in the material, and line 2 refers to the oriented material of the same composition but after grinding of the "back" side. Consequently, we can conclude that the constant b in formula (3) does not de- pend on the character of the fiber arrangement in the base (warp) and the weight ratios of fibers and film of plasti- cized PVC in the material .

Processing the experimental data for all series using the minimum squares method shows that b can be taken as approximately equal to 20. Thus, for AVP based on cotton the t ime-strength relationship can be expressed in the following form:

ts = Be-2~ (6)

As Table 4 and Figs. 5-8 show, the magnitude of B (and with it the durability) largely depends on the arrange- ment of the fibers in the warp and the weight ratios between the fiber and film in the material. With increase inthe

141

~'o,5~ tB, sec

3 2

\ ~0

1,0

I |

5N I | l i pi iN IN

0

k \ \

\

/,2 /.3 1,4 log ~.Mn/m ~

Fig. 8. Relationship between durabi l i ty

and strain for unground and ground spec- imens from series 2 (or iented warp) and 12

( crossed warp).

logtB, e d 2 ) 4 5

\ \ \ \ \ \ \ \ \ \

3.o

x\'A\

U Z2 1.31og ~Mn/m z

Fig. 9. Diagram of durable strength

of AVP with crossed cotton warp, series 12. Probabili ty of fai lure, %: 1) 5; 2) 10; 3) 50; 4) 90; 5 )95 .

quantity of fibers in the mate r ia l of this type the durabil i ty increases

sharply for the same strain. Thus, the rat io of mean durabil i ty for specimens of oriented mater ia l in series 2 and 6 with the same strain is ( t B) series 2

955, while the quantity of fibers in series 2 mater ia l is ( t B) series 6

double that of the number in series 6, S imi lar ly for series 12 and 15

AVP on a crossed warp, with a difference in the fibers of 1.6 t imes,

�9 (t B) series 12 the rat io of durabi l i t ies with the same strain zs (-@B) series 15 ~ 72.5.

There is a very sharp rise in durabil i ty with the change from crossed warp to oriented of the same composit ion (with the strain "along the fibers"). Thus, with the same strain the ratio of durabil i ty

�9 (tB)series 2 of specimens in series 2 and 12 (m = 0.8) ts (tB)series-- -~2 ~ 9350.

Thus, the characterist ics of durabil i ty in AVP with a static con- stant load are much more sensitive to changes in the number of fibers and their arrangement in the warp than the rupture strength obtained from short- term standard machine testing [34, 35]. The simplest

method of getting a sudden increase in the durabi l i ty is to increase the number of fibers in the warp.

The data obtained permit us to assess the effect on the durabil i ty of AVP of grinding the "back" sides of the specimens, i . e., the in- f luence of cuts on the surface of the specimens obtained by corundum saw No. 60. As Tables 1-2 and Figs. 6-8 show, grinding great ly re- duces the durabil i ty of the specimens. Thus, for series 2 and 2-grind (m = 0.8) the ratio of durabi l i ty with the same strain is ( t B) series 2 (t B) series 2-grind ~ 70, while the ratio for mean values of rupture

strength obtained from standard machine tests is only 1.12.

It is of interest to analyze the nature of scatter of the durabil i ty results for various types of AVP. The scatter character ized by the mean square deviat ion S ( log t B) with a reduction in the strain diminishes for a l l series of oriented AVP studied when testing "along the fibers." For mater ia ls based on a crossed warp we note a reverse tendency; the

mean square deviat ion increases with reduction in strain. Thus, the nature of the scatter for durabil i ty of AVP under prolonged static test-

ing may be connected with the degree of anisotropy of the specimens. When tests are made on anisotropic mate r ia l which has been cut in the direct ion of highest r igidi ty, the scatter of the durabil i ty values diminishes with reduciion in the strain, and when the tests are done with quasi- isotropic AVP the scatter of the values for durabil i ty increase with reduction in strain.

In conclusion we observe that the exis tence of curves for the distribution of durabil i ty for different levels of strain makes it possible to draw comple te diagrams for the durable strength of the mater ia ls being studied from the pa ramete r of the probabil i ty of fai lure . This diagram for AVP based on crossed cotton warps series 12 is shown in Fig. 9.

L I T E R A T U R E C I T E D

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A l l a b b r e v i a t i o n s of p e r i o d i c a l s in the a b o v e b i b l i o g r a p h y are l e t t e r - b y - l e t t e r t r a n s l i t e r -

a t i o n s of the a b b r e v i a t i o n s as g i v e n in the o r i g i n a l R u s s i a n journal . Some or all o f th i s per i -

od i ca l l i t e ra ture m a y wel l be a v a i l a b l e in E n g l i s h t ranalat ion. A c o m p l e t e l i s t o f the c o v e r - t o -

c o v e r E n g l i s h t r a n s l a t i o n s appears at the back o f t h i s i s s u e .

143