Proceedings of the Institution of Mechanical Engineers, Conference Proceedings-1963-Serensen-3-93-8

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DOI: 10.1243/PIME_CONF_1963_178_046_02

1963 178: 3-93Proceedings of the Institution of Mechanical Engineers, Conference ProceedingsS. V. Serensen and V. S. Strelayev

Paper 77: Creep Resistance and Low-Cycle Fatigue of Fibreglass Plastics

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3-93

Paper 77

CREEP RESISTANCE AND LOW-CYCLE FATIGUE OF

FIBREGLASS PLASTICS

By S.

V.

Serensen and V. S. Strelayev*

WHEN

ESIGNING CONSTRUCTION

PARTS

made of fibreglass

plastics one should take into account their creep and

low-cycle fatigue resistance. Different theoretical and

experimental relationships have been developed to de-

scribe the properties of high polymer materials under

various loading taking into consideration the influence of

time and temperature I>~-- IO).

There is some difficulty, however, in applying the

data obtained for designing constructions because the

results of mechanical testing show large scattering. This

scattering is connected with considerable size effect in

failure conditions as a result of the instability of the

properties of these materials.

Warm hardened plastics were put to the test both on

epoxide a,= 42-46 kg/mm 2) and pheno l-formaldehy de

(ultimate strength cr = 20-25 kg/mmz) binding with

oriented fibreglass reinforceme nt in two norma l directions.

T h e testing was carried o ut on the machines with auto-

matic constant load control and creep deformation

measu remen t. Th e cross-sectional area of a specime nvaried

between

25

and 100mm2. A sufficient num ber of specimens

were tested to permit the statistical treatment of results.

The creep-rupture curve of the specimen with the cross

section of 25 mm2 is plotted in Fig. 77.1 for different

values of failure probability. T h e data obtained show that

at low probability the slope of the curve to the axis T

diminishes and th e creep life only slightly depends on the

value of stress. The mean curve is linear for large stress

values but for the stress values less than 05-060 this

curve deviates from the line according to the expression

Th e point corresponding to the short time tension test is

situated high above the curve. This fact appears to be

accounted for by the varying of stress during loading and

The M S .

of

thispaper was received at the Institution on 25th March

Academy of Sciences, Ukrainian

S.S.R., Kiev U.S.S.R.

t 4 numrrical list of references s

given

in Appendix 77.1.

= Ae-c'

IY63

(A) .

the data

of

such a test cannot be compared with those of a

constant and uniformly distributed stresses test of the

same duration.

As is indicated in Fig. 77.2 the creep test data show

that the deformation ceases when the stress falls to

0.5-0.60,. It is possible to express the equation

of

a

creep curv e for fibreglass plastics in th e following form :

the parameters of this expression for epoxide plastics

being C = 4.515 x

m

= 2-4706 and n = 0.2531, and

for phenol-formaldehyde plastics

C =

9 4 3 ~

o-', m

=

1.61 and

n

= 0.342.

A

comparison was made between creep deformation

and creep-rupture curves (150-170 h for phenol plastics

and 250-300 h for epoxide plastics). T h e comparison

shows that the ceasing of creep deformation and the

deviation from linear dependence o-log T arise nearly at

the same time. The creep curves for fibreglass plastics

do not have the third part and the rupture occurs after

exhausting high elastic deformation. The mechanism of

creep deformation seems to be an activation process, and

at stress less than

0.50,

the materials do not break and

creep deformation stops at the time when all the loading

passes on to th e fibreglass and the binding m aterials cease

resisting.

The statistical treatment

of

data on the basis of the

linear correlating analysis (the dispersion of the lifetime

slightly depends on the stress level) gives the coefficient

of correlation between the stress and the logarithm of

time within

0.65-045,

i.e. there exists a close linear

dependence between these values.

It

is possible to use

both the exponential and the power equation for the

creep-rupture curve because the time dependence is low.

T he linearity of dependence 0-log

T

enables one to use

for practical purposes the parametric expression of the

following type :

o

= a - C . p

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3-94

S.

V. SERENSEN AND V.

S.

STRELAYEV

40

i

25

2ooc

1

P

= 95

2 0I

10

lo2

10.

lo4

1

o5

r -m in

Fig.

77.1.

Creep-rupture curves

o

an epoxide jibreglass pla stic

fo r

different probabilities o rupture

where p

=

T(c+log T ~ arson-Millers parameter (12)~

for evaluating t he lifetime of fibreglass plastics at mode rate

temperature.

Cree p-rup ture curves for fibreglass specimens of

different size and different stress concentration are illus-

crated in Fig. 77.3. The effect

of

stress concentration on

the creep-rupture curves is moderate. It is probable that

the stress concentration diminishes as a result of re-

distribution in the notch during the first minutes of

loading and later on the rupture is determined by the

action of constan t value stress close to th e nominal.

Different slopes of creep-rupture curves for smooth

specimens are accounted for by the size effect on the

rupture under the continuous static loading. Hence

it

is

possible to utilize the statistical interpretation of results.

As stated above

(11),

it is possible to describe the size

effect at th e tension test of fibreglass oriented plastics by

Weibulls theory of brittle fracture 13). T he experimental

data show that for different times of rupture the size

effect

in

the case of rupture under continuous static

loading is fairly well described by th e expression:

following from Weibulls statistical relationships. Here

uF1 and uFzare the rupturing stresses for the given times

of loading of th e specimens with th e cross sections F and

F 2

and

M

is the index of Weibulls function. T he points

theoretically calculated are plotted in Fig.

77.3.

T h e testing un der cyclic loading was carried out u nder

repeated tension by pulsating cycle. The frequency of

loading ranged from 10 to 400 cycles/min.

It

was found

that comparatively low loading frequency (200 cycles/min)

gives rise to a marked heating of fibreglass plastic speci-

mens when th e deformation amp litude rises as high as

0.8

per cent. This effect is connected with a hysteresis loop

that results from the form of a cyclic stress-strain dia-

gram under cyclic loading.

Low-cycle fatigue curves are plotted in Figs 77.4 and

40

m 30

9

0

X

C

c

L

P 10

LIPl--_Pl

0 40 80 12

5 - hou rs

calculated data.

x experimental points.

Fig. 77.2.

Creep deformation curves

of

a

phenol jibreglass

plastic

77.5. The statistical treatment of the experimental data

show that th e left-hand part of the fatigue curves can be

described by th e following expression:

umN= constant

the index m varying between 8 and 20 depending on the

type of material and the frequency of loading.

T he sca ttering of fatigue life decreases with th e increase

of maximum stress value as is the case with metals.

Fig. 77.6 shows the scattering of fatigue life of phenol

and epoxide plastics.

As

evidenced by th e data in th e case

of the above materials, their experimental results deviate

from linear dependence

in

the co-ordinates the prob-

ability of rupture plotted against the log of the number of

cycles, when the value of stress falls to 0 . 7 ~ ~ .h e foregoing

evidence indicates that a m inimum fatigue life does exist.

This minimum fatigue life is observed for metals at the

stress level close to the fatigue limit. In accordance with

this the probability distribution of fatigue life is described

by Weibulls expression :

N-No

pN= 1-exp -T)




CREEP

RESISTANCE AND LOW-CYCLE FATIGUE O F

FIBREGLASS

PLASTICS

3-95

L

10

10 lo3 lo4 1o5

h n

1

one-oriented fibreglass, cross section

40 mmz;

2

and

10

-fibres

in

two

normal directions;

2 and 8 cross section

25 mmz;

3

and

9

cross section

50

mm2;

4

cross section

100

mm2;

5 -

cross section 25

ma

two-sided notch with

p

=

2 9

mm;

6 -with p = 1.25;

7

-with

p

=

0.25;

10 120

mm2;

x

- calculated data.

Fig.

77.3.

Creep-rupture curves of epoxide

(2,

3

4, 5,

6 and

7 )

and phenol-formaldehyde I , 8,

9

and

10

plastics

32

N 28

E

E

m

I

.

24

20

I

2

I

A 10

cl rnin

r = o i

200

1 -P=95

2--P=50

3 - P =5

___

lo2 1

o3

lo4

l o 5 106

Fig.

77.4.

Low-cycl e fat igue curves of epoxide jibreglass fo r difJerent frequencies of loading

where PN = he cumulative probability of ruptu re;

N

=

the number of cycles before rupture which

corresponds to a given probability;

No=

he m inimum fatigue life;

N = he number of cycles corresponding to the

probability of rup ture

63.2

per cent; and

nz = he slope of the distribution curve in the co-

ordinates 'the probability of rup tur e plotted

against the log of the number of cycles'.

The probability of rup ture was determined in terms of

i-

0.5

n

where = he ordinal number

of

a specimen in the series

along the increasing fatigue life, and

Fig.

77.7

shows that the distribution curves are linear

in the co-ordinates P,v--log (N-No). After introducing

the minimum fatigue life the index

m

only slightly depen ds

on the level

of

stress. Th e upp er curves in Figs 77.4 and

77.5 correspond to th e probability

of

failure

95

per cent,

the medium 50 per cent, the lower 5 per cent. One can see

from these figures that under cyclic loading,

as

well as

under continuous static loading, the lifetime depends only

slightly

on

the stress level and the low probability of

rupture.

n =

the total number of specimens tested.




3-96

S. V.

SERENSEN

A N D V. S . STRELAYEV

1o3 1o4 lo5 1 6

N

Fig. 77.5.

Low-cycle fatig ue curves of a phenol-formaldehyde

jibreglass plastic

for

different probability of rupture

5

l o3

5 lo4

5

105 5

N

1

vmdx=

32

kg/mm2; 2 30 kg / m m a ;

3

27 kg mm2

Fig. 77.6. Distribution curves of fatig ue lives of a n

epoxide jibreglass plas tic PN

og N

4 25

k g / m 2 .

It

is of great interest to compare the results of creep

rupture and fatigue tests taking into account the pre-

dominating influence of time on the rupture of fibreglass

plastics under static and cyclic loading. Under the

conditions of continuous testing, and assuming the rupture

processes in fibreglass plastics with high polymer binding

to be irreversible, one can determine the fatigue life

of

materials under cyclic loading on the basis of the creep-

rupture curve assuming the cumulative damage effect to

be in the following form 15):

j;$=l

where

T

= the lifetime for the given condition of loading

and

T~ = the lifetime according to the creep-rupture

curve for stress level

a

(on the left the creep-

rupture curve is described by the expression

T = Ae- ).

Substituting the sinusoidal form of cycle for the triangle

in the case of cyclic tension loading one can put

N =

1

2jOTi2:

where T = the period of loading and

N

= number of cycles.

a

T

1

Therefore T =

2 1-exp

(-+a T)

where = the velocity of loading and unloading;

T = the lifetime under cyclic loading with the

amplitude

After simplification one obtains

i.e. the calculated lifetime under cyclic loading aa times

greater than the lifetime under static loading.

Fig. 77.8 gives the creep-rupture curves in comparison

U

=

U,in+UT

=

~ C T T ~

98

95

85 __

75

65

55

45

35

25

2 0

15

1

a>

5

2

102 5 lo4

5

10

5

106

N No

Fig. 77.7. Distribution curves of fatig ue lives




CREEP RESISTANCE AND LOW-CYCLE FATIGUE

O F

FIBREGLASS PLASTICS

3-97

5

103

5

104 5 1 6

Fig.

77.8. Creep-rupture curves of an epoxide

(1-

crosr section 25

mm2;

2

-cross

section 55 mm2;

3

-cross

section

100

mm2)

and phenol-

formaldehyde

(7

cross section 25 mm2; 8 cross section 50 mm2; 9 -

cross section 120 mm2)Jfbreglassplastics in comparison with low-cycle atig ue

curves 4 frequency 10 cycles min; 5 200 cyclesimin; 6 - 400

cyclesjmin-epoxide fibreglass plastics;

10 200

cyclesjmin-phenol

fibreglass)

10 5

lo2

'min

I

10 102 1o3 l o 4

00

trnin

A -calculated data.

Fig. 77.9.

The comparison

of

experimental fatigue curves with the results obtained

by calculating equ ivalen t ruptur ing stresses according to creep-rupture curves

with the fatigue curves plotted v e r w the t ime up to the

rupture in terms

of

the double logarithmic co-ordinates.

As is clear from Fig. 77.8 under the same level of stress

th e lifetime und er cyclic loading is much lower than under

continuou s static loading. Th us, w ith increase in frequency,

the difference increases. Not only the time of loading bu t

also th e cyclic effect connected w ith heating influences the

lifetime.

Cyclic deformation takes place mainly at somewhat

higher temperature. The refore the eva luation of equivalent

static stress values was carried ou t according to th e creep-

rup ture curves corresponding to the temperatures at each

level of stress under cyclic loading.

The results obtained are shown in Fig.

77.9.

T h e

calculated points are situated near the experimentaI

curves. Th e upper curve corresponds to t he frequency of

10

cycles/min, the medium 200 cycles/min and the lower

400

cyclesimin.




3-98

S. V. SE REN SEN AND V. 9 STRELAYEV

CONCLUSIONS

1) For fibreglass plastics with oriented fibres the creep-

rupture curve at stresses higher than 0.5-0*6aU s de-

scribed both by means of exponential and power equations.

For the evaluation of rupturing stresses Larson-Millers

parameter can be used. The creep deformation curves

in this area can be considered to be similar and the value

of deformation is expressed by the power function versus

time and stress.

2) The creep-rupture curve at stresses lower than 0.5-

0 . 6 ~ ~

s blocked and the time necessary for rupture is

indefinitely increased; the creep processes in this area

cease.

3) The value of rupturing stress under continuous

loading decreases with the increase in the size of speci-

mens according to Weibulls statistical theory of brittle

fracture.

(4)

The low-cycle fatigue curve is described by means

of power expressions and the probability of rupture is des-

cribed by the straight portion of the normal log distribu-

tion line after introducing the minimum fatigue life.

(5)

The main factor determining the rupture under

cyclic loading is the time. The fatigue curves can be

obtained from the creep-rupture curves on the basis of

the linear cumulative damage law.

APPENDIX 77.1

REFERENCES

(I) JURKOFF,

S.

N. e t al Journ Techn Physics

(Russian)

1953

(2)RABINOWITCH,. L. High Molecular Combinations

1959 N7.

(3)

BARTENEFF,

.

M.

Journ. Techn. Physics

(Russian)

1954

24.

4) FINDLEY,

.

5) HSISAO, . J Polymer Sci.

1960

44.

6)

GOLDFEIN,

. Mod. Plast.

1954

32,

N4.

7)

REGEL,W. R.

Journ.

Techn. Physics (Russian)

1951

21.

8) BELIANKIN,

. P.

9 )

ARRHEMINS,

.

23,

N10, 1.

Mod. Plast.

1957

34,

N7.

Deformation and Resistance

of

Wood,

Acad. Scien. Ukr.

S.S.R. 1957.

Zeitschrift Physic. Chemie

1889

4.

10)HAGEN, .

(11)

SERENSEN,

. V.

et al. Westnik Machinostrojenia J . mech.

12)

LARSON,. and MILLER,

Trans.

Amer. SOC.Mech.

Engrs.

(13)

WEIBULL,W. Proc. roy. Swed. Znstit. Eng. Research

1939

14) REGEL,W.

R.

Some problems on the strength

of

a

solid

15)

BAILEY,

.

Kunststoffe

1959

Bd.

49, 3.

Engng

1962

N3.)

1952.

N151.

body, Akad. Scien.

U.S.S.R. 1957.

Glass. Znd.

1939

20,

Nl.


Proceedings of the Institution of Mechanical Engineers, Conference Proceedings-1963-Serensen-3-93-8

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