Polymer Testing 6 (1986) 37-45

One-Day Test to Predict Long-Term Mechanical Behaviour of Plastics for a Yeart

A. V. Shenoy and D. R. Saini

Polymer Science and Engineering Group, Chemical Engineering Division, National Chemical Laboratory, Pune 411 008, India

SUMMARY

A new method is suggested for determining the long-term mechanical behaviour of plastics through short-term tests. A procedure for coalescing curves of stress versus log time creep data for various polymers is shown. The master curves generated have been shown to be independent of the percentage strain and temperature at which the creep data were obtained. The advantage of the master curve is in predicting the creep behaviour of a particular specimen for a year through the generation of creep data for only a day. The suggested approach has immense utility in design calculations and a high order of economic benefits.

1. INTRODUCTION

Plastics are being increasingly used in load-bearing applications and hence their dimensional stability in long-term performance becomes an essential feature of design calculations. The basic data necessary to predict the capability of a rigid plastic object of withstanding modest tensile or compressive loads for long periods of time without change in dimensions or shape are provided by creep as well as stress-relaxation tests.

t NCL Communication No. 3681.

37

Polymer Testing 0142-9418/86/$03-50 (~) Elsevier Applied Science Publishers Ltd, England, 1986. Printed in Northern Ireland

38 A. V. Shenoy, D. R. Saini

Creep is the time-dependent relative deformation which results from the application of a constant stress to a solid at a constant temperature, whereas in a stress-relaxation test, the specimen is deformed by a fixed amount and the stress required to maintain this deformation is measured for a period of time. The applied stress may be in the form of tension, compression, flexure or shear, depending on the proposed use of the material, and may be varied from very small values up to stresses approaching the breaking strength of the material. Creep, as well as stress relaxation, is measured as a function of time ranging from a fraction of a second to days and even years. The cost of the experiments needed to generate stress/strain/ time functions for an elapsed time of a few years is very high, and an evaluation of one sample cannot be applied to every grade and over a wide range of ambient conditions.

It would thus be very attractive if a method was evolved by which tests of shorter duration could be carried out and results carefully analysed to predict long-term performance. The present communica- tion is directed with this objective in mind. An attempt is made to study carefully the characteristic behaviour pattern of a number of different polymers through existing stress/ strain/time functions and then provide a method for coalescing the stress versus time curves in order to obtain master curves which could then be used for performance prediction.

2. B A C K G R O U N D

Identification of common patterns of behaviour through careful and accurate background experiments, as well as the principle of super- position to obtain master curves, are not new and have been tried by earlier investigators during their study of long-term mechanical strength of plastics. It was Turner I who found that creep curves of polyethenes have a particularly simple form of two straight lines of different slope when plotted as log strain versus log time, with a well-defined point of change. He found the slope in the latter portion to be almost constant and independent of sample density as well as of ambient temperature. Identification of such regularities was useful to enable data for one grade of polyethene to be converted into data for a different grade provided certain key relationships were known.

Test to predict long-term mechanical behaviour of plastics 39

Similarly, Turner z has shown that log strain versus log time creep curves for a homopolymer and a 15% ethylene copolymer of polypropylene show similarity in shape. Thus, if one basic set of matrix and stress/strain/time data is available for one grade of PP, it should be possible to modify it by appropriate graphical translation through a spacing parameter by which the relevant stresses can be assigned.

The idea of t ime-temperature superposition as suggested by Leaderman 3 and later demonstrated by Williams e t al . 4 and Tobolsky, 5 and Ferry 6 has shown that it is possible to convert stress-relaxation data at widely different temperatures to a single curve covering many decades of time at some reference temperature. The curves are first corrected (reduced) for density and temperature. An arbitrary temperature is selected as the reference temperature. The reduced curves are shifted one at a time, with respect to the reference curve, until portions of the curves superimpose to give a master curve. The amount each reduced modulus has to be shifted along the logarithmic time axis in making the master curve is the so-called shift factor which is a function of temperature as given by Williams e t al . 4 If the t ime-temperature equivalence principle is applied to creep behaviour, it is known to lead to shift factors which are practically identical to those obtained from stress relaxation.

3. PRESENT A P P R O A C H

Turner's approach, 1'2 discussed above, of identifying the regularities in the behavioural patterns of a particular grade of polymer, only instils confidence for some bold extrapolation. However, the errors involved in such performance prediction could be high in some cases. On the other hand, the prediction from a master curve obtained through a t ime- temperature equivalence can be more accurate but involves a cumbersome procedure of determining the shift factor and is also specific to the reference temperature or time.

The present approach is an effective combination of the two discussed above but is much more effective because of the relative simplicity in generation of the master curve as well as in performance prediction through bold extrapolation. Though it is known that creep experiments are presented in three different ways--strain versus time

40 A. V. Shenoy, D. R. Saini

(or log time), stress versus strain at various times (constant time sections across creep curves) and stress versus time or log time (constant strain section across creep curves)--we use only the last type of presentation to demonstrate our coalescence approach. Through a careful behavioural pattern study of stress versus log time curves of various polymers such as polyvinyl chloride, polypropylene, acetal copolymer and polymethyl methacrylate, it was deduced that the set of curves for each polymer could be coalesced into a single master curve through a normalizing factor, namely the stress value at an elapsed time equivalent to one day.

4. RESULTS AND DISCUSSION

Figure 1 shows creep isometric data for pipe-grade PVC at 20 °C. The data presented here are for very low values of strain (0.005- 0.02%) that are relevant for the final application of pipes. Each of the curves in Fig. 1 was normalized by the respective stress value at an elapsed time of one day, ao, and replotted to give Fig. 2. It can be seen that the four different curves of Fig. 1 show an apparent regularity and fall on the single curve shown in Fig. 2 through this simple normalizing technique.

Figure 3 shows the isometric stress versus log time curves at 20 °C for a polypropylene homopolymer. Here the data presented are for

Fig. 1.

60

E

Z 40

~) ¢/) Lu 20 n, I-- ol

0

POLYVINYL CHLORIDE AT 2O°C

~ 0"020 S 0 '015 T O'OIO R

- - - - - - - - " ~ ~ 0"005 I N

I I I I i i I 1

10 2 10 4 IO s I0 a

TIME (see)

%

Isometric stress versus log time curves for pipe-grade PVC at 20 °C under various low strain conditions (taken from ref. 7).

Test to predict long-term mechanical behaviour of plastics 41

| "~ I I P o ~ v,~Y~ c.LoR,oE .T 20"C

! t 1.3

1.7 | i l l l l l I I I11111 II I

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o, IIIIII il]tl lllllll IIII11 I lllllllt ]1~ 100 101 102 103 104 105

t/~o

IIIII

II111 Illl llll

lo 6

Fig. 2. Coalesced plot of normalized stress versus normalized time for PVC at 20 °C under various low strain conditions using the stress value corresponding to one

day, Oo, as the normalizing factor.

much higher strains (ranging from 0-5 to 3.0%) in comparison with the low strains in Fig. 1. Despite this difference in the strain range, the coalescence of the curves through a plot of O/Oo versus log t/ao in Fig. 4 is quite satisfactory. However, it is seen that the scatter on the master curve in Fig. 4 is much greater than in Fig. 2, leading to an apparent conclusion that the suggested approach is probably more effective at lower strains.

The creep data on the above two polymers were available at room

Fig . 3 .

20

~<~16 " ~ ~

~12

~4

o 10 ~

I I K

POLYPROPYLENE AT 20°C r /

-0"5

lo4 ld id io T io 8

TIME (sec)

Isometric stress versus log time curves for polypropylene homopolymer at 20 °C under various high strain conditions (taken from ref. 7).

42 A. V. Shenoy, D. R. Saini

1 ' 6

1"4

1"2

b

O ' B

0 - 6

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i 0 I

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POLYPROPY'ENE A--O'~ S AT 20"C111111 B -- 1.0 T

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Coalesced plot of normalized

IIlllll t fJlrJJ I IrllJ

111111 IIIflll

i 0 8

Fig. 4. stress versus normalized time for polypropylene homopolymer at 20 °C under various high strain conditions using the

stress value corresponding to one day, Oo, as the normalizing factor.

temperature (20 °C). It would be interesting to check the validity of the present approach even at higher temperatures. For this purpose, acetal copolymer stress versus log time data for median strain range (0.5-1.5%) at 60 °C are considered (Fig. 5). Again, the plot of tr/tr0 versus t/ao is seen to give a good coalesced curve as can be seen from Fig. 6.

The polymethyl methacrylate data shown in Fig. 7 are used to establish the propriety of the present technique to be independent of data temperature. Figure 8 shows how the coalescence is rather effective, even for data from 20 to 80 °C.

In each of the coalesced curves given in Figs 2, 4, 6 and 8, it is seen that the general trend is the same. Essentially, there exist two straight lines joined by a plateau at o/or0 = 1. This plateau is seen to occur in the time scale value of t/Oo from 103 tO 105. The scatter of points below t/tro = 103 is seen to be greater, but this region is of less relevance as it corresponds to a time scale of less than a day. In the region of t/Cro > 104, the master curve has been drawn through the points so that the maximum scatter is below the line. This way, if a

Test to predict long-term mechanical behaviour of plastics 43

Z

i f )

n¢

I . -

I I0 10 2 I 0 3

\ \

10

\ \

AL COPOLYMER 60°C

Fig. 5.

]

O I 0 I01 I 0 2 10 3 10 4 10 5 10 6 10 7. 10 8

T i M E ( S E e )

Isometric stress versus log time curves for acetal copolymer at 60 °C under various medium strain conditions (taken from ref. 8).

value of Oo is de te rmined and used for regenerating the relevant curve of interest f rom the master curve, it would only result in an overdesign.

5. C O N C L U S I O N

The present work demonst ra tes an effective method for coalescing existing stress versus log time creep data of polymers through a convenient normalizing factor Cro. The resulting master curves are

44 A. V. Shenoy, D. R. Saini

" I IIIIII fIIrJH frrJN

,., IN ! t 1111111 IIIIIII <~ "' II Illlt I'i'i,t~1 IIIIIII ~> ": l llllll I IIIi¢1 "-,~ IIIIIII I '1 "~

t . . . . . " rill,,, ,.o o . , . 'Jlil[ N~I!i 0.9 t = SEC

o, 1 illIiil 0.7

,o' ,o ~ ,o 3 io'

IIIIIIII I Illlilll I IIIIIIII IIIIIIIII I

ACETAL COPOIYMER AT 60eC

IHl ~-°~ ~ JH 8--'1.0 ,~%

INi o-'o ~ llJ rlrN[ JlJJrlr ItINl rlllill illlli i[LINI

NrlJl .- IIINI

I IIIIrl I llllll

I lllll IIIIILI rllrl Ilillil

iiilllJ IllJIH IIIIlll I Illllr Jllllll i IIIllJ illIIJi I lliill IllllN l i i l l l l IIIIIII IIIII)1

I11111t IIIIi~1"- ,o '~ ,6" ,0 8

t / O " o

10 s

Fig. 6. Coalesced plot of normalized stress versus normalized time for acetal copolymer at 60 °C under various medium strain conditions using the stress value

corresponding to one day, Oo, as the normalizing factor.

Fig. 7.

9 0

7O

z

50 t/J ¢,n ILl

~ 3o

I 0

~ M E T H A C R Y L A T E

~ 2 o ' c

:o°:: I I I I I I I I

101 1 0 3 10 5 1 0 7

T I M E ( S E C )

Isometric stress versus log time curves for polymethyl methacrylate at various temperatures (taken from ref. 7).

seen to be independent of percentage strain as well as tempera ture . The benefits of such master curves are that creep test p rogrammes can be curtailed to a day and then easily used for predicting the per formance behaviour for a year quite accurately for the purposes of design calculations.

Test to predict long-term mechanical behaviour of plastics 45

1.2

I . I

1,O

0 . 9

O.8

0 . 7

lo °

5 !!

|01 10 2 10 3

t / o " o

ii llflllll I I1111111

;o' ~o ~ lo ~

Fig. 8. Coalesced plot of normalized stress versus normalized time for polymethyl methacrylate at various temperatures using the stress value corresponding to one

day, Oo, as the normalizing factor.

R E F E R E N C E S

1. Turner, S. (1964). British Plastics, 37, 501. 2. Turner, S. (1981). Mechanical Properties of Polymers. London, Iliffe. 3. Leaderman, H. (1943). Elastic and Creep Properties of Filamentous

Materials and Other High Polymers. The Textile Foundation, Washing- ton, D.C.

4. Williams, M. L., Landel, R. F. and Ferry, J. D. (1955). J. Amer. Chem. Soc., 77, 3701.

5. Tobolsky, A. V. (1960). Properties and Structure of Polymers. New York, Wiley.

6. Ferry, J. D. (1970). Viscoelastic Properties of Polymers. New York, Wiley.

7. Ogorkiewicz, M. (ed.) (1974). Thermoplastic Properties and Design, pp. 38, 56, 234. New York, Wiley.

8. Powell, P. C. (1983). Engineering with Polymers, p. 77. New York, Chapman and Hall.