Deformation Recovery Behavior of a Solid Polymer After Tensile Yielding

GIOVANNI RIZZO and GIUSEPPE SPADARO

lstituto di lngegneria Chimica University of Palermo

ltaly

The deformation recovery at room temperature of a polycar- bonate after large tensile deformation and subsequent stress relaxation is measured as a function of time. The effect of the main parameters which affect the amount of recovered defor- mation is analyzed. This suggests a plot of the recovery versus time curves by means of proper coordinates which allow shift- ing of all curves towards a single master curve, thus indicating that most of the phenomena involved in the recovery process are taken into account.

INTRODUCTION is work encompasses the wide subject of pol- Th ymer processing in the solid state as an alter-

native to processing in the molten state (1-6). Solid- state processing, usually adopted for metals, could offer significant advantages in the rate of produc- tion. Furthermore, the orientation produced in the polymer could induce new and somehow better properties with respect to melt processing (7, 8).

In studying the solid-state processability of a pol- ymer, it is critically important to analyze the me- chano-viscoelastic behavior of the material at large deformations (9-13). In particular the deformation recovery after unloading and its relation with me- chanical and thermal history are obviously signifi- cant.

The aim of this work is to study the deformation recovery phenomenon after large tensile deforma- tion at room temperature as illustrated by an amor- phous polymer. The effect of three parameters, yet pointed out in a previous work (9), is here analyzed: i) the sample deformation ratio, e, just before un- loading; ii) the initial deformation rate, ai, during sample loading; iii) the time t" the sample is kept at the deformation ratio e.

The data clearly indicate the influence of these parameters on the amount of recovered deforma- tion. This suggests a plot of the recovery versus time curves by means of proper groups which take into account most of the phenomena involved, and thus shift all curves towards a single master curve.

EXPERIMENTAL The material used was Lexan, a bisphenol A pol-

ycarbonate (4,4' dioxydiphenil-2,2 propane car- bonate) manufactured by General Electric, sup- plied in pellet form.

The samples for tensile tests were prepared in a

laboratory Carver press, keeping the poIymer at 190°C and 2.5 X lo-' GPa for ten minutes. A subsequent rapid cooling was obtained by running cold water through the press platens. With this procedure, sheets 3 mm thick were prepared. They were then subjected to a thermal treatment above the glass-transition temperature, Tg P 150°C, in order to erase internal stresses. This was accom- plished as follows. The samples were slowly (48 hours) heated up to 150°C under vacuum and then quickly heated up to 190°C and kept for 24 hours at this temperature. After this the sheets were com- pressed again in the press at 19O0C, rapidly cooled and finally subjected to a second thermal treatment. This consisted in slowly heating to 190°C within 24 hours and holding this temperature for 24 hours,

This unusual procedure was necessary in order to gradually eliminate the air which was included in the sheets in the form of microbubbles. This trouble appeared in a previous thermal treatment consisting of a rapid heating of the molded sheets up to 190°C under vacuum, thus producing a rapid expansion of air which, because of the high viscosity of the ploymer, remained included in the form of large bubbles. The above described procedure, on the contrary, allowed gradual drawing out of the air, eliminating the discontinuity produced in the material.

In order to avoid necking and thus to obtain an homogeneous deformation of samples after tensile yielding, the sheets were rolled. Some preliminary tests showed that a minimum deformation ratio of 1.18 in the drawing direction was necessary. Sheets were prepared with a deformation ratio e, = l'/& between 1.18 and 1.24, where 1' is the ultimate value of the sheet length in the rolling direction and lo its initial value. The deformation ratio in the direction perpendicular to the rolling direction on the sheet plane was between 1.01 and 1.04.

1429 POLYMER EffiIUEERING AND SCIENCE, DECEMBER, 1984, V d . 24, No. 18

Giovanni Rizzo and Giuseppe Spadaro

Strip samples were cut from the preoriented sheets, 10 cm long in the rolling direction and 1 cm wide. The distance between grips was 4 cm.

The deformation recovery tests after sample un- loading were made at room temperature (-25°C) by an Instron machine model 1115 with a trans- ducer connected to the machine cross-head. The aim of these tests was to deform the samples up to a fixed value of deformation ratio and then, after unloading, to measure the amount of deformation recovered. Because of the viscoelastic behavior of the polymer, the recovery process was not instan- taneous, but went on with decreasing rate. In order to obtain a recovery curve versus time sample, unloading was not achieved by releasing the grips, but by moving the machine cross-head up to reduce the load close to zero and measuring its displace- ment by the transducer. After this first recovery ramp, the tendency of the sample to further recov- ery was revealed by an increase of the load. A load control system in the Instron machine was able to maintain the load to a small prefixed value by mov- ing the cross-head, thus allowing a record of the recovery curve versus time. As a consequence of the control system sensitivity, a load of 3 kg was kept during the recovery tests. The transducer- bridge-recorder system allowed measuring dis- placements of the order of magnitude of mm. Some preliminary tests showed data reproducibility within 5 percent.

The effect of three parameters was tested: e, the deformation ratio just before the recovery test with respect to the length of the virgin (be- fore both rolling and drawing) sample; a,, the initial deformation rate during the sample loading, the ratio between the cross-head veloc- ity and the length of the rolled sample; to , the time the sample is kept at the deformation ratio e before unloading. It has to be observed that the stresses developed

during cold rolling are extremely complicated and thus the material cannot be adequately character- ized by its resultant elongation ratio e. On the other hand e can be accepted as a comparative measure of the deformation between the tests presented here, since the deformation history before elonga- tion is substantially the same for all of the samples.

The following values of the parameters were tested: e = 1.4, 1.6, 1.8; a, = 3 , 30 h-'; t" = 60, 103, 104 , 1.6 x 105.

RESULTS AND DISCUSSION

Typical stress-strain curves relative to tensile tests on samples cut from different sheets are shown in Fig. I. It is worth noting that all curves super- impose after yielding, thus confirming that the stress-strain behavior after yielding is not signifi- cantly affected by the value of prestrain induced by rolling.

The stress relaxation behavior of this material was examined and is the subject of a previous work (1 2). The effect of the parameters e, ai, and t" considered here is a decrease of the residual stress n" on

decreasing e, and on increasing both at and the relaxation period t".

As for recovery tests, they were performed by loading the sample with a prefixed deformation rate a, up to a fixed value of the deformation ratio e (corresponding to point A in Fig. 2), letting the material relax from the stress for a fixed period t" (A-B), and finally unloading it and measuring the recovered deformation versus time. The sample was not unloaded instantaneously (B-C) but by means of the load control system of the Instron machine, which allowed the sample to reach and keep a fixed small value of the load (B-D). This needed a time, t,, which was dependent on the cross-head velocity. At the end of the time, t,, a first recovery AZ, was measured.

The fact that during time t, the material went on relaxing with a velocity dependent on a,, e, and t " was misleading on comparing tests relative to dif- ferent values of these parameters. The maximum cross-head velocity allowed by the control system was 2 cm/min; this resulted in t, values between 4 and 6 seconds. As the stress relaxation rate in the time interval t, decreased on increasing to , the minimum value of t" used in the tests was 60 seconds, i.e., ten times the maximum value oft,.

After this first recovery step, recovery versus time curves were obtained by means of the load control system and the transducer-bridge-recorder assembly.

Figure 3 shows the influence of deformation ratio, e, on the recovery behavior at different values of to. The data are plotted as AZ/l versus time t, where

I ' 1

Fig. 1 . True stress, a, versus deformation ratio, e, for tensile tests performed at deformation rate ai = 3 h-'.

i" A

Fig. 2. Typical stress versus time curve during a recovery test.

1430 POLYMER ENGINEERING AND SCIENCE, DECEMBER, 1984, Vol. 24, No. 78

Deformation Recovery Behavior of a Solid Polymer aft.. Tensile Yielding

1 -

'i

10 10' 10' ld Fig. 3. Effect of deformation ratio, e, on recovered deformation versus time curves for tests performed at ai = 3 h-' for different values of relaxation period t'.

to = 60 sec O e = 1 . 4 A e = l . 6 O e = 1 . 8 to = 103 e = 1 . 4 x e = 1 . 6 * e = 1 . 8 to = 1 0 4 CDe=1.4 O e = 1 . 6 V e = 1 . 8

All1 is the recovered deformation with respect to the sample length 1 after tensile deformation and t is measured from point B (see Fig. 2) just after stress relaxation period. It can be observed that, for each value oft', the larger the deformation ratio e, the larger the recovery.

The influence of ai is shown in Fig. 4 for samples deformed up to two different values of deformation ratio, e: a larger deformation rate results in a smaller recovered deformation.

A marked effect of t' is evidenced in Fig. 5, where the curve relative to the smallest period t 4 = 60 sec is well above that relative to the largest period t' = 1.6 X lo5 sec.

All data seem to indicate that the amount of recovered deformation is related to u', the residual stress at the end of the relaxation period t'. In fact, on decreasing e and on increasing ai and t', the values of both u' and Al/l decrease. This suggests a plot of the recovery data as Al/(l.u") versus t (see Fig. 6). The normalization of this data brings all of these curves into a rather wide band. It can be derived that correcting the recovery data by means of stress u4 takes into account the effect of all of the parameters, but only in part. On the other hand, the curves in Fig. 6 are grouped in sub-bands char-

I I

10 10' lo' ti Fig. 4. Effect of deformation rate a' on recovered deformation versus time curves for tests petformed at to = 60 sec.

ai, h-' e 0 3 1.4 0 30 1.4 A 3 1.6 A 30 1.6

10 lo' lo3 10'

Fig. 5. Effect of relaxation period, to , on recovered deformation uersus time curves for tests performed at ai = 3 h-' and e = 1.6. A, t" = 60 sec; X , to = lo3; 0, t = lo4; +, to = 1.6 X 105.

5

0.1

. - 'A P O

"4 t 0 0 V O

V O 0 A * r c 0 0

0 1 . ¶ec

1 lo loz Id lo'

Fig. 6. Normalized recovered deformation versus time. Key for symbols as in Figs. 3, 4, and 5.

acterized by different shapes, according to the value oft'. This suggests a further use of the param- eter t' as a normalizing factor. In Fig. 7 it is intro- duced as the dimensionless abscissa t/t", thus grouping all of the curves into a narrow S-shaped band (within 20 percent variation of ordinate) in which the sub-bands of different shape, relative to

1431 POLYMER ENGINEERING AND SCIENCE, DECEMBER, 1984, Vol. 24, No. 18

Giovanni Rizzo and Giuseppe Spaduro

1 . :

1/1'

tos m4 w1 lo" 10' 1 10

Fig 7. Normalized recovered deformation versus dimensionless time Key for symbols as in Figs. 3, 4 , and 5

different values of t o , are welded. The coordinate t / t o takes into account the fact that the stress relax- ation in the polymer occurs according to a spectrum of relaxation times, which correspond to the attain- ment of an equilibrium configuration through mo- lecular rearrangements more and more hindered. Consequently it is reasonable to study the defor- mation recovery process after relaxation using as a time scale factor the time t" during which the material relaxed.

CONCLUSIONS The recovery tests after tensile deformation and

subsequent stress relaxation, performed for differ- ent values of the deformation ratio e, the deforma- tion rate a, and the relaxation period t o show that on decreasing e and on increasing a, and t o the amount of recovered deformation decreases. As these parameters affect the residual stress uo in a similar way at the beginning of the recovery stage (point B in Fig. 2 ) , the recovered deformation Al/ l is normalized by dividing it by u". Furthermore, taking into account the relaxation period t o in the dimensionless abscissa t / t " , all recovery curves shift into a narrow band (within 20 percent variation of the ordinate).

Although all curves do not superimpose into a single master curve, the results seem to indicate that the factors used in the normalized coordinates take into account most of the phenomena involved in the recovery process.

The interest in such a normalizing procedure lies i n the possibility of predicting the amount of re- (hovered deformation for any set of parameters by means of the "recovery master curve" of the mate- rial. In this work it was presented for an amorphous polymer which was previously rolled. If it could be generalized, it would be obviously useful in study- ing polymer processing in the solid state.

Finally it is worth noting that, as solid-state proc- essing is generally performed at temperatures higher than room temperature, it would be inter- esting to analyze also the effect of temperature on the recovery behavior.

REFERENCES 1.

2.

3.

4. 5.

6. 7.

8.

9. 10. 11.

12. 13.

L'

D. M. Bigg, E. G. Smith, M. M. Epstein, and R. J. Fiorentino, Polym. Eng. Sci., 18, 908 (1978). A. E. Zachariades, P. D. Griswold, and R. S. Porter, Polym. Eng. Sci., 19, 441 (1979). P. S. Hope, A. G. Gibson, B. Parsons, and I. M. Ward, Polym. Eng. Sci., 20, 540 (1980). P. S. Hope and B. Parsons, Polytn. Eng. Sci., 20,5589 (1980). P. D. Coates, A. G. Gibson, and I. M. Ward, J. Muter. Sci., 15,359 (1980). G . Rizzo and G. Titomanlio, Rheol. Acta, 20, 133 (1981). B. S. Thakkar, L. J. Broutman, and S. Kalpakayian, Polym. B i g . Sci., 20, 756 (1980). D. M. Bigg, E. G. Smith, M. M. Epstein, and R. J. Fiorentino, Polym. Eng. Sci. , 22, 27 (1982). C . Titomanlio and G. Rizzo, Polymer, 19, 1355 (1978). G. Rizzo and G. Titomanlio, Polym. Bull. 1, 743 (1979). G. Rizzo and G. Titomanlio, in "Rheology," C. Astarita, G. Marrucci and L. Nicolais Ed.s, Vol. 3 page 199, Plenum Press, New York (1980). C. Titomanlio and G. Rizzo, Polynz. Bull. 4, 351 (1981). R. K. Mittal arid I. P. Singh, Polym. Eng. Sci., 22,358 (1982).

NOMENCLATURE = deformation ratio just before the re-

covery test with respect to the length of the virgin (before both rolling and

c - drawing) sample, lo.

e, = Z'/& = deformation ratio induced by rolling. 10

1' 1

tion. A l,

riod, t,. A//l

1. All([ . uo) = normalized recovered deformation. t = recovery time. 1 , = unloading period. t o

t / t " T&! = glass transition temperature. a1

= length of the virgin (before both rolling

= sample length after rolling. = sample length after tensile deforma-

= grips displacement in the unloading pe-

= recovered deformation with respect to

arid drawing) sample.

= relaxation period before sample un-

= normalized recovery time.

= initial deformation rate during the sam- ple loading, ratio between the cross- head velocity and the length of the rolled sample.

loading.

uo = residual stress before unloading

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