213

Goloh et al., Brittle Fracture and Spinnability o/ Viscous Materials

From the Institute /or Chemical Research, Kyoto-University Takatsuki, Osaka (Japan)

Brittle Fracture and Spinnability of Viscous Materials By R e m p e i Gotoh, H i r o s h i A i d a , Soichi H a y a s h i and N i s h i o H i r a i With 5 figures and 2 tables

(Received May 11, 1958)

It has been known that there are solid or plastic materials which show various types of fracture in accordance with the rate of extension. ]~rittle fracture is an extreme case. In this case, the separation is normal to that surface of separation with almost no deformation as a whole (2, 3). The fracture of this type can be seen above a critical velocity of extension at a definite temperature or below a critical temperature, i. e. the brittle temperature, at a relatively lower rate of extension. This critical velocity for brittle fracture may be called "the brittle velocity" in contrast to "the brittle temperature". At higher temperature, those materials liquefy and make drops on separation. This is another extreme case of fracture. ]3etween these two extreme cases, we can find the creeping or spinning condition with respect to the rate of extension and temperature as well as composition. The present authors intended to investigate the critical conditions for brittle fracture and dropping break-down of various viscous materials such as rosin dissolved in olive oil and bitumens. The spinning conditions of some aqueous solutions were also discussed.

Experimental The brittle velocity was measured with the apparatus shown diagrammatically in fig. 1. Thermostat ..........

7

Rack and P/n/on

S~ L..

. . . . . . . . . . . .

oo

t

Reduct/on Oear

Motor Osc~Ibgraph Fig. 1. Extension apparatus

A hollow space of a dum-bell type in a brass block was filled up with the plastic or highly viscous specimens. The block consisted of four separable parts, and the cylindrical part of the specimen was 6 mm in diameter

and 5 mm long. While the one half of the block was fixed to a strain gauge, t h e other half could be pulled by a rack and pinion with a constant velocity. The pulling velocity could be varied from 0.06 to 230 cm per second. The change in tensile force during extension of the specimen was recorded on a rotating film of an electro-magnetic oscillograph.

Glass Rod

~ Specm / ~n Thermostat

Fig. 2. Pulling-up apparatus

Spinning and brittle break-down were observed with the apparatus shown in fig. 2. When a glass rod dipped into a viscous material to a definite depth, about 1 mm, was pulled up vertically at a certain constant velocity, the material showed brittle fracture above a certain critical velocity, Vb, but below this velocity it showed spinning. At higher temperature and a definite velocity of pulling Vd, the material became less viscous and was broken down making drops at their ends. This critical velocity Vd m a y be called the dropping velocity at t h a t temperature.

Results 1. Process o/ Extension and Brittle Velocity Fig. 3 shows an example of the process of extension obtained with rosin dissolved in olive oil at various velocities of extension. In a relatively slow extension, the tensile force

C6

Rheologica Acta, Band 1, Nr. 2-3 (1958)

214

reached a maximum and then decreased, being followed by necking or spinning. As the rate of extension was increased, maximum point came sooner, and became higher. When the maximum tensile force reached a definite value, F~, the brittle fracture occurred as shown by a dotted line in fig. 3 6 FB 5

Brittle ~ Fracture

Rosin-Olive Oil 185%) 35~

0

oD5

olo

X

Straight Blown A1 Blown H 5 Blown Higashiyama Blown A 5 Semi-blown

Y

46 40 40 39 31 45

13 12 12 12 ]0 15

• • • • • •

P*(25~ 103 10 a 103 l0 S 10 ~ 103

25,0 8,1 7,0 3,3 1,6 --

increased slightly at a very low rate of shear. The viscous resistance at the brittle velocity was assumed to be equal to ~ Vb/r, r being the radius of the specimen. The numerical values of this viscous resistance took nearly the same order of magnitude with the brittle strength F~.

~2 +1

Bitumens

* P : P e n e t r a t i o n (mm/5see); load = 100g.

4 "/J!-v 1

Table 2

Bitumens

U

o15

020

time (cm/secJ Fig. 3. Change in tensile force during extension of rosin-olive oil. R a t e of extension (cm/seo): I: 0.6; I I : 2.5; III. 6.0; IV: 10.0; V: 14.4; VI: 20.4

and only little extension was observed. F~ remained almost constant at higher rates of extension, and it may be called the brittle strength. From fig. 3 we obtain the relation between tensile force and elongation from which we can estimate the energy for their deformation at the brittle fracture or spinning break-down. The velocity at brittle fracture gives the brittle velocity, Vb. I t was shown t h a t Vb increased exponentially with increasing temperature and can be expressed by the relation, y log Vb = X - -T- '

where X and Y are certain experimental constants characteristic of the specimen and its dimension and T the absolute temperature. Table 1 and 2 show the numerical values of those constants for rosin-olive oil and bitumens. Shear viscosities, ~, of the specimens were measured with a concentric cylinder viscometer at various temperatures and were shown to be nearly Newtonian, though t h e y

2. T e m p e r a t u r e R a n g e o[ S p i n n i n g F l o w .

I t was confirmed by the pulling-up method t h a t the specimen showed spinning within a certain range of temperature at a definite rate of pulling-up. Below a lower critical temperature, brittle fracture occurred and above a higher critical temperature dropping separation was observed. The relations be-

90~

t

3o t

~1ot I

4o

, so

s'o

16o

Temperature (~ Fig. 4. Break-down limits of rosin-olive oil. - - 9 brittle limit; - - O - - dropping limit

tween the critical velocity and the temperature at the brittle limit and droppin glimit are shown in fig. 4, and given by the relation respectively Vb = A e-BIT;

Va = ae-biT ,

where A, B, a and b are certain experimental constants, and T the absolute temperature. Thus, the range of spinning m a y be given by the region between two straight lines, log Vb - 1

Table 1

100%

and log Va

1

T"

Rosin-olive oil

Cone. ofl~osin%

X

75 80 85 90

63 41 30 21

3. S p i n n a b i l i t y H i r a i , one of the present authors, proposed

Y 18 12 9 7

• • • •

10 ~ 103 103 103

a simple rheological theory of spinnability for viscous liquids such as aqueous solutions of glycerine, cane sugar, glucose and glycols

Gotoh et al., Brittle Fracture and S~innability o/ Viscous Materials

(4). These liquids are v e r y viscous at high c o n c e n t r a t i o n s and low t e m p e r a t u r e s , a n d become spinnable a t certain rates of extension. Spinnability can be o b s e r v e d b y m e a n s of the pulling-up m e t h o d . A t higher t e m p e r a t u r e s or lower r a t e of extension, the liquids show d r o p p i n g b r e a k - d o w n as s h o w n b y the experiments m e n t i o n e d above. T h r o u g h these facts, it m a y be suggested t h a t spinnabilit y of viscous liquids depends largely u p o n t h e viscosity a n d the surface tension as well as the rate of extension. I n o t h e r words, in the process of extension the surface tension leads the liquid t h r e a d to b r e a k a n d to f o r m drops, b u t their viscosity keeps it f r o m breaking.

~ e ~

co~

oo~~

~5 ,J

~4

'~'2

1 -50

-30

40

-I0

I0

Temperature

30

50

70

$0

(~

Fig. 5. Spinning temperature Since the shrinking effect b y the surface tension of liquids m a y be considered ana- logous to the effect of elasticity, an a p p a r e n t relaxation time, X, can be defined b y a relation, 71So" where 7 is the surface tension a n d R 0the radius of liquid thread. Considering t h a t the relaxation time 2 means t h e life of liquid t h r e a d during which the liquid can be spun, the spinning length of liquid L m a y be given b y a relation L = v~ = v R o ~ / 7 , where v is the rate of extension. I f the spinnability S is defined b y L/Ro, a dimensionless q u a n t i t y , t h e n L s = ~

= v ~/~.

A s s u m i n g t h a t the liquid is spinnable for S > 1, t h e spinning condition can be derived as follows v ~ /y _= l or ~ ~ 7/v . P l o t t i n g ~ a n d y/v against the t e m p e r a t u r e respectively as shown in fig. 5, the spinning

215

t e m p e r a t u r e of the liquids at various concentrations can be d e t e r m i n e d b y the cross points of the curves ~ - - T a n d y / v - - T , where the m a n u a l spinning v e l o c i t y was t a k e n to be 1/1o cm per second. As the surface tension of viscous liquids could n o t be m e a s u r e d directly, it was e s t i m a t e d from the relation of R a m s a y - S h i e l d s . The spinning t e m p e r a t u r e s at various c o n c e n t r a t i o n s of the aqueous solutions of glycerine, cane sugar, glucose, a n d p r o p y l e n e glycol were observed a n d those e x p e r i m e n t a l results showed a g o o d a g r e e m e n t a p p r o x i m a t e l y with the value e x p e c t e d from the t h e o r y m e n t i o n e d above. Conclusion In both eases, brittle fracture and dropping breakdown, only very little deformation or elongation was observed in the experiments mentioned above, and limiting conditions were obtained reproducibly with respect to rate of extension and temperature. The brittle limits give the condition where the viscous resistance due to locally concentrated stress, i. e. the grip effect (5) exceeds cohesion of the materials, and development of the surface of separation is followed. At the dropping limits, the viscosities of the liquids may be too small to resist shrinking by surface tension with respect to the rate of extension. Although the theory of spinnability proposed here may be only tentative, it can be pointed out that surface tension plays some important role in spinning of viscous liquids of lower molecules. Concerning higher molecules, rubber-like elasticity as well as viscosity may become more important (6). Zusammen/assung Ffir beide Falle, spr6den Brueh und stufenweiser Bruch, wurde nur sehr geringe Deformation oder Verl/~ngerung beobaehtet und Grenzbedingungen hinsiehflieh Dehnungsgeschwindigkeit und Temperatur reproduzierbar erhalten. Die Bruchgrenzen geben die Bedingungen, bei denen der viskose Widerstand entsprechend den lokalen Spannungskonzentrationen, d. h. entsprechend den ,,grip"-Effekt die Kohasion des Materials tibersteigt, und die Entwickelung der Trennfl/~che wird verfolgt. Bei der Grenzbelastung ffir das Absinken der S.pannung mag die Viskosit/~t tier Fliissigkeiten zu gering sein, um dem Sehrumpfen durch Oberfli~chenspannung im Vergleich mit der Dehnungsgesehwindigkeit entgegen zu wirken. Obgleich die Theorie der Spinnbarkeit, hier vorgesehlagen, nur einen Versuch darstellt, kann behauptet werden, dab die Oberfl/ichenspannung beim Spinnen viskoser Fltissigkeiten mit kleineren Molekiilen eine wichtige Rolle spielt. Fiir h6hermolekulare Substanzen wird neben der Viskosit/~t auch die Gummielastizit~t ausschlaggebend. Be/erences 1) Gotoh, R. et al., Bull. Inst. Chem. l~es. 35, 26 (1957). 2) Reiner, M., Deformation and Flow (London 1949) 296. 3) A1]rey, T., Mechanical Behavior of High Polymers (New York 1948) 490. 4) Hirai, N., J. Chem. Soe. Japan 75, 1021 (1954). 5) Reiner, M., Research on the l~heological Proper~ies of Bitumen and Asphalt (Jerusalem 1948) 5. 6) Shishido, S. and Y. Ito, J. Chem. Soc. Japan 78, 203, 608 (1957).