The Fracture Energy of Low Molecular Weight Fractions of

7 The Fracture Energy of Low Molecular Weight Fractions of Polystyrene

Downloaded by AUBURN UNIV on December 26, 2017 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/ba-1976-0154.ch007

RICHARD E. ROBERTSON Scientific Research Staff, Ford Motor Co., P. O. Box 2053, Dearborn, Mich. 48121

The fracture energies (G ) of narrow fractions of low molecular weight polystyrene were measured. The fracture energy of the highest molecular weight fraction (111,000) depends on the nature of the crack formed, a phenomenon thought to arise from subsidiary crazing. The lowest frac ture energy for this fraction was 27.4 J/m which is lower than obtained previously on similar materials and may repre sent the absence of subsidiary crazing. The fracture energy of the lowest weight fraction studied (3550) was still about four times that needed to create the surfaces of the crack, though the energy seems to extrapolate to this value at monomeric molecular weights. Only a thin layer of the material is needed—particularly advantageous when only small amounts (< 1 g) of polymer are available. 1c

2

An important strength characteristic of all brittle materials is the fracture energy. This is the energy required to propagate the already formed cracks or crack nuclei which always exist in real materials. The fracture energy is obtained from an energy balance with the strain energy available to initiate crack growth. Because the fracture energy is independent of crack or flaw size, unlike the tensile strength, it describes strength better than the tensile strength does for new experimental materials, for example, where large flaws may arise from impurities or from unrefined molding and shaping procedures. Until now, however, the techniques for measuring the fracture energy required larger amounts of material than are usually available with a new material. In this report we describe a method of measurement that requires less than 1 g of material (often much less) and that can also be used for very brittle polymers. 89 Deanin and Crugnola; Toughness and Brittleness of Plastics Advances in Chemistry; American Chemical Society: Washington, DC, 1976.


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To illustrate the advantages of the technique, we apply it to narrow molecular weight fractions of low molecular weight polystyrene. The technique involves sandwiching the material between two pieces of a different polymer. The general requirements for the second polymer are: (a) that it be incompatible with the first, (b) that it have a similar thermal expansivity over the temperature range for which the two polymers are glassy to avoid shrinkage stresses, and (c) that there exist for the two a good, low-boiling, common solvent. Also, a clear sandwiching material would enhance measuring the layer thickness and viewing the crack. Poly (methyl methacrylate) is eminently suitable as the sandwiching material for studying narrow molecular weight fractions of polystyrene, and methylene chloride is an appropriate common solvent. Experimental Specimen Preparation. The polystyrenes examined are described in Table I. Each was tested and found to be incompatible with the poly(methyl methacrylate); another polystyrene of molecular weight ca. 2000 was not incompatible and could not be used. The poly (methyl methacrylate) (PMMA) used for sandwiching the polystyrene was Acrylite cast sheet (American Cyanamid Co.) of molecular weight 3.1 million. The cast sheet has a surface roughness that is much less than the thickness of the polystyrene layers (about 10 /xm). A ^-inch thick sheet was used, but later it had to be thinned to improve the accuracy of the measurements. After cutting to 2% X 2% inch and removing burrs, the protective paper was removed, and the pieces were washed in two changes of methanol—each with 2 min of ultrasonic agitation to ensure complete removal of the pressure sensitive adhesive used to bond the protective paper. Then the pieces were rinsed in distilled water, and the water droplets were removed by a stream of Freon gas. The sandwiches were made by dissolving the polystyrene (PS) in methylene chloride and by squeezing a layer of this solution between two pieces of PMMA. The final polystyrene layer was approximately 10 /xm thick. To ensure that a ternary solution did not develop between the PS, PMMA, and methylene chloride, which might phase separate to leave P M M A particles in the PS, solution concentrations were used for which the expanded polystyrene molecules tended to overlap. The overlap of the PS coils seems to avoid a ternary solution because even the two parts of PS-PMMA block copolymers seem to avoid each other in solution (I). An estimate of the concentration at which the polystyrene coils in methylene chloride overlap and essentially fill the entire solution space can be obtained by assuming that the radius of the coil is approximately equal to the radius of gyration of the molecule in a Flory or theta solution. The radius of gyration equals ((r )/6) , where (r ) is the mean end to end distance. The latter for polystyrene is 0.670 M A, where M is the molecular weight (2). The concentration at which the coils of molecular weight M fill the whole solution space in a Flory solution is 0

2

1/2

0

2

172

1/2

x

(o

=

19.4/M

1/2

Deanin and Crugnola; Toughness and Brittleness of Plastics Advances in Chemistry; American Chemical Society: Washington, DC, 1976.

(1)

7.

Fracture Energy

ROBERTSON

Table I. Molecular Peak

Weight

M

w

3,550 10,300 20,500 34,500 111,000

MiN

4,000 3,100 (10,300 ± 3%) 20,800 20,200 36,000 33,000 111,000 111,000

91 Polystyrene Fracture Energy. J/m

Xfo, g/ml

0.325 0.191 0.135 0.104 0.0581

2

0.360 0.248 0.149 0.132 0.0664

0.34 0.60 0.94 1.64 27.4-166.

Source °

WA AL WA WA WA


° WA = Waters Associates; AL = ArRo Laboratories. The values for x for each molecular weight are given in Table I. Concentrations lower than these will still give complete overlap in a good solvent like methylene chloride because the coils are more expanded. In our previous work with this technique for measuring fracture energy (3), we found that a growing crack would not stabilize within layers less than about 1 fxm thick. Hence, to ensure that the crack would grow only within the layer, a thickness of around 10 /*m was desired; it also required solution concentrations of 0.1 g/ml. For measuring the layer thickness, 0.12 mg/ml of rhodamine B dye was added to each solution. At 460 nm, 1 ftg/ml of rhodamine B in methylene chloride has an absorbance of 0.19 in a 1-cm thick cell. After assembling, the P M M A - P S - P M M A sandwiches were dried for one week at room temperature and then for 4 days at 60 °C. There was a tendency for the lower molecular weight polystyrene sandwiches to fracture from shrinkage while drying. These were rebonded in a vacuum oven. The specimens were clamped between glass plates with spring loaded clamps and placed in the oven. The oven was evacuated and then heated to approximately 150 °C for V2 hr before air was readmitted. After another 15 min at this temperature, the oven was allowed to slowly return to room temperature. After drying (and rebonding when necessary), the 2*4 X 2% inch sandwiches were cut into specimens approximately %-inch wide. A groove 1.4 mm wide and 6 mm deep was machined in one end, which removed the PS layer and adjacent PMMA, to allow insertion of the cleavage wedge. The other end was machined flat to act as a base. The specimens were clamped across the PS layer during the machining to avoid fracture. Mechanical Tests. The method for measuring fracture energy is shown in Figure 1. The cleavage wedge is driven into the top of the double-cantilever-beam specimen, forcing the two ends apart. Until a critical separation between the ends is reached, which depends on the length of the crack, c, the crack remains stationary. On reaching this separation, the crack begins to grow, but will come to rest again, or is arrested, at a new length c' if the separation of the ends is constant. By driving the wedge further into the specimen a new critical separation is reached, and the crack grows again; this is followed by growth arrest. In this way a series of measurements of critical separation and crack length corresponding to both crack growth initiation and arrest can be obtained t0


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CRACK Figure 1. Cleavage experi ment: the wedge is driven downward into the specimen and the crack is initiated be fore the experiment begins. Parameters to compute the fracture energy: c, the length of the crack below the appli cation of the stress at the top; d , the distance between the outside edges of the specimen at the top as the crack begins to grow.

BOND LINE

c

///////////////

from the same specimen. This method of cleavage superimposes a compressive stress parallel with the crack path which helps to keep the crack from running off to the side of the specimen. The critical separation is determined by measuring with a micrometer the total distance across the top of the specimen, d and by subtracting the thickness of the beams, 2h. The crack length, c, from where the stress is applied at the top of the specimen is measured with a cathetometer. The fracture energy can be obtained from these measurements of d and c by using an expression derived by Kanninen (4). When the crack tip is no closer to the end of the specimen than the thickness, 2h, a suitable approximation, which also accounts for the groove in the top of the specimens, is (3) C9

c

Gio =

3 (d - 2h) E ft — 16 c [l +0.64/i/c] c

4

2

3

4

where h is the thickness of the beam on each side of the crack; h! is the thickness on each side of the groove; I is the depth of the groove, and E is Youngs modulus of the beam material (the P M M A ) . The subscripts of G refer to mode I fracture, to the mode characteristic of cleavage, and to the condition of crack growth. The symbol G i without the subscript c refers to the rate, with respect to crack growth, at which the strained specimen releases strain energy which may or may not be sufficient to


7.

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Fracture Energy

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initiate crack growth. Note that the dimension perpendicular to the plane of Figure 1, the width, does not enter the expression; it is assumed to be constant for the full length of the specimen. The characteristic of fracture conveyed by G is sometimes expressed in two other ways. Thefirstis the fracture toughness, K , which is related to Gic by the equation u

l c

K

=

Ic

(E

G yJ

LU

QC 3 O < 1.0

0.5 0.2 0.1

• i i ii

I0

3

2

5

10

2

5

111

10

MOLECULAR WEIGHT

Figure 2. Measured fracture energy (G ) vs. molecular weight (distribution peak) for narrow molecular weight fractions of polystyrene [c


TOUGHNESS A N D BRITTLENESS O F PLASTICS

94 7

=

Oic/2

(4)

The factor of 2 arises from the fact that as the crack advances, the exposed surface area increases twice as rapidly as the area of the crack because each side of the crack is counted separately. The use of y is mainly historical and is significant only in the rare instance when the crack growth criterion is dominated by the energy required to create new surface. Results The fracture energies for polystyrene computed from the measurements of c and d with Equation 2 are shown in Figure 2 as a function of molecular weight. All of the individual fracture energies obtained from propagating a single crack in a specimen (as many as 14) were averaged; they are plotted in Figure 2. Also shown by line segments are plus and minus one standard deviation. Once a crack was formed in a specimen, approximately the same energy was required to advance it further each time. Hence, the standard deviation for the set of measurements was generally little more than 1 0 % of the mean fracture energy, and this variation arose in part from the following two experimental problems: (a) with the more brittle polymers, where the cleavage pressure needed for crack growth is small, just the measurement of the distance across the top with the micrometer can change the separation; (b) the increases in cleavage pressure to initiate crack growth sometimes could not be made in small enough increments, especially with the more brittle polymers. On the other hand, crack propagation can vary over the specimen; this was reflected in subtle changes in the almost featureless fracture morphology. The average fracture energies are included in Table I.


c

Discussion For the four lower molecular weight materials in Figure 2, the two or three specimens that were tested gave essentially the same fracture energy. For the highest molecular weight, however, different cracks gave different fracture energies; though within 9 9 % confidence limits, the five data points in the range 2 0 - 4 0 J/m are consistent with the average fracture energy of 27.4 J/m . The eight data points for this molecular weight were obtained from five specimens. In the specimens used for more than one datum, the crack was healed between tests by heating above 1 0 0 ° C for y hr and then reinitiated. It is not uncommon for different cracks to yield different fracture energies (5, 6 ) . Marshall et al. (6) note that the fracture energies obtained by various workers, including themselves, on various styrene homopolymers of commerce have varied from approximately 200 to 7200 J/m . Though some of this 2

2

2

2


7.

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Fracture Energy

95

variation may arise from material difference, much of it depends on the multiplicity of crazing that accompanies crack growth (5, 6). 27.4 J/m is the lowest fracture energy reported for a polystyrene molecular weight above 10 . Hence it may represent the minimum fracture energy that occurs in the absence of subsidiary crazing. The three data points at higher energy may then represent the inclusion of some subsidiary crazing. It is possible that the occurrence of subsidiary crazing requires a minimum polystyrene layer thickness. The layer thickness of the specimens giving the three highest fracture energies was around 10/xm; for those giving smaller energies, it was around 7.5 /mi. 2


5

MOLECULAR WEIGHT Figure 3.

Fracture energy vs. molecular weight of poly styrene and poly(methyl methacrylate)

In the only other studies of fracture energy vs. molecular weight known to us, Berry (7) and Kusy and Turner (8) examined poly (methyl methacrylate) (see Figure 3). The rapid fall in fracture energy below a molecular weight of 10 is characteristic of both polymers. 5

The fracture energy of polystyrene is a combination of the plastic energy needed to form crazed material from uncrazed material, the energy to create the exposed surface in the craze, the elastic strain energy stored in the craze, and the energy to create new surface when the craze ruptures (5, 9). As the molecular weight decreases, the amount of crazing and


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each of the contributions to the fracture energy decrease, except that needed to form the surface of the crack. We estimated the energy required to form new surface by using the surface energy extrapolated to 20°C from that for molten polystyrene obtained by Wu (10), which is 0.0407 J/m . Our lowest molecular weight specimen, with a contour length of approximately 85 A, has a fracture energy that is still approximately four times that needed to form the surface area of the crack. However, the fracture energy for polystyrene seems to extrapolate to the energy needed to form the crack surface (0.082 J/m ) at monomeric molecular weight (see Figure 3). 2


2

Literature Cited 1. Utiyama, H., Takenaka, K., Mizumori, M., Fukuda, M., Macromolecules (1974) 7, 28. 2. Kurata, M., Stockmayer, W. H., Fortschr. Hochpolym.-Forsch. (1963) 3, 196. 3. Robertson, R. E.,J.Adhesion (1975) 7, 121. 4. Kanninen, M. F., Int. J. Fracture (1973) 9, 83. 5. Murray,J.,Hall, D.,J.Mater. Sci. (1971) 6, 1277. 6. Marshall, G. P., Culver, L. E., Williams, J. G., Int. J. Fracture (1973) 9, 295. 7. Berry, J. P.,J.Polym. Sci. (1964) A2, 4069. 8. Kusy, R. P., Turner, D. T., Polymer (1974) 15, 394. 9. Kambour, R. P.,J.Polym. Sci., Part A-2 (1966) 4, 349. 10. Wu, S.,J.Adhesion (1973) 5, 39. RECEIVED October 18, 1974.


The Fracture Energy of Low Molecular Weight Fractions of

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