Fracture mechanics parameters for polystyrene under high speed impact

Fracture Mechanics Parameters for Polystyrene Under High Speed Impact

D. G . COOK and A. RUDIN”

Department of Chemical Engineering University of Waterloo

Waterloo, Ontario, Canada N2L 3G1

and

A. PLUMTREE

University of Waterloo Waterloo, Ontario, Canada N2L 3G1

A series of commercial polystyrenes was tested using an instrumented impact tester to determine the fracture toughness K , and critical strain energy release rate G,. Over the range of M , 201,000 to 336,000, K, increased from 1.38 MN/ m3I2 to 1.76 MN/m3l2 and G, from 0.92 kJ/m2 to 1.60 kJ/m2. A linear correlation for K , and G, was seen with melt index, and an inverse relationship was obtained against molecular weight. Examination of the fracture surfaces revealed the presence of crack growth bands corresponding to the crack tip plastic zone size. It is suggested that these bands are the consequence of variations in crack growth along crazes that form in the crack tip stress field. As the crack propagates, the stress is relaxed locally, decreasing the growth rate allowing a new bundle of crazes to nucleate along which the crack advances. The spacing of these bands corresponds to the craze length formed in the plastic zone, and the band spacing increases with molecular weight.

INTRODUCTION

raditional methods of measuring polymer impact T performance involve use of an Izod or Charpy device as detailed in ASTM method D 256 (1). Impact values measured by these methods are dependent on the particular test used as well as test specimen size and geometry, and the results are difficult to interpret in a rigorous way. Also, these methods give results with poor reproducibility: often small differ- ences in impact toughness are lost.

More recently, the concepts of fracture mechanics have been employed to interpret the fracture pro- cesses in many plastics. The fundamental principle of fracture mechanics is that all materials contain flaws or cracks, and that fracture occurs by their extension. The resistance to crack extension (K,) and the energy required to extend cracks (G,) are the basic parameters measured. These parameters are formu- lated from a specific analysis of the fracture process and are true material properties if measured prop- erly.

This study focused on a series of fully characterized polystyrenes covering the commercial range of melt indices. Fracture properties were measured un-

* To whom communications should be addressed

596

der impact conditions (i.e., high speed hammer strike]. K , (also called the “fracture toughness”) and G, (“critical strain energy release rate”) were determined and correlated to polymer parameters. An examination of the fracture morphology was also un- dertaken.

EXPERIMENTAL

The polystyrenes used are described in Table 1. These were commercial products and were used as received. These materials had no mineral oil additive, except for sample D. (Mineral oil is commonly added to polystyrene as a flow aid in injection molding.)

The results of gel permeation chromatography analyses are also listed in Table 1 . The number- average molecular weight (Gn) data were taken from universal calibration based on differential refractive index detector measurements, while weight-average (M,) and Z-average (az) molecular weights were obtained from use of a low-angle laser light scattering detector. I t can be seen that the materials have essentially the same polydispersity (i.e., similar M,/M,, and M J M , ratios).

Half-sized Charpy (75 mm by 12.5 mm by 6.2 mm) test specimens were prepared using a 50-ton injec-

POLYMER ENGINEERING AND SCIENCE, MAY 1990, Yo/. 30, No. 10

D. G. Cook, A. Rudin a n d A. Plumtree

Table 1. Test Polystyrenes.

Melt Sample Index* Mn M w Mz AIM" MJMW

A 4.6 133,000 336,000 521,000 2.52 1.55 B 11.9 107,000 262,000 424,000 2.44 1.62 C 14.7 85,000 242,000 408,000 2.85 1.69 D t 39.9 86,000 201,000 350,000 2.33 1.74 E 25.2 84,000 210,000 325,000 2.50 1.55 F 26.3 74,000 202,000 323,000 2.73 1.60 G* 20.9 (81,000) (230,000) - 2.82 -

' ASTM D 1236-82 (2) condition 230/3 8. t Contains rnlneral oil

A blend of 80 wt % F and 20 wt % A Molecular weights are calculated

tion molder. Molding conditions that gave adequate mold filling without overpacking or other mold de- fects were used. Some typical operating conditions were

barrel temperature: 180-220°C; injection time: 2.4 s; injection pressure: 3000 psi; mold temperature: 50°C; total cycle time: 55 s.

One difficulty that arose during early molding trials was that of residual stress in the Charpy bars. This is always a factor in molding (3, 4), particularly for thick sections, and arises because the molded part cools unevenly. Also, flow stresses are not relieved when the section cools quickly. After some experi- mentation, the following procedure was used to re- lieve this stress: the freshly made parts were placed on glass plates in an oven set close to the glass- transition temperature (92- 100°C) for 18-24 h. There was no significant residual stress seen in the annealed pieces on examination with crossed polar- ized lenses for birefringence (5).

A precise cutting device, consisting of a cutting wheel driven by a DC motor and sample positioning crosshead, was used to notch the annealed specimens. The samples were notched (30 degree angle) from 0.5 to 5-mm depth, taking at least two samples for each depth. Subsequently, a very sharp razor blade was pressed into the apex of each notch to obtain a sharp crack profile.

An instrumented Charpy tester was used for fracture testing. This device allowed the transient peak loads and total fracture energy to be measured directly. The basic frame and hammer assembly were designed and constructed according to ASTM D 256 specifications. In addition, a fast response load cell (PCB Piezotronics, Model 200A04) with titanium nose was attached to the hammer, and a photocell velocity measuring device added to the hammer. The output from these two devices was fed to a microcomputer with a Rapid Systems Model 4004B high speed analog to digital board. In this manner, both load cell response and hammer position versus time information could be collected over the very fast fracture event. These data were used to calculate load, velocity, kinetic energy, and other parameters.

POLYMER ENGINEERING AND SCIENCE, MAY 1990, Vol. 30, No. 10

The sample pieces were tested using the following

A. The impact velocity was set at 1.0 m/s by releasing the hammer from a calibrated height.

B. The Charpy anvil points and hammer nose were coated with a light grease. Grease has been used (6) to reduce oscillation effects during high speed impact testing (7, 8).

C. Care was taken that the hammer impact point was directly opposite the notch on the other side. [This ensured a straight, perpendicular fracture.) Careful alignment of the anvil was carried out before testing.

The main parameter determined was the load at the specimen fracture point. The fracture stress in- tensity K , under Charpy-type fracture is calculated by the equation (9)

precautions and conditions:

where K , = fracture toughness, N/m3/'; Y = shape factor (see below); P = load at fracture, N; L = distance between span supports, 0.040 m; B = specimen thickness, m; D = specimen width, m; and a = crack depth, m.

The shape factor Y is a function of LID ratio. In this case, Y is given by (1 0)

Y = 1.93 - 3.07(a/D) + 14.53(a/D)'

- 25.1 l(a/D)3 + 2 5 . 8 0 ( ~ / D ) ~ .

The independent variable in Eq 1 is the crack depth "a"; hence, varying crack depth and plots of l/& versus measured (3/2) Y(PL/BD') values result in a line with slope K,.

The critical strain energy release rate G, is calculated from the method of Plati and Williams [ 1 1):

where U, = specimen fracture energy, B = specimen depth, D = specimen width, and 4 = calibration factor (1 l), function of a/D and specimen geometry. The fracture energy U,was determined by loss of hammer kinetic energy, as calculated from hammer velocities computed from hammer position (from photocell) versus time data.

RESULTS

A typical computer display load versus time trace is shown in Fig. 1. It can be seen that the event is quite fast (approx 0.5 ms) and that the response is essentially elastic. A typical plot for the determina- tion of K , is shown in Fig. 2. Linear regression was used to calculate the slope, with the intercept forced to zero. A representative G, plot is shown in Fig. 3. The K , and G, data for all polystyrene samples calculated from such plots are summarized in Table 2.

Scanning electron microscopy was carried out on the fracture surfaces of the Charpy specimens. A typical surface is seen in Fig. 4, which shows the

597

Polystyrene Under H i g h Speed Impact

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

. , . . I I . , . I I I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- 5 1 6 . 0 0 UI .ib!OOO Us . U84.00 us d . 0 0 UI 1 . h HI 1.481

Fig. 1 . Load cell response during a fracture event. The load cell response is 20 lbs (88.9 NI per division on the graph: the time scale is 40 msldivision. The small oscillation seen in the initial load cell response is due to specimen bounce, whereas the high frequency oscillation after thefracture point is due to resonance in the load

80.0 ’””1

-1/2 l / 6 , m

Fig. 2. A typical K , plot, in this case for material A. The plot of 3 /2Y(PL/BD2) versus has slope K,.

0.240

0.200

0.160

i 0.080

0.040

I

0.000 I

due to fibril pullout from the surface (Fig. 6). Further along the fracture surface, the bands become smaller and the surface smoother, although the hackles re- mained (Fig. 7).

Table 2. Calculated Fracture Toughness, K,, and Strain Energy Release Rate, G,.

K C GC Polystyrene (MN/m3/*) (kJ/m2)

A 1.76 1.60 B 1.68 1.46 C 1.60 1.43 D 1.38 0.92 E 1.53 1.35 F 1.51 1.20 G 1.54 1.30

Note: estimated error in K. is 20.07 MN/m31Z, estimated error in G, is kO.10 kJ/m2.

0 0 2 0 40 6 0 8 0 100 120 140

B W ~ , m2 lo5

Fig. 3. G, plot for material E. The plot of hammer impact energy loss versus BDm has slope G,.

front edge of the fracture area. There are “bands” on the surface that occur with distinct regularity, consisting of a rough leading edge followed by a smooth region. Higher magnification (Fig. 5) of the smooth area showed evidence of “hackles” that seem to be

Fig. 5. SEM of smooth area between bands showing fibril pullout areas f o r sample D. Fracture from top to bottom in photo lmagntfication = 370 XI. The lowest part of the micrograph shows a sharp division for next rough band.

598 POLYMER ENGINEERING AND SCIENCE, MAY 7990, Vol. 30, No. 70

D. G. Cook, A. Rudin and A. Plumtree

I .Do- 0.90- 0.80-

DISCUSSION rene. The data in Table 2 indicate that molecular

I .Do- 0.90- 0.80-

Fracture Parameters

2.00 1.90-

2 1.50 1.80- 1.70: I60 Fig. 7. SEM of surface near end of fracture ligament. Fracture is from top to bottom (magnification = 430 X). N

2”: 140 5- 2 1.30- Y a 1.20-

Table 3. Measured K, Values for Polystyrene From Literature. “ 0

K C 1.10-

(MN/m3’*) Molecular Weight Reference 1.20-

0.75-1.1 Various, not stated Williams (12) (1984) 0.90-

weight has an influence on the observed K,, and this may explain some of the diversity (although Greco

+ K c 0 Gc

I-:-::::::::

The data in Tables 1 and 2 indicate that both K , and G, increase with molecular weight over the range of 200,000 to 300,000 M,. By way of comparison, some K , literature values are given in Table 3.

It is apparent from Table 3 that there is consider- able variation in the reported value of K, for polysty-

and Ragosta (13) found that K , did not vary with molecular weight). It should be noted also that the notching method, as shown by Marshall, e t al. (1 5) had a substantial effect on K,.

The critical strain energy release rate, G,, has been found to vary from 1.0 kJ/m2 to 2.0 kJ/m2 in other studies (16); the data in Table 2 are within this range. These are typical values for polystyrene within the commercial molecular weight range: G, does change significantly below a critical molecular weight (see Fig. 1 I).

From the data in Tables 1 and 2, the best correlation of K , was with melt index as shown in Fig. 8: a simple linear relationship is followed (by regression, R 2 = 0.97 for K,; 0.95 for Gc). Conversely, a plot of M,, versus K , [Fig. 9) showed a sharp dropoff at M , = 200,000. Closer examination shows that the drop is due primarily to one sample: D, the mineral oil- containing polystyrene. Mineral oil is known to increase the melt index of polystyrene (1 7). The inter- esting results seen here show that K , and G, values correlate more closely to factors that contribute to the higher melt index (i.e., melt viscosity properties) than to molecular weight itself.

Fig. 8. Fracture toughness K, and critical strain energy release rate G, versus melt index.

POLYMER ENG/N€ER/NG AND SCIENCE, MAY 1990, Vol. 30, No. 10 599

Polystyrene Under High Speed Impact

A reasonable correlation of K, and G, to l/Mw (ex- cepting sample D) is shown in Fig. 10. Many of the physical properties of polystyrene with similar molecular weight distribution follow this type of relationship (18). A comparable relationship has been found for poly(methy1 methacrylate) (19). At an infinite molecular weight, K, and G, for polystyrene ex- trapolate to 2.1 MN/m3I2 and 1.9 kJ/m2 respectively. Conversely, extrapolation of melt index versus K, and G, (Fig. 8) to zero melt index (hence infinite molecular weight) gives values that are somewhat lower (1.79 MN/m3I2 and 1.70 kJ/m2, respectively).

In summary, all the above data indicate that there is a relationship between molecular weight or melt index and K , and G, values. The photomicrographs also show that crazing (fibril formation and rupture) is the prominent process in fracture (24) and that the fracture features are related to molecular weight (see below).

The molecular weight effect on crazing seems to be due to changes in entanglement density (20) in polystyrene. Bersted (21) has developed a model, sup- ported by experiments, showing that tensile impact properties increased with "fineness" and density of the entanglement network for polystyrene. Donald and Kramer (20) showed that entanglements were essential for craze and fibril stability in glassy polymers. Fibril strength and extensibility are determined by the entanglement network within the fibril. Hence, changes in the fibril strength and extension result in changes to the failure stress and ultimately to G, and K,. The entanglement of molecules also explains why the fracture parameters correlate to melt index, since melt properties such as viscosity (22) or melt index are dependent on entanglements in the melt.

The above discussion implies that fracture energy should be significantly lower at molecular weights below the critical molecular weight for entanglement. Data from Wool, et al. (16) and Robertson (23) for G, as a function of molecular weight are shown in Fig. 1 1. A sharp dropoff in G, below the critical molecular weight (about 70,000 to 90,000) is seen. The ration- ale for these results is that at low molecular weights,

2.20 I I

2.00 j I 0 Kc + Gc

5 1.201 +

+

0 . 6 0 - / , , , , , , , I , , , , , , , I 2.40 2.80 3.20 3.60 4.00 4.40 4.80 5.20 5.60

_ - I -6 Mw x 10

Fig. 10. Fracture toughness K , and critical strain energy release rate G, uersus I/M,.,.

only Van der Waal's forces need be ruptured during fracture, whereas a sharp increase is seen as the critical molecular weight for entanglement is reached. The polystyrenes used in this study cover the range well above the critical molecular weight. It is of interest, however, that G, values still increase at molecular weights well above the critical molecular weight region, as shown here.

Fractography

The bands seen on the fracture surfaces have been seen by other researchers (13, 24) and have been explained by a "stick-slip" or "stop-start" cracking process. The fibrils arise from crazing in the plastic zone area ahead of the growing crack. The crack fractures through the craze fibrils (25) and then mo- mentarily stops at the end of the craze region. New crazes form in the plastic region ahead of the crack and the process repeats.

This mechanism is similar to that forming discon- tinuous crack growth bands in fatigue testing, where it is found that the growth band lengths are equal to the plastic zone length (26). While analogous to fatigue bands, it must be emphasized that the features observed are not due to a fatigue mechanism from, for example, repeated hits of the hammer on the specimen. High speed tensile (extension rates of 1 m/s) testing of the same polymers also show banding, as seen in Fig. 12. The tensile draw is a continuous process without any hammer bounce.

The plastic zone length is given by (Dugdale model ReJ. 27):

(3)

where r, = plastic zone length and uC = craze stress. The craze stress is not known at the high strain

rates for the Charpy. The static craze stress is about 30 MPa (28), but will be higher at higher strain rates, as has been shown for poly(methy1 methacrylate) (29). To determine the craze stress at these high strain rates, notched tensile specimens were placed

3.50 i ,- o data from Wool et a l

+present study 3.00 4 doto f rorn Robertson

2.50 1 (u 2.00

E -- 1.50

1.00

0.50

\

W

d

I I " ' "

4.60 5.00 540 5.80

LOG G w Fig. 1 1 . Log-log plot of G, versus molecular weight (M,.,). Data from Wool, et al. (16) and Robertson (23). Results from present study are also shown.


D. G. Cook, A. Rudin a n d A. Plumtree

in a high speed tensile apparatus (extension rate = 0.8 m/s) and fractured. The stress at fracture was recorded, and the broken specimens examined for signs of crazing throughout the specimen. The notch depth was varied to change the fracture stress. The results of many fractures are shown in Table 4 for polystyrene F.

The above indicates that the crazing stress is between 52.6 and 54.5 MPa under these conditions, or about 53 MPa. The strain rate for this test is in the order of 5.5 s-' which is somewhat lower than in the Charpy test (50 s - I ) . The approximate craze stress was determined for all of the polymers, and with this information, the plastic zone size was calculated and compared with the observed band spacing, as shown in Table 5. It can be seen that the plastic zone size is indeed approximately equal to the observed band spacing.

Proposed Fracture Mechanism

A zone of plasticity develops at a stress concentration when a load is applied to the material. Plastic zones having the form of a wedge-shaped layer have been observed (23) in glassy polymers such as polystyrene.

From the present observations, it is clear that the original notch (and later the resulting crack) nucleate

Fig. 12. SEMof high speed tensiZefracture surface. Frac- ture is from top to bottom in photo.

Table 4. High Speed Tensile Drawing of Polymer F.

Fracture Stress Crazing in (MPa) Broken Specimen

45.4 45.9 49.5 51.6 52.6 54.5 56.8 57.3 57.8 58.3

None observed None observed None observed None observed None observed Small amount Massive Massive Massive Massive

Table 5. Calculation of Plastic Zone Sizes for Different Polystyrenes and SEM Band Spacing.

Band Spacing Craze Stress Calculated Plastic Polystyrene (mm) (MPa) Zone Size (mm)

A 0.430 58 0.364 B 0.354 58 0.326 C 0.345 56 0.318 D 0.233 55 0.250 E 0.249 55 0.302 F 0.291 53 0.305 G 0.331 52 0.342

It can be seen that the plastic zone size is indeed approximately equal to the ObSeNed band spacing.

a set of crazes close to the highest stress concentration at the notch root (and crack tip). The crack then propagates along one of the bundle of crazes that formed in the stress field. The fine mottled structure on the fracture surface shown in Figs. 4 and 5 corresponds to islands of craze layer that adhere to one flank or the other of the craze-matrix interface. Since the craze tapers from the maximum to a very thin section at the extremity of the plastic zone, the size of the craze layer islands becomes finer as the crack approaches the craze tip. The size and distribution of the patches show that the crack has advanced in steps from the rough multifaceted region to the next (Fig. 3 ) . In each step, as the craze becomes progres- sively thinner, the patches become finer resulting in a smoother fracture surface until the crack encoun- ters a new bundle of crazes, which produce the next step. These repeated steps or bands correspond to crack advance that initially occurs on more widely spaced levels at the maximum craze width and then coalesces as it progresses through the craze, which tapers down to its tip, producing a smoother region on the fracture surface. The length of each step will be determined by the stress level and the length of the crazes which, in turn, corresponds to the amount of plasticity occurring at the crack tip. Similar fracture surface morphologies have been observed on other polymers (20).

During the fracture process, the stress concentration at the crack tip (or initial notch root) quickly rises to the craze stress. Although the resulting craze is capable of supporting reduced loads, the crack will advance through the weakened region. As the crack propagates on different levels through the craze, the stress will be relaxed locally, reducing the effective stress concentration causing the crack to slow down within the wider part of the craze. However, as the craze tapers down to its limit, the amount of in-plane crack advance increases as coalescence takes place and the stress increases to nucleate a bundle of new crazes. The crack then advances along one of these, and the process of stress relaxation, crack retarda- tion, and crazing is repeated.

The spacing of the bands on the fracture surface will depend on those parameters that are related to the kinetics of craze growth in a polymer and on the nature of the applied stress. On kinematical grounds, ~~~

POLYMER ENGINEERING AND SCIENCE, MAY 1990, Vol. 30, No. 70 601

Polystyrene Under H i g h Speed Impact

the total craze strain in the polymer can be written

t = Ctzz (4)

where t is the tensor crazing strain for a volume element in which an applied tensile force in the z direction has produced a volume of lenticular crazes with their plane normals parallel to the z direction and tZz is the transformation strain resulting from internal fibrillation of the craze. All other compo- nents except tzz are zero. From elementary consider- ations, the axial transformation strain can also be g' iven as

tZZ = x - 1

where X is the limiting extension ratio of the craze fibrils. Greater extensibility of craze fibrils at higher molecular weights will result in greater craze strains. This permits the maximum craze width to increase. The plastic deformation and fracture behavior is best characterized by the maximum length of stretched fibrils and, hence, the maximum craze width, which is quantitatively described by the Dugdale model.

Using the model, it can be shown that the relationship of maximum width to length is dependent on the properties of the material. The present work has indicated that as the molecular weight of polystyrene increased, the fracture band width increased, which is related to a greater maximum craze width and higher limiting extension ratio of the craze fibrils.

(5)

CONCLUSIONS

The present results indicate that fracture toughness of polystyrene is dependent on molecular weight. There is also dependency on melt index; this suggested that entanglement networks within the polystyrene are an important variable, as implied in other studies.

Fracture morphology gave evidence of a stepwise mechanism, as evidenced by the formation of a series of bands that contained multiple rough and smooth regions. The fracture mechanism may be explained by initial crazing in the stress field at the crack tip, and as the crack propagates along the craze, the stress is relaxed locally decreasing the growth rate and allowing bundles of new crazes to be nucleated ahead of the main crack. One of these crazes formed normal to the applied stress provides the preferred path for continuing crack growth.

ACKNOWLEDGMENT

The authors would like to thank the Natural Sci- ences and Engineering Research Council and the Dow Chemical Company for financial support of this research. We would also like to thank J. Pronovost

for contributing to the design and construction of the instrumented impact tester.

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Fracture mechanics parameters for polystyrene under high speed impact