Crack arrest in a wire-reinforced polymer composite

Materials Science and Engineering, 43 (1980) 261 - 266 © Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands

Crack Arrest in a Wire-reinforced Polymer

261

Composite

C. R. BARNES and A. R. ROSENFIELD Metal Science Section, Battelle Memorial Institute, Columbus, Ohio 43201 (U.S.A.) (Received June 21, 1979; in revised form November 13, 1979)

SUMMARY A n experimental method o f investigating rapid crack propagation and crack arrest in dynamically loaded fiber composites was developed. The reinforcement geometry and the impact energy are the major variables influencing the crack velocity v and the crack length Aa at arrest. However, there is a unique relation between v and Aa independent o f the imposed variables.

1. INTRODUCTION Over the past few years there has been considerable interest in defining the conditions under which a rapidly propagating crack arrests. Research in this laboratory has involved the measurement of the crack velocity and the crack arrest length in slowly loaded rectangular specimens. By the use of stiff loading systems, the data are obtained under essentially fixed-grip conditions. As a result, no work is done on the system during crack propagation and the elastic energy initially stored in the specimen is converted mainly into fracture energy. The specimens are provided with a blunt starter notch so that the elastic energy stored in its arms exceed the a m o u n t available at the Kic level of the material. In this way long crack jumps are produced. Both one- and two-dimensional dynamic analyses have been developed to describe the data and good agreement has been found between theory and experim e n t [1]. The present program was undertaken in order to extend the dynamic fracture experiments in two directions: (1) to use wirereinforced composites in order to study the effect of reinforcement geometry on crack

arrest; (2) to use impact loading in order to investigate non-fixed-grip situations. In addition, estimates were made of the crack propagation energy using subsidiary experiments. In this paper we outline the procedures adopted and report some preliminary experimental results.

2. PROCEDURE 2.1. Specimen preparation Figure 1 is a diagram of the transverse wedge-loaded specimens used in these experiments. They were fabricated using Clear Cast (a liquid casting plastic available from American Handicrafts, Columbus, Ohio). Since the specimens were cast, the incorporation of the wires within the specimens presented no special problem. Individual layers of wire (7/0 music wire of nominal diameter 0.08 mm) were w o u n d round a hollow rectangular casting frame which served as the side walls of the mold into which the plastic could be cast; multilayer composites were built up by adding thin wooden laths to the frame and winding around them. In most of the reinforced specimens the wires were aligned normally to the crack plane with a spacing of 1.25 m m in the thickness direction and a spacing of 0.5 mm in the crack propagation direction. Some specimens were tested in which the wires were aligned at +45 ° to the crack plane using the same spacing. For convenience the specimens are referred to as having n rows in the thickness direction. Finally the liquid plastic was poured around the array. The specimens were cast so that they were oversized and they were then ground to the finished dimensions; the pinhole was bored, the side groove was

262

/

indicated in Fig. 1, for sensing by the transducers. ~-AI foil

Velocity grid-I-~mm

. ~ - 7 / 0 musicwire ::r~ (nom dio O.08mm)

m

I-

A

89mm

I

"1

Fig. 1. The specimen design.

ground to 50% of the specimen thickness and the starter slot was cut to approximately 2.5 mm short of the desired length. The root radius of the starter slot was then produced by extending the starter slot about 3 mm with a 0.15 mm jewelers' saw. In order to m e a s u r e t h e crack velocity, the finished specimens had a resistor array deposited directly on the fiat surface opposite the side groove [2]. This array consisted of four grids of four or five lines, each line composed of a combination of gold and a Pt-C composite. The individual resistance of each line ranged from 3 to 12 k~2 so that the circuit could be powered by a 12 V battery without excessive current drain. (This resistance range also produces approximately equal voltage drops across the grid as the crack front fractures each line successively.) Each of the four grids was then wired into a branch of a simple Wheatstone bridge containing a resistor in parallel with the grid so that the bridge was in balance when all the lines were broken. The load-point displacement was measured with transducers placed a short distance from the edge of the specimen even with the center point of the load hole. Thin pieces of aluminum foil were bonded to the specimen, as

2.2. Instrumentation The instrumentation for these experiments consisted of a dual-channel transient recorder, two piezoelectric transducers, a dual-channel oscilloscope and a four-channel high speed tape recorder, all monitoring the specimen simultaneously. The signal from the velocity grid and one of the transducers monitoring the arm motion were wired to separate channels of the transient recorder and into two channels of the tape deck using T connectors. The second transducer monitoring the arm displacement was connected directly into an additional channel of the tape deck. In this way records of the load-point motion and the crack length were synchronized. An advantage of having the information permanently on tape is that the information can be played back through the transient recorder at various sample intervals. This allows the signals to be viewed over different time spans and perhaps additional information to be retrieved that otherwise might have been lost. 2.3. Loading arrangement Figure 2 is a schematic diagram of the drop tower. The transverse wedge arrangement is the same as the system used for slow loading [1]. The mass B and the drop height A can be varied to provide various impact energies and impact velocities.

Fig. 2. A schematic diagram of the loading arrangement (the support has been omitted for clarity).

263

3. B A S E P R O P E R T I E S

Velocity grid

Q

i~lr5

Displacement transducer

Fig. 3. An oscilloscope trace o f t h e e x p e r i m e n t a l r e c o r d (-+45 ° r e i n f o r c e m e n t ) .

The specimens were loaded in the following manner. The support plate F was first leveled using machine screws located at each corner of the plate. These screws also acted as a support for the base. The pinhole of the specimen E was then aligned with the hole in the support plate F. After lubricating the split pins D and the wedge C they were inserted as a unit into the pinhole. The rod A was then adjusted so that it was exactly vertical. The weight B was dropped from various heights, sliding down the rod A and striking the wedge C, thus driving the split pins apart and loading the specimen. The c o m p o n e n t s labeled G are the piezoelectric transducers that monitor the arm m o t i o n of the test specimens. Cracks propagated in the opening m o d e (mode I); however, the arrested crack front was longer on the top surface because of a bending c o m p o n e n t introduced by the wedge loading. Figure 3 shows a typical trace of a fracture event that was stored in the digital recorder and was played back on an oscilloscope where it was photographed. The upper trace represents the velocity grid. Each step on the y {ordinate) axis represents a change in voltage which corresponds to the rupture of a single line. The trace also indicates the point at which all the lines of the first grid have fractured. This occurs at the point of maximum voltage deflection. The steps in descending order represent the fracture of lines in the second grid. The lower trace represents the deflection of one arm of the specimen (the trace of the other arm deflection, together with the velocity grid, is still stored in the tape recorder at this point). Each division on the y axis represents 0.2 mm of arm deflection. The x axis has units of 200 ~s division -1 for both the velocity grid and the arm deflection.

OF THE COMPOSITE

In addition to the crack propagation and arrest data, subsidiary information was obtained in order to provide information on the crack propagation energy of the composite. The fracture energy Ew associated with a reinforcing wire is assumed to be composed of pull-out and fracture contributions. Accordingly Ew

=

Ep + E~

(1)

where Ep is the pull-out energy and E~ is the fracture energy of the wire. Each of the terms was calculated from the results of independent experiments. For pull-out Ep =

~r dlp2Tp

(2)

where d is the wire diameter, lp the pull-out length and rp the shear stress opposing pullout. The exposed length of wire extending o u t from the fracture surface was measured on crack propagation specimens separately made for the purpose. Figure 4 shows that the length distribution roughly is log-normal with an average of a b o u t 1.25 mm. The shear stress opposing pull-out was determined by pulling a wire o u t of a cylinder which had been cast around it. The value of rp measured in this way was found to be 1.93 MN m -2. {This value may be an underestimate for rapid

96 95 90 ~80

~7o ,--so =o4o

5 2 t.3

l

[

1.0

Z.O

2.3

Log Pullout Length ( i n )

Fig. 4. T h e c u m u l a t i v e d i s t r i b u t i o n o f pull-out lengths (for a w i r e - r e i n f o r c e d plastic crack arrest specimen) w h e r e 2 is t h e m e a n l e n g t h a n d a t h e s t a n d a r d deviat i o n o f l e n g t h : log 2 = 1.7 (2 = 0.05 in), log a = 0.39.

264

Fig. 5. The fracture surface of a double-cantilever-beam fracture specimen of wire-reinforced composite. (Magnification, 80x .)

crack propagation because of strain rate effects.) Combining these two values Ep = 3.7 X 10 -4 J from eqn. (2). For wire fracture

Ef =-~ofefd2h

4. RESULTS AND DISCUSSION

(3)

where o~ is the wire fracture stress, e~ the fracture strain and h the length of the necked region. The measured value of o~ was 2.57 X 103 MN m -2, while ef and h were approximated as 0.02 and d respectively. Combining these values, we obtain Ef = 2.2 X 10 -5 J. The sum Ew (eqn. (1)) of the energies Ep and E~ then becomes 4 X 10 -9 J, which is a first estimate of the fracture energy. It should be noted that the value of the pull-out length lp measured in the crack propagation specimen is considerably smaller than anticipated from the tensile pull-out results. The source of this discrepancy is not clear. It may be caused by the higher pull-out rates associated with fast fracture or by the bending stresses associated with the doublecantilever-beam geometry. The bending stresses may also be the origin of another observation: the formation of cracks parallel to the wire, as shown in Fig. 5. These secondary cracks contribute an u n k n o w n a m o u n t of additional energy which it is not possible to estimate.

The results of the drop weight experiments are given in Table 1 and in Figs. 6 and 7. The low toughness of the unreinforced polymer manifests itself in the relatively high crack velocities and in the absence of crack arrest, i.e. the specimens broke completely in two even using the lowest mass and drop height. In turn, reinforcement at -+45° is less effective than reinforcement normal to the crack plane. Possibly the reason is that the inclined wires are subject to relatively high shear stresses facilitating pull-out; this appears to be the dominant energy-absorbing mechanism, as discussed above. A more detailed analysis of the energy absorption during crack propagation is n o t possible because of the "bridging" effect described by Bowling and Groves [3, 4]. This effect arises because of the relatively large crack face separations required to attain complete pull-out and wire fracture (Fig. 4). As a result, energy is dissipated n o t only at the crack tip but also for some distance behind it. Furthermore, the energy absorption must increase from the onset of crack growth until the wire "bridging" nearest the original notch has been broken. Mathematically the fracture energy must be considered to be dependent on the a m o u n t of crack growth. However, there are some similarities to

265 TABLE Crack

1 propagation

Specimen number

and arrest

data

Drop parameters Mass (kg)

Height

0.45 0.45 0.45 0.45

305 305 76 38

Initial crack length

Arrest crack length

Average crachlvelocity

a0

a,

(ms

(mm)

(mm)

1

(mm)

Unreinforced 7 11

12 13

53 54 53 54

333 235 98 96

Wires normal to crack plane 1

2 3 4 5 6

0.45 0.45 0.45

610 914

0.45 0.45

305 305 152 457

0.45 0.45 0.45 0.45

152 305 76 38

0.91 0.91

152 76

0.91

51 50 51 51 51 51

103 109 102 72 88 102

51 ‘51 50 50 49 50

102 128 94 a4 137 113

34 95 45 _ 23 46

Wires +45” 1

2 3 4 5 6

41 81 _ 120 36

aNo arrest.

0

DropEnergy.J Fig. 6. The crack velocity in unreinforced inforced polymer specimens.

and re-

materials in which energy dissipation is independent of the crack growth length. For example, the data from both reinforcement designs collapse onto one curve when the crack velocity is plotted against the crack arrest length. Similar behavior has been observed in steel double-cantilever-beam

0

I

I

I

I

I

2 3 Drop Energy, J

4

Fig. 7. The length of crack propagation reinforced polymer specimens.

5

in wire.

specimens where cracks propagate under fixed-grip conditions and has been found to be in agreement with a solid mechanics analysis [5] which assumes that fracture energy depends only on the crack velocity. The observed relation is shown by Fig. 8, full line. The present results lie on a parallel curve

266

relation. Whether a mechanics analysis predicts such behavior has not yet been determined.

0.10

s,o,,0

/

//'

o/_..~ j] 1.0

ACKNOWLEDGMENTS

We are grateful to the United States Army Research Office for sponsoring this research under Project P-11691-MS (Grants DAHCO475-G-0080 and DAAG29-77-G-0019). We also thank P. R. Held for fabricating the specimens. f

3.0

2.0

4.0

REFERENCES

~a/a 0

Fig. 8. The v e l o c i t y - a r r e s t length r e l a t i o n f o r reinforced polymer specimens where v is the average

velocity, Co the bar wave speed, Z~a the total crack growth and a 0 the initial crack length. The curve labelled Static loading defines the theoretical and experimental relation for steel [2 ].

displaced to longer crack lengths at arrest. The difference can lie either in the additional energy supply provided to the specimen after crack initiation in the impact case or in the different nature of the fracture energy

1 G. T. Hahn, A. R. Rosenfield, C. W. Marschall, R. G. Hoagland, P. C. Gehlen and M. F. Kanninen, in N. Perrone, H. Liebowitz, D. Mulville and W. Pilkey (eds.), Fracture Mechanics, University of Virginia Press, Charlottesville, 1978, pp. 205 - 227. 2 G. T. Hahn, R. G. Hoagland and A. R. Rosenfield, Metall. Trans. A, 7 (1976) 49 - 54. 3 J. Bowling and G. W. Groves, J. Mater. Sci., 14 (1979) 431 - 442. 4 J. Bowling and G. W. Groves, J. Mater. Sci., 14 (1979) 443 - 449. 5 G . T . Hahn, R. G. Hoagland, M. F. Kanninen and A. R. Rosenfield, in G. C. Sih (ed.), Dynamic Crack Propagation, Noordhoff, Leyden, 1973, pp. 649 662. -