Dynamic fracture of a quartz-phenolic composite under stress-wave loading in uniaxial strain

’

I

Dynamic Fracture of a Quart<-phenolic Composite Under Stress- waue Loading in Uniaxial Strain

by L. J. COHEN

and

H. M. BERKOWITZ

Advance Structures and Mechanical Department McDonnell Douglas Astronautics Company Huntington Beach, California

ABSTRACT

:

A two-dimensionally

to a high-amplitude dynamic

fracture

plate-impact material defined:

techniques.

the visual

of connected These

This

loading

The direction

threshold,

quartz-phenolic condition condition

composite

material is subjected

in u&axial

strain

is achieved

by using

of wave propagation direction

and a microscopic

through

of reinforcement. threshold

to determine

the thickness

Two failure

represented

its

exploding-foil of the

levels

are

as the lower limit

delamination. that the macroscopic

O-degree shingle-angle,

duration,

dependent phenolic

loading

to the principal

data indicate

laminated, pulse

behavior.

is normal

reinforced

stress-wave

amplitude,

aspects are found

of

impulse

the spallation

to obey failure

reflect the effects of tensile-puke

and microscopic

quartz-phenolic and shape threshold theories

duration,

composite

at the spa16plane of

which

peak

spallation

two-dimentionally are rate-process

tensile stress,

thresholds

are sensitive

of the

to the tensile-

location.

The

reinforced

timequartz

oriented,

an,d which

tensile impulse

and tensile

pulse shape.

I. Introduction In recent years, there has been a steady increase in the number of investigations centered upon the characterization of the mechanical behavior and fracture of materials subjected to stress-wave loading in both uniaxial stress and strain (l-5). Development of the plate-impact experiment has facilitated the study of material behavior and failure under high-amplitude (N 100 kbars), short-time (< 1 x lO-‘j see) duration loads in uniaxial strain. A recent summary of the nuances of plate-impact testing is presented in (6). The test model for all standard plate-impact tests assumes that a plane wave front is produced by normal impact of a plane flyer upon a plane target (Fig. 1). If impact is truly planar, the central regions of the laterally finite flyer and target theoretically behave, during early response times, as if they are laterally infinite. The impact produces a high-amplitude, shortduration pressure pulse that propagates through the thickness of the target at a finite propagation velocity. If the compressive pulse reaches the backface of the target material, a reflected tensile stress is produced. For homogeneous materials, a primary damage mode under wave propagation loading conditions is spallation, which is produced by the interaction with the

25

L. J. Cohen and H. A!. Berkowitz material of rarefaction waves following impulsive loading. Even though the stress attenuation that has taken place prior to the reflection of tensile waves may decrease the peak stress by an order of magnitude, the resulting tensile

OIRECTION

OF

DIRECTION

FLIGHT

j]

WAVE

OF

PROPAGATION

_

FLYER

FIG. 1. Idealization

TARGET

of plate impact condition.

stress pulse may still be large enough to produce material spallation. A photomicrograph of spa11 in 6061-T6 aluminum subjected to plate-impact stresswave loading in uniaxial strain is illustrated in Fig. 2. Failure of composite materials resulting from passage of stress waves is a relatively more complex situation than spallation of homogeneous materials. From an engineering viewpoint, the principal modes of stress-wave-induced damage of fiber-reinforced composites fall into one, or a combination of, the following four categories : (1) S
26

Journal

of The Franklin

Institute

Fracture of a Quartz-phenol& Composite Under Stress-wave Loading included in the models (7) and (8). The modeling of all such effects is not always precise, but it usually is sufficient for engineering purposes. There are a number of investigations which have been directed toward obtaining an understanding of spallation in homogeneous materials, and toward the development of applicable failure criteria (9-17). Recent investigations, notably those reported in Refs. (3), (Q), (14), (15) and (17), have attempted to describe spallation of homogeneous materials (e.g. aluminum and copper) ,

I

PLANES OF LAMINATION DELAMINATION

DIRECTION IMPACT

OF

II

Iizr (Al SPALLATION

ISI DELAMINATION VIRGIN

/i E

INCREASING IMPULSIVE

E DEFORMATION

Cl

FRONTFACE

SPALLATION

DEGRADATION OF MECHANICAL PROPERTIES (01

FIG. 3. Categories of stress-wave-induced

damage for composite materials.

under wave-propagation conditions by postulating criteria which combine more than one parameter (e.g. peak-tensile stress vs. tensile-impulse and/or tensile-pulse duration, or peak-tensile stress vs. stress gradient). In Ref. (Q), a failure criterion is proposed for spallation of homogeneous materials which implicitly recognizes the functional dependence of the spallation criterion upon such parameters as peak-tensile stress, tensile impulse, tensile-pulse duration and pulse shape. Supporting data for this criterion are presented in Ref. (9) for 6061-T6 aluminum for tensile-pulse durations as short as 60 nsec. The failure criterion reported in (9) was formulated by employing Eyring’s theory of absolute reaction rates (18). In contrast to the state of the art of failure prediction for homogeneous materials, only a few investigations present analytical or experimental treatments for fracture of composite material under stress-wave loading conditions. Warnica and Charest (19) report dynamic fracture data under uniaxial strain conditions for a two-dimensional reinforced zero-degree shingle-angle quartz-phenolic composite. * The damage mode evidenced for this material is primarily delamination.? The durations of tensile pulses * The term “shingle angle” is conventionally defined aa the inclination of the lamination planes to the laded surface. t For this material, the spallation and delamination damage modes are synonymousthe planes of lamination are parallel to the impact surface of the material.

vol.

293, No.

1, January

1972

27

L. J. Cohen and H. M. Berkowitz experimentally produced in (19) cover approximately O-9-2 psec for tensilepulse stresses from about 0.2 to 2.0 kbars. For the tensile-pulse durations and pressures reported, it is concluded in (19) that the failure of twodimensional zero-degree quartz phenolic is solely a function of the maximum tensile stress produced in the reflected tensile pulse; i.e. failure of this material is governed by a critical tensile-stress criterion (11). The concept of material failure, termed the Constant Critical Stress Theory (i.e. a unique value of material strength), has been experimentally refuted for many homogeneous materials, both polymeric and metallic, over various regimes of loading, but not for a composite material. Its survival over the years has been justified by several investigators in the area of dynamic fracture. They reasoned that it is, by far, the simplest dynamic fracture theory to employ, and by conducting a set of simple experiments its validity can be readily ascertained for some materials, The present investigation was undertaken to determine the appropriate failure criteria for zero-degree shingle-angle quartz phenolic for tensilepulse durations less than those employed in (19), for pulse shapes which are not square; and, further, to validate the chosen failure criterion in prooftest configuration. Two-dimensionally reinforced, zero-degree shingle-angle quartz phenolic was chosen as the study material because characterization data exist in both uniaxial stress and strain conditions (20) ; and because of the simplicity of its failure mode, i.e. spallation. Also, as discussed in (20), the material studied admits modeling as a homogeneous material and can be analyzed with the same mathematical model as a homogeneous, isotropic material, although it is actually heterogeneous and anisotropic.

II.

Experiment

Preparation of Specimens and Characterization Tests Twelve linear yards of J. P. Stevens Co. 581 quartz fabric, impregnated with Monsanto Corporation SC-1008 phenolic resin, were procured from American Reinforced Plastics, Inc. (Adlock 301 PHQ 38-in. width). A 12 by 10 in. 0.35 in. thick, zero-degree shingle-angle flat panel was fabricated. In laying up the flat panel, first the warp and then the fill direction of a ply of quartz cloth alternately coincided with the long axis of the laminate. This technique was used to construct laminates which had the same material properties in both of the in-plane directions of reinforcement. The panel was cured under pressure in a universal flat press. After curing, the panel was rough cut into several plate-slap and characterization specimens. These specimens were subjected to a 4-day post cure.* The 16 specimens used for subsequent plate-slap testing were fine machined to 1.25 by 1.25 by 0.25 in.; the specimens used for other characterization tests on two-dimensional quartz phenolic were all machined to a thickness * The cure and post cure for the fabricated Ref. (23).

28

specimens are described in detail in

Journal of The Franklin Institute

Fracture of a Quartz-phenolic Composite Under Stress-wave Loading of 0.25 in. A summary of all the pretest plate-slap characterization tests which were performed on specimens selected from the flat panel, and the resulting data, are summarized in Table I. The void content of the specimens was computed using the algebraic relationships described in Ref. (21). The acoustic velocities were determined using a through-transmission technique. TABLE I Sunzmary of composite characterization data for two-dimensionally reinforced quartz phenolic

I$(%) w7n(%) Open porosity* (%) Average longitudinal wave velocity Perpendiculer to direction of reinforcementt (cm/set) (F) C W c, f, m, v

= = = =

1.68 61.02 38.98 1.44 0.3043

bar over symbol denotes average value. volumeric content. weight content. indices which denote composite, fiber, resin and voids, respectively.

* No correction is made for micropores less than 0.012 p. No correction mede for closed pores. t Average of four frequencies-0.5, 1.0, 2.25 and 5.0 MHz.

The values indicated in Table I are averages for a minimum of five specimens. In addition, 1 in. long by + in. diameter cylindrically shaped specimens were fabricated from pure SC-1008 phenolic resin to obtain characterization data on the behavior of the phenolic constituent. The SC-1008 phenolic resin specimens were cured at ambient pressure and at a variable temperature cycle. The SC-1008 phenolic resin cannot presently be cured at the high pressures and temperatures used to fabricate the quartz-phenolic panels. It is not presently known how these differences in cure influence the mechanical behavior or pure SC-1008 phenolic relative to the in situ phenolic in the composite. The specimens were tested in compression in an Instron universal tester over the strain-rate regime 1O-4 < g < 10-l see-l or time duration loo < t < lo3 sec. Figure 4 is a plot of the deformational behavior of pure SC-1008 phenolic resin as a function of strain rate. Figure 5 is a plot of the ultimate compressive strength as a function of the time to failure. Test Procedure The plate-slap test technique employed in the present study to obtain spallation threshold data for two-dimensional zero-degree quartz phenolic

Vol. 293, No. 1. January

1972

29

L. J. Cohen and H. M. Berkowitz is known as the exploding-foil technique. In this technique, a flyer plate is propelled against a target material at high velocity to produce the impact condition of uniaxial strain stress-wave loading. The launch of the flyer plate “I

PERCENT

FIG. 4. Compressive stress-strain

STRAIN

deformational

-E

behavior of SC-1008

phenolic resin.

60

50

40

xl’

I

1x 100

,,I

I

1

x

I

10'

,I

1

x

1 XlOJ

IO”

TIME WC’

FIG. 5. Ultimate

stress vs. time to failure-SC-1008

phenolic resin.

occurs with the sudden vaporization of a metal foil. The exploding-foil facility used to generate the fracture data reported in this study is described in detail in Refs. (9) and (20). A brief summary of the test setup, operational conditions and instrumentation of this facility is presented below.

30

Journal of The Franklin

Institute

Fracture of a Quartz-phenolic Composite Under Stress-wave Loading The basic circuit diagram of the exploding-foil apparatus used in this study is illustrated in Fig. 6. * With a foil connected across the capacitor bank, the switch is closed and the capacitor bank is charged to the desired voltage (nominally 16 to 20 keV). The capacitor bank consists of 16 12-mfd, SO-keV capacitors, each connected to a common bus by a circular connector

i DASH POT

FIG. 6. Schematic of MDAC-West

exploding-foil

facility.

threaded on the capacitor terminal. At 20 keV, the combined energy of the capacitor is 40 kJ. When the capacitor bank is fully charged, the switch is opened to disconnect the power supply. Air ionization is initiated by a pulse from the trigger generator situated between the capacitor bank electrodes. The breakdown of the spark gap initiates a discharge of the capacitor bank through the foil. The high-amplitude current that flows in the foil causes the foil to explode. Two types of foil assemblies were used to obtain fracture threshold data for two-dimensional zero-degree quartz phenolic. The singleplate assembly explodes the foil, and generates a pressure pulse which causes a polymeric projectile (i.e. Mylar) to tear out of a polymeric sheet and accelerate with very little tilt. After a free run, the projectile strikes the target. The region between the projectile plate and the test specimen, and the area completely surrounding the target and foil assembly, are evacuated to a pressure of about 8 x 1O-5 torr. This type of assembly was used to test 5-mil Mylar flyers in the velocity range O-61--1.18 mm/see. The double-plate assembly is a combination of the single-plate flyer configuration and a Lucite moderator block. The single-plate assembly is used to propel a flyer plate into a moderator material. The second moderator plate has a flyer greased on the opposite surface. The flyer is accelerated across a free run by momentum trapping. * The facility used in the present study is the McDonnell Douglas Astronautics Company

Vol.

(MDAC)

293, No. 1,

plate-slap

Jannary 1972

facility.

31

L. J. Cohen and H. M. Berkowitz After impact, the target is caught in a 2 lb/ft3 polystyrene foam catcher to minimize secondary wave effects. A simultaneous streak and framing camera recorded the motion of the flyer as it impacted the target. The camera is focused on the rear side of the flyer, and is operated at 800,000 frames/set. Simultaneity of impact is evaluated from framing pictures. Velocity measurements are not obtained from framing pictures because the finite shutter speeds cause a blurring of the flyer image. Consequently, the streak record is used to determine the flyer velocity. The technique consists of measuring the angle formed by the streak of the flyer and the horizontal streak formed by a stationary object in the field of view. Exploding-Foil

Testing

Sixteen exploding-foil tests were conducted on the MDAC exploding-foil facility to establish two points on the visual and microscopic thresholds of spallation of the zero-degree shingle-angle material. The two Mylar projectile plate thicknesses used were 5 and 14 mils thick. All specimens were impacted with 1 in2 Mylar projectile plates. The flyer velocity range was 0*38-1.11 mm/psec. Table II is a summary of the exploding-foil tests performed. Indicated on this table are the flyer velocity and post-test description of the specimens. Post-impact Examination Following the impulsive load failure testing all of the specimens were examined visually at a macroscopic level of approximately 4 x . Several of the specimens which showed no discernible visual damage were subsequently sectioned and polished for microscopic examination at magnitudes of lo-120 x . These examinations were made to determine the visual and microscopic spallation thresholds of the specimen. Tables II and III summarize the macroscopic and microscopic observations at 4-120 x . Figures 7-10 are photomicrographs representative of several of the sectioned specimens. Those which showed visual damage had distinct planes of spallation near the back-face of the specimen, microcracking perpendicular to the direction of reinforcement and some evidences of uncoalesced cracks. For the specimens which showed no visual damage, high-magnitude photomicrographic examination revealed distinct coalesced and uncoalesced cracks parallel to the plane of reinforcement running through fiber bundles and the fiber-matrix interface near the backface. Additionally, photomicrographic examination revealed cracks in the specimens which tended to line up along preferred planes. All specimens tested possessed the common characteristic of a poorly defined spallation plane, i.e. the lack of a single plane along which an opening traversed. All the specimens that showed some degree of spa11 exhibited it over a band approximately 30-100 mils from the backface of the specimens. In view of these damage characteristics two failure thresholds were adopted which characterized zero-degree shingle-angle quartz phenolic under stress-wave

32

.Joumal of The Franklin

Institute

Fracture of a Quartz-phenolic Composite Under Stress-wave Loading TABLE II Composite

summary

Specimen No.

Flyer thickness (mils)

13

of ex$oding-foil data for two-dimensionally-reinforced quartz-phenolic

Post-test

evaluation

Velocity

-

(mm/cLsec)

Macroscopic inspection

Photomicrographs

5

O-966

Discontinuities - 10 x

17

5

0.966

18

5

1.11

15

5

0.98

19

5

0.98

25

5

0.77

No discernible damage N 4 x No discernible damage - 4 x N 30 mm rear surface detached, spalled portion exhibits delamination - 4 x No discernible damage on back and front face, edge delamination - 4 x No discernible damage on back, front or edge of specimen N 4 x No discernible damage

23

5

0.66

No discernible damage

24

5

0.61

No discernible damage

14

14.7

0.75

21

14.7

0.41

20

14.7

0.38

26

14.7

0.59

- 30 mm rear surface detached, spalled portion exhibits multiple delaminations -4x No discernible damage N 4 x No discernible damage N 4 x Slight bulge in center of rear surface

22

14.7

0.57

28*

14.7

-

No discernible damage

27

14.7

0.39

No discernible damage

1st

14.7

-

No discernible damage

Slight bulge in center of rear surface

Discontinuities - 10 x

Two major discontinuities across width of specimen Discontinuities N 10 x

No discernible damage - 10 x No discernible damage - 10 x No discernible damage - 10 x

No discernible damage - 10 x No discernible damage - 10 x Major discontinuity near backface N 10 x Major discontinuity near backface N 10 x No discernible damage - 10 x Multiple planes of delamination N 10 x No discernible damage N 10 x

* Arc over, shot data not applicable. t Flyer disintegrated.

Vol. 293, No. 1, January

1972

33

.L. J. Cohen and H. M. Berkowitz TABLE III Summary

Specimen no. 51,44 46, 63

of post-test

Flyer thickness (mils)

Flyer velocity (mm/pet)

-

-

examination

of quartz-phenolic

Magnification 25, 75 100x

24

5

0.61

100 x

23

5

0.66

100x

25

5

0*77

65 x

13

5

0.966

30x

17

5

0.966

30, 100x

15

5

0.980

30x

19

5

0.980

30, 100x

20

14

0.38

30, 100x

34

specimens

Observation Control-no evidence of resin and/ or fiberor fiber cracking, matrix delamination Discontinuous cracks at fibermatrix interface in middle of specimen near backface Continuous cracks through fiber bundles and at fiber-matrix interface in middle of specimen near backface. Slight microcracking perpendicular to plane of reinforcement Continuous cracks through fiber bundles and fiber-matrix interface near backface. Microcracking perpendicular to plane of reinforcement, primarily in matrix Distinct planes of delamination near backface extending over middle portion of specimen. Slight micro-cracking perpendicular to plane of reinforcement Distinct delamination plane across middle portion of specimen near rearface. Slight micro-cracking perpendicular to plane of reinforcement Distinct delamination plane across width of specimen near rearface. Some evidence of uncoalesced cracks Distinct delamination plane across width of specimen near rearface. Heavy micro-cracking in matrix extending from the frontface to backface of the specimen through Slight micro-cracking resin and fiber bundles over middle portion of specimen near backface. Several uncoalesced cracks parallel to plane of reinforcement running through fiber bundles and fiber-matrix interface

Journal

of

The

Pranklin

Institute

Fracture of a Quartz-phenolic Composite Under Stress-wave Loading TABLE III

Specimen no.

Flyer thickness (mils)

Flyer velocity (mm/pet)

(con&L)

Magnification

Observation micro-cracking through Heavy matrix and several fiber bundles over middle portion of specimen near backface. Distinct coalesced cracks running through fiber bundles and fiber-matrix interface Several disconnected cracks running through matrix and fibermatrix interface. Cracks tend to line up along a preferred plane parallel to direction of Slight microreinforcement. cracking in resin perpendicular to direction of reinforcement Distinct delamination plane over middle portion of specimen near backface. Micro-cracking perpendicular to direction of rematrix and inforcement in through fiber bundles Slight micro-cracking perpendicular to direction of reinforcement through resin Distinct plane of delamination parallel to direction of remforcement over middle portion of specimen near backface. Connected cracks run through fiber bundles and fiber-matrix interface and resin

27

14

0.39

33, 50 160x

21

14

0.41

30, 100x

22

14

0.57

30x

28

14

26

14

-

0.59

30x

30 x

propagation-the visual threshold, and a microscopic threshold represented as the lower limit of coalesced cracks parallel to the direction of the reinforcement. For the 5 and 14-mil Mylar impactors, the visual thresholds were estimated to be O-960 and 0.57 mm/pseo, respectively. The microscopic thresholds for the 5- and 14-mil Mylar impactors were estimated to be 0.600 and O-390 mm/psec, respectively. Figures 7-10 are photomicrographs of each of the specimens which were impacted near or at the visual and microscopic threshold for both 5- and 14-mil Mylar impaction. III.

Analysis

of Test Results

Material Strength Theories for Wave Propagation Several failure criteria are currently employed by various investigators to predict spallation of materials. The commonly used criteria are : (1) constant

Vol. 293, No. 1, January

1972

35

L. J. Cohen and H. M. Berkowitz critical tensile stress (11) ; (2)stress rate or stress gradient (17) and (22) ; (3) empirical algebraic relationships between stress and impulse or time (la), (15) and (23) ; and (4) rate process criterion (9) and (23). The functional forms of each of these criteria are summarized in Ref. (9). The criterion employed in the present study to predict dynamic fracture (spallation) of two-dimensional zero-degree quartz phenolic under uniaxial wave-propagation loading is rate-process oriented. A fuller discussion of the rate-process-oriented failure criterion, or any of the other aforementioned criteria, may be found in Refs. (9) and (23). Rate-process-oriented failure criteria are generally presented in the functional forms t = AeBg

(1)

or a = C+Dlogt. The form of Eq. (1) is derivable from the application of Eyring’s rate process theories (18) and is attributed to Ref. (24) for polymers and Ref. (25) for metals. This criterion has been demonstrated experimentally for a wide variety of polymeric and metallic materials in uniaxial stress conditions over several decades of time duration of load; i.e. time durations as low as 1O-5 set and as long as lo* sec. It has been applied successfully to the failure of multiphase particulate-void polymeric composites in uniaxial stress over the time duration loading regime 1 x 1O-2 < t < 1 x lo2 min-l in the work of Cohen and Ishai (26). Previous work by the authors (9), reports experimental data for spallation of 6061-T6 under uniaxial strain for time durations of loading of 0.06
(2)

where K is a pulse-shape constant, I is the tensile impulse, u the peak tensile stress of the pulse and t the duration of the tensile pulse. Substituting Eq. (2) in Eq. (l), algebraic manipulation relates impulse to failure stress in the following manner

36

Journal of The Franklin Institute

Fracture of a Quartz-phenolic Composite Under Stress-wave Loading where I and a are constants for a given material and pulse shape. Rewriting Eq. (3) in experimental form

[J=[i+X~[~]* Reduction of Exploding-foil

(4)

Data

If flyer and target thickness, flyer and target constitutive relations and flyer velocity producing a damage mode are known, a wave-propagation analysis can be conducted to determine any of the basic variables in which one desires to express a failure criterion. Several computer codes are available for analyzing the problem of wave propagation under uniaxial strain (‘7 and 8). A modified version of the one-dimensional elastic-plastic-hydrodynamic wave-propagation code PUFF (7) was chosen for the study material. This selection was prompted by the minimal amount of two-dimensional stress-wave effects for wave propagation through a zero-degree shingle-angle composite ; the lack of experimental data to formulate a tensor equation of state to account for possible multidimensional wave effects ; and the relative simplicity of the failure mode for two-dimensional zero-degree quartz phenolic, i.e. spallation. Determining failure criteria for composite materials over a spectrum of shingle angles (from 0 to 90 deg) would most likely involve use of a multidimensional wave-propagation code, in view of the possible role that propagating shear waves would play in the failure mechanism. Constitutive data are reported in Refs. (20) and (23) for the present study material (the same cure and percent constituents). The constitutive relationship employed in the work of Berkowitz and Cohen (20) and (23) assumed the material could be modeled as an elastic-plastic, strain-rate-insensitive, isotropic work-hardening material, without a Baushinger effect. Experimental confirmation for the assumed material modeling was obtained employing the results of thin-pulse attenuation tests on two-dimensional zero-degree quartz phenolic which were instrumented with quartz-crystal gages. The model used incorporates the Mie-Gruneisen equation of state in the form (27):

(5)

a=p+s

with

p=

[CP+DP2+XP3]

d=

and

+Gfi

1s 1 = QY

[

l-2

1

if IsI < +Y (elastic), otherwise (plastic),

+p,,I’E

(6) (7)

where a = axial stress,

p = mean pressure, s = stress deviator, .4 = deviator rate,

Vol. 293, No.

1,January 1972

37

L. J. Cohen and H. M. Berkoud t.~= condensation, fi = condensation

rate,

p. = initial density, P = Gruneisen coefficient, E = internal energy, C, D, S = empirical constants, G = elastic shear modulus, Y = yield stress in uniaxial stress = Y, + C, j 1dpp 1, cup= plastic strain measure. Table IV lists the parameters used for the Mylar flyer (28) and the twodimensional zero-degree quartz-phenolic (20) and (23). TABLE IV

Constitutiveparameters for the study material

Material Mylar (28) Zero-degree quartz-phenolic

(&

(k:,

(k:)

I?

PO Wcm3)

71.3 95

131 740

200 3700

O-448 O*llO

1.39 l-67

(k2, 0 38.3

0 0.40

0 10

The failure threshold data points analyzed were the two visual and two microscopic threshold values delineated by testing under this study (described in the preceding section). Another two points on each threshold were obtained by analyzing the data reported in (19) for laminated, zerodegree shingle-angle quartz phenolic.* The impact conditions analyzed using PUFF are summarized in Table V. Tables VI and VII show the mean values of the various parameters which were selected from this output to represent the failure parameters to use with the various criteria. Tables VI and VII indicate that the two-parameter failure space (i.e. 0 and I/o) appears to subdivide naturally into two regions. In one region, spallation occurs at a constant tensile stress, and is independent of the tensile-pulse time duration. In the other region, the spallation process appears to be sensitive to the duration of the tensile pulse, i.e. the failure is time dependent. The rate-process failure criterion [Eq. (4)] was chosen for use to fit the data in the region which exhibits time-dependent spallation. A constant tensile-stress criterion appeared appropriate for use to fit the * The constituent distribution for the material of Ref. (19)was C, = 45 per cent, C, = 55 per cent and yr = 1.79. Information pertaining to the composite cure is presently not known.

38

Journal of The Franklin Institute

Fracture of a Quartz-phenolic Composite Under Stress-wave Loading TABLE Assumed impact condition

V

producing threshold data points Threshold velocities

Thickness

Flyer material Mylar * Mylar* Quartz phenolic,t 0” orientation (19) Quartz phenolic,? 0” orientation (19)

Microscopic

Flyer (mils)

Target (mils)

Visual (mn+sec)

5 14 125

250 250 225

960 560 473

600 390 213

60

125

473

213

(mn+sec)

* Spa11 planes located over a band extending from about 30 to 100 mils from backface of target. t Spa11 plane located at approximately one-half of the target thickness.

TABLE Failure parameters

VI

for visual threshold

Tensile pulse parameters Flyer thickness (mils) 5

Impulse I

Stress o (kbars)

Ilo (psec)

1.44

0.685

3.45 1.05 1.05 = 1 bar-psec.

0.492 0.906 1.570

(taps)* 987

:: (19) 1700 950 125 (19) 1650 * 1 tap = 1 dyne-sec/cmx

TABLE Failure parameters

VII

for microscopic

threshold

Tensile pulse parameters Flyer thickness (mils) 5 ;: (19) 125 (19)

Impulse I

I

(taps)*

Stress o (kbars)

(psec)

460 1080 515 900

0.835 2.51 0.55 0.55

0.549 0.429 0.938 1.64

* 1 tap = 1 dyne-sec/cmz

= 1 bar-psec.

in the other region. Other relations could have been used to fit the data; however, the authors favored this selection in light of the physical aspect of the theory and in view of previous successful use of this theory, which data

TTol. 293.No.1,January1972

L. J. Cohen and H. M. Berkowitz has been reported in Ref. (9). The resulting visual and microscopic then, are given by

criteria,

where

I

(taps) 5300 4200

Visual delamination Microscopic delamination

0 W)

7 (psec)

0, W)

6.10 6.78

0.730 0.572

1.05 0.55

These results are plotted in Figs. 11 and 12. From Fig. 12, it is seen that the time-dependent portion of the criteria produces a multivalued threshold.

MONSANTO

I

FIG. 11. Estimated

0.2

m4

0%

0e8

’ .O I z;.!J=c

SC1008

PHENOUC

2.0

RESlN

-

40

51.9

V/O

eo

8.0

10.0

delamination thresholds zero-degree shingle-angle quartz phenolic.

This reflects a pulse-shape effect. For a given impulse, the criterion essentially permits brief durations of the pulse peak to occur without failure at intermediate stress levels, but will indicate failure for long durations at a low-peak stress or short durations at a high stress. Extremely low stresses of any duration will not produce failure. It is not physically unreasonable to expect this type of behavior. In this case, the data points producing these multivalued curves lie to the left of the peak of the curve (Fig. 12). However, the authors (9) used the same criterion as the above Eq. (8) for 6061-T6 aluminum and, for the rate-dependent portion, curves were defined by points lying to the right of the peak. Not enough data are presently available for these materials to completely validate use of Eq. (2) in either case.

40

Journal of The Franklin

Institute.

Fracture of a Quartz-phenolic Composite Under Xtress-wave Loading We can only infer that by data falling to the crests, we have some sufficient data become

because such multivalued curves have been generated left and in another case to the right of the respective support that such cresting will be evidenced when available.

---T

-F -c

.

0 ELAMINATI(

\

\

k-

?EGION

T

1;

4

I, = 5.300 0,

TAPS

=6lOKbar

REG,ON

I

OF NO VISUAL

;

OEILAMINATIOF

(NO CROSS-HATCH) I

0

2

4

6 0, PEAK

FIG. 12. Visual delamination

IV.

Validation

of Failure

I

8 TENS,

LE STRESS,

10

IL

Kbar

threshold zero-degree shingle-angle quartz phenolic.

Criterion

by Proof

Testing

The preceding sections described how the study material was characterized and how exploding-foil impact data were utilized to construct a failure criterion for two-dimensional zero-degree quartz-phenolic which implicitly recognizes the dependence of failure upon several stress-pulse parameters. In order to validate the chosen criterion, a proof-test configuration was designed which would employ the chosen criterion to establish the impact condition to produce spallation. The configuration chosen was nominally that of a t-in. thick, laminated, zero-degree shingle-angle, quartz-phenolic target, backed by a &in. 6061-T6 aluminum block and impacted by a 5-mil Mylar flyer. The aluminum backup block was not bonded to the quartzphenolic target, but the interface of the two items was coated with vacuum grease to insure adequate transmission to the aluminum of the compression pulse produced by the impact. This configuration was designed to exhibit the following features during wave propagation : (1) The initial compression pulse would first travel through the quartz phenolic. The pulse would be partially transmitted to the aluminum and partially reflected back into the quartz phenolic (as another compression wave), then travel back through the quartz phenolic. When it reached the free impacted face, the pulse would be reflected

Vol. 293, Xo.

1, January

1972

41

L. J. Cohen and H. M. Berkowitz and, therefore, produce a tensile pulse. This tensile pulse would then be the cause of any visual or microscopic spallation that would subsequently be observed. (2) The aluminum block would be sufficiently thick that it would not spall, for conditions producing spa11 of the quartz phenolic. interface was essentially a zero(3) The quartz-phenolic/aluminum tensile-strength connection, i.e. the aluminum block acted as a momentum trap. TABLE VIII Post-test Specimen number

Impact velocity

Pl

1.72

P2

1.47

P6

1.07

P3

2.05

P4

2.20

P5

2.30

WmlcLsec)

examination

of proof-test

Visual observation

ape&men

Microscopic examination

No visual damage

Continuous internal cracks through fibers and matrix30 x , between 60 and 100 mils from frontface No visual damage High degree of coalesced microcracks between 60 to 100 mils from frontface100 x Uncoalesced microcracks No visual damage parallel to plane of reinforcement-200 x &in. thin crack or Continuous internal spallascratch on one edge, tion from 60 to 100 mils approximately 90 mils from frontfacex from frontface Distinct cracks visible Continuous internal spallaall edges N 83 mils tion from 70 to 90 mils from frontface from frontfacex Continuous internal spallaNo visual damage tion from 60 to 100 mils from frontface -30 x

This test configuration was modeled in the PUFF code using the properties listed in Table IV; available characterization data for 6061-T6 (29), and the failure criteria described by Eq. (8). The result predicted in each case (visual and microscopic) was that the first spallation plane would occur about 80 mils in front of the impacted face at the following velocities: (1) Visual spallation at between 2.1 and 2.2 mm/psec. (2) Microscopic spallation at between l-3 and 1.4 mm/psec. Six shots were fired. The velocity range was varied to encompass the regime predicted to include microscopic spallation through visual spallation. Table VIII lists the impact conditions and the results of post-test examination. Table VIII indicates that visual spa11 occurred for specimen P4 at 2.20 mm/psec, at approximately 83 mils from the frontface of the target, as had been predicted. However, specimen P5, which was impacted at a

42

Journal of The Franklin

Institute

Fracture of a Quartz-phenolic Composite Under Stress-wave Loading

l

1 high&,velocity than P4, showed no edge cracks at this depth. The occurrence of visual damage at one level and no visual damage at a higher level is characteristic of many plate-slap test results (9), and is attributed to the statistical variations of material strength, combined with statistical variations of flyer impact conditions, e.g. planarity and simultaneity. There was the possibility that specimen P3 also exhibited a visual crack on one edge. Further examination of the sectioned specimen up to 200 x revealed that the observed discontinuity was more likely a scratch. Specimens Pl, P2 and P6, when sectioned, clearly revealed the presence of internal microcracking. Considering the connected cracks seen in specimen P2, but not in specimen P6, it was concluded that the microscopic threshold was between 1.07 and 1.47 mm/psec. This bracketed the predicted microscopic threshold. Thus, the proof tests have shown that it is possible to predict specified levels of damage, both visual and microscopic, with engineering accuracy, using the fracture criterion formulation described herein. V. Conclusion

The present experimental data and supporting analysis lead to several conclusions concerning the dynamic fracture (spallation) of two-dimensionally reinforced, zero-degree shingle-angle quartz-phenolic under stress-wave loading in uniaxial strain: (1) Two damage thresholds for zero-degree shingle-angle quartz phenolic have been defined: the visual threshold, and a microscopic threshold represented as the lower limit of connected cracks. (2) The spallation threshold of zero-degree shingle-angle quartz-phenolic is as high as 3.45 and 2.51 kbars for visual and microscopic spallation, for tensile pulse durations as short as 0.492 and O-429 psec, respectively, and as low as 1.05 and 0.55 kbars, for visual and microscopic spallation, respectively, for pulse durations as long as 1.57 and 1.640 psec. (3) The spallation criterion for zero-degree shingle-angle quartz-phenolic was composed of a time-dependent and a time-independent portion. The time-dependent aspects of the spallation threshold of zero-degree shingle-angle quartz-phenolic were found to obey a failure criterion which was rate-process-oriented, such as (I/II) = (u/oJ exp ( - (T/u~), which combine the effects of tensile-pulse duration, stress or impulse and pulse shape. (5) The time-independent aspect of the fracture process was approximated reasonably well by a critical tensile stress criterion, as observed in Ref. (19). (6) The engineering criterion, based on rate-process considerations, was used in conjunction with a constitutive model to predict the visual and microscopic failure levels of a proof-test configuration. Experimental results agreed reasonably well with the prediction. (4)

Vol.293,No.l, Jannary 1972

43

L. J. Cohen and H. M. Berkowitz

(7) One

result of proof-testing is that if the ratio of post-test to pretest. acoustic velocity for each specimen is plotted vs. impulse delivered to the specimen, the points fall very close to or lie on a negatively sloped straight line which intersects the normalized acoustic velocity ordinate at a value of unity for zero-impulsive load ; since the acoustic velocity of the impulsive loaded specimen decreased with increasing impulsive load, it may also be reasoned that the mechanical behavior of the material is also degraded, e.g. strength and modulus.

Acknowledgements The work presented in this paper was sponsored by the Air Force Materials Laboratory, Wright-Patterson Air Force Base, Dayton, Ohio, under Contract No. F33615-68-C-1414. The authors wish to express their appreciation to Mr. S. A. Schechter of McDonnell Douglas Astronautics Company, for his valuable technical assistance, and to Mr. D. C. MacKallor also of McDonnell Douglas Astronautics Company, for conducting the exploding-foil tests.

References

(1) “Mechanical (2) (3)

(4)

(5)

(6)

(7)

(8)

(9)

(16) (11)

(12)

44

Behavior of Materials Under Dynamic Loads”, (ed. by U. S. Lindholm), New York, Springer Verlag, 1968. I. C. Skidmore, “An introduction to shock waves in solids”, Appl. Materials Res., pp. 131-147, July 1965. B. M. Butcher, L. M. Barker, D. E. Munson and C. D. Lundergan, “Influence of stress history on time-dependent spa11 in metals”, AIAA Journal, Vol. 2, pp. 977-990, June 1964. G. E. Duvall, “Shock waves in solids”, in “Shock Metamorphism of Natural Materials” (ed. by B. M. French and N. M. Short), pp. 19-29, Baltimore, Maryland, Mono Book Corp., 1968. J. H. Oscarson and K. F. Graff, “Summary report on spa11 fracture and dynamic response of materials”, Batelle Memorial Inst. (Columbus, Ohio). Rep. No. BAT-49-083 OSA-3176, Mar. 21 1968. L. J. Cohen and H. M. Berkowitz, “A study of plate-slap technology: Part II. The nuances of plate-slap testing of composite materials”, Air Force Materials Lab., Wright-Patterson AFB, Dayton, Ohio, AFML-TR-69-106 Part II, June 1969. P-PUFF-66 computer proR. N. Brodie and J. E. Hormuth, “The PUFF-66 TR-66-48, Air Force Weapons Lab., Kirtland AFB, New grams”, AFWL Mexico, May 1966. L. D. Berthoff and S. E. Benzley, “Toody-11 A computer program for twodimensional wave propagation”, Sandia Labs., Albuquerque, New Mexico, SC-RR6841, Nov. 1968. L. J. Cohen and H. M. Berkowitz, “Time dependent spallation of 6061-T6 aluminum under stress wave loading in uniaxial strain”, 1nnt.J. Fracture Mech., Vol. 7, No. 2. pp. 183-196, June 1971. F. A. Field, “A simple crack extension criterion for time dependent spallation”, Aerospace Corp., San Bernardino, Calif., Nov. 1969. J. R. Penning, D. M. Young and J. H. Prindle, “Negative equation of state and spall criteria, “Air Force Res. and Tech. Div., RTD-TDR-63-3039, AD420-509, Sept. 1963. D. R. Keller and D. M. Young, “A method for determining spallation criteria in Air Force Special Weapons Center, Kirtland solids”, AFSWC-TRD-61-102, AFB, New Mexico, Nov. 1961.

Journal of The Franklin

Institute

Fracture of a Quartz-phenolic Composite Under Stress-wave Loading 113) JI H. Gilman, “Dislocation (14) (15)

(16)

(17) (18) (19) (20)

(21) (22) (23)

(24) (25)

(26)

(27)

(28) (29)

dynamics and the response of materials to impact”, _4ppl. Mech. Rev., Vol. 21, No. 8, Aug. 1968. F. R. Tuler and B. M. Butcher, “A criterion for the time-dependence of dynamic fracture”, Int. J. Fracture Mech., Vol. 4, No. 4, pp. 486-491, Dec. 1968. J. C. Peck, H. M. Berkowitz and L. J. Cohen, “The relationship of the critical stress vus. impulse theory of spa11 fracture to stress gradient or stress-rate Santa Monica, Calif., Sept. 1968. theories”, Douglas Paper 5318, MDAC-WD, 1nt. J. Fracture Mech., Vol. 5, No. 4, Dec. 1969. R. L. Warnica, “Spallation thresholds of S-200 beryllium, ATJS graphite and isotropic boron nitride 75’F, and 500’F and 1000°F”, General Motors Tech. Center, Warren, Mich., July 1968, MSL-68-18. R. B. Bried, C. L. Mader and D. Venable, “Technique for the determination of dynamic-tensile-strength characteristics”, J. appl. Phye., Vol. 38, p. 977, 1964. H. Eyring, “Viscosity, plasticity and diffusion as examples of absolute reaction rates”, J. them. Ph,ys., Vol. 4, p. 283, 1936. R. L. Warnica and J. A. Charest, “Spallation thresholds of quartz-phenolic”, BSD-TR-67-24, Ballistic Systems Div., Norton AFB, Calif., Feb. 1967. H. M. Berkowitz and L. J. Cohen, “High amplitude stress-wave propagation in an anisotropic quartz-phenolic composite”, MDAC Paper WD 1179, McDonnell Douglas Astronautics Co., Huntington Beach, Calif., May 1970. Presented at the AIAA 9th Aerospace Sciences Meeting, New York City, Jan. 25-27, 1971. L. J. Cohen and 0. Ishai, “The elastic properties of three phase composites”, J. Composite Materials, Vol. 1, No. 4, pp. 391-403, Oct. 1967. P. Whiteman, Report No. UNDEX 445, Atomic Weapons Research Establishment, England, 1962. H. M. Berkowitz and L. J. Cohen, “A critical evaluation of plate-slap technology, Part I of Final Rep.: A study of plate-slap technology”, AFML-TR-69-109 Part I, Air Force Materials Lab., Wright Patterson AFB, Dayton, Ohio, June 1969. F. Bueche, “Physical properties of polymers”, New York, Interscience, pp. 246256, 1962. Z. N. Zhurkov and T. P. Sanfirova, ‘Study of the time-temperature dependence of mechanical strength”, Soviet Physics-Solid State, Vol. 2, No. 6, pp. 933-938, Dec. 1960. L. J. Cohen and 0. Ishai, “Delayed yielding of three-phase epoxy composites”, Meeting Preprint 711, ASCE Annual and National Meeting of Structural Engineering, Sept. 30-Oct. 4, 1968, Pittsburgh, Pa. (Published ASCE-EM, Dec. 1970, pp. 867-876.) M. H. Rice, R. G. McQueen and J. M. Walsh, “Compression of solids by strong shock-waves”, in Solid State Physics, Vol. 6 (ed. by F. Seitz and D. Turnbull), pp. l-63, New York, Academic Press, 1958. F. W. Davies and S. R. Penning, Rep. D2-9516, The Boeing Co., Aerospace Div., Seattle, Wash., 1968. C. D. Lundergan and W. Hermann, “Equation-of-state of 6061-T6 aluminum at low pressure”, J. appl. Phye., Vol. 31, p. 2016, July 1963.

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