Deformation Analysis of Composites Exhibiting Large · PDF fileDeformation Analysis of...

45

Deformation Analysis of Composites Exhibiting Large Strain-Rate Effects

D. C. PREVORSEK, H. B. CHIN and Y. D. KWON

Allied-Signal Inc., Research and Technology, PO Box 1021, Morristown, New Jersey 07962-1021, USA

ABSTRACT

Viscoelastic high modulus composites exhibit excellent impact damage tolerance, a material characteristic which is essential to achieve the survivability of structures and equipment when these are exposed to high speed projectiles, explosions, etc. Relevant properties and characteristics of viscoelastic ultra-high strength polyethylene fiber reinforced composites are discussed to identify their inherent advantages resulting from the strain dependent behavior of the reinforcing .fiber. The focus of this paper is the theoreticalrand experimental deformation analysis of viscoelastic composites involving farge strains caused by a ballistic impact.

INTRODUCTION

Viscoelastic composites subjected to large deformation are rapidly becoming materials of choice for applications where survivability of equipment and people is a key factor. With regard to overall properties and mathematical analysis, this class of materials falls between two well investigated categories of composites: the composites with elastomeric matrices such as pneumatic tires and the rigid composites in which glass, carbon or aramid fibers are embedded in a high modulus rigid matrix. In the latter case, the typical matrix materials are epoxies, bismaleimides, and high performance thermoplastic resins such as PEEK, etc.

The mechanics of rubbery composites has been a field of major scientific 617

I. H. Marshall (ed.), Composite Structures© Elsevier Science Publishers LTD. 1991

618 D. C. Prevorsek, H. B. Chin and Y. D. Kwon

endeavor for many years. Temperature rise, strain and strain rate dependence of properties, non-linear behavior, etc., must be taken into consideration to arrive at satisfactory analytical solutions for deflection and performance analysis.! For rigid composites the deformations are so small that linear, elastic approximation yields satisfactory results. 2

The focus of this paper is on a new type of 'semi-rigid' damage tolerant composite. A typical representative of these composites consists of high performance PE fibers of Spectra@ type 3 embedded in a matrix of a block copolymer containing rigid and rubbery segments, or a matrix of an interpenetrating network exhibiting similar properties as a PE matrix. These composites are frequently used to protect other structures and their primary function is to absorb energy. They must, therefore, be capable to undergo large deformations without failure and exhibit outstanding properties at the extremely high deformation rates encountered in explosions, ballistic impact, etc.

The behavior of these composites can neither be treated by the mechanics and experimentation developed for rigid composites used, for example, in aircraft structures nor by the methods to treat elastomeric composites as is done in tire mechanics. The mechanics of viscoelastic ballistic composites is therefore a field requiring new and special experimental as well as analytical procedures.

In this paper we review our progress in the ballistic mechanics of viscoelastic composites and discuss our experimental and computational scheme to predict the performance of these composites at extreme rates of deformation. The focal point of our study is the mathematical and experimental analysis of the interaction of a projectile with flat plate viscoelastic composites reinforced with fibers exhibiting large viscoelastic effects.

PROJECTILE ARMOR INTERACTION: THE METHODOLOGY

A quantitative analysis ofprojecti\e viscoelastic armor interaction is a very complex task because of: (a) a lack of property data of components at these extreme rates of deformation; (b) a lack of failure criteria; (c) the existence of multiple modes of failure depending on projectile characteristics. Because of the unmatched potential of Spectra® PE fibers in damage tolerant structures we are involved in long range research to solve some of these problems and develop reliable predictive capabilities for advanced armor design.

Deformation of Composites Exhibiting Large Strain-Rate Effects 619

To achieve this goal we developed an experimental and analytical plan which should provide data for use in various computational codes. Our plan includes quantitative determinations or analysis of:

(1) adiabatic heating, (2) heat transfer, (3) fiber properties as a function of deformation rates using high speed

testing equipment, (4) transverse impact of fibers with projectiles, (5) transverse impact of composite plaques with projectiles.

TEMPERATURE EFFECTS DURING BALLISTIC IMPACT

In order to develop a satisfactory approach to solve the problems of interaction between a projectile and a composite material we must first establish :

(1) whether the material is strain rate dependent, (2) the magnitude of the strain rate effects, (3) whether the material wil1 exhibit a temperature change during

impact, (4) the magnitude of the temperature rise.

In viscoelastic rubber composites such as pneumatic tires the temperature rise during use may be very large. Temperature rises exceeding 100°C, caused by deformations, are not uncommon and must, therefore, be taken into consideration in the stress, deformation and failure analyses.

With carbon, aramid or glass fiber composites used in aircraft and other structures the difference between the temperature during use and the ambient temperature is too smal1 to require consideration in the analysis. The magnitude of the temperature rise of Spectra® fiber composites during bal1istic impact, however, needs clarification. Since there is experimental evidence as wel1 as theoretical predictions that these temperature rises may be significant or even critical for the armor performance, we present below a quantitative analysis of this problem.

The quantitative determination of temperature rise associated with severe deformation is particularly critical with the thermoplastic composite whose properties are very sensitive to temperature changes. With PE fiber composites it is therefore desirable to know the temperature within an accuracy of ± lO°e.


The issue of temperature rise is further confounded by the appearance of molten filaments in the impact zone. It is not uncommon that a microscopical examination of the ballistically impacted area reveals sections of fibers that appear to have melted on impact. These findings seem to agree with the theoretical work of Smith.4 This author proposes that under stresses approaching the breaking stress the PE fibers experience a crystal melt transition causing a melting point depression which ultimately leads to failure.

Evidence contradicting this stress-induced melting failure is provided by the observation that the projectiles are stopped regardless of whether the molten filaments are observed or not and the lack of correlation between the appearance of molten filament and armor performance. Most importantly, PE fiber composites retain their terminal ballistic potential at temperatures which greatly exceed those at which a substantial drop in properties is observed at standard rates of deformations.

In discussing the adiabatic temperature changes in polymeric materials caused by severe straining, it is frequently overlooked that during adiabatic stretching the temperature change with sample length, L, is given by

(OT) (OF) Cp oL = T oT

p,ad p,L

(1)

where Tis the temperature, Cp the heat capacity and Fthe retractive force. The adiabatic temperature change with length is related to the

temperature coefficient of the retractive force. Since the modulus of the crystalline domains decreases with increasing sample temperature, (oF/oT) is negative and the sample temperature should decrease on straining.

However, the fibers are not 100% crystalline. About 25% of the fiber volume behaves like rubber. The amorphous domains exhibit on straining a viscous loss that can be accurately determined by a variety of viscoelastic testing techniques and expressed as loss modulus or tan 15. In order to estimate the fraction offiber breaking energy that is converted into heat, we have determined the loss tangent (tan (5) of Spectra® fiber using a large strain dynamic viscoelastometer of the RJS type. 5

A 1200-denier yarn of Spectra ® 900 was subjected to a sinusoidal cyclic strain of strain amplitude ,1y = ± 0'0025, at a frequency of 10 Hz at 40°C. The energy loss per cycle was found to be 3-7 x 105 erg/g (or 3-63 x 105

erg/cm 3). The energy loss per cycle (that equals energy converted into heat), Q, is given by

Q = nE* ,1y2 sin 15 (2)


b

A

t:.-y = strain amplitude

* E = complex modulus

c

2 t:.-y

'Y. STRAIN

?-<l N

*. W

B

FIG. I. Viscoelastic hysteresis of Spectra' fiber.

where E* is the complex modulus. By means of eqn (2) we found sin <5 (or tan (5) to be 0·026.

Referring to Fig. 1, the quantity in eqn (2) corresponds to the area of the hysteresis loop. Defining the loss factorJas the ratio of this loop area to the area of triangle ABC in Fig. l,Jindicates the fraction of the energy input in straining the specimen by 211,)" which is lost by the hysteresis. ThusJis given by

J = (n/2) sin <5 (3)

Substituting sin <5 = 0'026,f is found to be 0·041. The temperature rise by adiabatic straining is obtained by applying one

half of theJvalue (because there is no contraction process in the case of yarn breaking) to the energy to break (501/g) to obtain the amount of heat which is generated in the process. This yields 0-44°C.

Consequently these experimental data show that the adiabatic heating in ultra-strong PE fibers is negligible and that the property changes as function of temperature and strain rate reflect only the viscoelastic characteristics of the fiber with no interference from secondary straininduced temperature effects. During testing fibers are essentially at ambient temperature, even at a very high rate of deformation. In the analysis of ballistic impact of Spectra H) composites it is, therefore, justified to assume that the polyethylene fiber composite is at the ambient temperature during the entire period of projectile target interaction.


To make the above conclusion credible we must still explain the existence of molten filaments in composites that were struck by a projectile. In a systematic investigation of plaques which were struck with deformable projectiles, we noticed that the molten filaments are observed only in the cases where the projectile is stopped by the armor. Since the molten filaments are not present in targets that were penetrated by projectiles, it follows that the melting of filaments is not caused by the adiabatic straininduced heating but by the heat transfer from the hot projectile after the projectile is stopped.

FIBER MODULUS AS A FUNCTION OF STRAIN RATE

In the performance analysis of a damage tolerant structure, the modulus of the fibers and composites and the strain propagation rate J(Ejp) (E is modulus and p is density) are as important as strength and energy to break. Experimentally, modulus E and strain propagation rate are much easier to determine than strength and energy to break. High speed impact testing and transverse ballistic impact testing yielded the plot of modulus change with the strain rate shown in Fig. 2. A three-fold increase in tensile modulus resulting from the deformation rate increases from 10 to 104 min -1 shows the magnitude of the strain rate effects which we can expect for all the

4000.,-----------------,

C III

~ 3000 .. ::l :i 'tI o ::i! 2000 .!! 'iii c ~

1000

• Gauge Length 2.5 em • 7.5 em & 25 em

&

& & • • • •

• •

10 102 103

Strain Rate (Min-I)

• • • •

&

•

FIG. 2. Effect of strain rate on tensile modulus for Spectra" 1000 fiber.


engineering moduli appearing in the constitutive relationship of the composite.

In addition, it is obvious that in the case of an armor which slows down and stops the projectile, the properties of the armor (PE composite) will change as a function of the material deformation rate. At deformation rates exceeding 105 min - 1 the modulus of ultra-strong PE fibers (such as Spectra® 1000) becomes insensitive to strain rate changes. The recorded value of 320 GPa is close to the theoretical modulus of deformation and the longitudinal stress wave velocity is '" 18 000 mis, which is comparable to diamond and is significantly higher than that of any polymeric material.

The quantity (E/p) is very important in ballistic mechanics because it determines the amount of material which participates in absorbing the kinetic energy of the projectile. The extremely high modulus of PE fibers and their low density are the key factors making these materials so effective in damage tolerant structures.

PROJECTILE SPECTRA® ARMOR DEFORMATION ANALYSIS

The deformation of Spectra® composites subjected to ballistic impact was foIl owed by a high-speed camera. The experimental set-up allowed determination of the following quantities:

(1) projectile velocity and its deceleration during impact, (2) transverse deformation of the target, (3) compaction and damage of the target, (4) projectile deformation during impact.

The experimental observations provide the background for a theoretical analysis of the ballistic impact on the Spectra(~) composites. In the theoretical analysis special attention was paid to account for the strain rate dependence of the Spectra® fiber properties. The effective elastic moduli of Spectra(!Y composites were estimated by means of the Halpin- Tsai 6

semiempirical relationship for composites and lamination theory using the experimentally determined properties and their strain rate dependence whenever possible. Unknown properties were initially estimated and then adjusted to better match the observed deformations of the target.

The ballistic impact is a time-dependent problem and its governing equation has the foIlowing matrix differential form:

[M]ii + [C]u + [K]u = [F] (4)


Yes 6.0/0 ~c:

FIG. 3. Ballistic impact analysis scheme.

where [M] is the mass matrix, [C] the damping matrix, [K] the stiffness matrix and [F] the external force vector. The displacement vector is D, and the upper dots denote differentiation with respect to time. This equation was solved using a general finite element computer program, MARC, developed by Marc Analysis Research Corporation. Detailed discussion regarding the solution method of the above dynamic equation is given by Prevorsek and Chin.7

Since the strain rate during ballistic impact is not known a priori, an iterative solution method is employed, as schematically shown in Fig. 3. The ballistic event is divided into several time intervals, and then the analysis is performed in a stepwise manner. Briefly, the analysis procedure proceeds as follows:

(1) Estimate the strain rate in the first time interval. (2) Obtain the fiber and matrix properties at that strain rate from

experimentally measured strain rate dependent properties. (3) Calculate the effective properties of the Spectra® composite using

the properties in step 2.


TABLE I Effective moduli and Poisson's ratio of [0/90 j Spectra® composite

Moduli (GPa)

Strain rate (min - 1) 10 500 1000 5000 10000

Exx 38 49 54 81 98 Eyy 38 49 54 81 98 Ezz 6·3 6·6 6·7 7·0 7·1 GXY 3-7 3-8 3-9 4·0 4·0 GyZ 3-7 3-8 3-9 4·0 4·0 Gzx 3-7 3-8 3-9 4·0 4·0

Poisson's ratio

Strain rate (min -1) 10 500 1000 5000 10000

vxy 0·058 0·048 0·045 0·032 0·028 Vyz 0·3 0·3 0·3 0·3 0·3 Vxz 0·3 0·3 0·3 0·3 0·3

(4) Perform the impact analysis by solving eqn (4). (5) Calculate the strain rate from the solution in step 4 and compare

with the estimated strain rate in step l. Also calculate the deformation of the target.

(6) Repeat steps 2 through 6 until the strain rate has converged within the prescribed convergence criteria and the calculated deformation agrees with the observed deformation.

(7) Proceed to the next time interval and repeat steps 2 through 6.

Using the computational scheme shown in Fig. 3 and by analyzing the results of several projectile target interactions, we established by iterative procedures that the effective engineering moduli and Poisson's ratio of (0/90) Spectra@ composites listed in Table 1 yield the deformations of the target which match, within experimental error, the deformations recorded by high-speed photographic techniques.

CONCLUSIONS

Viscoelastic composites exhibiting large strain rate effects are the materials of choice in damage tolerant structures and a variety of armor.


Ballistic mechanics treating such structures must take into consideration

-adiabatic heating, -strain rate dependence of properties, -existence of mUltiple failure mechanisms.

By subdividing the time period of impact into smaller intervals and by varying the properties of the composites in a stepwise fashion, the strain rate dependence of composite properties can be taken into account.

REFERENCES

1. PREvORSEK, D. c., BERINGER, C. w., KWON, Y. D. and SHARMA, R. K., Bias passenger tires: effect of construction on the cord deformation and temperature rise during rolling. ASTM Special Technical Publication 694,1979, pp. 298-325.

2. HALPIN, J. c., Primer on Composite Materials: Analysis. Technomic Publishing Co., Lancaster, PA, 1984.

3. PREVORSEK, D. c., Ultrahigh modulus/ strength polyethylene fibers and composites. In Reference Bookfor Composites Technology, Vol. J, ed. S. M. Lee. Technomic Publishing Co., Lancaster, PA, 1989, pp.167- 74.

4. SMITH, K. J. Jr, The breaking strength of perfect polymer fibers. Polymer Engineering and Science, 30(8) (1990) 437-43.

5. KWON, Y. D., SHARMA, R. K. and PREVORSEK, D. C., Viscoelastic properties of tire cords under conditions of rolling tires. ASTM Special Technical Publication 694, 1979, pp. 239-62.

6. HALPIN, J. C. and TSAI, S. W., Effects of environmental factors on composite materials. Air Force Material Laboratory Technical Report, AFML-TR-67-423, 1967.

7. PREVORSEK, D. C. and CHIN, H. 8., Properties of spectra fibers and composites at ballistic rates of deformation. 21st International SAMPE Technical Conference, 25-28 September 1989, Atlantic City, New Jersey.

Deformation Analysis of Composites Exhibiting Large · PDF fileDeformation Analysis of...

Documents

Transcript of Deformation Analysis of Composites Exhibiting Large · PDF fileDeformation Analysis of...