NASA Technical Memorandum 83694

Dynamic Stress Analysis of Smoothand Notched Fiber CompositeFlexural Specimens

P. L. N. Murthy and C. C. ChamisLewis Research CenterCleveland, Ohio

Prepared for theSeventh Conference on Composite Materials: Testing and Designsponsored by the American Society for Testing and MaterialsPhiladelphia, Pennsylvania, April 2-5, 1984

NASA

https://ntrs.nasa.gov/search.jsp?R=19840017702 2018-08-10T09:39:04+00:00Z

TABLE OF CONTENTS

PAGE

SUMMARY 1INTRODUCTION " . . 1ANALYSIS 2

Specimen Geometry 2Finite Element Idealization 2Direct Transient Response Analysis 3Composite Systems Analyzed 4

RESULTS AND DISCUSSION ... 4Load Conditions 4Natural Frequencies and Normal Modes 4Displacement and Stress Wave Propagation 5Transient Response of Smooth Specimens 6Static and dynamic Stress Contours 7

Smooth Specimen 7Notched Specimen 7

GENERAL DISCUSSION 7SUMMARY OF RESULTS 8REFERENCES 9

DYNAMIC STRESS ANALYSIS OF SMOOTH AND NOTCHED FIBER

COMPOSITE FLEXURAL SPECIMENS

P. L. N. Murthy and.C. C. ChamlsNational Aeronautics and Space Administration

Lewis Research CenterCleveland, Ohio 44135

SUMMARY

A detailed analysis of the dynamic stress field 1n smooth and notchedfiber composite (Charpy-type) specimens 1s reported 1n this paper. The analy-sis 1s performed with the aid of the direct transient response analysis solu-tion sequence of MSC/NASTRAN. Three unidirectional composites were chosen forthe study. They are S-Glass/Epoxy, Kevlar/Epoxy and T-300/Epoxy composite

<NJ systems. The specimens are subjected to an Impact load which 1s modeled as a£j triangular Impulse with a maximum of 2000 Ib and a duration of 1 ms. The re-^ suits are compared with those of static analysis of the specimens subjected to

a peak load of 2000 Ib. For the geometry and type of materials studied, thestatic analysis results gave close conservative estimates for the dynamicstresses. Another Interesting Inference from the study 1s that the ImpactInduced effects are felt by S-Glass/Epoxy specimens sooner than Kevlar/Epoxyor T-300/Epoxy specimens.

INTRODUCTION

Smooth and notched flexural specimen testing continues to be popular 1nthe composites community for characterizing and/or qualifying fiber composites.Reasons for the popularity are: (1) simplicity, (2) adaptability to adverseenvironments, (3) availability of simple equations for data reduction, and (4)availability of written ASTM standard testing procedures. In addition tothese reasons, flexural specimen testing forces the material to respond like astructure by simultaneously subjecting 1t to tensile, compresslve and shearstresses. Furthermore, the notched flexural specimen (Charpy Impact testspecimen) testing enables easy determination of fracture toughness and Impactresistance.

Fracture 1n general (be 1t static, quasi-static or dynamic) 1s a dynamicevent and, as such, 1s a very complex process. Fracture progression 1n aflexural specimen is controlled by the local dynamic stress field which 1s alsocomplex. The local dynamic stress field 1s characterized by the stress waveswhich are normal, shear, flexural and surface waves. Each of the dynamicstresses can Initiate failure (or a defect) at a point and/or propagate thisdefect to fracture. For a complete understanding of these phenomena a detaileddescription of the local dynamic stress field 1s a prerequisite. This requiresthe use of a complex transient analysis Involving direct time Integration asopposed to the standard modal synthesis methods such as those available 1nsome general purpose finite element structural analysis codes. Solution 27(direct transient response) of MSC/NASTRAN 1s one of the available tools forsuch analyses. The objective of the present paper 1s to report a detailedanalysis of the dynamic stress field 1n smooth and notched Charpy specimens.

Although the notched Charpy test specimen has been used for years 1n test-Ing metals and recently 1n testing composites, no analysis has been performedto determine the detailed dynamic stress state variation 1n the notch vicinity.In general, the physical problem of the notched Charpy test specimen 1s dynamicand nonlinear; solution of this problem 1s difficult. However, a good firstorder approximation may be obtained by assuming linear behavior and a quasi-static load. Reference 1 reports such an analysis which uses the static solu-tion sequence of COSMIC NASTRAN. The main conclusions of reference 1 are: 1)the stress state Is biaxial, and 2) the Charpy test specimen 1s not suitablefor assessing the Impact resistance of nonmetalUc fiber composites directly.In the present work the effort 1s directed towards understanding the stresswave propagation and the attendant dynamic stress field 1n fiber compositesmooth and notched flexural specimens.

ANALYSIS

In this section, the specimen geometry, the finite element Idealization,the finite element analysis method, and the composite systems analyzed aredescribed.

Specimen Geometry

The geometry of the Charpy test specimen (ASTM STO E23-7) 1s shown 1nfigure 1. As can be seen 1n this figure, the overall length of the specimen1s 2.164 1n. and the length between supports 1s 1.574 1n. The specimen width1s 0.394 1n. The specimen unnotched depth 1s 0.394 1n. and the depth at thenotch 1s 0.315 1n. The notch 1s 0.079 1n. deep and has a 45° opening.

Finite Element Idealization

Two finite element Idealizations of Charpy test specimens — one withouta notch (smooth specimen) and one with a notch were selected for the presentstudy. The details of the meshes are shown 1n figures 2 and 3. The materialproperties are assumed to be uniform, orthotroplc, and obey a linear stress-strain law throughout the analysis. In addition, the specimen 1s assumed tobe 1n a state of plane stress. The plane stress assumption 1s also justifiedfrom the physics of the problem. The width restraints at the notch-tip arenegligible because of the very low value of the respective Polsson's ratio.For the present analysis, the plane stress assumption Implies that the stressesare permitted to vary along the specimen length and through the thickness butnot across the width. This reduces the stresses to be calculated to three,two normal and one shear.

With these assumptions, plane stress finite elements can be used to modelthe Charpy test specimen. For the smooth specimen all the elements are quad-rilateral. The notched specimen 1s modeled with both triangular elements andquadrilateral elements. The triangular elements are used as transition ele-ments 1n the areas around the the supports, the load application point and thenotch. These are the regions where maximum stress concentrations are expectedto occur and therefore are provided with a finer mesh. The boundary conditionsprescribed are such that the node at the left support 1s constrained from x, yand z displacements, and the node at the right support 1s constrained from y

and z displacements. In addition, for the notched specimen, three nodes clos-est to the right support are constrained from displacement In the y direction.The specimens are subjected to an Impulse loading. The form of Impact 1s atriangular function with peak load of 2000 Ib occurlng at 500 ys of a totalcontact time of 1000 ys.

The statistics of the finite element representation for the smooth andnotched specimens are as follows:

1) Smooth Specimens.Number of nodes or grid points 1147Number of displacement degrees of freedom (DOF) (2 degrees

of freedom per node) 2294Number of quadrilateral plate elements (CQUAD4) 1080DOF eliminated using the boundary conditions (2 from u = 0

and v = 0 at the left support and 1 from v=0 at theright support) 3

Number of free DOF (2294 - 3) 2291

2) Notched Specimens.Number of nodes or grid points 656Number of displacement degrees of freedom (DOF) 1312Number of quadrilateral plate elements (CQUAD4) 544Number of triangular plate elements (CTRIA3) 82Total number of elements (544 * 82) 626DOF eliminated using the boundary conditions (2 from u = 0

and v = 0 at the left support and 3 from v = 0 for threenodes at the right support) 5

Number of free DOF (1312 - 5) 1307

Finite Element Analysis Method

The MSC/NASTRAN general purpose structural analysis finite element com-puter program 1s used for the finite element analysis. The specific elementsused are Identified as CTRIA3 and CQUAD4. They are Isoparametric constantstrain elements. NASTRAN obtains the solution using a displacement formulationvia rigid format solution sequence No. 27. This solution sequence employs adirect time Integration scheme to obtain the transient response of a structure.

The solution sequence No. 27 of MSC/NASTRAN uses the Integration algorithmbased upon the Newmark Beta method (ref. 2). It provides stable results forthe widest possible spectrum of practical problems without sacrificing eitheraccuracy or efficiency. For complete details of the MSC/NASTRAN analysis(ref. 3) should be consulted. A brief description 1s given 1n the followingparagraphs.

The differential equations of a linear structural problem may be writtenIn the general matrix form

[P2M * pB + K] {u} = {F} (1)

where p = d/dt. M and K are the mass and stiffness matrices, B 1s asso-ciated with the damping matrix, u 1s the vector of displacements and F 1sthe load vector. The numerical Integration 1s achieved by replacing p^ andp by finite difference operators and then using explicit Integration. The

outputs of the transient analysis module Include velocities, and accelerationsas well as displacements. The output can be requested at even multiples ofthe Integration time step. This feature affords some economy 1n output datapreparation 1n cases where small time step 1s needed for greater accuracy.

Composite Systems Analyzed

Flexural (Charpy-type) test specimens made from three typical compositesystems are analyzed. They are: T-300/Epoxy, Kevlar/Epoxy, and S-Glass/Epoxycomposites. The specimens are all unidirectional composites with the fibersparallel to the length (x-ax1s, fig. 1) of the specimen.

The plane stress-strain relationship (stiffness) coefficients required toInput to NASTRAN are summarized 1n table I. These properties are obtained byusing the resident data-bank 1n the composite mechanics computer code ICAN(ref. 4). The relationships between the NASTRAN stiffness coefficients (G's),and the usual engineering constants are:

= Em/(1 -

G12 = V!121

22

33

13

= Ea22/(1 -

G22 = G21

121

= G !L12

= G = G = G23 31 32

(2)

(3)

(4)

(5)

(6)

The notation 1n equations (2) to (5) 1s as follows: Ejm denotes the longi-tudinal modulus, E^22 the transverse modulus, 6^12 the shear modulus, w^]2the major Polsson's and «j21 the minor Polsson's ratios. For an elasticmaterial the two Polsson's ratios are related by the well known relation

(7)

RESULTS AND DISCUSSION

Load conditions

Two types of load conditions are used 1n obtaining the results. The first1s a static loading where a force of 2000 Ib 1s applied at the center of thespecimen on the top surface. The second 1s an Impulse loading. This 1smodeled as a triangular pulse with a peak value of 2000 Ib 1n the middle. Thepulse 1s modeled to last for 1000 ys. The transient response 1s, however,obtained for three contact time periods (I.e., 3 ms). A separate normal modesanalysis 1s used to determine the first five natural frequencies.

Natural Frequencies and Normal Modes

The NASTRAN normal modes analysis module (Solution 3) 1s utilized to de-termine the first five natural frequencies and the associated mode shapes for

the Charpy test specimens. They are shown 1n figure 4. The results are shown1n table II for S-Glass/Epoxy specimens. The frequencies are used to determinethe time periods which aid 1n determining the Integration time step for thetransient analysis. A time step of 5 ys 1s chosen for the transient analysisbased upon the time periods shown 1n table II.

Displacement and Stress Wave Propagation

The bulk wave and shear wave velocities are normally much higher comparedto the flexural wave velocities. In order to capture the characteristics ofpropagation of these waves a much smaller time step of Integration (0.1 ys) 1schosen. The output of displacements and stress contours at various time Inter-vals are saved and displayed graphically 1n figures 5 to 10. Figures 5 to 7depict the dynamic displacement propagation 1n S-Glass/Epoxy, Kevlar/Epoxy andT-300/Epoxy specimens. Two bulk wave velocity parameters and one shear wavevelocity parameter are defined below to aid the following discussion of thedisplacement wave propagation results:

CB11 = 6l.l'' (8)

= G22/p (9)

CS]2 = G]2/p (10)

where p 1s the mass density of the material.

The computed values of Cgn , C&22> and CS12 are shown 1n table III forthe three composite systems under study. The velocities are expressed 1n1n./ps. The trend Indicated by Cg22 f°r *ne three materials (the transverseshock wave travels fastest 1n S-Glass/Epoxy and slowest 1n Kevlar/Epoxy) 1sseen clearly 1n figures 5 to 7 specifically the frames after 3 and 5 ys. Arough estimate of the normal wave velocity can be obtained by counting thenumber of elements that appear to be affected by the Impact from the figures 5to 7. The normal wave velocity estimates from the 1 and 3 sec frames are shownbelow:

Composite system Number of elements Velocity Average1 ysec 3 ysec 1 ysec 3 ysec

S-Glass/Epoxy 10 25 0.1313 0.1094 0.1204T-300/Epoxy 7 16 .0788 .0700 .0744Kevlar/Epoxy 5 12 .0657 .0520 .0589

These values are 1n close agreement with the theoretical values shown 1ntable III under Cg22- Tne same trend 1s also seen for the 3 and 5 y secframes. It can be concluded that the Initial shock travels with the bulk wavevelocity CB22 along the direction of Impact.

Once the normal shock reaches the bottom of the beam, the wavefront ap-pears to be moving 1n the longitudinal direction forming a flexural wave. Thevelocities of the waves traveling 1n the longitudinal direction can also bedetermined approximately with the same technique mentioned earlier. The fol-lowing are the details for the frame after 13 ys:

Composite system Number of Velocityelements

S-Glass/Epoxy 11 0.0510 1n/psecT-300/Epoxy 9 .0416 1n/ysecKevlar/Epoxy 7 .0320 1n/ysec

The above velocities appear to have the same trend as depicted by the wavevelocity parameter C$i2 shown 1n table III. However, the waves along thelongitudinal direction appear to move significantly slower than that Indicatedby C$i2- This 1s probably due to the coupling between the flexural wave andthe shear wave. The flexural wave velocity 1s significantly slower than theshear wave velocity. For example, the smooth S-Glass/Epoxy specimen understudy has a flexural wave velocity given by

Cp = 2af = 0.0137

where 8. 1s the length between the supports, f 1s the first fundamentalfrequency. (It 1s assumed that the wave number 1s 1 and the beam deflects Intoa half wave.)

The transient stress response after one percent (10 ps) of the contacttime are shown 1n figures 8 to 10 1n the form of stress contours. All stressesare localized at this early time. The longitudinal stress («n) 1n theKevlar/Epoxy and T-300/Epoxy composites 1s of about the same magnitude whilethat 1n the S-Glass/Epoxy 1s about half as much. The normal stress (022) an<*shear stress (012) are of about the same magnitude for all three composite sys-tems. It appears from these stress results that, under the same Impact condi-tions, the stress 1n the Kevlar/Epoxy and the T-300/Epoxy will reach fiberfracture stress magnitudes considerably earlier (about half the time) than 1nthe S-Glass/Epoxy composite. Two implications follow relative to the samestress magnitude: (1) the S-Glass/Epoxy composite will sustain greater Impactload prior to fracture than the T-300/Epoxy, and (2) the rapid compressivestress built up will cause longitudinal compression failure accompanied bysubstantial bending deflection 1n the Kevlar/Epoxy composite thus increasingthe Impact required to induce fracture.

Transient Response of Smooth Specimens

The displacements, velocities, accelerations and stresses are obtained fora total contact time of 1000 ys for S-Glass/Epoxy smooth specimens. In thesecomputations a time step of 5 *is 1s used. The output 1s saved for every twotime steps. Two points A and B as shown 1n figures 2 and 3 are selected forstudy. A is the load point and B 1s the opposite point at the bottom forsmooth and at the notch-tip for notched specimens.

The transient response results appear 1n figures 11 to 16. Figures 11 to13 show the longitudinal (axial) and the transverse (bending/f lexural) com-ponents of displacement, velocity and acceleration of point A plotted againsttime. The corresponding results for point B are not shown as they are similarto point A response both qualitatively and quantitatively. It can be concludedfrom these figures that the response 1s primarily 1n the first flexural mode.For example (from fig. 11) the number of cycles in 1 ms 1s counted as a little

over 6. From table II the first fundamental time period 1s 161.3 ys whichImplies that 6.2 (1000/161.3) cycles of response 1n first mode can be expected.

The stress response results are shown graphically 1n figures 14 to 16.Each figure contains the stress response of elements near points A and B. Thelongitudinal stress behavior appear to be primarily the first flexural moderesponse. However, the magnitude of stress near point A 1s about one and ahalf times greater than the magnitude of stress near point B. This 1s to beexpected because of stress concentration near the load point A. The transversenormal (022) and the shear (o ) stress Increase linearly to a peak when theload takes the maximum value of 2000 Ib and then decrease linearly to a zero.The corresponding stresses for the element near point B are Insignificant andtherefore can not be shown distinctly when drawn to the same scale.

The response after the load removal 1s not shown 1n the above figures.The computations, however, are conducted for three contact time periods. It1s found that, for all practical purposes, the specimen remains static. Atypical response curve Is shown 1n figure 17 for point A.

Static and Dynamic Stress Contours

Smooth specimen. - The static stress contours under a load of 2000 Ib andthe dynamic stress contours at the peak load of 2000 Ib are shown 1n figures18 to 20. They appear to be Identical. The peak values for the dynamic loadcase, however, are slightly lower than those for the static case. While themaxima for the longitudinal stress (a-\-\) occur at the center of top and thebottom, the transverse normal stress and the transverse shear stress have themaxima almost adjacent to each other near the load application point. Thetransverse shear stress and the axial stress distribution 1s seen to approachthe classical Euler-BernoulU theory predictions away from the load applicationpoint. Steep stress gradients are observed near the load application point.

Notched specimen. - The results for notched S-Glass/Epoxy specimen areshown 1n figures 21 to 23. The static and dynamic stress contours at the peakload show similar trend as observed 1n the case of smooth specimens. Figure 24shows the stress Intensity near notch-tip 1n relation to the far fieldstresses. This distance from the notch-tip 1s measured along the longitudinaldirection towards the left support. It 1s seen that all the three stressesattain very high peaks, Indicating severe local stress Intensities near thenotch-tip. As the stress allowables for 022 and <*-\2 are generally an orderof magnitude lower than that for a-\-\, one can expect a matrix Initiated fail-ure followed by fiber fractures at this location.

GENERAL DISCUSSION

The response analysis of smooth and notched Charpy-type flexural specimenssubjected to a triangular Impulsive load provides Insight Into the nature ofstress wave propagation, failure mechanisms and the relation between the staticand dynamic responses. The contact time of the Impact load 1s approximately 6time periods of the first flexural mode. The bulk wave velocities C$-\-\ andCg22» and the shear wave velocity C$i2 are very high compared to the flexuralwave velocity for the materials and the geometry under study. Hence, the re-sponse 1s observed at early times of the Impact event (of the order of a micro-second). It shows that the Initial waves travel with a bulk wave velocity

7

CB22 till they reach the bottom surface of the specimen. The waves thenappear to travel longitudinally towards the supports. The approximate calcu-lations based upon the deformations at various times Indicated that the wavevelocity 1s significantly lower than the shear wave velocity C$i2 but muchhigher than the flexural wave velocity. The wavefront appears to Induce aflexural wave as 1t progresses towards the supports.

At longer times, the response 1s primarily 1n the first flexural mode. Acomparison with the static response Indicates that little or no differenceexists 1n the magnitude for stresses at the peak load. The static predictions,however, are on the conservative side.

The response of notched fiber composite specimens show severe stress In-tensities near the notch region Indicating local failures 1n shear and trans-verse tension Initially followed by fiber fractures since the longitudinalstresses approach fracture stress magnitudes.

The response after the load removal reduces to mere noise; the structureremains practically static.

SUMMARY OF RESULTS

The results of the study on static, dynamic and transient response ofsmooth and notched, fiber composite, Charpy specimens are listed below:

(1) The wave propagation velocities can be estimated from the early timedisplacement propagation response; the estimates are In fair agreement withthe theoretical predictions.

(2) The first five flexural mode shapes and frequencies show couplingeffects from the thickness stretch and the transverse shear type modes; thefrequencies are not Integer multiples of the fundamental frequency.

(3) The dynamic and static peak load stress contours are almost Identi-cal. The static peak load stress magnitudes are slightly higher. Stress pre-dictions based upon a quasi-static approach lead to conservative estimates.

(4) The transient displacement and velocity response appear to be pri-marily 1n the first flexural mode. The acceleration response shows contribu-tions from higher modes.

(5) The structure responds for the load duration time period only. Thesteady state response after the load removal appears to be negligible.

(6) The transverse normal and shear stresses vary linearly with time andfollow the load path.

(7) The notch-tip region develops severe stress concentrations and anyof the three stresses could cause or Initiate a failure.

(8) Based upon the transient stress response, 1t appears that the fail-ures 1n Charpy specimens are Initiated at the notch-tip by the shear stressesand the transverse tensile stresses followed by fiber fractures. However, the

failures 1n smooth specimens are probably Initiated by a combined stress statenear the load application point followed by local Interply delamlnatlons.

REFERENCES

1. Chamls, C. C., "Failure Mechanics of Fiber Composite Notched CharpySpecimens," NASA TM X-73462, National Aeronautics and SpaceAdministration, Lewis Research Center, Cleveland, OH, Sept. 1976.

2. Newmark, N. M., American Society of C1v1l Engineers. Journal of theEngineering Mechanics Division. EH-3, July 1959, pp. 67-94.

3. MacNeal, R. H., "The NASTRAN Theoretical Manual, (Level 15.5)," MacNeal-Schwendler Corp., Los Angeles, CA, Dec. 1972.

4. Murthy, P. L. N. and Chamls, C. C., "ICAN: Integrated Composite Analyzer:Users and Programmers Manuals, NASA TP; No. to be assigned, NationalAeronautics and Space Administration, Lewis Research Center, Cleveland,OH, 1984.

TABLE I. - NASTRAN PLANE STRESS - STRAIN RELATIONSHIPS

Compos Hesystem

S-Glass/EpoxyKevlar

/EpoxyT-300

/Epoxy

Mass density

(xlO4)

(Ib.sec2/1n4)

1.813

1.249

1.405

Stress-strain coefficient

Gn

8.7900

12.385

17.896

G12 - G21

1.1700

.20082

.30275

G22

(xlO6 ps1)

3.2600

.57377

1.1318

Orthotropy Ratios

G33

1.2700

.31635

.50871

G11/G22

2.70

21.59

15.81

Gn/G33

6.92

39.15

35.18

TABLE II. - NATURAL FREQUENCIES AND TIME

PERIODS FOR S-GLASS/EPOXY SMOOTH AND

NOTCHED SPECIMENS

Specimentype

Smooth

Notched

Modenumber

1234512345

Frequency(cycles/sec)

6200.6711659.5419993.0231062.843913.029030.1614631.3324596.5627775.8636685.27

Time period(PS)

161.385.850.232.222.8110.768.340.736.027.3

TABLE III. - WAVE VELOCITY PARAMETERS

FOR THE SELECTED COMPOSITE SYSTEMS

Parameter\

MaterialBll "512

S-Glass/EpoxyKevlar/EpoxyT-300/Epoxy

0.2201.3149.3569

0.1341.0678.0698

0.0837.0503.0602

a 394x

*-2.164-

a 394

0.315

0.787-1.082-

^Ly^UEND SUPPORT

Figure 1. - Geometry of ASTM Charpy test specimen.(All dimensions in inches.)

Figure 2. - Finite element idealization of smooth specimen.

Ptt)A

B

Figure 3. - Finite element idealization of notched Chappyspecimen.

L f = 6200.67 Hz. 1. f = 9030.157 Hz.

2. f = 11659. 54 Hz. 2. f = 14631.33 Hz.

3. f = 19993.02 Hz. 3. f = 245%. 56 Hz.

4. f = 31062. 80 Hz. 4. f = 27775.86 Hz

5. f = 43913.02 Hz. 5. f = 36685.27 Hz.

Figure 4 - Natural frequencies and mode shapes forS-glass/epoxy smooth and notched flexural specimens.

3 Msec

10 Msec

13 Msec

5 usec

6 usec

15 Msec

18 Msec

9 Msec 20 Msec

Figure 5. - Dynamic displacement propagation in S-glass/epoxy composite flexural specimen. (Triangular impulse:2000 Ib maximum 1000 Msec duration.)

Ipsec

n * • i • •ihibJ]

Hi5 Msec

10 Msec

13 Msec

15 Msec

6 Msec 18 Msec

20|jsec

Figure 6. - Dynamic displacement propagation in Kevlar/epoxy composite flexural specimen. (Triangular impulse:2000 Ib maximum 1000 Msec duration.)

Ijisec

3|isec

6|osec

10 p.sec

13 ysec

15p.sec

IStisec

20|isec

Figure 7. - Dynamic displacement propagation in T-300/epoxy composite flexural specimen. (Triangular impulse:2000 Ib maximum 1000 usec duration.)

SYMBOL VALUES, psi

1 -L 328899E+032 -L143674E+033 -9.584489E+024 -7.732237E+025 -5 879985E+026 -4.027733E+027 -2.175482E+028 -3.232298E+019 1.529022E+02

10 3.381274E+02

SYMBOL VALUES, psi

1 -2.362948E+032 -2.065930E+033 -L768912E+034 -L 471895E+035 -1.174877E+036 -a 778589E+027 -5 308411E+028 *838233E+029 L 319453E+0110 3.102123E+02

(a) 0ji Contours.

1 -L052444E+032 -9.068754E+023 -7.613066E+024 -6.157379E+025 -4J01691E+026 3.246003E+027 1.790316E+028 3.346283E+019 1.121059E+02

10 2.576747E+029 lO

(a) QH Contours.

1 -1.913533E+032 -8.775216E+023 -7.415100E+024 -6.054964E+025 -4694862E+026 -3.334752E+027 -L974635E+028 -6.W5193E+019 7.455969E+01

10 2.105713E+02„ 10 P(t)

(b) 022 Contours.

1 -5.760680E+022 -4.970201E+023 -4120802E+024 -3.689114E+025 -2.998825E+026 -1.808336E+027 -1.017847E+028 -2.273584E+019 5.631304E+01

10 1.353619E+0210 IP f t )

o22 Contours.

1 7.771991E+022 -*. 946070E+023 -5.920160E+024 -4.994229E+025 -4.068309E+026 -3.142388E+027 -2.216458E+028 -1.290548E+029 -3.646273E+01

10 5.612931E+01

10 l - .P f t )

Figure & - Dynamic stress contours inS-glass/epoxy composite flexuralspecimen after 1 percent contact time.

(c) o12 Contours.

Figure 9. - Dynamic stress contours inKevlar/epoxy composite flexural specimenafter 1 percent of the contact time.

SYMBOL VALUES, psi

1 -2.200180E+032 -L 907888E+033 -L615597E+034 -1.323305E+035 -L 031014E+036 -7.387221E+027 -4464305E+028 -1.541389E+029 1.381526E+02

10 4.304442E+02

Pit)

(a) Ojj Contours.

123456789

10

-1. 019H7E+03-8. 816818E+02-7. 442470E+02-6. 068122E+02-4693774E+02-3. 319426E+02-1. 945078E+02-6. 707301E+01a 036180E+011 177966E+02

10 8

v^1t6

<

Pft)

(b) 022 Contours.

123456789

10

-7.026985E+02-6.178950E+02-5.830914E+02-4 482878E+02-3.634842E+02-2.786306E+02-1. 938771E+02-L 090725E+02-2.426991E+016.053367E+01

10

Figure 10. - Dynamic stress contours inT-300/epoxy composite flexural specimenafter 1 percent contact time.

, 1.0

' .8

o30.

—5_j<

=3

o30.

to

.6

.4

.2

0

-.2

.5

0

-.5

-1.0

-1.5

-2.0

-2.5

-3.0

-3.50 .2 .4 .6 .8

TIME, msec1.0

Figure 11. - Displacement responseof point A for S-glass/epoxysmooth flexural specimen.

oo

oo

o:UJ

.2 .4 .6 .8TIME, msec

1.0

Figure 12. - Velocity response ofpoint A for S-glass/epoxy smoothflexural specimen.

LUCMO *->o S< -~-

oo

OO

.2 .4 .6 .8 1.0TIME, msec

Figure 13. - Acceleration responsefor S-glass/epoxy smooth flexuralspecimen.

1.0

xX

o

UJa: -.5

-1.0

-1.5

BOTTOM

.2 .4 .6TIME, msec

.8 1.0

Figure 14 - Axial stress oxx re-sponse of top and bottom elementsnear points A and B for S-glass/epoxy smooth flexural specimen.

toco

10

-1

l~ -2o •=>

ffi°5; -4z

1— "'

-6

r BOTTOM\

\ I

.2

MOP

I I.4 .6

TIME, msec

.8 1.0

Figure 15. - Transverse normalstress Oyy response of top andbottom elements near points Aand B for S -glass Jepoxy smoothflexural specimen.

.5

0

-.5

2J.E -1.0CO £

" > , -L5

COCOLUOHI—CO

o:LU O

-ao-a 5-3.0

\'BOTTOM FIBER

I I I I I0 .2 .4 .6 .8

TIME, msec1.0

Figure 16. - Transverse shear stressoxy response of top and bottomelements near points A and B forS-glass/epoxy smooth flexuralspecimen.

0 .5 1.0 1.5 2.0 2.5 3.0TIME, msec

Figure 17. - Displacement responseof point A for three contact timeperiods of S-glass/epoxy smoothflexural specimen.

SYMBOL VALUES, psi

123456789

10

-1.494680E+05-1.216115E+05-9.375496E+04-6. 589843E+04-3.804191E+04-1.018539E+041.767114E+044 552766E+047.338418E+041.012407E+05

SYMBOL VALUES, psi

2000 Ib

(a) Static stress contours.

123456789

10

-1.480251E+05-1.205350E+05-9. 304484E+04^. 555471E+04-3.806458E+04-1.057445E+041.691569E+044 440582E+047.189595E+049.938608E+04

2000 Ib

123456789

10

-5. 259623E+04-4. 533239E+04-3. 806855E+04-3. 080471E+04-2. 354087E+04-1.627703E+04-9. 013191E+03-1.749351E+035. 514490E+031. 277833E+04

10 |. 2000 Ib8 J3M 21'y /i5'3/ ( V

(a) Static stress contours.

1 -5. 248293E+042 -4523803E+043 -3. 799313E+044 -3.074823E+045 -2. 350333E+046789

10

-1.625843E+04-9. 013535E+03-1. 768636E+035.476263E+031. 272116E+04

10 }, 2000 Ib8^%!

Q:(b) Dynamic stress contours.

Figure 18. - Comparison of static and dynamicaxial stress oxx contours at peak load forS-glass/epoxy smooth flexural specimens.

(b) Dynamic stress contours.

Figure 19. - Comparison of static and dynamictransverse normal stress Oyy contours atpeak load for S-glass/epoxy smooth flexuralspecimen.

SYMBOL VALUES, psi

SYMBOL VALUES, psi123456789

10

-2. 867220E+04-2.474687E+04-2.082155E+04-1.689622E+04-1. 297089E+04-9. 045565E+03-5.129230E+03-1. 194911E+032.730416E+036.655744E+03

910

123456789

10

-a 175306E+04i 182584E+046. 540473E+041.089836E+051. 525625E+051.961414E+052. 397203E+052.832992E+053.268781E+053.704570E+05

2000 Ib

(a) Static stress contours.

(a) Static stress contours.

1 -2.125020E+042.137141E+046.399302E+04

123456789

10

-2.850863E+04-2.461521E+04-2.072178E+04-1.682836E+04-1.293493E+04-9.041510E+03-5.148086E+03-1.254662E+032.638762E+036.532187E+03

9 10

4 1.066146E+055 1.492362E+056 1.918579E+057 2.344795E+058 2.771011E+059 3.197227E+05

10 3.623443E+05

.8

|, 2000 Ib

(b) Dynamic stress contours.

Figure 20. - Comparison of static and dynamictransverse shear stress oxy contours atpeak load for S-glass/epoxy smooth flexuralspecimen.

(b) Dynamic stress contours.

Figure 21. - Comparison of static anddynamic axial stress oxx contoursnear the notch region at peak loadfor S-^lass/epoxy notched flexural

SYMBOL VALUES, psi

1 -4.934123E+039.081599E+032.309732E+04

4 3.711304E+045 5.112877E+046 6.514449E+047 7.916021E+048 9.317593E+049 L 071917E+05

10 1.212074E+05

SYMBOL VALUES, psi

1 -9.067550E+042 -7.053295E+043 -5.039041E+044 -3.024786E+045 -1.010531E+046 1.003724E+047 3.017979E+048 5.032234E+049 7.046488E+04

10 9.060743E+04

(a) Static stress contours. (a) Static stress contours.

123456789

10

-4. 830871E+03a 877968E+032.258681E+043.629565E+045.000448E+046.371332E+047.742216E+049.113100E+041.048398E+051.185487E+05

1 -a881748E+042 -6. 911646E+043 -4941543E+044 -2.971441E+045 -1.001339E+046 9.687638E+037 2.938866E+048 4 908969E+049 6.879071E+04

10 a 849173E+04

(b) Dynamic stress contours.

Figure 22. - Comparison of static anddynamic transverse normal stressOyy contours near the notch regionaf peak load for S-glass/epoxynotched flexural specimen.

(b) Dynamic stress contours.

Figure 23. - Comparison of static anddynamic transverse shear stress0^ contours near the notch regionat peak load for S-<jlass/epoxynotched flexural specimen.

300 r—

200

-100.0 .5

DISTANCE FROM NOTCH TIP. in.

Figure 24 - Stress intensity distribution near the notch tip for S-glassfepoxy notchedflexural specimen.

1. Report No.

NASA TM-83694

2. Government Accession No. 3. Recipient's Catalog No.

4. Title and Subtitle 5. Report Date

Dynamic Stress Analysis of Smooth and Notched FiberComposite Flexural Specimens 6. Performing Organization Code

505-33-5B

7. Author(s)

P. L. N. Murthy and C. C. Chamis

8. Performing Organization Report No.

E-2152

10. Work Unit No.

9. Performing Organization Name and Address

National Aeronautics and Space AdministrationLewis Research CenterCleveland, Ohio 44135

11. Contract or Grant No.

12. Sponsoring Agency Name and Address

National Aeronautics and Space AdministrationWashington, D.C. 20546

13. Type of Report and Period Covered

Technical Memorandum

14. Sponsoring Agency Code

15. Supplementary Notes

P. L. N. Murthy, NRC-NASA Research Associate. Prepared for the SeventhConference on Composite Materials: Testing and Design, sponsored by theAmerican Society for Testing and Materials, Philadelphia, Pennsylvania,April 2-5, 1984.

16. Abstract

A detailed analysis of the dynamic stress field in smooth and notched fiber com-posite (Charpy-type) specimens is reported in this paper. The analysis is per-formed with the aid of the direct transient response analysis solution sequenceof MSC/NASTRAN. Three unidirectional composites were chosen for the study. Theyare S-Glass/Epoxy, Kevlar/Epoxy and T-300/Epoxy composite systems. The specimensare subjected to an impact load which is modeled as a triangular impulse with amaximum of 2000 Ib and a duration of 1 ms. The results are compared with those ofstatic analysis of the specimens subjected to a peak load of 2000 Ib. For thegeometry and type of materials studied, the static analysis results gave closeconservative estimates for the dynamic stresses. Another interesting inferencefrom the study is that the impact induced effects are felt by S-Glass/Epoxy speci-mens sooner than Kevlar/Epoxy or T-300/Epoxy specimens.

17

19

Key Words (Suggested by Author(s))

Fiber composites; Stress wave propagation;Flexural specimen; Dynamic stressanalysis; Frequencies; Mode shapes;Transient response analysis; Fracturetoughness; Smooth specimen; Notchedspecimen; Triangular impulse

18. Distribution Statement

Unclassified - unlimitedSTAR Category 24

Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of pages 22. Price*

Unclassified Unclassified

'For sale by the National Technical Information Service. Springfield. Virginia 22161

National Aeronautics andSpace Administration

Washington. D.C.20546

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