MTL MS 86-3 rAI iI

SWORK-IN-PROGRESS PRESENTED AT THE

-. ARMY SYMPOSIUM ONSOLID MECHANICS, 1986 -

LIGHTENING OF THE FORCE

::.:' : SEP 2 218

October 1986

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WORK-IN-PROGRESS PRESENTED AT THE ARMY Final ReportSYMPOSIUM ON SOLID MECHANICS, 1986 - ______________

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Work-In-Progress presented at the Army Symposium on Solid Mechanics, 1986-Lightening of the Force, held at the U.S. Military Academy, West Point,New York, 7-9 October 1986.

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Acceleration Gunfire Rotating BandsAdhesives Guns Rotor BladesAircraft Helicopters Shaped ChargesAirframes High Temperature Shear PropertiesAluminum Alloys Impact SheltersBallistics Inertia ShipsCeramic Materials Intensity Shock (Mechanics)Collisions Joining SpectraComposite Materials Joints Statistical AnslysisComputerized Simulation Kinetic Energy Strain (M4echanics)Confidence Level Landing Gear Strain RateCopper Life (Durability) Strength (General)Corrosion Lightweight Stress CorrosionCrack Propagation Loads (Forces) StressesCrashes Measurement Structural ResponseCrash Resistance Mechanics StructuresDefects (Materials) Metals Survival (General)Displacements Mines (Ordnance) Telemeter SystemsDynamic Response Models TemperaturesDynamics Moisture Thermal StressesEnergy Absorbers Nondestructive Testing ThreatsEnvironments Plastic Properties Time DependenceExplosives Plates TitaniumFabrication Predictions TransientsFailure Pressure VibrationFatigue (Materials) Probability VulnerabilityFighter Aircraft Projectiles Wpapon SystemsFragmentation ProtectionFuselages Reliability

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PREFACE

The Army Symposium on Solid Mechanics, 1986, represents thetenth in the series of Iienniel meetings of researchers fromgovernment, academia and industry working in the field of solidmechanics in support of Army, Navy and Air Force systems.

This document contains the extended abstracts of work-in-progress selected for presentation at the 1986 symposium andinclusion in the proceedings. A companion document contains thefull technical manuscripts of completed work selected for presen-tation at the meeting.

%

Initially organized in 1966 to answer the needs of Armyresearchers for a forum for presentation and critical review ofwork being accomplished by Army laboratories and their contrac-tors, the symposium was expanded in 1968 to include the partici-pation of the Navy, Air Force and other government agencies activein areas of Army interest. During the ensuing years the symposiumfulfilled its original purpose by providing an excellent opportu-nity for the interaction of mechanics researchers in the threeservices as well as the Departments of Energy and Transportation.

For each meeting the symposium committee selects a centraltheme representing a technical or system-related area of currentmajor interest to the Army. The theme "Lightening of the Force"selected for this, the tenth symposium, represents a major Armypriority in order to enhance both fighting capability on thebattlefield and the capability for rapid deployment of fightingforces to remote locations. The full papers and extended ab-stracts selected for presentation and/or inclusion in the proceed-ings are representative of the extensive research and advance de-velopment being carried on in support of this central theme.

Although centered on the applied research (6.?) area, thearea of interest of the symposium spans the range from basic (6.1)research through advanced development (6.4). The papers selectedfor this symposium provide this broad mixed coverage of the cen-tral theme.

On this tenth anniversary a review of the record of the ArmySymposium on Solid Mechanics shows that it is an appropriate andpopular event that has filled an important need over the twentyyears of its existence. It is fitting now to acknowledge theforesight and guidance of the individuals who initiated and stead-fastly supported the symposium from the beginning. Therefore toJoseph I. Bluhm, who throughout his career was the leading advo-cate of solid mechanics research and engineering in the Army; andto the late Dr. John M. Slepetz who led and guided the ArmyMaterials Technology Laboratory and the Army to and through theintricacies of advanced composites.

iii

: 5 " , - "" " "" *,** \* '; .I # %,WWL " ' .,' 't ,

PREVIOUS DOCUMENTS IN THIS SYMPOSIA SERIES

Proceedings of the Army Symposium on Solid Mechanics, 1169, AWMRCMS 68-09, September 1968, AD 675 463

Proceedings of the Army Symposium on Solid Mechanics, 1970:Lightwieght Structures,

AMMRC MS 70-5, December 1970, AD 883 455L

Proceedings of the Army Symposium on Solid Mechanics, 197?:The Role of Mechanics in Design - Ballistic Problems,

AMMRC MS 73-2, September 1973, AD 772 827

Work-In-Progress Presented at the Army Symposium on Solid Mechanics, 1974:The Role of Mechanics in nesign, Structural Joints,

AMMRC MS 74-9, September 1974, AD 786 524

Work-In-Progress Presented at the Army Symposium on Solid Mechanics, 1976:Composite Materials: The Influence of Mechanics of Failure o6 Design,

AMMRC MS 76-3, September 1976, AD A029 736

Ongoing Case Studies Presented at the Army Symposium on Solid Mechanics, 1978:Case Studies on Structural Integrity and Reliability

AMMRC MS 78-4, September 1978, AD A059 605/6GI

Work-In-Progress Presented at the Army Symposium on Solid Mechanics, 1980:Designing for Extremes: Environment, Loading, and Structural Behavior,

AMMRC MS 80-5, September 1980, AD A090685

Work-In-Progress Presented at the Army Symposium on Solid Mechanics, 1982:Critical Mechanics Problems in Systems Designs,

AMMRC MS 82-5, September 1982 AD A119497

Proceedings of the Army Symposium on Solid Mechanics, 1q84:Advances in Solid Mechanics,

AMMRC MS 84-3, September 1984 AD A150042

|*

These documents may be ordered from the National Technical InformationService, Li. S. Department of Commerce, Springfield, VA 22161.

iv

SYMPOSIUM COMMITTEE

R. SHEA, Chairman, MTLJ. MESCALL, Vice Chairman, MTLJ. M. MCINTOSH, Coordinator, 11%

CPT .). LESKO, LngisticsD. M. RETLLY, Administrative CoordinatorK. SHOEMAKER, Administrative Coordinator

TECHNICAL PAPER; AND PROGRAM

J. ADACHI, Chairman, MTLR. BARSOIIM, MTL

J. F. MESCALL, MTL0. M. NEAL, MTLH. RAY, MTLR. SHEA, MTL

0. M. TRACEY, MTLT. Y. TSUI, MTL

WORK-IN-PROGRESS SESSION

G. E. MADDUX, Co-ChAirman, Air Force Flight Dynamics LaboratoryS. SerAbian, Co-Chairman, MTL

V

.... CONTENTS ;,

"]) MPUTED NEUTRON TOMOGRAPHY AND CODED APERTURE HOLOGRAPHY FROM REALTIME NEUTRON IMAGE. ,,, .................................................... I

M. F. Sulcoski, ;i t-y of-Irgi ni a

SPATIAL STRENGTH VARIATION AND STATISTICAL SIZE OF LAMINATEDORTHOTROPIC COMPOSITE MATERIALS,, ..

E. Samaras and M. Shinozuka, \University of GQoumbiA-

A DIRECT METHOD TO OBTAIN CONSTITUTIVE MODEL CONSTANTS FROM CYLINDERIMPACT TEST RESULTS} K . .................................................... 7

1

T. J. Holmquist y~d G. R. Johnson,Honeywell eft7 'sp Systems Division

-ASTIC STRAIN LOCALIZATION BETWEEN VOIDS IN SHEAR DEFORMATIONFIEL.......................................................13

.. Tracey, C. E. Freese, and P. J. Perrone,- Army Materials Technology Laboratory

A STUDY OF THE CRACK TIP PARAMETERS THAT GOVERN ENVIRONMENTALLYASSISTED CRACKING BY USE OF THE RISING DISPLACEMENT TES. ............... 21

R. Mayville, T. Warren and P. Hilton,Arthur D. Little Incorporated

L XPLICIT AND IMPLICIT SOIL MODELLING FOR DYNAMIC SOIL-STRUCTURE

INTERACTION PROBLEMS; .............. 27

A. Das Gupta, ArmJyBallistic Research Laboratory

OMPOSITE MATERIALS APPLICATIONS PROGRA5 AT THE US ARMY BALLISTICRESEARCH LABORATORY ........................... . ......... 2q

R. B. Murray, E. M. Patton, L. . Burton, and R. P. KasteArmy Ballistic s arch Laboratory

EFFECTIVE TREATMENT OF MEMBRANE AND SHEAR LOCKING PHENOMENA IN CURVEDSHEAR-DEFORMABLE AXISYMMETRIC SHELL ELEMENT .............................. 3

A. Tassler and L. Spiridigliozzi,

Army Materials Technology Lahoratory

PLANE STRAIN FINITE ELEMENT ANALYSIS OF RU4BER TRACK PAD .................. 37

A. R. Johnson and C. J. Quigley,Army Materials Tpchnology Laboritory

vii

ANALYSIS AND TESTING OF PREDAMAGED SHELL STRUCTURES .......... 41

R. E. Keefe, Kaman Sciences Corporation, andE. Reece, Sandia National Laboratories-

'3RITO 5-0N CONTROL BY COMPOSITE MATERIAL SUBSTITUTION WITH APPLICATIONTO THE M-939 5 TON TRUCK' ........ ................... 45

P Jong._ ra.""pfor( ion Systems Center

DURABILITY OF POWDERED ALUMINUM STURCTURE ............................. 49

K. Severyns and M. Artley,Air Force Wriqht Aeronaut- a oratories

SOME MECHANICS CONSIDERATIONS IN CERAMIC GUN BARREL LINERS. ............. 53

R. Barsoum, P. Perrone, P. WongArmy Materials Technology Laboratory,

andE. Bunning, SACO Defensp Incorporated

AUTHOR INDEX .............................................................. 61

viii

VL-T,,- W'V'w JV ¢ < - I ;, . &9 * ,. .'- o ,, .2~ ~'- -

COMPUTED NEUTRON TOMOGRAPHYAND

CODED APERTURE HOLOGRAPHYFROM REAL TIME NEUTRON IMAGES

*

MARK F. SULCOSKIUniversity of Virginia

P. 0. Box 7432Charlottesville, Virginia 22906

EXTENDED ABSTRACT

Neutron radiography is well known as a non-destructive examination(NDE) technique for low atomic number materials. The increased interestin lightweight composite materials using low atomic number elements(such as carbon) require modern imaging techniques such as computedneutron tomography and coded aperture neutron holography to complementother NDE techniques. The unique interaction mechanisms of neutronradiation as compared to x-rays allow higher detection structures, adhe-sive bonding layers in laminated structures and delamination detectionin composite structures.

The purpose of the continuing work described herein is to developand investigate the uses of neutron tomography and holography for NDEapplications. Much of the early work in neutron tomography was limitedby slow and tedious methods of optical densitometer scanning of staticneutron radiographs to obtain data. The use of boron trifluoride coun-ters rather than film improved the usefulness. This paper describesthe use of a real time neutron imaging system coupled with a dedicatedimage processing system to obtain neutron tomographs.

Experiments to date have utilized a Thomson-CSF neutron cameracoupled to a Digital Equipment Corporation LSI 11/23 based system usedfor image processing. Experiments have included the following:

Configuration of a reactor neutron beam port for neutronimaging.

Development and implementation of a convolution methodtomographic algorithm suitable for neutron imaging.

Results to date have demonstrated the proof of principal ofthis neutron tomography system:

Tomographs from real time images of 1.6 cm (0.63 in) woodentest objects have achieved near theoretical resolution of1.3 mm (0.051 in) voids using 200 projections with no image

processing.

Computation time of approximately 30 seconds per projection.

Preliminary benefits of image processing before tomography

data acquisition investigated.

Future work is planned to include the following:

Investigation of alternate algorithms to reduce the numberof projections necessary for a given resolution.

Investigation of combinations of image processing techniques

and other data preprocessing algorithms to allow largerobjects to be imaged and to increase resolution.

More studies of void detection and delamination detectionfor various materials and structures.

Coded aperture neutron holography is under investigation using acadmium Fresnel zone plate as the coded aperture and the real timeimaging system as the detection and holographic reconstruction system.Coded aperture imaging utilizes the zone place to encode scatteredneutron radiation from the entire volume of an object. The scatteredradiation pattern recorded at the detector is used as input data to aconvolution algorithm which reconstructs the scattering source (object).Thus, ideally, all the tomography planes of the object are recorded

simultaneously allowing a three dimensional neutron image of the object.This technique has not yet been successfully implemented and is

still under development. Current ongoing work includes:

Investigation of techniques to increase object scatteredneutron flux and/or increased detector sensitivity.

Comparison of several methods to improve signal-to-noiseratio of the neutron detection system.

Present address: U. S. Army Foreign Science and

Technology Center220 Seventh Street N. E.Charlottesville, Virginia 22901

2

I--" pI I I1K

SPATIAL STRENGTH VARIATION AND STATISTICALSIZE EFFECT OF LAMINATED ORTHOTROPIC

COMPOSITE MATERIALS

ELIAS SAMARASAssistant Professor of Civil Engineering

MASANOBU SHINOZUKARenwick Professor of Civil Engineering

Both at the Department of Civil Engineering and Engineering MechanicsColumbia University, New York, NY 10027

ABSTRACT

Resisting strength and other properties of engineering materials usedfor the production of laminated orthotropic composites are known to ,ivvconsiderable spatial variations. In the present study, a particular emphasisis placed, however, on the probabilistic model for spatial variation of mate-rial strength and on the corresponding statistical size effect. The principalidea lies in the interpretation that the material strength can be idealized asa multidimensional random field. This interpretation together with the re-cently developed method of digital simulation of multidimensional randomtelds by use of ARMA models makes it possible to demonstrate the statis-tical size effect in terms of numerical examples. Tha ARMA model methodmentioned above uses a recursive equation whose coefficient matrices aredetermined in accordance with the prescribed autocorrelation function ofthe multidimensional random field. Using the recursive equation with thesecoefficient matrices, we can generate with substantial computational ease,sample functions of the field over a large two- or three- dimensional do-main. An alternative method for the digital simulation of multidimensionalrandom fields is the well-known Fast Fourier Transform (FFT) method. Itshould be pointed out however, that the ARMA model method is consider-

3

ably more efficient in terms of computational time.

Consider now a specific example of a laminated orthotropic compos-

ite plate consisting of two laminae. Each lamina is divided into an equal

number of elements (4 6 = 24 for the case considered - see Fig. 1).

Fig. 1 Division of plate into 48 elements

Therefore the whole plate is divided into 2 24 = 48 elements. We

can now assign values for the material strengths in the three principal di-

rections (longitudinal, transverse and shear strengths respectively) for each

one of the 48 elements. This can be achieved by considering that for each

lamina the material strengths in the three principal directions consist a

three-variate two-dimensional (3V-2D) random field. In this way, each one

of the 46 elements is assigned with a different triad of values for the material

strengths in the three principal directions.

Considering now uniaxial stress of the laminated orthotropic composite

plate, we can start from a very small stress-level a and check whether one or

more of the 48 elements fail under the given stress o. The Tsai-Hill failure

criterion shown below in Eq. (a), can be used to perform this check. It

should be noted that this failure check is performed 48 times, once for each

element. The Tsai-Hill failure criterion is given by

11MCR 11,, , ,'L .4

cos40 1- 1 2 2 0 + in 4 0 1(a)XY- + (S 2 X 2 )CO8s O in y2 -- 2

where X, Y, S are the strengths in the three principal directions (longitu-

dinal, transverse and shear respectively), a is the externally applied axial

stress and 0 is the angle between the principal direction X and the directionof application of the uniaxial stress a. Of course, any other failure criterioncan be used instead of the Tsai-Hill one, by making slight modificationsto the above procedure. For example some other failure criterion might

involve only two independent strengths instead of the three of the Tsai-Hillcriterion. In this case, a two-variate two-dimensional random field has to

be generated.

If no failure is detected at the original stress-level, the stress-level canbe increased by steps up to the point where some element(s) fails for the firsttime. The value of the externally applied uniaxial stress at this level canbe considered as the strength of the whole laminated orthotropic compositeplate in uniaxial tension.

Using Monte Carlo techniques the above-described procedure can berepeated a number of times for different realizations of the 3V-2D randomfield describing the strengths of the laminated composite plate in the threepricipai directions. In this fashion several different values for the strength ofthe whole laminated plate can be obtained. Then, the distribution functionof those values can be estimated by the use of some test of goodness of fit(e.g. probability paper).

Finally, in order to examine the statistical size effect, the followingprocedure can he followed. The same problem as the one described aboveto find the strength of the whole laminated composite plate is solved againby considering in the beginning twice the area of the original laminatedplate, then thrice and so on, however always using the same autocorrela-tion function for the 3V-2D random field describing the material strengthvariability in the three principal directions. In this way, conclusions can bedrawn about the statistical size effect due to the spatial strength variation.

5

A DIRECT METHOD TO OBTAIN CONSTITUTIVE MODEL CONSTANTSFROM CYLINDER IMPACT TEST RESULTS

TIM J. HOLMQUISTDevelopment Engineer

GORDON R. JOHNSONPrincipal Engineering Fellow

Honeywell Defense Systems DivisionEdina, MN 55436

INTRODUCTION

The cylinder impact test was introduced by G. I. Taylor in 1948. Since that timethe merits of this test have been debated. Some would argue that this test should notbe used to obtain constitutive data because a wide range of unknown strains, strainrates, temperatures, and stresses vary throughout the test specimen, and throughoutthe duration of the test. It is better, they would say, to obtain data from dynamic tension,compression, and/or torsion tests, in which the variables are better defined, and thenuse the cylinder impact test to provide an independent check of the data.

Others would argue that dynamic tension, compression, and/or torsion testsrequire expensive test facilities and that these tests are limited in their ability to achieve.the range of strains and strain rates of interest. Conversely, the cylinder impact testis simple, inexpensive, and provides data for the appropriate range of strains and strainrates. During the past twenty years, several researchers have used this test to esti-mate dynamic flow stresses for various materials.

The work reported in this paper is directed at developing an explicit method (asopposed to previous trial-and-error methods) to obtain constants for computational con-stitutive models.

DISCUSSION AND RESULTS

Figure 1 shows a comparison of cylinder impact test results and correspondingEPIC-2 computational results for OFHC copper. The test data are from Reference 1(Johnson and Cook, Proceedings of the Seventh International Symposium on Ballistics,1983). The adiabatic stress-strain relationships are given in Figure 2 and the strengthmodel constants used for the four cases are given in Table I. The adiabatic stressesare shown only to the maximum strains attained in the computed results.

7

;I--- 22M

r_ - " 1 r - r - Ir-

CASE A CASE B CASE C CASE D

S -a 0.. 11.4-f 0 1 a--- 0 -*4

NOTES:

* OFHC COPPER CYLINDER (L 0 = 25.4mm, o= 7.6mm, L=16.2mm. D = 13.5mm)

* IMPACT VELOCITY - 190 m/a

* TEST RESULTS INDICATED BY DOTS e000

* EQUIVALENT PLASTIC STRAIN CONTOURS SHOWN AT INTERVALS OF 0.5

Figure 1. Comparison of Test Results with Computed Results Using VariousStrength Model Constants

1000 ,

2 CASE 8

CASED (10 51*510 )

o0 - CASE C

0_ .5 1.0 1.5 2.0 4.5 5.0 5.5

I.,,CASE i % A

EQUIVALENT PLASTIC STRAIN. C

Figure 2. Adiabatic Stress-Strain Relationships for the Various Strength Models

8

Table I. Strength Model Constants for the Computed Results

CASE A CASE B CASE C CASE D

STRENGTH CONSTANTS FOR

[,=[+0 ,+C~111 -T.-,]A (MPG) 250 160 103 98a (MPG) 0. 400 469 368

fn - 1.00 .65 .70C 0. 0. 0. .026m - - 1.00 1.09

ii$=ift 0 FORi0=I.0 S - 1

T$= (T - TROOM) I (TMELT - TROOM)

For Case A the length, L, of the deformed cylinder is matched with the computa-tional result. Because only one deformed dimension is matched, only one independentstrength constant (representing a constant flow stress) can be obtained. It can be seenthat there are significant discrepancies between the test and computational resultsat the deformed end of the cylinder.

Case B provides for linear strain hardening. By matching both the deformedlength, L, and the maximum diameter, D, it is possible to obtain the two constantsfor the linear hardening. Here the computed result is in good general agreement withthe test result. If this model would be applied to larger strains than those experiencedin the computed results of Case B, however, it would probably lead to excessively highstresses. It is well known that thermal softening tends to decrease the rate of strainhardening at large strains. In general, if the basic model accurately represents materialbehavior, then the results can probably be extrapolated beyond the data base.

Cases C and D are based on the following model for the von Mises tensile flowstress (Reference 1):

stressRefernce1) o=[A + B_"][1 + Cln i*][1 - T*] (1)

where F is the equivalent plastic strain, * = Ui. is the dimensionless plastic strainrate for ii, = 1.0s - 1, and T* is the homologous temperature. The five material con-stants are A, B, n, C, m. The first three constants (A, B, n) represent the strain harden-ing characteristics of the material and are the ones which are determined from thetest results. Because there are now three constants, it is possible to match three deformeddimensions-the length, L, the maximum diameter, D, and an intermediate diameter,W. The strain rate constant, C, and the thermal softening constant, m, must beapproximated or obtained from other sources.

9

Ai r w,9iii'j

Case C is the result obtained if nothing is known about the strain rate or ther-mal softening characteristics of the material. Here, the strain rate constant is set toC = 0, and the thermal softening is assumed to be linear, or m = 1.0. Case D uses strainrate and thermal softening data from Reference 1. Even though there is little appar-ent difference between Cases C and D for this problem, for some other problems (withwider ranges of strain rates and temperatures) the Case D constants will probably pro-vide better results.

METHOD TO OBTAIN CONSTANTS

The method consists of applying the following equation in an iterative manneruntil a satisfactory set of constants is attained:

{Ax} = [K]{Ay} (2){AA) (ALI~where {Ax} = AB and {Ay} = AD

An IAW

For a given set of material constants (A, B, n) it is possible to compute the deformedgeometrical dimensions (L, D, W). These deformed dimensions are compared to thedimensions of the test specimen and the differences are expressed as AL, AD, and AW.These differences can then be used to find the corresponding material constant changeswhich will lead to improved material constants. This is accomplished through a3 x 3 operator matrix, [K], where Kij is the change in material constant, Axi, due toa unit change in the deformed geometry, Ayj.

The operator matrix, [K], can most easily be attained by first developing the in-verse to this matrix. This is accomplished by running a series of four computer simu-lations with different material model constants. The first simulation is a baselinecomputation which uses an initial estimate of the constants. The next three simula-tions vary each of the three constants independently (A', B', n'). This procedure, andthe generation of the [K] ', is shown in Figure 3.

The operator matrix assumes a linear relationship between incremental materialconstant changes and incremental deformed dimension changes. This is not a validassessment because the operator matrix is actually nonlinear. However, the linearassumption can produce accurate, converging results if the four simulations used togenerate the operator matrix are sufficiently close to the final solution.

For the limited number of solutions obtained to date, convergence was experiencedafter several iterations. In these cases, the initial operator matrix was used for all iter-ations. The rate of convergence can eventually be increased by implementing improvedtechniques that continually update the operator matrix after every simulation.

10

81UATION MATERIAL DEFORMED CYLINDER

CONSTANTS DIMENSIONS

I (BASELINE) A a n . L1 D 1 WI

2 A' B In L 2 D 2 W2

3 A 0' n - L3 03 W3

4 A B n' - L4 D 4 W4

Li - L2 L1- L3 L I L 4

A-A' B-B' n_-n-r

[K] 1 = D1-D2 01- D 3 01 - 4

W1-W 2 W1-W 3 W1-W 4

_-BBA - A' - n-n

Figure 3. Summary of Computer Simulations Required to Generate Inverse ofOperator Matrix

SUMMARY AND CONCLUSIONS

It has been demonstrated that it is possible to directly obtain constitutive modelconstants from cylinder impact test results. Future work will be directed at improvingthe convergence of the method, and applying the method to other models and materials.

ACKNOWLEDGEMENT

This work was funded by a Honeywell Independent Development program.

11

PLASTIC STRAIN LqCALIZATION nETWEEN VOIDSIN SHEAR DEFORMATION FIELDS

D. ft. Tracey, C. E. Freese, and P. J. Perrone

U. S. Army Mati-rials Technology LaboratoryWatertown, Massachusetts, 02172-COC1

ABSTRACT

I!let3lloqraphic studies have shown that crack prnoaoqtion

occurs by a plastic shear instability mechanism in high strength

martensitic alloy steels. On the microscale, propagation occurs

in a non-planar fashion following bands which develop alona the

shear directions. Voids evidently play a major role in this

fracture orocess, with microcracks developino between interactinn2

voids. In shear tests of high strength 4340 steel , voids have

been found within shear bands at debonded sub-micron sized grain

refinement particles. It has been speculated that the microcracks

linking such voids form as a result of the coalescence of voids

which nucleate at smaller scale strengthening particles. It is

likely that this secondary void nucleation results from the strain

intensification caused by the dominant voids. Fracture is

expected after a critical number of microcracks are forme,.

The present mechanics study is being conducted in suooor

an alloy development research program attempting to producF

ultra-high strength steel alloy (300-350 ksi) with fracture

toughness sufficiently high (6V-120 ksiV'in) to allow a wide range

of structural applications. Success of this program will provide

an important new material selection option for lightweight

fracture resistant metallic structures. The mechanics work is

directed to establishing a quantitative understanding of the

void-softening mechanism in shear. This information will be used

to guide alloy design to achieve low shear banding propensity.

The key to understanding how microscopic voids deteriorate q

plastically deforminq metal is knowledge of the void region

stress/ strain elevation over the uniform levels that would exist

13

in the absence of voids. Particularly useful would be knowledne

of the void region state when the remote uniform field simulates

the deformation occuring in a band of locnlized flow. This is the

analytical problem addressed here. A set of elastic-Dlastic

finite element analyses has been conducted to estahligh the local

field between a pair of voids close enouqh to produce siqnificant

interactions.

The analyses were conducted using lqrqe scale computational

facilities and an elastic-plastic finite element formulation for3

non-hardening Prandtl-Reuss constitutive theory . The formulation

is an incremental secant stiffness method that guarantees

satisfaction of the yield condition at each grid point. An

adaptive incrementation scheme is employed to automate load step

size selection and to control load path discretization error. The

formulation traces the spread of plasticity by adjusting element

stiffnesses as the imposed displacement is incrementally

increased. The mesh used to model the void pair in a plane strain

deformation band is shown in Figure 1. There are approximately

150C nodes (3000 degrees of freedom) in the mesh drawn. However,

symmetry allows half of the model in simple shear analysis and A

quadrant for uniaxial extension. All four sides of the band were

constrained according to nominal deformation mode. In simple

shear, the edges were constrained against vertical displacement,

while in uniaxial extension, nodes on all four edges were

constrained against horizontal motion. Thus, in the absence of

the voids, the solutions would be uniform shear (no normal strain)

and constant uniaxial extension (a single non-zero strain

component).

The plastic zone development for the simple shear case is

illustrated in Figure 2. In the early stages of loading, plastic

deformation is restricted to regions at the void surfaces, rouqhly

45 degrees from the ligament. As these surface zones develop, a

separate distinct plastic zone develops along the liqampnt. Once

the zones link, plastic strain localization occurs between the

voids. Figure 3 illustrates the fact that over the early stages

of loading, straining is fairly uniform over the interior of the

14

%' " ... " " .€ € - " 5

ligament, but a maximum is seen to develop at a distance of C.3 D

ahead of the voids. The value of the maximum local shear strain

is plotted versus nominal strain in Fiqure 4. Th P rate of

increase of local strain with respect to qpplied strnin

continually rises with the final intensification rate in excess of

thirty.

The plasticity and interaction for the case of uniaxial

extension is much different than the above simple shear case. The

plastic zone at a uniaxial strain value 1.27 Y/E is shown in

Figure 5. Also shown in Figure 5 is that portion of the plastic

zone that satisfies the near isocloric condition that the

magnitude of the normal strain increments differ by less than 6'.

Plasticity spreads from the void surfaces and excessive strain

intensification occurs once the zones merge. The numerical data

agrees with the logarithmic spiral distribution expected from

slipline theory, Figure 7. Consistent with the plastic zone

development, the maximum strain in this loading case is seen to

occur at the void surfaces. The very significant intensification

of strain suggests that substantial void growth will occur, in

agreement with known results for the growth of isolated voids in

triaxial stress fields

In summary, the plasticity results for the test cases studied

are consistent with experimental observations of void sheet

development in shear and void growth in tension. Further work is

being oursued to establish interaction features over a ranno of

particle distribution parameters. The results suoqest that the

goal of establishing alloy development guidelines to minimiz-

shear banding propensity using micromechanics is achievable and

likely to be very worthwhile.

15

REFERENCES

1. J .Van Den Avyle, " Correlation of Fractogrziphy, Ilicrostructurp,and Fracture Toughness Behavior of High 5trenoth Alloys," Ph.).Thesis, fill, Cambridge, MIA, 1975.

2. ti. Azrin, J. Cowie, qnd G. Olsen, private communica tion, ArmyMaterials Technology Laboratory, 1986.

3 . D. M. Tracey and C. E. Freese, "Adaptive Load Incrementition inElastic-Plistjc Finite Element Analysis," Compute-rs aind ',tructures,13, po. 45-53, 198).

4. J. R. Rice and 0. '1. Trqccy, "The Ductile Enlaroement of Voids inIriaxial Stress Fields," J. Mechs. Phys. Solids, 17, po. 2fl1-2f?,1969.

16

FIGURE 1 -Pair of voids in deformation band

17

FIGURE 2 Development of plastic instability between voidpair under simple shear. Plastic zones at nominalshear strain levels 60, 77, and 91% of -yield

18

6-

a/ YIELD 09

a--08

6. 66.5 1.6 1.5 2.6 2.5 3.6

FIGURE 3 -Shear strain distributions On ligament betweenvoids under nominal simple shear

16-

1"YIELD

YNOl /YYIELD

6.0 6.2 6.4 6.6 6.3 1.6 1.11

FIGURE 4 - Strain intensification between voids undernominal simple shear

19

I E01~1.27 Y/E

(B)

FIGURE 5 -(A) Plastic zone under nominal uniaxiat strainlevel 1.27 Y/E

(B) Ful1. developed near-isoctoric portion ofplastic zone shown in (A)

20

11.5V,

Y

X/D

0.61.01.S 8. .6

FIGURE 6 -Numerical dat~a for normal stress On ligament atnominal UniaXiat strain 1.27 Y/E compared with3lipline theory logarithmic spiral distribution

E, W 1. 27 WE4

Y//

0.76

S.S

0.0 1.0 .5 8.0.6 38

FIGURE 7 -Normal strain distribution on ligament betweenvoids under nominal untaxial strain

21

A Study of the Crack Tip Parameters that Govern Environmentally

Assisted Cracking by Use of the Rising Displacement Test

by

R. Mayville, T. Warren and P. Hilton

A.D. Little, Inc., Cambridge, MA

Abstract

There is an increasing interest in the use of rising displacement or load

tests, similar to K-R or J-R resistance curve tests, to characterize

environmentally assisted cracking (EAC) in metal/environment systems.

These tests have been used to determine KIEAC (KIScC) and to study the

effect that crack tip parameters, such as Ki, dJ/dt and d6/dt, have on EAC.

This investigation is an experimental study of the effect a wide range of

applied displacement rates has on EAC for AISI 4340 with a 0 - 1095 MPa (159

ksi) in flowing synthetic seawater. Cantilever beam - constant load -

tests were performed to obtain KIEAC - 98 MPa v/m. Rising displacement

tests were performed over four orders of magnitude with 25mm thick compact

tension specimens under ambient conditions and in environment to generate

J-R curves and to determine crack velocities. Under ambient conditions the

4340 exhibits substantial stable tearing. In environment, the J-R curves

were identical to the ambient J-R curve except for the slowest test, which

lasted over a week. The J-R curve for this specimen was substantially

lower than the ambient curve and K I converted from J IC was found to agree

very well with K IEAC The J-R curves are shown in Figure 1. Two experi-

ments were also performed in environment in which the displacement - stroke

- was held constant after some stable crack extension had occurred. The

crack velocities from these and the other compact tension tests are plotted

in Figure 2 against KI and indicate that the a-KI relationship is unique

for environmental cracking for KI > KIi (from ambient J IC In addition,

the environmental a-KI curve is

23

parallel to the ambient a-K curve suggesting that the ambient mechanicalcracking mechanisms play a major role in environmental cracking for this

system. This is supported by very similar ductile rupture fracture

surfaces for the two cases. This work has been supported by the National

Science Foundation and by the Arthur D. Little Corporate Fund.

Key words for Army Symposium: fracture mechanics, experimental methods,

life prediction.

24

- C

0Ci

~~t c nqto.- N 8

~ir 4060

4. . r4

to _

0)

00

E-

In co

N --

25

10-4

* 0.25mm/min (Ambient)

10-5 0

0.125mm/mn (Environment)

10-6-

100

00

U00

10-8 0 0.00125 mm/min (Environment)0.015m /i(Abet

00 , SteRt=0 (Evrnet

1 0/

00

- 0J

L&.430IO 09 ~

I M 0avl-

oiue2rakVlct Dat from troe Romate(nionmSeen026

EXPLICIT AND IMPLICIT SOIL MODELLING FOR DYNAMIC SOIL-STRUCTUREINTERACTION PROBLEMS

Aaron Das Gupta, Ph.D.US Army Ballistic Research Laboratory

Aberdeen Proving Ground, Maryland 21005-5066

ABSTRACT

Increased application of nonlinear viscoelastic materials in structuresand consideration of operating environments require modeling of interactionof such structures with the surrounding soil medium which significantlyinfluences the dynamic response when subjected to an impulse or blast over-pressure loading. The need is currently accentuated by the rapid advancesin numerical modeling of dynamic problems using either finite-differenceor finite element techniques of structural analysis.

While various models are available to describe the deformation and failureprocesses, scarcity of dynamic experimental data at high strain rates is aserious handicap for a majority of representative soil materials. As aresult, many computations are still made using static or low strain ratedata. In order to overcome this critical shortcoming in soil-structure inter-action problems, an explicit modeling technique could be improvised byrepresenting the soil with an equivalent mechanical model consisting of aspring and a dashpot in parallel and connecting the model to the structuralmodel using node-tie element. In this spring support condition, the baseof a structure in contact with soil could be flexibly supported using anappropriate value of the spring stiffness while the top of the structurecould be loaded directly.

The implicit modeling technique where nodal tie elements are used tomodel the base support as nonlinear springs for shallow buried structuresto simulate the soil medium suffers from a serious shortcoming in sofarasthe indirect loading of the structure through shock waves passing throughthe soil and overpressure loading attenuation effects are not adequatelymodeled resulting in unrealistic soil-structure interaction and erroneousresults. Hence an explicit modeling technique is recommended whereby afew layers of soil surrounding the base of the structure are modeled asan assembly of elements in contact with the structure. The interfacingcantact elements for both structure and soil are allowed to stick, slideor seperate from each other to simulate the appropriate boundary condi-tions.

The explicit modeling technique using a finite element code requirecharacterization of constitutive relationship of geological materials fromshock compression behavior of such materials and their Hugoniot charac-teristics. Although the equations-of-state in the form of pressure-density relationships for shock propagation in such mediums can be non-linear, the characterization technique in this investigation is currentlyrestricted to materials with linear Hugoniot characteristics at allpressure ranges.

27

~ '>~''I

Jul ' 17:20 1986 india Page 2

Three representative ?,oil mediums i.e., saturated and unsaturatedtuff, oil shale and sand are selected for this study. Under the assumptionof unidimensional shock propagation and conservation law of mass, momentumand energy, the equations-of-state could be transformed to bulk moduliversus volumetric strain relationship using the methodology described inthis paper. The transformed characterization is compatible with thetension cutoff curve description material model available in the ADINAnonlinear dynamic finite element analysis program. However, the charac-terization of sand is valid in this study only at very high pressureregimes where sand behaves like quartz due to solid phase transitionand a linear Hugoniot curve fit to the shock velocity versus particlevelocity data is feasible.

The method could be readily extended to partially saturated soil withnonlinear characteristics through multilinear approximation during theloading and unloading phase. The resulting constitutive relationship willfacilitate explicit modeling of the surrounding medium around shallow-buried structures and realistic simulation of dynamic soil-structurpinteraction which can significantly alter the dynamic response behaviorof such structures.

28

-. V .e~*j' ' IK d ~ X'~

ABSTRACT

.CONPOSITE MATERIALS APPLIC ATIONS PROGRAM

AT THE US ARfY BALLISTIC rESEARCH LABORATORY

WORK IN PROGRESS

RICHARD B. MURRAYMechanical Engineer

Mechanics and Structures BranchUS Army Ballistic Research Lab

EDWARD N. PATTONTeam Leader, Material ApplicationsMechanics and Structures BranchUS Army Ballistic Research Lab

LARRY W. BURTONMechanical Engineer

Mechanics and Structures BranchUS Army Ballistic Research Lab

ROBERT P. KASTEMechanical Engineer

Mechanics and Structures BranchUS Army Ballistic Research Lab

EXTENDED ABSTRAT

The Mechanics and Structures Branch of the Interior Ballistics Division of theBallistic Research Laboratory has embarked upon a mission program tailored to

understanding _mposite materialsjand their potential application to Armysystems. The intent of the program is to provide the Army with design techniquesand prediction methodologies specifically aimed at the problems peculiar to Armysystems. These problems include high rates of loading, including ballisticloadings and blast loadings; high and low cycle fatigue; corrosion and erosionresistance; and the necessity to predict structural rebponse of thick sections toall loading environments. The intent is also to attempt to apply new andemerging materials developed at other Army laboratories, under other Armyprograms, and those materials available in the commercial sector. The approachto this broad scoped and general program has been to decide which issues are themost important to the designers of some specific systems and components, andinitially concentrate upon those aspects of the material systems which are not

yet well understood. Three of these aspects of composite material behavior havebeen selected as the most critical current predictive techniques for composite

materials. They are: structural response to high rates of loading, predictingstructural response of thick sections of laid-up laminated structures, andfailure criteria for thick laminates. The remainder of this abstract will focuson the work in progress in these three critical areas.

29

OL Dwl II

HIGH RATE IDADIII

We are developing an instrumented projectile that can be launched from a 37mmgun housed in an indoor range at BRL. This gun/projectile system can be usedto ballistically test a sample encased within the instrumented projectile. Bychanging the charge and/or mass and/or geometry of the projectile, a widerange of ballistic loading rates and states of stress of interest can beinvestigated. It is intended that samples of composite materials will be madeup and loaded in the instrumented projectile for tests. Data such as strainand strain rate in several directions and at several locations within thesample will be taken. These data will then be correlated with finite elementstructural simulations of the tests to determine the efficacy of a particularmodelling method, and also to benchmark that method. In this way, predictivetechniques of structural response at the rates of loading of interest can bedeveloped and benchmarked before being applied to full scale Army systems andcomponents.

THICK SCTIOIN

Army structural components tend, in general, to be larger, thicker, and moremassive than do structural components for agencies such as the Air Force orNASA. The major studies to date that have been performed, and a majority ofthe structures which have manufactured have been for those two agencies.These structures tend to be two dimensional curved or cylindrical structureswith or without stiffening ribs. Army Structures, such as howitzer componentsand armored vehicle hulls, tend to be made of thick, strong, massivecomponents. To date, very little analytical work has been. performed for thistype of structure.

A major portion of the composite material application program has had to dealwith just this problem. How does one predict structural response of a thicklaminated section. Laminated plate theory fairly accurately predicts theresponse of thin structural components such as wing skins or rocket motorhousings, but the theory fails to accurately predict the response of thicklaminates. We have therefore taken a broad approach to attacking thisproblem. First, several experts from within and outside of the Army labora-tories have been contacted. Experts from two of the pre-eminent centers forcomposites have been brought under contract to derive failure criteria. Thiswill be discussed later in this abstract.

Secondly, a small laboratory is being set up which is specifically gearedtoward constructing samples of thick sections for testing. Both an injectionmolding machine and a small autoclave will be used to make up test samples ofthick sections for mechanical testing and benchmarking of structural pre-dictive techniques.

30

e .P. I )R"',

FAILURE CRITERIA

All of the structural response predictions that can be made are worthlessunless we can predict whether or not the structure survives its loadingenvironment. One of the most important parts of this program is, therefore,the prediction of failure, and the criteria whereby that failure is predicted.There are many schools of thought concerning failure prediction in laminatedstructures. There are almost as many as there are experts predicting thefailure. They can, however, be broken into two general categories; maximumstress criteria and maximum strain criteria. Experts from both the Air ForceMaterials Lab and Lawrence Livermore Laboratories are working under contracton one or the other of these general criteria. It is intended that theresults of these two studies will be integrated into a design tool for use byArmy systems designers which will allow these designers to accurately predictthe response and failure of structural components. Enough intelligence will bebuilt into this predictive tool to allow the designer to select from severalapproaches to laying up a laminate, and several approaches to predicting theresponse and/or failure of the component in question.

.ClSURE

We have embarked on a long term and intentionally aggressive program for thedevelopment of predictive techniques and design methodologies for applicationof composite materials to Army structural components and systems. The programhas elements of pure research into predictive techniques for thick sectionsand failure of components, and elements of experimental work in high rates ofloading common to Army Ballistic comonents. The program has a very broadscope, but is focused upon the peculiar needs of Army component and systemsdesigners. It meshes well with ongoing programs at other major Army labora-tories in composite materials development, and it also has brought together alarge body of knowledge from outside experts in an effort to capitalize on asmuch of the present knowledge and technology of composite materials aspossible.

31

EFFECTIVE TREATMENT OF MEMBRANE AND SHEAR LOCKING PHENOMENA IN CURVEDSHEAR-DEFORMABLE AXISYMMETRIC SHELL ELEMENT

A. Tessler and L. SpiridigliozziU.S. Army, Materials Technology Laboratory

Watertown, Massachusetts 02172

Wide varieties of structural shells exhibit geometric and mate-rial symmetry. As such, they are best modeled by appropriate shell ofrevolution finite elements which are intrinsically one-dimensional.Thus, computationally efficient analyses are possible owing to thesmall bandwidth and dramatically reduced number of degrees-of-freedom,as compared to the alternative discretizations with more 'expensive'two-dimensional shell elements.

Design requirements for thin and moderately thick shells and inparticular those made of laminated organic composite materials neces-sitate accurate modeling of the shell geometry and proper account of

the effects due to shear deformation and, in dynamics, rotary inertia.To be effective, therefore, an element should be able to accommodatethese higher-order effects and closely approximate the meridian curva-ture. Additionally, nodal simplicity is commonly desired, especiallyif computationally involved nonlinear analyses are warranted.

A major difficulty intrinsic to shear-deformable bending elementsis due to a mathematical deficiency called 'shear. locking'; (the termrefers to nearly trivial kinematic patterns manifested in the thinregime due to an overly stiff model). A mathematically analogousphenomenon known as 'membrane locking' is a common hindrance in curvedbending elements. Thus, formulating a curved shear-deformable elementrequires simultaneous resolution of the two locking phenomena.

In this paper we present a simple, yet extremely effective,two-node, displacement-type, axisymmetric shell element derived fromNaghdi's refined shell theory [I] with the aid of the Marguerre shal-lowness equations [2]. This work is an extension of the conical shellelement discussed in [3] and the Timoshenko-Marguerre beam [4]. Here,we adopt the anisoparametric kinematic approximations which employdistinctly different degree polynomials for the kinematic variables,rather than uniform interpolations as in the conventionalisoparametric procedure. Owing to these approximations, both themembrane and shear strains, which serve as penalty constraints in thethin-element regime, possess physically admissible penalty modes. Theformulation is further enhanced by an innovative treatment of the twopenalty parameters (nondimensional multipliers of the shear and mem-brane strain energies), giving rise to the appropriate relaxation ofthe penalty straining for coarsely discretized models. To focus onthe core issues, only the axisymmetric response of linearly elasticisotropic shells is considered; note that extensions to asymmetricresponse and laminated composites are straightforward once the 'lock-ing issues' have been conceptually resolved.

33

- ~ '%

The main features of this two-node, six degrees-of-freedom shellelement are summarized as follows (refer to Fig. 1 for the shellnotation):

1. The meridian variation of the element geometric descriptionis taken as cubic and is given in terms of two nodal slopes 0o and 01,which are assumed to be small (i.e., the geometry is shallow in theMarguerre sense).

2. The kinematic variables u (membrane displacement), w (trans-verse displacement) and e (cross-sectional rotation about the normalto the meridian) are interpolated in the meridian direction by quar-tic, quadratic and linear polynomials , respectively. The quartic uis coupled in terms of ui, wi, and 80 (i=0,1) degrees-of-freedom; thequadratic w is coupled in terms of wi and 81 degrees-of-freedom; andthe linear 8 is solely dependent upon its nodal values 8.. In theparticular case of a straight meridian, u reduces to an independentlinear function in terms of uL degrees-of-freedom.

3. Because of the specific choice of the kinematic approximat-ions, the membrane strain, bending curvature and shear strain actingin the meridian direction are constant. Thus, only one-point Gaussianquadrature is needed to integrate the corresponding strain energiesexactly.

4. Element stiffness and consistent mass matrices, and consis-tent load vector are derived via Hamilton's variational principlewhere full Guassian quadratures are employed on all energy terms.

5. The shear and membrane relaxation parameters depend exclu-sively upon element geometric and material properties and yield awell-conditioned stiffness matrix for any shell thickness. Important-ly, these relaxation measures give rise to notable accuracy enhance-ments in coarsely discretized models.

Numerical studies are carried out focusing on the element model-ing capabilities in free vibration problems.

II

I \ 0w

oi

Fig. 1. Shallowly curved axisymmetric shell element.

134

- % V %%V % -

REFERENCES

1. Naghdi, P.M. "Foundation of elastic theory", in Progress inSolid Mechanics, (eds. I.N. Sneddon and R. Hill), North-Holland,Amsterdam, Vol. IV, Chap. 1, 1963.

2. Marguerre, K. "Zur Theprie der gekrummten Platte grosserFomenderung", Proc. 5 Internat. Congress of Applied Mechanics,693-701, 1938.

3. Tessler, A. "An efficient, conforming axisymmetric shell elementincluding transverse shear and rotary inertia", Computers andStructures, 15, 567-574, 1982.

4. Tessler, A. and Spiridigliozzi, L. "Curved beam elements withpenalty relaxation", to appear in Internat. J. Numer. Meth.EngrR. (1986).

.35

'IA'A'.

PLANE STRAIN FINITE ELEMENT ANALYSIS OFRUBBER TRACK PADS

A. R. Johnson and C. J. QuigleyUnited States Army Laboratory CommandArmy Materials Technology Laboratory

Watertown, MA 02172-0001

EXTENDED ABSTRACT

Rubber track pads used on Army tanks are subjected to large loads.The loading environment consists of repeated compression loads applied bythe road wheels, penetration by rocks or metal debris, scuffing andcutting. Failure modes include chunking, subsurface cracking and blowoutfrom hysteretic heating. It is not practical to try and model all possibleloading situations to which a track pad may be exposed. Instead, to screennew material candidates, laboratory tests and analyses of samples can bemade. These tests and analyses should subject the material to the variousmodes of loading expected so that materials which perform better than thecurrent standard can be identified.

During the past two years MTL has started a research program todevelop finite element analysis capabilities for determining the largedeformations and stresses in elastomer (rubber) materials used in vehicles.The finite element programs developed can be used to analyze and design thelaboratory tests mentioned above. In this effof) a total Lagrangianpotential energy formulation with a Valanis-Landel form for an energydensity function was used to model elastomers. A nonlinear finite elementalgorithm was developed which used bilinear three node triangular elementsto minimize the potential energy. Elastomer cylinders load " 4Noth endthrust and by a probe along the cylinder axis were analyzed ' ' Morerecently, a modified fo) of the classical Mooney-Rivlin energy densityfunctional was derived which allows for computation of rubberdeformations without the hydrostatic pressure as an independent variable.Also, a 6 5uadratic six node finite element formulation has beendeveloped . (2-6)

The analyses of axisymmetric deformations of rubber can bemodified to allow for the computation of plane strain rubber deformations.In this effort we show the plane strain formulation and present numericaldata obtained for a two dimensional model of an Army T-156 track pad. Thenotation used to describe the stretching of the material is shown in Figure1. Both three node bilinear and six node biquadratic elements are shown inFigure 2. One half of a finite element model for a T-156 track pad isshown in Figure 3. The energy density functions used are as follows:

VALANIS-LANDEL

3 J

w 2 Z .(lnA.-I) + -A[ln( 2A3Ai=1 1 2 3

37

p.1 1. If 1 1 . 1

MODIFIED MOONEY-RIVLIN

c(i-3K/3 c(J-3K2/3 1 2K

c2( ) + -An21 2 2

where w = energy per unit undeformed body,

A. = the i'th stretch ratio,II XI2+X 2+X3

,

1 2 2~22 22 22

J = X 2 +X2X+X X1 2 2 3 31222

K= X X2X31 2 3'

AP, A = the Lame constants,

and cl, c2 = material coefficients from classical Mooney-Rivlin

energy density functional.

REFERENCES

1. K. C. Valanis and R. F. Landel, "The strain energy function of ahyperelastic material in terms of the extension ratios", J. of AppliedPhysics, Vol. 38, No. 7, June 1967, 2997 -3002.

2. A. R. Johnson, C. J. Quigley and I. Fried, "Large Deformations ofelastomer cylinders subjected to end thrust and probe penetration", ThirdArmy Conf. on Applied Math. and Computing, Georgia Inst. Tech., Atlanta,Georgia, 1985.

3. A. R. Johnson, C. J. Quigley and I. Fried, "Stretching in an elastomercylinder during an axial probe penetration", Thirty-Second Sagamore ArmyMaterials Research Conference, Lake Luzerne, NY, July 1985.

4. A. R. Johnson, C. J. Quigley and I. Fried, "Computer modeling of solidelastomer cylinders used in material performance tests", US Army SurvivableTire Symposium 85, Ormsby House, Carson City, Nevada, November 1985.

5. I. Fried, A. R. Johnson and C. J. Quigley, "Admissible Elastic EnergyDensity Functions for Rubber-Like Solids", Fourth Army Conference onApplied Mathematics and Computing, Cornell University, May 1986.

6. I. Fried and A. R. Johnson, "Nonlinear computation of axisymmetricsolid rubber deformation", submitted to Computer Methods in AppliedMechanics and Engineering.

38

y

ds ds' A

1

p 2

a x

undeformed deformed

A (6) = (-- )1ds

Find A 2 . 1 [b[(-)2+421/

1 2 1/

A2 . 1 [a+b-[(a-b) 2+4c 2 1/

3

where a x 2 + y 2,a ,a

b x 2 + y2

c x x + y y, CL ,a,

Figure 1. Description of material line deformation and stretch ratios.

39

P,Y O,y

3' 3'

3

1 2 4 2

ax a, x

bilinear biquadratic

= integration point.

Figure 2. Bilinear and biquadratic elements used to discretize thepotential energy.

/1\ - rubber

aluminumste yBa

Figure 3. Plane strain T-156 tank track pad finite element model.

40

P*

ANALYSIS AND TESTING OF PREDAMAGED SHELL STRUCTURESRichard E. Keeffe

Sr. Research ScientistKaman Sciences Corp.

Colo Spgs, Colo 80907

Eric ReeceMember Technical Staff

Sandia National LaboratoriesAlbuquerque, New Mexico 87185

EXTENDED ABSTRACT

A predamaged shell structure may undergo significant reduction in loadcarrying capacity, dependent upon( e location, size, and shape of the damagedarea. Kaman Sciences Corporation (KSC) and Sandia National Labs (SNLA)under direction from the U.S. Army Strategic Defense Command are investigatinganalytic and experimental methods for evaluation of these effects. This paperreviews some results of work in progress and planned structural test effortsaimed at supplying data for analytic correlations.

Of primary concern are thin walledcylindrical and conical shell frustra whichhave locally damaged areas as indicated inFigure 1. Note that these damages are TENSION

idealized and that in general, damages may COMPRESSION

be irregular in nature. As shown, threebasic loading conditions are of interest. MOMENT

1. Axial Tension2. Axial Compresison3. Lateral Bending FIGURE 1

Note that two bending configurations will DAMAGEDSHELLGEOMETRYbe studied; one with the damaged area intension, the second with the damaged areain compression.

The basic analysis tool currently being considered for these studiesinvolves application of the nonlinear finite element code ABAQUS, developedand maintained by HIBBITT, KARLSSON and SORENSON, INC. The code capabilitiesinclude static and dynamic modeling of solid, beam, and shell elements, andprovides accurate modeling for arbitrary magnitudes of displacement, rotation,and strain. Preliminary assessment of the applicability of the ABAQUS formula-tion has been applied to tension ano, ompression test results obtained on6061-T6 seamless aluminum cylinders . Slot damages were machined in one

(1) This work is being performed under Contract DASG60-85-C-0051 for theUSASDC Huntsville, Alabama. Mr. Owen Bender (USASDC) is the contractmonitor.

(2) This Testing was performed at Southwest Research Institute, San Antonio,Texas under subcontract to Kaman Sciences Corporation.

41

I L ,ev l 'r , d F11 1. 1

side of these cylinders and compression andtension tests (with clamped ends) wereperformed to large deformation and frac-ture. Axial load vs total axial deflectionpredicted using ABAQUS are compared to testresults in Figure 2. The comparison shownwas obtained using an initial radialimperfection of .01 inches (.254 mm) at theshell midplane. Additional variations ininitial imperfections are being analyzed.The final deformed mesh geometry (X2.5)predicted by ABACUS is presented in Figure3(a), along with a photograph of the posttest shell specimen (Figure 3b). Ingeneral the comparisons between test andtheory are promising for this single shell 80'0 1' 1, o' I I CE o a

geometry.FIGURE 2

ANALYSIS TEST COMPARISON

r,

I.I

(a)(b)

4 FIGURE 3SHELL DEFORMATION

A more ambitious combined analysis and test program involving two layeredconical frustra is currently underway. Table I presents a conical frustratest matrix planned for FY 1986-87. The initial tests will incorporatesingle, circular hole damage patterns. Additional tests planned for 1987 willinclude multiple hole patterns and non circular damages. Actual testing willbe performed by the Sandia National Laboratories in Albuquerque, New Mexico.

42

.l a

TABLE ICONICAL FRUSTRA TEST MATRIX

NUMBER OF TESTS FORDAMAGE* EACH DAMAGE HOLE TYPE NUMBER TEST DATE

TEST TYPE LEVEL CIRCULAR SIMULATED IRREGULAR OF HOLES FY86FY87

15% 1 1 125% 1 1 1

AXIAL 25% 1 2 1TENSION 15-25% 1 1 1 2

25% 1 1 2 235% 1 1 1 2

15% 1 1 125% 3 1 3

AXIAL 25% 1 2 1COMPRESSION 15-25% 1 1 1 2

25% 1 1 2 235% 1 1 1 2

15% 1 125% 1 1 1

BENDING 25% 1 2 1(DAMAGE HOLE 35% 1 1 1IN TENSION) 15-25% 1 1 1 2

25% 1 1 2 235% 1 1 1 2

15% 1 1 125% 1 1 1

BENDING 25% 1 2 1(DAMAGE 35% 1 1 1HOLE IN COM- 15-25% 1 1 1 2PRESSION) 25% 1 1 2 2

35% 1 1 1 2

TEST SUBTOTALS 4 36• Max Circumferential Removal

U

43

CORROSION CONTROL BY COMPOSITE MATERIAL SUBSTITUTION WITH

APPLICATION TO THE M-939 5 TON TRUCK

PIN TONG, Chief Structures and Dynamics Division

TRANSPORTATION SYSTEMS CENTER

CAMBRIDGE, MA 02142

In an effort to improve the corrosion resistance of the 5-ton M-939 truck and to

lighten its weight, the Army is evaluating the replacement of structural

components which have high potential for environmental deterioration with

equivalent composite components. As a part of this overall effort, several graphite

epoxy chassis were fabricated by Ewald Associates. A schematic of the chassis is

shown in figure 1. These chassis were designed to match the strength and stiffness

characterisitcs of the steel chassis and weigh about 50% less. One of the chassis

has been installed in an actual truck and is being used for demonstration purposes.

The present study involves the evaluation of the prototype chassis both as

fabricated and as installed in the 5-ton truck for corrosion resistance, structural

integrity, and damage tolerance. Of interest is the sensitivity of the composite

frame mechanical details to stress concentrations, fracture, shock and vibration

and environmently produced degradation particularly from moisture and abrasion.

Additionally, other structural components which are critically sensitive to

corrosion and may afford a great weight saving potential will be identified and

alternative composite designs developed. Finally, a prototype truck employing as

many light weight corrosion resistant components as possible will be designed,

fabricated, and tested.

In the initial phase of this project a methodology has been developed to evaluate

the composite frames. This methodology involves identifying stress sensitive

locations, characterizing static strength and dynamic flexibility of the composite

frame, and evaluating the in service stresses. The first step has been to compare

the stiffness characteristics, as well as. the first bending and warping naturalfrequencies of the composite frame with the steel frame. In addition, the worst

case loading conditions have been identified and a simple dynamic model proposed.

Estimates are developed for the effect of the assembly modifications made to the

Ewald frame currently installed in an actual truck.

45

Test plans for the truck with the composite chassis include estimating the principle

connection stiffness and damping characteristics of an assembled truck. These

parameters are required for the dynamic model of the truck in conjuction with road

spectrum data, for the prediction of life cycle estimates. Of critical concern is

the potential for environmental deterioration of the frame especially at or near the

mechanical fasteners. Tests conducted on coupons or sample mechanical details

are planned to evaluate effects such as moisture content and operating

temperature (-25OF to +1250F). These tests will include sensitivity to freeze-thaw

cycles and mechanical abrasion.

Numerous truck components have been identified as corrosion sensitive with some

potential for weight reduction, also, designs for these components will be

developed and evaluated for structural capacity, particularly in reference to

abrasion, environmental deterioration, and damage tolerance. The final phase of

the project will be the fabrication, assembly and service testing of a prototype

truck encompassing all the light weight corrosion resistant components developed.

46

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Durability of Powdered Aluminum Structures

by

Karen SeverynsMargery Artley

Air Force Wright Aeronautical LaboratoriesAFWAL/FIBEC

WPAFB, Ohio 45433

For presentation atArmy Symposium on Solid Mechanics, 1986

U.S. Military Academy, West Point, New YorkOctober 7-9,1986

Many high strength, low density powdered metals are beingdeveloped for aerospace applications. Advantages in mechanicalproperties, such as lower density, higher fracture. toughness, and muchhigher strength, in powdered metallurgy wrought products are due tothe fine grain structure resulting from rapid solidification achievedby powder atomization. Powdered metallurgy (P/M) offers signficantimprovements in material properties over ingot metallurgy (I/M).

Although the physical and mechanical properties of P/M materialsare still being quantified, properties of P/M alloys are promisinggreater load-carrying capability and/or reduced weight in high-stress,fracture critical airframe applications. Even with this promisingoutlook, the applicabilty of powdered metals in fracture criticalaerospace components is uncertain. In order to help maximize theperformance of military aircraft, this research program is beingconducted to investigate the crack growth characteristics of arepresentative powdered aluminum, and to characterize the initialquality and fatigue crack growth rates of P/M aluminum for durabilityand damage tolerance analysis. In addition to determining iftraditional crack growth fracture mechanics analysis is possible, thisprogram will ensure that structures made of P/M aluminum can bedesigned to ensure structural integrity.

This research program investigates the characteristic propertiesof extruded bar stock 7091 T7E69, a first generation, high strengthP/M aluminum produced by ALCOA. The test specimens of dimensions4"x.5"x48" have several different flaw geometries including eloxcenter starter notches of approximately .1" (figure 1A), open holes0.25" in diameter (figure IB), open holes 0.25" in diameter withcorner flaws (figure IC), and open holes 0.25" in diameter with thru-the-thickness flaws (figure ID). The flaw geometries were preparedsixteen inches (16") apart to ensure no load interaction between thetwo holes or notches.

49

11,111~ $ r 1,

The test plan includes four tensile tests to determine themechanical properties of 7091, and ninety-four fatigue crack growthtests of constant amplitude and variable amplitude load histories.The variable amplitude load history being used is a programmed F-16load history containing predominately tension-tension cycles as wellas a few compression cycles with each block representing 400 flighthours.

To date, all tensile tests and twenty-five fatigue tests have beencompleted. The fatigue test specimens show extreme out of planecracking and tunneling (figure 2). Believing that the out of planecrack growth was due to the thickness of the specimen (.5") andresidual surface stresses, the specimens were modified. In an attemptto alleviate surface stresses and to control the non-planar crackgrowth, the specimens were milled to 3.9"x.4"x48". Then the maximumstress level was reduced from 30 KSI to 25 KSI. In the thinnerspecimens, the crack growth rate decreases, and the total life isincreased by twenty six blocks on the average. Also the angle, 0, atwhich the crack deviates from the plane of the flaw is decreased byforty percent on the average (figure 3). The thinner specimensappear to exhibit better crack growth, yet this crack growth stillexhibits extreme non-planar growth and tunneling.

The fatigue crack growth of P/M 7091 is extremely consistent. Thecharacteristic nature of non-planar crack growth and tunneling ispresent in all of the fatigue test specimens. The non-planar crack

growth and tunneling is not dependent on the thickness of thespecimen or the maximum stress level. For this reason, it is believedthat the non-planar crack growth is completely normal for P/M 7091 andthat linear elastic fracture mechanics may not apply to P/M metals. Anew method must be developed to analyze the fatigue crack growth ofP/M 7091 and all other P/M metals.

Tensile tests showed that P/M 7091 demonstrates an average yieldstrength of 72.7 KSI, an average ultimate strength of 83.9 KSI, and anaverage modulus of elasticity of 9.9xI0 PSI. I/M 7075 T7 demonstratesa yield strength of 59 KSI, an u)timate strength of 80 KSI, and amodulus of elasticity of 10.4x0 PSI. Therefore P/M 7091 has animproved yield strength and ultimate strength over I/M 7075, but adecreased modulus of elasticity.

Before any more fatigue testing is performed, life predictionswill be developed for P/M 7091 using the Walker equation. Thentesting will be resumed to check the accuracy of the developedequation. Adjustments to the equation will be made if necessary.

Conclusions of this research on the durability of powderedaluminum structures will be documented when the fatigue test programis completed.

50

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Some Mechanics Considerations in Ceramic Gun Barrel Liners*

R. Barsoum, P. Perrone, P. WongU.S. Army Materials Technology Laboratory

Watertown, MA

E. BunningSACO Defense, Inc.

SACO, ME 04072

The problem of erosion and wear of gun barrels has long beenrecognized. Ceramic materials offer the most favorablecombination of high hardness, compressive strength, erosionresistance and chemical inertness at high temperature. Inrecognition of the potential of ceramics for gun barrel lifeimprovement, MTL and DARPA contracted with SACO Defense SystemsDivision to investigate the feasibility of a ceramic-linedbarrel.

This work-in-progress report describes the analysis andfailure evaluations of the tests performed on three potentialceranric liner materials. The ceramic lined gun barrel testassembly is shown in Figure 1. The ceramic liners have aninterference fit. They are assembled by a shrink fitting processfirst to the steel sleeve, then to the steel jacket. Shrinkfitting is performed in order to introduce favorable compressivestress in the ceramic, which could negate any tensile stressesarising during firing. Finally, the liner retainer and nozzleattachments are assembled. Following that the ceramic liner isthoroughly inspected using a boroscope before the firing tests.After each firing the ceramic liner is also inspected for anycracks.

The three ceramic materials tested werec(-SiC, Si3 N4 and PSZ/TS.Table 1 gives a summary of the firing test results and failuremodes observed.

In order to understand the cause of failure in each case, afinite element analysis was performed. The finite elementanalysis ati-empted to simulate the shrink fit operations andfiring conditions. It should be mentioned that SACO performed aLame analysis in order to evaluate the interference fit andfiring stresses,. The finite element model in Figure 2 emphasizedthe details at muzzle end of the ceramic liner where most of thefailures occurred.

Figures 3 to 8 show the hoop and axial stresses due to shrink fitand firing and are used in the failure analysis.

*This program is Co-sponsored by MTL and DARPA.

53

The presentation will discuss the analysis results for theassembly operation and firing. The failures observed ot thethree materials are correlated with the analysis results. Itwill also cover the use of the finite element results in aWeibull analysis to evaluate the probability of failures.Dynamic effects, design changes and recommendations for improvedperformance will be discussed also.

54

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AUTHOR INDEX

Artley, 4. Air Force Wright Aeronautical Laboratories WPAFI1, OH

Barsoum, R. Army Materials Technology Laboratory Watertown, 041

Running, F. SACO) Dpfense Incorporated Saro, 11FBurton, L. W. Army Rallistics Research Laboratory Ahprdpon, Mn

flas Gupta, A. Army Ballistics ResParch Laboratory Ahrr'lcn, kin

Freese,. C. E. Army Materials Technology Lahoratory Watprtow-n, MAX

Hilton, P. Arthur fl. Little Incorporated ramhridgp, 11A

* Holmquiist, T. J. Honpywell Incorporated 17Edina, 'INDefense Systems Division

,Johnson, A. R. Army Materials Technology Lahoratory W-atertown, I/s

,Johnson, G. R. Honeywell Incorporated 'Ii N *M

Defense Systems Division

Kaste, R. P. Army Rallistics Research Laboratory Aherdpen, "IO

Keefe, R. E. Kaman Sciences Corporation Colorado Springs, CO

Mayville, R. Arthur 0. Little Incorporated Cambridge, 11A

Murray, Q. B. Army Ballistics Research Laboratory Abordee-n, 1.1

Patton, t. M. Army Ballistics Research Laboratory Aberdeen, MD1

Perrone, P. ). Army Materials Technology Laboratory WAtprtown, MA

Quigley, C. I. Army Materials Technology Laboratory Watertown, MA

Reese, E. Sandia National Laboratories Albujqierque, NIII

Saiarase,E. Columbia University New York, NY

Soveryns, K. Air Force Wright Aeronautical Laboratories WPAFR, IIH

Shino7uka, M. Columbia 1University Ne-w York, NY

Spiridigliozzi, L. Army Materials Technology Laboratory Watertown, PIA

Sulcoski, M. F. University of Virginia Charlottesville, VIA

Tessler, A. Army Materials T,:chnology Laboratory Watertown, 1 A

Tong, P. Transportation Systems Center Cambridge, MA

Tracey, D. 11. Army Materials Tfechnology LaborAcory Watertown, MA

Warren, T. Arthur 0. Little Incorporated Cambridge, MA

Wong, P. Army Materials Technology Laboratory Watertown, MA

61

- -F..-117,