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C E NT EIR-and L________
I... TECHNICAL. REPORT
NO. 13004 I,II III
Reproduced FromBest Available Copy
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THEORETICAL AND EXPERIMENTAL ''VESIGATI•N
OF MECHANICALLY FASTE!;ED AOMPOSITESJ1'Lv 94I , I
C tr. 6o Enayat Mah82- --I,
Pedro H .,,- .,• • • M1,.hria;, it,-?• Uriversity| :
Bby . .•i,, 48823-1226 , " l,'1
M i_ _ _ , ',.-
DISTPJIBLMON STATEMENTA
u J
U.S. ARMY TANK-AUTOMOTIVE COMMANDRESEARCH AND DEVELOPMENT CENTERWarren., Michigan 48090
-4, .. . . . . '."' : .' -" •" ""• ." ."'"• -'' " ".'. • •-"; '.;" -. " "..; "...•: .'. .'..V. "' " •.".. .. "....• ." -,
INOTICES
i This report is not to be construed as an official Department of the Armyposition.
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Mention of any trade names ,or manufacturers in this report shall not beconstrued as an official indorsement or approval of such products orcompanies by the US Government.
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Destroy this report when it is no longer needed. Do not return ft to theoriginator.
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rECJRlTY CLASSIFICATION OF THIS PAGE
REPORT DOCUMENTATION PAGE
'a. RdPOJT SECj8I.TY CLASSIFICATION 1 b. RESTRICTIVE MARKINGSunclassified jaNone
2a. SECURITY CLASSIFICATION AUTHORITY 3. DISTRIBUTIQN/ AVAILABIUIY OF RYEPORTApproved for publiC re ease distribution2b. DECLASSIFICATION / r:WNGRADING SCHEDULE unlimited,
4. PERFORMING ORGANIZATION REPORT NUMBER(S) 5. MONIhORiNG ORGANIZATION REPORT NUMBER(S)
TACOM T.R. #13004
"* 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORINtC ORGANIZATION
Michigan State University TACOM AMSTA-RiCKM
6c. ADDRESS (City, State, and ZIPCode) 7b. ADDRESS (Clt, State, s.ed ZIP Code)
Dept. of Met. Mech. & Mat. Sci. TACOMMichigan State University Attn: AMSTA-RCKME. Lansing. MI 48824-1226 Warren, MI 48690
Ba. NAME OF FUNDINGISPONSORING l8b. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBERORGANIZATION *Of applicable)
Same as 7 Contract DAAEO7-82-K-4002St. ADCRESS (City, State, WW ZIP Code) 10. SOURCE OF FUNDING NUMBERS
PROGRAM PROJE TASK IWORK UNITELEMENT NO. NO. NACCSSION NO.
S11. TITLE (Include Security Catication)
Theoretical and Experimental Investigation of MIechanically Fastened Compositesi. PERSONAL AUTHQR(S)
Clotd, Gary; Sikarskie, David; Mahajerin, Enayat; and Herrera, Pedro13a. TYPE OF REPORT 13b. TIME CVRED I14. DA jOF REPORT (Yepar,16Month, Da)I .PAGE COUNT
Final FROM 9ilvl TO 9/83 7984 July16. SUPPLEMENTARY NOTATION
17. COSATI CODES 18. SUBJECT TERMS (Continue an reverie if necesauM and identify by block number)
FIELD GROUP SUB-GROUP
11,. ABSTRACT (Continue on revorse of neceusavy and identifyb &~bock number)
* "The mechanics of fasteners in composites were studied it a combined experimental-'theoretical research program. The objectives were to gain fundamental insight into thestress-strain field near pin-type fasteners and to provide guidance to designers responsiblefor the selection and sizing of fasteners. The primary experimental method utilizes Moireinterference with optical Fourier processing of grid photoplates. A new technique usingoptical interference to generate gratings in three directions was developed togain a factor*of 10 in sensitivity. The constitutive properties of the materi al studied were measured.For the analytical work, a boundary element method (BEM) was deveToped, a compact and ..efficient compnter, code written, and the method compared with the finite-element method.
- (FEM).- cor the problems investigated, the BEM is more efficient. The material used wasfiber g9ass-epoxy laminate with woven fibers. The analytical and experimental forces werebrought to. bear on the problem of a loaded pin snugly fit in a hole. Results from the two
,approaches agreed well for the specific composite.20. DISTRiUUTION/AVAILABILiTY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION
(3UNCLASSIFIEODJNLIMITEO 0 SAME AS RFT.' C OTIC USERS
J2&. P AME OF RESPONSIBLE INDIVIDUAL 22b. TELEPHONEVInuI~d Area Cbde)f 22c. OFFICE SYMBOL
Avery'H. Fisher 313-574-5879 AISTA-RSC00 FORM 1473.MMAR 83 APR edition may be used until exhausted. SECURIT LASSIFICATION OF, TIS PAGE
All other editions we o bsWlft.
ol.........
"PREFACE
The research described in this report was conducted at Michigan State
University in the Department of Metallurgy, Mechanics and MaterialsScience and in the Center for Composite Materials and Structures.Investigators were Dr. Gary Cloud, Professor; Dr. David Sikarskie,Chairman; Dr. Enayat Mahajerin, Post-doctoral Student; and Mr. Pedro
i Herrera, Doctoral Candidate. Manuscript preparation was by Ms. ArleneKlingbiel.
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E L TEC T E.....MAR6 1985 .
B . )•3'K '.,"-.?,
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TABLE OF CONTENTS
Sect.ion Page
1.0. INTRODUCTION* * * ** **.****1
1.2. Pakroject Summar . . . . . . . . . . ............. *1
2.0. ANALYTICAL DEVELOPMENT, RESULTS AND COMPARISON . ~.....122.1. Problem Statement . . . . . .. . . . . . . ... ........ 122.2. BEM Formulation . . . . . . . . . ** *** . .... . . . 132.3. Example Problems . . .18
2.4. Comparison of BEM andFEM . . . .* . . . . . . . . . .. 18
3.0. EXPERIMENTAL METHODS AND RESULTS. . . . .. . . . .273.1 Introduction ... .. ..... . . . . . . . . . 273.2. Specimen Fabrication and Material Specification .!*' .. 283.3. Specimen Cratings . .... 283.4. Printing Gr4atlong Onto Specimen . *.* 313.5. Grid Photography . ~.....313.6. Summary of Optical Processing to Create Fringe Patterns . 343.7. Experimental Results . 353.8. Experimental Evaluation of Elastic Constants for Composite 463.9. Experimental Results and Discussion . . . 473.10. High-sensiti~vity Interferometric Moire Technique ... 49
4.0. COMPARISON BETWEEN EXPERIMENTAL AND NUMERICAL RESULTS . . . . . 52
REFERENCES . . . . . . . . . . . . . * 54
APPENDIX A FUNDAMENTAL SOLUTIONS .. . . A-i
APPENDIX BTHE COMPUTER PROGRAM NBEM .. . . . . . . . . .. .. .. 8-1
APPENDIX C SIMPLE OPTICAL PROCESSING OF MOIRE-GRATING PHO~TOGRAPHS .C-i
DISTRIBUTION LIST . . . . . . . . 0-1
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.................................... ,. ..........
LIST OF FIGURES
Figure Page
2-1. Geometry for the Boundary Element Method . . . . . . . . . . . 14
2-2. Geometry for Computation of a' y's 16
2-3. Double-lap Mechanical Joint . . . . . . . . . . . . . . . . . 19
2-4. Geometry for the Example Problem ...... . .. .... 20
2-5. Schematic of, Boundary Element Subdivisions. . . . . . . . . . 21
2-6. FEM and BEM Subdivision Schemes for the Mechanicai Jc..IntProblem . . . . . . . .. 26
3-1. Dimensions of the Test Coupon . .............. . 29
3-2. Grating Produ rocess to .e.......... . 32
3-3. Set-up for Grating Photography. ......... .*... 33
3-4. Photograph of Moire Pattern Showing Displacements Perpendicularto Load Line for Zero Load with Pitch Mismatch . . . . . . . . 36
3-5. Photograph of Moire Pattern Showing Displacements Perpendicularto Load Line for 400 lbs. Load with Pitch Mismatch . . . . . .. 37
3-6. Photograph of Moire Pattern Showing Displacements Parallelto Load Line for Zero Load with Pitch Mismatch . . . . . . . . 38
3-7. Photograph of Moire Pattern Showing Displacements'Parallelto Load Line for 400 lb. Load with Pitch Mismatch . . . 39
3-8. Strain, Perpendicular to Load Axis (ex) Along Several Livesin the Ligaments of Fastener Hole . 0.. . * . . . 40
3-9. Strai Perpendicular to Load Axis (ex) Along Several Linesin Bearing.Region tiear Hole ........ . . . . . . . . 41
3-10. Strain Parallel to Load Axis (ey) Along Several LinesEncompassing a Ligament Region ....... . .... ... 42
3-11. Strain Parallel to 'l.oad Axis (e1 Along Several Lines isand Opposite to the Bearing Region . . . ,* ..... ... 43
3-12. Specimen Showing Location of Strain Gages ...... . 44
7,,%
,, -
• ° . .. . "-"". . . . '"- . ."- . ,' . " ' . • " o ",q' , .. ' .- . .o , -, ."• -. --I"W. -- •" % .. . " . • . .. - , , . ,- ,. . ' ,.' - ' ., - .'' - .- -.- - -. -, . - . .. • ,. - .. - .
Figure Page
3-13,. Typical Tensile Stress-strain Plots for Determination ofMechanical Properties of Orthutropic Composite usea in thisProject .. . .. .... ... ... .. ... . .. .. . .. 45
3-14. Distribution of Tensile and Compressive Strain (ey) Nearthe Fastener Hole . . . . . . . . . . . . . . .. . . 48
3-15. High Sensitivity Moire Fringes Showing DisplacementsPerpendicular to the Direction of Loading for No Load withRotational Mismatch . . . . . . ...... .... . .. . . 50
3-16. High Sensitivity Moire Fringes Showing DisplacementsPerpendicular to the Direction of Loading for a 130 lb. Loadwith Rotational Mismatch .... . . . . . . . .. ... ... 51
4-1. Comparison of Stress Concentration Factors Obtained byNumerical and Experimental Techniques . .. .. .. .. . .. . 53
%N?
LIST OF TABLES .
Table Page
2-1. Stresses along the ligamert l 4 ne ab for an orthotropiccomposite. Uniaxial Tension, d/w = .5, N 60 (boundarysubdivisions) d = 0.5, e a 0.5, h = 1.5, w 1.0 ....... 22
2-2. Stresses along the ligament line ab for an 'wt!otropiccomposite. Cosine distribution of tractions on the upperhalf of the hole, d/w - .5, N - 60 (boundary subdivisions)d = 0.5, e = 0.5, h a 1.5, w 1.0 .. . . .. .& .. . . * 23
2-3. Stresses along the lijament line ab for an orthotropiccomposite. Cosine di.,tribution of tractions on the upperhalf of the hole, d/w :- .2, N - 60 (boundary subdivisions)d - 0.2, e - 0.5, h a 1.5, w - 1.0 . . . . . ......... . 24
2-4. Stresses along the ligament line ab for -n orthotropiccomposite. Fixed pin case, d/w - .5, N - 60 (boundarysubdivisions) d 0.5, e - 0.5, h - 1.5, w - 1.0 ....... 25
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1.0. INTRODUCTION
1.1. Background
There has been a dramatic increase ir. the use of composite materials. Thecenter of gravity of this growth has been in aerospace and defense-relatedindustries. As composite material developments continue to increase,resulting in decreases in cost, -use of these materials will naturallyspread to other industries.
One of the attractive features of composites as opposed to metals is theirability to be molded into complex "final shape.' Important advantages ofthis approach include requiring a minimum number of fasteners as well asbeing able to locate the necessary fasteners in regions of low stress,Because of cost, however, such elaborate design is usually possible onlyfor sophisticated structures, e.g., military aircraft. While fastenerproblems are significant in these structures, it is expected that theirimportance will increase as composites usage spreads to lesS-sophisticatedapplications.
The fastening of composites poses some special problem. In the fastening |of metals, normal metal plasticity acts' as an "averaging' mechanismtending to relieve both high local stresses and uneven load distributionin fastener patterns. .In general, composites are considerably morebrittle, more sensitive to stress concentrations, and have much lowerstrain to failure. Fastener techniques which distribute bearing loadsmore evenly (reduce stress concentrations) result in higher-strengthjoints. Techniques which distribute bearing loads include fastenerarrays, interference-fit fasteners, glued fasteners, and hybrid adhesive-mechanical joints. A typical example involves replacing lead-alignedgraphite fibers near the fastener hole with lower-odulus glass fibers.Stress concentration relief in the interference-fit fastener case isderived from a matrix Osoftening" in the vicinity of the hole. Thissoftening is actially an inter-or intra-ply separation which can occurwithout fiber breakage.
1.2. Project Sumary
The contractors conducted a one-year study of the mechanics of fastenersin composites. It should be noted that the analytical and experimentaltool' used in this study are fairly novel, particularly in the context of,composite fastening, and in that sense are unique contributions in their 0own right. The theoretical effort concentrates on the extension ofboundary element methods to determine stresS-strain fields for complexmultiply-connected and three-dimensional geometries with anisotropicmaterials. Experimental approaches include a Noire method involving "high-resolution grating replicition, Fourier optical processing of gratingreplicas, and digital Cata reduction. ,
This report describes the ,methodOlogy developed for both the analyticaland experimental studies. The techniques developed were used to determdne
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stresses and strains in the vicinity of a single-pin loose-fit lap jointin an actual glass-epoxy composite; these results are reported. Theproperties of the composite were measured so that theory and experimentcould be compared. The comparison, which is described in Section 4.0.showed good agreement for the furdamental case studied.
While this ore-year effort was successful in terms of methodology andresults, it was viewed fror. the start by the researchers involved as theearly steps in a more comprehensive research program. A unique aspect ofthis program is that the experimental and analytical techniques aresimultaneously being developed and used by researchers in the same group.This work is necessary before systematic fabrication of structures fromcomposites can be successful in engineering and economic terms. Theeffort is considerably enhanced by having the theoretical and experimentalresearchers together. Significant progress has been made after the closeof the one-year contract because the contractxe-'s were comMtted to theIdeas agd the people involved. The researchers feel strongly that themaor benefits will come from research yet to be done, and they suggestthat continued support is appropriate for proper re&lization of the
L resources and personnel already developed.
2.0. ANALYTICAL 'DEYELOPMENT, RESULTS AND COMPARISON
. 2.1. Problem Statement
This section presents the analytical developln 't of a boundary elementformulation for calculating stresses and deformations in mechanicallyfastened composites. 7ae purpose of this development results from thefollowing observations. In a vast majority. of the composites literaturein which stress and/or deformation calculations are required,. the finiteelement method (FEN) is used. This method is, of course, very powerfuland has the advantage of access to well developed codes. It is notnecessarily the most efficient numerical procedure, however. Numerousauthors have shown ()* that the boundary element method is, for certainclasses of problems. considerably more efficient than the FEM. The mainpurpose of this section is to develop a boundary element method (BEl) codepertinent to a mechanically fastened composite structure. This code will
* then be directly compared with a current state-of-the-art FEN code to seeIf significant improvement in efficiency is possible. For comparative
Y.- purposes both codes are run on the same computer, a Prime 250. In termsof problem selection for comparative purposes there are a number of
. possible boundary value problems to look at in the composite fasteningarea., Examples include multiple fasteners, interference fit fasteners,
: softening strips, etc. For this example, a simple lap Joint, single pin,loose fit connector is considered, and results using both numerical
. methods are compared. If improvements can be shown in the simple case, it-.is reasonable to expect improvement in more complicated situations.
; *Numbers in parenthesis refer to references given at the end of Section4.0.
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However, code development for the more complicated situations are coveredunder future proposed research. The next subsection will explain the BEMformuiation. This is followed by the solution of some example problemsand a comparison of BEM and FEM.
"- 2.2. OEM Formulation
Let an anisotropic body (Figure 2-1) occupy a finite open plane region Dbounded by a single smooth contour 3D which admits a representation in theform xi - xj(s). The parameter s is the length along, 3D, rom an arbitrary
":- origin, and xi are cartesian coordinates (see Figure 2-1). For the"'-7 well-known mixed boundary value problem of anisotropic elastostatics:
"" SaoytS uy,•60 0 in D
*"yny - "o on 30t (1)Su0 - 0 on 30u
- 0,,y , 1,2 30 3 Dt + 3 0 u0
u yrepresents the displacement components, the coma denotesdIfferentiation with respect to the arguments after the comma, aoy is a
.-- component of stress, t its the corresponding traction vector, ny is a- -. component of the unit outward normal to the boundary aD, and Smoy6 denotes
"the "stiffness tensor" for the material. To solve this problem by ani indirect boundary element method, one can apply the initially unknown-: . layer of body forces Ry to the boundary of the embedded region and use the
-* principle of superposition to obtain (2):•:'000M fa();J Hao, (Cx')Ry(x')ds (2)
uO(M) - Uoy (Cx')Ry(x')ds (3)
where C-u(*C1,C2), x*-(x y') are field point and source point respectively.- U8 and H 0 are the fundamental displacement and stress solutions* for a
po nt load In the y direction in an infinite medium. As .C approaches aSboundary point.from inside the region, equation (2) reduces to an. integral
equation of the second kind for which the intefral is defined in a Caichyprincipal value (CPY) sense. For equation (3) the corresponding boundary
-- integral is of the first kind and need not be considered as a CPV. Forsimplie.ity, a general boundary integral equation covering several casescan be written as:
p6(s) a Soy R(s) +f' Goy (ss'),ry(s')ds' (4)3D
St8,y U 1,?
*These fundamental solutions are given in detail In Appendix A.
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I-.
1.i
p.p.
tt
41,
•24
Pon
Node
AD
m"D
-. 14
we consider three cases:
U (I)The pure displacement problem
a 0
PS UB
(ii) The pure traction problem
a -1/2
(iii) The mixed problem '(i.e.,j displacements are prescribed on 3Du andtr&ctions are prescribed on 30t) requires an appropri'atecombination of case Mi and case (ii).
In the numerical solution of equation (4) one can replace 30 by Ni straightline segments 30j, j - .10.000 N on which the point loads R (sj are,approximated by piecewise constant functions Ry(sj). T , - 193 = i 00N. If the boundary conditions are satisfied at th~e center of each segmentIthen equation (4) reduces to a system of 2N simulataneous linear algebraicequations denoted by:
A R b, 5
where A i~s a 2Nx2N coefficient matrix, R=(R 19R2 .... R2)T are the unknownpoint loads and b=(bjbl,bZ..bZ)T are the pres~cribed boundary conditions.The essence of t~e computation is the construction of A. From, the
* discretized version of equation (4) it can be seen that A is N blocks ofWx matrices having elements:
"12 88Y A~ J,
(a O-i f ,Y(si s')nPd' i J()_
(a'o-f)jj I j*&fi - U oy (sjs 6)ds' i j (7)
3%
where (a* Oy) , B ,f 1,2 have been computed analytically using F~Iure 2-2
15
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Ia
Field
FIGJM 2-2. Gc&etry for Ccbuptatcam of a *
163
aCO 0 -h/
* .. *.....-... ... ~. **.**d.* *. ~ .16
o-.
for both isotropic and orthotropic materials. In Figure 2-2, h, is themesh length. As a+O, the field point approaches the boundary point andthe integrals over this mesh length become singular. The integrals areevaluated by first assuming that the unknown traction components Rt, Rnare constant over the mesh length. Rt. Rn can then be taken outside theintegrals, and the resulting integrals car. then be evaluated analyticallyfor a$O. The resulting values of (a*oy)jj are obtained by taking thelimit as a+O. The results are:
PL M() For the isotropic case
. (a*ll)jj = 2Q hj(ln(hj/2)-1) + hjcos 2 *j
(a*12)jj = (a*21)jj a hjsincjcosgtj
(a*22)jj = 2Qhj(ln(hj/2)-1) + hjsin2,cj
with Q = (3-v)/2(1+v), where v is the Poisson's ratio for material.
0(i) For the orthotropic case
(a*ll)jj a -{(clAl-c3A2 )cos 2Gj + (c4Al-c 2A2)sin2ajlhj(ln(hj/2)-11/2
(a*12)jj = -((c1A1+c2A2-c3A2-c4A1)cosajsinuj)hj(ln(hj/2)-1)/2
(a*21)jj a (a*12)jj
(a*21jj -[(clA1-c3A2)sin"aj + (c4 A1-c2A2)sin2 Ij ]hj(ln(hj/2)-l)/2
where c's and A's have been defined i,, Appendix A.
The integrals in equations (6) and (7) have been computed ;,:a.7-ricallyusing a four-point Harris-Evans quadrature formula (3). This quadrature"is useful when the integral is singular. In this formulation (thesingular case), inj has been excluded, but in the adjacent segments (near"singularities) this quadrature is helpful.
Once the system (5) is solved for R,.stresses and displacements at anyinternal field point can be compuld from the discretized form ofequations (2) and (3). The boundary element method is unable to predictstresses and displacements at boundary points. However, by excludingsingular points (i.e., evaluating elastic fields analytically) andemploying the Harris-Evans quadrature for the rest of the points, we can
°*D predict boundary fields (especially the stress concentratfon, factors inSthe example problems)'quite accurately.
" The corresponding computer program, BEM (see Appendix 8), is based on theformulation explained here and is written in FORTRAN 77.
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* *.-.....* .. . . . ... .* ,~** * ,, ' ..-. '- .- . k f :.
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2.3. Example Problems
A number of example problems were solved using the BEM program. Allproblems have a common geometry, namely, the lower section of the simplelap mechanical joint (see Figure 2-3.). Making use of the symmetry of thespecimen (for the principal material and coordinate axis coincident), thefinal geometry analyzed is s!town in Figure 2-4. Figure 2-5. is aschematic of the boundary ý.-lement subdivision used. Both isotropic andorthotropic problems were4 solved; however, only orthotropic results arepresented. All orthotropic problems were based on a particularglass-epoxy composite hating the following compliances:
cll = 5.OOx1O08 1/psi
SC12 - -1.05x1O- 8 1/psi (8)
c22 - 4J6x10"7 1/psi
c33 = 1.18x10" 6 1/psi
These compliances were measured for the laminate used in the experimentalstrain analysis phase of this project (see Section 3-8.).
Two items were investigated in this limited numerical- study. The firstinvolved hole size, i.e., the d/w ratio, and the second was the effect ofvarious boundary conditions. Tables 2-1. through 2-4. shown with theenclosed figures are self explanatory and give selected solutions forthese parameters. Full field stresses were computed but only ligamentline (the line from the edge of hole to the edge of the specimen) stressesare presented. These stresses are particularly useful for two reasons:the maximum stress concentration is along this line (at thi hole edge) andthe appropriate summation of these stresses' (forces) 'is a check on overallequilibrium. All computations were done on a Cyber 750 computer. Notethat in the following subsection in which BEM is compared to FEMN bothprograms were run on the Prime 250 system.. This system had graphicscapability which permitted graphic display of computed data.
2.4. Comparison of BEM and FEM
As discussed earlier, one of the main objectives of this work is to make acomparison of BEM and FEM numerical procedures. For this purpose it wasuseful to run both programs on the same computer. The FEM computer code.was available on the Prime 250 system., For this reason, the' BEN code wasadapted to the Prime 250 computer system. For this contract FEM-SEM.comparison has been done only fcr the case of isotropic'material with the'simple joint in tension. This is the isotropic version of the results inTable 2-1, The comparison was based on a common boundary subdivision,i.e., in the BEM code 57 boundary elements corresponded to 134 quadraticFEN elements, see Figure 2-6. For this case, the stress concentrationalso is "known* (4). Results are summarized in Figure 2-6. and below:
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". . .. . .. . ..... . •.... .. '... .. .. ..." ."."'" ..... ... a. -> ..... •....-....... * * .' . -. * . . .,.....
F Ff2 Ff2
i44i
FIUR 2-3 -obeLp Meh a Jont
11
-44
6ty
4,
iie
-w/2
F=Mui 2-4.. Gesr fo~r the M.X~pVJ Problem
20
S . . . . . . ..,.,m m
bondaryelement
rodeA
SN.-
FI~3E 2~5. Shsmtc ofBoudaryElui Su,,vi-.us
21'
So'.,
TABLE, 2- 1. t 00 t s2L.
Stresses aiong the ligament. line ab
for an orthotropic ccmposite.
Lkniaida1 TArý.:, ion, d/w - .5,0 - bN-= 60 kCbouiOArxy subdivisions)
d = 0.5
e -=0.5 t no.A
h =1.5
w' 1.0
_ _ LOx _
.M2 1.5 .0070 .0015 -. 1135
.%4 1.5 .1593 .0091 ..2379
.06 1.5 .=279 .0145 .5569
.08 1.5 .2861 .0189 .8721
.1. 1.5' .3509 .0225 1.1847
.12. 1.5. .4174 .0251 1.5085
.14 1.5 .4794 .0269- 1.8589
* .. 16 135 ..5289 .0275 2.0496
$18 1.5 .5543 .0270 2. 7191.
.2 .51 .5391 ' .0243 3.2888
ý.21 1.5 .5095 ..0299 3.6290
.22 1-'~ .4616 '0186 ý4.0195
.23 1.5 .3990 .0139 4.4765
.24 1.5 .3812 .0072 5.03. j
* .25 1.! -1.4308 .0082 6.4621
22
~ ~~ *i* - i:
.1"
TABLE 2-2. -o. ..-
Stresses along, the ligament line ab e,_ , o -
for an orthotropic composite. ___ ty
Cosine distribution of tractions on Ct 11F
the uppez half of the hole, d/w- .5,N 60 (boundary subdivisions) 4 *•-o-
d 0.5 k=Q ty=@.
e 0o. 0.5 tyw o.
h =1.5
w = O.1.0 t" 0 .w- 1.0 %j -I ] "
x y "1
.02 1.5 .2160 -. 1639 .7849
.04 1.5 .1100 -. 1734 .9807
.06 1.5 .1555 -. 1826 1.1347-
.08 1.5 .2200 -. 1826 L.281.3
.1l 1.5 .2775 -.1799 1.4318
.12 1.5 .3224 -.1643 1.5958
.14 1.5 .3531 -. 1495 1.7830
.16 1.5 .3669 -. 1323 2.0057
.!8 1.5, .3575 -. 1137 2.2820
.2 1.5 .3088 -. 0949 2. 6403'
.21 1.5 .2595 -. 8586 2.8645
.22 1.5 .1848 -. 0770 3.1305
.23 1.5 .0826 -. 0678 3.4528
.24 1.5 -r.0037 -. 0583 3.8640
.25 .1.5 -. 9524 -. 2265 5.7545
........ ,
'23 ';;
-• L -'- - . . .," - .r .-- .* . ," o• .- W •," .," ' '. _, " ' ' -" •. ; '' " "• '. . . -" 2 r ."'.• .• - - - " , -4 -: -. -__ _ -,. • ,. •'
p..
TABKE 2-3. ± = ty -0.Stresses along the. ligmt line ab :-I - 'e%for an orthotropic caoposite. t, .Cosine distribution of tractions on- OL 6the upper half-of the hole, d/% .2,N- 60 (bo:-dary subdivisirms) "-d =0.2 a.' "yiO. 1 x "e -0.5 tyo= ty ""-
h 1. 5w = 1.0
ty=-±.. :
* ,11?x I'rtr.032 1.5 .0494 .0626 .5133
.064 1.5 .0343 .0343 .5494
.096 1.5 .0415 .0189 .5899
.128 1.5 .0553 .0227 .6100
.160 1.5 .0727 .0332 .6496
.192 1.5 .0934 .01:60 .6787
.224 1. -1198 .0616 ..7285
.256 1.1 .1554 .0766 .7978
.288 1. .2066 .0909 .9296
.320 1.. .2816 .1045 1.0894
.336 1. .3284 .116 1.2948'
.352 1. .3752 .1190 1.4420
.4006 .1250 1.97J5
384 1. .3269 .1103 2.4196.384
.400 1. .4279 .2449 3.3944
'40 A.
24
TIAKE 2-4. tyoStresses along the ligaamet line ab V.. Gf.or an orthotropic composite.' 'AYu 0.
Fixed pin case, d/w =.5, 6.N =60 (bowndary subdivisions)
.. -
d-0.5e'-0.5
A/a@h 1.5 t~0 y0w=1.0
1 (rzx 14__ __ _
.215.0019 -. 0077 .8061
.4 15.0232 -'.0728 8.8W8
.06 1.5 .0324 -.1015 .9069
.08 1.5 .0390 -. 1029 .9600
.1 1.5 .0442 -1022 1.0203
.12 1.5 .0464 -.1007 -1.0930
.14 1.5 .0432 -.0972 1.1815
.16 1.5 .0310 -. 0913 1.3077
,8 1.5 £0040 -. 758 -1.4794.2 1.5 -. 0501 -.0467 1.7377
.11.5 -.0946 .0221 1.9236..22 1.5 -. 1584. -0116 2.175 .9
.23 1.5 -.24-80 - -.0527 2.5430,
.24 1.5 -.3886 -.1264 3.2133
.25 1.L-.9566 -.9854 * 9.7269
25
1. FINrIM FLEM~r( (ANSYS)
( d = .2, 0.5, h - 1.5. w 1.0)
N - 134 Qiadratic F.e ts
Results: For d/w - .2 K, 3.1102
STotal CU time: 177 see.
-,2. BONDR EEMC (BMi
( d TM .2, e -0.5 , h -1.5 , w -1.0 )
N4 57 Con~stant Elements
*Results: Ford4w - .2 Ki 3.O0951*Total CPU t~me: 27 sec.
FIO Z!-6. FM. and BEM Subdivision Schms for the +ectimdCAJ JOint
Problem.
26
4"
, * . . . p .. -.. ...-. . -_ -- •
I
FEM EXACT E4
Ki u 3.1102 KI , 3.1352 Ki - 3.0951
CPU time - 177 sec. CPU time - 27 sec.
Note that BEM represents a significant reduction in computer time over"FEM. This savings depends to some extent on the particular case, how manyfield points are required, and so on.
3.0. EXPERIMENTAL METHODS AND RESULTS
3.1. Introduction
The experimental components of this investigation encoipassed two phases.Techniques appropriate to the problem and the material were developed.Some studies of composite pin-loaded specimens were carried out. Inactuality, both phases ran simultaneously, so the program was rathercomplex and open-ended.
The primary experimental method uses Moire interference with Fourieroptical processing of grid photographs.* Rugged grids are applied to thespecimen, by vacuum-deposition, and these grids are recorded usinghigh-resolution 'techniques for each state of the specimen. Sequentialrecording of grating replicas and subsequent coherent optical processingto obtain eahanced fringe patterns, often with multiplied seinsiftivty,allow quantitative comparisons between any two states of the specimen atany later time. Such a procedure is especially advantageous innonreversible structural testing.
A publica•ion (5) discussing the theoretical basis and showing anapplication of this Moire technique is duplicated in Appendix C. Completedescriptions appear in Air Force reports and papers by Cloud's group (6 to12) so further description is not needed here.
It is worth noting that this version of the Moire method can be. used mna"dirty' environment. It is tolerant of poor quality or course grids andpoor photographic reproduction of the gratings. The approach has beenused in difficult situations involving high temperatures (up to 1,S00"F)long tfmes (1,000 hours) and in the presence of convection currents,vibrations, and so on (6).. The procedures appear to have great promisefor application in field investigations of displacement and Strain Instructures of any material.
It soon became clear that the Moire technique as summarized above has a. strain sensitivity which is marginal for work on composites, as wasexpected. Consequently, while this method was being used on the first
Win this report, 2ratinq means a set of parallel lines, while grid means apair of orthogonal gratings -25 sets of lines at 90".
27
*.. .. .. "" " " . . ... " AtM' .'.'-.: " -.. '" . t * ' .
J
specimens in this project, a program to extend the sensitivity by a factorof 10 or more was begun. Both endeavors were successful. In order tocompare theoretical and experimental ressIlts in this project, theconstitutive properties of the material studied had to be measured. Thisaspect of the experimental work was also successful.
This section describes first the specimen materials and preparation,including the creation of Moire grids. The essential details of the Moireprocess leading to plots of strain are then outlined. Results obtained inthis way are given, and interesting aspects of these data are discussed.The experiments to determine material properties for the composite are
Z described and the results given. Finally, the high-sensitivity techniquesZ are described in brief, and some results which illustrate the promise andI flexibility of the method are reported.
3.2 Specimen Fabrication and Material Specification''
The material used for this investigation was fiberglass-epoxy laminatewith woven fibers (R1500/1581, 13 plies, 0.14 in. thick) supplied by
- CIBA-GEIGY, Composite Materials Department, 10910 Talbert Avenue, Fountain.. Valley, California 92708.
The dimensions of the specimens are shown in Figure 3-1. It has beenshown by Horgan (13) that, when working with composites, the end effectspersist over distances of the order of several widths of the specimen.This stress channelling does not seem to be so severe in this case basedon the results of the Moire patterns obtained, probably because of the
* reinforcing in t',e transverse direction. To be safe, however, thespecimens were designed to be quite long and narrow.
"* The specimen was cut with the fiber oriented along the direction of theloading. Grating application techniques are described in section 3.3.Subsequent to applying the gratings, the fiducial marks, identifers, andcode marks were applied with Presstype lettering. The specimen was thenready for recording a baseline Moire grating photograph, loading throughthe hole by means of a pin, and recording at-strain grating images.3.3.' Specimen Gratings
Application of the Moire effect to any problem depends on the successfuldeposition of line grids (or dots) on the specimen material.
The photoresist approach to creating grids on the specimens was chosen* because it Is fairly simple, requires minimal special equipment, and is
well proven in the contractors' laboratory. Photoreststs for Moireapplications have oetn studied and described in detail by Luxmoore,Holister and Hermann (14,15,16). Cloud and co-workers (6 to 12) 'ave usedthis approach successfully.
The photc.'esist chosen was Shipley AZ1350J provided by the Shipley Co.,
28
* * .*.*,** ** . ... .*.... .. , * .. . .... ~
S
in 1 .0
FIDUCIAL MARKS
IS
3/8 DRILL THRII 8.00
n
.s 1.00
Figure 3-1. Dimensions of the test coupon..
'29
,.:......;..:.... . ., ...... . . . . ,. .... . .. .. .* .. . . . .
Newton, Mass. The companion thinner and developer were purchased with theresist.
"It is desired for Moire work, as with most other photoresist usage, thatthe resist co4ting be thin and uniform. Common application methods"include spinning, dipping,spraying, wiping and roller coating. Thespinning and wiping techniques were found deficient in that they alwaysleft some build-up near the hole of the fastener boundary, that is, in theregion of greatest interest.
Attention settled, therefore, upon the spraying method. An artist'sairbrush was obtained and a spraying technique which gave satisfactoryuniformity and coating thickness was worked out by trial and error.Superior results were obtained by thinning the resist. Testing wasconducted to establish a balance of resist-thinner proportions, airpressure, airbrush nozzle opening, spraying distance, and brush motion.
In order to produce coatings of the desired thickness, the photoresistrequired thinning. The proportions arrived at through trial and errorwere by volume, one part AZ1360J to two parts AZ thinner. The air
* pressure provided by "canned air* sold in art supply stores wassatisfactory for the Paasche type H-3 airbrush. The best nozzle settingfor the airbrush used was 1-1/2 to 4 full turns open from the closedposition. The spraying procedure which was developed called for laying"the clean and dry specimen inclined at about 80" to the horizontal. Theairbrush containing the resist was held about 12 in. from the specimen.
.. Flow of the atomized resist was begun and allowed to stabilize for aboutone or two seconds, after which the spray was quickly shifted onto thespecimen. At the range the air flowýd, it was necessary to sweep thebrush from left to right to cover the whole surface. Care was taken to
* assure that the spray fan did not overlap the previously applied wetcoating, otherwise small bubbles of photoresist started to form, yieldinga nonuniform surf4ce. It was absolutely necessary to start the spray wellbefore bringing it to bear on the specimen, as some coarse droplets areexpelled at the beginning of flow.
*: Coating thickness was controlled by spraying time and number of strokes(or coatings). Best results were obtained with one single layer ofresist.
' .If the coating did not appear satisfactory, itwas removed using eitherthinner or acetone. This operation was performed as quickly, as possible"to avoid dissolving the surface of the specimen. The surface was then
* Immediately washed with running water to get rid of any excess of acetone.After the specimen dried at room temperature, another coating ofphotoresist was' applied. The coated specimens were placed inside alight-tightcontaines to await exposure and development of the gratingimage.
I
30
* •. *•••• •• .°.. .. •`* .....................* ~ ... ~ . .* ** * *. **** ~ S. S. . **S* .**
3.4. Printing Grating onto Specimen.
The Moire grid was printed on the photoresist coating on the specimen by asimple contact printing procedure in which a grid master was held in closecontact with the sr -cimen and the assembly exposed to ultraviolet lightfrom a Mercury lamq 1, Figure 3-2. summarizes the process of applying thegrids.
The master grid used to print the grid on the specimen was made by using afine metal mesh with an orthogonal array of holes. In.this study, Nickelmesh with 2,000 lines per in. was used. First, a Nickel mesh was held inclose contact with a piece of flat glass by spreading soap solution overit and then removing the surplus with filter paper. Then the corners ofthe piece of mesh were fastened to the glass with adhesive tape.
The Mercury lamp which was used has a, power of 200 Watts. The distancefrom the lamp to the master grating-specimen assembly was 20 in. The timeof exposure was 30 seconds. The-newly exposed photoresist was developedaccording to manufacturer's instructions in the standard Shipley AZdeveloper diluted with water.
Next the specimen with its photoresist grid was placed in a vacuumdeposition unit (Denton D.V. 502 high vacuum evaporator) and a film ofaluminum was deposited over the whole surface. The result is a reliefgrid in the metal -coating with excellent reflectivity. Aluminum waschosen because of its ability to resist tarnishirg, its high reflectivityin thin films, and its low cost.
3.5. Grid Photography
The complete state of strain throughout an extended field can bedetermined from Moire fringe photographs obtained through superposition ofa submaster grating with deformed and undeformed (baseline) specimen gridreplicas. Such superposition yields baseline Moire fringes and data (atstrain) fringe patterns.
The set up used to accomplish the high resolution photography of thespecimen grid is sketched.in Figure 3-3. The camera used was a Horseman4XS bellows model. The lens was a Carl Z•iss S-planar with focal lengthof 120ram and a maximum aperture of S.F., The system rested upon a graniteoptical table and the camera was set up -to give a magnification factor ofone. The specimen was placed in the loading frame (loaded under" tension).The 1ight'sources were two flash lamps which were activated by anelectronictriggering mechanism.
Focus of the specimen image was very critical in this high resolutionsituation. The ground glass of the camera was not satisfactory for thiscritical work because it was too coarse and because such focus plates areoften not exactly in the photoemulsion plane. For focusing, a blank plateof the thickness and type used in the photography was developed and fixedand then mounted in a 4XS plate holder which had the separator removed,
31
.... . . .. *3 1 * * .
1) .._-SPR
SPECIMEN
2) SUBMASTER
SPECIMEN
3)
SPECIMEN
SS PEC IM E N,
SPR 5 Shipley Photo Resist
Figure 3-2. Grating production process*,.
32 ,,
S. . S *.*. S* S S * . . , .. * - ,a=,,•. - p ,. . • 'i*• = . .
TOP VIEW
.. I
* Strobes
Specimen 4x5 View Camera
SIDE VIEW/
I2
/ 450
Specimen __4 x5 iew Camera
Figure 3-3. -Set-up, for grating photography.
I * *33
l dX
The im,.- of the specimen in the emulsion was examined with a 160Xmicros-,.r which had been focused first on the image of the specimensurface.. ,his process facilitated bringing emulsion and image into the
* same L
After c-'ýcking that the image of'the specimen was perfectly focused overits entire area and that the desired magnification was correct, the camerawas locked in place to avoid losing the focus during the loading of thephGto-plate.
The right 'xposure was determined by trial and error using Kodakhigh-speed holographic film (type SO-253, 4X5 in.). After getting thebest grid-replica from Koa film, the data and baseline grids wererecorded by using Kodak high speed holographic plates (type 131-02, 4X5in.). In order to get the right exposure, the imaximum aperture was usedto avoid losing sharpness of the grating, and the intensity of the flashlamps was reduced by adding ground glass pieces in front of theflashlamps. These glasses cut down the intensity of the light by roughlyone f-stop per piece. Alsoi it is worth noting here that the angle ofincidence of the illumination was chosen by trial and error to give thebest contrast in the grating image. Shadows of the three-dimensional gridstructure evidently play an important role in grating visibility. Theexposed 131-02 plates were individually developed in Kodak HRP developerfor three minutes and fixed in Kodak fixer for the same amount of time.
After completion, each grating plate was examined and inspected forS diffraction efficiency to assure that the photography had been successful.
It was labelled with specimen number, loading, and magnificationconditions for future reference and stored in a rack to await opticalconstruction of Moire fringe patterns.
3.6. Summary of Optical Processing to Create Fringe Patterns
The grating photographs of this experiment produced an assembly ofphotographic plates of the undeformed (baseline) and deformed (data)specimen gratings as well as a submaster grating having an integermultiple of the specimen's grating spatial frequency., The creation ofMoire fringe patterns from these plates and the reduction of Moire fringedata have been described in detail (9 to 12). The steps required toproduce Moire fringe photographs from these grid records were as follows:
1. A photoplate of the undeformed specimen grid was superimposedwith a master grating having a spatial frequency of 1000 lpi(which was'half the spatial frequency of the specimen grating)plus or minus a small' frequency mismatch.
2. The superimposed gratings were clamped together and placed in acoherent optical processor and adjusted to produce a correct baseline (zero strain), fringe pattern at the processor'output, whereit was photographed. This photograph corresponded to thesuperposition of the 2nd'diffraction order of the master grating
34
* *o • * * *.* * *p * .a • ° . . .- , ,** --..- - - - - -
I
with the first diffraction order of the corresponding specimengrating.
3. Steps 1 and 2 were repeated for the other component of thespecimen grid i.e. the grating at 90" to the first one.
4. Steps 1 to 3 were repeated with the photographs of the deformed-grid in order to create the *data" or *at straina fringepatterns. The same submaster plate was used.
5. The' fringe patterns were enlarged and printed with high contrastin a convenient size equivalent to about 5 times the actualspecimen dimensions.
6. The prints were sorted and coded for identification.
7. Computer digitizing, data reduction, and plotting were performedon each photograph.
8. Digital processing of Moire data finished the analysts.
Digitization of the fringe patterns and subsequent data reduction followedthe procedures described in detail by Cloud and colleagues (9 to 12).Some of the essentials are reproduced in Appendix C.
3.7 Experimental Results
In this investigation, the specimen had a two-way gratfng (a grid). Byusing the optical processor, a, Moire fringe pattern was formed separatelyfor each direction. One pattern was formed to get horizontal fringes,(perpendicular to the direction of loading), and this fringe pattern wasused to measure strain in the direction of loading. The other pattern wasformed with vertical fringes (same as direction of loading); fringes fnthis direction were used to measure transverse strain (perpendicular tothe direction of the load). The photograph of ,the fringe pattern wasrecorded separately for each direction and for each loading step. Samplephotographs of the Moire fringe patterns obtained from the compositematerial fastener specimen for the horizontal and vertical directions areshown in Figures 3-4. to '3-7.
Figures 3-8. through 3-11. show the measured strain ex and e for severaldifferent lines on the specimen. The whole-field nature of .he Moiremethod means that a great deal of data are generated. Such data arealways difficult to present and assimilate. The plots shown here are areasonable compromise between completeness and confusion. The next step -
is to develop strain contour maps, wnich would be easier to understand ata glance. Such a step was not within the scope of this 'project. Programsfor three dimensional computer graphics representations of the straincontours are being developed by the investigators.
354t
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3.8. Experimental Evaluation of Elastic Constants for the Composite
In order to compare theory and experiment, it Is necessary to know withprecision the material properties of the composite usede An experiment todetermine these parameters was conducted.
There are two goals in the design and test of a tensile specimen. First,the existence of a statically determinant, uniaxial state of stress withinthe test section must be assured; however, producing such a state ofstress in the laboratory is not a trivial task. Several analyticalstudies have revealed that the first goal may be accomplished byestablishing the specimen geometry such that the length-to-width ratio isa practical maximum (13, 17, 18). In the current study the maximum lengthwas chosen to be 12 in. and the width one in. The second goal of thedesign and test of the tensile specimen is to assure that the elasticresponses in the in-plane shear and traverse tension modes are constantand that failure will occur within the specimen test section.
Determination of El, E2 and v is quite straight forward. Two tensiletests are required, and for this purpose two specimens were constructed:one with the warp fibers oriented along the direction of the loading (for
determination of E1 and v12) and the other with woven (weft) fibers in thedirection of loading (for determination of EZ and v2 1 ).
As shown in Figure 3-12., four single-element strain gages of typeEA-13-075AA-120 from Micromeasurements were used to check the uniformityof the stress field. Strain gage rosettes on both faces ef the specimen
were also used (type CEA-06-062UR-120), first to determine any effect ofbending on the specimen and then to obtain the measurements needed toperform the calculations. Effects of transverse sensitivity were checkedand found negligible.
The specimens were mounted in a loading frame using grips especiallydesigned to avoid any clamping of the ends and to allow rotations, thusavoiding any end effects.
Every specimen was loaded in increments up to 500 lbs and then unloadedand reloaded to the same stress. The tests were at room temperature(75F.). The strain readings were made with a. digtal strain indicatorfrom Northern Technical Services, Inc.
Figure 1-13. shows typical plots of stress vs strain obtained from thisexperiment.
The results obtained for Young's modulus and Poisson's ratio are asfollows:
El w 3.188 x 106 psi E2 - 3.0824 x 106 psi
V12 0.11 V21 0.11
44
.., .,* *-
~ *~ I..A. &:. :k:~ ~ ~ ~ ~ * . * ***~*
AT
V1
La 12 IN* 5:1I IN
1 2F..75. IN
1;- 4 Single element
S strain gage
. L
L O 05-6 Rectangular strain
* 1.0gage rosette31.
ok k.0
I U
"Figure 3-12. Specimen showing location of strain gages.
45
"* -. ' *k.75.:. IN*
I Q,a C
E4~
.4-
. ~ ~4. 4)0
to 0.
to
SI~a, .=
c 4
00
CL
fn
S41
L._
46
.. . . . . ..- . . . . . . . • .- . ; . . . - .- - . .. . - 1.• . • . . ' - . . - . . - . . . 0. . . . - .:.. ..... ... .'.... ...... ..... .. .. ....... .•... ... .• , .. •,'. '•, .: .' - -• -, "• '. -. • - .' .-. -. -. -... . .- :. ... '...,•4.'-.- .-S .. . ... • . ... ... ...... .. .. ... • . ... . . ,• -• .- • .. • .•. .,• • '•'..:..:,. . •:. '..'.. ..,'..:,. .. ,• .'.•',•..,., ,........
A test which is planned for subsequent study is to use an Instron machineto perform the tensile test under different room humidity and roomtemperatures. It is suspected that humidity and temperature affect the
material properties of this specific composite.
3.9 Experimental Results and Discussion
A typical composite pin-loaded joint exhibits a strong coupling betweenaxial strain and bearing capacity at any given pin location.
In this investigation, the specimen had a two-way grating. By using theoptical processor, the Moire fringe patterns were formed separately foreach direction. One pair (Figures 3-4. and 3-5.) was formed with verticalfringes (direction parallel to the load) and these fringe patterns wereused to measure strain Ex in the traverse direction (perpendicular to thedirection of the load). The other pair (Figures 3-6. and 3-7.) wereformed with horizontal fringes (perpendicular to the loading direction);fringes in this direction were used to measure strain ey in the samedirection as the load.
Both the photographs of the horizontally-oriented (from the horizontalgrating) fringe patterns and the vertically-oriented (from the verticalgrating) fringe patterns yielded some interesting results.
Li Figure 3-8. and Figure 3-9., plots of cx vs position are shown. InFigure 3-10. and Figure 3-11. Cy vs position are shown.
From Figures 3-10. and 3-11. we can notice that, in the area of contactbetween pin and composite, ey is, highly compressive; but, as we move awayfrom. the edge of the hole towards the end of the specimen, its valuedecreases to an average value.
* Now, looking at the right hand edge of the hole, iy is of tensile nature;as we move away from the edge of the hole towards the edge of the specimenit decreases to an average value (shown by lines x3 to x7 in Figure.3.11.).
Figure 3-14. shows a distribution of strain based on the results from thethe Moire fringes. This figure is developed from Figures 3-10. and 3-11.plus similar strain plots created for additional lines on the specimen.
Much more information useful to the designer can be extracted from theseMoire photographs. As an example, examine the areas shown in Figure 3-14.where the normal strain, i.e., Cy, changes from tensile to compressive.Along that interface, we find a very high shear strain which in some. cases'ce!% produce delamination and/or faillure by shearing, (especially along thetrý:osition zone from high compressive strain to tensile strain near thefastener. Such features of the Moire results allow the designer to getvery useful information anywhere on the surface of the specimen providingbetter criteria for the determination of the optimum combination of
47
Figu ,re 3-14. Distribution of tensile and compressive str'ain (c )near the-fastener hole.
%%
S" C+ (+48
• . . . . . . . . . . . .
*45 -... "
______(+)_ * 4-.+)4
parameters such as distance from hole to edge, ratio of pin to hole
diameters, fiber orientation, lay-up sequence, etc.
3.10. High-sensitivity Interferometric Moire Technique
From the results for ex (the smaller strain component), it clear that theMoire technique has a marginally low strain sensitivity for work oncomposite materials. This idea is suggested on Figure 3-8. which showspoor agreement between values of ex at areas located at the right and leftof the specimen (shown by lines xO to x2 and xA to xC respectively).
The Moire ntwhod yields full-field information of the in-plane surfacedisplacernents. It has great potential for the macroscopic strain analysisof composites, and this method does not suffer any limitation due toanisotropy, inhomogeneity, or inelasticity of composite material.Successful Moire strain analysis requires that the sensitivity, which isgoverned by the grating frequency, be matched to a degree with themagnitude of the deformation which is to be measured. Thus an extensiveprogram to extend the sensitivity by a factor of 10 or more was begun.
An interferometric technique similar to that described by Fost (19, 20) .and Walker, Mckelvie and McDonach (21) was developed in this laboratory.It is evident that this technqiue for measuring the strain distributionshould operate over a sufficiently short gage length to elucidate thedetails of the strain distribution, while at the same time giving anoverall picture of the material behavior. In this tnterferometric Moire -
technique, the specimen grating is a phase-type grating. The analysis iscarried out by using overlapping beams of coherent light to create thespecimen grating and the master grating which is projected onto thedeformed specimen.
The particular virtues of the system developed for this investigation
are:
1. The efficiency of light use is very high.*
2. No rigid connection is required between the specimen and thesystem. This last feature is relevant in view of the convenienceof performing measurements-in environments which are not so idealas a vibration-free'optics laboratory.
3. Measurements can be performed In three different directions,yielding a map of strains in the same number of directions andallowing calculations of maximum strains. In composites, it doesnot make much sense to talk about principal directions, sincethey depend on the material directions; still', information inthree directions will provide very useful information forspecific situations of fastener design.
Preliminary testing of this technique has been conducted and the resultsappear to be very promising. Figures 3-15. and 3-16. show Moire fringes
49
9 U'4
cC6
0.
06
5. c
- _0.0-
16-
-- .mO
4j~q
•* 5
• g =
""4
CC
C=Cc
up 44.is
--- --- ---
of displacement in the x-direction (perpendicular to the direction of theloading). Notice the difference between these fringe patterns and thoseobtained by the traditional Moire technique (Figures 3-4. and 3-5.).
4.0. COMPARISON BETWEEN EXPERIMENTAL AND NUMERICAL RESULTS
Section 3 describes the methodology of obtaining strain In the actualcomposite material by Moire techniques which are self-',alibrating and -,which do not depend on assumptions of material behavior. Typical resultsare reported. Section 2 described a boundary-element approach to the --problem and gives results from that method. Some finite element resultsare also computed and used for comparison of the two numericalapproaches.
It Is instructive and valuable to designer, theoretician, and ±7
experimentalist to compare the results from these widely diverseapproaches to the problem. Since the methods are so different, goodagreement of results would imply that the results are probably correct.Disagreement would give an idea of the magnitudes of errors in either orboth sets of results.
To perform the comparison, some strains measured by Moire were convertedto stress by use of generalized Hooke's law. This procedure inserts anhassumption of material behavior into the experimental findings, but itdoes facilitate comparison. It is probably more reasonable, but also moredifficult, to use Hooke's law to convert the numerical results to strain,The canversion of experimental data was carried out for ey at selectedpoints along the ligament line between hole boundary and specimen edge.These stresses were normalized, then plotted. They are compared with thematching finite element values. The comparison is shown graphically inFigure 4-1. The agreement between numerical and experimental findings isexcellent, especially when one considers the fact that these composites doshow some nonhomogeneity, i.e., properties vary slightly from point topoint.
This comparison is not extensive, but it does indicate that the work andthe results are probably correct. Comparisons for other critical areas ofthe stress field are planned. In addition, it would be advisable toobtain a measure of the inhomogeneity of the material so that a "scatterband" of expected stress for a given load situation can be established. ,The results presented suggest that numerical and experiment results wouldboth lie within any such scatter band.
52 '"
Finite Element-Method -
5 I Ofoiri Technique
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0 .1 23
REFERENCES
1. C.A. Brebbia (ed), Proceeding of the 3rd International seminar onBoundary Element Methods, Pub. Springer-Verlag, 1981.
2. N.J. Altiero and D.L. Sikarskie "An Integral Equation Method Appliedto Penetration Problems in Rock Mechanics,• Boundary Integral EquationMethod: Computational Applications in Applied Mechanics, AMD-Vol. 11,ASME, 1975. 119-141.
3. C.G. Harris and W.B. Evans, "Extension of Numerical Quadrature Formulato Cater for End Point Singular Behavior Over Finite Integrals,""Intern. J. Computer Math. 6B, 1977, 219-277.
4. R.E. Peterson, Stress Concentration Factors, John Wiley, 1974.
S. Cloud, G., "Simple Optical Processing'df Moire-grating Photographs,"E4p. Mech., 20, 8, 265-272 (Aug. 1980).
6. G. Cloud, Radke, R., 3nd Peiffer, J. 'Moire Gratings for HighTemperatures and Long Times.• Exp. Mech. Vol. 19, No. 10, 19N-21N."Oct. 1979.
"7. Cloud, G., Paleebut, "The Dimensional Nature of Strain Field NearColdworked Holes." AFWAL-TR-80-4204, Wright-Patterson AFB, Ohio(1980).
8. Paleebut, Somnuek, "An Experimental Study of Three-dimensional StrainAround Cold Worked Holes and in Thick Compact Tension Specimens,*Ph.D. Thesis, Michigan S.ate University, Department of Metallury,Mechanics and Materials Science, 1982.
9. Cloud, G., "Residual Surface Strain Distributions Near Holes Which areCold Worked to Various Degrees, Technical Report AFML-TR-78-153,Wright-Patterson AFB, Ohio (1980).
10. Cloud, G., "Measurement of Strain Fields Near Cold Worked Holes,'Experimental Mechanics, 20, 2, 9-16, (January 1980).
11. Cloud, G., and Sulaimana, R., *An Experimental Study of Large"Compressive Loads Upon Residual Strain Fields and the InteractionBetween Surface Strain Fields Created by Cold Working Fastener Holes,'"Technical Report AFML-TR-80-4206, Wright-Patterson AFB, Ohio (1980).
- 12. Cloud, G., and Tipton, M., 'An.Experimental Study of the Interactionof Strain Fields Between Coldworked Fastener Holes,* Technical Report,AFML-TR-80-4205, Wright-Patterson AFB, Ohio (1980).
"13. Horgan C.O., 'Saint-Venant End Effects in Composites," Journal of* Composite Materials, Vol. 16, Sept. 1982 pp. 411.
.54I"
* *, *. . ' , .
14. Luxmoore, A. and Hermann, R., *An Investigation of Photoresists ForUse in Optical Strain Analysis," Jrnl. of Strain Anal.., 5, 3, 162 July
Z 1970.
15. Holister, G.S., and Luxmoore, AR. OThe Production of High densityN Moire Grids," Exp. Mech. 8, 210, May 1968.
16. Luxmoore, A.R., and Hermann R., "The Rapid Deposition of Moire Grids,85 Exp. Mech, 11, 5, 375, August 1971.
17. Pagano, N.J., and Halpin, J.C., 'Influence of End Constraint in theTesting of Anistropic Bodies," J. Composite Materials, Vol. 2 (1969)p. 18.
18. R.B. Pipes., 0On the Off-Axis Strength Test for AnisotropicMaterials," Journal of Composite Materials, Vol. 7 (April 1973), p.
' 246.
19. Post, D., "Optical Interference for DeformationMeasurements-Classical, Holographic and Moire' InterferometryoMechanics of Nondestructive Testing Proceedings edited by W.V..Stnchcomb,-Plenum Publishing Corp., NY (1980).
20. Post, 0. and Baracat, W.A., NHigh Sensitivity Moire Interfero te~ry-ASimplified Approach," Exp. Mech. 21, 3, 100-104 (March 1981).
3 21. McDonach, A., McKelvie, J., Mackenzie, P., and Walker, C.A.,Proceedings of the V International Congress on ExperimentalMechanics, Montreal, Canada June 10-15,1984 pp. 308-313.
*1S
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.9A
APPENDIX. A
FUNDAMENTAL SOLUTIONS
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•. . ........ .. . . . . . . . . . . . . . . . .
- - . . . . . . . . . . . * ,S . .
'. * * . .*. S .. . . . . * . * . . . ..... ,- !* ~ S .***
SV •. -o* * .S ~ * *
0
For the isotropic case
The stress and displacement fields at a point (x.y) due to a unit pointload acting at the origin of coordinates in the x-direction in an infiniteplate with material properties G and v under plane stress are:
4 G Ux Qlnr 2 + y 2 /r 2
4G Uy -xy/r 2
1+vHxx x(P + x2 1r 2 )lr 2
- Hxy y(P + x2 /rZ)/rZ
Hyy x(-P + y2 1r 2 )/r 2
where P - (1-v)/2(1+v), Q - .5 + 2P and r 2 - x2 + y2 . For a unit load inthe y-direction, the results are:
4G Ux -xy/r 2
4G Uy Q lnr 2 + x2/r 2
1+v•Hxx yl-p + x2 /r 2 )/r 2
* Hxy x(P + y 2 /r 2 )lr 2
Hy y(P + y2 /r 2 )1r 2
;- The tractions are:
.Txk = Hxxk cosa + Hxy,k sina
Tyk a Hxyk cosa + Hyyk Sin•
where k a either x or y and a - angle that the exterior normal makes withthe x-axis.
For the orthotropic case
"For a unit load in the x-direction
A-3
•Io D . • . , *. . *o_•ae p~. * . •. • ~ -•,- *. .. . ., .,',
A
-Uxx (cA 1 In r2 - c3A2 In rj)/2
Uyx AIA 2(*1-0 2)/c 22
Hxxx (clr2 - c3r1)x-k
Hxyx (clr2-c3rl)y
Hyyx (S1c3rl - 82clr2)x
'For a unit load in the y-direction
uXY A1A2(*!-#2)/c22
Uyy (c4A1 InrI - c2A2 lnr2)/2
Hxxy - k (c2r2 - c4rl)y
Hxyy (Slc4rl - 82c2r2)x
Hyyy (81c4r1 - 82c2r2)Y
withk 1/2M162-61),
-r 1/(Six2 +y2 ), 1-1,2
Al c12 - 61 C22, i-1,2
41 - 2 sin-l[yx'lr2 (072- M .Cl /'T2 (1-c12/c22),
.2 czV (z-61c12/c11),'
C3 1 (52-c12/C22)U
C4 " v (1-62C12/cll).
81 and 62 are the roots of the characteristic equation of the material;
C22 82 -(2c124c33)6 + C11 0
Note that 8's are either real or complex. tf they are real, then since6182 c11/c 12 > 0, they are either both positive or both negative. For
.clearness, the V's are taken to be real. For complex V's, 82 isnecessarily the conjugate of 51 and the C's obtained above are substitutedin (ii) to obtain' the equivalent complex forms of the fundamentalsolution', the real parts of which represent U's and H's.
| A-4
APPENDIX B 4
THE COMPUTER PROGRAM *BEM*
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B
*.......-.* .v:*..;'.:-.�. 4 *: � -. ___________________________________ P .�. *..'�Vj?'�. � �t.'w'� *�* �***** .t .. �t k... .. �,
Major steps in constructing BEM computer program
Step 1. Provide the following data:
Boundary points coordinator (XB, YB)
The angles that outward normal at boundary nodes make with+x-axis (T)
Field points coordinates (XFYF)
Boundary conditions in X and Y (BC),BC = 0 displacement prescribedBC - 1 stress prescribed
Boundary values (B)
Integration nodes and weights (ZW)
Compliances, (c's)
Step.2. Construct the influence matrix, A
Step 3. Solve AX =,B(stores results in B) .*
Step 4. Calculate displacements and stresses at given field points
Remark:
The computer program BEM is developed for real 81 and 62. The complex
version of BEM follows directly from the discussion given in Appendix 1.
.-
-Y
'1-3'-
PROGRAM 8EM(INPU1,OUTPUT)
PARAMETER CN:60 N2=2*N9M=26)REAL XB(k.1),YBCN.1),TCN) Xt~Y(~B(2)AN929(2,
*Z(A)#UC4)READ*, CllvCl2qC22*C33READS, (Z (I) ,I=194ft)C'idI)9I=1v4)
REAO.,(XF(I).YF(I),I1=1M)PT =3 14 1592 653 589
C COMPUTE CONSTANTS IN THlE FUNCAPENTAL SOLUTIONSP1(CC12+*5*C33 )/C22
CN=2.*PI*CX2-Xl)-A1=C2-X1'C22- ...... ...
A2=C12-X2*C22-C1=(Xl-Cl2/C22)*SQRTCX2)C2=C1.-Xl*Cl2/Cll)*SQRT(X2)
* --C3=(X2-C12/C22)SQRT(Xl) - ---- .-..
- . C4-Cl -.X2*C12/Cll)*SQRTCX'l)
'-'C CONSTRUCT THE INFLUENCE MATRIX, A00 -10'0 I=IPN
CT=COSCTCIY ).~ST:SIICTCI))
,.FY.5e&CYBCI*1)*YB(l))*0000J=19N
'AXtXB8( J 41) -x 8( JAY=YB(J+1)-YSCJ)H=SQRTCAX*AX+AY*AY)
IF CI.EQ.J) GOTO 50UXX=UXY=UyyHmx~Cx2xXYXHYYX=I3XY=HXyY2hyyy=0.DO 7 K19214
v~. ~ k..- ~X=FX-AXkeZ(K)-XBCJ),-Y=FY-A"-Z(K)-YflCJ)R121./CX1*X*X+Y*Y)R2=lo/(X2*X*X-*Y*Y)UXX=UXX,.5*(C1.A1*ALCG( R2)-C3*A2.ALOG(R1) )*H*Wd(K)UXY=UXYA1.A2e.ASIN(X*Y*X3*SQRT(Rle'R2))/C22.H.*W(K)"HXXXtftXXX".( Cl#R2-C 3*R1)*X *H* W K)HYYX.:HYYX,(CX1*C3*R1-X2*Cl*R2)*X*H* (K)
HXYY=HXIY.( X1*C4*K1-X2*C2*R2)*X*H*W(K)7 HYYY:HYYY.(XI*C,*RI-X2*C2*R21*Y*H.W(K)IF(BC(I1)*EQ.0.),GOTO 10A(11,2*,J-1)=MXXX.CT*CTHYYX*ST*ST.2.**XYX*CT*STGO~TO 20 )IiXYC*CTHYYY*ST*ST,2..IIXYY*CT*ST
10 A(I1,2ivj-1)=UXX*CT*UXY*STA (Xl 2.i ):LXY*CT*UYY*ST
* 20 IF(BC(I2).EQ*0.) GWO 30AC(12,2*,J-1)=(HYYX-HXXX)*CT*SI+HXYX*(CTiCT-ST*ST)A(12,2*J)=(HYYY-HXXY)*CT*STIgXYY*CCT*CT-ST*ST)*07 GOO 10
30 A(1292*,J-1)=UXY*CT-UXX*STA(12'92*,J)=UYY*CT-UXY*STGOTO 10'0
.50 A(11,2*j-l)=95*CN*(BCC I1))*C1,(1.-18CCI1)).QT..(Cl*A1-C3 A2)*CTA( 1,92*J).5*CN*eC(Il).ST.1e-ecdii)).QI*(Cl'A1-C3*A2) ST
A(1292*J,)= 9CN-*CBC(12 ) )*CT.'4l1.C(12) )*'§I'(C4*A1-C2*A )*CT2litj CONTIMUE
CC SOlLVE A*X P
CALL MATX(:4.*A~jb)
ORI NIT 5u'
* . - - * . . * -* * . .
C CALCULATE C I :SPLACEMENTS AND STRES$3ZS AT GIVEN FIELD POINTSD0 3500 I-1,MUX=UY=TXX:TXY=TYYCo.CT=CCS(T(I))ST:SINCTCI) )
K=2%
H=SQRT(AX*AXAY*AY)* . IF((XF(I)-.5*(XBCJ.1),XB(J))).*2.(YF(I).-ýi*(Y8IJ.+1).eYBJ) ) )**2
*LE.I.E-e) GOTO 15000 110 L=194SX=XF (11 At*-ZCL)-XB J)Y=YFCI)-ZtL)*AY-YB(J)R1~1 ./CX1*X*XY*Y)R2=1.i(X2*X*X,.Y*Y)UXX~.5*(Cl*Al*ALOG,,(R2)-C3*A2'tALOG;(Rl))UXY=Al*A2*ASIN(X*Y*X3*SQRTCR I*R2) )/C221IYY=.5*ICC4*A1*ALOG(RZ)-C2*A2.ALOG(R2)),HXXX=(Cl*R2-C3*Rl)*XHXYX=(Cl*R2-C3*RliJ!YI$YY-X=( X*C3*Rl-X2*C1*R2) *XHXXY=(C2*R2-C4*Rl1*YHXYY=(X1*CI*R1.X2*C2..R2) *XMHYYY--CX1.C4*Ri--X2*C2*R2)*YUX=UXCB IK-I) *IXX,8( K) *UXY)* C (L)
* . TXX=TXX. (B(K-1)*HXXXBCK)*HXXY)*H*w(L)T7XY.:TXY.(8(-K-l)*HxX,8 B(K)*HXIY)*H*W(L.)
- TYY=*TYY.(8CK-1)*HYYX+eB (K) *HYYt)*H*WCLJ* liC CCNTINUE
GOTO 200i5o or=-m*(ALCG(H)-l.)
LXX=GI*( (Cl*A1-C3*A2)*CT**2.CC4*Al-C2*A2)*St**2)UXY=QI.(Cl*AIC2*A2-C3*A2-C4.Al )*CT*STLYY=Gl*( (Cl*Al-C3w42)*ST**2. (C4*AlC2*A2)*CT**2)LX=UX+UXX*B(K-1)+UXY*B(K)UY=UY+UXY*BCK-I)*UYY*B(K)TXX=TXX,.5*CN* (CT*E(K-i)-ST*B(k))TXYzTXY..5-*CN*(-CT*8(K-IST.eK))TYY=TYY..5*CN*(ST*8(K-l).CT~ecK))
20~0 CONTINUE 1300 PR~INT 40C 1,XF(I)9YF(I),UX9LYtTxXTXYTYY400 FCRr'AT'(lHe,5XI2,.!X,2(4XF864),6X,2(,XFl2e8),6X,3c4XFl2.a))500 FORMAT( '(i'5X, N0' ,T21,'X,9T!2,'Y ,T52,'UX' ,T68,'UY'
*,T90,'TXX',TlO6,'TXY', r122,'.TYYO/)
C INPUT DATAS-*EGF
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APPENDIX C -
SIMPLE OPTICAL PROCESSING OPMO IRE-GRATING PHOTOGRAPHS
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Simple Optical Processing ofMoire-grating Photographs
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*1*
APPENDIX 0DISTRIBUTION LIST
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DISTRIBUTION LIST
CDR 15Defense Technical Information CenterBldg. 5 Cameron ANNEXAttn: DOACAlexandria, VA 22314
Manager 2Defense Logistic StudiesInformation Exchange,Attn: AMXMC-D LFt. Lee, VA 23801
DirectorU.S. Army Materials & MechanicsResearch CenterAttn: AMXMR-M 2
AMXMR-ER 2AMXMR-S 2
Watertown, MA 02172
PLASTECPicatinny ArsemalDover, NJ 07801 ,
CDR 1Air Force Maberials LabAttn: LTM VAttn: LLN 1Attn:. FIBEC 1Wr4 -ht-Patterson AFB, OH 45433
CDRU.S. Army TACOMAttn: AMSTA-TSL 2
AMGTA-R 1AMSTA-RCKM 2AMGTA-G 1 -
AMGTA-CR 1Warren, MI, 48090
SNaval Materiel Command 1Cede C(MT0424Washington, D.C. 20360
Hdq., Dept. of ArmyDeputy Chief of Staff,For Research, Development and AcquisitionWashington, DC 20310Attn: DAMA-ARZ-E
D-3'.
CDR 1U.S. Army Materi'l CmdAttn: AMCMT-MAlexandria, VA ,22333
Grumman Aerospace Corp. "Bethpage N.Y. 11714Attn. Mr. Sam Baskin
Dr. Gary Cloud 25Dept. of Met. Mech. & Mat. Sci.Michigan State UniversityEast Lansing, MI 48823
Dr. David Sikarskie 25
Dean of EngineeringMichigan Technological UniversityHoughton, MI 49931
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