NBSIR 73-201

Composite-Overlay Reinforcement of

Cutouts and Cracks in Metal Sheet

Richard A. Mitchell, Ruth M. Woolley, and Daniel J. Chwirut

Engineering Mechanics Section

Mechanics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

February 1973

Final Report

Prepared for Lang ley Research Center

National Aeronautics and Space Administration

Hampton, Virginia 23365

NBSIR 73-201

COMPOSITE-OVERLAY REINFORCEMENT OF

CUTOUTS AND CRACKS IN METAL SHEET

Richard A. Mitchell, Ruth M. Woolley, and Daniel J. Chwirut

Engineering Mechanics Section

Mechanics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

February 1973

Final Report

Prepared for Langley Research Center

National Aeronautics and Space Administration

Hampton, Virginia 23365

U. S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

CONTENTS

Page

1. INTRODUCTION 2

2. FINITE ELEMENT ANALYSES 5

2.2.

2.1.

Planform

Finite Element

Analysis

Formulation '5

12

a. Analysis of a Reinforced Cutout 14

b. Analysis of a Reinforced Cutout-with-Crack 17

c. Analysis of a Reinforced Crack 17

2.3. Longitudinal Cross-Section Analysis 18

2.4. Nonlinear-Shear Analysis 21

2.5. Progressive-Debond Analysis 23

3. DESCRIPTION OF LABORATORY TESTS 23

3.1. Specimen Materials 24

3.2. Specimen Configurations 25

a. Material Property Specimens 25

b. Unreinforced Sheet Specimens 25

c. Reinforced Cutout Specimens 26

d. Reinforced Cutout-with-Slit Specimens 26

e. Reinforced Transverse-Slit Specimens 26

f. Double-Lap Joint Specimens 26

3.3. Specimen Fabrication 27

3.4. Instrumentation 27

3.5. Test Procedures 28

a. Quasi-Static Tension Tests 28

b. Tension-Tension Fatigue Tests 28

4. TEST RESULTS AND CORRELATIONS WITH ANALYSES 29

4.1. Material Properties 29

4.2. Unreinforced Sheet 29

4.3. Reinforced Cutout 3q

4.4. Reinforced Cutout-with-Slit 32

4.5. Reinforced Transverse Slit 34

4.6. Double-Lap Joints 34

4.7. Discussion of Results 37

5. CONCLUSION 38

6. REFERENCES 39

1

COMPOSITE-OVERLAY REINFORCEMENT OF COUTOUTS

AND CRACKS IN METAL SHEET

Richard A. Mitchell, Ruth M. Woolley, and Daniel J. Chwirut

ABSTRACT

Finite element computer programs were

developed for the planform analysis and the

longitudinal cross-section analysis of metal

sheet reinforced by adhesively bonded overlays

of composite material. The analyses articulate

the separate responses of the metal sheet,

the composite overlays, and the adhesive layers.

All materials are assumed to be orthotropic and

linear elastic, with the provision that nonlinear

interlaminar shear deformation can be approximated by a series of stepwise- linear solutions.

The computer programs were developed specifically

for the study of three general configurations:

(1) a sheet with a reinforced cutout; (2) a sheet with a reinforced cutout with two

symmetrical transverse cracks, within the sheet,

radiating away from the cutout edge; and (3) a sheet with a reinforced transverse crack.

The programs are also suitable for the study

of bonded lap joints. The principal output

of the computer programs is a set of contour

plots of stress and strain fields throughout

the sheet, the overlays, and the adhesive

layers.

A series of laboratory tests was conducted

to demonstrate the validity of the analyses.

Strains measured on the surfaces of specimens

representing the general configurations studied

were, for the most part, in good agreement

with strains predicted by the finite element

analyses. Significant correlations between

certain failure modes and the stresses computed

by the finite element analyses were apparent.

Similarities between the modes of failure under

static and fatigue loading were also evident.

Key Words: Adhesively bonded joints; composite

materials; composite-overlay reinforcement;
contour plotting; cracks, reinforcement of;

cutouts, reinforcement of; debond analysis,

progressive; finite element analysis; joints,

adhesively bonded; nonlinear analysis, shear;

reinforcement, composite overlay; reinforcement,

cutouts and cracks; shear analysis, nonlinear.

1. INTRODUCTION

An overlay of high-strength, high-stiffness composite material

offers an efficient means of achieving local reinforcement of cutouts

and cracks in metal sheet. This concept can be used in the design of

new structures or it can be used to strengthen existing structures.

Where a crack is anticipated, on the basis of stress analysis or service

experience, a composite overlay can be used to reduce the stresses that

might otherwise initiate a fatigue crack. Where a crack already exists,

a composite overlay can be used to bridge across the crack and stop or retard its growth.

The primary objectives of the work reported here were to develop

methods of analysis of composite- reinforced cutouts and cracks and to

demonstrate the validity of the analyses by laboratory testing. Finiteelement computer programs were developed (in FORTRAN V code) for the

study of three general configurations: (1) a sheet with a reinforced

cutout, (2) a sheet with a reinforced cutout with two symmetrical

transverse cracks within the sheet radiating away from the cutout edge,

and (3) a sheet with a reinforced transverse crack. The computer

programs generate contour plots of the computed stress, strain, and

stress-direction fields for the entire region including and adjacent to

the reinforced area. This form of computer output enables one to

visualize the interaction between the metal sheet and the reinforcement.

The contour plots can also indicate the presence of stress conditions

that might initiate or drive a crack or a debond.

Sixteen test specimens, representing the general configurations

simulated by the finite element analyses, were instrumented with

resistance strain gages and loaded to failure in quasi-static tension.

Strains measured on the surfaces of these specimens were, for the most

part, in good agreement with the finite element analyses. Thirteen

similar specimens were tested to failure in low-cycle tension-tension

fatigue. There were significant similarities in modes of failure of

specimens of the same design, whether subjected to static or fatigue

loading. There were also significant correlations between certain

failure modes and the stresses computed by the finite element analyses.

The experimental results suggest that the finite element analyses would

be appropriate and useful for the design of reinforcement where either

static or fatigue loading is involved.

2
This work was done at the National Bureau of Standards under the

sponsorship and with the financial assistance of the National

Aeronautics and Space Administration, Langley Research Center.

LIST OF SYMBOLS

Ag area of the shear stiffness element in the x-y plane;

[aJ matrix relating nodal point displacements to generalized

displacement coordinates;

a, b dimensions of a finite element;

[b] matrix relating components of strain to generalized

displacement coordinates;

C parameter defining the linear range of a nonlinear stress-strain

curve;

'11' ^22 ^^^'^s's moduli in the longitudinal and transverse principal

material directions of an orthotropic lamina, respectively;

column matrix of forces applied to a structure;

{f} column matrix of forces acting at the nodal points

of a triangular finite element;

|fg[ column matrix of shear forces acting in the adhesive

layer of a shear-stiffness element;

G shear modulus;

i, j, k index symbols for corners of triangular finite

elements;

K shape parameter of a nonlinear stress-strain curve;

[k] matrix relating the forces applied to a structure to the

resulting nodal-point displacements;

[k] matrix relating nodal point forces to nodal point

displacements of a triangular finite element;

[kgj matrix relating nodal point forces to nodal point

displacements of a shear-stiffness element;

3
n shape parameter of a nonlinear stress-strain curve;

[}] stress-strain matrix for an orthotropic lamina,

referred to the principal material axes;

[qJ stress-strain matrix for an orthotropic lamina,

referred to the axes x,y;

T, -1 superscripts indicating matrix transposition and

inversion, respectively;

^, t^, t^ thickness of sheet, adhesive, and overlay, respectively;

u nodal point displacement in the x direction;

u X component of relative displacement of an overlay

with respect to a sheet;

v nodal point displacement in the y direction;

V y component of relative displacement of an overlay with

respect to a sheet;

V volume of a triangular finite element;

|w[ column matrix of nodal point displacements;

|Wg| column matrix of relative displacements of an overlay

with respect to a sheet;

(x, y, z) rectangular coordinates;

a a generalized displacement coordinate;

Y shear strain;

e normal strain;

^12 > ^21 major and minor Poisson's ratios, respectively;

o normal stress;

T shear stress;

6 angle between the major material axis of a lamina and the x axis

4
2. FINITE ELEMENT ANALYSES

Separate finite element computer programs were developed for the

planform analysis and the longitudinal cross-section analysis of metal

sheet reinforced by overlays of composite material. The analyses are formulated to articulate the separate responses of the metal sheet, the

composite overlays, and the adhesive layers. Although the basic finite

element formulation is linear, the computer programs permit nonlinear

shear deformations and progressive debonding to be approximated by a series of stepwlse-linear solutions.

The analyses were coded in FORTRAN V and run on a UNIVAC 1108

computer. Computed results were contour plotted using an SC A020

plotter.

2.1. Finite Element Formulation

In a finite-element analysis the continuum structure is subdivided

into a network of elements that are connected to adjacent elements only

at common nodal points. Displacements within individual elements are assumed to be defined by generalized functions that assure displacement

compatibility at common boundaries of adjacent elements. The stiffness

matrix of each element, relating nodal point forces and displacements,

is then computed in terms of the assumed displacement functions,

dimensions, and material properties of the element. The stiffness

matrix of the entire structure, relating applied external forces to

nodal point displacements throughout the structure, is formed by

superposing the element stiffness matrices.

Figure 1 shows a representative network of triangular finite

elements as might be used in a planform analysis of a reinforced cutout.

Syimnetry is assumed about the horizontal (x) and vertical (y) axes of

the cutout and, therefore, only one quadrant is analyzed. The sheet and

the overlay are each divided into separate networks of triangular

elements that are connected to adjacent elements of the same adherend

only at common nodal points. Within the bonded-overlay region the

triangular networks of the two adherends are congruent and the tv70 networks are coupled together by an array of special shear-stiffness

elements linking conjugate pairs of nodal points.

Figure 2 shows a representative network of triangular finite

elements as might be used in a cross-section analysis of a reinforced

transverse crack. Symmetry is assumed about the vertical (z) axis.

Such a network can be used for the cross-section analysis of either

singly reinforced or doubly reinforced sheet. For the case of a doubly

reinforced sheet, symmetry about the horizontal (x) axis is imposed.

5
A general triangular finite element of the type used in both the

planform and the cross-section analyses is shown in Fig. 3. In this

formulation the state of strain within a triangular element is assumed

to be uniform. Therefore, the displacement of any point within the

triangle can be expressed by

1 X y 0 0 0

0 0 0 1 X y

as

^6

(1)

in which

u = displacement in the x direction,

V = displacement in the y direction,

= a generalized coordinate.

A particular generalized coordinate represents either the x or y

component of displacement of nodal point i or a rate of change of a displacement component with respect to x or y. The assumed displacement

functions (eq.(l)) give linear variations in displacement along element

boundaries and, therefore, complete displacement compatibility between

adjacent elements. Stresses within adjacent elements are not, in

general, in equilibrium along common boundaries, but the resultant

forces acting at nodal points are required to be in equilibrium.

Substitution of nodal point coordinates (defined in Fig. 3) into eq.(l)

gives the following equation for nodal point displacements in terms of

the generalized coordinates:

u

1 u

'<

i v

1

I V .

1 0 0 0 0 0

1 ab . 0 0 0

1 k

0 0 0

0 1 0 0

0 0 0 1 a

a^^k

b

0 0 0 1 b

ai

a2

lot3

I at^ ^5

,^6

(2)

or lw( = [A]ja}. (3)

6
Element strains are obtained by applying the definitions of strain from

elasticity theory to eq.(l) as follows:

xy

6u

6x

6v

6y

6u 6v

6y 6x

0 1 0 0 0 0

0 0 0 0 0 1

0 0 10 10

a2

^5

^5

(4)

or f^f = t^] • (5)

In this analysis, all stiffness computations for triangular finite

elements are formulated to accommodate generally orthotroplc materials

as defined by four Independent elastic constants In two-dimensional

stress states. A composite overlay can consist of several lamina, each

having an arbitrary orientation of the two orthogonal material axes that

lie within the mldplane of the lamina. The assumed stress-strain

relationship for a particular orthotroplc lamina In a state of plane

stress, as presented In Ref.l, Is

In which

^1

02

"^12

Qii Qi2 0

Qi2 Q22 0

0 0 Q66

£2

Yl2

(6)

Qii =

1 - Vi129 V

Q22 = ^22

1 - Vi 9 V 12 ^21

Q12 - V12 E22

1 - V12 V21

Q,, = G12 . 66

7
Ej^l and E22 ^^£1 respectively, the Young's moduli in the longitudinal

and transverse directions; \>i2 and V21 are, respectively, the major

and minor Poissons' ratios; and G12 is the shear modulus. Only four

of the five material constants are independent since

^21 En - V12 E22

The stress-strain relationship given by eq.(6) is referred to the

material axes 1,2 of a lamina. As described in Ref. 1, eq.(6) can be

transformed to give the following stress-strain relationship for the

lamina referred to the axes x, y of the finite element analysis:

xy/

Qll Q12 Q16

Qa2 Q22 Q26

Q16 Q26 Q66_ xy

(7)

or

in which

(8)

Qll = Qu cos'+e+2(Qi2+2Q5 5) sin^e cos2e+Q22 sin^e

Q22 = Qll sin^e+2(Qi2+2Q66) sin^e cos2e+Q22 cos'+B

Q12 = (Q11+Q22 - ^Qee) sin^e cos2e+Qi2 (sin'^e+cos'+e)

Q66 = (Q11+Q22 - 2Qi2 - 2Q6s) sin^e cos^e+Qgg (sin^G+cos^e)

Q16 = (Qll - Q12 - 2Q66) sine cos39+(Qi2 - Q22+2Q66) sin^GcosO

Q26 = (Qll - Q12 - 2Q66) sin^e cose+(Qi2 " Q22+2Q66) sinGcos^e

and 0 is the angle between the major material axis of the lamina and

the X axis.

By equating internal to external virtual work, using eqs . (3),

(5), and (8), the general equation for nodal point stiffness of a triangular finite element can be shown to be (see Refs.2 and 3)

8

(9)
in which V is the volume of the element and the superscripts T and -1

indicate matrix transposition and inversion, respectively. The

stiffness matrix [k] relates the six components of force ]f| acting at the

three nodal points of a trianj^ular finite element to the six components

of nodal point displacement|w| by the expression

)f( = [k]iw[ . (1

A different formulation is required for computation of the special

shear-stiffness elements that couple conjugate pairs of nodal points in

the two adherends. Figure A (a) and 4(b) show, respectively, schematic

plan and cross-section views of a region of an overlay-reinforced sheet.

In Fig. 4(b) the x axis is a line of symmetry in the doubly reinforced

case; it is a free boundary in the singly reinforced case. In the

shear-stiffness element formulation the interlaminar shear stress is

assumed to vary as shown in Fig. 4(c). That is, the shear stress is

assumed to have a uniform maximum value at the adhesive layer (c to d)

and to decrease uniformly to zero at a free surface (a or f) or at a plane of symmetry (a) . The area of a shear-stiffness element in the x-y

plane is equal to one-third of the sum of the bonded triangular areas meeting at an overlay nodal point. For example, the shear-stiffness

element areas for nodal points (1) and (2) in Fig. 4(a) are equal to the areas within the dashed rectangles. The specific shapes of the shearstiffness elements, in plan, are not defined in the analysis.

The nodal point stiffness matrix for a shear-stiffness element [k^J

relates the two components of shear force |f

| acting in the adhesive

layer to the two components of relative dispfacement of the overlay with

respect to the sheet ]^ [ by the expression

f k 0 1 u sx sx ) ^

f 0 k ) V

sy sy 1 ^ (11)

in which u^ and v^ are, respectively, the x and y components of

the difference in displacement of the midplanes of the overlay and the

sheet. It is assumed that the shear moduli are uniform within the

sheet, within the adhesive, and within the overlay, and that each shearstiffness element is deformed in pure shear. With these assumptions.

9
the relative displacement within a shear-stiffness element can be

approximated by an integral of the form (see Fig. 4(d))

(13)

in which

m = a in the case of a doubly reinforced sheet,

m - b in the case of a singly reinforced sheet,

(Ug) = difference between x components of displacement at

points e and ra (point a or b in Fig. 4(b)),

s me

and > '^a ' ^^'^ ^o ^^^» respectively, the shear moduli of the

sheet, the adhesive, and the overlay. In the doubly-reinforced case,

integration of eq.(13) between points a and e and substitution into

eq.(ll) gives the shear-stiffness coefficient

k

(14)

SX -, t t g t

J- __s a 3 o

•

. 2 G G 8 G

s a o

in which

Ag = the area of the shear stiffness element in the x-y plane,

tg = one-half the thickness of the doubly- reinforced sheet,

t^ = the thickness of the adhesive,

t^ = the thickness of the overlay.

In the singly-reinforced case, integration of eq.(13) between points b

and e (Fig. 4(b)) and substitution into eq.(ll) gives the shear-stiffness

coefficient

k

A

s

J s a J o v-LJ-' 8 G G 8 G

s a o

10
xii wiiiun xb tne cocax tnicicness ot the singly-reinforced sheet, and

the other symbols are defined as above.

The stiffness matrices of the' various finite elements ,[kj in eq,(9)

and [l^gj in eq.(12), are superposed to form the stiffness matrix of the

entire structure. This is done by adding the stiffness matrix elements

that relate displacements to resulting forces for common or adjacent

nodal points of adjacent elements. The resulting stiffness matrix of

the entire structure [kJ relates the external forces applied to the

structure I f|- to the resulting nodal point displacements according to

the equation

1f} = [K] {w( (16)

This equation can be solved for nodal point displacements{w[ throughout

the structure. In the work reported here, eq.(16) was solved by GaussSeidel iteration with overrelaxation and group relaxation as described

by Wilson [4).

After the nodal point displacements have been computed, the strains

and stresses within the elements can be computed by the use of eqs.(3),

(5), (8), and (12). The strains within the triangular finite elements

are given by

{.(=[b] [a-1] )w( , (17)

and the corresponding element stresses are given by eq. (8) . The

adhesive shear stresses q\ are obtained by dividing the adhesive shear

forces |f Ihy the shear area A (see eq.(14)); that is

' s> a

T k 0 u sx sx s

T _ 1

0 k V

sy A

s sy s

(18)

The adhesive shear stress components and t: can be added

vectorially to give the resultant adhesive shear stress at each

nodal point within the bonded area.

An approximate value for a stress or strain component at the

location of a nodal point can be determined by a process of averaging

11
the stress or strain values already computed for the triangular elements

surrounding the nodal point. In the work reported here, weighted

average values of nodal point stresses were computed by the following

formulas recommended by Wilson

(19)

(20)

(21)

in which the element dimensions are as defined in Fig. 3, and N is the

number of surrounding elements that are averaged. Some stress

components are discontinuous at an interface between two materials of

different stiffness. Therefore, for nodal points located at an interface between the adhesive material and either the sheet or the

overlay, separate weighted averages were computed for each material.

Nodal point strains were computed by a similar process of averaging

element strains. These nodal point stresses and strains are the

quantities that were contour plotted. The locations of the contour

lines were linearly interpolated between pairs of adjacent nodal points.

2.2. Planform Analysis

A single finite element computer program was developed for the

planform analysis of all three of the general configurations

12
studied. The program computes the in-plane stresses and strains in both

the sheet and the overlay and the shear stress in the adhesive. The

computer program generates the triangular element networks from input

data in the form of gross dimensions, and it controls an electron beam

plotter which produces contour plots of the computed stress and strain

fields. A plot of the triangular network (FINITE ELEMENT MESH) and

contour plots of the following stress and strain fields are produced:

ADHESIVE SHEAR STRESS - The resultant i of the two adhesive shear

stress components, t^^ and "^gy* given fy eq.(18).

ADHESIVE SHEAR ANGLE - The angle between the direction of the adhesive

shear stress resultant x and the x axis.

s COMPOSITE X-STRESS - The x component of normal stress (a ) in the

overlay.

METAL X-STRESS - The x component of normal stress (a^) in the sheet.

COMPOSITE Y-STRESS - The y component of normal stress (a ) in the

overlay. ^

METAL Y-STRESS - The y component of normal stress (a ) in the sheet.

y

COMPOSITE XY-STRESS - The xy component of shear stress (x ) in the

overlay.

METAL XY-STRESS - The xy component of shear stress (t^^^) in the sheet.

COMPOSITE MAX-STRESS - The maximum principal stress in the overlay.

METAL MAX-STRESS - The maximum principal stress in the sheet.

COMPOSITE MIN-STRESS - The minimum principal stress in the overlay.

METAL MIN-STRESS - The minimum principal stress in the sheet.

SURFACE X-MICROSTRAIN - The x component of normal strain ( ) on the

exposed surface of the overlay and the surrounding sheet.

SURFACE Y-MICROSTRAIN - The y component of normal strain (e ) on the

exposed surface of the overlay and the surrounding sheet.

SURFACE XY-MICROSTRAIN - The xy component of shear strain (Y ) on the

exposed surface of the overlay and the surrounding sheet.

The following three specific examples serve to describe the planform

analysis for the three general configurations.

13
a. Analysis of a Reinforced Cutout

Figure 5 is a computer-generated plot of the finite element network

and the input data for an analysis of a boron/epoxy-reinforced cutout in

an aluminum-alloy sheet. The x axis is horizontal and the y axis is

vertical. In the table of input data (Fig. 5) , all length dimensions are given in inches, stresses and elastic moduli in pounds-force per square

inch, and angles in degrees. The following definitions of the terms

used in the table of data serve to describe, in part, the scope and

character of the analysis:

PLATE - Length, width, and half- thickness of the metal sheet in the

first quadrant.

COMPOSITE - Length, width, and maximum thickness of a single composite

overlay in the first quadrant.

ADHESIVE - Adhesive thickness. (In this particular plot the number

0.0020 is incorrect. It should be equal to the adhesive depth (ADH

DEPTH) of 0.003 given elsewhere in the table.)

CUSHION - Cushion thickness. A cushion is a rectangular layer of

unreinforced polymer that, in some cases, reduces the peak adhesive

shear stresses at the edge of an overlay. In the analysis reported here

the cushion is assumed to have the same material constants as the

adhesive. Cross sections of two cushions are shown in Fig. 6 and a cross section of one is shown in Fig. 2.

HOLE CUSHION X - The x coordinate of the right edge of a rectangular

cushion surrounding a cutout.

HOLE CUSHION Y - The y coordinate of the upper edge of a rectangular

cushion surrounding a cutout.

X CUSHIONS - The x coordinates of the vertical edges of two rectangular

cushions. Both cushions extend the full width of the overlay. The

first is adjacent to the y axis; the second is adjacent to the vertical

edge of the overlay.

Y CUSHION - The y coordinate of the horizontal edge of a cushion

adjacent to the horizontal edge of the overlay. If there is no cushion,

the coordinate of the overlay edge is given.

X TAPER - The x coordinate of the beginning of a step taper in the x direction. In the analysis the actual step taper is approximated by a uniform taper as indicated by the dashed line in Fig. 6. To compute the

stiffness matrix [k] of a triangular planform element in a tapered region.

14
it is assumed that the element has uniform thickness equal to its

tapered thickness at the centroid of the triangle.

Y TAPER - The y coordinate of the beginning of a step taper in the y

direction. If there is no taper, the coordinate of the overlay edge is

given.

X WIDTH OF HOLE - The maximum x dimension of the cutout in the first

quadrant. The computer program permits the analysis of the general

class of rectangular cutouts with n-degree-elliptical corner fillets.

Y WIDTH OF HOLE - The maximum y dimension of the cutout in the first

quadrant.

X AXIS OF ELLIPSE - The half-length of the x axis of an elliptical

cutout, or the x dimension of an elliptical fillet of a rectangular

cutout.

Y AXIS OF ELLIPSE - The half-length of the y axis of an elliptical

cutout, or the y dimension of an elliptical fillet of a rectangular

cutout

.

DEGREE OF ELLIPSE - The degree n of an ellipse defined by an equation of

the form

CRACK LENGTH - The length of a through crack in the sheet radiating away

from the cutout along the y axis. The overlay bridges over the crack.

The crack is simulated by providing a free boundary condition for each

cracked nodal point, with the exception that shear stiffness coupling

with the overlay, eq.(12), is maintained.

NO. DEBOND AREAS - The number of rectangular regions of debonded

overlay. The analysis permits up to two rectangular regions throughout

which the shear-stiffness elements are disconnected. This is

accomplished by setting kg = 0 in the debonded regions. If there are debonded regions, the coordinates of their boundaries are listed here.

DATE - A date that is read in as data.

X BOUNDARY X-STRESS - The x component of normal stress distributed along

the vertical x boundary of the sheet. A uniformly distributed stress is

15
approximated by statically equivalent forces applied at the boundary

nodal points.

X BOUNDARY Y-STRESS - The y component of shear stress distributed

uniformly along the vertical x boundary of the sheet.

Y BOUNDARY X-STRESS - The x component of shear stress distributed

uniformly along the horizontal y boundary of the sheet.

Y BOUNDARY Y-STRESS - The y component of normal stress distributed

uniformly along the horizontal y boundary of the sheet.

NONLINEAR K-C-N - The constants K, C, and n of a nonlinear shear stressstrain relationship of the form

= !2iz + K(t - C)"" . xz Gxz

The three constants are given for the adhesive (ADH) and the overlay

(COMP) . The analysis permits nonlinear x-z shear response of both the

adhesive and the overlay to be approximated by a series of stepwiselinear solutions.

METAL - The orthotropic properties of the sheet (Ell, E22, V12, G12)

,

the half-thickness of the sheet (DEPTH) , and the angle in the x-y plane

between the major material axis of the sheet and the x axis (ANGLE).

ADH - The orthotropic properties, the total thickness, and the material

axis orientation of the adhesive layer.

COMP - The orthotropic properties, the maximum thicknesses, and the

material axis orientations of one or more stacked layers making up a single overlay. A layer consists of one or more lamina having the same orthotropic properties and material axis orientation. In the analysis,

the orthotropic properties for each layer, with respect to the_m.aterial

axes, are first transformed by eq.(8) to give the properties [q J with

respect to the axes x,y. The effective (weighted average) orthotropic

properties are then computed for each finite element according to the

thicknesses of the separate layers at the centroid of the element.

Figures 7 through 13 are a sample of the fifteen different contour

plots produced for the case defined in Fig. 5. Figure 7, a plot of the

resultant adhesive shear stress, indicates that there are peak adhesive

shear stresses near the edge of the cutout and near the corner of the

16
overlay. Figure 8, a plot of shear stress within the overlay, indicates

a longitudinal ridge of high shear stress intersecting the cutout.

Figures 9 and 10, plots of the maximum principal stresses in the overlay

and sheet, respecively, indicate high tensile stresses at the edge of

the cutout. Figures 11 through 13 are plots of strain components in the

overlay and in the surrounding sheet.

b. Analysis of a Reinforced Cutout-with-Crack

Figures 14 through 17 are plots of the finite element network and

three stress fields for a case that is identical to the one defined in

Fig. 5, except for a through crack in the sheet radiating away from the

cutout along the y axis (CRACK LENGTH 0.210). The x axis is horizontal

and the y axis is vertical. The crack is simulated by providing a free

boundary condition for the first two sheet nodal points on the y axis

and adjacent to the cutout, with the exception that shear-stiffness

coupling with the overlay, eq.(12), is maintained for these two points.

The third nodal point on the y axis is made to coincide with the end of

the crack; therefore, the finite element networks shown in Figs. 5 and 14

differ slightly.

Figure 15 is a plot of the resultant adhesive shear stress and

Figs. 16 and 17 are plots of the maximum principal stress in the overlay

and in the sheet, respectively. The stress contours for this case

(Figs. 15, 16, and 17) approximate those for the corresponding stress

fields for the uncracked case (Figs. 7, 9, and 10) except for the region

adjacent to the crack. A comparison of Figs. 7 and 15 indicates that,

according to the analysis, the crack causes a significant increase in

the peak adhesive shear stress. A comparison of Figs. 9 and 16 indicates

that the crack causes a significant increase in the maximum principal

stress within the part of the overlay that directly bridges over the

crack. The greatest value of maximum prinicpal stress within the sheet

adjacent to the crack, according to this analysis (Fig. 17), is less than

the peak value at the edge of the uncracked cutout (Fig. 10). The finite

element network used here to represent the cracked sheet (Fig. 14),

however, is far too coarse to indicate the actual peak stresses near the

end of the sharp crack.

c. Analysis of a Reinforced Crack

Figure 18 is a computer-generated plot of the finite element

network and the input data for the analysis of an aluminum sheet with a transverse crack that is reinforced by an overlay of boron/epoxy. The x

axis is horizontal and the y axis is vertical. The format of the data

table is the same as for the other planform analyses (Fig. 5). The

definitions of the terms used in the data table (Fig. 18) that are

17
actually applicable to the cracked sheet analys Is are the same as given

above for the cutout analysis (Fig. 5). The CRACK LENGTH given in Fig. 18

is the half-length of the crack. Data terms given in Fig. 18 that are actually not applicable to the cracked sheet analysis are given

numerical values that are consistent with the concept of a zero size

cutout.

For the case defined in Fig. 18, Fig. 19 is a plot of the resultant

adhesive shear stress and Figs. 20 and 21 are plots of the maximum

principal stresses in the overlay and in the sheet, respectively. The

stress contours are roughly parallel to the direction of the transverse

crack for a large part of the overlay region. This suggests that a finite element analysis simulating the response within a longitudinal

cross-section (an x-z plane) would be useful in the study of reinforced

transverse cracks in metal sheet.

2.3. Longituninal Cross-Section Analysis

A single finite element computer program was developed to simulate

the response within a longitudinal cross-section of a sheet with a reinforced transverse crack. The program computes displacements,

stresses, and strains (in the x-z plane) within the sheet, the overlay,

and the adhesive layer. The triangular analysis network is generated by

the program from input data in the form of gross dimensions. The

program controls an electron beam plotter which produces a plot of the ^ analysis network (FINITE ELEMENT MESH) and contour plots of the

following stress fields:

X-STRESS - The x component of normal stress i^^)-

Z-STRESS - The z component of normal stress ^)

XZ-STRESS - The xz component of shear stress (t ).

MAX-STRESS - The maximum principal stress.

MIN-STRESS - The minimum principal stress.

MAX-SHEAR - The maximum shear stress.

MAX-STRESS ANGLE - The angle between the direction of the maximum

principal stress and the x axis.

Figure 22 is a computer-generated plot of the finite element

network and the input data for an analysis of an aluminum-alloy sheet

with a transverse crack that is doubly reinforced with an overlay of

boron/epoxy. The x axis is horizontal and the z axis is vertical. The

18
z axis scale is magnified to twenty times the x axis scale. The left (z

axis) boundary of the plot was lost in a photographic process; it should

be continuous and straight as in Fig. 2. The crack extends along the z axis for the full thickness of the sheet. In this doubly reinforced

case symmetry is imposed about both the x and z axes. In a singly

reinforced case symmetry is imposed about the z axis and the x axis is a free boundary. Although the cross-section program was developed for the

study of a sheet with a reinforced transverse crack, the analysis can accurately be interpreted as simulating the response of a bonded joint

in which the overlay is either a lapped adherend or a splice plate.

The general definitions of the terms used in the table of input

data (Fig. 22) are listed below. In the table of data, all length

dimensions are given in inches, stresses and elastic moduli in poundsforce per square inch, and angles in degrees.

PLATE - Length and thickness of the metal sheet in the first quadrant.

COMPOSITE - Length and maximum thickness of a single composite overlay

in the first quadrant.

ADHESIVE - Adhesive thickness.

DATE - A date that is read in as data.

CUSHION - Cushion thickness (Fig. 6).

CUSHION 1 - The x coordinate of the right end of a cushion located

adjacent to the z axis.

CUSHION 2 - The x coordinate of the left end of a cushion located

adjacent to the right edge of the overlay.

X TAPER - The x coordinate of the beginning of a step taper in the x direction. The actual step taper is approximated by a uniform taper as i:idicated by the dashed line in Fig. 6.

NO. DEBOND AREAS - The number of areas of debonding at the interface

between the sheet and the adhesive. Debonding is simulated by

disconnecting the finite elements having common boundaries along a debonded interface. If there are debonded areas, the x coordinates of

their ends are listed here,

X STRESS - The normal stress distributed along the vertical x boundary

at the right end of the sheet, A uniform distributed stress is

approximated by statically equivalent forces applied at the boundary

nodal points.

19
NONLINEAR K-C-N - The constants K, C, and n of a nonlinear shear stressstrain relationship of the form

T n

xz = ^ + K(t

G

- c) xz

xz

The three constants are given for the adhesive (ADH) and the overlay

(COMP) .

METAL - The orthotropic properties of the sheet (Ell, E22, V12, G12)

,

the thickness of the sheet in the first quadrant (DEPTH), and the angle

in the x-y plane between the major material axis of the sheet and the x axis (ANGLE)

ADH - The orthotropic properties, the total thickness, and the material

axis orientation of the adhesive layer.

COMP - The orthotropic properties with respect to the material axes, the

maximum thicknesses, and the material axis orientations of one or more stacked layers making up a single overlay. A layer consists of one or more lamina having the same orthotropic properties and material axis

orientation. In the analysis, the orthotropic properties given here are

first transformed by eq.(8) to give the properties []Q]with respect to

the axes x,z. Then the effective (weighted average) orthotropic

properties are computed for each triangular finite element according to

the cross sectional areas of the separate layers within the triangular

element. For example, the effective orthotropic properties for the

element defined by the dashed triangle ijk in Fig. 6 would be weighted

according to the sub-areas of different ply-angle located within the

triangle.

Figure 23 is a contour plot of the maximum principal stress for the case defined in Fig. 22. This plot illustrates the nature of the

discontinuities in a stress field at the interface between different

materials

For the case defined in Fig. 22, Fig. 24 gives a plot of three shear

functions that can be related to the shear-stiffness computations,

eqs.(ll) through (14), of the planform analysis. An effective shear

stiffness k' can be computed from the results of the cross-section

S X analysis by the formula

T A

k' xz s (22) sx u

s

20
in which ^ ^ ^^^^^^^^ ^^^^^.^^ 3^3^, 3tress at the interface

between the adhesive and the sheet,

A - thlarea over which the shear stress xs acting,

: Te Tcollor^ent of the difference in ciisplace.en

^

of the midplanes of the overlay and the sheet, that

is, the relative x displacement.

Ihe stiffness ratio plotted in Fig. 24 the ratio of the shear^^^^^^^^

stiffness k',, computed by e, (22) to the shea

^^^^

bv eq.(14). Between x = 1 and x J, i-ig.^'+, l

^ T Ind u are too near zero to permit meaningful numerical

xz s , ^, f

^ t 1^ roughly approximates k

computation of k . ine race cnat ^

& y f^^^n „„p reasonably

suggests that the' assumptions on which eq.(l4) was based are reasonably

consistent with the cross-section analysis.

2.4. Nonlinear-Shear Analysis

Both the planform analysis and the cross-section analysis permit

nonlinear interlaminar shear deformation to be approximated by a converging series of stepwise- linear finite element

assumed that the nonlinear shear properties of each material are detinea

by analytical stress-strain relationships [5] of the type represented

schematically in Fig. 25. That is,

Gl 9

(23)

T . Gi2

K(t - C) n

T > C (24)

in which C defines the linear range and the parameters K and n define

the slope of the curve in the nonlinear range. The other orthotropic

constants (En, E22» and ^12 ) assumed to be unaffected by the

nonlinear shear deformation.

In the planform computer program, nonlinear shear deformation is

permitted only in the interlaminar shear-stiffness elements (see eq.(12)

and Fig. 4). Only linear elastic deformation is permitted in the

triangular elements (eq.(lO) and Fig. 3). The following stepwise-linear

procedure is used:

1. Obtain an initial finite element solution using the linear elastic

material constants throughout the network of triangular

and shear-stiffness elements.

21
2. For each shear-stiffness element, compute the resultant adhesive

shear stress by the use of eq.(18), and select single

representative values of the interlaminar shear stresses

within the sheet and the overlay. In this analysis, the

selected effective shear stresses are the values midway

; . between the limits of integration in eq.(13) for the stress

distribution shown in Fig. 4(c).

3. For each shear-stiffness element, compute the shear strains

within the adhesive, the sheet, and the overlay by

substituting into eq.(23) or (24) the shear stresses

from step 2.

4. Compute trial effective shear moduli G , G , and G as

s a o the ratios of stresses from step 2 to strains from step 3.

5. Recompute the shear stiffness coefficients by substituting

into eq.(14) or (15) the shear moduli from step 4.

6. Obtain a finite element solution using the shear-stiffness

coefficients from step 5.

7. Repeat steps 2 through 6 until the process converges

satisfactorily. Figure 25 shows, schematically, a progression

of three iterative cycles for one material of a shear-stiffness element.

In the cross-section computer program, nonlinear shear

deformation is permitted throughout the sheet, the adhesive, and the

overlay. The following stepwise-linear procedure is used:

1. Obtain an initial finite element solution using the elastic

material constants throughout the network of triangular

elements

2. For each element compute the shear stress component by

the use of eq. (8)

3. For each element compute the shear strain by substituting

into eq.(23) or (24) the shear stress component from step 2.

4. Compute trial effective shear moduli ^iz as the ratios

of the stresses from step 2 to the strains from step 3.

5. Recompute the nodal point stiffnesses using the effective

shear moduli from step 4.

6. Obtain a finite element solution using the shear stiffness

from step 5.

22
7. Repeat steps 2 through 6 until the process converges

satisfactorily.

2.5. Progressive-Debond Analysis

In the planform analysis, progressive adhesive debond can be

approximated by a series of finite element solutions. This analysis is

based on the premise that the adhesive bond will fail at any point where

tne resultant adhesive shear stress ^ reaches a critical value. The

following procedure is used in the computer program:

1. Obtain an initial finite element solution for an arbitrary

set of uniformly distributed boundary stresses.

2. For each shear-stiffness element, compute the resultant

adhesive shear stress by the use of eq.(18).

3. Determine which shear-stiffness element has the greatest

resultant adhesive shear stress. Scale the uniformly

distributed boundary stresses up or down to make the

greatest value of adhesive shear stress equal the critical value

required to cause debond.

4. Remove the critically stressed shear-stiffness element

from the finite element network, thus debonding the

conjugate pair of nodal points in the sheet and overlay.

5. Obtain a new finite element solution for the network as reduced in step 4 and subjected to the uniformly distributed

boundary stresses as scaled in step 3.

6. Repeat steps 2 through 5 as many cycles as desired.

3. DESCRIPTION OF LABORATORY TESTS

A total of 34 specimens were designed, fabricated, instrumented,

and tested. These consisted of the following:

1. Four 0.5 in (1.3 cm) wide boron/epoxy coupon tensile

specimens for determination of the elastic constants Ei2»

E 2 2 » and v 1 2 •

2. One 3.0 in (7.6 cm) diameter boron/epoxy thin-tube torsion

specimen for determination of the elastic constant G12 .

23
3. Three 6.0 in (15.2 cm) wide aluminum sheet specimens with

no composite reinforcement; one with a circular cutout, one with a circular cutout and sawed slits radiating away

from each side of the cutout, and one with a transverse

symmetrical sawed slit. The sawed slits were intended to

simulate cracks.

• 4. Six 6.0 in (15.2 cm) wide aluminum sheet specimens with circular

cutouts reinforced with overlays of boron/epoxy.

5. Five 6.0 in (15.2 cm) wide aluminum sheet specimens with circular

cutouts and slits reinforced with overlays of boron/epoxy.

6. Six 6.0 in (15.2 cm) wide aluminum sheet specimens with

transverse slits reinforced with overlays of boron/epoxy.

7. Nine 1.0 in (2.5 cm) wide double lap joint specimens

consisting of two aluminum sheets spliced together by

_ overlays of boron/epoxy.

Ten of the 6.0 in (15.2 cm) wide specimens were tested in static tension

and ten were tested in low-cycle tens ion- tens ion fatigue. Six of the

1.0 in (2.5 cm) wide specimens were tested in static tension and three

were tested in low-cycle tens ion- tens ion fatigue. The 6.0 in (15.2 cm)

wide and 1.0 in (2.5 cm) wide specimens were designed on the basis of

computer analyses. The specimens were not optimized with respect to

structural efficiency, however, since the prime consideration was that

they give definitive data for the evaluation of the computer analyses.

: . ^ -z .

: .; v:. 3.1. Specimen Materials

The composite material used in the test specimens was 3M* SP-292

unidirectionally reinforced boron/epoxy. This was purchased in 3.0 in

(7.6 cm) wide continuous prepreg tape form with nominally 212 filaments

per inch (83 filaments per cm) of tape width. The boron filaments are nominally 0.004 in (0.1 mm) in diameter and preimpregnated with PR-279

epoxy resin. Each ply of boron/epoxy had a glass fiber scrim backing

0.001 in (0.03mm) thick. The cushion material used in some specimens

(see Fig. 6) was unreinforced PR-279 epoxy resin.

*The identification of the suppliers of materials used in

these tests is for information purposes only and is not intended

to indicate endorsement by the National Bureau of Standards, nor does it imply that the material x-zas necessarily the best

available.

24
The metal sheet used in three of the 1.0 in (2.5 cm) wide test

specimens was cut from a single sheet of 0.126 in (0.320 cm) thick 2024-

T4 bare aluminum alloy. The metal sheet used in all other specimens was

cut from a single sheet of 0.124 in (0.315 cm) thick 7075-T6 bare

aluminum alloy.

The adhesive used to bond the composite overlays to the metal sheet was Armstrong C-4 epoxy and activator W mixed in a 1:1 ratio.

3.2. Specimen Configurations

a. Material Property Specimens

The elastic constants En, E22, and V12 the boron/epoxy

material were determined by static tensile tests of 8-ply thick by 0.5

in (1.3 cm) wide by 12 in (30 cm) long coupon specimens. Glassreinforced-plastic tabs, 3.0 in (7.6 cm) in length, were bonded to each

end of the specimens. Two specimens used for the determination of E^^

and V12 had the boron filaments oriented in the longitudinal

direction. The average thickness per ply for these two longitudinal

specimens was 0.0056 in (0.142 mm). Two specimens used for the

determination of E22 had the boron filaments oriented in the transverse

direction.

The shear modulus G22 foi^ the boron/epoxy material was determined

by a torsion test of a 4-ply thick by 3.0 in (7.6 cm) diameter by 10 in

(25 cm) long hollow cylindrical tube specimen. The boron filaments were

oriented in the longitudinal direction.

The elastic constants E and v for the aluminum-alloy materials

were determined by averaging strain measurements made on ten of the 1.0

in (2.5 cm) wide and 6.0 in (15.2 cm) wide specimens. These strains

were measured in a region of approximately uniform stress, between the

composite-overlay region and an end tab or grip.

The elastic constant E for the epoxy adhesive material was determined by a compression test of a 0.5 in (1.3 cm) diameter by 1.5 in

(3.8 cm) long solid cylindrical specimen (Ref.6). A value of 0.35 was assumed for the elastic constant v on the basis of the manufacturer's

literature.

b. Unreinforced Sheet Specimens

Details of the three 6.0 in (15.2 cm) wide unreinforced specimens

are given in Fig. 26. The first two digits of the specimen designations

CUUl, CCUl, or CRUl (Fig. 26) indicate, respectively, the specimen

25
configuration CUtout, £utout-with-^rack, or CRacked. The third digit

indicates that the specimen is Unreinforced , The fourth digit is a serial number for specimens of the same design.

c. Reinforced Cutout Specimens

The details of the aluminum sheet of the six 6.0 in (15.2 cm) wide

reinforced cutout specimens are the same as those for the unreinforced

cutout specimen (CUUl) given in Fig. 26(a). The 1.50 in (3.81 cm)

diameter cutouts were reinforced on both surfaces of the specimen with

composite overlays of one of the designs detailed in Fig. 27. Three

specimens (CUAl, CUA2, and CUA3) were reinforced with overlays of Design

A (a = 45°) and three specimens (CUBl, CUB2, and CUBS) were reinforced

with overlays of Design B (

ct = 30°).

•

, . . d. Reinforced Cutout-with-Slit Specimens

The details of the aluminum sheet of the five 6.0 in (15.2 cm) wide

reinforced cutout-with-slit specimens are the same as those for the

unreinforced cutout-with-slit specimen (CCUl) given in Fig. 26(b). The

1.50 in (3.81 cm) diameter cutouts with 0.20 in (0.51 cm) long

transverse radial slits were reinforced on each side by composite

overlays of one of the designs detailed in Fig. 27, the same as the

overlays that were used to reinforce the cutout specimens. Two

specimens (CCAl and CCA2) were reinforced with overlays of Design A (a = 45°) and three specimens (CCBl. CCB2, and CCB3) were reinforced with

overlays of Design B ( = 30°).

'''-[ e. Reinforced Transverse-Slit Specimens

The details of the aluminum sheet of the six 6.0 in (15.2 cm) wide

reinforced transverse-slit specimens are the same as those for the

unreinforced transverse-slit specimen (CRUl) given in Fig. 26(c). The

2.4 in (6.1 cm) long transverse slits were reinforced on each side by

composite overlays of one of the designs detailed in Figs. 28 and 29.

Three specimens (CRAl, CRA2, and CRA3) were reinforced with overlays as detailed in Fig. 28 and three specimens (CRBl, CRB2, and CRB3) were

reinforced with overlays as detailed in Fig. 29.

f. Double-Lap Joint Specimens

The nine 1.0 in (2.5 cm) wide double-lap joint specimens consisted

of two 12 in (30 cm) long aluminum-alloy sheets, spliced together, end

to end, with 6-ply by 1.0 in (2.5 cm) wide by 12.0 in (30.5 cm) long

unidirectional 0° boron/epoxy overlays bonded to each surface. The four

different overlay configurations detailed schematically in Fig. 30 were

26
represented in the nine specimens. Three specimens (PAl, PBl, PB2) were spliced with plain, fully bonded, uniform- thickness overlays

(Fig. 30(a)). Three specimens (DAI, DBl, DB2) were spliced with plain,

uniform-thickness overlays that were adhesively bonded over only twothirds of their contact surfaces (Fig. 30(b)). Two specimens (CBl, CB2)

were spliced with fully bonded, uniform-thickness overlays with 1-ply

thick cushions at the center and at each end (Fig. 30(c)). One specimen

(TAl) was spliced with a fully bonded step-tapered overlay (Fig. 30(d)).

The aluminum-alloy sheet of three specimens (PAl, DAI, TAl) was 2024-T4;

for the other six specimens it was 7075-T6.

- 3.3. Specimen Fabrication

Each boron/epoxy overlay or coupon tensile specimen was laid up and

fully cured as a unit before being adhesively bonded to another

material. The boron/epoxy was cured in a heated platen press using

pressures and temperatures recommended by the manufacturer of the

composite prepreg tape.

The aluminum-alloy surface was degreased with acetone and/or methyl

ethyl ketone and chemically neutralized with an acidic conditioner and

alkaline neutralizer before bonding of the boron/epoxy overlay.

The overlays were bonded to the aluminum-alloy sheet using the

epoxy adhesive and a nominal confining pressure, and the specimen was

allowed to cure at room temperature for at least seven days before

testing.

The boron/epoxy thin-tube torsion specimen was laid up on a pxastic-covered wooden mandrel. A heat-shrinkable fluorocarbon plastic

tube was then shrunk over the laminate. The specimen was cured using

the temperature-time cycle recommended by the manufacturer of the

boron/epoxy tape. This fabrication process is described in greater

detail in Ref.7.

3.4. Instrumentation

The four boron/epoxy coupon tensile specimens were each

instrumented with four resistance strain gages, two longitudinal and two

transverse, mounted back to back to permit bending corrections. The

boron/epoxy torsion specimen was instrumented with fifteen resistance

strain gages grouped in three-gage 45° rosette configurations.

The 6.0 in (15.2 cm) wide specimens were each instrumented with

from four to forty-seven resistance strain gages, and the 1.0 in (2.5

cm) wide specimens were each instrumented with from four to twenty-one

gages.
For most tests, strains were recorded by a multi-channel data

acquisition system. Figure 31 shows a test setup using this system.

For some tests involving relatively few strain gages, a single-channel

strain indicator and a switching box were used.

; 3.5. Test Procedures

a. Quasi-Static Tension Tests

The four boron/epoxy coupon specimens were statically loaded to

failure in tension using a hydraulic universal testing machine. The

boron/epoxy torsion specimen was loaded only within the elastic range

using a torsion testing machine.

Ten 6.0 in (15.2 cm) wide specimens were statically loaded to

failure in tension using an elect rohydraulic testing machine in a setup

similar to the one shown in Fig. 31. Steel tab plates were bolted to

each end of a specimen, and the load was applied to the tab plates

through 1.0 in (2.5 cm) diameter steel pins.

Six 1.0 in (2.5 cm) wide double-lap joint specimens were statically

loaded to failure in tension using a hydraulic testing machine. The

load was applied directly to each end of a specimen by wedge grips.

In all static tests loads were applied slowly in increments and

surface strains were measured at each increment. The duration of

loading in a material property test was no more than several minutes.

The duration of loading in the other static tests, however, was typically thirty minutes or more.

b. Tension-Tension Fatigue Tests

Ten 6.0 in (15.2 cm) wide specimens were tested to failure in

tension-tension fatigue using an electrohydraulic testing machine in a setup similar to the one shown in Fig. 31. Three 1.0 in (2.5 cm) wide

specimens were similarly tested in an electrohydraulic testing machine

of smaller capacity.

In all fatigue tests the minimum cyclic load was one-tenth the

maximum load (R = 0.1). Fatigue loading frequencies of from 1 to 4 Hz

were used. Maximum cyclic loads were chosen that were expected to cause failure in less than 100,000 cycles.

Fatigue cycling was interrupted several times during each test and

a single cycle of quasi-static load was applied. At maximum cyclic load

(static) the specimen was visually examined for any indication of damage

and strains were recorded from the resistance gages attached to the

specimen.
4. TEST RESULTS AND CORRELATIONS WITH ANALYSES

4.1. Material Properties

The elastic constants determined by tensile tests of the four

boron/epoxy coupon specimens were:

Ell = 28.6 X 10^ Ibf/in^ = 197 x 10^ N/m^

E22 = 2.10X 10^ Ibf/in^ = 14.5 x 10^ N/m^

Vi2 = 0.168

The average tensile strength of the two specimens with longitudinal

fiber orientation was 195000 lbf/in^(1340 x 10%/m2). The average

tensile strength of the two specimens with transverse fiber orientation

was 5400 lbf/in^(37 x lO^/m^).

The shear modulus determined by a torsion test of the boron/epoxy

tube specimen was:

G12 = 0.759 X 10° Ibf/in- = 5.22 x 10^ N/m^

The elastic constants determined by averaging strain measurements

made on the surfaces of seven specimens made with 7075-T6 aluminum alloy

were

:

E = 9.92 x 10^ Ibf/in^ = 68.4 x 10^ N/m^

V = 0.318

The value of Young's modulus determined by averaging strain measurements

made on the surfaces of three specimens made with 2024-T4 aluminum alloy was

:

E = 10.40 X 10^ Ibf/in^ = 71.7 x 10^ N/m^

It was assumed that Poisson's ratio for the 2024-T4 alloy was the same

as that determined for the 7075-T6 alloy.

The value of Young's modulus determined by a compression test of a cylindrical specimen of the epoxy adhesive material was:

E = 0.27 x 10^ Ibf./in^ = 1.9 x 10^ N/m^

The value of Poisson's ratio for the adhesive was assumed to be 0.35.

4.2. Unreinforced Sheet

Figure 32 shows the three unreinforced aluminum sheet specimens

after they were tested to failure in static tension.

29
The cutout specimen (CUUl) failed at a surprisingly high load of

46000 Ibf (205000 N). This was a ductile failure with visible

elongation of the cutout and necking of the specimen in both the

thickness and width directions. A lower bound on the maximum tensile

stress at the failure surface can be computed by dividing the failure

load by the net cross sectional area. This computation gives a value of

82500 Ibf /in^ (569 x 10^ N/m^) which is slightly higher than the handbook

value of ultimate tensile strength for this material CRef.S). This

suggests that the tensile stresses were distributed rather uniformly

across the net cross section just before failure.

The cutout-with-slit specimen (CCUl) failed at a load of 19900 Ibf

(88500 N) and the transverse slit specimen (CRUl) failed at a load of

18750 Ibf (83400 N)

Strains measured on the surface of the three unreinforced specimens

can be compared directly with strains predicted by the planform finite

element analysis. Figure 33 indicates the locations and orientations of

strain gages on the specimens, the measured microstrains (in

parentheses), and the microstrains predicted by the analysis, for an applied tensile load of 4000 Ibf (17800 N) . The multiple numbers (in

parentheses) indicate microstrain measurements from strain gages

symmetrically located in different quadrants of a specimen. The

analytical strains were linearly interpolated from the contour plots of

strain components. For comparison with strains measured by gages

oriented at an angle, the analytical strains were computed from the x and y components of normal strain and the xy component of shear strain.

4.3. Reinforced Cutout

Figures 34 and 35 show the six reinforced cutout specimens after

they were tested to failure in static tension or tension-tension

fatigue. During the static tensile test of specimen CUAl there was a shear failure of the tab bolts at one end at a load of 38250 Ibf (170100

N) . The sudden release of load caused failure of one overlay without

failure of the aluminum sheet (Fig. 34).

The maximum tensile loads (static or fatigue) and the cycles to

failure (fatigue) for all seven cutout specimens (including the

unreinforced cutout) are given in Table 1. The table also gives certain

stress components, computed by the planform finite element analysis,

that have been scaled to correspond to the applied maximum tensile load

for the particular specimen. The x and y coordinates of the point at

which a stress is acting are given below the stress. Some of these

stress components may be related to the failure modes evident in Figs. 34

and 35. Notice, for example, the very high values of tensile stress in

the composite at the edge of the cutout for specimens CUA2 and CUBl and

the corresponding tensile failure modes evident in the photographs.

30
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31
Longitudinal splitting and debonding of the boron/epoxy overlays is

evident in all six reinforced cutout specimens (Figs. 34 and 35). In the

three fatigue specimens the splitting and debonding was visible long

before fatigue failure. In specimen CUB2, for example, after only 500

fatigue cycles the splitting and debonding had progressed to the extent

that there was little effective reinforcement from the overlay on one side of the specimen. The contour plots of xy shear stress in the

composite indicate longitudinal ridges of high stress in the locations

of these splitting failure surfaces. See, for example. Fig. 8 which is

from the analysis of specimen CUBl.

Strains measured on the surfaces of specimens CUAl and CUBl were

compared with strains computed by the finite element analysis for an applied load of 11250 Ibf (50040 N) . Figures 36 and 37 indicate the

locations and orientations of strain gages on the specimens, the

measured microstrains (in parentheses), and the microstrains predicted

by the analysis.

4.4. Reinforced Cutout-with-Slit

Figures 38 and 39 show the five reinforced cutout-with-slit

specimens after they were tested to failure in static tension or tension-tension fatigue. The maximum tensile loads (static or fatigue)

and the cycles to failure (fatigue) for all six cutout-with-slit

specimens (including the unreinforced cutout-with-slit) are given in

Table 2. The table also gives certain stress components, computed by

the planform finite element analysis, that have been scaled to

correspond to the applied maximum load for the particular specimen. The

X and y coordinate of the point at which a stress is acting are given

below the stress. Some of these stress components may be related to the

failure modes evident in Figs. 38 and 39. The relatively low failure

load for specimen CCBl may be related to the presence of an air pocket,

roughly 0.8 in^(5 cm^) in area, in the adhesive layer near one end of an overlay.

A combination of tensile failure, splitting, and debonding is

evident in the three fatigue specimens (Figs. 38 and 39). Splitting and

debonding were observed during fatigue testing in only one specimen

(CCB3) . That occurred in a corner of one overlay midway through the

fatigue test and then apparently remained stable until failure of the

specimen.

In all three fatigue specimens, the extent of crack growth before

failure is clearly visible on the fracture surface of the aluminum-alloy

sheet. The lengths of crack growth in the three specimens were 0.10,

0.24, 0.30, 0.30, 0.47, and 0.53 in (2.5, 6.1, 7.6, 7.6, 12.0, 13.5 mm).

There was no tensile failure evident in the boron/epoxy overlay near the

0.10 in (2.5 mm) crack extension. There was tensile failure in the

overlays near the five longer crack extensions, however.

32
in o o o m o o o o

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33
Strains measured on the surfaces of specimens CCAl and CCBl were

compared with strains computed by the finite element analysis for an applied load of 11250 Ibf (50040 N) . Figures 40 and 41 indicate the

locations and orientations of strain gages on the specimens, the

measured microstrains (in parentheses) , and the microstrains predicted

by the analysis.

,

. 4.5. Reinforced Transverse Slit

Figures 42 and 43 show the six reinforced transverse-slit specimens

after they were tested to failure in static tension or tension-tension

fatigue. The maximum tensile loads (static or fatigue) and the cycles

to failure (fatigue) for all seven transverse crack specimens (including

the unreinforced transverse crack) are given in Table 3. The table also

gives certain stress components, computed by the planform finite element

analysis, that have been scaled to correspond to the applied maximum

load for the particular specimen. The x and y coordinates of the point

at which a stress is acting are given below the stress. Some of the

stress components may be related to the failure modes evident in Figs. 42

and 43.

The relatively low failure load and the mode of failure for

specimen CRBl was caused by the inadvertent inclusion of a sheet of

plastic release material between two plies of one overlay. The outer

four plies popped off the specimen and the remaining two plies failed in

tension.

In all four fatigue specimens, the extent of crack growth before

failure is clearly visible on the fracture surface of the aluminum-alloy

sheet. The lengths of fatigue crack growth in the four specimens ranged

from 0.02 to 0.28 in (0.5 to 7.1 mm). There was no apparent correlation

between length of fatigue crack growth and either strength or mode of

failure for these specimens.

Strains measured on the surfaces of specimens CRAl and CRBl were

compared with strains computed by the finite element analysis for an applied load of 11250 Ibf (50040 N) . Figures 44 and 45 indicate the

locations and orientations of strain gages on the specimens, the

measured microstrains (in parentheses) , and the microstrains predicted

by the analysis.

4.6. Double-Lap Joints

Figures 46 through 49 show the nine double-lap joint specimens

after they were tested to failure in static tension or tens ion- tens ion

fatigue. The maximum tensile loads (static or fatigue) and the cycles

to failure (fatigue) for all nine double- lap joint specimens are given

in Table 4. The table also gives certain stress components, computed by

34
en

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35
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36
the longitudinal cross-section finite element analysis, that have been

scaled to correspond to the applied maximum load for the particular

specimen. The x and z coordinates of the point at which a stress is

acting are given below the stress.

The tensile failure evident in one tapered boron/epoxy overlay of

specimen TAl (Fig. 49) was probably a secondary failure that occurred

after debonding of the other overlay. The two specimens with single-ply

cushions (both static and fatigue, Fig. 48) failed in a combination of

debond and delamination. The delaminations occurred between the first

and second inner plies and apparently were precipitated by the inner

cushions. The other six double-lap joint specimens (both static and

fatigue, Figs. 46 and 47) failed by debonding of the overlays in two or three quadrants.

The progression of debonding was clearly visible during each of the

three fatigue tests. It began at the end of an overlay and grew toward

the center of the specimen. In specimen FBI, for example, debonding

over a length of about 1 in (3 cm) was observed after 4000 fatigue

cycles; just before failure at 14000 cycles there was visible debonding

over a length of about 4 in (10 cm) in two quadrants.

Longitudinal strains measured on the surface of specimens PB2, DAI,

CB2, and TAl were compared with strains computed by the longitudinal

cross-section analysis for an applied load of 2500 Ibf (11120 N)

Figures 50 through 53 are plots of the longitudinal surface strain

distributions as predicted by the analysis (continous curve) and as measured (data points).

4.7. Discussion of Results

Strains measured on the surfaces of the test specimens are, for the

most part, in good agreement with strains computed by the finite element

analyses. Agreement is best in the reinforced transverse-slit specimen

(CRAl) which had relatively thin 4-ply overlays. There is apparent

systematic disagreement at two locations in both the cutout and cutoutwith-slit specimens. On the x axis, adjacent to the cutout, the

measured strains on five specimens (CUUl, CUAl, CUBl, CCAl, CCBl) are, on the average, only 58 percent of the corresponding computed strains.

On the y axis, adjacent to the cutout, the measured strains on the same

five specimens are, on the average, 82 percent of the corresponding

computed strains.

Examination of the specimens after testing indicates significant

similarities in modes of failure of specimens of the same design,

whether subjected to static or fatigue loading (Figs. 34, 35, 38, 39, 42,

43, 46, 47 and 48). These similarities are more clearly evident in the

37
transverse-slit specimens and the lap-joint specimens than In the cutout

and the cutout-wlth-sllt specimens. Examination of the debonded

surfaces suggests that there was considerable variation In bond quality

from specimen to specimen and within a single specimen.

Finite element computer programs have been developed to analyze the

reinforcement of cutouts and cracks In metal sheet by adhesively bonded

overlays of composite materials. The programs are also suitable for the

analysis of adhesively bonded lap joints. The analyses articulate the

separate responses of the bonded adherends and the adhesive.

The outputs from the computer programs Include contour plots of

stress and strain fields throughout each of the constituents of a bonded

system. This form of output enables one to visualize the Interactions

between the different elements of the total system. The contour plots

can also Indicate the presence of a stress condition that might Initiate

or drive a crack or a debond.

The computer programs can accommodate the analysis of a broad class

of relnf orced-cutout , relnf orced-crack, and lap-joint configurations.

Such special features as cushions, tapers, and debonded regions can be

explicitly studied. The computer programs generate the finite element

networks from input data in the form of gross dimensions. These

characteristics of the programs make them efficient for use in design

studies

A series of laboratory tests was conducted to demonstrate the

validity of the analyses. Strains measured on the surfaces of a wide

variety of test specimens were, for the most part, in good agreement

with strains predicted by the analyses. Significant correlations

between some failure modes and the stresses computed by the analyses

were apparent. Some similarities in modes of failure of similar

specimens, whether subjected to static or fatigue loading, were evident.

The following valuable contributions to this work are greatfully

acknowledged:

Technical review and consultation - Leonard Mordfln

5. CONCLUSION

k

Computer programming

Specimen fabrication

Instrumentation

- Saul M. Baker

- Robert L. Breeden

- Robert E. Snyder.

38
6. REFERENCES

Ashton, J.E., Halpin, J.C., and Petit, P.H., Primer on Composite

Materials: Analysis (Technomic, 1969).

Clough, R.W. , The finite element method in structural mechanics,

chapter 7 of Stress Analysis, Eds. Zienkiewicz, O.C. and Hollster,

G.S. (Wiley, 1965).

Zienkiewicz, O.C, The Finite Element Method in Engineering Science

(McGraw-Hill, 1971).

Wilson, E.L., Finite Element Analysis of Two-Dimensional

Structures, Structures and Materials Research Report No. 63-2, U.

of Calif. Berkeley (June 1963).

Osgood, W.R., Stress-Strain Formulas, J. Aeronautical Sci. 13, No.l,

45-48 (Jan. 1946).

Halsey, N. , Mitchell, R.A. , and Mordfin, L., Evaluation of GRP Rod

and Rope Materials and Associated End Fittings, NBSIR 73-129 (Dec.

1972)

.

Marlowe, D.E., Torsional Instabilities in Composite and CompositeReinforced Aluminum-Alloy Thin-Walled Cylinders, NBS Technical Note

728 (June 1972).

Metallic Materials and Elements for Aerospace Vehicle Structures,

MIL-HDBK-5A (Aug. 1972).

39



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51

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Figure 3 - General triangular finite element.

OVERLAY REiNFORCED UNREINFORCED

(ajpiNITE ELEMENT MESH (PLAN VIEW

i i i

_) , 1. _

; ADHESIVE

SHEET

xz

(b) CROSS SECTION (c)SHEAR STRESS (d) DISPLACEMENT

(ASSUMED) (RELATIVE)

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i.-

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£

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Figure 6 - Schematic cross-section of an overlay-reinforced sheet.







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Figure 24 - Plots of three shear functions for the case defined in Fig. 22.
II

I- IIi
SHEAR STRAIN

Figure 25 - Schematic stress-strain curve for a nonlinear shear-stiffness material.

Figure 26 - Details of the unreinforced sheet specimens. Sheet material is

0.124 in (0.315 cm) thick 7075-T6 aluminum alloy. Dimensions shown are

in inches (1 in = 2.54 cm).

i
1..
Figure 27 - Details of the composite overlays used to reinforce the cutout and

cutout-with-slit specimens. Dimensions shown are in inches (1 in = 2.54 cm)

EZZZL

0.5—»| hF7ZT

5^

0^

1

•F777

•CUSHION

< 0.5

Ezza

T

ALUM. ALLOY

4.0

-3.0

-2.0

2.4

iJ

3.0

Figure 28 - Details of the composite overlays used to reinforce three of the

transverse-slit specimens (CRAl, CRA2, CRA3). Dimensions shown

are in inches (1 in = 2.54 cm).

0.5

-45'

V77X

IF"

< *-

CUSHION

0.5

-ALUM. ALLOY

4.0

3.0

2.0

240

Figure 29 - Details of the composite overlays used to reinforce three of the

transverse-slit specimens (CRBl, CRB2, CRB3) . Dimensions shown

are in inches (1 in = 2.54 cm).
]

I

I

i
ADHESIVE 6-PLY BORON/EPOXY

(a) PLAIN OVERLAY SPECIMENSCpA 1, PBl,PB2)

1 --i*-

A

BONDED

ADHESIVE

2 —

BONDED

6-PLY BORON/EPOXY

K-1

ib)PARTIALLY'BONDED OVERLAY SPECIMENS(DAl, DBl, DB 2)

Figure 30 - Schematic details of the double-lap-joint specimens. (Continued)

(d)TAPERED OVERLAY SPECIMEN (TAI)

Figure 30 - Schematic details of the double-lap-joint specimens.

Figure 31 - Test setup using a multi-channel data acquisition

system and an electrohydraulic testing machine.
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U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR 73-201

2. Gov't Accession

No.

3. Recipient's Accession No.

|

4. TITLE AND SUBTITLE

(Composite-Overlay Reinforcement of Cutouts

and Cracks in Metal Sheet

5. Publication Date Feb. 19 73

6. Performing Organization Code

7. AUTHOR(S)

Richard A. Mitchell, Ruth M. Woolley, Daniel J. Chwiri

8. Performing Organization t NBSIR 73-201

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2130446

11. Contract/Grant No. L-48, 857

12. Sponsoring Organization Name and Address Langley Research Center

National Aeronautics and Space Administration

Hampton, Virginia 23365

13. Type of Report & Period Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) Finite element computer programs Were developed

for the planform analysis and the longitudinal cross-section analysis of metal sheet

reinforced by adhesively bonded overlays of composite material. The analyses

articulate the separate responses of the metal sheet, the composite overlays, and the

adhesive layers. All materials are assumed to be orthotropic and linear el^istic, with

the provision that nonlinear interlaminar shear deformation can be approximated by

a series of stepwise-linear solutions. The computer programs were developed specifically for the study of three general configurations: (1) a sheet with a reinforced

cutout; (2) a sheet with a reinforced cutout with two symmetrical transverse cracks,

within the sheet, radiating away from the cutout edge; and (3) a sheet with a reinforced transverse crack. The programs are also suitable for the study of bonded lap

joints. The principal output of the computer programs is a set of contour plots

of stress and strain fields throughout the sheet, the overlays, and the adhesive

layers. A series of laboratory tests was conducted to demonstrate the validity of

the analyses. Strains measured on the surfaces of specimens representing the general

configurations studied were, for the most part, in good agreement with strains

predicted by the finite element analyses. Signigicant correlations between certain

failure modes and the stresses computed by the finite element analyses were apparent.

Similarities between the modes of failure under static and fatigue loading were also

evident

Key Words: Adhesively bonded joints; composite materials; composite-overlay

reinforcement; contour plotting; cracks, reinforcement of; cutouts, reinforcement of;

debond analysis, progre-q-qi ve ; fim'fp plpmpnf analycig; -irn'rifg,—adhesively bonded;

17. KEY WORDS (Alphabetical order, separated by semicolons) analysis, shear; reinforcement,

composite overlay; reinforcement, cutouts and cracks; shear analysis, nonlinear.

18. AVAILABILITY STATEMENT

M UNLIMITED.

I I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19, SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

20. SECURITY CLASS

(THIS PAGE)

21. NO. OF PAGES

22. Price

UNCLASSIFIED

USCOMM-DC 66244-P7J
1