EFFECT OF PIN REINFORCEMENT ON BUCKLING OF DELAMINATED

SANDWICH BEAMS

BY

BRIAN T. WALLACE

A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING

UNIVERSITY OF FLORIDA

2000

ii

ACKNOWLEDGEMENTS

I would like to acknowledge the contribution that both my advisors, Dr. Peter Ifju

and Dr. Bhavani Sankar, have made to my academic career. Both gentlemen have

become personal friends as well as offering academic and professional guidance.

I would also like to thank Ryan Merrit for his contribution to this effort. Ryan

conducted the fracture toughness experiments contained in this study as part of the

University Scholars Program here at the University of Florida.

I should also recognize the contribution that my family has made to my academic

success. Their support and patience has played a key role in my achievement.

iii

TABLE OF CONTENTS page

ACKNOWLEDGEMENTS……………………………………………….. ii ABSTRACT…………………………………………………….…………. v CHAPTERS 1 INTRODUCTION…………………………………………….………… 1 1.1 Motivation……………………………………………….…………. 1 1.2 Literature Survey…………………………………………………... 4 2 MATERIALS AND SPECIMEN FABRICATION…………………….. 6 2.1 Material Systems…………………………………………………… 6 2.2 Specimen Preparation……………………………………………… 7 3 EXPERIMENTAL STUDY…………………………………………….. 12 3.1 Experimental Setup………………………………………………… 12 3.2 Preliminary Study………………………………………………….. 13 3.3 Edgewise Compressive Loading…………………………………… 19 3.4 Circular Delamination Testing…………………………………….. 30 3.5 Effect of Reinforcement on Mode I Fracture Toughness………….. 33 3.6 Experimental Results/Discussion………………………………….. 35 4 FINITE ELEMENT MODELING…………………………….………… 41 4.1 Geometric Modeling……………………………………………….. 41 4.2 Material Modeling……………………………………….………… 46 4.3 Finite Element Analysis…………………………………………… 50 4.4 FEA Results/Discussion…………………………………………… 53

iv

5 DISCUSSION AND FUTURE WORK………………………………… 67 5.1 Discussion…………………………………………………………. 67 5.2 Future Work……………………………………………………….. 75 REFERENCES …………………………………………………………… 78 BIOGRAPHICAL SKETCH……………………………………………… 80

v

Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering

EFFECT OF PIN REINFORCEMENT ON BUCKLING OF DELAMINATED

SANDWICH BEAMS

By

Brian T. Wallace

December 2000

Chair: Bhavani Sankar Co-chair: Peter Ifju Major Department: Aerospace Engineering, Mechanics and Engineering Science

The purpose of this thesis was threefold: to better understand the buckling

behavior of delaminated sandwich structures, to develop a reinforcement technique to

increase the post-buckling load of these beams, and to develop a method to accurately

model the behavior of delaminated sandwich beams. Experiments were conducted to

identify the effect of geometric parameters on the ultimate post-buckling load. These

specimen configurations then were reinforced using two methods. The first method was a

traditional Z-pin method using cylindrical graphite pins. The second method, “C-

pinning,” was developed during the course of this study. “C-pinning” involves using

reinforcement that is integral with the facesheets. In order to accurately predict the

behavior of sandwich beams, a nonlinear finite element study also was conducted. It was

determined that a nonlinear analysis that considers plastic deformation in the facesheet

provided good correlation between modeling and experimental data.

1

CHAPTER 1 INTRODUCTION

1.1 Motivation The drive to create structures that are lighter and stronger has led to tremendous

interest in sandwich construction. The availability of advanced core materials and

improved bonding techniques has allowed for more efficient sandwich structures. The use

of laminated composites, such as graphite/epoxy, for facesheet materials has extended the

range of strength and stiffness for these types of structures.

One barrier to the widespread acceptance of sandwich structures is debonding of

the facesheet. Debonding of the facesheet can occur during manufacture or service.

Structures with debonded facesheets have significantly lower load carrying capacity. In

severe cases, the reduced capacity can drop below the service loads leading to a

catastrophic failure. This phenomenon is especially true when the sandwich beam is

loaded in axial compression.

Delamination is a problem associated with all types of laminated materials. In a

sandwich structure, this problem typically is encountered at the facesheet/core interface.

Honeycomb core materials are attractive because of their high specific strength.

Unfortunately, they also provided little surface area for bonding resulting in a weak

facesheet/core interface. During the service life of a structure, debonding of the facesheet

from the core can occur. There are several common instances where this debonding can

occur including foreign matter being inserted inadvertently during manufacturing, tool-

drop during maintenance operations, and impact events, especially for aerospace

structures.

2

Advanced composite materials are a new class of materials. Traditional materials

such as wood, concrete, and steel have been in use for hundreds of years. The behavior

of these materials has been well characterized. This understanding of the behavior of a

material system leads to confidence among the engineers who specifies materials. For

advanced composite materials to gain widespread acceptance, there are several major

hurdles to overcome. One of the technical challenges in the use of composite materials is

improving the through-the-thickness strength of laminated composite structures.

Laminated composites have high in-plane stiffness and strength but weak interlaminar

strength. It is this weak interlaminar strength that results in delamination problems.

Figure 1-1. The X-33 technology demonstrator from NASA and Lockheed Martin

suffered a failure of its sandwich composite fuel tank.

The technical problems associated with laminated composites affected even the

most recent, high-tech projects. NASA is currently working with Lockheed Martin to

develop the X-33. The X-33 is a technology demonstrator and precursor to the

VentureStar Single-Stage-To-Orbit vehicle. The original X-33 design called for a

composite honeycomb fuel tank designed and built by Lockheed Martin SkunkWorks and

3

Alliant TechSystems (Hazen 2000). Unfortunately, during the first full pressurization test

the tank failed. A portion of the external facesheet delaminated. The failure is believed

to be the result of cryo-pumping that occurs during cryogenic loading of the fuel tank.

The tank holds liquid hydrogen at -425 degrees fahrenheit. This failure ignited

controversy within the project as to the safety and reliability of composite sandwich

structures. Engineers disagreed about the statistical significance of test data from

coupons and how well that information scaled to a full size structure. The design was

since changed to include an aluminum fuel tank.

Two techniques to improve the through-the-thickness properties of laminated

composites, including sandwich construction emerged in recent years: stitching and Z-

pinning. Through-the-thickness stitching has been shown to improve through-the-

thickness properties, particularly Mode I fracture toughness (Sharma and Sankar, 1996).

Aramid and glass yarns are commonly used to provide continuous reinforcement to a

laminated composite. This continuity of reinforcement reduces the introduction of stress

concentrations into the structure. One major limitation to the use of stitching of large

scale structures is that stitching requires access to both sides of a structure. Being able to

access both sides of today's large, complex sandwich structures may be impractical or

impossible. The use of composite materials allows for monolithically casting an aircraft

fuselage. To stitch a structure this size would require a stitching machine as large as the

aircraft itself. Structures that have complex geometries may be impossible to stitch

regardless of size.

The effects of Z-pinning of composite sandwich structures is the focus of this

project. The Z-pinning involves the insertion of individual pins through-the-thickness of

a laminate or sandwich structure. This project investigated the effect of reinforcement

and reinforcement spacing on the buckling load of a debonded sandwich beam.

4

1.2 Literature Survey

Many studies were performed to understand buckling of delaminated composite

beams and plates. Much of the early work was done in the area of laminated composites

and more recently was extended to sandwich structures.

Early analytical work dealing with the effects of delaminations on the ultimate

load capacity of beam-plates was done by Simitses et al. (1985). Yin et al. (1986)

worked in the same area but included the post-buckling behavior and energy release rate

calculations to predict delamination growth. Kassapagolou (1988) used a series solution

approach to solve for large deflections in a delaminated facesheet specimen. The

delaminations in this study were between facesheet plies, not at the facesheet/core

interface. The effect of elliptical delaminations on buckling and post-buckling was

studied.

The compressive failure of sandwich panels with different core materials was

studied by Minguet (1987). The study identified three failure modes: core failure,

facesheet debond, and facesheet fracture. The test results were used to develop non-

linear failure models for each of the observed failure modes. An analysis of various

numerical techniques for determining the buckling load of delaminated sandwich panels

was considered by Sleight and Wang (1995). The results from the various techniques

were compared to plane finite element analysis. The authors determined that accurate

models could be generated using 2-D, plane strain finite element analysis. Hwu and Hu

(1992) extended the work of Yin et al. (1986) to include delaminated sandwich beams.

This model provides good results for beams that fail in global buckling modes.

Kardomateas (1990) performed an experimental study aimed at understanding the

buckling and post-buckling of delaminated Kevlar/epoxy laminates. During the study,

the load-displacement behavior, deformed shape, and crack growth were recorded.

Avery (1998) and Avery and Sankar (2000) performed a parametric experimental

5

study to quantify the effect of facesheet thickness, core thickness, delamination length,

and core density had on the ultimate post-buckling load of a delaminated sandwich beam.

The delaminations in this study were at the facesheet/core interface. A Graeco-Latin

Square test plan was used to derive a test matrix from which the influence of each

parameter could be calculated. Narayanan (1999) performed a non-linear finite element

analysis study of the specimens used by Avery. During the finite element analysis, the

influence of core yielding and crack propagation on the post-buckling behavior of

delaminated sandwich beams was explored.

All the complexities of the current study have been previously investigated

individually. However, to gain a strong understand of reinforcement of delaminated

sandwich beams, all factors must be consider simultaneously to capture the interactions

between them. The current study aims to evaluate the performance of pin reinforcement

in sandwich beams with a delamination at the facesheet/core interface.

6

CHAPTER 2 MATERIALS AND SPECIMEN FABRICATION

2.1 Materials System

A typical sandwich construction consists of a high stiffness, facesheet material

separated by a lightweight core. By providing this separation between the facesheets, the

stiffness of a sandwich structure can be 30 times higher than a monocque structure of the

same weight (Zenkert, 1997). The advantages of using sandwich structures must be

weighed against the additional problems associated with these structures. Poor resistance

to localized loading and poor interlaminar strength are two main concerns for designers of

sandwich structures.

In this study, the facesheet material used was a plain weave, graphite epoxy pre-

preg material manufactured by Cytec-Fiberite (HMF 5-322/97714AC). The core material

was an aramid honeycomb core from Euro-Composites. Core materials used in this study

were 0.25, 0.375, and 0.5 inch thick. All core materials had a 0.125 inch cell diameter. A

typical delaminated sandwich beam is shown in Figure 2-1. Manufacturer’s data for the

facesheet material is shown in Table 2-1.

Figure 2-1. A typical sandwich beam showing edge to edge delamination at the

facesheet/core interface.

7

Table 2-1. Manufacturer’s data for Cytec-Fiberite HMF 5-322/97714AC used for facesheet material

Tensile strength 97 ksi

Tensile Modulus 7.7 Msi

Flatwise tensile strength 693 psi

Fiber volume fraction 0.59

2.2 Specimen Preparation

The methods used to reinforce specimens in this study can be divided into two

categories: Z-pins and “C-pinning”. Z-pins are cylindrical, graphite/epoxy pins. “C-

pinning” involves inserting strips of uni-directional, graphite/epoxy pre-preg into the

sandwich construction pre-form.

In the case of Z-pins, the reinforcement was cured prior to being introduced into

the sandwich pre-form. The Z-pins in this study were constructed from 6-K graphite fiber

tows from Aircraft Spruce and Specialty. Since the Z-pins were to be co-cured with the

sandwich pre-form, the resin selected for manufacturing pins must not degrade at the cure

temperature of the sandwich composite. A room temperature cure resin would degrade at

elevated temperature leading to poor adhesion between the pins and the facesheets. A

Shell Epoxy system was chosen using SU-3 resin, Curing Agent W, and 828 Resin mixed

to a ratio of 3:3:7 by weight.

The fiber tows were wetted out in a vacuum oven. The wetted fibers were then

transferred to a fixture which was used to apply tension and could be rotated to twist two

individual tows together to form 12K graphite/epoxy rods. These rods were

approximately 0.03" in diameter. The cured rods were then cut to form graphite/epoxy

8

pins used for reinforcement. Typical sandwich construction techniques were used in

preparing the pre-forms. Individual facesheets were layed-up and mechanically debulked.

The Nomex® honeycomb core was cut to the appropriate panel dimensions and facesheets

were applied. Prior to applying the second facesheet, a strip of non-porous Teflon® was

inserted to create a delamination of the appropriate length. The resulting delamination

extends across the width of the specimen and lies at the facesheet/core interface. Once the

delaminated sandwich beam was assembled, pins were inserted through-the-thickness as

shown in Figure 2-2.

Figure 2-2. Z-pins inserted through-the-thickness of sandwich pre-form. An aluminum

fixture was used to allow a pilot hole to be punched through the preform prior to inserting the graphite pins. The fixture forced the facesheet to remain flat while the pins were inserted.

The second method of translaminar reinforcement used in this study was “C-

pinning.” This reinforcement technique is illustrated in Figure 2-4. With this

reinforcement technique, initially a single ply of facesheet material was applied to each side

of the honeycomb core. Again, a thin strip of nonporous Teflon® was applied underneath

one facesheet to create the appropriate delamination. Using a small sewing needle, thin

strips of uni-directional, graphite-epoxy pre-preg were inserted through-the-thickness of

the sandwich beam. The pre-preg strips are cut leaving 1/8 inch section protruding from

either side of the beam. This procedure was repeated until the entire beam had been

9

reinforced at the proper spacing. The exposed pre-preg was folded flat and the remaining

facesheet plies were applied to the sandwich beam. With this reinforcement technique, the

head of the pin is now integral with the facesheet.

Figure 2-3. “C-pinning” technique involves insertion of uncured, uni-directional pre-preg

strips through-the-thickness of the sandwich beam during lay-up.

After the sandwich panels were layed-up and the appropriate type and spacing of

reinforcement was inserted, the sandwich pre-form was vacuum bagged. A flat aluminum

tool was covered with non-porous Teflon®. The panel was placed on the tool and a

second layer of non-porous Teflon® was applied over the specimen. In a typical vacuum

bagging procedure for composite panels, a layer of bleeder material is inserted to allow

excess resin to flow out and increase the fiber-volume fraction of the cured panel. In this

case, the bleeder material was intentionally omitted to allow excess resin to flow into the

structure. This excess resin helps to secure the pins in the facesheet. Next, a layer of

breather material was placed on top of the panel and tool to allow for a complete vacuum

over the entire sandwich panel. After placing dam tape around the perimeter of the tool,

the vacuum bag and valve are applied. Care is taken to ensure that the bag is applied so

Outer plies

Inner ply

“C-pinning” reinforcement

Outer plies

10

that it is kept as flat as possible to avoid wrinkling. If the bag wrinkles when the vacuum

is applied, a resin-rich crease will be formed in the sandwich panel. Prior to curing, the

complete vacuum bag assembly is tested to ensure a good seal. A typical panel was 5

inches by 10 inches and when cured would yield five specimens. A completed vacuum bag

assembly is shown in Figure 2-4.

Figure 2-4. Specimens with vacuum applied prior to curing in modified convection oven.

The sandwich panels were cured in a modified convection oven. An electronic

controller regulated the temperature and pressure during the curing cycle. The curing

profile used in this study is shown in Figure 2-5. A three stage curing cycle was used. In

the first stage, the vacuum was applied and the temperature ramped at 5 degrees per

minute until reaching 260º F. During the second stage, the vacuum is maintained and the

temperature is held constant at 260º F for 4.5 hours. The third stage was a cool-down

stage. The oven used in this study did not have the ability to adjust the cooling rate. The

specimens were cooled back to room temperature, and the vacuum was released.

11

0

50

100

150

200

250

300

0 100 200 300 400 500 600

Time (minutes)

Tem

pera

ture

(F

)

Figure 2-5 Curing cycle used for all specimens in this study.

After curing the 5 inch by 13 inch sandwich panels were cut into 4 inch by 2 inch

compression specimens using a diamond coated masonry saw. Prior to testing the

specimens were maintained in an environmental chamber for conditioning. The specimens

were conditioned at 23ºC and 50% relative humidity in accordance with ASTM C364.

12

CHAPTER 3 EXPERIMENTAL STUDY

3.1 Experimental Setup

All tests were performed on an MTI Phoenix 30,000 lb, screw-driven, testing

machine. A PC-based data acquisition system was used to collect load and displacement

information. A Revere 12,000 lbs. capacity load cell was used for load measurements. A

Lucas-Schaevitz, 2000HR LVDT was used for displacement measurements. Compression

tests were run in displacement control using the ASTM recommended crosshead velocity

of 0.02 inch/min.

The fixtures used in the edgewise compressive loading tests, shown in Figure 3-1,

were constructed to provide a fixed boundary condition to the bottom 0.5 inch of the

specimen. This configuration is consistent with both the previous experimental and

numerical studies on which this work is based. The fixture constructed for this study did

not apply lateral force to the specimen, it merely restricted lateral displacement of the

specimen.

The attachment of the LVDT to the fixture, shown in Figure 3-2, is an important

consideration in taking accurate displacement measurements. The fixture design allowed

for attachment of the LVDT as close as possible to the edge of the specimen. The upper

attachment point for the LVDT was integral with the plate that contacts directly with the

specimen. The lower LVDT bracket was adjustable to provide a means for alignment of

the core and rod. The lower bracket was attached to the side of the fixture just below the

bearing surface of the fixture. By attaching the LVDT close to the bearing surfaces, errors

due to the compliance of the fixtures and testing machine can be eliminated. Aluminum

13

tabs were attached to the specimens to prevent crushing of the ends of the facesheet. The

tabs were 0.125 inch thick, 0.5 inch tall, and 2.0 in wide.

Figure 3-1. The loading fixture used in the preliminary and edgewise compressive studies.

Without a specimen, the LVDT can be observed behind the fixture.

3.2 Preliminary Study Preliminary testing was performed using experimental sets defined in Avery

(1998). Four sets were chosen for this study. The sets chosen were considered

representative of the design space from Avery. The four sets were Set 6, 8, 13, and 15.

The properties for these sets are shown in Table 3-1. These four sets represented the

permutations of thick/thin facesheet and thick/thin core. This subset was chosen to

investigate the effects if pin reinforcement over a wide spectrum of sandwich structure

configurations.

14

Figure 3-2. A rear view of the loading fixture used in this study shows how the LVDT

was attached to avoid the introduction of machine compliance in the displacement measurements.

Figure 3-3. Edgewise compressive test specimen in the testing fixture.

15

The purpose of the preliminary study was to gain some initial understanding of the

effect of pin reinforcement on the buckling of delaminated sandwich beams. This

understanding was then used to develop an improved technique for reinforcing sandwich

beams. An experimental baseline was created by choosing a subset of the work done by

Avery (1998).

Table 3-1. Parameters used in preliminary study. The set numbers correspond to those

used in Avery (1998).

Set Facesheet thickness

(in) Core thickness

(in) Core density

(pcf)

Delamination length

(in)

6 3 x 0.0087 0.25 6 1.0

8 3 x 0.0087 0.50 3 2.0

13 7 x 0.0087 0.50 6 0.5

15 7 x 0.0087 0.25 3 1.5

Table 3-2. Experimental results for Z-pin reinforced specimens from Avery.

Set Non-reinforced (# of specimens)

COV

Graphite pin reinforced,

0.5 inch spacing (# of specimens)

COV % Increase in ultimate

load

6 495 (16) 12.4 637 (11) 19.5 28

8 320 (5) 8.4 495 (7) 24.4 54

16

During the preliminary study, both experimental and numerical studies were being

performed concurrently. While the numerical study included all four sets from Avery, the

preliminary experimental study focused on Sets 6 and 8. Both non-reinforced specimens

and specimens reinforced with Z-pins were considered in the preliminary study. Table 3-2

shows the experimental results for the four categories of specimens considered.

Much of the early work in this study involved specimens from Set 6. This set had

3 ply facesheets, a 0.25 inch core thickness, 6 pcf core density, and a 1 inch delamination

length. The average failure load for non-reinforced specimens was 495 lb/in. Specimens

reinforced with Z-pins at 0.5 inch pin spacing failed at 637 lb/in. This represented an

average increase in ultimate load of 28%. Some typical load vs. end-shortening curves for

Set 6 are shown in Figure 3-4. The failure mode for all specimens was pin pullout.

Before failure, local buckling occurred between adjacent pins. Visually, a pin cushion

effect could be observed. The pins were providing reinforcement to the structure locally,

however, transverse displacement between the pins was not restricted. Failure would

occur when the pin force reached the critical pin pullout force for the facesheet thickness.

Specimens for Set 8 from Avery were also tested. This set had 3 ply facesheet

thickness, 3.0 pcf core density, 0.5 inch core thickness, and a 2 inch delamination length.

Non-reinforced specimens from this set failed at only 320 lb/in. Reinforcing the specimens

with 0.5 inch reinforcement spacing increased the failure load to 495 lb/in. Z-pin

reinforcement was able to provide a 54% increase in ultimate load.

17

0

100

200

300

400

500

600

700

0 0.01 0.02 0.03 0.04 0.05

End-shortening (in)

Lo

ad (

lb/in

)

Figure 3-4. Typical load vs. end-shortening curves for Set 6 Z-pin reinforced and non-reinforced specimens.

During the course of this study, a new reinforcement technique was developed.

“C-pinning”, as described in Chapter 2, involves inserting reinforcement during the lay-up

of the sandwich structure. The reinforcement is co-cured with the sandwich panel. The

resulting pins are integral with both facesheets, significantly increasing the critical pin

pullout force.

Set 6 specimens reinforced with the “C-pinning” technique showed significant

increases in ultimate load. These results are shown in Table 3-3. The ultimate failure load

of specimens with 0.5 inch reinforcement spacing was 65% higher than the non-reinforced

specimens. Specimens with 0.25 inch reinforcement spacing exhibited an increase of

257%. The ultimate failure load used for comparisons is the average failure load for non-

reinforced specimens that came from the same panels as the “C-pinning” reinforced

specimens themselves.

The failure mechanism of “C-pinning” reinforced specimens was different from the

Z-pin reinforced specimens. While a “pin cushion” effect was visible in the Z-pin

18

reinforced specimens, this was absent in the “C-pinning” specimens. The effect of

reinforcement was not as localized as it had been in earlier tests. The “C-pinning”

specimens actually restricted the local buckling of the delaminated region. There was a

combination of local buckling in the delaminated region as well as global buckling of the

beam itself.

The local buckling effects seen in the Z-pin reinforced specimens was not totally

absent in the C-pin reinforced specimens. It was present during the test but was not the

trigger that led to the collapse of the sandwich beams. Two competing modes were

present during the tests, a local buckling of the delaminated portion of the facesheet and a

global buckling of the beam. This reinforcement method restricted the displacement of the

facesheet and arrested the local buckling mode.

Table 3-3. Failure load and coefficient of variations for Set 6 specimens with “C-pinning” reinforcement.

Reinforcement spacing (inch)

Failure load (lb/in)

COV (%)

0.25 1252 6.4

0.5 580 10

Non-reinforced 350 3.1

19

0

200

400

600

800

1000

1200

1400

0 0.02 0.04 0.06 0.08

End-shortening (in)

Lo

ad (

lb/in

)

Figure 3-5. Typical load vs. end-shortening curves for Set 6 with and without “C-

pinning” reinforcement. The high-density reinforcement is far superior to both the low density reinforcement as well as the non-reinforced.

3.3 Edgewise Compressive Loading

Avery used a Graeco-Latin Square factorial plan to organize tests. This approach

provided a method to determine the influence of four parameters on the ultimate load.

The four parameters investigated were facesheet thickness, core thickness, core density,

and delamination length. Analysis of the results was made difficult by the fact that no two

experimental sets differed by only one parameter. It was impossible to make a one-to-one

comparison between any two data sets.

Without a strong foundation of understanding of buckling of delaminated sandwich

structures, a parametric study of their behavior is difficult to conduct. The inclusion of pin

reinforcement into sandwich structures only increases the complexity of their behavior.

To better understand the buckling of reinforced sandwich structures, a simpler, more

streamlined test matrix was created. The test matrix is shown in Table 3-4. In this test

20

matrix, delamination length and pin spacing were the only parameters varied. Based on

the results of the preliminary study, “C-pinning” was chosen as the reinforcement

technique to be investigated. The delamination lengths considered were 0.5, 1.0, and 1.5

inch. The pin spacings considered in this study were 0.25 and 0.5 inch. Non-reinforced,

no-delamination specimens were included to provide a baseline. A few off-design sets

were included to investigate the influence of thick facesheets on this particular type of

reinforced sandwich beam. All specimens in the current study have 3 ply facesheet, a core

thickness of 0.375 inch, and a core density of 6 pcf. The dimensions for all specimens

were 2 inch wide by 4 inch tall. Experimental results are shown in Table 3-5.

Typical load vs. end-shortening curves for all experimental sets in the edgewise

compressive loading study are shown in Figure 3-6 through Figure 3-17.

As expected, the ultimate load of a delaminated sandwich beam decreased with

increasing delamination length. In the case of low density reinforcement, the short

delamination specimens (H30) carried an ultimate load of 997 lb/in. A medium length

delamination (H31) reduced the ultimate load to 965 lb/in. The ultimate load dropped to

841 lb/in. when a long delamination (H35) was created. In the case of high density reinforcement, the benefits of translaminar

reinforcements were similar. A specimen with a short delamination (Q30) had an ultimate

load of 1524 lb/in. The medium delamination case (Q31) carried 1346 lb/in. A high

density reinforcement, long delamination (Q35) was able to carry 1158 lb/in.

The ultimate post-buckling load also increased as pin density increased. A non-

reinforced sandwich beam with a short delamination (N30) had an ultimate load of 962

lb/in. This is just 62% of the non-delaminated beam’s ultimate load of 1537 lb/in. With

low density pin reinforcement (H30), the ultimate load increased slightly to 997 lb/in. A

significant increase was observed when the pin spacing was decreased to 0.25 in. A

21

sandwich beam with high density pin reinforcement had an ultimate load of 1524 lb/in.

This trend of increasing load with increasing reinforcement density was repeated over all

delamination lengths in this study.

In all cases, the failure of these specimens was sudden and catastrophic. There

were no outward signs of failure prior to collapse. In some cases, intermittent internal

cracking could be heard prior to failure. This is most likely due to minor variations in the

fixation of the pin/facesheet interface. Pins with poor interface conditions would tear

away from the facesheet internally. Ultimately, a failure mechanism similar to pin-pullout

occurred. Rather than a cylindrical Z-pin being pulled from the facesheet, the head of the

“C-pinning” reinforcement was torn from beneath the facesheet.

Crack propagation along the facesheet/core interface occurred during testing.

Whether or not crack propagation occurred prior to collapse of the sandwich beam could

not be determined experimentally.

22

Table 3-4. Test matrix used during edgewise compressive loading study.

Set Facesheet Thickness (in) Reinforcement spacing

(in) Delamination length

(in)

ND 3 x 0.0087 n/a n/a

N30 3 x 0.0087 n/a 0.50

N31 3 x 0.0087 n/a 1.00

N35 3 x 0.0087 n/a 1.50

Q30 3 x 0.0087 0.25 0.50

Q31 3 x 0.0087 0.25 1.00

Q35 3 x 0.0087 0.25 1.50

H30 3 x 0.0087 0.50 0.50

H31 3 x 0.0087 0.50 1.00

H35 3 x 0.0087 0.50 1.50

N75 7 x 0.0087 n/a 1.50

Q75 7 x 0.0087 0.25 1.50

23

Table 3-5. Experimental results for edgewise compressive loading study.

Experimental Set Failure load

(lb/in) # of specimens COV

ND 1537 4 12.5

N30 962 5 24.1

N31 579 5 10.4

N35 681 5 23.4

N75 2055 5 22.4

Q30 1524 4 30.7

Q31 1346 5 20.8

Q35 1158 5 8.52

Q75 3416 5 7.20

H30 997 5 24.6

H31 965 5 7.0

H35 841 5 16.0

24

Panel ND

0

500

1000

1500

2000

2500

3000

0 0.01 0.02 0.03 0.04 0.05 0.06

End shortening (in)

Lo

ad (

lb/in

) ND_01

ND_02

ND_03

ND_04

ND_05

Figure 3-6 Load vs. end-shortening curves for non-reinforced, no-delamination specimens with 3 ply facesheets (ND).

Panel N75

0

500

1000

1500

2000

2500

3000

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

End shortening (in)

Lo

ad (

lb/in

) N75_01

N75_02

N75_03

N75_04

N75_05

Figure 3-7. Load vs. end-shortening curves for non-reinforced specimens with 7 ply

facesheets and a 1.5 inch delamination (N75).

25

N30 Panel

0

200

400

600

800

1000

1200

1400

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

End shortening (in)

Load

(lb

/in) N30_01

N30_02

N30_03

N30_04

N30_05

Figure 3-8. Load vs. end-shortening curves for non-reinforced specimens with 3 ply

facesheets and a 0.5 inch delamination (N30).

N31 Panel

0

100

200

300

400

500

600

700

0 0.01 0.02 0.03 0.04 0.05 0.06

End shortening (in)

Lo

ad (

lb/in

)

N31_01

N31_02

N31_03

N31_04

N31_05

Figure 3-9. Load vs. end-shortening curves for non-reinforced specimens with 3 ply

facesheets and a 1 inch delamination (N31).

26

N35 Panel

0

100

200

300

400

500

600

700

800

900

1000

0 0.01 0.02 0.03 0.04 0.05 0.06

End shortening (in)

Lo

ad (

lb/in

) N35_01

N35_02

N35_03

N35_04

N35_05

Figure 3-10. Load vs. end-shortening curves for non-reinforced specimens with 3 ply

facesheets and a 1.5 inch delamination (N35).

H30 Panel

0

200

400

600

800

1000

1200

1400

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

End shortening (in)

Lo

ad (

lb/in

) H30_01

H30_02

H30_03

H30_04

H30_05

Figure 3-11. Load vs. end-shortening curves for specimens with 0.5 inch reinforcement

spacing, 3 ply facesheets and a 0.5 inch delamination (H30).

27

H31 Panel

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05

End shortening (in)

Lo

ad (

lb/in

)

H31_01

H31_02

H31_03

H31_04

H31_05

Figure 3-12. Load vs. end-shortening curves for specimens with 0.5 inch reinforcement

spacing, 3 ply facesheets and a 1 inch delamination (H31).

H35 Panel

0

200

400

600

800

1000

1200

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

End shortening (in)

Lo

ad (

lb/in

) H35_01

H35_02

H35_03

H35_04

H35_05

Figure 3-13. Load vs. end-shortening curves for specimens with 0.5 inch reinforcement

spacing, 3 ply facesheets and a 1.5 inch delamination (H35).

28

Panel Q30

0

500

1000

1500

2000

2500

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

End shortening (in)

Lo

ad (

lb/in

) Q30_02

Q30_03

Q30_04

Q30_05

Figure 3-14. Load vs. end-shortening curves for specimens with 0.25 inch reinforcement

spacing, 3 ply facesheets and a 0.5 inch delamination (Q30).

Panel Q31

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

End shortening (in)

Lo

ad (

lb/in

) Q31_01

Q31_02

Q31_03

Q31_04

Q31_05

Figure 3-15. Load vs. end-shortening curves for specimens with 0.25 inch reinforcement

spacing, 3 ply facesheets and a 1 inch delamination (Q31).

29

Panel Q35

0

200

400

600

800

1000

1200

1400

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

End shortening (in)

Lo

ad (

lb/in

)

Q35_01

Q35_02

Q35_03

Q35_04

Q35_05

Figure 3-16. Load vs. end-shortening curves for specimens with 0.25 inch reinforcement

spacing, 3 ply facesheets and a 1.5 inch delamination (Q35).

Panel Q75

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

End shortening (in)

Lo

ad (

lb/in

)

Q75_01

Q75_02

Q75_03

Q75_04

Q75_05

Figure 3-17. Load vs. end-shortening curves for specimens with 0.25 inch reinforcement

spacing, 7 ply facesheets and a 1.5 inch delamination (Q75).

30

3.4 Circular Delamination Testing

The delamination introduced during both the preliminary study and the edgewise

compressive loading study was an edge-to-edge delamination at the facesheet/core

interface. This type of delamination problem is useful for research purposes but is not

necessarily representative of delamination due to damage. Typical delamination in

structures that are in service are, more often, circular in shape and internal to the

structure. In the case of aerospace sandwich structures, these types of delaminations are

often the result of impact damage such as bird strikes or tool drops. Since these types of

damage are difficult to detect and repair, it is important for the sandwich structure to have

increased resistance to impact damage.

Fabrication of circular delamination specimens was similar to that of the edge-to-

edge delamination specimens. Rather than inserting a Teflon® strip the length of the

panel, a 1 inch circular piece of non-porous Teflon® was placed onto the facesheet prior

to applying the facesheet to the core. The outer surface of the facesheet was marked so

that the position of the delamination was known after the facesheet was applied. Once the

facesheet was applied, the delamination was no longer visible. After the panel was cured,

specimens were cut based on the facesheet markings. Using the outer markings assured

that the delamination was in the center of the specimen. The outer markings also served

as a guide when inserting pin reinforcement. Earlier results had shown that pin placement

can have a measurable impact on the performance of the reinforcement.

Circular delamination specimens had the same material properties as the specimens

presented earlier. The size of the circular delamination specimens was increased to

accommodate an internal delamination. The width of the specimens was 3 inch. This

larger width allowed for a 1 inch delamination with 1 inch of undamaged facesheet/core

interface from the delamination to the free edge. Creating a 1 inch delamination in the

previous specimen configuration of 2 inch width would be subject to edge effects and not

31

accurately portray the full-scale behavior of this type of sandwich structure.

The panel nomenclature used for this part of the study was as follows: C3N for

non-reinforced circular delamination panels, C3H for 0.5 inch reinforcement spacing

circular delamination panels, and C3Q for 0.25 inch reinforcement spacing circular

delamination panels.

The experimental results of testing circular delamination panels are shown in Table

3-6. These results were consistent with those in the earlier studies. Non-reinforced

specimens carried an ultimate load of 1210 lb/in. As was the case earlier, the reinforced

specimens showed a significant increase in capacity. Circular delamination specimens with

0.5 in reinforcement spacing had an ultimate load of 1630 lb/in. High density pin

reinforced, circular delamination specimens (C3Q) had an ultimate load of 1611 lb/in.

Load vs. deflection curves for all circular delamination specimens are shown in

Figure 3-18 through Figure 3-20.

Table 3-6. Experimental results for circular delamination specimens.

Experimental Set Failure load (lb/in) (# of specimens)

COV

C3N 1210 (3)

22.7

C3H 1630 (2)

15.8

C3Q 1611 (3)

4.7

32

Panel C3N

0

200

400

600

800

1000

1200

1400

1600

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

End shortening (in)

Lo

ad (

lb/in

)

C3N_01

C3N_02

C3N_03

Figure 3-18. Load vs. deflection curves for non-reinforced specimens with 3 ply

facesheets and a 1 inch circular delamination (C3N).

Panel C3H

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

End shortening (in)

Lo

ad (

lb/in

)

C3H_01

C3H_02

C3H_03

(facesheet cracked near top end)

Figure 3-19. Load vs. deflection curves for specimens with 0.5 inch reinforcement

spacing, 3 ply facesheets and a 1 inch circular delamination (C3H).

33

Panel C3Q

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.01 0.02 0.03 0.04 0.05 0.06

End shortening (in)

Lo

ad (

lb/in

)

C3Q_01

C3Q_02

C3Q_03

(tab failure)

Figure 3-20. Load vs. deflection curves for specimens with 0.25 inch reinforcement

spacing, 3 ply facesheets and a 1 inch circular delamination (C3Q).

3.5 Effect of Reinforcement on Mode I Fracture Toughness

The issue of the effect of pin reinforcement on the Mode I Fracture Toughness of a

composite sandwich structure was also considered in this study. Specimens were

fabricated with a 1 inch delamination at one end by placing a strip of non-porous Teflon

at the facesheet/core interface. Each specimen was 1 inch wide and 6 inches long. A

double cantilever beam test fixture was used to apply the loads.

The results were consistent with the author’s expectations. Non-reinforced and

reinforced specimens were fabricated using a core material with a density of 3 pcf. Non-

reinforced specimens using a core material with a density of 6 pcf were also fabricated.

The non-reinforced 3 pcf specimens had a fracture toughness of 6.0035 lb-in/in2. Low

density pin reinforcement increased the fracture toughness by 21% to 7.29325 lb-in/in2. A

34

more significant increase was observed with high density (1/4 inch pin spacing). High

density reinforced specimens had a fracture toughness of 9.20925 lb-in/in2, a 53% increase

over the non-reinforced specimens.

The 6 pcf (stiff) core material specimens had an average fracture toughness of

3.598 lb-in/in2. This was only 60% of the 3 pcf core material specimens. Lower density

core materials tend to be more compliant. This compliance absorbs energy under loading

and contributes to a higher fracture toughness. The stiff core does not deform and the

energy is concentrated at the facesheet/core interface. The results for the 6 pcf core

material represent the average of 6 specimens. The test sets that used 3 pcf core material

represent the average of 8 specimens per set.

Mean Value for Fracture Toughness

0

1

2

3

4

5

6

7

8

9

10

G (

lb-i

n/in

2 ) 3 pcf non-reinforced

3 pcf 1/2 in spacing

3 pcf 1/4 in spacing

6 pcf non-reinforced

Figure 3-21 Average experimental results for fracture toughness of pin reinforced and non-reinforced specimens.

35

3.6 Experimental Results/Discussion

This study focuses on increasing the post-buckling load of delaminated sandwich

beams. In order to understand the effect of translaminar reinforcement, it is important not

only to know the failure load of the delaminated beam but also to know the theoretical

failure for the non-delaminated case. Using these values, it is possible to evaluate the

effectiveness of the reinforcement techniques presented. Simply comparing the reinforced

specimen to the non-reinforced only gives insight into the increase in ultimate load from

the damaged state. To understand how effective a technique is in terms of restoring the

structure to it’s original capacity, the ultimate failure load of the undamaged specimen

must also be considered. In the next chapter, a finite element model will be developed to

predict the response of sandwich beams with and without reinforcement or delamination.

Whitney (1987) presents the following equation for the critical buckling load of an

undamaged sandwich composite.

+−

=2

2

1

1'

ππ

SS

crNNcr

where

213

112

2

11 ,'ahG

DS

aDcrN ==

π

Theoretical buckling loads are shown in Table 3-7. Values for specimens from both the

preliminary study and the edgewise compressive study are presented. The values

presented are ultimate buckling loads for specimens with the same geometric configuration

as the states set but without the delamination. An ideal reinforcement technique could

restore the delaminated sandwich beam to its theoretical maximum buckling load.

36

Table 3-7. Theoretical buckling loads for specimens from preliminary and edgewise

compressive studies. These sets listed in the figure represent the same geometric configurations as previous sets without delaminations.

Set Buckling load

(lb/in)

6 2323

8 8905

ND 5092

ND7 12113

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.5 1 1.5 2

Delamination length (in)

Lo

ad (

lb/in

)

N

H

Q

Figure 3-22. Graphic representation of the relationship between ultimate load and delamination length.

37

The technique of inserting Z-pins through-the-thickness of the sandwich composite

was able to increase the ultimate load of a delaminated sandwich beam. However, pin

pullout type failures presented some limitations to their ability to improve the load

capacity of the beam. Two important curves can be derived from the results of this study.

The first curve, shown in Figure 3-22, represents the relationship between load and

delamination length. The second curve, shown in Figure 3-23, illustrates the relationship

between load and reinforcement spacing.

In a Z-pin reinforced sandwich structure, the Z-pins transfer load from the

damaged facesheet to the undamaged facesheet. In the case of Z-pins, this load transfer is

done by shear. The critical pin pullout force is a function of the surface area of the head

of the pin. There are basically two options to increase the critical force for this type of

pin: increase the diameter of the pin or increase the density of reinforcement. Neither of

these alternatives are particularly

desirable for laminated composites. In the case of lightweight aerospace structures,

reducing the thickness (and therefore the weight) of the facesheet is a design goal. This

presents the designer with a tradeoff: reducing the thickness reduces weight but decreases

the effectiveness of the translaminar reinforcement.

The preliminary study showed that translaminar reinforcements can be effective in

increasing the ultimate buckling load, however they do not present an ideal solution. The

mechanism by which the pin transfers load, as discussed above, presents one major limit to

the effectiveness of this technique. Another limitation lies in the fact that the Z-pins

protrude entirely through-the-thickness of the laminate. Many applications for structural

38

sandwich composites are in pressurized structures, such as fuel tanks. Inserting

reinforcement through the vessel wall to provide translaminar reinforcement creates other

problems. The point where the pin protrudes through the facesheet becomes a crack

nucleation site. Again, a designer is faced with an undesirable decision. If the pin

diameter is increased the through-the-thickness properties, the amount of damage done to

the laminate is increased. All of the techniques described reduced the in-plane properties

of the composite to some extent.

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.2 0.4 0.6 0.8 1 1.2

Reinforcement spacing (in)

Lo

ad (

lb/in

)

0.5 in

1.0 in

1.5

Figure 3-23. Graphic representation of the relationship between ultimate load and

reinforcement spacing.

The “C-pinning” technique was developed during this study to overcome some of

the limitations of Z-pin reinforcement. By fabricating specimens such that the

reinforcement is integral with the facesheet, the critical pin pullout force is no longer a

function of the surface area of the pin. Since the pin is internal to the facesheet, the

stresses being developed are distributed over a larger portion of the structure. The

39

laminate/pin/laminate interface is much stronger than the pin/facesheet interface. In this

study, the facesheets were relatively thin. In a large structure with thick facesheets, the

designer has the depth of reinforcement as an additional design variable when developing a

reinforced structure.

By co-curing the “C-pinning” reinforcement with the sandwich panel, problems

associated with fabrication of Z-pin reinforced panels can be avoided. Adhesion problems

between the cured Z-pins and the uncured sandwich preform can be avoided.

The advantages of using “C-pinning” reinforced was evident in the experimental

data. By using high density reinforcement, a sandwich beam with a short delamination

was able to carry 99% of the ultimate load of the undamaged sandwich beam.

The experimental results for the edgewise compressive study showed that C-

pinning has promise as a method of translaminar reinforcement. There was one anomaly

in the non-reinforced data. The results for Sets N30, N31, and N35 should have been a

monotonically decreasing function. The ultimate load should have decreased as

delamination length increased. The expected result was realized in all other data sets. In

the nonreinforced data, this was not the case. There are two possible explanations, either

the N31 value is too low or the N35 value is too high.

One possible explanation for the discrepancy is the influence of the fixture on

specimens with a long delamination. In this study, the overall specimen length was 4

inches. With 0.5 inch of fixed boundary condition on either end, there was only 3 inches

of unsupported distance. In specimens with a 1.5 inch delamination, there is only 0.75

inch between the edge of the delamination and the fixture. This is in the ideal case. If the

delamination is slightly longer is either direction this problem will be exaggerated. It is

possible when working with honeycomb core that slight misalignment of the Teflon strip

or poor bonding between the core and facesheet can result in a delamination that is slightly

longer than predicted. If the poor adhesion takes place, the next adhesive boundary is one

40

cell diameter (0.125 inch) away. As the distance between the edge of the delamination

and the fixture decreases, the influence of the fixed boundary condition changes. The

specimen will become artificially stiffer as the distance decreases.

The trends evident in the edgewise compressive study were reflected in the circular

delamination study. The results indicate that the increases in ultimate post-buckling load

observed in the edge-to-edge delamination panels can be realized in specimens that more

closely mimic real world damage. Specimens with 0.5 inch reinforcement spacing showed

a 34.7% increase in ultimate load. The trend of increasing ultimate load with increasing

pin density did not hold in the case of circular delamination specimens. Circular

delamination specimens showed only a 33% increase in ultimate load. This result would

suggest that there is an upper limit to pin density. Beyond this upper limit, the pins no

longer increase the ultimate post-buckling load. The data set available from this study is

not large enough to develop a conclusion about the relationship between pin density and

allowable crack length.

One factor that was not studied was the effect that the pins had on the in-plane

properties of the sandwich beams. The failure modes observed during the testing indicate

that this did not play a role in the failure of the specimens studied. However, in order to

develop a complete understanding of the buckling of delaminated sandwich beams, this

issue should be explored.

During the experimental study, pin reinforcement was repeatedly shown to

increase the ultimate post-buckling load of a sandwich beam. The “C-pinning” technique

developed during this study proved to be the most effective technique for reinforcing these

types of structures.

41

CHAPTER 4 FINITE ELEMENT MODELING

A detailed finite element analysis of the post-buckling behavior of delaminated

sandwich beams was conducted in conjunction with the experimental study described

earlier. The purpose of the finite element analysis was to develop a model that could

accurately predict the post-buckling behavior of a delaminated sandwich beam. Another

goal of the study was to evaluate the effect that geometric parameters, such as

delamination length and reinforcement spacing, had on the ultimate buckling load of the

beams.

The models in this study were generated using MCS/PATRAN. The analysis and

post-processing of finite element results were performed using ABAQUS/Standard and

ABAQUS/Post, respectively.

4.1 Model Generation

The generation of the finite element models used in this study can be broken into

four main steps: geometric modeling, element generation, load/boundary conditions, and

material modeling. The first three steps will be covered in this section. The formulation

of an appropriate material model for sandwich beams is considered in the following

chapter.

Geometric modeling involves the creation of points, curves, and surfaces that

define the shape and dimensions of the specimen being studied. All specimens in this

42

study were 2 inches by 4 inches. The thickness dimension of the specimens was varied

during the preliminary study. Core thickness and facesheet thickness were two of the

parameters varied during the preliminary study. The combination of these two

parameters determined the overall thickness of the specimen. During the edgewise

compressive study, the core thickness and facesheet thickness did not vary. All

specimens had a core thickness of 0.375 inch and a facesheet thickness of 3 plies (0.0261

inch).

The first step in building the model is to create points by assigning a set of

Cartesian coordinates that describe the location of the point. Once the appropriate

number of points has been created, the points are then connected by curves. The curves

are created by specifying both an initial and a terminating point.

At this point in the process, a wireframe representation of the specimen exists. To

move from a wireframe representation to a solid model, the curves are used to define

surfaces. The edge method was used in this study. In this method, four edges are

specified to define the surface boundaries. The advantage of the edge method is that it

allows for a surface to be generated from four curves without regard to the normal vector

for each curve. A positive, normal vector is assumed and combined with the four

specified curves to generate a surface. After the surfaces have been created, the

geometric definition of the model is complete.

Once the geometry has been established, the finite element work begins. Creating

a finite element mesh in PATRAN is a two-step process. First, a mesh seed is defined for

every curve in the model. A mesh seed divides each curve into segments. These

segments will determine the shape and distribution of the mesh.

43

When creating a mesh seed, the user has the option of using a uniform mesh seed,

a one-way bias seed, or a two-way bias seed. In order to create a purely rectangular mesh

in which all the elements have the same size, a uniform mesh would be applied to all

sides of the surface. Using a one-way bias mesh seed allows for the creation of mesh

refiement toward one end of a surface while leaving a sparse mesh at the opposite end.

This technique of biasing is beneficial by allowing a more localized mesh refinement.

Rather than increase drastically the computational effort required by refining the mesh

over the entire model, a one-way bias mesh seed can refine the mesh in a particular

region of interest. Two-way bias mesh seed works in much the same way. The main

difference between one-way and two-way bias is that the mesh can be refined in both

directions simultaneously. Care must be taken in defining the mesh seed to avoid

creating elements that have a high aspect ratio.

The second step in the finite element phase of the model generation is to create

the actual mesh. The specimens in this study were modeled using eight-node, bi-

quadratic plain strain elements. All the sandwich beam models in this study have a unit

width. The assumption of a plane strain condition is consistent with the structural

applications of composite sandwich structures.

After creating a mesh on each surface, a number of duplicate nodes existed. To

remove these duplicate nodes, an "equivalence" method was applied. During

equivalencing, the model is traversed and any nodes that fall within a tolerance cube are

merged into one node. The tolerance value can be specified by the user in terms of the

dimensional units of the model. If a large number of nodes will be collapsed, PATRAN

generates a warning message to verify that the tolerance value is correct.

44

Interface cracks can be inserted using the "equivalence method". When removing

duplicates nodes, the user has the option to specify both a value for the tolerance cube

and a list of nodes to exclude from the "equivalence" operation. In the current study, the

nodes at the facesheet/core interface that fell within the crack boundaries were excluded

from this process. All other duplicate nodes along the interface were removed.

The load and boundary conditions used in the models were intended to represent

the actual conditions from the experiments. Figure 4.1 shows both the experimental

setup and the finite element model equivalent. In the model, one end of the specimen

was fixed and lateral displacement was restricted for 0.5 inches along either side. The

other end of the specimen was modeled to correspond to the crosshead end of the

experimental specimen. In order to distribute the load over the entire thickness of the

model, a multi-point constraint was used. A linear relationship was created between all

the nodes along the left end of the model and the node at the top left corner of the model.

This created a dependency in which all nodes along the edge were forced to have the

same u displacement as the one independent node. Any displacement boundary condition

could then be applied to the independent node. This type of boundary condition

simplifies greatly the modeling of axial compressive loading fixtures.

Three different techniques were used in understanding the effects of pin

reinforcement. In the first model, the pins were modeled as truss elements and located

between the inner surfaces of the face sheets. These pins were normal to the facesheets.

This model was designed to create an interaction between the facesheets. This concept

was based on the idea that local buckling of the delaminated facesheet would create an

axial force in the pin, which would then be transferred to the undamaged facesheet. This

45

reinforcement model produced only minor increases in load carrying capacity, regardless

of pin size or spacing.

Figure 4-1. Comparison of load/boundary conditions in experiments and FEM. Length

of constrained end was 0.5 inch.

In the second model, the reinforcement was inclined with respect to the normal to

the facesheets. This arrangement created a truss type structure within the sandwich

beam. Although this arrangement could not be realized in practice since the damage

done to the core would far outweigh any advantage the reinforcement might provide, it

did show a significant increase in the load carrying capacity. This model yielded

tremendous insight into the behavior of the sandwich structure with translaminar

reinforcements. This model indicates that the effect of transverse stiffness of the

reinforcement, rather than the axial stiffness of the reinforcement, is critical to increasing

the compressive load carrying capacity of the beam.

46

In the third model, the reinforcement was modeled as shear-deformable beam

elements, thus providing flexural as well as transverse shear stiffness. The reinforcement

penetrated both facesheets thus connecting the outer surfaces of both facesheets and

restricted rotation at the pin/facesheet connection. This model closely represents the test

specimens. Further, the interaction between the facesheets and reinforcement can be

predicted in this model. Since reinforcement now protruding into the facesheet, the beam

element model also provided additional information about the effect pin reinforcement

had on the stress distribution in the facesheet.

In all models, the pins were inserted at either 0.25 or 0.5 inch spacing in a rectangular array.

4.2 Material Modeling

The ability to accurately model the behavior of sandwich structures has been

hindered by the difficulty in describing the behavior of the core material. This study, like

other previous studies (Narayanan, 2000), attempts to model the core as a continuum. In

actuality, honeycomb core materials are a structure rather than a continuum. Honeycomb

structures undergo phenomenon such as buckling or cell wall collapse that cannot be

explicitly captured in a continuum model. Rather, the continuum model is adjusted so

that the structural effects are mimicked.

During the preliminary study, the facesheets were modeled as isotropic materials.

While the core material was modeled as an elastic orthotopic material. The effects of

plasticity were not considered during this study. The numerical results of the preliminary

study are shown in Table 4-1. The correlation between the results in Table 4-1 and

experimental results is poor. From these results, it was clear that a better representation

47

of the material behavior needs to be develop. The test matrix of the edgewise

compressive loading study was determined to be a better test bed for development of a

new approach.

Table 4-1. FEM results for preliminary study

Set 6 8 13 15

0.25 inch pin spacing

2156 1256 9734 3161

0.5 inch pin spacing

943 678 8652 1964

No pins 894 398 8512 1613

During the edgewise compressive study, the addition of plasticity in the material

model was explored. The load/displacements results from early models were

qualitatively similar to experimental results. However, the finite element models were

failing at consistently higher loads. A comparison of experimental results and linear

elastic finite element models is shown in Figure 4-2. Plastic deformation in either the

core, the facesheet or both were considered as possible explanations for the premature

failure.

The simplest option for describing plasticity in an ABAQUS model is to use the

default *PLASTIC option . The default case for this commands assumes isotropic

plasticity. The arguments that must be specified are yield stress and plastic strain. This

option allows for the definition of the flow rule as a function of temperature, however,

temperature dependence was not considered in this study. With only one yield

48

stress/plastic strain pair specified, an elastic-perfectly plastic material model is created.

A more complex flow rule can be created by specifying more yield stress/plastic strain

pairs. Since the complex flow rule is defined in terms of discrete values, ABAQUS will

interpolate linearly between specified pairs.

0

200

400

600

800

1000

1200

1400

0.00 0.01 0.02 0.03 0.04 0.05

Displacement (in)

Lo

ad (

lb/in

)

FEM

Experimental

Figure 4-2. Experimental and linear elastic finite element results were only qualitatively

similar in the preliminary study. To determine the yield stress for material model, the no delamination case was

used as a reference case. The experimental failure load for this set was 1537 lb/in. The

models used to determine the proper yield stress values for facesheet plasticity and core

plasticity are shown in Table 4-2 and Table 4-3, respectively.

Determining the appropriate yield stress for facesheet plasticity involved

analyzing models with yield stresses ranging from 15 ksi to 60 ksi. An iterative

49

approach was used to bracket the optimal value. In the case of facesheet plasticity, the

optimal yield stress was determined to be 28 ksi. A model using only facesheet plasticity

and a yield stress of 28 ksi had an ultimate load of 1534 lb/in.

Determining the appropriate yield stress for core plasticity models followed the

same approach. Yield stresses ranging from 15 psi to 40 psi were analyzed until a value

of 34 ksi. was determined to be optimal. A model using only core plasticity and a yield

stress of 34 psi had an ultimate load of 1524 lb/in.

The default plasticity option uses isotropic plasticity regardless of what type of

elastic material definition is present. At the onset of yield, the material switches from an

elastic orthotopic material to an isotropic plastic material. This method requires that a

material yield the same in all directions. While this technique can capture the onset of

yield, a method to accurately represent the post-yield behavior must be explored.

Table 4-2. Determination of ultimate yield stress using facesheet plasticity in non-delaminated model.

Yield stress (ksi)

Failure load (lb)

15 854

25 1380

27 1483

28 1534

30 1636

45 2401

60 3175

50

Table 4-3. Determination of ultimate yield stress using core plasticity in non-delaminated model.

Yield stress

(psi) Failure load

(lb/in)

15 795

20 1021

25 1196

30 1394

34 1524

35 1558

40 1709

4.3 Finite Element Analysis

The finite element analyses performed in this study fall into two types: linear

buckling analysis and non-linear post-buckling analysis. The non-linear post-buckling

analyses including both geometrical and material non-linearities.

The linear buckling analysis demonstrated the effect of delamination length and

reinforcement spacing on the buckling loads and mode shapes of the specimens. During

the linear buckling analysis, the first three eigenvalues and their corresponding mode

shapes were obtained. Some typical mode shapes are shown in Figure 4-3. These mode

shapes would be used to create imperfections to trigger buckling in the non-linear

analysis.

The non-linear post-buckling analysis was performed to simulate compressive

testing of delaminated sandwich beams with and without reinforcement. Most of the

analyses were performed according to the following method:

1) An eigenvalue buckling analysis was performed to determine the possible buckling

loads and mode shapes.

51

2) The mode shape from the linear buckling analyses was used as an imperfection in the

non-linear post-buckling analysis. The imperfection created a perturbed geometry

required for the post-buckling analysis. To create this imperfection, the mode shape

must be multiplied by an appropriate scale factor. The scale factor used in this study was

based on facesheet thickness. Typically 10% of the facesheet thickness was sufficient to

trigger buckling and obtain convergence of the solution.

3) A geometrically non-linear load displacement analysis of the delaminated sandwich

beam was performed using the Riks method.

Figure 4-3. Typical mode shapes obtained during linear buckling analysis.

52

The Riks algorithm is an incremental, iterative solution strategy to solve

geometrically non-linear problems in buckling and post-buckling. The Riks algorithm is

based on the Newton-Rhapson method. This method is used in non-linear finite element

analysis because it is both accurate and minimizes computation time. Rather than apply

an incremental displacement and determine the load at which a stable equilibrium is

obtained, the Riks algorithm using load magnitude as an additional unknown. In order to

track the progress of the solution, an additional quantity known as the 'arc length' is

maintained. This algorithm can provide solution for both stable and unstable problems.

Loading in the Riks algorithm is proportional. All loads that exist at the

beginning of an analysis step will be treated by ABAQUS as "dead" loads. Loads applied

during the current step will be ramped according to the load proportionality factor from

the "dead" load value to the reference load value. There are several cases in which the

analysis will be terminated:

1) The minimum arc length value has been violated. 2) The maximum arc length value has been violated. 3) The reference load has been reached. 4) The maximum numbers of iterations has been reached. When solving this type of problem, the tangent stiffness matrix will become

singular when the solution reaches an instability point. Conventional algorithms have

difficulty in traversing these instability points. A goal of non-linear finite element

analysis is to be able to trace both the pre and post-critical load path of the structure. By

using load magnitude as an additional unknown, the Riks algorithm is able to traverse

these instability points.

Not all models were analyzed using the imperfection-based method. A second,

similar method was used to model the effect of misalignment of a specimen during

53

testing. In this case, no linear buckling analysis was performed. Instead, an additional

loading step was added to non-linear model. This additional load step consisted of a

lateral displacement of one end of the specimen. The displacement was intended to

simulate the effect of misalignment of the loading fixture during compressive testing.

Figure 4-4 shows the non-linear model after the initial misalignment has been applied.

The displacement of the 'misaligned' model in Figure 4-4 has been magnified for

visibility.

Figure 4-4. Nonlinear finite element model after simulated misalignment has been

applied.

4.4 FEA Results/Discussion

Before embarking on the experimental program, it was decided to perform some

preliminary finite element analysis in order to under the effects of pin reinforcement in

sandwich beams. The purpose of the finite element study was to determine the

effectiveness of pin reinforcement and the effect of pin spacing on suppressing the

buckling of debonded facesheets.

The first reinforcement model used truss elements that did not penetrate the

facesheet. This type of reinforcement model did not restrict rotation at the pin/facesheet

interface but rather used a pin-pin connection. It was quickly determined that this model

did not accurately represent the reinforcement behavior or boundary condition and the

model was discarded.

54

The second reinforcement model involved inserting reinforcement that was

inclined with respect to the facesheet. This reinforcement scheme created a truss type

structure internal to the sandwich beam. The truss-type reinforcement model drastically

increased the ultimate failure load. This model yielded tremendous insight into the

mechanism by which translaminar reinforcement can be effective. Figure 4-5 shows the

load vs. end-shortening curve for the inclined pin model. Also shown are curves for the

delaminated, non-reinforced and the no-delamination specimens. These two additional

curves provide an upper and lower bound to the sandwich beam performance.

Previous models with reinforcement at nodal points showed little or no increase in

ultimate load. Models in which reinforcement did not fall at nodal points showed

increased load but not as significant as the increases seen in models using the inclined

pins. The advantage of the inclined pin model is the component of stiffness that restricts

axial displacement of the facesheet. The type of reinforcement provides both lateral and

axial stiffness. It was initially thought that restricting the lateral displacement of the

facesheet was key in increasing the ultimate post-buckling load. However, both

modeling and experiments suggest that the restriction of axial displacement is more

important.

The model that was determined to best represent both the pin/facesheet boundary

conditions as well as the reinforcement behavior was the third model. This model used

shear deformable beam elements to represent the reinforcement.

55

0

1000

2000

3000

4000

5000

6000

0 0.02 0.04 0.06 0.08

End-shortening (in)

Lo

ad (

lb/in

)

Inclined

N31

ND

Figure 4-5. Load vs. end-shortening curve for sandwich beam with inclined pin

reinforcement. During the preliminary study, the initial finite element results were discouraging.

Modeling of Set 6 specimens using beam elements to model the reinforcement showed

only minor increases in ultimate load. A reinforcement spacing of 0.5 inch resulted in an

increased of ultimate load of 28%.

This results turned out to be an anomaly. The delamination length in Set 6 is 1

inch. Since the delamination is centered in the model, using a 0.5 inch reinforcement

spacing would result in three pins falling within the delaminated region. One pin would

fall at each crack tip while the third pin would fall at the centerline of the delamination.

The mode shape for Set 6 was locally symmetric. In this particular case, the pins were

located at nodal points. These points have only transverse displacement, not axial

displacements. This result reinforces the belief that restriction of axial displacement of

the facesheet is critical in increasing the load carrying capacity of the sandwich beam.

56

A point of confusion between experimental and numerical results is the

observation from models that a sandwich beam with 0.5 inch reinforcement spacing has

minimal increase in ultimate load, while experimental data show an increase of 28%.

This discrepancy is the result of human factors in the manufacture of specimens. In the

finite element models, the placement of reinforcement is ideal. Pins are located exactly at

nodal points. In the fabrication of specimens, the location of pins has some small

variance. This variance, no matter how small, can have an impact on the effectiveness of

the reinforcement. This sensitivity to pin placement is consistent with the results of the

inclined pin reinforcement. The reinforcement is most effective if placed where the axial

displacement of the facesheet is maximum. Figure 4-6 shows the axial displacements of

the delaminated facesheets after buckling.

In the preliminary study, only the elastic material model was considered. The

correlation between finite element results and experimental results was poor. The

relative error between experimental and numerical results is presented in Table 4-4.

These results clearly indicate that a purely elastic model is not capable of capturing the

complex behavior of delaminated sandwich structures.

For the sake of comparison, the specimens used in the edgewise compressive

study were modeled using the elastic material model. The results again were

significantly higher than the experimental failure load.

Models that used a linear elastic material model for both the core and facesheet

consistently overpredicted the ultimate post-buckling load of a delaminated sandwich

beam. This approach did not capture the complex behavior of the sandwich structure.

One possible cause of the failure was yielding of the constituent materials. Three cases

57

of yielding were considered: yield in the facesheet, yield in the core, and yield in both

facesheet and core. Table 4-6 shows the finite element results using an elasto-plastic

material model for the facesheet, core or both facesheet and core. Load vs. deflection

curves for the results of finite element modeling considering facesheet plasticity are

shown in Figures 4-6 through Figure 4-17.

In several cases using plasticity in both the facesheet and the core, the ultimate

post-buckling load was lower than either the case of facesheet-only or core-only

plasticity. At first glance, this would seem incorrect. Typically, the value is lower than

that of core-only plasticity. This phenomenon occurs when the facehsheet begins to yield

and the stresses are redistributed. If the core material is also considered as elasto-plastic,

the core will almost immediately yield and failure of the specimen will occur. This is not

seen in the case of facesheet-only plasticity because the specimen continues to take load

even after the onset of yield in the delaminated facesheet.

In the case of Set Q35, the ultimate post-buckling load for facesheet plasticity is

lower than that for core plasticity. Because the high density reinforcement allows the

specimen to maintain its stiffness, the specimen fails in a globally symmetric mode. In

this situation, the facesheet stresses are much higher than the core stresses. Therefore,

the introduction of facesheet plasticity will have a drastic and immediate effect on the

ultimate load.

58

Table 4-4. Finite element results for edgewise compressive study using elastic material model.

Model Linear buckling

load (lb/in)

Post-buckling load

(lb/in)

Experimental failure load

(lb/in) % difference

N30 1816 2746 962 -65

N31 644 1328 579 -56

N35 324 659 681 -3

H30 1816 1852 997 -46

H31 1468 1360 965 -29

H35 1350 1290 841 -35

Q30 3105 2746 1524 -44

Q31 3020 2891 1346 -53

Q35 2776 2696 1158 -57

ND 5313 5059 1537 -69

N75 2913 3154 2055 -35

Q75 8212 7953 3416 -57

59

Table 4-5. Finite element results for the edgewise compressive study using an elasto-

plastic material model.

Set Facesheet plasticity

Core plasticity

Both

N30 1022 722 718

N31 849 438 438

N35 602 367 367

H30 1022 722 718

H31 1002 767 828

H35 982 852 828

Q30 1397 1322 1253

Q31 1396 1241 1199

Q35 1374 1428 1277

ND 1534 1524 1498

ND7 3486 1179 1179

N75 2312 1266 1261

Q75 3473 2946 2364

60

ND Results

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.01 0.02 0.03 0.04 0.05

Displacement (in)

Lo

ad (

lb/in

)

Figure 4-6. Load vs. deflection curve for non-delaminated, non-reinforced specimens

(ND).

ND7 Results

0

500

1000

1500

2000

2500

3000

3500

4000

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Displacement (in)

Lo

ad (

lb/in

)

Figure 4-7. Load vs. deflection curve for non-delaminated, non-reinforced specimen with

7 ply facesheets (ND7). This set was included in the finite element modeling to characterize the effect of pin reinforcement on specimens with thick facesheets.

61

N75 Results

0

500

1000

1500

2000

2500

0.00 0.01 0.02 0.03 0.04

Displacement (in)

Lo

ad (

lb/in

)

Figure 4-8. Load vs. deflection curve for non-reinforced specimen with 7 ply facesheet

and a 1.5 inch delamination (N75).

N30 Results

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Lo

ad (

lb/in

)

Figure 4-9. Load vs. deflection curve for non-reinforced specimen with 3 ply facesheets

and a 0.5 inch delamination (N30).

62

N31 Results

0

100

200

300

400

500

600

700

800

900

0.00 0.01 0.02 0.03 0.04

Displacement (in)

Lo

ad (

lb/in

)

Figure 4-10. Load vs. deflection curve for non-reinforced specimen with 3 ply facesheets

and a 1 inch delamination (N31).

N35 Results

0

100

200

300

400

500

600

700

0.00 0.01 0.02 0.03 0.04 0.05

Displacement (in)

Lo

ad (

lb/in

)

Figure 4-11. Load vs. deflection curve for non-reinforced specimen with 3 ply facesheets

and a 1.5 inch delamination (N35).

63

H30 Results

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Lo

ad (

lb/in

)

Figure 4-12. Load vs. deflection curve for a specimen with 0.5 inch reinforcement

spacing, 3 ply facesheets and a 0.5 inch delamination (H30).

H31 Results

0

200

400

600

800

1000

1200

0.00 0.01 0.02 0.03 0.04 0.05 0.06

D i s p l a c e m e n t ( i n )

Figure 4-13. Load vs. deflection curve for a specimen with 0.5 inch reinforcement spacing, 3 ply

facesheets and a 1 inch delamination (H31).

64

H35 Results

0

200

400

600

800

1000

1200

0.00 0.01 0.02 0.03 0.04 0.05

Displacement (in)

Lo

ad (

lb/in

)

Figure 4-14. Load vs. deflection curve for a specimen with 0.5 inch reinforcement

spacing, 3 ply facesheets and a 1.5 inch delamination (H35).

Q30 Results

0

200

400

600

800

1000

1200

1400

1600

0.00 0.01 0.02 0.03 0.04 0.05

Displacement (in)

Lo

ad (

lb/in

)

Figure 4-15. Load vs. deflection curve for a specimen with 0.25 inch reinforcement

spacing, 3 ply facesheets and a 0.5 inch delamination (Q30).

65

Q31 Results

0

200

400

600

800

1000

1200

1400

1600

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Lo

ad (

lb/in

)

Figure 4-16. Load vs. deflection curve for a specimen with 0.25 inch reinforcement

spacing, 3 ply facesheets and a 1 inch delamination (Q31).

Q35 Results

0

200

400

600

800

1000

1200

1400

1600

0.00 0.01 0.02 0.03 0.04 0.05

D i s p l a c e m e n t ( i n )

Figure 4-17. Load vs. deflection curve for a specimen with 0.25 inch reinforcement spacing, 3 ply facesheets and a 1.5 inch delamination (Q35).

66

Q75 Results

0

5 0 0

1 0 0 0

1 5 0 0

2 0 0 0

2 5 0 0

3 0 0 0

3 5 0 0

4 0 0 0

0 .0 0 0 .0 1 0 .0 2 0 .0 3 0 .0 4 0 .0 5

D i s p l a c e m e n t ( i n )

Figure 4-18. Load vs. deflection curve for a specimen with 0.25 inch reinforcement

spacing, 7 ply facesheets and a 1.5 inch delamination (Q75).

67

CHAPTER 5 DISCUSSION AND FUTURE WORK

5.1 Discussion The experimental program conducted during this study set out to quantify the

effects of pin reinforcement on the post-buckling behavior of delaminated sandwich

beams. In the process of this investigation, a new technique for sandwich beam

reinforcement was developed. The technique developed is called "C-pinning". It differs

from traditional pin reinforcement techniques by creating reinforcement that is integral

with the facesheet. The experimental study has shown that the "C-pinning" technique is

effective in increasing the ultimate post-buckling load of sandwich beams. This

technique has also been shown to be far superior to the traditional, cylindrical Z-pin.

Insight was also gained into how the reinforcement of the delaminated sandwich

beam occurs. Both modeling and experimental results suggest that the restriction of axial

displacements is key to increasing the ultimate post-buckling load. Rather than having a

uniform force distribution among pins, reinforcement in a region of large axial

displacement will carry a significantly higher portion of the load than reinforcement that

is at or near a nodal point in the buckled shape.

In general, the comparison of models using facesheet plasticity and experimental

results provided good correlation. The only aberration in the experimental data was in

Set N31, as discussed in Chapter 3. All the models with 0.5 and 1.0 inch delamination

lengths had relative errors of less than 10% when compared to experimental data. The

68

models with longer delamination lengths had slightly higher relative errors but were still

below 20%. It is reasonable to assume that as the delamination length increases, the role

that the core material plays in predicting the ultimate post-buckling load increases. As

the delamination length increases, locally symmetric buckling modes become dominant.

These mode shapes have large mid-plane rotations, which lead to high compressive

stresses in the core. Eventually, these compressive stresses lead to cell wall collapse and

core crushing.

Table 5-1 Relative error between models using facesheet

plasticity and experimental results.

Set FEM

Facesheet plasticity

Experimental Relative error

N30 1022 962 -6.24

N31 849 579 -46.63

N35 602 681 11.60

H30 1022 997 -2.51

H31 1002 965 -3.83

H35 982 841 -16.77

Q30 1397 1524 8.33

Q31 1396 1346 -3.71

Q35 1374 1158 -18.65

ND 1534 1537 0.20

ND7 3486

N75 2312 2055 -12.51

Q75 3473 3416 -1.67

69

The consideration of plastic deformation of the facesheet seems to provide good

correlation with experimental data over a range of delamination lengths and

reinforcement spacings. The combination of plastic material model and shear-

deformable pin model is a reasonable method of predicting the complex behavior of

reinforced, sandwich structures. Figures 5-1 through Figure 5-12 show comparisons

between the experimental results from the edwise compressive loading study and the

finite element analysis. From the figures, good correlation between experimental and

modeling can be observed for both ultimate failure load and initial tangent stiffness

across the range of geometric configurations.

ND Results

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Displacement (in)

Lo

ad (

lb/in

)

Experimental

FEM

Figure 5-1. Comparison of FEM results and experimental results for non-delaminated, non-reinforced specimens with 3 ply facesheets (ND).

70

N75 Results

0

500

1000

1500

2000

2500

3000

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Displacement (in)

Lo

ad (

lb/in

)

Experimental

FEM

Figure 5-2. Comparison of FEM results and experimental results for non-reinforced

speccimens with 7 ply facesheets and a 1.5 inch delamination (N75).

N30 Results

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Lo

ad (

lb/in

)

Experimental

FEM

Figure 5-3. Comparison of FEM results and experimental results for non-reinforced

specimens with 3 ply facesheets and a 0.5 inch delamination (N30).

71

N31 Results

0

100

200

300

400

500

600

700

800

900

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

Displacement (in)

Lo

ad (

lb/in

)

Experimental

FEM

Figure 5-4. Comparison of FEM results and experimental results for non-reinforced specimens with 3 ply facesheets and a 1 inch delamination (N31).

N35 Results

0

100

200

300

400

500

600

700

800

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Displacement (in)

Lo

ad (

lb/in

)

Experimental

FEM

Figure 5-5. Comparison of FEM results and experimental results for non-reinforced

specimens with 3 ply facesheets and a 1.5 inch delamination (N35).

72

H30 Results

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Lo

ad (

lb/in

)

Experimental

FEM

Figure 5-6. Comparison of FEM results and experimental results for specimens with 0.5

inch reinforcement spacing, 3 ply facesheets and a 0.5 inch delamination (H30).

H31 Results

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Lo

ad (

lb/in

)

Experimental

FEM

Figure 5-7. Comparison of FEM results and experimental results for specimens with 0.5

inch reinforcement spacing, 3 ply facesheets and a 1 inch delamination (H31).

73

H35 Results

0

200

400

600

800

1000

1200

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

Displacement (in)

Lo

ad (

lb/in

)

Experimental

FEM

Figure 5-8. Comparison of FEM results and experimental results for specimens with 0.5

inch reinforcement spacing, 3 ply facesheets and a 1.5 inch delamination (H35).

Q30 Results

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

Displacement (in)

Lo

ad (

lb/in

)

Experimental

FEM

Figure 5-9. Comparison of FEM results and experimental results for specimens with 0.25

inch reinforcement spacing, 3 ply facesheets and a 0.5 inch delamination (Q30).

74

Q31 Results

0

200

400

600

800

1000

1200

1400

1600

0 0.01 0.02 0.03 0.04 0.05 0.06

Displacement (in)

Lo

ad (

lb/in

)

Experimental

FEM

Figure 5-10. Comparison of FEM results and experimental results for specimens with

0.25 inch reinforcement spacing, 3 ply facesheets and a 1 inch delamination (Q31).

Q35 Results

0

200

400

600

800

1000

1200

1400

1600

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

D i s p l a c e m e n t ( i n )

Expe r imen ta l

F E M

Figure 5-11. Comparison of FEM results and experimental results for specimens with

0.25 inch reinforcement spacing, 3 ply facesheets and a 1.5 inch delamination (Q35).

75

Q75 Results

0

500

1000

1500

2000

2500

3000

3500

4000

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

D i s p l a c e m e n t ( i n )

Expe r imen ta l

F E M

Figure 5-12. Comparison of FEM results and experimental results for specimens with

0.25 inch reinforcement spacing, 7 ply facesheets and a 1.5 inch delamination (Q75).

5.2 Future Work An obvious next step in the experimental program would be to re-test the non-

reinforced specimens. This would confirm or deny the assumptions made in Chapter 3

about the source of the discrepancy between Sets N31 and N35. To investigate the

influence of specimen length on the results presented here, the specimens used in this

study could be lengthened so that the delaminated region represented a small portion of

the overall length of the specimen.

By using longer specimens, it would be possible to investigate the behavior of

long delaminations. Delaminations that are much larger than the reinforcement spacing

may have a different behavior. In this type of configuration, problems associated with

76

nodal points would be lessened. This arrangement would also increase the number of

pins per specimen providing more robust reinforcement.

Additionally, now that a reasonably accurate method of predicting the ultimate

post-buckling load of delaminated sandwich beams exists, this method could be applied

to a more complicated test matrix. The influence of parameters such as core density and

core thickness could be revisited. While the method presented here provide good results,

the complex interaction of facesheet and core will certainly change as the specimen

geometry changes. The influence of geometric parameters on both the performance of

pin reinforcement and the applicability of the model presented here should be

investigated.

While "C-pinning" has been shown to be effective in increasing the post-buckling

load, it's effect on the in-plane properties of the sandwich beam were not quantified in

this study. While the "C-pinning" technique is less intrusive than the Z-pin technique, it

still does some level of damage to the facesheet. The effects of the reinforcement on

tensile strength and bending stiffness should be investigated.

The “C-pinning” technique developed in this study has not been implemented in

commercial manufacturing of sandwich structures. Due to the complex nature and

custom configurations common in composite structures, the fabrication of the structures

is often labor intensive and expensive. “C-pinning” adds another dimension to the

complexity of manufacturing this type of structure.

Automating the process of “C-pin” reinforcement involves being able to insert the

pre-preg through-the-thickness of the sandwich panel and cut the reinforcement to the

appropriate length. Current technology in automated tape-laying machines and cutters

77

would be useful in manufacturing this type of part. Whether the facesheet material was

cut to the appropriate dimensions by an automated cutter or put in place by a tape-laying

machine, the manufacture of the core/1-ply sub-assembly could easily be automated.

Inserting the pins would require a stitching machine that included a cutter whose actuator

was parallel to the surface of the sandwich preform. During the downstroke of the

stitching machine, the lower arm of the cutter would insert next to the pre-preg. When

the stroke is complete and the needle has returned to the up position, the pre-preg would

be cut between adjacent pins by the lower arm. This technique is similar to traditional

stitching but would include an additional step break the continuity of the stitch material,

thus forming individual pins.

78

REFERENCES

Avery, J.L., 1998, “Compressive Failure of Delaminated Sandwich Composites,” Master

of Science thesis, Department of Aerospace Engineering, Mechanics and Engineering Science, University of Florida, Gainesville, Florida.

Avery, J.L., and Sankar, B.V., 2000, “Compressive Failure of Sandwich Beams with

Debonded Facesheets,” J. Composite Materials, 34(14): 1176-1199. Hazen, Judith Ray, “Composite Hydrogen Tank is under investigation,” High

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BIOGRAPHICAL SKETCH I was born in Orlando, FL, on July 5, 1974. I am the younger of two sons born to

Guy and Patty Wallace. My brother, Shawn, and parents still reside in Orlando. I

married Robin Book of Fernandina Beach, FL, on August 15, 1998. My son, Parker, was

born on November 13, 1998, and my daughter, Taylor, was born on April 26, 2000.

I graduated from William R. Boone High School in June 1992. While pursuing a

bachelor’s degree in civil engineering, I was employed by Post, Buckley, Schuh, and

Jernigan and the Florida Department of Transportation Structural Research Center. This

practical engineering experience has been beneficial during my career as a graduate

student. I earned my bachelor’s degree from The Florida State University in December

1997. In January 1998, I began my graduate studies in the Aerospace Engineering,

Mechanics, and Engineering Science department at the University of Florida. My

research into delaminated sandwich structures over the last two years is represented by

this thesis. This thesis was defended on November 7, 2000.

I am concurrently pursuing a Master of Engineering in computer engineering. I

plan to graduate from computer engineering in December 2001.