design allowables for composite aerospace structures

195 Pages·2013·14.13 MB·English

DESIGN ALLOWABLES
FOR COMPOSITE AEROSPACE
STRUCTURES

Paul R Spendley

Submitted for the Degree of Doctor of Philosophy

Faculty of Engineering and Physical Science
University of Surrey
Guildford, Surrey, GU2 7XH

© Paul Spendley, 2012
ACKNOWLEDGEMENTS

Patience and tolerance are two words that spring to mind when writing these
acknowledgements. My principle supervisors, Paul Smith and Steve Ogin have been
extremely patient and understanding in waiting for this piece of work. I am grateful for their
confidence in me and their continuous support and conveyance of the importance and real
value of this work. For this I am eternally in their debt. I also owe thanks to Andrew Clarke
of Qinetiq for his industrial support. David Jesson and Peter Haynes of the University of
Surrey have been a constant source of support through prescriptive doses of humour and Earl
Grey and I would like to give them special thanks. Finally, I would like to thank Emma
Payne for her encouragement at the final hurdle and her unwavering love and support.
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DEDICATION

I would like to dedicate this work to my two boys Noah and Toby who have, like everyone
around me, been waiting for me to finish this Thesis. They will be thrilled that I have
achieved time traveller status and become a Doctor. Indeed, like all PhD candidates, the
ability to time travel would have been an extreme advantage in conducting this study.

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ABSTRACT

Recent developments in aircraft design have seen the Airbus A380 and the Boeing
Dreamliner employ significant amounts of advanced composite materials. There is some
thought however, and the motivation for this current work, that these materials continue to
suffer a weight penalty. In this work tests required to generate design allowables which
accommodate environmental effects and holes are performed on Carbon/epoxy quasi-
isotropic laminates. The test data is treated statistically to provide B-basis allowables for
each specimen type and condition. It was seen that the notched specimens (coupons
containing a centrally placed through hole) displayed significantly less scatter in strength
than unnotched specimens. This is significant when considering the widespread use of
deterministic knock-down factors as an alternative route to obtain design allowables which
accommodate environmental effects and/or holes. This results in an over-conservative design
allowable being employed in subsequent structural design calculations. The possibility for
using notched coupons to determine design allowables was explored using the CDG (Critical
Damage Growth) model. This showed that, given two of the three parameters, the unnotched
and notched strength, and fracture toughness the variation in strengths could be reasonable
predicted. This leads to a more representative design allowable by maintaining the statistical
nature of the B-basis allowable. During the statistical treatment of the test data it was also
seen that although current aerospace guidelines recommend a particular distribution model
(i.e. the Weibull distribution) this can also leads to an artificially reduced design allowable.
These findings suggest that the use of notched specimens can lead to a reduced development
test programme and reduced structural weight.
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NOMENCLATURE

a Single edge notch or crack length
a Whitney Nuismer average stress criterion characteristic
0
Characteristic dimension of energy intense region of the Waddoups, Eisenmann and
a
1
Kaminski model
Average characteristic dimension of energy intense region of the Waddoups,
a
2
Eisenmann and Kaminski model
A A Basis allowable (95% of strength values obtained experimentally)
b Point strength model characteristic distance
1
b Minimum strength model characteristic distance
2
B B Basis allowable (90% of strength values obtained experimentally)
c Straight crack half-length
c Critical damage zone length predicted by the Critical Damage growth Model
0
C Critical value for MNR model
d Circular centre hole or notch diameter

d Whitney Nuismer Point Stress Criterion
0
E Young’s modulus
E Longitudinal young’s modulus
1
E Transverse young’s modulus
2
E Young’s modulus of matrix material
m
E Young’s modulus of fibres
f
E Young’s modulus along x co-ordinate
x
E Young’s modulus along y co-ordinate
y
F Correction factor for cracks growing from a circular hole
0
F The standard Normal distribution function using the Anderson-Darling model
AD
G Laminate shear modulus
12
G Critical energy release rate or Toughness
c
H Fracture toughness equivalent parameter in the Mar-Lin model
c
j Indicates jth rank of specimen strengths considered in Weibull plot
k Kim et al. (1995) notch sensitivity factor
k Tolerance factor used with an A basis allowable
A
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k Tolerance factor used with an B basis allowable
B
k Karlak fitting parameter relating d to R
0 0
K Critical stress intensity factor or fracture toughness
c
K0 Fracture toughness of the 0° plies
c
K Stress concentration factor for a plate of finite width
T
K ∞ Stress concentration factor for a plate of infinite width
T
l Length of critical damage zone on the left hand side, in the schematic model
l
l Length of critical damage zone on the right hand side, in the schematic model
r
m Pipes, Wetherhold and Gillespie exponential parameter
M Mass fraction of fibre material
f
M Mass fraction of matrix material
m
M Mass of sample weighed in air
sa
∆M Mass difference of specimen when weighed in air and water
s
n The number of specimens considered in test or analysis
N Total number of ranked specimens considered in Weibull plot.
P Maximum load
Max
Ps Probability of survival
R Circular hole radius
R Pipes, Wetherhold and Gillespie reference radius
0
S S-basis allowable
t The quantile of the t-distribution with n -2 degrees of freedom and
V Mean value obtained from tabulated data for a 95% confidence level
V Volume fraction of fibre material
f
V Volume fraction of matrix material
m
w Width of critical damage zone on the left hand side, in the schematic model
l
w Width of critical damage zone on the right hand side, in the schematic model
r
W Coupon/Sample width
Y Finite width correction factor
1
x The ith smallest sample observation
(i)
µ The sample average (mean failure strength).
Y Finite width correction factor for a crack emanating from a hole
2
SD Standard deviation
α The statistical significance level applied to the Anderson – Darling model
αˆ The maximum likelihood estimators for scale parameters.

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ˆ
β The maximum likelihood estimators for shape parameters.

ε Strain
ε Failure strain
f
ε Strain at the geometrical mid-plane of the laminate
f 0
ε Longitudinal strain
l
ε Transverse strain
t
η Factor relating to the stress in the laminate to the stress in the 0° plies
λ Ellipse opening ratio
ν Poisson’s ratio
ν Longitudinal Poisson’s ratio
12
ν Transverse Poisson’s ratio
21
ρ Density of fibres
f
ρ Density of matrix
m
ρ Density of specimen
s
ρ Density of water
w
σ Strength of a specific specimen
σ Unnotched laminate strength
0
σ Remote applied stress
1
σ Applied stress for shear modulus determination
app
σ Mean strength of laminate
m
σ Notched laminate strength of a finite plate
N
σ Notched laminate strength of an infinite plate
N∞
σ Normal stress ahead of notch
y
Z Ranked strength value using the Anderson – Darling model

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CONTENTS
CHAPTER 1 INTRODUCTION ................................................................................................................. 1
1.1 Background ........................................................................................................................................ 1
1.2 Aims .................................................................................................................................................... 4
1.3 Structure of Thesis ............................................................................................................................. 4
CHAPTER 2 LITERATURE REVIEW ..................................................................................................... 5
2.1 Introduction ........................................................................................................................................ 5
2.2 Materials qualification of composite structures .............................................................................. 5
2.2.1 Background to certification ........................................................................................................ 5
2.2.2 Considering the effect of environment and holes in certification ............................................... 8
2.3 Considering the failure strength variation in laminates ................................................................. 9
2.3.1 Overview of strength variation in composite laminates ............................................................. 9
2.3.2 Determining the best-fit distribution ........................................................................................ 14
2.3.3 Observation on fibre architecture and environment on the variation in strength. ................... 16
2.4 Strength of notched CFRP laminates ............................................................................................. 18
2.4.1 Overview of stress in CFRP Laminates .................................................................................... 18
2.4.2 Stress concentration factor ....................................................................................................... 19
2.4.3 Considering the failure in notched (open-hole) laminate coupons .......................................... 20
2.4.4 Considering damage development in notched tensile laminates .............................................. 22
2.4.5 Considering damage development in compression in notched laminates ................................ 24
2.4.6 Environmental effect on strength of notched laminates............................................................ 25
2.5 Models for notched strength of laminates ...................................................................................... 28
2.5.1 Overview................................................................................................................................... 28
2.5.2 A Critical Damage Growth Model ........................................................................................... 30
2.5.3 Considering the prediction of notched strength using micro-mechanics modes in HW
and CD conditions .................................................................................................................................. 32
2.5.4 Using notched strength models in the derivation of design allowables .................................... 33
2.6 Methods for obtaining static strength allowables .......................................................................... 33
2.7 Summary and concluding remarks ................................................................................................ 35

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CHAPTER 3 EXPERIMENTAL METHODS ......................................................................................... 37
3.1 Introduction ...................................................................................................................................... 37
3.2 Material properties and sample fabrication .................................................................................. 38
3.2.1 Introduction .............................................................................................................................. 38
3.2.2 Material properties................................................................................................................... 38
3.2.3 Sample size ............................................................................................................................... 38
3.2.4 Sample fabrication ................................................................................................................... 39
3.2.5 Fibre Volume Fraction Determination ..................................................................................... 42
3.3 Test arrangement and specimen preparation ................................................................................ 43
3.3.1 Test arrangement ...................................................................................................................... 43
3.3.2 Specimen preparation ............................................................................................................... 45
3.3.3 Tabbing requirements ............................................................................................................... 49
3.3.4 Coupon machining ................................................................................................................... 51
3.3.5 Measurement of strain .............................................................................................................. 51
3.3.6 Finite element analysis – strain gauge position ....................................................................... 53
3.3.7 Environmental pre-conditioning of hot-wet specimens ............................................................ 55
3.4 Mechanical testing ........................................................................................................................... 56
3.4.1 Introduction .............................................................................................................................. 56
3.4.2 General test arrangement ......................................................................................................... 56
3.4.3 Room temperature tests ............................................................................................................ 57
3.4.4 Hot-wet tests ............................................................................................................................. 57
3.4.5 Cold-dry tests ........................................................................................................................... 58
3.5 Summary .......................................................................................................................................... 59
CHAPTER 4 EXPERIMENTAL RESULTS: PLAIN, UNNOTCHED SPECIMENS ........................ 60
4.1 Introduction ...................................................................................................................................... 60
4.2 Unnotched tensile properties........................................................................................................... 60
4.2.1 Room temperature conditions (PTRT) ...................................................................................... 60
4.2.2 Hot wet conditions (PTHW) ..................................................................................................... 65
4.2.3 Cold dry conditions (PTCD) .................................................................................................... 68
4.3 Unnotched compressive properties ................................................................................................. 72
4.3.1 Room temperature conditions (PCRT) ..................................................................................... 72
4.3.2 Hot wet conditions (PCHW) ..................................................................................................... 76
4.3.3 Cold dry conditions (PCCD) .................................................................................................... 81
4.4 Unnotched: Discussions ................................................................................................................... 85
4.5 Unnotched: Concluding remarks ................................................................................................... 86
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CHAPTER 5 EXPERIMENTAL RESULTS: NOTCHED SPECIMENS ............................................ 88
5.1 Introduction ...................................................................................................................................... 88
5.2 Notched tensile properties ............................................................................................................... 88
5.2.1 Room temperature conditions (OHTRT) .................................................................................. 88
5.2.2 Hot wet conditions (OHTHW) .................................................................................................. 92
5.2.3 Cold dry conditions (OHTCD) ................................................................................................. 97
5.3 Notched compression ..................................................................................................................... 101
5.3.1 Room temperature conditions (OHCRT) ................................................................................ 101
5.3.2 Hot wet conditions (OHCHW)................................................................................................ 108
5.3.3 Cold dry conditions (OHCCD) ............................................................................................... 113
5.4 Notched: Discussions ..................................................................................................................... 119
5.5 Notched: Concluding remarks ...................................................................................................... 120
CHAPTER 6 MECHANICAL DATA AND STATISTICAL COMPARISON .................................. 121
6.1 Introduction .................................................................................................................................... 121
6.2 Mechanical response ...................................................................................................................... 122
6.2.1 Failure strength of conditioned specimens ............................................................................. 122
6.3 Statistical comparison .................................................................................................................... 124
6.3.1 Generalised strength distribution ........................................................................................... 124
6.3.2 Failure strength and specimen extraction .............................................................................. 126
6.3.3 B-Basis and the strength distribution ..................................................................................... 126
6.3.4 Sample size ............................................................................................................................. 130
6.3.5 Considering the effect of environment on the B-basis ............................................................ 130
6.3.6 Considering the Weibull plot of the test data ......................................................................... 134
6.4 Summary and concluding remarks .............................................................................................. 142
CHAPTER 7 PREDICTIVE MODEL: RELATIONSHIP BETWEEN UNNOTCHED AND
NOTCHED STRENGTH ................................................................................................ 143
7.1 Introduction .................................................................................................................................... 143
7.2 A damage growth/fracture mechanics model for notched strength .......................................... 143
7.2.1 Introduction of the DG/FM Model ......................................................................................... 143
7.2.2 Estimation of Fracture toughness - Kc ................................................................................... 146
7.2.3 Variation in test data .............................................................................................................. 151
7.3 Concluding remarks ...................................................................................................................... 152

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