Analysis of Failure in Fiber Polymer Laminates: The Theory of Alfred Puck

208 Pages·2008·7.75 MB·English

by  Martin Knops Dr.-Ing. (auth.)

Analysis of Failure in Fiber Polymer Laminates
Martin Knops
Analysis
of Failure
in Fiber Polymer
Laminates
The Theory of Alfred Puck
123
Dr.-Ing. Martin Knops
REpower Systems AG
Rotorblattentwicklung
Hollesenstraße 15
24768 Rendsburg
Germany
[email protected]

ISBN 978-3-540-75764-1 e-ISBN 978-3-540-75765-8

DOI 10.1007/978-3-540-75765-8

Library of Congress Control Number: 2008921124

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Foreword
In 1948 when I began to study mechanical engineering in the ruins of the
School of Engineering in Hamburg common opinion was that designing of
components was not a science but an art. Since then things have changed
significantly. There is no doubt that a designer of composite components
needs a lot of practice and a certain “artistic” skill but he also needs a good
understanding of fundamental theory. Unfortunately still some people feel
that theory is far away from practice. Personally I refer to great researchers
such as the famous chemist A.L. Lavoisier (1743–1794) and the well
known German scientist and teacher in aerodynamics L. Prandtl (1875–
1953); it was him who said “There is nothing more practical than a good
theory!” Possibly this can be a modification of the much older statement of
Lavoisier: “There is nothing more practical than a good hypothesis!”
An FRP-laminate is a very sophisticated multilayered structure with
skillfully tailored anisotropy. Analyzing the fracture processes in FRP-
laminates needs a theory which is able to describe the different fracture
mechanisms fundamentally correctly. I use as a “good hypothesis” the one
created by Otto Mohr (1835–1918): “The fracture limit of a material is
determined by the stresses on the fracture plane.” From time to time some
authors have proposed to apply this hypothesis to brittle composites. This
was most forcibly argued by Hashin [Hashin 1980]. But time had not yet
come for that approach. That is to say a certain computing capacity has to
be available to identify the orientation of the fracture plane, which is un-
known a priori.
First one had experimentally to investigate whether or not a modified
Mohr-Hypothesis would be acceptable for UD-composites. Parallel to my
theoretical approaches I found invaluable help for the experimental task
from Ph-D candidates of the Aachen Technical University. Very often I
told these young colleagues about my feelings that there is an excessive
production of theories but a considerable lack of reliable experimental
results. Unfortunately nowadays experimental work is not appreciated as
much as it should be. Nevertheless the young colleagues from Aachen
have chosen the experimental problems proposed by me as the subject of
their dissertation. This way they supplied the experimental verification of
my theory. I am extremely grateful for this assistance and therefore I want
VI Foreword
to list the names of all the experimenters: Dirk Huybrechts (1996), Jochen
Kopp (2000), Martin Knops (2003), author of this book, Oliver Fischer
(2003), Martin Mannigel (2007) and Erik Kuhnel (2008)1.
My theory has now “arrived” in practice. Also the incorporation of my
theory into the Guideline VDI 2014 (Verein Deutscher Ingenieure) as well
as into guidelines of Germanischer Lloyd and Det Norske Veritas shows
the same acceptance. For the readers of this book, VDI 2014 Part 3 “De-
velopment of Fiber Reinforced Plastic Components, Analysis” can be
a very helpful supplement. It is written throughout in German and English.
The reason that my theory has been treated in VDI 2014 so profoundly and
prepared for use in practice is mainly the credit of my cooperation with
Mr. Günther Lutz, who is a very experienced designer and developer of
FRP-Couplings and large FRP-Drive shafts for fast ships.
In the future the Composite Technology will play an important role for
the development of energy saving vehicles and technologies for environ-
ment and climate protection. The author of this book is working in this
field already, developing large rotor blades for wind turbines. The fact that
design engineers, using composites, have an enormous freedom in the de-
sign of “custom made materials” for special needs is a fascinating experi-
ence. Nevertheless this fascination should not stop us from thinking about
the ultimate usage of our products. As can be expected one can find many
composites in modern weapon systems including intercontinental ballistic
missiles. It should not be our goal to develop even more weapons or make
them “more effective”. The problem will ever be: “How can we get rid of
them before everyone will have them?”
I hope that the book of Martin Knops will satisfy many interested and
critical readers. I am confident that the readers will have some delightful
“ahaa… experiences”. For myself I hope that for quite a while I will still
be privileged to stay in contact with young composite engineers. We
should never stop learning! What I already know for a long time, is: Mo-
dern composites are black and not easy to be looked through but they are
not at all products of “black magic”! We can understand them, if we care-
fully try to think about their internal construction. However thinking alone
is not enough, of equal importance are smart experiments.
Immenhausen, January 2008 Alfred Puck

1 The year in brackets is the year of the publication of the dissertation (see also
References in the book)
Preface
In 2003 I was encouraged by Alfred Puck himself to write this book about
his failure model and the Puck fracture criteria. The motivation was that
Puck’s own book from 1996 was written in German and did not cover the
major progress especially in the field of validation which was achieved
since. There was no comprehensive presentation of Puck’s work in Eng-
lish language and several people asked for an English book with such
content.
I had at the time just finalized my dissertation about the gradual failure
process for which I had worked closely together with Alfred Puck as
a senior adviser. He considered me as one of the best experts and the right
person to write such a book. That was of course a high honor to me and
I agreed to start the project being supported and encouraged by the man-
agement of my employer, the Institute for Plastic Processing (IKV),
namely Walter Michaeli and Ernst Schmachtenberg.
Originally it was planned to publish in 2004, but as often in such projects
this was a too optimistic assumption and after I changed from university to
industry in early 2005 and started a family at the same time it became hard to
find enough time for the project. I am grateful to Petra Jantzen from Springer
who – always polite but with the right pressure – set deadlines and pushed
me to work. After all, the elongation of the project offered the opportunity to
implement the latest work in the field which was conducted in the recent
years. Thus, value was added to the overall project. On the other hand, there
are still wishes which have not been met. For sure a broader presentation of
the applications of Puck’s failure model would have been desirable. But now
it is time for publication and this part is left out for the moment.
There is a list of people who have made this book possible. First to
name is of course Alfred Puck, who teached and advised me for years and
who also revised this book. Günther Lutz – one of the co-authors of the
VDI2014 guideline on the development of FRP components – has been the
main reviser of the text. I thank not only for this but also for the great
profit I got from the work on the VDI2014.
Additional thanks go to Walter Michaeli and Ernst Schmachtenberg
who encouraged me to write this book during my time at the IKV. Besides
I am very grateful to Dieter Merkle and Petra Jantzen from Springer for
VIII Preface
making this book possible. Last but not least I thank my wife Claudia for
her understanding and patience during all the hours I worked for this
book.
I dedicate this book to my children Paula Liane and Peter Elias.
Rendsburg, January 2008 Martin Knops
Contents
1 Introduction................................................................................ 1
2 Failure of laminates.................................................................... 5
2.1 Laminate structure............................................................... 5
2.2 Micro-cracks........................................................................ 6
2.3 Inter Fiber Fracture (IFF).................................................... 7
2.3.1 Different forms of Inter Fiber Fracture (IFF)........... 10
2.3.2 Relevance of IFF....................................................... 13
2.4 Delamination....................................................................... 14
2.5 Fiber Fracture (FF).............................................................. 16
2.6 Laminate Failure.................................................................. 18
2.7 Summary of chapter............................................................. 19
3 Stress and strength analysis: Basics and definitions............... 21
3.1 Coordinate systems, stresses and stressings........................ 21
3.1.1 Natural coordinate system of the UD-lamina........... 21
3.1.2 Coordinate system of the laminate............................ 22
3.1.3 Stresses of the UD-lamina........................................ 22
3.1.4 Stressings of a UD-element...................................... 23
3.1.5 Stresses on the fracture plane,
adapted coordinate system......................................... 24
3.1.6 Coordinate system for the visualization
of fracture bodies...................................................... 25
3.2 Stress analysis...................................................................... 27
3.3 Strength analysis.................................................................. 28
3.3.1 Introduction............................................................... 28
3.3.2 Fracture condition, fracture criterion and the term
“stress exposure”....................................................... 28
3.3.3 Distinguishing residual and load
determined stresses................................................... 32
3.3.4 Margin of safety and reserve factor of the Composite
materials structure..................................................... 33
3.4 Summary of chapter............................................................. 34
4 Puck’s action plane fracture criteria........................................ 37
4.1 Fiber fracture criteria........................................................... 37
4.2 Inter fiber fracture (IFF) criteria.......................................... 40
X Contents
4.2.1 Motivation................................................................. 40
4.2.2 Different IFF-fracture modes.................................... 43
4.2.3 Fracture hypotheses.................................................. 44
4.2.4 Fracture resistance of the action plane...................... 46
4.2.5 Visualization of the stress/strength problem............. 51
4.2.6 Universal 3-D-formulation of the action plane
related IFF-criteria.................................................... 65
4.2.7 Analytical 2-D-formulation for plane states
of stress..................................................................... 79
4.3 Extensions to the IFF-criteria.............................................. 83
4.3.1 Inclusion of stresses not acting on the fracture plane
in the action-plane-related inter-fiber
fracture criteria.......................................................... 83
4.3.2 Calculation of the stretch factor f L of the load-
S
determined stresses when residual stresses
are present................................................................. 97
4.4 Visualization of fracture bodies........................................... 108
4.5 Summary of chapter............................................................. 114
5 Analysis of the gradual failure process..................................... 117
5.1 Approaches for the modeling of the gradual
failure process...................................................................... 119
5.2 Puck’s approach for the analysis of the gradual
failure process...................................................................... 121
5.2.1 Degradation procedure for cracks due to IFFMode A... 122
5.2.2 Degradation procedure for cracks due to IFFMode B
and IFFMode C............................................................. 123
5.2.3 Puck’s method from 1969......................................... 125
5.2.4 Degradation method used in the
“World Wide Failure Exercise”................................ 128
5.2.5 New degradation method (2007).............................. 128
5.2.6 Laminates with unsound loading conditions............. 129
5.3 Implementation of the Puck theory for the gradual failure
process in a software code................................................... 130
5.4 Summary of chapter............................................................. 133
6 Experimental work..................................................................... 137
6.1 Verification of the fracture hypotheses and calibration
of the fracture body.............................................................. 137
6.1.1 Experiments with Three Dimensional Stress States. 137
6.1.2 Experiments with plane
(σ , τ )-stress combinations..................................... 143
2 21
6.2 Experimental determination of degradation curves............. 150
6.2.1 Degradation of E t and G for fracture Mode A...... 151
⊥ ⊥||
6.2.2 Degradation of E and G for fracture Mode B....... 156
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