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Is There Really No Need
to Be Able to Predict Matrix Failures
in Fibre-Polymer Composite Structures?
Dr. L. J. Hart-Smith
by
Informal Lectures in Europe and the UK, April and September, 2016
Summary of the Problem
Fibre-polymer composites, such as carbon-epoxy, are very strong when the
fibres dominate their behaviour, but equally weak when premature matrix failures
prevent the fibres from developing their full strength.
Several reliable analysis models can predict fibre-dominated failures, but not
even one of the popular failure theories is capable of predicting matrix failures.
How could this happen after composites have been around for decades?
There are some very widely accepted composite failure theories believed to be
capable of predicting matrix failures, by all those people with insufficient
knowledge of the mechanics of composites to recognize that every such theory
was based on a false simplifying assumption – that the distinct fibre and resin
constituents could be replaced by an allegedly “equivalent” homogeneous
anisotropic solid. This process simplified the mathematics, but actually
precluded all possibility of ever predicting matrix failures.
Unfortunately, these defective failure models were proposed by highly
recognized composites experts, marketed extensively through short courses,
and embedded deeply in structural analysis computer codes. Their many
disciples continue to promote these theories.
The few engineer/scientists who understood what was really happening have
been unable to get their message through. The composites establishment
strenuously refuses to accept it.
Objective of this Presentation
Past papers explaining the problems have been ignored. It is as if the reigning
experts place no importance on predicting matrix failures.
The first theory ever developed, circa 2000, that was capable of explaining both
fibre and matrix failures, SIFT (Strain Invariant Failure Theory), has gained some
support around the world, but with no acknowledgement that it invalidated the
bogus theories, which continue to be used.
A different approach is needed to get the message through.
This presentation demonstrates the fallacies in the accepted models by an
analogy with steel-reinforced concrete beams and columns.
A physical explanation is provided of the origin of intense residual thermal
stresses in the matrix, which cannot exist in a truly homogeneous material – and
cannot be accounted for in any homogenized theory. These stresses consume
about 50 percent of the intrinsic matrix strength at room temperature, and even
more in the cold environments of high-altitude jet flight.
The bulk of the presentation consists of real-world situations, mainly from
aerospace, where matrix failures dominate, all of which failed to be predicted by
the existing theories.
The goal of this presentation is to encourage academia to stop defending (and
teaching) the bogus theories, and to put more effort into developing new theories
that obey, rather than violate, the laws of physics.
The Problems of Matrix Failures in Fibre-Polymer Composites Explained
in the Context of a Simple Skin-Doubler Combination, and Impact Damage
Skin-Doubler Combination: All the load carried in the doubler
can pass to or from the skin ONLY through the thin resin interface.
SkinDoubler Pure Resin Interface
Run-Out Zone
Impact
Broken Fibres
Delamination
Impact Damage: All the load carried in the broken fibres must unload
through a layer of resin. If it cannot, the delamination will spread.
An Example of Just How Deeply the Misunderstanding
About the Nature of Fibre-Polymer Composites Is Ingrained
If one engineer were to propose that the riveted stringer-stiffened wing skins on
large transport aircraft be replaced by adhesively bonded structure with no
fasteners, his suggestion would be treated with disdain. Everyone “knows” that
a 0.125 mm (0.005 inch) thick layer of glue cannot transmit as much load as a
series of 1 cm (0.4 inch) titanium bolts.
Yet, if another engineer were to propose that the aluminium skins and extruded
stringers be replaced by carbon-epoxy laminates, and that there was no need for
any fasteners, since the skin and stringers would be cured together in a single
cure cycle, he would probably be hailed as a visionary, nowadays.
Ironically, the load-transfer capability of the ultra-thin layer of resin between the
skin and stringers would be less than 1/10th of the strength of the layer of
adhesive that was universally deemed to be inadequate.
Why is this so? Fibre-polymer composites are so misunderstood that the
stiffened composite wing skin is regarded as equivalent to an integrally stiffened
machined aluminium plank, rather than the bonded structure it actually is –
because fibre-polymer composites have been defined to be “homogeneous.”
The Empirical Original Maximum-Strain And
Truncated Maximum-Strain Models
nxy > nLT
a = ARCTAN(n LT)
Vertical Limits for
0o Fibers,
Horizontal Cut-Offs
for 90o Fibers
0
e 2
- eLc
eLt
Original Maximum-Strain
Model
e 1a
a
Truncated Maximum-Strain Model
(1 +nLT)eLt
e 1
45o
e 2
0
45o Sloping Cut-Offs for
Both Fiber Directions
eLt
- eLc
- eLc
- eLc eL
t
eLt
a
anxy < nLT
Typical Interactive Composite Failure Model
0
Matrix-Dominated
Transverse
Tension Strength
Fibre-Dominated
Longitudinal Tensile
Strength
Undefined
Geometry-Dependent
Transverse Compression
Strength
Fibre-Dominated
But Matrix-Influenced
Longitudinal
Compressive Strength
?
What is Happening at
the Off-Axis Points?
Which Constituent
is Failing?
An Equally Meaningless Curve Drawn Through
Unrelated Data Points
0
Number of Rocks on
the Moon
Number of Waves in
the Ocean
Number of Trees in
the Forest
Number of Stars in
the Sky
?
What is the Physical
Meaning of All the
Intermediate Points?
A Point To Ponder About Hashin’s Failure Model
Hashin’s two-equation failure model is widely used because it is believed that
one equation covers fibre failures, while the other addresses matrix failures,
avoiding the inherent limitation of the single-equation Tsai-Wu Model.
(However, Hashin’s equations are not independent; they are coupled by the in-
plane shear stresses.)
Hashin’s model is deeply embedded in all structural analysis computer codes.
Yet, Hashin has declared in writing that his theory does not work; this is why he
declined to participate in the World Wide Failure Exercise. In doing so, he also
stated that he believed that no one else’s theory worked, either. To reinforce his
message, he switched to a totally unrelated field for all his subsequent research.
Why won’t anyone believe him?
Failure Envelope for Unidirectional Ply Deduced from SIFT
Properties, on Lamina Stress Plane
Unattainable fibre
strengths preceded
by matrix failures
Distortional (gvM)
Failures in Fibers,
(Insensitive to
Environment)
Longitudinal
Stress0
Transverse StressDilatational (J1)
Failure of Matrix,
(Varies with
Environment)
Note greatly expanded
transverse stress scale,
about 10:1, for clarity
Note that each portion of the failure envelope refers to one distinct constituent
and is fully defined by the single data point needed to characterize each of the
two non-interactive failure mechanisms. Fibre-failure envelope locally
truncated by matrix-failure cut-off.
0o Lamina
Tension Test
90o Lamina
Tension Test
Physical Model of Unit Cell of a
Steel-reinforced Concrete Slab
Steel Rods
Concrete Slab
Mathematical Model of Layered Unit Cell
of a Steel-reinforced Concrete Slab
Steel Plates
Concrete
Layers
The “Lamina Properties” for Steel-Reinforced Concrete
According to Interactive Models Used for Composite Materials
0
Concrete-Limited
Transverse
Tension Strength
Steel-Dominated
Longitudinal Tensile
Strength
Concrete Limited
Transverse Compression
Strength
Steel-Dominated
Longitudinal
Compressive Strength
?
How does encasing the steel rods in
concrete increase their longitudinal
compressive strength when subjected to
transverse compression ?
Why is it so obvious that the concept of a
homogenized “equivalent” steel- reinforced
concrete model makes no sense while it is
insisted that exactly the same model is
appropriate for fibre-reinforced resin
composites?
Contrarian Model of Layered Unit Cell of Fibre-Polymer
Composite Laminate With Interfacial Layers of Resin
Homogenized 0o Lamina
Homogenized 0o Lamina
Homogenized
90o Lamina
Homogenized
+45o Lamina
Homogenized -45o Lamina
Very Thin, but Finite Interfacial Resin Layers Between Laminae
Traditional Model of Layered Unit Cell of Fibre-Polymer
Composite Laminate, Without any Interfacial Layers of Resin
Homogenized 0o Lamina
Homogenized 0o Lamina
Homogenized
90o Lamina
Homogenized
+45o Lamina
Homogenized -45o Lamina
Zero-Thickness Interfaces Between Layers
Are Fracture Mechanics Analyses Relevant to Delaminations
and Matrix Cracking in Fibre-Polymer Composites?
Fracture mechanics analyses cannot possibly predict the initiation of matrix
damage; they require the presence of a pre-existing crack. (SIFT can!)
Fracture mechanics analyses require the presence of a singularity in the model to
even be applicable. It appears that the prediction of singularities in the matrix of
fibre-polymer composites is the result of over-simplified structural models, as a
consequence of never-justified homogenization.
Some delaminations occur away from any free edges, where there is no
possibility of predicting a singularity.
Have fracture mechanics analyses, as applied for homogeneous materials, ever
been validated for use in heterogeneous materials?
Fracture mechanics analyses have been just as ineffective in predicting potential
matrix failures as have the interactive composite failure models. (Non-interactive
models were never expected to be capable of doing so.)
It is clear that the very use of fracture mechanics in solving matrix failures in
fibre-polymer composites analyses needs to be thoroughly re-assessed.
Shrinkage of Resin Matrix Around Fibres
Length
Essentially
Unchanged during
Cool-Down after Cure
Contraction in Thickness
Matrix
Fibres
Transverse Contraction Due to
Resin Shrinkage
Distribution of Internal Residual Stresses in Polymer Matrices Caused by
Thermal Contraction During Cool-Down after High-temperature Cure
Resin MatrixFibres Surrounded by High
Tensile Hoop Stresses and
Radial Compressive Stresses
Caused by Residual Thermal
Stresses in Matrix
High Tensile Residual Thermal
Stress Along Fibre Direction
Throughout ALL the Matrix
Interstices,
where the
Fibres are
Furthest
Apart.
Regions of
High Triaxial
Tension
Residual
Thermal
Stresses,
but Low
Mechanical
StressesInter-fibre Regions, Where Fibres are Closest Together, and Stresses
from Transverse Loads and Residual Thermal Loads are Highest
Fibre
Transverse
Mechanical
Load
Explanation of Size Effect (Tow Size) in Transferring Interfacial
Shear Loads Between the Matrix and the Embedded Fibres
Axially Loaded Bundle (Tow) of Fibres Shearing
End Load into Surrounding Resin Matrix
Shear Stress Proportional to Ratio of Fibre
Bundle Cross Section to Its Perimeter, i.e.
Directly Proportional to Tow Size, for a
Common Applied Lamina-Level Stress
Small Tow Size Associated with
Low Interfacial Shear Stress
Large Tow Size Associated with
Excessive Interfacial Shear Stress
This is why large noodles are a liability, not a
desirable design feature. They separate from
the rest of the stiffener by delaminating,
starting at the ends, which move continuously
as the delamination progresses.
Edge Delaminations, or Worse, Caused by
Excessive Blocking of Parallel Plies
4-Ply Stacks,
45o and 90o Angle Changes,
Some Delaminations
4-Ply Stacks,
45o Angle Changes,
No Delaminations
0o Fibres
+45o Fibres
-45o Fibres
90o Fibres
Thick 8-Ply Stacks,
45o Angle Changes,
Total Delaminations
AS-4/3501-6 Carbon/Epoxy, 0.005 in. (0.0125 mm) UD Plies
Through-the-Thickness Layer Splitting Leading to Interfacial
Delaminations Caused by Excessive Blocking of Parallel Plies
Crack Initiation
Crack Grows to
Interfaces
Crack Spreads as Delaminations
Damage Propagation in Fibre-Polymer Composites
Initial damage, in the matrix, is self arresting when the surrounding stress and
strain field is lower than the region where such damage initiates. This is the
source of the added strength of bolted composite joints above predictions based
on linear elastic analysis of homogenized laminae. This damage is benign and is
taken advantage of in establishing strengths.
Initial damage will spread unrestrained whenever the surrounding region is just as
highly stressed, and strained, as the damaged region. The rate of spreading is
really unimportant. Immediate repair is necessary before the residual strength
with damage drops to unacceptable levels. Such repair is not always possible, as
with large noodles in stiffeners. It is never easy.
Test coupons for delaminations from impact damage are customarily free from
typical in-plane loads in real structures. This assumes that there is no interaction.
Has this ever been verified?
The model of long stable crack growth associated with the fatigue of thin-skin
2024 aluminium structures has no parallel in fibre-polymer composites.
Predicting in-service inspection intervals for composite structures on this basis is
questionable at best.
Typical Example of Defective Stiffener Run-Out
Designs, with Co-Cured Hat Stiffeners
Hinge Screws
Tie-down Screw Holes
A
A
Rubber
Mandrel
Extraction
Retrofitted
Bolt-On
Doublers
Beam Not Attached to
Supporting Structure
Delaminations Section A-A Enlarged and Inverted
Support
Structure
An Example of a Structurally Sound Stiffener Run-Out
Basic Cross Section
Stiffener Formed
around Removable
Rubber Mandrel
Metal Hinge
One-Piece Co-Cured Panel
Tie-Down
Screw Holes
Expansion Joints
in Composite Pre-
preg Located to
Reinforce Beam
Edge
Doubler
Intensity of Stress Concentration Factor
at Poorly Designed Stiffener Run-Out
h
t skin
Stiffener run-out design
to be avoided
Stiffeners should not
be terminated short of
the very ends of panels
Fatigue-crack or
delamination site
Edge of skin
Co-cured (or integral)
stiffener
stiffeners blade forgeneral inskin
stringert
skinstringer
stringert 1 , 1
t
hk
tt
Ak
k t h
t skin
Original Co-Cured Design for Large Composite Tail Cone, of
High Cost Because of Complexity of Each of the Few Parts
Open-Ended Segmented
Co-Cured Hat Stringers
Skin from Two Integrally
Stiffened Half-Shells
2 Rows of 3/16-inch Fasteners
Composite Tail-Cone,
Looking Aft
Metallic Substructure,
Bottom Half Pre-Assembled
Secondarily Bonded Lattices
of Stiffening Beads
Secondarily Bonded Lattices
of Stiffening Beads
Z-Section
Sheet-Metal
Intercostals
Sheet-Metal Frames
C-Section Machined
Intercostals
One-Piece Unstiffened
Composite Skin
Improved Secondarily Bonded Design for C-17 Tail Cone,
of Far Lower Cost than Original Co-cured Design
Bonded-Beaded Hollow-hat Stringers
for Composite Fuselages
Cross Section
Region of Double Thickness
Stringer Centreline
Frame Centreline
Note: Double-Thickness (Overlap)
Regions are Necessary for
Manufacture as Well As Strength
Basic Cross Section
Is Precisely Semi-
Circular
Features to be Avoided in Composite Aircraft Wing Splices
Upper Metallic
Splice Plate
Lower Metallic Splice Plate
Composite
Skin
Co-Cured Stringer0o NoodleInitiation Point
for Delamination
Delamination Spreads, and is
Arrested as Bolts Pick Up the
Load between Skin and
Stringer, but Usually Not Until
after the Delamination has
Migrated from Interface into
Composite Skin
Stiffener
Terminated
Short of End
of Skin PanelBolt
Holes
Co-Cured
Spacer
Shearout of Plugs of Composite Bolted Joints
With an Excessive 0o Fibre Fraction
Test
Coupon Bolt
Hole
Full-Thickness Block Sheared Out,
Regardless of Edge Distance,
when Excess 0o Plies Are
Uniformly Interspersed
Bolt
Hole
Bolt
Hole
Test Coupon B
Test Coupon A
Concentrated
Blocks of 0o Plies
Sheared Out
Separately
Thermal Contraction of Angle Between Flanges in Composite
Angles (and Other Shapes)
Contraction of Angle between Flanges
during Cool-down after CureOpening Up of Angle between Flanges
during Prying Apart
Delaminations on
Inside of Corner
This problem cannot possibly be solved by fracture-mechanics analyses,
since the delaminations originate away from the ends of the components.
Delaminations Caused by Bolting Together
Composite Parts That Don’t Quite Fit
Spar
Skin
RibFasteners
Delaminations most likely
to occur where shaded, in
the skin or the root of the
rib flange, depending on
the relative stiffnesses
Original Positions of
Skin and Rib Flange
Original Gap
Concluding Remarks
Not even one of the traditional fibre-polymer composite failure models is
capable of predicting when matrix failures will occur, because of the
patently false and never validated assumption that it is permissible to
replace the individual fibre and polymer constituents by an “equivalent”
homogeneous anisotropic solid, to simplify the mathematics. It is not!
There is no such thing as a “composite material”; only composites OF
materials.
The problems have been made clear by an analogy with the standard
analyses for steel-reinforced concrete.
The answer to the question posed by the title of the paper is “Yes, there is
a need.” And it is about time that the composites establishment and
academia paid serious attention to this issue.
People designing and building such structures encounter considerable
difficulty as the result of unanticipated matrix failures occurring before
the fibres (actually it was the laminae) were predicted to fail.
The SIFT (Strain Invariant Failure Theory) model that has separate
expressions governing dilatational and distortional failures in the two
constituents does satisfy this need, but it is being treated as just another
theory, not as the revolutionary change it actually is.