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.