Dr. L. J. Hart-Smith Informal Lectures in Europe and the UK, April - - PowerPoint PPT Presentation

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. Skin Doubler 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

e 2

• eL

c

eL

t

Original Maximum-Strain Model e 1 a a Truncated Maximum-Strain Model

(1 +nLT)eL

t

e 1

45o

e 2

45o Sloping Cut-Offs for Both Fiber Directions

eL

t

• eL

c

• eL

c

• eL

c

eL

t

eL

t

a a nxy < nLT

Typical Interactive Composite Failure Model

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

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

• ne 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 Stress Transverse Stress Dilatational (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

• f a Steel-reinforced Concrete Slab

Steel Plates Concrete Layers

The “Lamina Properties” for Steel-Reinforced Concrete According to Interactive Models Used for Composite Materials

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 Matrix Fibres 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 Stresses Inter-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

• n 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 for general in

skin stringer t skin stringer stringer t

1 , 1 t h k t t A k     

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

• f Stiffening Beads

Secondarily Bonded Lattices

• f 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,

• f 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 Stringer 0o Noodle Initiation 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

• f Skin Panel

Bolt 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 Cure Opening 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 Rib Fasteners 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.