Is There Really No Need to Be Able to Predict Matrix Failures in Fibre-Polymer Composite Structures? by Dr. L. J. Hart-Smith 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 Doubler Pure Resin Interface Skin Run-Out Zone Skin-Doubler Combination: All the load carried in the doubler can pass to or from the skin ONLY through the thin resin interface. Impact Delamination Broken Fibres 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 1/10 th 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 Vertical Limits for e 2 0 o Fibers, e 2 45 o Sloping Cut-Offs for a = ARCTAN( n LT ) Horizontal Cut-Offs Both Fiber Directions for 90 o Fibers e L e L t t 45 o a a (1 + n LT ) e L t n xy < n LT e 1 - e L - e L e L a c a c t 0 0 e L e 1 t n xy > n LT - e L - e L c c Original Maximum-Strain Truncated Maximum-Strain Model Model
Typical Interactive Composite Failure Model Matrix-Dominated Transverse Tension Strength Fibre-Dominated But Matrix-Influenced Longitudinal Compressive Strength 0 Fibre-Dominated Longitudinal Tensile Strength ? What is Happening at the Off-Axis Points? Undefined Geometry-Dependent Which Constituent Transverse Compression is Failing? Strength
An Equally Meaningless Curve Drawn Through Unrelated Data Points Number of Rocks on the Moon Number of Stars in the Sky 0 Number of Waves in the Ocean ? What is the Physical Number of Trees in Meaning of All the the Forest 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 Transverse Stress Dilatational ( J 1 ) Failure of Matrix, Unattainable fibre (Varies with strengths preceded Environment) by matrix failures 90 o Lamina Tension Test Longitudinal Stress 0 Distortional ( g vM ) 0 o Lamina Failures in Fibers, Tension Test (Insensitive to 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.
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 Why is it so obvious that the concept of a homogenized “equivalent” steel - reinforced concrete model makes no sense while it is Concrete-Limited insisted that exactly the same model is Transverse appropriate for fibre-reinforced resin Tension Strength composites? Steel-Dominated Longitudinal Compressive Strength 0 Steel-Dominated Longitudinal Tensile Strength ? How does encasing the steel rods in Concrete Limited concrete increase their longitudinal Transverse Compression compressive strength when subjected to Strength transverse compression ?
Contrarian Model of Layered Unit Cell of Fibre-Polymer Composite Laminate With Interfacial Layers of Resin Homogenized +45 o Lamina Homogenized 0 o Lamina Homogenized -45 o Lamina Homogenized 90 o Lamina Homogenized 0 o 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 +45 o Lamina Homogenized 0 o Lamina Homogenized -45 o Lamina Homogenized 90 o Lamina Homogenized 0 o Lamina Zero-Thickness Interfaces Between Layers
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