From atoms to aeroplanes – high performance composite design
Fibre-reinforced composites are everywhere in the modern world. Since the world’s first fibreglass boat hull was built in the 1930s, composites have found uses in countless industries, including military, aerospace, automotive, civil engineering and consumer markets. Among the explosion of different applications and uses, the standout performer for stiff, strong, light and durable structures has been carbon fibre reinforced epoxy (CFRE).
Surprisingly, the design of composite laminates has changed very little in the last three decades. The near infinite tailorability of composites is accompanied by a similarly astronomical cost to test and validate the mechanical properties of every newly devised fibre, resin and lay-up combination. It is for this reason that fibre orientations for the vast majority of parts are still selected from only four possible directions, regardless of optimal design.
Predicting the end
The biggest hurdle limiting the use of highly optimised composite laminates is the poor ability to predict their strength. The complexity of failure in composite materials has spurred years of research into failure theories. These theories generally predict failure by comparing a particular stress state in each ply of the laminate to a set of strength terms calibrated from test data. These theories are all based on similitude. As long as the calibrating tests are performed under similar conditions to the real engineering problem, the results will be reasonable.
The weakness of similitude-based theories is that the real world is much more complex than the test laboratory. What role does the heterogeneity and volume fraction of the fibre-resin system play in the engineering properties? What is the effect of temperature or loading rate? Should failure predictors be based on stress or strain? To answer all these questions, there is a need for a physics-based failure theory. The theory must capture the physics of the constituent materials, their geometric relationship within the composite and the effects of temperature, while the method must be applicable to as many composite systems as possible.
Researchers at Boeing and The University of New South Wales (UNSW), Australia, have developed such a theory, known as Onset Theory – so called because it predicts the onset of irreversible damage in the composite. It represents a revolution in composites failure prediction, as it is consistent across all scales – from the molecular structure to the engineering component.
Composites are not metals
Much of the early work predicting the failure of composite materials was inspired by work in the metals field. The von Mises yield surface, in particular, was extended to fit the orthotropic properties of composites. The elliptical yield surfaces are still at the core of the vast majority of popular failure theories today. The influence of the truncated elliptical failure surface approach to composites design is so entrenched, that only in recent years have researchers realised it is based on fundamentally flawed science.
The failure of a laminate or ply of composite material cannot be determined from the global stress state alone. It can easily be shown that the loads on the constituents do not follow the same trends as the loads at the ply level, meaning either the constituent must have very exotic properties or the traditional approaches are incorrect.
The behaviour of glassy polymers in a composite is governed by the intrinsic polymer behaviour, as well as the restraint provided by the fibres, which limits any plastic fl ow processes and restricts failure to brittle failure modes. It has been shown by other researchers that failure in this state is governed by two strain invariants. The first critical invariant is related to the degree of volume change (dilatation) and the second to shape change (distortion). The two invariants are independent – the polymer fails by one or the other, not a combination of the two.
If it has been established that local resin failure was predicted by two independent and competing failure mechanisms, the question still remains: what physical processes govern each failure mechanism? To answer this, it was necessary to investigate the polymer at another, smaller length scale, along with the mechanics and dynamics of the polymer molecules.
Molecular modelling was performed on small repeating cells for a range of polymer systems. The cells were loaded to rupture by applying degrees of dilatational and distortional strain to the boundaries in a molecular mechanics simulation. It was shown that at molecular level, the two failure processes were driven by independent physical phenomena. Dilatational failures were driven by the rupture of intramolecular bonds, while distortional failures were driven by conformation changes to the polymer backbone and relaxing of the intermolecular forces.
Rebuilding the composite
What use is this to a composites design engineer? It is obviously an intractable problem to predict the true strain state, even within a single ply that may include many millions of fibres embedded randomly in resin. For this to be of any use to the design of a real structure, it is necessary to have a method of calculating the resin strains from globally-obtained ply strains from analytical solutions of finite element analysis.
Instead of modelling each fibre discretely within the composite, a modelling technique has been developed that uses the constituent fibre and resin properties to build idealised heterogeneous composite models (see Fig 1). By systematically loading these models, a table of micro-mechanical enhancement (MME) factors can be constructed, which link the local strain distribution within the matrix to the global strain. The micro-mechanical modelling approach has the additional benefit of capturing the influence of temperature on the local strain distribution within the ply, due to the thermal expansion mismatch between resin and fibres after curing. It has been shown that the MMEs provide an excellent predictor for the behaviour of the statistically distributed fibres within each ply.
To ascertain validity of Onset Theory at engineering level, tests were carried out on unidirectional off-axis test coupons. These tests were selected as the baseline because the initiation of resin failure and the complete part failure coincide. These tests have been conducted for a range of glassy epoxy-carbon fibre systems including IM7/977-3, K3B/977-3 and T800s/3900-2.
The average strain-to-failure for each fibre angle was converted to a critical distortion and dilatational strain using the MME approach described above. The results for each invariant were normalised against the largest result. It is strikingly evident that at fibre angles of less than 20° the failure is driven by distortional strain, while at angles greater than 20° the failure is driven by dilatational strain. The crossover at 20° shows that the two mechanisms are completely independent.
Onset Theory is a robust, physics-based tool to aid designers of composite components, and represents a paradigm shift in the understanding of composite failure. Although implementation of the theory is initially challenging, changes to material systems and part lay-up can be made within a short time and without the need for excessive testing. A more comprehensive failure theory will allow designers to maximise strength while minimising structural weight.