Royal Society

Alan Arnold Griffith

Everest of fracture surface [By Kaspar Kallip (CC BY-SA 4.0), via Wikimedia Commons]

Some of you maybe aware that I hold the AA Griffith Chair of Structural Materials and Mechanics at the University of Liverpool.  I feel that some comment on this blog about Griffith’s seminal work is long overdue and so I am correcting that this week.  I wrote this piece for a step in week 4 of a five-week MOOC on Understanding Super Structures which will start on May 22nd, 2017.

Alan Arnold Griffith was a pioneer in fracture mechanics who studied mechanical engineering at the University of Liverpool at the beginning of the last century.  He earned a Bachelor’s degree, a Master’s degree and a PhD before moving to work for the Royal Aircraft Establishment, Farnborough in 1915.

He is famous for his study of failure in materials.  He observed that there were microscopic cracks or flaws in materials that concentrated the stress.  And he postulated that these cracks were the source of failure in a material.  He used strain energy concepts to analyse the circumstances in which a crack or flaw would propagate and cause failure of a component.  In order to break open a material, we need to separate adjacent atoms from one another, and break the bonds between them.  This requires a steady supply of energy to do the work required to separate one pair of atoms after another and break their bonds.  It’s a bit like unpicking a seam to let out your trousers when you’ve put on some weight.  You have to unpick each stitch and if you stop working the seam stays half undone.  In a material with a stress raiser or concentration, then the concentration is quite good at delivering stress and strain to the local area to separate atoms and break bonds.  This is fine when external work is being applied to the material so that there is a constant supply of new energy that can be used to break bonds.  But what about, if the supply of external energy dries up, then can the crack continue to grow?  Griffith concluded that in certain circumstances it could continue to grow.

He arrived at this conclusion by postulating that the energy required to propagate the crack was the work of fracture per unit length of crack, that’s the work needed to separate two atoms and break their bond.  Since atoms are usually distributed uniformly in a material, this energy requirement increases linearly with the length of the crack.  However, as the crack grows the material in its wake can no longer sustain any load because the free surface formed by the crack cannot react against a load to satisfy Newton’s Law.  The material in the wake of the crack relaxes, and gives up strain energy [see my post entitled ‘Slow down time to think (about strain energy)‘ on March 8th, 2017], which can be used to break more bonds at the crack tip.  Griffith postulated that the material in the wake of the crack tip would look like the wake from a ship, in other words it would be triangular, and so the strain energy released would proportional to area of the wake, which in turn would be related to the crack length squared.

So, for a short crack, the energy requirement to extend the crack exceeds the strain energy released in its wake and the crack will be stable and stationary; but there is a critical crack length, at which the energy release is greater than the energy requirements, and the crack will grow spontaneously and rapidly leading to very sudden failure.

While I have followed James Gordon’s lucid explanation of Griffith’s theory and used a two-dimensional approach, Griffith actually did it in three-dimensions, using some challenging mathematics, and arrived at an expression for the critical length of crack. However, the conclusion is the same, that the critical length is related to the ratio of the work required for new surfaces and the stored strain energy released as the crack advances.  Griffith demonstrated his theory for glass and then others quickly demonstrated that it could be applied to a range of materials.

For instance, rubber can absorb a lot of strain energy and has a low work of fracture, so the critical crack length for spontaneous failure is very low, which is why balloons go pop when you stick a pin in them.  Nowadays, tyre blowouts are relatively rare because the rubber in a tyre is reinforced with steel cords that increase the work required to create new surfaces – it’s harder to separate the rubber because it’s held together by the cords.

By the way, James Gordon’s explanation of Griffith’s theory of fracture, which I mentioned, can be found in his seminal book: ‘Structures, or Why Things Don’t Fall Down’ published by Penguin Books Ltd in 1978.  The original work was published in the Proceedings of the Royal Society as ‘The Phenomena of Rupture and Flow in Solids’ by AA Griffith, February 26, 1920.

A tiny contribution to culture?

img-20161204-wa00031112This year I would like to think more and do a little less. Or, in other words, to make a better job of fewer things.  This resolution has caused me to think about why I write this blog and whether I should continue to do so.  I started writing it in 2012 as part of an outreach effort mandated by a Royal Society Wolfson Research Merit Award that I held for five years until February 2016. So, the original motivation for writing a weekly blog has expired but obviously I have continued – why?

Well, a number of reasons come to mind, first: loyalty to my readers – in 2015 visitors to this blog would have filled six New York subway trains [see my post of January 21st, 2016].  The number of visitors more than doubled in 2016 so that now you would fill a small Premier league football stadium.  It’s difficult to disappoint this number of readers.

Second: the annual doubling of the blog’s readership perhaps suggests that I am doing something worthwhile – making a small contribution to our culture and society.  To quote the neuroscientist Vittorio Gallese in conversation with Stefan Klein ‘by passing on just a little bit of knowledge, every human being makes a contribution to that culture’.   Most of the time this is an altruistic motivation but occasionally it is converted into an inner warm glow when I meet someone who says ‘I read your blog and …’

The third reason is purely selfish: the process of writing is therapeutic and provides an opportunity to collect, order and record my thoughts and ideas.  My editor thinks that I focus too much on re-blogging other peoples’ ideas and that more originality would bring a bigger increase in readership. She is probably right about the connection between originality and readership but original thinking is hard to do, especially on a weekly basis, so often the best I can do is to join dots in ways that perhaps you haven’t thought about.

My final reason is more pecuniary. As an academic researcher, I need to apply for funding to support my research group of about a dozen people.  Engagement in enhancing the public understanding of science and technology is an expectation of many funding bodies and so an established blog with a stadium-sized readership is an asset that justifies the investment of time.

The relative importance of these reasons varies with my mood and audience but together they are sufficient to ensure that writing a weekly post will be one of the fewer things that I plan to do better in 2017.  I guess that means fewer introspective posts like this one!

Best wishes for a happy and prosperous New Year to all my readers!

Source: Stefan Klein, We are all stardust, London: Scribe, 2015.

Opal offers validation opportunity for climate models

OrangeFanSpongeSmallMany of us will be familiar with the concept of the carbon cycle, but what about the silicon cycle?  Silicon is the second most abundant element in the Earth’s crust.  As a consequence of erosion, it is carried by rivers into the sea where organisms, such as sponges and diatoms (photosynthetic algae), convert the silicon in seawater into opal that ends up in ocean sediment when these organisms die.  This marine silicon cycle can be incorporated into climate models, since each step is influenced by climatic conditions, and the opal sediment distribution from deep sea sediment cores can be used for model validation.

This approach can assist in providing additional confidence in climate models, which are notoriously difficult to validate, and was described by Katharine Hendry, a Royal Society University Research Fellow at the University of Bristol at a recent conference at the Royal Society.  This struck me as an out-of-the box or lateral way of seeking to increase confidence in climate models.

There are many examples in engineering where we tend to shy away from comprehensive validation of computational models because the acquisition of measured data seems too difficult and, or expensive.  We should take inspiration from sponges – by looking for data that is not necessarily the objective of the modelling but that nevertheless characterises the model’s behaviour.



Super channel system

polina bayvelPerhaps we can be characterized by whether or not we believe we have an acceptable speed of internet access.  At home and work, I’m in the category that’s never satisfied by the speed provided.  Well, now there is a completely new standard: 1.125 Tb/s.  That’s 50,000 times faster than anything commercially available at the moment.  You could download a boxed set of the entire Games of Thrones saga in a second; at least that’s how Professor Polina Bayvel described her latest research in a recent conference that I attended at the Royal Society.  Professor Bayvel is head of the Optical Networks Group at University College London.  I think the UK government should abandon attempting to extend the current internet technology to everyone in the country and instead leap-frog the rest of the world by working on rolling out Prof Bayvel’s new technology.


Maher R, Xu T, Galdino L, Sato M, Alvarado A, Shi K, Savory SJ, Thomsen BC, Killey RI & Bayvel P, Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back propagation, Scientific Reports, 5:8214, 2015.

Small is beautiful and economic

tractorFarm tractors have been growing bigger and bigger, though perhaps not everywhere – the photograph was taken in Donegal, Ireland earlier this year.  The size of tractors is driven by the economics of needing a driver in the cab. The labour costs are high in many places, so that the productivity per tractor driver has to be high too.  Hence, the tractors have to move fast and process a large amount of the field on each pass.  This leads to enormous tractors that weigh a lot and exert a large pressure on the soil, which in turn results in between 1 and 3% of the farm land becoming unproductive because crops won’t grow in the severely compressed soil. But what happens if we eliminate the need for the driver by using autonomous vehicles? Then, we can have smaller vehicles working 24/7 that do less damage and are cheaper, which means that a single machine breakdown doesn’t bring work to halt. We can also contemplate tailoring the farming of each field to the local environmental and soil conditions instead a mono-crop one-size fits all approach. These are not my ideas but were espoused by Peter Cooke of the Queensland University of Technology at a recent meeting at the Royal Society on ‘Robotics and Autonomous Systems’.

It is a similar argument for modular nuclear power stations. Most of the world is intent on building enormous reactors capable of generating several GigaWatts of power (that’s typically 3 with nine zeros after it) at a cost of around £8 billion (that’s 8 with nine zeros) so about 50 pence per Watt. Such a massive amount of power requires a massive infrastructure to deliver the power to where it is need and a shutdown for maintenance or a breakdown potentially cuts power to about a million people. The alternative is small modular reactors built, and later dismantled, in a factory that leave an uncontaminated site at a lower capital cost and which provide a more flexible power feed into the national grid. Some commentators (see for example Editor’s comment in Professsional Engineer, November 2015)believe that a factory could be established and rolling modular reactors off its production line on the same timescale as building a GigaWatt station.

Regular readers will recognise a familiar theme found in Small is beautiful and affordable in nuclear powerstations on January 14th, 2015, Enabling or disruptive technology for nuclear engineering on January 28th, 2015 and Small is beautiful on October 10th, 2012; as well as the agricultural theme in Knowledge-economy on January 1st, 2014.