Month: April 2017

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.

Gone walking

Background and lock-screen pictures have become a feature of modern life.  Your computer and mobile device were probably delivered with some pre-loaded scenes from nature and some of us personalize our devices by up-loading photographs taken on holiday or a recent excursion into the countryside.  Perhaps, we do this intuitively, because recent research has shown that immersion in nature, even at the superficial level of viewing a picture can improve brain function.  Brisk walking stimulates the production of new neurons and, when you do it in an environment enriched with natural stimuli, the connectivity and stability of connectivity between neurons is increased.  For those us whose biological systems are in terminal decline, the opportunity to retard this decline by walking in the wild is too good to miss.  I have gone to the English Lake District to produce and connect some more neurons.  I’ll be back next week – feeling hopefully creative and empowered, as well as, probably rather damp but what else can be expected from northern England in April!

For those of you who want to immerse themselves vicariously in the damp natural environment of England in the rain could read ‘Rain: Four Walks in English Weather‘ by Melissa Harrison.


Susan Greenfield, A Day in the Life of the Brain, London: Allen Lane, 2016.

Atchley RA, Strayer DL & Atchley, Creativity in the wild: improving creative reasoning through immersion in natural settings, PloS One, 7:e51474, 2012.

Yao S et al, Physical exercise-induced adult neurogenesis: a good strategy to prevent cognitive decline in neurodegenerative diseases? Biomedical Research Intl., 2014, 403120.

Olson KA et al, Environmental enrichment and voluntary exercise massively increase neurogenesis in the adult hippocampus via dissociable pathways, Hippocampus, 16:250-260, 2006.

Attribute triplets

It’s curious how we latch on to three-word lists, or attribute triplets.  There’s the famous one attributed to Julius Caesar in a letter to the Roman Senate about one of his military victories: ‘Veni. Vidi. Vici.’ – I came. I saw. I conquered.  In my forthcoming MOOC on Understanding Super Structures, I cite the Roman architect and engineer, Vitruvius who recommended that structures should have ‘Firmatas. Utilitas. Venustas.’ – Durability. Utility. Beauty.   Perhaps these were the original soundbites.  In modern times, the concept has been taken down-market by realtors (estate agents) who talk about ‘Location. Location. Location.’  And, by my leadership coach at the Center for Creative Leadership, who told us that the three laws of leadership were ‘Communication. Communication. Communication.’  This seems to represent trading content for impact . So, I was surprised to see, on the frontpage of our weekend newspaper in large type, the following:  ‘Knowledge. Integrity. Discretion.’  I thought perhaps they were describing the attributes of a college tutor or a life mentor.  However, they were part of an advertisement for a realtor, who was claiming ‘to have unrivalled knowledge [and to] provide a trusted and personal service’.  Sounds like a college tutor again!  Maybe as college professors, we should promote ourselves as having ‘Knowledge. Skills. Understanding.’  Of course, we don’t offer these attributes to our students, only the opportunity to learn how to acquire them – a subtlety that’s missed by a substantial number of our students.

We are all citizens of the world

A longer post this week because I was invited to write an article for the Citizens of Everywhere project being organised by the Centre for New and International Writing at the University of Liverpool. The article is reproduced below:

Scientists seek to discover and describe knowledge, while engineers seek to apply and deploy the same knowledge by creating technology that supports our global society.  In their quests, both scientists and engineers are dependent on each other and on those that have gone before them.  On each other, because scientists increasingly need technology in order make discoveries, and because engineers need new scientific discoveries to drive innovation; and both groups stand on the shoulders of their predecessors, to mis-quote Isaac Newton who said he was able to see further by standing on the shoulders of his predecessors.  Scientists and engineers have to build on the achievements of their predecessors, otherwise nothing would be achieved in a single lifetime.  This process is enabled by the global dissemination of knowledge and understanding in our society, which does not recognise any boundaries and flows around the world largely unimpeded by the efforts of nation states and private corporations.  As Poincaré is reputed to have said ‘the scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful’.  The feeling of delight is a reward for hours of intense study; but, the realization that you are the first to recognise or discover a new scientific fact generates so much excitement that you want to tell everyone.  Scientists have always met to share their findings and discuss the implications.  As a young researcher, I had a postcard above my desk showing a photograph of the attendees at the 5th Solvay Conference in 1927 at which 29 scientists from around the world met to debate the latest discoveries relating to electrons and photons.  Seventeen of the 29 attendees at this conference went on to receive Nobel prizes.  Not all scientific meetings are as famous, or perhaps as significant, as the Solvay conference; but, today they are happening all around the world involving thousands of researchers from scores of countries.  Besides the bureaucratic burden of obtaining visas, national boundaries have little impact on these exchanges of scientific and technological knowledge and understanding.  If you are a researcher working in the subject with sufficient funding then you can attend; and if your work is sufficiently novel, rigorous and significant, as judged by your peers, then you can present it at one of these meetings.  You can also listen to the world’s leading experts in the field, have a discussion over a coffee, or even a meal, with them before going back to your laboratory or office and attempting to add to society’s knowledge and understanding.  Most scientists and engineers work as part of a global community contributing to, and exploiting, a shared knowledge and understanding of natural and manufactured phenomena; and in this process, as global citizens, we are relatively unaware and uninfluenced by the national boundaries drawn and fought over by politicians and leaders.  Of course, I have described a utopian world to which reality does not conform, because in practice corporations attempt to protect their intellectual property for profit and national governments to classify information in the national interests and sometimes restrict the movement of scientists and technologist to and from states considered to be not playing by the right set of rules.  However, on the timescale of scientific discovery, these actions are relatively short-term and rarely totally effective.  Perhaps this is because the delight in the beauty of discovery overcomes these obstacles, or because the benefits of altruistic sharing outweigh the selfish gain from restrictive practices.  (Of course, the scientific community has its charlatans, fraudsters and free-loaders; but, these counterfeiters tend to operate on a global stage so that even their fake science impacts on the world-wide community of scientists and engineers.)  Participation in this global exchange of ideas and information makes many of us feel part of a world-wide community, or citizens of the world, who are enfranchised by our contributions and interactions with other citizens and international organisations.  Of course, along with everyone else, we are also inhabitants of the world; and these two actions, namely enfranchisement and inhabiting, are key characteristics of a citizen, as defined by the Shorter Oxford English Dictionary.  Theresa May in her speech last October, at the Conservative party conference said: ‘If you believe you’re a citizen of the world, you’re a citizen of nowhere.’  If she is right, then she rendered many scientists and engineers as aliens; however, I don’t think she is, because citizenship of the world does not exclude us from also being citizens of other, local communities; even though politicians may want to redraw the boundaries of these communities and larger unions to which they belong.  However, in practice, it is hard to avoid the fact that we are all inhabitants of planet Earth and have a responsibility for ensuring that it remains habitable for our grand-children and great-grandchildren; so, we are all citizens of the world with its associated responsibilities.

When I was a student, thirty years ago, James Lovelock published his famous book, ‘Gaia’ in which he postulated that the world was a unified living system with feedback control that preserved its own stability but not necessarily the conditions for the survival of the human race.  More recently, Max Tegmark, in his book ‘Our Mathematical Universe’, has used the analogy of spaceship Earth stocked with large but limited supplies of water, food and fuel, and equipped with both an atmospheric shield and a magnetic field to protect us from life-threatening ultra-violet and cosmic rays, respectively.  Our spaceship has no captain; and we spend next to nothing on maintenance such as avoiding onboard explosions, overheating, ultra-violet shield deterioration or premature depletion of supplies.  Lovelock and Tegmark are part of a movement away from a reductionist approach to science that has dominated since Descartes and Newton, and towards systems thinking, in which it is recognised that the whole is more than the sum of the parts.  It’s hard for most of us to adopt this new thinking, because our education was configured around dividing everything into its smallest constituent parts in order to analyse and understand their function; but, this approach often misses, or even destroys, the emergent behaviour of the complex system – it’s like trying to understand the functioning of the brain by physically dissecting it.  Recently reported statements about citizens of the world and about climate change, suggest that some world leaders and politicians find it easier, or more convenient, to use reductionism to ignore or deny the potential for complex systems, such as our global society and planet Earth, to exhibit emergent behaviour.

Thomas L. Friedmann in his book, ‘The World is Flat’ warned that ‘every young American would be wise to think of themselves competing against every young Chinese, Indian or Brazilian’.  He was right; we cannot turn back the globalisation of knowledge.  The hunger for knowledge and understanding is shared by all and courses provided over the internet are democratizing knowledge to an unprecedented level.  For instance, I recently taught a course on undergraduate thermodynamics – not normally a popular subject; but, it was made available globally as a massive open on-line course (MOOC) and taken by thousands of learners in more than 130 countries.  The citizens of the world are becoming empowered by knowledge and simultaneously more networked.  Large complex networks are systems that exhibit emergent behaviour, which tends to be unexpected and surprising, especially if you only consider their constituents.