Listening with your eyes shut

I am in the London Underground onboard a train on my way to a conference on ‘New Approaches to Higher Education’ organised by the Institution of Engineering and Technology and the Engineering Professors’ Council.  The lady opposite has her eyes closed but she is not asleep because she opens them periodically as we come into stations to check whether it’s her stop.  I wonder if she is trying to reproduce John Hull’s experience of the depth of sounds as a blind person [see my post entitled ‘Rain brings out the contours in everything‘ on February 22, 2017].  For the second time in recent weeks, I close my eyes and try it for myself.  It is surprising how in a crowded train, I can’t hear anyone, just the noise made by the train.  It’s like a wobble board that’s joined by a whole percussion section of an orchestra when we go around a bend or over points.  The first time I closed my eyes was at a concert at the Philharmonic Hall in Liverpool.  My view of the orchestra was obstructed by the person in front of me so, rather than stare at the back of their head, I closed my eyes and allowed the music to dominate my mind.  Switching off the stream of images seemed to release more of my brain cells to register the depth and richness of Bach’s Harpsichord Concerto No. 5.  I was classified as tone deaf at school when I was kicked out of the choir and I learned no musical instruments, so the additional texture and dimensionality in the music was a revelation to me.

Back to the London Underground – many of my fellow passengers were plugged into their phones or tablets via their ears and eyes.  I wondered if any were following the MOOC on Understanding Super Structures that we launched recently.  Unlikely I know, but it’s a bit different, because it is mainly audio clips and not videos.  We’re trying to tap into some of the time many people spend with earbuds plugged into their ears but also make the MOOC more accessible in countries where internet access is mainly via mobile phones.  My recent experiences of listening with my eyes closed, make me realize that perhaps we should ask people to close their eyes when listening to our audio clips so that they can fully appreciate them.  If they are sitting on the train then that’s fine but not recommended if you are walking across campus or in town!

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.

Instructive report and Brexit

Even though this blog is read in more than 100 countries, surely nobody can be unaware of the furore about Brexit – the UK Government’s plan to leave the European Union.  The European Commission has been funding my research for more than twenty years and I am a frequent visitor to their Joint Research Centre in Ispra, Italy.  During the last decade, I have led consortia of industry, national labs and universities that rejoice in names such as SPOTS, VANESSA and, most recently MOTIVATE.  These are acronyms based loosely on the title of the research project.  Currently, there is no sign that these pan-European research programmes will exclude scientists and engineers from the UK, but then the process of leaving the EU has not yet started, so who knows…

At the moment, I am working with a small UK company, Strain Solutions Ltd, on a EU project called INSTRUCTIVE.  I said these were loose acronyms and this one is very loose: Infrared STRUctural monitoring of Cracks using Thermoelastic analysis in production enVironmEnts.  We are working with Airbus in France, Germany, Spain and the UK to transition a technology from the laboratory to the industrial test environment.  Airbus conducts full-scale fatigue tests on airframe structures to ensure that they have the appropriate life-cycle performance and the INSTRUCTIVE project will deliver a new tool for monitoring the development of damage, in the form of cracks, during these tests.  The technology is thermoelastic stress analysis, which is well-established as a laboratory-based technique [1] for structural analysis [2], fracture mechanics [3] and damage mechanics [4], that I described in a post on November 18th, 2015 [see ‘Counting photons to measure stress’].  It’s exciting to be evolving it into an industrial technique but also to be looking at the potential to apply it using cheap infrared cameras instead of the current laboratory instruments that cost tens of thousands of any currency.  It’s a three-year project and we’ve just completed our first year so we should finish before any Brexit consequences!  Anyway, the image gives you a taster and I plan to share more results with you shortly…

BTW – You might get the impression from my recent posts that teaching MOOCs [see ‘Slowing down time to think [about strain energy]’ on March 8th, 2017] and leadership [see ‘Inspirational leadership’ on March 22nd, 2018] were foremost amongst my activities.  I only write about my research occasionally.  This would not be an accurate impression because the majority of my working life is spent supervising and writing about research.  Perhaps, it’s because I spend so much time writing about research in my ‘day job’ that last year I only blogged about it three times on: digital twins [see ‘Can you trust your digital twin?’ on November 23rd, 2016], model credibility [see ‘Credibility is in the Eye of the Beholder’ on April 20th, 2016] and model validation [see Models as fables on March 16th, 2016].  This list gives another false impression – that my research is focussed on digital modelling and simulation.  It is just the trendiest part of my research activity.  So, I thought that I should correct this imbalance with some INSTRUCTIVE posts.


[1] Greene, R.J., Patterson, E.A., Rowlands, R.E., 2008, ‘Thermoelastic stress analysis’, in Handbook of Experimental Mechanics edited by W.N. Sharpe Jr., Springer, New York.

[2] Rowlands, R.E., Patterson, E.A., 2008, ‘Determining principal stresses thermoelastically’, J. Strain Analysis, 43(6):519-527.

[3] Diaz, F.A., Patterson, E.A., Yates, J.R., 2009, ‘Assessment of effective stress intensity factors using thermoelastic stress analysis’, J. Strain Analysis, 44 (7), 621-632.

[4] Fruehmann RK, Dulieu-Barton JM, Quinn S, Thermoelastic stress and damage analysis using transient loading, Experimental Mechanics, 50:1075-1086, 2010.

Slowing down time to think [about strain energy]

161-6167_imgLet me take you bungee jumping.  I should declare that I am not qualified to do so, unless you count an instructor’s certificate for rock-climbing and abseiling, obtained about forty years ago.  For our imaginary jump, pick a bridge with a good view and a big drop to the water below and I’ll meet you there with the ropes and safety gear.

It’s a clear early morning and the air is crisp and fresh – ideal for throwing yourself off a bridge attached to a rope.  The rope is the star of this event.  It’s brand new, which is reassuring, and arrived coiled over my shoulder.  A few days ago, I asked you how much you weigh – that’s your real weight fully clothed, at least I hope that’s the number you gave me otherwise my calculations will be wrong and you’ll get wet this morning!  I have calculated how much the rope will stretch when it arrests your free-fall from the bridge parapet; so, now I am measuring out enough rope to give you an exciting fall but to stop you short of the water.  I’m a professor of structural materials and mechanics so I feel confident of getting this bit right; but it’s a long time since I worked as an abseiling instructor so I suggest you check those knots and that harness that we’ve just tightened around you.

You’ve swung yourself over the parapet and you’re standing on the ledge that the civil engineers conveniently left for bridge jumpers.  The rope is loosely coiled ready with its end secured to a solid chunk of parapet.  As you alternate between soaking up the beautiful view and contemplating the chasm at your feet, you wonder why you agreed to come with me.  At this moment, you have a lot of potential energy due to your height above the sparkling water [potential energy is your mass multiplied by your height and gravitational acceleration], but no kinetic energy because you are standing motionless.  The rope is relaxed or undeformed and has zero strain energy.

Finally, you jump and time seems to stand still for you as the fall appears to be happening in slow motion.  The air begins to rush past your ears in a whoosh as you build up speed and gain kinetic energy [equal to one half your mass multiplied by your velocity squared].  The bridge disappeared quickly but the water below seems only to be approaching slowly as you lose height and potential energy.  In reality, your brain is playing tricks on you because you are being accelerated towards the water by gravity [at about 10 metres per second squared] but your total energy is constant [potential plus kinetic energy unchanged].  Suddenly, your speed becomes very apparent.  The water seems very close and you cry out in surprise.  But the rope is beginning to stretch converting your kinetic energy into strain energy stored by stretching its fibres [at a molecular level work is being done to move molecules apart and away from their equilibrium position].  Suddenly, you stop moving downwards and just before you hit the water surface, the rope hurls you upwards – your potential energy reached a minimum and you ran out of kinetic energy to give the rope; so now it’s giving you back that stored strain energy [and the molecules are relaxing to their equilibrium position].  You are gaining height and speed so both your kinetic and potential energy are rising with that squeal that just escaped from you.

Now, you’ve noticed that the rope has gone slack and you’re passing a loop of it as you continue upwards but more slowly.  The rope ran out of strain energy and you’re converting kinetic energy into potential energy.  Just as you work out that’s happening, you run out of kinetic energy and you start to free-fall again.

Time no longer appears to stationary and your brain is working more normally.  You begin to wonder how many times you’ll bounce [quite a lot because the energy losses due to frictional heating in the rope and drag on your body are relatively small] and why you didn’t ask me what happens at the end.  You probably didn’t ask because you were more worried about jumping and were confident that I knew what I was doing, which was foolish because, didn’t I tell you, I’ve never been bungee jumping and I have no idea how to get you back up onto the bridge.  How good were you at rope-climbing in the gym at school?

When eventually you stop oscillating, the rope will still be stretched due to the force on it generated by your weight.  However, we can show mathematically that the strain energy and deformation under this static load will be half the values experienced under the dynamic loading caused by your fall from the bridge parapet.  That means you’ll have a little less distance to climb to the parapet!

Today’s post is a preview for my new MOOC on ‘Understanding Super Structures’, which is scheduled to start on May 22nd, 2017.  This is the script for a step in week 2 of the five-week course, unless the director decides it’s too dangerous.  By the way, don’t try this home or on a bridge anywhere.

Popping balloons

Balloons ready for popping

Balloons ripe for popping!

Each year in my thermodynamics class I have some fun popping balloons and talking about irreversibilities that occur in order to satisfy the second law of thermodynamics.  The popping balloon represents the unconstrained expansion of a gas and is one form of irreversibility.  Other irreversibilities, including friction and heat transfer, are discussed in the video clip on Entropy in our MOOC on Energy: Thermodynamics in Everyday Life which will rerun from October 3rd, 2016.

Last week I was in Florida at the Annual Conference of the Society for Experimental Mechanics (SEM) and Clive Siviour, in his JSA Young Investigator Lecture, used balloon popping to illustrate something completely different.  He was talking about the way high-speed photography allows us to see events that are invisible to the naked eye.  This is similar to the way a microscope reveals the form and structure of objects that are also invisible to the naked eye.  In other words, a high-speed camera allows us to observe events in the temporal domain and a microscope enables us to observe structure in the spatial domain.  Of course you can combine the two technologies together to observe the very small moving very fast, for instance blood flow in capillaries.

Clive’s lecture was on ‘Techniques for High Rate Properties of Polymers’ and of course balloons are polymers and experience high rates of deformation when popped.  He went on to talk about measuring properties of polymers and their application in objects as diverse as cycle helmets and mobile phones.