mechanics

Press release!

A jumbo jet has about six million parts of which roughly half are fasteners – that’s a lot of holes.

It is very rare for one of my research papers to be included in a press release on its publication.  But that’s what has happened this month as a consequence of a paper being included in the latest series published by the Royal Society.  The contents of the paper are not earth shattering in terms of their consequences for humanity; however, we have resolved a long-standing controversy about why cracks grow from small holes in structures [see post entitled ‘Alan Arnold Griffith‘ on  April 26th, 2017] that are meant to be protected from such events by beneficial residual stresses around the hole.  This is important for aircraft structures since a civilian airliner can have millions of holes that contain rivets and bolts which hold the structure together.

We have used mechanical tests to assess fatigue life, thermoelastic stress analysis to measure stress distributions [see post entitled ‘Counting photons to measure stress‘ on November 18th, 2015], synchrotron x-ray diffraction to evaluate residual stress inside the metal and microscopy to examine failure surfaces [see post entitled ‘Forensic engineering‘ on July 22nd, 2015].  The data from this diverse set of experiments is integrated in the paper to provide a mechanistic explanation of how cracks exploit imperfections in the beneficial residual stress field introduced by the manufacturing process and can be aided in their growth by occasional but modest overloads, which might occur during a difficult landing or take-off.

The success of this research is particularly satisfying because at its heart is a PhD student supported by a dual PhD programme between the University of Liverpool and National Tsing Hua University in Taiwan.  This programme, which supported by the two partner universities, is in its sixth year of operation with a steady state of about two dozen PhD students enrolled, who divide their time between Liverpool, England and Hsinchu, Taiwan.  The synchrotron diffraction measurements were performed, with a colleague from Sheffield Hallam University, at the European Synchrotron Research Facility (ESRF) in Grenoble, France; thus making this a truly international collaboration.

Source:

Amjad K, Asquith D, Patterson EA, Sebastian CM & Wang WC, The interaction of fatigue cracks with a residual stress field using thermoelastic stress analysis and synchrotron x-ray diffraction experiments, R. Soc. Open Sci. 4:171100.

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Red to blue

Some research has a very long incubation time.  Last month, we published a short paper that describes the initial results of research that started just after I arrived in Liverpool in 2011.  There are various reasons for our slow progress, including our caution about the validity of the original idea and the challenges of working across discipline boundaries.  However, we were induced to rush to publication by the realization that others were catching up with us [see blog post and conference paper].  Our title does not give much away: ‘Characterisation of metal fatigue by optical second harmonic generation‘.

Second harmonic generation or frequency doubling occurs when photons interact with a non-linear material and are combined to produce new photons with twice the energy, and hence, twice the frequency and half the wavelength of the original photons.  Photons are discrete packets of energy that, in our case, are supplied in pulses of 2 picoseconds from a laser operating at a wavelength of 800 nanometres (nm).  The photons strike the surface, are reflected, and then collected in a spectrograph to allow us to evaluate the wavelength of the reflected photons.  We look for ones at 400 nm, i.e. a shift from red to blue.

The key finding of our research is that the second harmonic generation from material in the plastic zone ahead of a propagating fatigue crack is different to virgin material that has experienced no plastic deformation.  This is significant because the shape and size of the crack tip plastic zone determines the rate and direction of crack propagation; so, information about the plastic zone can be used to predict the life of a component.  At first sight, this capability appears similar to thermoelastic stress analysis that I have described in Instructive Update on October 4th, 2017; however, the significant potential advantage of second harmonic generation is that the component does not have to be subject to a cyclic load during the measurement, which implies we could study behaviour during a load cycle as well as conduct forensic investigations.  We have some work to do to realise this potential including developing an instrument for routine measurements in an engineering laboratory, rather than an optics lab.

Last week, I promised weekly links to posts on relevant Thermodynamics topics for students following my undergraduate module; so here are three: ‘Emergent properties‘, ‘Problem-solving in Thermodynamics‘, and ‘Running away from tigers‘.

 

Instructive Update

Six months ago I wrote about our EU research project, called INSTRUCTIVE, and the likely consequences of Brexit for research [see my post: ‘Instructive report and Brexit‘ on March 29th, 2017].  We seem to be no closer to knowing the repercussions of Brexit on research in the UK and EU – a quarter of EU funding allocated to universities goes to UK universities so the potential impacts will hit both the UK and EU.  Some researchers take every opportunity to highlight these risks and the economic benefits of EU research; for instance the previous EU research programme, Framework Programme 7, is estimated to have created 900,000 jobs in Europe and increased GDP by about 1% in perpetuity.  However, most researchers are quietly getting on with their research and hoping that our political leaders will eventually arrive at a solution that safeguards our prosperity and security.  Our INSTRUCTIVE team is no exception to this approach.  We are about half-way through our project and delivered our first public presentation of our work at the International Conference on Advances in Experimental Mechanics last month.  We described how we are able to identify cracks in metallic structures before they are long enough to be visible to the naked eye, or any other inspection technique commonly used for aircraft structures.  We identify the cracks using an infra-red camera by detecting the energy released during the formation and accumulation of dislocations in the atomic structure that coalesce into voids and eventually into cracks [see my post entitled ‘Alan Arnold Griffith‘ on April 26th, 2017 for more on energy release during crack formation].  We can identify cracks at sub-millimetre lengths and then track them as they propagate through a structure.  At the moment, we are quantifying our ability to detect cracks forming underneath the heads of fasteners [see picture] and other features in real aerospace structures; so that we can move our technology out of the laboratory and into an industrial environment.  We have a big chunk of airplane sitting in the laboratory that we will use for future tests – more on that in later blog posts!

INSTRUCTIVE is an EU Horizon 2020 project funded under the Clean Sky 2 programme [project no. 686777] and involves Strain Solutions Ltd and the University of Liverpool working with Airbus.

Statistics on funding from http://russellgroup.ac.uk/news/horizon-2020-latest-statistics/and https://www.russellgroup.ac.uk/media/5068/24horizon-2020-the-contribution-of-russell-group-universities-june-201.pdf

For other posts on similar research topics, see ‘Counting photons to measure stress‘ on November 18th, 2015 and ‘Forensic engineering‘ on July 22nd, 2015.

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.