Category Archives: mechanics

Graphite for Very High Temperature Reactors (VHTR)

One of the implications of the second law of thermodynamics is that the thermal efficiency of power stations increases with their operating temperature.  Thus, there is a drive to increase the operating temperature in the next generation of nuclear power stations, known as Generation IV reactors.  In one type of Generation IV reactors, known as the Very High Temperature Reactor (VHTR), graphite is designed to be both the moderator for neutrons and a structural element of the reactor.  Although the probability of damage in an accident is extremely low, it is important to consider the consequences of damage causing the core of the reactor to be exposed to air.  In these circumstances, with the core temperature at about 1600°C, the graphite would be exposed to severe oxidation by the air that could change its material properties and ability to function as a moderator and structural element.  Therefore, in recent research, my research group has been working with colleagues at the UK National Nuclear Laboratory (NNL) and at the National Tsing Hua University (NTHU) in Taiwan to conduct experiments on nuclear graphite over a range of temperatures.  Our recently published article shows that all grades of nuclear graphite show increased rates of oxidation for temperatures above 1200°C.  We found that large filler particles using a pitch-based graphite rather than a petroleum-based graphite gave higher oxidation resistance at these elevated temperatures.  This data is likely to be important in the design and operations of the next generation of nuclear power stations.

The work described above was supported by the NTHU-University of Liverpool Dual PhD Programme [see ‘Citizens of the world‘ on November 27th, 2019] and NNL.  This is the fifth, and for the moment last, in a series of posts on recent work published by my research group.  The others are: ‘Salt increases nanoparticle diffusion‘ on April 22nd, 2020; ‘Spatio-temporal damage maps for composite materials‘ on May 6th, 2020; ‘Thinking out of the box leads to digital image correlation through space‘ on June 24th, 2020; and, ‘Potential dynamic buckling in hypersonic vehicle skin‘ on July 1st, 2020.

The image is figure 5: SEM micrographs of the surface of petroleum-based IG-110 graphite samples oxidized at various temperatures from Lo IH, Tzelepi A, Patterson EA, Yeh TK. A study of the relationship between microstructure and oxidation effects in nuclear graphite at very high temperatures.  J. Nuclear Materials. 501:361-70, 2018.


Lo I-H, Yeh T-K, Patterson EA & Tzelepi A, Comparison of oxidation behaviour of nuclear graphite grades at very high temperatures, J. Nuclear Materials, 532:152054, 2020.

Potential dynamic buckling in hypersonic vehicle skin

The skin of an aircraft is supported on the inside by a network, or mesh, of ribs and stringers running approximately at right angles to one another; so that the skin is effectively a series of rectangular plates supported around their edges.   In hypersonic flight, above five times the speed of sound, these rectangular plates are subject to vibration and to high temperatures that vary spatially and with time.  The combined vibratory and thermal loading causes the plates to buckle out of plane which has two possible detrimental consequences: first, it causes the formation of fatigue cracks leading to catastrophic failure; and, second, it might influence the formation of the boundary layer in the flow over the skin of the aircraft and affect the aerodynamics of the aircraft.  In my laboratory, we have built a test-rig that allows us to subject rectangular plates to random mechanical vibrations up to 1000Hz and, at the same time, to temperature distributions upto 1000K that vary in time and space.  Earlier this year, we published an article in which we showed, by experiment, that an edge-reinforced rectangular plate behaved as a dynamic system in response to thermal loading.  In other words, when a constant temperature distribution is applied, the shape of the plate varies with time until an equilibrium state is achieved.  In addition, we found that the post-buckled shape of the plate is not proportional to the energy supplied but dependent on the in-plane temperature distribution.  Probably, both of these observed behaviours are a result of differential thermal expansion of the plate and its reinforcements.

The image shows point-wise temperature and displacement measurements (centre) at the centre and edge of a reinforced plate (top) subject to a localised strip of heating over time as shown by the temperature distributions (bottom).

This is the fourth in a series of posts on recent work published by my research group.  The others are: ‘Salt increases nanoparticle diffusion‘ on April 22nd, 2020; ‘Spatio-temporal damage maps for composite materials‘ on May 6th, 2020; and, ‘Thinking out of the box leads to digital image correlation through space‘ on June 24th, 2020.


Santos Silva AC, Lambros J, Garner DM & Patterson EA, Dynamic response of a thermally stressed plate with reinforced edges, Experimental Mechanics, 60:81-92, 2020.

Thinking out of the box leads to digital image correlation through space

This is the third in a short series of posts on recent engineering research published by my research group.  Actually, two have already been published: ‘Salt increases nanoparticle diffusion‘ on April 22nd, 2020; and ‘Spatio-temporal damage maps for composite materials‘ on May 6th, 2020 and then I got distracted.  This third one arose from the same project as the time-damage maps which was sponsored by the United States Air Force.  The time-damage maps allow us to explore the evolution of failure in complex materials; however, we already know that damage tends to initiate from imperfections or flaws in the microstructure in the material.  New continuous fibre reinforced composite (CFRC) materials based on ceramics are very sensitive to defects or anomalies in their microstructure, such as misalignment of fibres.  However, they are capable of withstanding temperatures in excess of 1500 degrees Centigrade, which offers the opportunity to use them in jet engines or nuclear power plants to help generate energy more efficiently.  Therefore, it is worthwhile investigating effective methods of inspecting their microstructure which we can do either destructively by repetitively polishing away the surface of a sample and viewing it in a microscope, or non-destructively using x-ray tomography.  In both cases, the result is hundreds of ‘images’ containing millions of data values from which it is challenging to extract useful information.  In our work, we have used a little lateral thinking, to show how digital image correlation, usually used to track deformation of structures using multiple images collected over time [see ‘256 shades of grey‘ on January 22nd, 2014] , can be used to track fibres through the multiple images of the layers of the microstructure.  The result is the sort of ‘stick’ diagram in the image showing the orientation of fibres through the sample.  We have demonstrated that our new algorithm was more reliable and 30 times faster than its nearest rival.

The image shows, at the top, a typical stack of images from the microscope of a ceramic matrix composite; and, at the bottom, a plot of 3d profiles of the fibres tracked using the DIC-based method with the fibres orientated nominally at ±45° from the sectioning (x-y) plane shown in red and green colours.


Amjad K, Christian WJR, Dvurecenska K, Chapman MG, Uchic MD, Przybyla CP & Patterson EA, Computationally efficient method of tracking fibres in composite materials using digital image correlation, Composites Part A, 129:105683, 2020.


Homework practical exercises in structural mechanics

Last week I wrote about the practical exercises that I have been setting as homework in my first year undergraduate course on thermodynamics.  The instruction sheets that I published had been used by thousands of learners on my MOOC, Energy! The Thermodynamics of Everyday Life; and slightly modified versions had been used by more than a thousand students at the University of Liverpool.  A few years ago, I produced another MOOC called ‘Understanding Superstructures’ which also contained three practical exercises for online learners to perform in their kitchens.  I have not used them as part of a blended undergraduate course but nevertheless they have been completed by hundreds of participants in the MOOC.  I have decided to share them for colleagues to use in support of first year courses on the Mechanics of Solids or the Mechanics of Structures.  There is strong food flavour and no additional equipment is needed. Please feel free to use them to support your teaching.

Instruction sheets for thermodynamics practical exercises as homework:

Structural collapse | Crushing and toppling of towers

Stress concentrations | Newspaper tension tests

Residual stresses | Bending carrots