Tag Archives: Royal Society

Scattering electrons reveal dislocations in material structure

Figure 9 from Yang et al, 2012. Map of plastic strain around the crack tip (0, 0) based on the full width of half the maximum of the discrete Fourier transforms of BSE images, together with thermoelastic stress analysis data (white line) and estimates of the plastic zone size based on approaches of Dugdale's (green line) and Irwin's (blue line; dimensions in millimetres).

Figure 9 from Yang et al, 2012. Map of plastic strain around the crack tip (0, 0) based on the full width of half the maximum of the discrete Fourier transforms of BSE images, together with thermoelastic stress analysis data (white line) and estimates of the plastic zone size based on approaches of Dugdale’s (green line) and Irwin’s (blue line; dimensions in millimetres).

It is almost impossible to manufacture metal components that are flawless.  Every flaw or imperfection in a metallic component is a potential site for the initiation of a crack that could lead to the failure of the component [see ‘Alan Arnold Griffith’ on April 26th, 2017].  Hence, engineers are very interested in understanding the mechanisms of crack initiation and propagation so that these processes can be prevented or, at least, inhibited.  It is relatively easy to achieve these outcomes by not applying loads that would supply the energy to drive failure processes; however, the very purpose of a metal component is often to carry load and hence a compromise must be reached.  The deep understanding of crack initiation and propagation, required for an effective and safe compromise, needs detailed measurements of evolution of the crack and of its advancing front or tip [depending whether you are thinking in three- or two-dimensions].  When a metal is subjected to repeated cycles of loading, then a crack can grow incrementally with each load cycle; and in these conditions a small volume of material, just ahead of the crack and into which the crack is about to grow, has an important role in determining the rate of crack growth.  The sharp geometry of the crack tip causes localisation of the applied load in the material ahead of the crack thus raising the stress sufficiently high to cause permanent deformation in the material on the macroscale.  The region of permanent deformation is known as the crack tip plastic zone.  The permanent deformation induces disruptions in the regular packing of the metal atoms or crystal lattice, which are known as dislocations and continued cyclic loading causes the dislocations to move and congregate around the crack tip.  Ultimately, dislocations combine to form voids in the material and then voids coalesce to form the next extension of the crack.  In reality, it is an oversimplification to refer to a crack tip because there is a continuous transition from a definite crack to definitely no crack via a network of loosely connected voids, unconnected voids, aggregated dislocations almost forming a void, to a progressively more dispersed crowd of dislocations and finally virgin or undamaged material.  If you know where to look on a polished metal surface then you could probably see a crack about 1 mm in length and, with aid of an optical microscope, you could probably see the larger voids forming in the material ahead of the crack especially when a load is applied to open the crack.  However, dislocations are very small, of the order tens of nanometres in steel, and hence not visible in an optical microscope because they are smaller than the wavelength of light.  When dislocations congregate in the plastic zone ahead of the crack, they disturb the surface of the metal and causing a change its texture which can be detected in the pattern produced by electrons bouncing off the surface.  At Michigan State University about ten years ago, using backscattered electron (BSE) images produced in a scanning electron microscope (SEM), we demonstrated that the change in texture could be measured and quantified by evaluating the frequency content of the images using a discrete Fourier transform (DFT).  We collected 225 square images arranged in a chessboard pattern covering a 2.8 mm by 2.8 mm square around a 5 mm long crack in a titanium specimen which allowed us to map the plastic zone associated with the crack tip (figure 9 from Yang et al, 2012).  The length of the side of each image was 115 microns and 345 pixels so that we had 3 pixels per micron which was sufficient to resolve the texture changes in the metal surface due to dislocation density.  The images are from our paper published in the Proceedings of the Royal Society and the one below (figure 4 from Yang et al, 2012) shows four BSE images along the top at increasing distances from the crack tip moving from left to right.  The middle row shows the corresponding results from the discrete Fourier transform that illustrate the decreasing frequency content of the images moving from left to right, i.e. with distance from the crack.  The graphs in the bottom row show the profile through the centre of the DFTs.  The grain structure in the metal can be seen in the BSE images and looks like crazy paving on a garden path or patio.  Each grain has a particular and continuous crystal lattice orientation which causes the electrons to scatter differently from it compared to its neighbour.  We have used the technique to verify measurements of the extent of the crack tip plastic zone made using thermoelastic stress analysis (TSA) and then used TSA to study ‘Crack tip plasticity in reactor steels’ [see post on March 13th, 2019].

Figure 4 from Yang et al, 2012. (a) Backscattered electron images at increasing distance from crack from left to right; (b) their corresponding discrete Fourier transforms (DFTs) and (c) a horizontal line profile across the centre of each DFT.

Figure 4 from Yang et al, 2012. (a) Backscattered electron images at increasing distance from crack from left to right; (b) their corresponding discrete Fourier transforms (DFTs) and (c) a horizontal line profile across the centre of each DFT.

Reference: Yang, Y., Crimp, M., Tomlinson, R.A., Patterson, E.A., 2012, Quantitative measurement of plastic strain field at a fatigue crack tip, Proc. R. Soc. A., 468(2144):2399-2415.

Spatio-temporal damage maps for composite materials

Earlier this year, my group published a new technique for illustrating the development of damage as a function of both space and time in materials during testing in a laboratory.  The information is presented in a damage-time map and shows where and when damage appears in the material.  The maps are based on the concept that damage represents a change in the structure of the material and, hence, produces changes in the load paths or stress distribution in the material.  We can use any of a number of optical techniques to measure strain, which is directly related to stress, across the surface of the material; and then look for changes in the strain distribution in real-time.  Wherever a permanent change is seen to occur there must also be permanent deformation or damage. We use image decomposition techniques that we developed some time ago [see ‘Recognizing strain‘ on October 28th, 2018], to identify the changes. Our damage-time maps remove the need for skilled operators to spend large amounts of time reviewing data and making subjective decisions.  They also allow a large amount of information to be presented in a single image which makes detailed comparisons with computer predictions easier and more readily quantifiable that, in turn, supports the validation of computational models [see ‘Model validation‘ on September 18th, 2012].

The structural integrity of composite materials is an on-going area of research because we only have a limited understanding of these materials.  It is easy to design structures using materials that have a uniform or homogeneous structure and mechanical properties which do not vary with orientation, i.e. isotropic properties.  For simple components, an engineer can predict the stresses and likely failure modes using the laws of physics, a pencil and paper plus perhaps a calculator.  However, when materials contain fibres embedded in a matrix, such as carbon-fibres in an epoxy resin, then the analysis of structural behaviour becomes much more difficult due to the interaction between the fibres and with the matrix.  Of course, these interactions are also what make these composite materials interesting because they allow less material to be used to achieve the same performance as homogeneous isotropic materials.  There are very many ways of arranging fibres in a matrix as well as many different types of fibres and matrix; and, engineers do not understand most of their interactions nor the mechanisms that lead to failure.

The image shows, on the left, the maximum principal strain in a composite specimen loaded longitudinally in tension to just before failure; and, on the right, the corresponding damage-time map indicating when and where damage developing during the tension loading.


Christian WJR, Dvurecenska K, Amjad K, Pierce J, Przybyla C & Patterson EA, Real-time quantification of damage in structural materials during mechanical testing, Royal Society Open Science, 7:191407, 2020.

Size matters

Most of us have a sub-conscious understanding of the forces that control the interaction of objects in the size scale in which we exist, i.e. from millimetres through to metres.  In this size scale gravitational and inertial forces dominate the interactions of bodies.  However, at the size scale that we cannot see, even when we use an optical microscope, the forces that the dominate the behaviour of objects interacting with one another are different.  There was a hint of this change in behaviour observed in our studies of the diffusion of nanoparticles [see ‘Slow moving nanoparticles‘ on December 13th, 2017], when we found that the movement of nanoparticles less than 100 nanometres in diameter was independent of their size.  Last month we published another article in one of the Nature journals, Scientific Reports, on ‘The influence of inter-particle forces on diffusion at the nanoscale‘, in which we have demonstrated by experiment that Van der Waals forces and electrostatic forces are the dominant forces at the nanoscale.  These forces control the diffusion of nanoparticles as well as surface adhesion, friction and colloid stability.  This finding is significant because the ionic strength of the medium in which the particles are moving will influence the strength of these forces and hence the behaviour of the nanopartices.  Since biological fluids contain ions, this will be important in understanding and predicting the behaviour of nanoparticles in biological applications where they might be used for drug delivery, or have a toxicological impact, depending on their composition.

Van der Waals forces are weak attractive forces between uncharged molecules that are distance dependent.  They are named after a Dutch physicist, Johannes Diderik van der Waals (1837-1923).  Electrostatic forces occur between charged particles or molecules and are usually repulsive with the result that van der Waals and electrostatic forces can balance each other, or not depending on the circumstances.


Giorgi F, Coglitore D, Curran JM, Gilliland D, Macko P, Whelan M, Worth A & Patterson EA, The influence of inter-particle forces on diffusion at the nanoscale, Scientific Reports, 9:12689, 2019.

Coglitore D, Edwardson SP, Macko P, Patterson EA, Whelan MP, Transition from fractional to classical Stokes-Einstein behaviour in simple fluids, Royal Society Open Science, 4:170507, 2017. doi: .

Patterson EA & Whelan MP, Tracking nanoparticles in an optical microscope using caustics. Nanotechnology, 19 (10): 105502, 2009.

Image: from Giorgi et al 2019, figure 1 showing a photograph of a caustic (top) generated by a 50 nm gold nanoparticle in water taken with the optical microscope adjusted for Kohler illumination and closing the condenser field aperture to its minimum following method of Patterson and Whelan with its 2d random walk over a period of 3 seconds superimposed and a plot of the same walk (bottom).

Thought leadership in fusion engineering

The harnessing of fusion energy has become something of a holy grail – sought after by many without much apparent progress.  It is the energy process that ‘powers’ the stars and if we could reproduce it on earth in a controlled environment then it would offer almost unlimited energy with very low environmental costs.  However, understanding the science is an enormous challenge and the engineering task to design, build and operate a fusion-fuelled power station is even greater.  The engineering difficulties originate from the combination of two factors: the emergent behaviour present in the complex system and that it has never been done before.  Engineering has achieved lots of firsts but usually through incremental development; however, with fusion energy it would appear that it will only work when all of the required conditions are present.  In other words, incremental development is not viable and we need everything ready before flicking the switch.  Not surprisingly, engineers are cautious about flicking switches when they are not sure what will happen.  Yet, the potential benefits of getting it right are huge; so, we would really like to do it.  Hence, the holy grail status: much sought after and offering infinite abundance.

Last week I joined the search, or at least offered guidance to those searching, by publishing an article in Royal Society Open Science on ‘An integrated digital framework for the design, build and operation of fusion power plants‘.  Working with colleagues at the Culham Centre for Fusion Energy, Richard Taylor and I have taken our earlier work on an integrated nuclear digital environment for the nuclear energy using fission [see ‘Enabling or disruptive technology for nuclear engineering?‘ on january 28th, 2015] and combined it with the hierarchical pyramid of testing and simulation used in the aerospace industry [see ‘Hierarchical modelling in engineering and biology‘ on March 14th, 2018] to create a framework that can be used to guide the exploration of large design domains using computational models within a distributed and collaborative community of engineers and scientists.  We hope it will shorten development times, reduce design and build costs, and improve credibility, operability, reliability and safety.  It is a long list of potential benefits for a relatively simple idea in a relatively short paper (only 12 pages).  Follow the link to find out more – it is an open access paper, so it’s free.


Patterson EA, Taylor RJ & Bankhead M, A framework for an integrated nuclear digital environment, Progress in Nuclear Energy, 87:97-103, 2016.

Patterson EA, Purdie S, Taylor RJ & Waldon C, An integrated digital framework for the design, build and operation of fusion power plants, Royal Society Open Science, 6(10):181847, 2019.