Category Archives: mechanics

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.

My Engineering Day

Photograph of roof tops and chimneys in Liverpool.Today is ‘This is Engineering’ day organised by the Royal Academy of Engineering to showcase what engineers and engineering really look like, celebrate our impact on the world and shift public perception of engineering towards an appreciation that engineers are a varied and diverse group of people who are critical to solving societal challenges.  You can find out more at https://www.raeng.org.uk/events/online-events/this-is-engineering-day-2020.  I have decided to contribute to ‘This is Engineering’ day by describing what I do on a typical working day as an engineer. 

Last Wednesday was like many other working days during the pandemic.  I got up about 7am went downstairs for breakfast in our kitchen and then climbed back upstairs to my home-office in the attic of our house in Liverpool [see ‘Virtual ascent of Moel Famau’ on April 8th, 2020].  I am lucky in that my home-office is quite separate from the living space in our house and it has a great view over the rooftops.  I arrived there at about 7.45am, opened my laptop, deleted the junk email, and dealt with the emails that were urgent, interesting or could be replied to quickly.  At around 8am, I closed my email and settled down to write the first draft of a proposal for funding to support our research on digital twins [see ‘Tacit hurdle to digital twins’ on August 26th, 2020].  I had organised a meeting earlier in the week with a group of collaborators and now I had the task of converting the ideas from our discussion into a coherent programme of research.  Ninety caffeine-fuelled minutes later, I had to stop for a Google Meet call with a collaborator at Airbus in Toulouse during which we agreed the wording on a statement about the impact our recent research efforts.  At 10am I joined a Skype call for a progress review with a PhD student on our dual PhD programme with National Tsing Hua University in Taiwan, so we were joined by his supervisor in Taiwan where it was 6pm [see ‘Citizens of the World’ on November 27th, 2019].  The PhD student presented some very interesting results on evaluating the waviness of fibres in carbon-fibre composite materials using ultrasound measurements which he had performed in our laboratory in Liverpool.  Despite the local lockdown in Liverpool due to the pandemic, research laboratories on our campus are open and operating at reduced occupancy to allow social distancing.

After the PhD progress meeting, I had a catch-up session with my personal assistant to discuss my schedule for the next couple of weeks before joining a MS-Teams meeting with a couple of colleagues to discuss the implications of our current work on computational modelling and possible future directions.  The remaining hour up to my lunch break was occupied by a conference call with a university in India with whom we are exploring a potential partnership.  I participated in my capacity as Dean of the School of Engineering and joined about twenty colleagues from both institutions discussing possible areas of collaboration in both research and teaching.  Then it was back downstairs for a half-hour lunch break in the kitchen. 

Following lunch, I continued in my role as Dean with a half-hour meeting with Early Career Academics in the School of Engineering followed by internal interviews for the directorship of one of our postgraduate research programmes.  At 3.30pm, I was able to switch back to being a researcher and meet with a collaborator to discuss the prospects for extending our work on tracking synthetic nanoparticles into monitoring the motion of biological entities such as viruses and bacteria [see ‘Modelling from the cell through the individual to the host population’ on May 5th 2020].  Finally, as usual, I spent the last two to three hours of my working day replying to emails, following up on the day’s meetings and preparing for the following day.  One email was a request for help from one of my PhD students working in the laboratory who needed a piece of equipment that had been stored in my office for safekeeping.  So, I made the ten-minute walk to campus to get it for her which gave me the opportunity to talk face-to-face with one of the post-doctoral researchers in my group who is working on the DIMES project [see ‘Condition-monitoring using infra imaging‘ on June 17th, 2020].  After dinner, my wife and I walked down to the Albert Dock and along the river front to Princes Dock and back up to our house.

So that was my Engineering Day last Wednesday!

 

Logos of Clean Sky 2 and EUThe DIMES project has received funding from the Clean Sky 2 Joint Undertaking under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 820951.  The opinions expressed in this blog post reflect only the author’s view and the Clean Sky 2 Joint Undertaking is not responsible for any use that may be made of the information it contains.

Poleidoscope (=polariscope + kaleidoscope)

A section from a photoelastic model of turbine disc with a single blade viewed in polarised light to reveal the stress distribution.Last month I wrote about the tedium of collecting data 35 years ago without digital instrumentation and how it led me to work on automation and digitalisation in experimental mechanics [see ‘35 years later and still working on a PhD thesis‘ on September 16th, 2020].  Thirty years ago, one of the leading methods for determining stresses in components was photoelasticity, which uses polarised light to generate fringe patterns in transparent components or models that correspond to the distribution of stress.  The photoelastic fringes can be analysed in a polariscope, of which the basic principles are explained in a note at the end of this post.  During my PhD, I took hundreds of black and white photographs in a polariscope using sheets of 4×5 film, which came in boxes of 25 sheets that you can still buy, and then scanned these negatives using a microdensitometer to digitise the position of the fringes.  About 15 years after my PhD, together with my collaborators, I patented the poleidoscope which is a combination of a polariscope and a kaleidoscope [US patents 6441972 & 5978087] that removes all of that tedium.  It uses the concept of the multi-faceted lens in a child’s kaleidoscope to create several polariscopes within a compound lens attached to a digital camera.  Each polariscope has different polarising elements such that photoelastic fringes are phase-shifted between the set of images generated by the multi-faceted lens.  The phase-shifted fringe patterns can be digitally processed to yield maps of stress much faster and more reliably than any other method.  Photoelastic stress analysis is no longer popular in mainstream engineering or experimental mechanics due to the simplicity and power of digital image correlation [see ‘256 shades of grey‘ on January 22nd, 2014]; however, the poleidoscope has found a market as an inspection device that provides real-time information on residual stresses in glass sheets and silicon wafers during their production.  In 2003, I took study leave for the summer to work with Jon Lesniak at Glass Photonics in Madison, Wisconsin on the commercialisation of the poleidoscope.  Subsequently, Glass Photonics have  sold more than 250 instruments worldwide.

For more information on the poleidoscope see: Lesniak JR, Zhang SJ & Patterson EA, The design and evaluation of the poleidoscope: a novel digital polariscope, Experimental Mechanics, 44(2):128-135, 2004

Note on the Basic principles of photoelasticity: At any point in a loaded component there is a stress acting in every direction. The directions in which the stresses have the maximum and minimum values for the point are known as principal directions. The corresponding stresses are known as maximum and minimum principal stresses. When polarised light enters a loaded transparent component, it is split into two beams. Both beams travel along the same path, but each vibrates along a principal direction and travels at a speed proportional to the associated principal stress. Consequently, the light emerges as two beams vibrating out of phase with one another which when combined produce an interference pattern.   The polarised light is produced by the polariser in the polariscope and the analyser performs the combination. The interference pattern is observed in the polariscope, and the fringes are contours of principal stress difference which are known as isochromatics. When plane polarised light is used black fringes known as isoclinics are superimposed on the isochromatic pattern. Isoclinics indicate points at which the principal directions are aligned to the polarising axes of the polariser and analyser.

Image: a section from a photoelastic model of turbine disc with a single blade viewed in polarised light to reveal the stress distribution.

Turning the screw in dentistry

Dental implant surgery showing implant being screwed into placeTwo weeks ago, I wrote about supervising PhD students and my own PhD thesis [‘35 years later and still working on a PhD thesis‘ on September 16th, 2020].  The tedium of collecting data as a PhD student without digital instrumentation stimulated me to work subsequently on automation in experimental mechanics which ultimately led to projects like INSTRUCTIVE and DIMES.  In INSTRUCTIVE we developed  low-cost digital sensors for tracking damage in components; while in DIMES we are transitioning the technology into the industrial environment using tests on full-scale aircraft systems as demonstrators.  However, my research in automating and digitising measurements in experimental mechanics has not generated my most cited publications; instead, my two most cited papers describe the development and application of results in my PhD thesis to osseointegrated dental implants.  One, published in 1994, describes the ‘Tightening characteristics for screwed joints in osseointegrated dental implants‘; while, the other published two years earlier provides a ‘Theoretical analysis of the fatigue life of fixture screws in osseointegrated dental implants‘.  In other words, the former tells you how to tighten the screws so that the implants do not come loose and the latter how long the screws will survive before they need to be replaced – both quite useful pieces of information for dentists which perhaps explains their continued popularity.

Statistics footnote: my two most cited papers received five times as many citations in the last 18 months and also since publication than the most popular paper from my PhD thesis. The details of the three papers are given below:

Burguete, R.L., Johns, R.B., King, T. and Patterson, E.A., 1994. Tightening characteristics for screwed joints in osseointegrated dental implants. Journal of Prosthetic Dentistry, 71(6), pp.592-599.

Patterson, E.A. and Johns, R.B., 1992. Theoretical analysis of the fatigue life of fixture screws in osseointegrated dental implants. The International journal of oral & maxillofacial implants, 7(1), p.26.

Kenny, B. and Patterson, E.A., 1985. Load and stress distribution in screw threads. Experimental Mechanics, 25(3), pp.208-213.

Logos of Clean Sky 2 and EUThe INSTRUCTIVE and DIMES projects have received funding from the Clean Sky 2 Joint Undertaking under the European Union’s Horizon 2020 research and innovation programme under grant agreements No. 685777 and No. 820951 respectively.

The opinions expressed in this blog post reflect only the author’s view and the Clean Sky 2 Joint Undertaking is not responsible for any use that may be made of the information it contains.

Image by володимир волощак from Pixabay.