Tag Archives: residual stress

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.

Slow start to an exciting new project on thermoacoustic response of AM metals

We held the kick-off meeting for a new research project this week.  It’s a three-way collaboration involving three professors based in Portugal, the UK and USA [Chris Sutcliffe, John Lambros at UIUC and me]; so, our kick-off meeting should have involved at least two of us travelling to the laboratory of the third collaborator and spending some time brainstorming about the challenges that we have agreed to tackle over the next three years.  Instead we had a call via Skype and a rather procedural meeting in which we covered all of the issues without really engendering any excitement or sparking any new ideas.  It would appear that we need the stimulus of new environments to maximise our creativity and that we use body language as well as facial expressions to help us reach a friendly consensus on which  crazy ideas are worth pursuing and which should be quietly forgotten.

Our new research project has a long title: ‘Thermoacoustic response of Additively Manufactured metals: A multi-scale study from grain to component scales‘.  In simple terms, we are going to look at whether residual stresses could be designed to be beneficial to the performance of structural parts used in demanding environments such as those found in reusable spacecraft, hypersonic flight vehicles and breeder blankets in fusion reactors.  Residual stresses are often induced during the manufacture of parts and are usually detrimental to the performance of the part.  Our hypothesis is that in additive manufacturing, or 3D printing, we have sufficient control of the manufacture of the part that we can introduce ‘designer stresses’ which will improve the part’s performance in demanding environments.  The research is funded jointly by the National Science Foundation (NSF) in the USA and the Engineering and Physical Sciences Research Council (EPSRC) in the UK and is supported by The MTC and Renishaw plc; you can find out more at Grants on the Web. The research will be building on our recent research on ‘Potential dynamic buckling in hypersonic vehicle skin‘ [posted July 1st, 2020] and earlier work, see ‘Hot stuff‘ on September 13th, 2012.  While the demanding environment is not new to us, we will be using 3D printed parts for the first time instead of components made by conventional (subtractive) machining and taking them to higher temperatures.

The thumbnail shows measured modal shapes for a subtractively-manufactured plate subject to the three temperature regimes: room temperature (left), transverse heating of the centre of the plate (middle) and longitudinal heating on one edge (right) from Silva, A.S., Sebastian, C.M., Lambros, J. and Patterson, E.A., 2019. High temperature modal analysis of a non-uniformly heated rectangular plate: Experiments and simulations. J. Sound & Vibration, 443, pp.397-410.


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





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.


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.