Tag Archives: plasticity

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.

Amazing innovation in metamaterials

Most manufactured things break when you subject them to 90% strain; however Professor Xiaoyu Rayne Zheng of the Department of Mechanical Engineering at Virginia Tech has developed additively-manufactured metamaterials that completely recover from being deformed to this level.  Strains are usually defined as the change in length divided by the original length and is limited in most engineering structures to less than 2%, which is the level at which steel experiences permanent deformation.  Professor Zheng has developed a microstructure with a recurring architecture over seven orders of magnitude that allows an extraordinary level of elastic recovery; and then his team manufactures the material using microstereolithography.  Stereolithography is a form of three-dimensional printing.  Professor Zheng presented some of his research at the USAF research review that I attended last month [see ‘When an upgrade is downgrading‘ on August 21st, 2019 and ‘Coverts inspire adaptive wing design’ on September 11th, 2019].  He explained that, when these metamaterials are made out of a piezoelectric nanocomposite, they can be deployed as tactile sensors with directional sensitivity, or smart energy-absorbing materials.

Rayne Zheng and Aimy Wissa [‘Coverts inspire adaptive wing design’ on September 11th, 2019] both made Compelling Presentations [see post on March 21st, 2018] that captured my attention and imagination; and kept my phone in my pocket!

The picture is from https://www.raynexzheng.com/

For details of the additively-manufactured metamaterials see: Zheng, Xiaoyu, William Smith, Julie Jackson, Bryan Moran, Huachen Cui, Da Chen, Jianchao Ye et al. “Multiscale metallic metamaterials.” Nature materials 15, no. 10 (2016): 1100

For details of the piezoelectric metamaterials see: Cui, Huachen, Ryan Hensleigh, Desheng Yao, Deepam Maurya, Prashant Kumar, Min Gyu Kang, Shashank Priya, and Xiaoyu Rayne Zheng. “Three-dimensional printing of piezoelectric materials with designed anisotropy and directional response.” Nature materials 18, no. 3 (2019): 234

Crack tip plasticity in reactor steels

Amplitude of temperature in steel due to a cyclic load with a crack growing from left to right along the horizontal centre line with the stress concentration at its tip exhibiting the peak values. The wedge shapes in the left corners are part of the system.

At this time of year the flow into my inbox is augmented daily by prospective PhD students sending me long emails describing how their skills, qualifications and interests perfectly match the needs of my research group, or sometimes someone else’s group if they have not been careful in setting up their mass mailing.  At the moment, I have four PhD projects for which I am looking for outstanding students; so, because it will help prospective students and might interest my other readers but also because I am short of ideas for the blog, I plan to describe one project per week for the next month.

The first project is about the effect of hydrogen on crack tip plasticity in reactor steels.  Fatigue cracks grow in steels by coalescing imperfections in the microstructure of the material until small voids are formed in areas of high stress.  When these voids connect together a crack is formed.  Repeated loading and unloading of the material provides the energy to move the imperfections, known as dislocations, and geometric features in structures are stress concentrators which focus this energy causing cracks to be formed in their vicinity.  The movement of dislocations causes permanent, or plastic deformation of the material.  The sharp geometry of a crack tip becomes a stress concentrator creating a plastic zone in which dislocations pile up and voids form allowing the crack to extend [see post on ‘Alan Arnold Griffith‘ on April 26th, 2017].  It is possible to detect the thermal energy released during plastic deformation using a technique known as thermoelastic stress analysis [see ‘Counting photons to measure stress‘ on November 18th 2015] as well as to measure the stress field associated with the propagating crack [1].  One of my current PhD students has been using this technique to investigate the effect of irradiation damage on the growth of cracks in stainless steel used in nuclear reactors.  We use an ion accelerator at the Dalton Cumbrian Facility to introduce radiation damage into specimens the size of a postage stamp and afterwards apply cyclic loads and watch the fatigue crack grow using our sensitive infra-red cameras.  We have found that the irradiation reduced the rate of crack growth and we will be publishing a paper on it shortly [and a PhD thesis].  In the new project, our industrial sponsors want us to explore the effect of hydrogen on crack growth in irradiated steel, because the presence of hydrogen is known to accelerate fatigue crack growth [2] which is believe to happen as a result of hydrogen atoms disrupting the formation of dislocations at the microscale and localising plasticity at crack tip on the mesoscale.  However, these ideas have not been demonstrated in experiments, so we plan to do this using thermoelastic stress analysis and to investigate the combined influence of hydrogen and irradiation by developing a process for pre-charging the steel specimens with hydrogen using an electrolytic cell and irradiating them using the ion accelerator.  Both hydrogen and radiation are present in a nuclear reactor and hence the results will be relevant to predicting the safe working life of nuclear reactors.

The PhD project is fully-funded for UK and EU citizens as part of a Centre for Doctoral Training and will involve a year of specialist training followed by three years of research.  For more information following this link.

References:

  1. 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.
  2. Matsunaga, H., Takakuwa, O., Yamabe, J., & Matsuoka, S., 2017, Hydrogen-enhanced fatigue crack growth in steels and its frequency dependence. Phil. Trans. R. Soc. A, 375(2098), 20160412