Research ArticleCONDENSED MATTER PHYSICS

Propagating bands of plastic deformation in a metal alloy as critical avalanches

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Science Advances  07 Oct 2020:
Vol. 6, no. 41, eabc7350
DOI: 10.1126/sciadv.abc7350
  • Fig. 1 Features of deformation bands from speckle images.

    (A) The raw subtracted speckle images showing two simultaneous PLC bands (top one during nucleation). (B) The stress-strain curves showing the responses of the samples and the serrations. (C) The effective strain rate map (time derivative of the speckle image intensity) ϵ·spec (see Materials and Methods for details) for one band inclination (top), the stress signal (middle), and the band velocity signals (bottom).

  • Fig. 2 Average band velocities.

    Top: The average velocities vb¯ of the bands decrease with strain ϵ. The inset shows the average velocities averaged over the strain rate vb¯ increasing as a power law (red symbols for experiments and blue for the ABBM model; the error bars represent the SD of band velocities obtained with a given strain rate). The black line is a power law vb¯ϵ·p with p = 0.6. Bottom: The average velocities (binned to strain intervals) scaled with ϵ·p decrease exponentially with strain (red symbols for experiments and blue for the ABBM model; the error bars represent the SD of band velocities in the given strain bin). The black line is an exponential relation vb¯ϵ·pexp(ϵϵ0) with ϵ0 = 0.16.

  • Fig. 3 Averaged band velocity profiles for a fixed duration.

    The averaged band velocity profiles for four different duration bins (red) showing the evolution of the shape from an inverted parabola to almost a flat constant velocity shape with increasing duration. As expected from the analytic results, this is reproduced by the ABBM model (blue).

  • Fig. 4 Statistics of the avalanche sizes.

    (A) The average avalanche size 〈S〉 for a fixed duration T for the experiments (red) and the ABBM model (blue). The third curve (magenta) is the fixed duration average for the size of the stress drop Δσ in the serrated stress-strain curve. (B) The avalanche size distribution from the experiments (red) and the ABBM simulations (blue). The black line represents the expected scaling of the distribution P(S)=A(1SL)Sα with α = 1, A=(S0L+lnLS01)1, and S0 = 2 mm. (C) The distribution of band velocities from the experiments (red) and the ABBM simulations (blue). The black line represents the expected exponential distribution P(vb)=k˜ek˜vb with k˜=0.04.

  • Fig. 5 The experimental setup.

    The sample is tensile-loaded and simultaneously imaged using the laser speckle technique. Here, the sample is illuminated by a diffuse laser at a slight angle, and the produced speckle pattern on the sample surface is imaged using a high-speed camera. Photo credit: Tero Mäkinen.

Supplementary Materials

  • Supplementary Materials

    Propagating bands of plastic deformation in a metal alloy as critical avalanches

    Tero Mäkinen, Pasi Karppinen, Markus Ovaska, Lasse Laurson, Mikko J. Alava

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