Research ArticlePHYSICS

Femtosecond quantification of void evolution during rapid material failure

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Science Advances  16 Dec 2020:
Vol. 6, no. 51, eabb4434
DOI: 10.1126/sciadv.abb4434
  • Fig. 1 Experimental arrangement at the LCLS and details of the initial Cu foil microstructure.

    (A) Experimental arrangement at LCLS. The XFEL beam impinges the Cu with substrate sample shortly after a laser shock pulse with a “clipped” leading edge. The WAXS data are recorded in the front detector and small angle (SAXS) data recorded in the rear detector. (B) (111) pole figure from EBSD; the intensity in the center of the pole figure refers to the foil normal (growth) direction. (C) Secondary electron scanning electron microscopy (SEM) imaged normal to the sputtered Cu surface, illustrating the nanoscale planar pores between grains, and (D) backscattered electron SEM imaged at a 70° tilt angle, highlighting the columnar grain microstructure through the foil thickness. Graphic design credit: Gregory Stewart, SLAC National Accelerator Laboratory.

  • Fig. 2 Evolution of scattering data as a shock wave propagates through a Cu foil and illustrative cartoon to aid interpretation.

    (ai to avi) From left to right: Sequential illustrations of the longitudinal strain profile and corresponding void distribution in the Cu foils, describing the shock loading cycle to failure as a shock wave propagates through the foil. (bi to bvi) From left to right: Azimuthally averaged scattering data illustrating the evolution of WAXS as the shock wave propagates through the foil and (ci to cvi) the corresponding SAXS profiles. The scattering data (bi) to (bvi) and (ci) to (cvi) correspond to the schematic of (ai) to (avi). t = 0 ps is defined at full material compression. An increasingly negative time means a shorter lag between the probe and pump, and the initial shock wave has progressed less through the foil. An increasingly positive time corresponds to the rarefaction wave returning through the foil. The peaks labeled 1 and 2 in (bii) correspond to diffraction from the unstrained region ahead of the shock front and strained region behind the shock front, respectively. The dashed vertical lines in (bi) to (bvi) are a reference for the initial {111} peak position. SAXS model fits to data are included as solid black lines (ci to cvi).

  • Fig. 3 Evolution of microstructure as a shock wave propagates through a Cu foil, deduced from SAXS model fits to experimental data.

    (A) Void volume fraction, (B) void minor dimension, and (C) void number density with increasing pump-probe delay times, deduced from SAXS model fits to the experimental data. t0 at 0 ps refers to the time in the shock event at which the sample was fully compressed. Exponential fits to the deduced parameters are included, as well as error bars of 10%, calculated from χ2 analyses of the fitting parameters.

  • Fig. 4 Comparison of experimentally determined high strain rate spall strengths for polycrystalline Cu samples.

    Buchar et al. (40) measured three different grain sizes: 94 μm (red data points), 139 μm (black data points), and 185 μm (green data points). Escobedo et al. (41) also determined the spall strength for samples with average grain size between 30 and 200 μm. The data of Kanel et al. (28) and the current work are fitted by a straight line on a log-log plot (spall strength = ε·m·10b, where m is the slope and b is the intercept point on the log plot).

  • Fig. 5 MD simulated evolution of microstructure, internal stresses, and scattering profiles as a shock wave propagates through a Cu foil.

    (ai to av) Representative snapshot images of selected foil regions (i.e., not the full foil) for the MD simulation foils at five sequential times of shock wave propagation, illustrating (i) initial compression, (ii) full compression, (iii) expansion, (iv) void nucleation, and (v) void coalescence. The closure of a grain boundary void (white) is shown in (ai), and void nucleation and expansion are also shown in (aiv) and (av). (bi to bv) The corresponding simulated internal longitudinal stress along the shock direction and the transverse stress averaged for the two normal directions along the full simulated foil, with a positive stress corresponding to compression. (ci to cv) The corresponding predicted WAXS profiles through the foil bulk. Peaks labeled 1 and 2 of (ci) correspond to scattering arising from the uncompressed and compressed regions, respectively.

Supplementary Materials

  • Supplementary Materials

    Femtosecond quantification of void evolution during rapid material failure

    James Coakley, Andrew Higginbotham, David McGonegle, Jan Ilavsky, Thomas D. Swinburne, Justin S. Wark, Khandaker M. Rahman, Vassili A. Vorontsov, David Dye, Thomas J. Lane, Sébastien Boutet, Jason Koglin, Joseph Robinson, Despina Milathianaki

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