Direct detection of plasticity onset through total-strain profile evolution

by   Stefanos Papanikolaou, et al.

Plastic yielding in solids strongly depends on various conditions, such as temperature and loading rate and indeed, sample-dependent knowledge of yield points in structural materials promotes reliability in mechanical behavior. Commonly, yielding is measured through controlled mechanical testing at small or large scales, in ways that either distinguish elastic (stress) from total deformation measurements, or by identifying plastic slip contributions. In this paper we argue that instead of separate elastic/plastic measurements, yielding can be unraveled through statistical analysis of total strain fluctuations during the evolution sequence of profiles measured in-situ, through digital image correlation. We demonstrate two distinct ways of precisely quantifying yield locations in widely applicable crystal plasticity models, that apply in polycrystalline solids, either by using principal component analysis or discrete wavelet transforms. We test and compare these approaches in synthetic data of polycrystal simulations and a variety of yielding responses, through changes of the applied loading rates and the strain-rate sensitivity exponents.



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  • (1) H. Schreier, J.-J. Orteu, and M. A. Sutton, Image correlation for shape, motion and deformation measurements: Basic concepts, theory and applications, Vol. 1 (Springer, 2009).
  • (2) A. Guery, F. Hild, F. Latourte, and S. Roux, Identification of crystal plasticity parameters using DIC measurements and weighted FEMU. Mechanics of Materials, 100, pp.55-71, (2016).
  • (3) N. Grilli, P. Earp, A. C. Cocks, J. Marrow, and E. Tarleton, Characterisation of slip and twin activity using digital image correlation and crystal plasticity finite element simulation: Application to orthorhombic -uranium. Journal of the Mechanics and Physics of Solids, 135, p.103800, (2020).
  • (4) A. Githens, S. Ganesan, Z. Chen, J. Allison, V. Sundararaghavan, and S. Daly, Characterizing microscale deformation mechanisms and macroscopic tensile properties of a high strength magnesium rare-earth alloy: A combined experimental and crystal plasticity approach. Acta Materialia, 186, pp.77-94, 2020.
  • (5) P. W. Anderson, Basic notions of condensed matter physics (The Benjamin-Cummings Publishing Company, 1984).
  • (6) G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. Vogt-Maranto, and L. Zdeborová, Machine learning and the physical sciences. Reviews of Modern Physics, 91(4), p.045002 (2019).
  • (7)

    E.P. Van Nieuwenburg, Y.H. Liu, and S.D. Huber, Learning phase transitions by confusion. Nature Physics, 13(5), pp.435-439 (2017).

  • (8) W. Hu, R. R. Singh, and R.T. Scalettar, Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination. Physical Review E, 95(6), p.062122, (2017).
  • (9)

    S.J. Wetzel, Unsupervised learning of phase transitions: From principal component analysis to variational autoencoders. Physical Review E, 96(2), p.022140 (2017).

  • (10)

    B.S. Rem, N. Käming, M. Tarnowski, L. Asteria, N. Fläschner, C. Becker, K. Sengstock, and C. Weitenberg, Identifying quantum phase transitions using artificial neural networks on experimental data. Nature Physics, 15(9), pp.917-920 (2019).

  • (11) C. Giannetti, B. Lucini, and D. Vadacchino, Machine Learning as a universal tool for quantitative investigations of phase transitions. Nuclear Physics B, 944, p.114639 (2019).
  • (12) W. Zhang, J. Liu, and T. C. Wei, Machine learning of phase transitions in the percolation and X Y models. Physical Review E, 99(3), p.032142 (2019).
  • (13) Q. Ni, M. Tang, Y. Liu, and Y.C. Lai, Machine learning dynamical phase transitions in complex networks. Physical Review E, 100(5), p.052312 (2019).
  • (14) L. Wang, Discovering phase transitions with unsupervised learning Phys. Rev. B 94 195105 (2016).
  • (15) C. Wang and H. Zhai, Machine learning of frustrated classical spin models. I. Principal component analysis Phys. Rev. B 96 144432 (2017).
  • (16) S. J. Wetzel, Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders Phys. Rev. E 96 022140 (2017).
  • (17) W. Hu, R R P Singh and R. T. Scalettar, Discovering phases, phase transitions, and crossovers through unsupervised machine learning: a critical examination Phys. Rev. E 95 062122 (2017).
  • (18) C. Ruscher, and J. Rottler, Correlations in the shear flow of athermal amorphous solids: A principal component analysis. Journal of Statistical Mechanics: Theory and Experiment, 2019(9), p.093303 (2019).
  • (19) D. Richard, M. Ozawa, S. Patinet, E. Stanifer, B. Shang, S. A. Ridout, B. Xu et al. Predicting plasticity in disordered solids from structural indicators. Physical Review Materials 4, no. 11, 113609 (2020).
  • (20) S. Pantelakis, E.P. Koumoulos, C.A. Charitidis, N.M. Daniolos, and D.I. Pantelis, Determination of onset of plasticity (yielding) and comparison of local mechanical properties of friction stir welded aluminum alloys using the micro‐and nano‐indentation techniques. International Journal of Structural Integrity, 4, 143-158 (2013).
  • (21) E. D. Cubuk, S. S. Schoenholz, J. M. Rieser, B. D. Malone, J. Rottler, D. J. Durian, E. Kaxiras, and A. J. Liu, Identifying Structural Flow Defects in Disordered Solids Using Machine-Learning Methods, Phys. Rev. Lett. 114, 108001 (2015).
  • (22) S. S. Schoenholz, E. D. Cubuk, D. M. Sussman, E. Kaxiras, and A. J. Liu, A structural approach to relaxation in glassy liquids, Nat. Phys. 12, 469 (2016).
  • (23) V. Bapst, T. Keck, A. Grabska-Barwińska, C. Donner, E. D. Cubuk, S. Schoenholz, A. Obika, A. Nelson, T. Back, and D. Hassabis et al., Unveiling the predictive power of static structure in glassy systems, Nat. Phys. 16, 448 (2020).
  • (24) P. Ronhovde, S. Chakrabarty, D. Hu, M. Sahu, K. Sahu, K. Kelton, N. Mauro, and Z. Nussinov, Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering, Eur. Phys. J. E 34, 105 (2011).
  • (25) E. Boattini, M. Dijkstra, and L. Filion, Unsupervised learning for local structure detection in colloidal systems, J. Chem. Phys. 151, 154901 (2019).
  • (26) E. Boattini, S. Marín-Aguilar, S. Mitra, G. Foffi, F. Smallenburg, and L. Filion, Autonomously Revealing Hidden Local Structures in Supercooled Liquids, Autonomously revealing hidden local structures in supercooled liquids arXiv:2003.00586.
  • (27) S. Patinet, D. Vandembroucq, and M. L. Falk, Connecting Local Yield Stresses with Plastic Activity in Amorphous Solids, Phys. Rev. Lett. 117, 045501 (2016).
  • (28) S. Patinet, A. Barbot, M. Lerbinger, D. Vandembroucq, and A. Lemaître, Origin of the Bauschinger Effect in Amorphous Solids, Phys. Rev. Lett. 124, 205503 (2020).
  • (29) M.A. Sutton, F. Hild, Recent advances and perspectives in digital image correlation Exp. Mech., 55 (2015), pp. 1-8.
  • (30) J.C. Stinville, W.C. Lenthe, M.P. Echlin, P.G. Callahan, D. Texier, T.M. Pollock, Microstructural statistics for fatigue crack initiation in polycrystalline nickel-base superalloys, Int. J. Fract., 208 (2017), pp. 221-240.
  • (31)

    D. Lunt, R. Thomas, M. Roy, J. Duff, M. Atkinson, P. Frankel, M. Preuss, and J. Quinta da Fonseca, Comparison of sub-grain scale digital image correlation calculated using commercial and open-source software packages, Materials Characterization 163 (2020) 110271.

  • (32) T. Mäkinen, P. Karppinen, M. Ovaska, L. Laurson, M.J. Alava, Propagating bands of plastic deformation in a metal alloy as critical avalanches, Science Advances, 6(41), p.eabc7350 (2020).
  • (33) J. Koivisto, M. J. Dalbe, M. J. Alava, and S. Santucci, Path (un) predictability of two interacting cracks in polycarbonate sheets using Digital Image Correlation, Scientific Reports, 6(1), pp.1-8 (2016).
  • (34) T. Mäkinen, A. Miksic, M. Ovaska, and M.J. Alava, Avalanches in wood compression, Physical Review Letters 115, 055501 (2015).
  • (35) Z. Yang, S. Papanikolaou, A.C. Reid, W.K. Liao, A.N. Choudhary, C. Campbell, and A. Agrawal, Learning to predict crystal plasticity at the nanoscale: Deep residual networks and size effects in uniaxial compression discrete dislocation simulations. Scientific reports, 10(1), pp.1-14 (2020).
  • (36) S. Papanikolaou, M. Tzimas, A. C. Reid, and S. A. Langer, Spatial strain correlations, machine learning, and deformation history in crystal plasticity. Physical Review E 99(5), 053003 (2019).
  • (37) S. Papanikolaou, Microstructural inelastic fingerprints and data-rich predictions of plasticity and damage in solids. Computational Mechanics, 66(1), pp.141-154 (2020).
  • (38) F. Roters, M. Diehl, P. Shanthraj, P. Eisenlohr, C. Reuber, S. L. Wong, T. Maiti, A. Ebrahimi, T. Hochrainer, and H.-O. Fabritius, Computational Materials Science 158, 420 (2019).
  • (39) R. Asaro and V. Lubarda, Mechanics of solids and materials (Cambridge University Press, 2006).
  • (40) S. Papanikolaou, P. Shanthraj, J. Thibault, and F. Roters, Brittle to quasi-brittle transition and crack initiation precursors in crystals with structural inhomogeneities, Materials Theory 5, 3(2019).
  • (41) A. Ma, and F. Roters, A constitutive model for fcc single crystals based on dislocation densities and its application to uniaxial compression of aluminium single crystals. Acta materialia, 52(12), pp.3603-3612 (2004).
  • (42) W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical recipes in C++. The art of scientific computing, 2, p.1002 (1992).
  • (43) C.A. Bronkhorst, S. R. Kalidindi, and L. Anand, Polycrystalline plasticity and the evolution of crystallographic texture in FCC metals. Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences, 341(1662), pp.443-477 (1992).
  • (44) S.B. Brown, K.H. Kim, and L. Anand, An internal variable constitutive model for hot working of metals, International Journal of Plasticity, 5(2), pp.95-130 (1989).
  • (45) Y.S. Chen, W. Choi, S. Papanikolaou, and J. P. Sethna, Bending crystals: emergence of fractal dislocation structures, Physical Review Letters, 105(10), p.105501 (2011).
  • (46) I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure. and Appl. Math., 41, 909-996 (1988).
  • (47) C. Chiann, P.A. Morettin, A wavelet analysis for time series, Nonparametric Stat., 10, 1-46 (1998).
  • (48) J.D. Scargle, T. Steiman-Cameron, K. Young, D.L. Donoho J.P. Crutchfield, J. Imamura, The quasi-periodic oscillations and very low frequency noise of Scorpius X–1 as transient chaos: a dripping handrail? Astron. J., 411, L91-L94, (1993).
  • (49) S. Papanikolaou, Y. Cui, and N. Ghoniem, Avalanches and plastic flow in crystal plasticity: an overview. Modelling and Simulation in Materials Science and Engineering, 26(1), p.013001 (2017).