Advertisement

Reduced-Order Microstructure-Sensitive Models for Damage Initiation in Two-Phase Composites

  • David Montes de Oca Zapiain
  • Evdokia Popova
  • Fadi Abdeljawad
  • James W. FoulkIII
  • Surya R. Kalidindi
  • Hojun Lim
Technical Article
  • 117 Downloads

Abstract

Local features of the internal structure or the microstructure dominate the overall performance of materials. An open problem in materials design with enhanced properties is to accurately identify and quantify salient features of the microstructure and understand its correlation with the material’s performance. This task is exacerbated when dealing with failure related properties that show strong correlations to higher-order details of the material microstructure. This paper presents a novel data-driven framework for quantitatively determining the highly complex correlations that exist between the higher-order details of the material microstructure and its failure-related properties, specifically its damage initiation properties. The enclosed work will address this challenge by significantly extending the Materials Knowledge Systems (MKS) framework and by leveraging concepts in extreme value distributions and machine learning. The developed framework was capable of successfully sorting nine different classes of synthetically generated two-phase microstructures for their sensitivity to damage initiation. The framework and approaches presented here open new research avenues for studying the microstructure-sensitive damage initiation properties associated with heterogeneous materials, and pave the way forward for practical multiscale materials design.

Keywords

Materials Knowledge System Damage 2-point statistics PCA Extreme value distributions 

Notes

Acknowledgments

Sandia National Laboratories is a multi-mission laboratory managed and operated by the National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

References

  1. 1.
    Adams BL, Kalidindi S, Fullwood DT (2013) Microstructure-sensitive design for performance optimization. Butterworth-Heinemann, WalthamGoogle Scholar
  2. 2.
    McDowell DL, Panchal J, Choi H-J, Seepersad C, Allen J, Mistree F (2009) Integrated design of multiscale, multifunctional materials and products. Butterworth-Heinemann, WalthamGoogle Scholar
  3. 3.
    Song K, Zhang Y, Meng J, Green EC, Tajaddod N, Li H, Minus ML (2013) Structural polymer-based carbon nanotube composite fibers: understanding the processing–structure–performance relationship. Materials 6(6):2543–2577CrossRefGoogle Scholar
  4. 4.
    McDowell DL, Ghosh S, Kalidindi SR (2011) Representation and computational structure-property relations of random media. JOM 63(3):45–51CrossRefGoogle Scholar
  5. 5.
    McDowell DL, Olson GB (2008) Concurrent design of hierarchical materials and structures. Sci Model Simul 15(1–3):207–240CrossRefGoogle Scholar
  6. 6.
    Olson GB (1997) Computational design of hierarchically structured materials. Science 277(5330):1237–1242CrossRefGoogle Scholar
  7. 7.
    Adams BL, Olson T (1998) The mesostructure—properties linkage in polycrystals. Prog Mater Sci 43(1):1–87CrossRefGoogle Scholar
  8. 8.
    N.R. Council (2008) Integrated computational materials engineering: a transformational discipline for improved competitiveness and national security. National Academies Press, Washington DCGoogle Scholar
  9. 9.
    J Oden, T Belytschko, J Fish, T Hughes, C Johnson, D Keyes, A Laub, L Petzold, D Srolovitz, S Yip (2006) Simulation-based engineering science: revolutionizing engineering science through simulation. Report of NSF Blue Ribbon Panel on Simulation-Based Engineering ScienceGoogle Scholar
  10. 10.
    N. Science, T. Council (2011) Materials genome initiative for global competitiveness, Executive Office of the President. National Science and Technology Council, Washington D.C.Google Scholar
  11. 11.
    Kalidindi SR (2015) Hierarchical materials informatics. Butterworth Heinemann, WalthamGoogle Scholar
  12. 12.
    Brechet Y, Embury J, Tao S, Luo L (1991) Damage initiation in metal matrix composites. Acta Metall Mater 39(8):1781–1786CrossRefGoogle Scholar
  13. 13.
    Brechet Y, Newell J, Tao S, Embury JD (1993) A note on particle comminution at large plastic strains in Al-SiC composites. Scr Metall Mater 28(1):47–51CrossRefGoogle Scholar
  14. 14.
    Caceres CH, Griffiths JR (1996) Damage by the cracking of silicon particles in an Al-7Si-0.4Mg casting alloy. Acta Mater 44(1):25–33CrossRefGoogle Scholar
  15. 15.
    Caceres CH, Griffiths JR, Reiner P (1996) The influence of microstructure on the Bauschinger effect in an Al-Si-Mg casting alloy. Acta Mater 44(1):15–23CrossRefGoogle Scholar
  16. 16.
    Wilkinson DS, Maire E, Fougeres R (1999) A model for damage is a clustered particulate composite. Mater Sci Eng A-Struct 262(1–2):264–270CrossRefGoogle Scholar
  17. 17.
    Wilkinson DS, Maire E, Embury JD (1997) The role of heterogeneity on the flow and fracture of two-phase materials. Mat Sci Eng A-Struct 233(1–2):145–154CrossRefGoogle Scholar
  18. 18.
    Segurado J, Gonzalez C, Llorca J (2003) A numerical investigation of the effect of particle clustering on the mechanical properties of composites. Acta Mater 51(8):2355–2369CrossRefGoogle Scholar
  19. 19.
    Nan CW, Clarke DR (1996) The influence of particle size and particle fracture on the elastic/plastic deformation of metal matrix composites. Acta Mater 44(9):3801–3811CrossRefGoogle Scholar
  20. 20.
    Gupta A, Cecen A, Goyal S, Singh AK, Kalidindi SR (2015) Structure–property linkages using a data science approach: application to a non-metallic inclusion/steel composite system. Acta Mater 91:239–254CrossRefGoogle Scholar
  21. 21.
    Paulson NH, Priddy MW, McDowell DL, Kalidindi SR (2017) Reduced-order structure-property linkages for polycrystalline microstructures based on 2-point statistics. Acta Mater 129:428–438CrossRefGoogle Scholar
  22. 22.
    Latypov MI, Kalidindi SR (2017) Data-driven reduced order models for effective yield strength and partitioning of strain in multiphase materials. J Comput Phys 346:242–261CrossRefGoogle Scholar
  23. 23.
    D Montes de Oca Zapiain, A Fadi, L Hojun, E Popova, SR Kalidindi (2017) 2-Phase composite damage initiation sensitivity dataset, https://matin.gatech.edu/resources/296
  24. 24.
    Brough DB, Kannan A, Haaland B, Bucknall DG, Kalidindi SR (2017) Extraction of process-structure evolution linkages from X-ray scattering measurements using dimensionality reduction and time series analysis. Integr Mater Manuf Innov 6(2):147–159CrossRefGoogle Scholar
  25. 25.
    CeCen A, Fast T, Kumbur E, Kalidindi S (2014) A data-driven approach to establishing microstructure–property relationships in porous transport layers of polymer electrolyte fuel cells. J Power Sources 245:144–153CrossRefGoogle Scholar
  26. 26.
    S Torquato (2013) Random heterogeneous materials: microstructure and macroscopic properties. Springer Science & Business MediaGoogle Scholar
  27. 27.
    Kroner E (1986) Statistical modelling. In: Gittus J, Zarka J (eds) Modelling small deformations of polycrystals. Elsevier Science Publishers, London, pp 229–291CrossRefGoogle Scholar
  28. 28.
    Kalidindi SR, Niezgoda SR, Salem AA (2011) Microstructure informatics using higher-order statistics and efficient data-mining protocols. JOM 63(4):34–41CrossRefGoogle Scholar
  29. 29.
    Niezgoda SR, Kanjarla AK, Kalidindi SR (2013) Novel microstructure quantification framework for databasing, visualization, and analysis of microstructure data. Integr Mater Manuf Innov 2(1):3CrossRefGoogle Scholar
  30. 30.
    Jolliffe I (2005) Principal component analysis, encyclopedia of statistics in behavioral science. Wiley, HobokenGoogle Scholar
  31. 31.
    Suh C, Rajagopalan A, Li X, Rajan K (2002) The application of principal component analysis to materials science data. Data Sci J 1:19–26CrossRefGoogle Scholar
  32. 32.
    Niezgoda SR, Yabansu YC, Kalidindi SR (2011) Understanding and visualizing microstructure and microstructure variance as a stochastic process. Acta Mater 59(16):6387–6400CrossRefGoogle Scholar
  33. 33.
    NH Paulson, MW Priddy, DL McDowell, SR Kalidindi (2017) Data-driven reduced-order models for rank-ordering the high cycle fatigue performance of polycrystalline microstructures, Submitted for reviewGoogle Scholar
  34. 34.
    Benesty J, Chen J, Huang Y, Cohen I (2009) Pearson correlation coefficient, noise reduction in speech processing. Springer, Berlin, pp 1–4Google Scholar
  35. 35.
    P. Sedgwick (2012) Pearson’s correlation coefficient. BMJ 345(7)Google Scholar
  36. 36.
    Bienias J, Debski H, Surowska B, Sadowski T (2012) Analysis of microstructure damage in carbon/epoxy composites using FEM. Comput Mater Sci 64:168–172CrossRefGoogle Scholar
  37. 37.
    Ghosh S, Moorthy S (1998) Particle fracture simulation in non-uniform microstructures of metal-matrix composites. Acta Mater 46(3):965–982CrossRefGoogle Scholar
  38. 38.
    Needleman A, Tvergaard V (1984) An analysis of ductile rupture in notched bars. J Mech Phys Solids 32(6):461–490CrossRefGoogle Scholar
  39. 39.
    Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Metall Mater 32(1):157–169CrossRefGoogle Scholar
  40. 40.
    Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth. 1. Yield criteria and flow rules for porous ductile media. J Eng Mater Trans ASME 99(1):2–15CrossRefGoogle Scholar
  41. 41.
    Rice JR, Tracey DM (1969) On ductile enlargement of voids in Triaxial stress fields. J Mech Phys Solids 17(3):201–217CrossRefGoogle Scholar
  42. 42.
    Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46(1):81–98CrossRefGoogle Scholar
  43. 43.
    Mirone G (2008) Elastoplastic characterization and damage predictions under evolving local triaxiality: axysimmetric and thick plate specimens. Mech Mater 40(9):685–694CrossRefGoogle Scholar
  44. 44.
    Mirone G (2007) Role of stress triaxiality in elastoplastic characterization and ductile failure prediction. Eng Fract Mech 74(8):1203–1221CrossRefGoogle Scholar
  45. 45.
    Mcclintock FA (1968) A criterion for ductile fracture by growth of holes. J Appl Mech 35(2):363–371CrossRefGoogle Scholar
  46. 46.
    Mcclintock FA (1968) Local criteria for ductile fracture. Int J Fract Mech 4(2):101–130CrossRefGoogle Scholar
  47. 47.
    Mackenzie AC, Hancock JW, Brown DK (1977) On the influence of state of stress on ductile failure initiation in high strength steels. Eng Fract Mech 9(1):167–188CrossRefGoogle Scholar
  48. 48.
    Cockcroft M, Latham D (1968) Ductility and the workability of metals. J Inst Met 96(1):33–39Google Scholar
  49. 49.
    P Brozzo, B Deluca, R Rendina (1972) A new method for the prediction of formability limits in metal sheets, Proc. 7th biennal Conf. IDDRGoogle Scholar
  50. 50.
    Clift SE, Hartley P, Sturgess C, Rowe G (1990) Fracture prediction in plastic deformation processes. Int J Mech Sci 32(1):1–17CrossRefGoogle Scholar
  51. 51.
    Zhang KS, Bai JB, François D (2001) Numerical analysis of the influence of the lode parameter on void growth. Int J Solids Struct 38(32):5847–5856CrossRefGoogle Scholar
  52. 52.
    Xue L (2007) Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading. Int J Solids Struct 44(16):5163–5181CrossRefGoogle Scholar
  53. 53.
    Xue L, Wierzbicki T (2008) Ductile fracture initiation and propagation modeling using damage plasticity theory. Eng Fract Mech 75(11):3276–3293CrossRefGoogle Scholar
  54. 54.
    Biffle JH (1993) JAC3D—a three-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method. Yucca Mountain Site Characterization Project, Sandia National Labs, AlbuquerqueGoogle Scholar
  55. 55.
    Ahsanullah M (2016) Extreme value distributions. Atlantis Press, ParisCrossRefGoogle Scholar
  56. 56.
    IF Alves, C Neves (2011) Extreme value distributions. 493–496Google Scholar
  57. 57.
    Jenkinson AF (1955) The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Q J R Meteorol Soc 81(348):158–171CrossRefGoogle Scholar
  58. 58.
    Bali TG (2003) The generalized extreme value distribution. Econ Lett 79(3):423–427CrossRefGoogle Scholar
  59. 59.
    Singh VP (1998) Generalized extreme value distribution, entropy-based parameter estimation in hydrology. Springer, Berlin, pp 169–183Google Scholar
  60. 60.
    Coles S, Bawa J, Trenner L, Dorazio P (2001) An introduction to statistical modeling of extreme values. Springer, BerlinCrossRefGoogle Scholar
  61. 61.
    Martins ES, Stedinger JR (2000) Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data. Water Resour Res 36(3):737–744CrossRefGoogle Scholar
  62. 62.
    Hosking J (1985) Algorithm as 215: maximum-likelihood estimation of the parameters of the generalized extreme-value distribution. J R Stat Soc: Ser C: Appl Stat 34(3):301–310Google Scholar
  63. 63.
    Niezgoda SR, Fullwood DT, Kalidindi SR (2008) Delineation of the space of 2-point correlations in a composite material system. Acta Mater 56(18):5285–5292CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society 2018

Authors and Affiliations

  1. 1.Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Sandia National LaboratoriesAlbuquerqueUSA
  3. 3.Sandia National LaboratoriesLivermoreUSA

Personalised recommendations