A void descriptor function to uniquely characterize pore networks and predict ductile-metal failure properties

Abstract

Porosity, a commonly occurring void defect in casting and additive manufacturing, is known to affect the mechanical response of metals, making it difficult or impossible to predict response variability. We introduce a new method of uniquely characterizing pore networks using a void descriptor function (VDF), which can be used to predict ductile-metal failure properties, namely, toughness modulus, ultimate strength, elongation, and fracture location. The VDF quantifies the inter-relationships of pores by accounting for pore location, size, and distance to free surface. Using a finite-element-modeling framework, 120 tensile specimens with statistically similar pore networks were simulated (virtually tested) to failure. The pore networks were characterized by the proposed VDF, which was then compared to the nominal location of fracture (defined as the fracture-initiation location corresponding to the dominant crack responsible for final rupture). The location of maximum VDF accurately predicted the fracture location (within ± 0.2 mm) for 91 (76%) of the 120 samples and proved to be a more reliable indicator than the location of maximum reduced cross-section area and the location of largest pore diameter for predicting fracture location. Furthermore, the maximum VDF value was found to be more highly correlated than fraction porosity, pore size, reduced-cross section area, and total number of pores to the ultimate tensile strength, elongation, and toughness modulus.

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Notes

  1. 1.

    The value of 120 was selected based on a formula from (Bellera and Hanley 2007), which is detailed further in Sect. 2.4.

  2. 2.

    The stress data reported in Ref. (Boyce et al. 2017) were based on width and thickness measurements for individual tensile samples using a Keyence IM-6225T optical measurement system and Mitutoyo Digimatic Micrometer, respectively.

  3. 3.

    The built-in function scipy.signal.find_peaks in SciPy v1.4.1 was used to identify all local maxima.

References

  1. Antou G, Montavon G, Hlawka F, Cornet A, Coddet C (2004) Characterizations of the pore-crack network architecture of thermal-sprayed coatings. Characterizations of the pore-crack network architecture of thermal-sprayed coatings. Mater Charact 53(5):361–372. https://doi.org/10.1016/j.matchar.2004.08.015

    CAS  Article  Google Scholar 

  2. ASTM Standard E8/E8M-13a (2013) Standard test methods for tension testing of metallic materials. Tech Rep https://doi.org/10.1520/E0008_E0008M-13A

  3. Bellera CA, Hanley JA (2007) A method is presented to plan the required sample size when estimating regression-based reference limits. J Clin Epidemiol 60(6):610–615. https://doi.org/10.1016/j.jclinepi.2006.09.004

    Article  Google Scholar 

  4. Boyce BL, Salzbrenner BC, Rodelas JM, Swiler LP, Madison JD, Jared BH, Shen YL (2017) Extreme-value statistics reveal rare failure-critical defects in additive manufacturing. Adv Eng Mater 19(8):1700102

    Article  Google Scholar 

  5. Cao TS, Mazière M, Danas K, Besson J (2015) A model for ductile damage prediction at low stress triaxialities incorporating void shape change and void rotation. Int J Solids Struct 63:240–263. https://doi.org/10.1016/j.ijsolstr.2015.03.003

    Article  Google Scholar 

  6. Chawla N, Deng X (2005) Microstructure and mechanical behavior of porous sintered steels. Mater Sci Eng A 390(1):98–112. https://doi.org/10.1016/j.msea.2004.08.046

    CAS  Article  Google Scholar 

  7. Chen X, Wu S, Zhou J (2013) Influence of porosity on compressive and tensile strength of cement mortar. Construct Build Mater. https://doi.org/10.1016/j.conbuildmat.2012.11.072

    Article  Google Scholar 

  8. Eichhubl P (2003) Aydin A (2003) Microcrack nucleation, growth, coalescence and propagation in the fatigue failure of a powder metallurgy steel. J Struct Geol 25(1):121–134. https://doi.org/10.1016/S0191-8141(02)00055-X

    Article  Google Scholar 

  9. Fan J, McDowell DL, Horstemeyer MF, Gall K (2003) Cyclic plasticity at pores and inclusions in cast Al’Si alloys. Eng Fract Mech 70(10):1281–1302. https://doi.org/10.1016/S0013-7944(02)00097-8

    Article  Google Scholar 

  10. Fritzen F, Forest S, Böhlke T, Kondo D, Kanit T (2012) Computational homogenization of elasto-plastic porous metals. Int J Plast 29(1):102–119. https://doi.org/10.1016/j.ijplas.2011.08.005

    CAS  Article  Google Scholar 

  11. Gunasegaram DR, Farnsworth DJ, Nguyen TT (2009) Identification of critical factors affecting shrinkage porosity in permanent mold casting using numerical simulations based on design of experiments. J Mater Process Technol. https://doi.org/10.1016/j.jmatprotec.2008.03.044

    Article  Google Scholar 

  12. Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth: part 1 - yield criteria and flow rules for porous ductile media. J Eng Mater Technol Trans ASME. https://doi.org/10.1115/1.3443401

    Article  Google Scholar 

  13. Hogan JD, Farbaniec L, Sano T, Shaeffer M, Ramesh K (2016) The effects of defects on the uniaxial compressive strength and failure of an advanced ceramic. Acta Materialia 102:263–272. https://doi.org/10.1016/j.actamat.2015.09.028

    CAS  Article  Google Scholar 

  14. Hogg R, McKean J, Craig A (2012) Introduction to Mathematical Statistics. Pearson Education. https://books.google.com/books?id=YdwsAAAAQBAJ

  15. Huang T, Gong Y (2018) A multiscale analysis for predicting the elastic properties of 3D woven composites containing void defects. Compos Struct 185:401–410. https://doi.org/10.1016/j.compstruct.2017.11.046

    Article  Google Scholar 

  16. Hyun S, Murakami K, Nakajima H (2001) Anisotropic mechanical properties of porous copper fabricated by unidirectional solidification. Mater Sci Eng A 299(1):241–248. https://doi.org/10.1016/S0921-5093(00)01402-7

    Article  Google Scholar 

  17. Jahed Armaghani D, Tonnizam Mohamad E, Momeni E, Narayanasamy MS, Mohd Amin MF (2015) An adaptive neuro-fuzzy inference system for predicting unconfined compressive strength and Young’s modulus: a study on Main Range granite. Bull Eng Geol Environ 74(4):1301–1319. https://doi.org/10.1007/s10064-014-0687-4

    CAS  Article  Google Scholar 

  18. Kabatova M, Dudrova E, WRONSKI AS (2009) Microcrack nucleation, growth, coalescence and propagation in the fatigue failure of a powder metallurgy steel. Fatigue Fract Eng Mater Struct 32(3):214–222. https://doi.org/10.1111/j.1460-2695.2009.01328.x

    CAS  Article  Google Scholar 

  19. Khademi F, Jamal SM, Deshpande N, Londhe S (2016) Predicting strength of recycled aggregate concrete using Artificial Neural Network, Adaptive Neuro-Fuzzy Inference System and Multiple Linear Regression. Int J Sustain Built Environ 5(2):355–369. https://doi.org/10.1016/j.ijsbe.2016.09.003

    Article  Google Scholar 

  20. Khdir YK, Kanit T, Zaïri F, Naït-Abdelaziz M (2015) A computational homogenization of random porous media: effect of void shape and void content on the overall yield surface. Eur J Mech A 49:137–145. https://doi.org/10.1016/j.euromechsol.2014.07.001

    Article  Google Scholar 

  21. Kramer SLB, Ivanoff TA, Madison JD, Lentfer AP (2019) Evolution of damage and failure in an additively manufactured 316L SS structure: experimental reinvestigation of the third Sandia fracture challenge. Int J Fract 218(1–2):63–84. https://doi.org/10.1007/s10704-019-00357-x

    CAS  Article  Google Scholar 

  22. Kramer SL, Jones A, Mostafa A, Ravaji B, Tancogne-Dejean T, Roth CC, Bandpay MG, Pack K, Foster JT, Behzadinasab M et al (2019) The third Sandia Fracture Challenge: predictions of ductile fracture in additively manufactured metal. Int J Fract 218(1–2):5–61

    CAS  Article  Google Scholar 

  23. Levine BG, Stone JE, Kohlmeyer A (2011) Fast analysis of molecular dynamics trajectories with graphics processing units’Radial distribution function histogramming. J Comput Phys 230(9):3556–3569. https://doi.org/10.1016/j.jcp.2011.01.048

    CAS  Article  Google Scholar 

  24. Li Z, Jing Y, Guo H, Sun X, Yu K, Yu A, Jiang X, Yang XJ (2019) Study of 3D pores and its relationship with crack initiation factors of aluminum alloy die castings. Metallurg Mater Trans B 50(3):1204–1212. https://doi.org/10.1007/s11663-019-01550-y

    CAS  Article  Google Scholar 

  25. Lyubartsev AP, Laaksonen A (1995) Calculation of effective interaction potentials from radial distribution functions: a reverse Monte Carlo approach. Phys Rev E 52:3730–3737. https://doi.org/10.1103/PhysRevE.52.3730

    CAS  Article  Google Scholar 

  26. Madison JD, Underwood OD, Swiler LP, Boyce BL, Jared BH, Rodelas JM, Salzbrenner BC (2018) In: AIP Conference Proceedings. https://doi.org/10.1063/1.5031506

  27. Masmoudi M, Kaddouri W, Kanit T, Madani S, Ramtani S, Imad A (2017) Modeling of the effect of the void shape on effective ultimate tensile strength of porous materials: numerical homogenization versus experimental results. Int J Mech Sci 130:497–507. https://doi.org/10.1016/j.ijmecsci.2017.06.011

    Article  Google Scholar 

  28. Orsini V, Zikry M (2001) Void growth and interaction in crystalline materials. Int J Plast 17(10):1393–1417. https://doi.org/10.1016/S0749-6419(00)00091-7

    Article  Google Scholar 

  29. Rao S, Cunningham R, Ozturk T, Rollett AD (2016) Measurement and analysis of porosity in Al-10Si-1Mg components additively manufactured by selective laser melting. Mater Perform Charact 5(5):20160037. https://doi.org/10.1520/MPC20160037

    Article  Google Scholar 

  30. Shahriari B, Swersky K, Wang Z, Adams RP, de Freitas N (2016) Taking the human out of the loop: a review of Bayesian optimization. Proc IEEE 104(1):148–175. https://doi.org/10.1109/JPROC.2015.2494218

    Article  Google Scholar 

  31. Sholl DS, Lively RP (2015) Defects in metal’organic frameworks: challenge or opportunity? J Phys Chem Lett 6(17):3437–3444. https://doi.org/10.1021/acs.jpclett.5b01135

    CAS  Article  Google Scholar 

  32. Slotwinski JA, Garboczi EJ, Hebenstreit KM (2014) Porosity measurements and analysis for metal additive manufacturing process control. J Res Natl Inst Stand Technol 119:494

    Article  Google Scholar 

  33. Smith M (2014) ABAQUS/Standard User’s Manual, Version 6.14. Dassault Systèmes Simulia Corp, United States

  34. Spear AD, Czabaj MW, Newell P, DeMille K, Phung BR, Zhao D, Creveling P, Briggs N, Brodbine E, Creveling C et al (2019) The third Sandia Fracture Challenge: from theory to practice in a classroom setting. Int J Fract 218(1–2):171–194

    Article  Google Scholar 

  35. Su X, Yang Z, Liu G (2010) Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials: a 3D study. Int J Solids Struct 47(17):2336–2345. https://doi.org/10.1016/j.ijsolstr.2010.04.031

    Article  Google Scholar 

  36. Tvergaard V (Elsevier, 1989), pp. 83 – 151. https://doi.org/10.1016/S0065-2156(08)70195-9

  37. Tvergaard V (1981) Influence of voids on shear band instabilities under plane strain conditions. Int J Fract. https://doi.org/10.1007/BF00036191

    Article  Google Scholar 

  38. Varna J, Joffe R, Berglund L, Lundström T (1995) Effect of voids on failure mechanisms in RTM laminates. Composit Sci Technol 53(2):241–249. https://doi.org/10.1016/0266-3538(95)00024-0

    CAS  Article  Google Scholar 

  39. Voisin T, Calta NP, Khairallah SA, Forien JB, Balogh L, Cunningham RW, Rollett AD, Wang YM (2018) Defects-dictated tensile properties of selective laser melted Ti-6Al-4V. Mater Des 158:113–126. https://doi.org/10.1016/j.matdes.2018.08.004

    CAS  Article  Google Scholar 

  40. von Lilienfeld OA, Ramakrishnan R, Rupp M, Knoll A (2015) Fourier series of atomic radial distribution functions: a molecular fingerprint for machine learning models of quantum chemical properties. Int J Quant Chem 115(16):1084–1093. https://doi.org/10.1002/qua.24912

    CAS  Article  Google Scholar 

  41. Watring DS, Carter KC, Crouse D, Raeymaekers B, Spear AD (2019) Mater Sci Eng A. https://doi.org/10.1016/j.msea.2019.06.003

    Article  Google Scholar 

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Acknowledgements

The authors wish to thank Drs. Jonathan Madison, Bradley Jared, and Brad Boyce for sharing the experimental data used to inform the numerical models in this work. Dr. Branden Kappes is gratefully acknowledged for fruitful discussions that influenced aspects of this work. This research is supported by the National Science Foundation under Grant No. CMMI-1752400 and by the Department of Defense Office of Economic Adjustment (ST1605-19-03). Numerical simulations were performed using resources provided by the University of Utah Center for High Performance Computing.

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Appendix

Appendix

See Tables 5 and 6.

Table 5 Sensitivity of predictions to VDF parameters. The 120 samples described in Sect. 2 were randomly divided into three data sets of 40 samples each. The VDF scaling parameters \(\alpha \) and \(\rho \) were optimized for each data set and used to blindly predict the fracture location for the remaining 80 samples not included in the optimization
Table 6 Condensed tabular input of plastic stress–strain curve

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Erickson, J.M., Rahman, A. & Spear, A.D. A void descriptor function to uniquely characterize pore networks and predict ductile-metal failure properties. Int J Fract (2020). https://doi.org/10.1007/s10704-020-00463-1

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Keywords

  • Porosity
  • Computational fracture mechanics
  • Ductile fracture
  • Finite-element modeling
  • Additive manufacturing