# Disorder is good for you: the influence of local disorder on strain localization and ductility of strain softening materials

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## Abstract

We formulate a generic concept model for the deformation of a locally disordered, macroscopically homogeneous material which undergoes irreversible strain softening during plastic deformation. We investigate the influence of the degree of microstructural heterogeneity and disorder on strain localization (formation of a macroscopic shear band) in such materials. It is shown that increased microstructural heterogeneity delays strain localization and leads to an increase of the plastic regime in the macroscopic stress–strain curves. The evolving strain localization patterns are characterized.

## Keywords

Fracture Microstructures Inhomogeneous material Numerical algorithms Probability and statistics## Notes

### Acknowledgements

Financial support of the Hungarian Scientific Research Fund (OTKA) under contract number PD-105256 and of the European Commission under Grant Agreement No. CIG-321842 are also acknowledged. DT is supported by a One Year scholarship program sponsored by the Free State of Bavaria for graduates of Central, Eastern and Southeastern European states. PDI is also supported by the János Bolyai Scholarship of the Hungarian Academy of Sciences. MZ acknowledges financial support of DFG under Grant No. Za171/8-1.

## References

- Adibi S, Sha Z, Branicio P, Joshi SP, Liu Z, Zhang Y (2013) A transition from localized shear banding to homogeneous superplastic flow in nanoglass. Appl Phys Lett 103(211):905Google Scholar
- Albaret T, Tanguy A, Boioli F, Rodney D (2016) Mapping between atomistic simulations and Eshelby inclusions in the shear deformation of an amorphous silicon model. Phys Rev E 93(053):002. doi: 10.1103/PhysRevE.93.053002 Google Scholar
- Albe K, Ritter Y, Sopu D (2013) Shear band formation, nanocomposites and nanoglasses investigated by molecular dynamics simulations. Mech Mater 67:94–103CrossRefGoogle Scholar
- Ashby M, Greer A (2006) Metallic glasses as structural materials. Scripta Mater 54(3):321–326. doi: 10.1016/j.scriptamat.2005.09.051 CrossRefGoogle Scholar
- Bako B, Groma I, Györgyi G, Zimanyi G (2006) Dislocation patterning: the role of climb in meso-scale simulations. Comput Mater Sci 38:22–28CrossRefGoogle Scholar
- Budrikis Z, Zapperi S (2013) Avalanche localization and crossover scaling in amorphous plasticity. Phys Rev E 88(062):403. doi: 10.1103/PhysRevE.88.062403 Google Scholar
- Cheng Y, Cao A, Ma E (2009) Correlation between the elastic modulus and the intrinsic plastic behavior of metallic glasses: the roles of atomic configuration and alloy composition. Acta Mater 57(11):3253–3267. doi: 10.1016/j.actamat.2009.03.027 CrossRefGoogle Scholar
- Das J, Tang M, Kim KB, Theissmann R, Baier F, Wang WH, Eckert J (2005) “Work-hardenable” ductile bulk metallic glass. Phys Rev Lett 94(205):501Google Scholar
- Groma I, Csikor F, Zaiser M (2003) Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics. Acta Mater 51(5):1271–1281. doi: 10.1016/S1359-6454(02)00517-7 CrossRefGoogle Scholar
- Hofmann DC, Suh JY, Wiest A, Duan G, Lind ML, Demetriou MD, Johnson W (2008) Designing metallic glass matrix composites with high toughness and tensile ductility. Nature 451:1085–1089CrossRefGoogle Scholar
- Ispánovity PD, Ádám Hegyi, Groma I, Györgyi G, Ratter K, Weygand D (2013) Average yielding and weakest link statistics in micron-scale plasticity. Acta Mater 61(16):6234–6245. doi: 10.1016/j.actamat.2013.07.007 CrossRefGoogle Scholar
- Kapetanou O, Weygand D, Zaiser M (2015) Stress and strain fluctuations in plastic deformation of crystals with disordered microstructure. J Stat Mech Theory Exp P08009Google Scholar
- Lennartz-Sassinek S, Main IG, Zaiser M, Graham CC (2014) Acceleration and localization of subcritical crack growth in a natural composite material. Phys Rev E 90(052):401. doi: 10.1103/PhysRevE.90.052401 Google Scholar
- Lin J, Saade A, Lerner E, Rosso A, Wyart M (2014) On the density of shear transformations in amorphous solids. EPL (Europhys Lett) 105(2):26003CrossRefGoogle Scholar
- Lin J, Gueudre T, Rosso A, Wyart M (2015) Criticality in the approach to failure in amorphous solids. Phys Rev Lett 115:168,001. doi: 10.1103/PhysRevLett.103.065501 CrossRefGoogle Scholar
- Qiao J, Yao Y, Pelletier J, Keer L (2016) Understanding of micro-alloying on plasticity in \(\text{CU}_{46}\text{ Zr }_{47}{-}x\text{ Al }_7dyx 0 \leqslant x \leqslant 8\) bulk metallic glasses under compression: based on mechanical relaxations and theoretical analysis. Int J Plast doi: 10.1016/j.ijplas.2016.02.002S0749641916300122
- Rodney D, Schuh C (2009) Distribution of thermally activated plastic events in a flowing glass. Phys Rev Lett 102(235):503Google Scholar
- Rodney D, Tanguy A (2011) Modeling the mechanics of amorphous solids at different length scale and time scale. Modell Simul Mater Sci Eng 19(083):001Google Scholar
- Sandfeld S, Budrikis Z, Zapperi S, Fernandez Castellanos D (2015) Avalanches, loading and finite size effects in 2D amorphous plasticity: results from a finite element model. J Stat Mech Theory Exp 2015(2):P02011CrossRefGoogle Scholar
- Schuh CA, Hufnagel TC, Ramamurty U (2007) Mechanical behavior of amorphous alloys. Acta Mater 55:4067–4109CrossRefGoogle Scholar
- Şopu D, Ritter Y, Gleiter H, Albe K (2011) Deformation behavior of bulk and nanostructured metallic glasses studied via molecular dynamics simulations. Phys Rev B 83(100):202. doi: 10.1103/PhysRevB.83.100202 Google Scholar
- Steif P, Spaepen F, Hutchinson JW (1982) Strain localization in amorphous metals. Acta Metall 30(2):447–455CrossRefGoogle Scholar
- Talamali M, Petäjä V, Vandembroucq D, Roux S (2012) Strain localization and anisotropic correlations in a mesoscopic model of amorphous plasticity. C R Mécanique 340(4–5):275–288. doi: 10.1016/j.crme.2012.02.010 (recent Adv Micromech Mater)CrossRefGoogle Scholar
- Wright W, Schwarz RB, Nix W (2001) Localized heating during serrated plastic flow in bulk metallic glasses. Mater Sci Eng A 319:229–232CrossRefGoogle Scholar
- Wu Y, Bei H, Wang Y, Lu Z, George E, Gao Y (2015) Deformation-induced spatiotemporal fluctuation, evolution and localization of strain fields in a bulk metallic glass. Int J Plast 71:136–145. doi: 10.1016/j.ijplas.2015.05.006 CrossRefGoogle Scholar
- Xu X, Wang Y, Guo A, Geng H, Ren S, Tao X, Liu J (2016) Enhanced plasticity by nanocrystallite in bulk amorphous \(\text{ AL }_2\text{ O }_3{-}\text{ ZrO }_2--\text{ Y }_2\text{ O }_3\). Int J Plast 79:314–327. doi: 10.1016/j.ijplas.2015.09.004 CrossRefGoogle Scholar
- Zaiser M (2006) Scale invariance in plastic flow of crystalline solids. Adv Phys 55:185–245CrossRefGoogle Scholar
- Zaiser M, Mill F, Konstantinidis A, Aifantis K (2013) Strain localization and strain propagation in collapsible solid foams. Mater Sci Eng A 567:38–45CrossRefGoogle Scholar
- Zaiser M, Aifantis EC (2006) Randomness and slip avalanches in gradient plasticity. Int J Plast 22(8):1432–1455. doi: 10.1016/j.ijplas.2005.07.010 (special issue in honour of Dr. Kirk Valanis)CrossRefGoogle Scholar
- Zaiser M, Moretti P (2005) Fluctuation phenomena in crystal plasticity—a continuum model. J Stat Mech Theory Exp 2015(08):P08004Google Scholar
- Zhou H, Zhong C, Cao Q, Qu S, Wang X, Yang W, Jiang J (2014) Non-localized deformation in metallic alloys with amorphous structure. Acta Mater 68:32–41CrossRefGoogle Scholar