Abstract
It is well known that the biological composites have superior mechanical properties due to their exquisite multilevel structural hierarchy. However, the underlying mechanisms of the roles of this hierarchical design in the toughness of the biocomposites remain elusive. In this paper, the deformation and fracture mechanism of multilevel hierarchical structures are explored by molecular dynamics simulations. The effects of the multilevel design on fracture toughness, nonlinear deformation of soft matrix, and the crack path pattern were quantitatively analyzed. We showed that the toughness of composites is closely associated with the pattern of the crack path and the nonlinear deformation of the matrix. Additionally, the structure with a higher level of hierarchy exhibit higher toughness, which is less sensitive to the geometrical change of inclusions, such as the aspect ratio and the staggered ratio. This work provides more theoretical evidence of the toughening mechanism of the multilevel hierarchy in fracture toughness of biological materials via new methods of analyzing fracture of multilevel structures and provides guidelines for the design of high-performance engineering materials.
References
1.
Ritchie
, R. O.
, 2011
, “The Conflicts Between Strength and Toughness
,” Nat. Mater.
, 10
(11
), pp. 817
–822
. 10.1038/nmat31152.
Jäger
, I.
, and Fratzl
, P.
, 2000
, “Mineralized Collagen Fibrils: A Mechanical Model With a Staggered Arrangement of Mineral Particles
,” Biophys. J.
, 79
(4
), pp. 1737
–1746
. 10.1016/S0006-3495(00)76426-53.
Okumura
, K.
, and De Gennes
, P.-G.
, 2001
, “Why Is Nacre Strong? Elastic Theory and Fracture Mechanics for Biocomposites With Stratified Structures
,” Eur. Phys. J. E
, 4
(1
), pp. 121
–127
. 10.1007/s1018901701504.
Gao
, H.
, Ji
, B.
, Jäger
, I. L.
, Arzt
, E.
, and Fratzl
, P.
, 2003
, “Materials Become Insensitive to Flaws at Nanoscale: Lessons From Nature
,” Proc. Natl. Acad. Sci. USA
, 100
(10
), pp. 5597
–5600
. 10.1073/pnas.06316091005.
Ji
, B.
, and Gao
, H.
, 2004
, “Mechanical Properties of Nanostructure of Biological Materials
,” J. Mech. Phys. Solids
, 52
(9
), pp. 1963
–1990
. 10.1016/j.jmps.2004.03.0066.
Ji
, B.
, and Gao
, H.
, 2006
, “Elastic Properties of Nanocomposite Structure of Bone
,” Compos. Sci. Technol.
, 66
(9
), pp. 1212
–1218
. 10.1016/j.compscitech.2005.10.0177.
Gao
, H.
, 2006
, “Application of Fracture Mechanics Concepts to Hierarchical Biomechanics of Bone and Bone-Like Materials
,” Int. J. Fract.
, 138
(1–4
), pp. 101
–137
. 10.1007/s10704-006-7156-48.
Ji
, B.
, and Gao
, H.
, 2006
, Handbook of Computational and Theoretical Nanotechnology
, M.
Rieth
, and W.
Schommers
, eds., Vol. 9, American Scientific Publishing
, Stevenson Ranch
, pp. 456
–497
.9.
Yao
, H.
, and Gao
, H.
, 2007
, “Multi-Scale Cohesive Laws in Hierarchical Materials
,” Int. J. Solids Struct.
, 44
(25–26
), pp. 8177
–8193
. 10.1016/j.ijsolstr.2007.06.00710.
Buehler
, M. J.
, Keten
, S.
, and Ackbarow
, T.
, 2008
, “Theoretical and Computational Hierarchical Nanomechanics of Protein Materials: Deformation and Fracture
,” Prog. Mater. Sci.
, 53
(8
), pp. 1101
–1241
. 10.1016/j.pmatsci.2008.06.00211.
Ji
, B.
, and Gao
, H.
, 2010
, “Mechanical Principles of Biological Nanocomposites
,” Annu. Rev. Mater. Res.
, 40
(1
), pp. 77
–100
. 10.1146/annurev-matsci-070909-10442412.
Zhang
, Z.
, Zhang
, Y. W.
, and Gao
, H.
, 2011
, “On Optimal Hierarchy of Load-Bearing Biological Materials
,” Proc. Biol. Sci.
, 278
(1705
), pp. 519
–525
. 10.1098/rspb.2010.109313.
Mirzaeifar
, R.
, Dimas
, L. S.
, Qin
, Z.
, and Buehler
, M. J.
, 2015
, “Defect-Tolerant Bioinspired Hierarchical Composites: Simulation and Experiment
,” ACS Biomater. Sci. Eng.
, 1
(5
), pp. 295
–304
. 10.1021/ab500120f14.
Munch
, E.
, Launey
, M. E.
, Alsem
, D. H.
, Saiz
, E.
, Tomsia
, A. P.
, and Ritchie
, R. O.
, 2008
, “Tough, Bio-Inspired Hybrid Materials
,” Science
, 322
(5907
), pp. 1516
–1520
. 10.1126/science.116486515.
Lapidot
, S.
, Meirovitch
, S.
, Sharon
, S.
, Heyman
, A.
, Kaplan
, D. L.
, and Shoseyov
, O.
, 2012
, “Clues for Biomimetics From Natural Composite Materials
,” Nanomedicine (Lond)
, 7
(9
), pp. 1409
–1423
. 10.2217/nnm.12.10716.
Peng
, J.
, and Cheng
, Q.
, 2017
, “High-Performance Nanocomposites Inspired by Nature
,” Adv. Mater.
, 29
(45
), p. 1702959
. 10.1002/adma.20170295917.
Ji
, B.
, and Gao
, H.
, 2004
, “A Study of Fracture Mechanisms in Biological Nano-Composites via the Virtual Internal Bond Model
,” Mater. Sci. Eng. A
, 366
(1
), pp. 96
–103
. 10.1016/j.msea.2003.08.12118.
Ji
, B.
, 2010
, “An Atomistic Study of the Strength of Protein–Mineral Interface of Biological Materials With a Biomimicking Model System at Nanoscale
,” J. Comput. Theor. Nanosci.
, 7
(7
), pp. 1265
–1271
. 10.1166/jctn.2010.147919.
Bai
, Z.
, Su
, Y.
, and Ji
, B.
, 2016
, “Buckling Behaviors of Staggered Nanostructure of Biological Materials
,” ASME J. Appl. Mech.
, 83
(3
), p. 031011
. 10.1115/1.403211620.
Liu
, G.
, Ji
, B.
, Hwang
, K.-C.
, and Khoo
, B. C.
, 2011
, “Analytical Solutions of the Displacement and Stress Fields of the Nanocomposite Structure of Biological Materials
,” Compos. Sci. Technol.
, 71
(9
), pp. 1190
–1195
. 10.1016/j.compscitech.2011.03.01121.
Ni
, Y.
, Song
, Z.
, Jiang
, H.
, Yu
, S.-H.
, and He
, L.
, 2015
, “Optimization Design of Strong and Tough Nacreous Nanocomposites Through Tuning Characteristic Lengths
,” J. Mech. Phys. Solids
, 81
, pp. 41
–57
. 10.1016/j.jmps.2015.04.01322.
Wu
, K.
, Song
, Z.
, He
, L.
, and Ni
, Y.
, 2018
, “Analysis of Optimal Crosslink Density and Platelet Size Insensitivity in Graphene-Based Artificial Nacres
,” Nanoscale
, 10
(2
), pp. 556
–565
. 10.1039/C7NR06748H23.
Wei
, X.
, Naraghi
, M.
, and Espinosa
, H. D.
, 2012
, “Optimal Length Scales Emerging From Shear Load Transfer in Natural Materials: Application to Carbon-Based Nanocomposite Design
,” ACS Nano
, 6
(3
), pp. 2333
–2344
. 10.1021/nn204506d24.
Mathiazhagan
, S.
, and Anup
, S.
, 2016
, “Influence of Platelet Aspect Ratio on the Mechanical Behaviour of Bio-Inspired Nanocomposites Using Molecular Dynamics
,” J. Mech. Behav. Biomed. Mater.
, 59
, pp. 21
–40
. 10.1016/j.jmbbm.2015.12.00825.
Khandelwal
, A.
, Kumar
, A.
, Ahluwalia
, R.
, and Murali
, P.
, 2017
, “Crack Propagation in Staggered Structures of Biological and Biomimetic Composites
,” Comput. Mater. Sci.
, 126
, pp. 238
–243
. 10.1016/j.commatsci.2016.09.02926.
Gao
, L.
, Nie
, G.
, and Zhang
, T.
, 2016
, “A Study of Hierarchical Biological Composite Structures Via a Coarse-Grained Molecular Dynamics Simulation Approach
,” Int. J. Appl. Mech.
, 8
(6
), p. 1650084
. 10.1142/S175882511650084827.
Michel
, J. A.
, and Yunker
, P. J.
, 2019
, “Structural Hierarchy Confers Error Tolerance in Biological Materials
,” Proc. Natl. Acad. Sci. USA
, 116
(8
), pp. 2875
–2880
. 10.1073/pnas.181380111628.
Shao
, Y.
, Zhao
, H.-P.
, Feng
, X.-Q.
, and Gao
, H.
, 2012
, “Discontinuous Crack-Bridging Model for Fracture Toughness Analysis of Nacre
,” J. Mech. Phys. Solids
, 60
(8
), pp. 1400
–1419
. 10.1016/j.jmps.2012.04.01129.
Dimas
, L. S.
, Bratzel
, G. H.
, Eylon
, I.
, and Buehler
, M. J.
, 2013
, “Tough Composites Inspired by Mineralized Natural Materials: Computation, 3D Printing, and Testing
,” Adv. Funct. Mater.
, 23
(36
), pp. 4629
–4638
. 10.1002/adfm.20130021530.
Dimas
, L. S.
, and Buehler
, M. J.
, 2013
, “Tough and Stiff Composites With Simple Building Blocks
,” J. Mater. Res.
, 28
(10
), pp. 1295
–1303
. 10.1557/jmr.2013.8831.
Xie
, Z.
, and Yao
, H.
, 2014
, “Crack Deflection and Flaw Tolerance in “Brick-and-Mortar” Structured Composites
,” Int. J. Appl. Mech.
, 6
(2
), p. 1450017
. 10.1142/S175882511450017332.
Gao
, H.
, and Ji
, B.
, 2003
, “Modeling Fracture in Nanomaterials Via a Virtual Internal Bond Method
,” Eng. Fract. Mech.
, 70
(14
), pp. 1777
–1791
. 10.1016/S0013-7944(03)00124-333.
Dimas
, L. S.
, and Buehler
, M. J.
, 2012
, “Influence of Geometry on Mechanical Properties of Bio-Inspired Silica-Based Hierarchical Materials
,” Bioinspir. Biomim.
, 7
(3
), p. 036024
. 10.1088/1748-3182/7/3/03602434.
Dimas
, L. S.
, and Buehler
, M. J.
, 2014
, “Modeling and Additive Manufacturing of Bio-Inspired Composites With Tunable Fracture Mechanical Properties
,” Soft Matter
, 10
(25
), pp. 4436
–4442
. 10.1039/c3sm52890a35.
Libonati
, F.
, Cipriano
, V.
, Vergani
, L.
, and Buehler
, M. J.
, 2017
, “Computational Framework to Predict Failure and Performance of Bone-Inspired Materials
,” ACS Biomater. Sci. Eng.
, 3
(12
), pp. 3236
–3243
. 10.1021/acsbiomaterials.7b0060636.
Gao
, H.
, 1996
, “A Theory of Local Limiting Speed in Dynamic Fracture
,” J. Mech. Phys. Solids
, 44
(9
), pp. 1453
–1474
. 10.1016/0022-5096(96)00038-537.
Plimpton
, S.
, 1995
, “Fast Parallel Algorithms for Short-Range Molecular Dynamics
,” J. Comput. Phys.
, 117
(1
), pp. 1
–19
. 10.1006/jcph.1995.103938.
Sheppard
, D.
, Terrell
, R.
, and Henkelman
, G.
, 2008
, “Optimization Methods for Finding Minimum Energy Paths
,” J. Chem. Phys.
, 128
(13
), p. 134106
. 10.1063/1.284194139.
Stukowski
, A.
, 2010
, “Visualization and Analysis of Atomistic Simulation Data With OVITO—The Open Visualization Tool
,” Modell. Simul. Mater. Sci. Eng.
, 18
(1
), p. 015012
. 10.1088/0965-0393/18/1/01501240.
Falk
, M. L.
, and Langer
, J. S.
, 1998
, “Dynamics of Viscoplastic Deformation in Amorphous Solids
,” Phys. Rev. E
, 57
(6
), pp. 7192
–7205
. 10.1103/PhysRevE.57.719241.
Shimizu
, F.
, Ogata
, S.
, and Li
, J.
, 2007
, “Theory of Shear Banding in Metallic Glasses and Molecular Dynamics Calculations
,” Mater. Trans.
, 48
(11
), pp. 2923
–2927
. 10.2320/matertrans.MJ20076942.
Wu
, Y.
, Shao
, Z.
, and Wang
, F.
, 2012
, “Study on Wood Fracture Parallel to the Grains Based on Fractal Geometry
,” Int. J. Fract.
, 176
(2
), pp. 163
–169
. 10.1007/s10704-012-9732-043.
Dlouhý
, I.
, and Strnadel
, B.
, 2008
, “The Effect of Crack Propagation Mechanism on the Fractal Dimension of Fracture Surfaces in Steels
,” Eng. Fract. Mech.
, 75
(3–4
), pp. 726
–738
. 10.1016/j.engfracmech.2007.03.03844.
Su
, Y.
, and Lei
, W. S.
, 2000
, “Relationship Between Fracture Toughness and Fractal Dimension of Fracture Surface of Steel
,” Int. J. Fract.
, 106
(3
), pp. L43
–L48
.45.
Celli
, A.
, Tucci
, A.
, Esposito
, L.
, and Palmonari
, C.
, 2003
, “Fractal Analysis of Cracks in Alumina–Zirconia Composites
,” J. Eur. Ceram. Soc.
, 23
(3
), pp. 469
–479
. 10.1016/S0955-2219(02)00148-646.
Restuccia
, L.
, Reggio
, A.
, Ferro
, G. A.
, and Kamranirad
, R.
, 2017
, “Fractal Analysis of Crack Paths Into Innovative Carbon-Based Cementitious Composites
,” Theor. Appl. Fract. Mech.
, 90
, pp. 133
–141
. 10.1016/j.tafmec.2017.03.01647.
Lyu
, S.
, Zhu
, X.
, and Qi
, Z.
, 1994
, “Correlation Between the Fractal Dimension of Fracture Surfaces and Fracture Toughness for Ductile Polymer Materials
,” J. Polym. Sci., Part B Polym. Phys.
, 32
(13
), pp. 2151
–2154
. 10.1002/polb.1994.09032130348.
Karperien
, A.
, 1999–2013
, “FracLac for ImageJ
,” http://rsb.info.nih.gov/ij/plugins/fraclac/FLHelp/Introduction.htm, Accessed June 24, 2019.49.
Schneider
, C. A.
, Rasband
, W. S.
, and Eliceiri
, K. W.
, 2012
, “NIH Image to ImageJ: 25 Years of Image Analysis
,” Nat. Methods
, 9
(7
), pp. 671
–675
. 10.1038/nmeth.208950.
Murali
, P.
, Bhandakkar
, T. K.
, Cheah
, W. L.
, Jhon
, M. H.
, Gao
, H.
, and Ahluwalia
, R.
, 2011
, “Role of Modulus Mismatch on Crack Propagation and Toughness Enhancement in Bioinspired Composites
,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.
, 84
(1 Pt 2
), p. 015102
. 10.1103/PhysRevE.84.01510251.
Gorbatikh
, L.
, Lomov
, S. V.
, and Verpoest
, I.
, 2010
, “Original Mechanism of Failure Initiation Revealed Through Modelling of Naturally Occurring Microstructures
,” J. Mech. Phys. Solids
, 58
(5
), pp. 735
–750
. 10.1016/j.jmps.2010.02.00752.
Zhang
, Z.
, Liu
, B.
, Huang
, Y.
, Hwang
, K.
, and Gao
, H.
, 2010
, “Mechanical Properties of Unidirectional Nanocomposites With Non-Uniformly or Randomly Staggered Platelet Distribution
,” J. Mech. Phys. Solids
, 58
(10
), pp. 1646
–1660
. 10.1016/j.jmps.2010.07.004Copyright © 2020 by ASME
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