双层金属纳米板界面能密度的尺寸效应
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摘要
界面能密度是表征纳米复合材料与结构界面力学性质的重要物理量.采用分子动力学方法计算了不同面心立方金属晶体构成的双材料纳米薄板结构的界面能密度,分析了界面晶格结构形貌变化及界面效应对原子势能的影响.结果表明:双材料纳米薄板界面具有周期性褶皱状疏密相间的晶格结构形貌,界面上原子势能亦呈现周期性分布特性,而靠近界面的两侧原子势能与板内原子势能具有明显差异.拉格朗日界面能密度和欧拉界面能密度均随双层薄板厚度的增加而增加,最终趋向于块体双材料结构的界面能密度.
The interface free energy density is an important quantity characterizing the mechanical property of interface in nanocomposite systems. In this paper, molecular dynamics simulation method is adopted to investigate the interface energy density of different FCC metallic bi-nano-scaled plates. The morphology of the interface crystal structure and the interface effect on the atomic potential are analyzed. It is found that interface atoms have periodically wrinkled rarefied or serried configurations, and the potential energy of interface atoms is also periodically distributed. The potential energy of atoms near the interface is obviously different from that of atoms inside the nano-plates. Both the Lagrange interface energy and the Eulerian one increase with the increase of the thickness of the bi-material, which approach the interface energy of a bulk bi-material finally.
The interface free energy density is an important quantity characterizing the mechanical property of interface in nanocomposite systems. In this paper, molecular dynamics simulation method is adopted to investigate the interface energy density of different FCC metallic bi-nano-scaled plates. The morphology of the interface crystal structure and the interface effect on the atomic potential are analyzed. It is found that interface atoms have periodically wrinkled rarefied or serried configurations, and the potential energy of interface atoms is also periodically distributed. The potential energy of atoms near the interface is obviously different from that of atoms inside the nano-plates. Both the Lagrange interface energy and the Eulerian one increase with the increase of the thickness of the bi-material, which approach the interface energy of a bulk bi-material finally.
引文
1 Gleiter H.Nanostructured materials:Basic concepts and microstructure.Acta Materialia,2000,48(1):1-29
2 Muller P,Saúl A.Elastic effects on surface physics.Surface Science Reports,2004,54(5-8):157-258
3 Ibach H.The role of surface stress in reconstruction,epitaxial growth and stabilization of mesoscopic structures.Surface Science Reports,1997,29(5-6):195-263
4张玉龙.纳米复合材料手册.北京:中国石化出版社,2005(Zhang Yulong.Handbook of Nano-composites.Beijing:China Petrochemical Press,2005(in Chinese))
5 Gurtin ME,Murdoch AI.Surface stress in solids.International Journal of Solids and Structures,1978,14(6):431-440
6 Gurtin ME,Murdoch AI.A continuum theory of clastic material surfaces.Archive.for Rational Mechanics and Analysis,1975,57(4):291-323
7 Sharma P,Ganti S.Size-dependent Eshelby's tensor for embedded nano-inclusions incorporating surface/interface energies.Journal of Applied Mechanics,2004,71(5):663-671
8 Mogilevskaya SG,Crouch SL,La Grotta A,et al.The effects of surface elasticity and surface tension on the transverse overall elastic behavior of unidirectional nano-composites.Composites Science and Technology,2010,70(3):427-434
9 Duan H,Wang J.Huang Z,et al.Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress.Journal of the Mechanics and Physics of Solids,2005,53(7):1574-1596
10 Li Z,Lim C,He L.Stress concentration around a nano-scale spherical cavity in elastic media:Effect of surface stress.European Journal of Mechanics-A/Solids,2006,25(2):260-270
11 Li P,Wang Q,Shi S.Differential scheme for the effective elastic properties of nano-particle composites with interface effect.Computational Materials Science,2011,50(11):3230-3237
12 Dai M,Gao C-F.Non-circular nano-inclusions with interface effects that achieve uniform internal strain fields in an elastic plane under anti-plane shear.Archive of Applied Mechanics,2016,86(7):1295-1309
13 Huang Z,Wang J.A theory of hyperelasticity of multi-phase media with surface/interface energy effect.Acta Mechanica,2006,182(3-4):195-210
14 Wang Z-Q,Zhao Y-P,Huang Z-P.The effects of surface tension on the elastic properties of nano structures.International Journal of Engineering Science,2010,48(2):140-150
15 Gao X,Huang Z,Qu J,et al.A curvature-dependent interfacial energy-based interface stress theory and its applications to nano-structured materials:(1)General theory.Journal of the Mechanics and Physics of Solids,2014,66:59-77
16 Miller RE,Shenoy VB.Size-dependent elastic properties of nanosized structural elements.Nanotechnology,2000.11(3):139
17 Mi C.Jun S,Kouris DA,et al.Atomistic calculations of interface elastic properties in noncoherent metallic bilayers.Physical Review B,2008,77(7):075425
18 Paliwal B,Cherkaoui M.Atomistic-continuum interphase model for effective properties of composite materials containing nanoinhomogeneities.Philosophical Magazine,2011,91(30):3905-3930
19 Chen S,Yao Y.Elastic theory of nanomaterials based on surfaceenergy density.Journal of Applied Mechanics,2014,81(12):121002
20 Yao Y,Chen S,Fang D.An interface energy density-based theory considering the coherent interface effect in nanomaterials.Journal of the Mechanics and Physics of Solids.2017,99:321-337
21 Shuttleworth R.The surface tension of solids.Proceedings of the Physical Society.Section A,1950,63(5):444
22 Cammarata R.Surface and interface stress effects on interfacial and nanostructured materials.Materials Science and Engineering:A,1997,237(2):180-184
23 Johnson R.Alloy models with the embedded-atom method.Physical Review B.1989,39(17):12554
24 Plimpton S.Fast parallel algorithms for short-range molecular dynamics.Journal of Computational Physics,1995,17(1):1-19
25 Zhang C,Yao Y,Chen S.Size-dependent surface energy density of typically fcc metallic nanomaterials.Computational Materials Science,2014,82(3):372-377
26 Dingreville R,Qu J.Interfacial excess energy,excess stress and excess strain in elastic solids:planar interfaces.Journal of the Mechanics and Physics of Solids,2008,56(5):1944-1954
27 Spearot D,Capolungo L,Qu J.et al.On the elastic tensile deformation of(100)bicrystal interfaces in copper.Computational Materials Science,2008,42(1):57-67
28 Ouyang G,Liang L,Wang C,et al.Size-dependent interface energy.Applied Physics Letters,2006,88(9):091914
29 Jiang Q,Li J,Chi B.Size-dependent cohesive energy of nanocrystals.Chemical Physics Letters,2002,366(5):551-554
2 Muller P,Saúl A.Elastic effects on surface physics.Surface Science Reports,2004,54(5-8):157-258
3 Ibach H.The role of surface stress in reconstruction,epitaxial growth and stabilization of mesoscopic structures.Surface Science Reports,1997,29(5-6):195-263
4张玉龙.纳米复合材料手册.北京:中国石化出版社,2005(Zhang Yulong.Handbook of Nano-composites.Beijing:China Petrochemical Press,2005(in Chinese))
5 Gurtin ME,Murdoch AI.Surface stress in solids.International Journal of Solids and Structures,1978,14(6):431-440
6 Gurtin ME,Murdoch AI.A continuum theory of clastic material surfaces.Archive.for Rational Mechanics and Analysis,1975,57(4):291-323
7 Sharma P,Ganti S.Size-dependent Eshelby's tensor for embedded nano-inclusions incorporating surface/interface energies.Journal of Applied Mechanics,2004,71(5):663-671
8 Mogilevskaya SG,Crouch SL,La Grotta A,et al.The effects of surface elasticity and surface tension on the transverse overall elastic behavior of unidirectional nano-composites.Composites Science and Technology,2010,70(3):427-434
9 Duan H,Wang J.Huang Z,et al.Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress.Journal of the Mechanics and Physics of Solids,2005,53(7):1574-1596
10 Li Z,Lim C,He L.Stress concentration around a nano-scale spherical cavity in elastic media:Effect of surface stress.European Journal of Mechanics-A/Solids,2006,25(2):260-270
11 Li P,Wang Q,Shi S.Differential scheme for the effective elastic properties of nano-particle composites with interface effect.Computational Materials Science,2011,50(11):3230-3237
12 Dai M,Gao C-F.Non-circular nano-inclusions with interface effects that achieve uniform internal strain fields in an elastic plane under anti-plane shear.Archive of Applied Mechanics,2016,86(7):1295-1309
13 Huang Z,Wang J.A theory of hyperelasticity of multi-phase media with surface/interface energy effect.Acta Mechanica,2006,182(3-4):195-210
14 Wang Z-Q,Zhao Y-P,Huang Z-P.The effects of surface tension on the elastic properties of nano structures.International Journal of Engineering Science,2010,48(2):140-150
15 Gao X,Huang Z,Qu J,et al.A curvature-dependent interfacial energy-based interface stress theory and its applications to nano-structured materials:(1)General theory.Journal of the Mechanics and Physics of Solids,2014,66:59-77
16 Miller RE,Shenoy VB.Size-dependent elastic properties of nanosized structural elements.Nanotechnology,2000.11(3):139
17 Mi C.Jun S,Kouris DA,et al.Atomistic calculations of interface elastic properties in noncoherent metallic bilayers.Physical Review B,2008,77(7):075425
18 Paliwal B,Cherkaoui M.Atomistic-continuum interphase model for effective properties of composite materials containing nanoinhomogeneities.Philosophical Magazine,2011,91(30):3905-3930
19 Chen S,Yao Y.Elastic theory of nanomaterials based on surfaceenergy density.Journal of Applied Mechanics,2014,81(12):121002
20 Yao Y,Chen S,Fang D.An interface energy density-based theory considering the coherent interface effect in nanomaterials.Journal of the Mechanics and Physics of Solids.2017,99:321-337
21 Shuttleworth R.The surface tension of solids.Proceedings of the Physical Society.Section A,1950,63(5):444
22 Cammarata R.Surface and interface stress effects on interfacial and nanostructured materials.Materials Science and Engineering:A,1997,237(2):180-184
23 Johnson R.Alloy models with the embedded-atom method.Physical Review B.1989,39(17):12554
24 Plimpton S.Fast parallel algorithms for short-range molecular dynamics.Journal of Computational Physics,1995,17(1):1-19
25 Zhang C,Yao Y,Chen S.Size-dependent surface energy density of typically fcc metallic nanomaterials.Computational Materials Science,2014,82(3):372-377
26 Dingreville R,Qu J.Interfacial excess energy,excess stress and excess strain in elastic solids:planar interfaces.Journal of the Mechanics and Physics of Solids,2008,56(5):1944-1954
27 Spearot D,Capolungo L,Qu J.et al.On the elastic tensile deformation of(100)bicrystal interfaces in copper.Computational Materials Science,2008,42(1):57-67
28 Ouyang G,Liang L,Wang C,et al.Size-dependent interface energy.Applied Physics Letters,2006,88(9):091914
29 Jiang Q,Li J,Chi B.Size-dependent cohesive energy of nanocrystals.Chemical Physics Letters,2002,366(5):551-554