Effects of interface effects on the macroscopic elastoplastic properties of nanoporous materials

doi:10.3969/j.issn.1000-1565.2021.02.008

Abstract

Abstract: For the porous materials with nanoscale voids, the interface effect between the solid matrix and the void has a great influence on the macroscopic elastoplastic properties of such material. Through the theoretical analysis, this work treated the typical mathematical interfacial model describing the interface effects as the interfacial phase model with a certain thickness, and developed a material model of the interfacial phase model using the UMAT subroutine of ABAQUS software. On this basis, the finite element numerical method is employed to study the effects of porosity, pore size and interfacial residual stress on the macroscopic elastoplastic tensile and compressive mechanical properties of nanoporous metals. The results show that the increasing porosity causes the effective elastic modulus and the yield strength to decrease in magnitudes when the pore size and the interfacial residual stress keep constant. the increasing pore size leads to the increase of the effective yield strength and the flow stress when the porosity and the interface residual stress are constant. The interfacial residual stress induces the asymmetry of the tension-compression- DOI:10.3969/j.issn.1000-1565.2021.02.008界面效应对纳米多孔材料宏观弹塑性力学性能的影响马连华^1,2,周靖博²,曹亚阔²(1.河北大学质量技术监督学院,河北保定 071002;2.河北大学建筑工程学院,河北保定 071002)摘要:当多孔材料的孔洞为纳米尺度时,基体/孔洞的界面效应会对这种材料的弹塑性力学性能产生较大影响.本文通过理论分析将描述界面效应的传统数学界面模型等效为具有一定厚度的界面相模型,并基于ABAQUS的UMAT子程序开发了界面相材料模型.以此为基础,采用有限元数值模拟的方法,研究了孔隙率、孔径尺寸及界面残余应力对纳米多孔金属材料宏观弹塑性拉伸-压缩性能的影响.结果表明,孔径尺寸和界面残余应力一定时,孔隙率增大引起有效弹性模量和屈服强度减小;若孔隙率与界面残余应力保持不变,孔径尺寸增大会引起有效屈服强度和流动应力增大;界面残余应力会导致纳米多孔金属拉伸-压缩曲线存在明显的不对称现象;由于界面相的负刚度效应,当纳米多孔金属变形到一定程度时呈现出软化现象,即宏观应力随变形增加而减小.关键词:纳米多孔材料;弹塑性;界面效应;有限元;应力软化中图分类号:O341 文献标志码:A 文章编号:1000-1565(2021)02-0161-05Effects of interface effects on the macroscopic elastoplastic properties of nanoporous materialsMA Lianhua^1,2, ZHOU Jingbo², CAO Yakuo²(1. School of Quality and Technical Supervision, Hebei University, Baoding 071002, China;2. College of Civil Engineering and Architecture, Hebei University, Baoding 071002, China)Abstract: For the porous materials with nanoscale voids, the interface effect between the solid matrix and the void has a great influence on the macroscopic elastoplastic properties of such material. Through the theoretical analysis, this work treated the typical mathematical interfacial model describing the interface effects as the interfacial phase model with a certain thickness, and developed a material model of the interfacial phase model using the UMAT subroutine of ABAQUS software. On this basis, the finite element numerical method is employed to study the effects of porosity, pore size and interfacial residual stress on the macroscopic elastoplastic tensile and compressive mechanical properties of nanoporous metals. The results show that the increasing porosity causes the effective elastic modulus and the yield strength to decrease in magnitudes when the pore size and the interfacial residual stress keep constant. the increasing pore size leads to the increase of the effective yield strength and the flow stress when the porosity and the interface residual stress are constant. The interfacial residual stress induces the asymmetry of the tension-compression- 收稿日期:2020-03-14 基金项目:国家自然科学基金面上项目(11572109);2019年度河北省引进留学人员资助项目(C20190318);河北省教育厅在读研究生创新能力培养项目(CXZZSS2020009);河北省高等学校科学技术研究重点项目(ZD2017006) 第一作者:马连华(1979—),男,河北衡水人,河北大学副教授,博士,主要从事复合材料力学研究.E-mail:lhma@hbu.edu.cn第2期马连华等:界面效应对纳米多孔材料宏观弹塑性力学性能的影响curves of the nanoporous metal, and due to the negative stiffness of the interfacial phase, the nanoporous metal exhibits the stress softening phenomenon. That is the macroscopic stress decreases as the deformation increases when the material deforms to a certain degree.

Key words: nanoporous material, elastoplasticity, interface effect, finite element method, stress softening

CLC Number:

O341

MA Lianhua, ZHOU Jingbo, CAO Yakuo. Effects of interface effects on the macroscopic elastoplastic properties of nanoporous materials[J]. Journal of Hebei University(Natural Science Edition), 2021, 41(2): 161-165.

References

[1] DUAN H L, YI X, HUANG Z P. et al. A unified scheme for prediction of effective moduli of multiphase composites with interface effects. Part I: Theoretical framework[J].Mech Mater, 2007, 39(1): 81-93. DOI:10.1016/j.mechmat.2006.02.009.
[2] DUAN H L, WANG J, KARIHALOO B L, et al. Nanoporous materials can be made stiffer than non-porous counterparts by surface modification[J]. Acta Mater, 54(11): 2983-2990. DOI:10.1016/j.actamat.2006.02.035.
[3] DUAN H L, WANG J, KARIHALOO B L. Theory of elasticity at the nanoscale[M] //Advances in Applied Mechanics. Amsterdam:Elsevier, 2009: 1-68. DOI:10.1016/s0065-2156(08)00001-x.
[4] DUAN H L, WANG J, HUANG Z P, et al. Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress[J]. J Mech Phys of Solids, 2005,53(7): 1574-1596. DOI:10.1016/j.jmps.2005.02.009.
[5] FENG X Q, XIA R, LI X D, et al. Surface effects on the elastic modulus of nanoporous materials[J]. Appl Phys Lett, 2009, 94(1): 011916. DOI:10.1063/1.3067999.
[6] SOYARSLAN C, HUSSER E, BARGMANN S. Effect of surface elasticity on the elastic response of nanoporous gold[J]. J Nanomech Micromech, 2017, 7(4): 04017013. DOI:10.1061/(asce)nm.2153-5477.0000126.
[7] ZHANG W X, WANG T J. Effect of surface energy on the yield strength of nanoporous materials[J]. Appl Phys Lett, 2007, 90(6): 063104. DOI:10.1063/1.2459115.
[8] DORMIEUX L, KONDO D. Non linear homogenization approach of strength of nanoporous materials with interface effects[J]. Int J Eng Sci, 2013, 71(11): 102-110. DOI:10.1016/j.ijengsci.2013.04.006.
[9] MONCHIET V, KONDO D. Combined voids size and shape effects on the macroscopic criterion of ductile nanoporous materials[J]. Int J Plast, 2013, 43:20-41. DOI:10.1016/j.ijplas.2012.10.007.
[10] BRACH S, CHERUBINI S, KONDO D, et al. Void-shape effects on strength properties of nanoporous materials[J]. Mech Res Commun, 2017, 86:11-17. DOI:10.1016/j.mechrescom.2017.10.009.
[11] MOSHTAGHIN A F, NAGHDABADI R, ASGHARI M. Effects of surface residual stress and surface elasticity on the overall yield surfaces of nanoporous materials with cylindrical nanovoids[J]. Mech Mater, 2012, 51: 74-87. DOI:10.1016/j.mechmat.2012.04.001.
[12] DORMIEUX L, LEMARCHAND E, BRISARD S. Equivalent inclusion approach for micromechanics estimates of nanocomposite elastic properties[J]. J Nanomech Micromech, 2016, 6(2): 04016002. DOI:10.1061/(asce)nm.2153-5477.0000104.
[13] WANG W, ZENG X, DING J. Finite element modeling of two-dimensional nanoscale structures with surface effects[J]. International Journal of Civil and Environmental Engineering, 2010, 46:12-20. DOI:doi.org/10.5281/zenodo.1055040
[14] JIN H. Surface stress on the effective Young’s modulus and Poisson’s ratio of isotropic nanowires under tensile load[J]. AIP Adv, 2015, 5(11): 117206. DOI:10.1063/1.4935439.
[15] TIAN L, RAJAPAKSE R K N D. Finite element modelling of nanoscale inhomogeneities in an elastic matrix[J]. Comput Mater Sci, 2007, 41(1):44-53. DOI:10.1016/j.commatsci.2007.02.013.
[16] QIU Y P, WENG G J. A theory of plasticity for porous materials and particle-reinforced composites[J]. J Appl Mech, 1992, 59(2): 261-268. DOI:10.1115/1.2899515.
[17] JIN HJ, WEISSMÜLLER J, FARKAS D. Mechanical response of nanoporous metals: A story of size, surface stress, and severed struts[J]. MRS Bull, 2018, 43(1):35-42. DOI:10.1557/mrs.2017.302. (