The present study investigated the geometrically necessary dislocation (GND) with the influence of the surface roughness by establishing the relation of roughness in GND for indentation. The single crystal copper with (111) oriented surface plane was chosen and polished to various roughness levels ranging from 32.7 to 224 nm and subjected to indentation. The increase in surface roughness revealed to increase in the GND and statistically stored dislocation density. As the indentation force decrease from 9.8 to 0.245 N, the plastic strain gradient related to GND increase from 0.0001 up to 0.0017 µm−1 for each 1 nm increment of surface roughness.
NixWDGaoH.Indentation size effects in crystalline materials: a law for strain gradient plasticity. J Mech Phys Solids. 1997;46(3):411–425.
2.
LiuYNganAHW.Depth dependence of hardness in copper single crystals measured by nanoindentation. Scr Mater. 2001;44(2):237–241.
3.
HuangYZhangFHwangKCA model of size effects in nano-indentation. J Mech Phys Solids. 2006;54(8):1668–1686.
4.
KimJYLeeJJLeeYHSurface roughness effect in instrumented indentation: a simple contact depth model and its verification. J Mater Res. 2006;21(12):2975–2978.
5.
PetitFVandeneedeVCambierF.Relevance of instrumented micro-indentation for the assessment of hardness and Young's modulus of brittle materials. Mater Sci Eng A. 2007;456(1–2):252–260.
McElhaneyKWVlassakJJNixWD.Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments. J Mater Res. 1998;13(5):1300–1306.
8.
DemirERaabeDZaafaraniNInvestigation of the indentation size effect through the measurement of the geometrically necessary dislocations beneath small indents of different depths using EBSD tomography. Acta Mater. 2009;57(2):559–569.
9.
KysarJWGanYXMorseTLHigh strain gradient plasticity associated with wedge indentation into face-centered cubic single crystals: geometrically necessary dislocation densities. J Mech Phys Solids. 2007;55(7):1554–1573.
10.
TangDZhaoLWangHThe role of rough surface in the size-dependent behavior upon nano-indentation. Mech Mater. 2021;157(March):103836.
11.
KimJYKangSKLeeJJInfluence of surface-roughness on indentation size effect. Acta Mater. 2007;55(10):3555–3562.
12.
ChuahHGRipinZM.Quantifying the surface roughness effect in microindentation using a proportional specimen resistance model. J Mater Sci. 2013;48(18):6293–6306.
13.
JiangWGSuJJFengXQ.Effect of surface roughness on nanoindentation test of thin films. Eng Fract Mech. 2008;75(17):4965–4972.
14.
BerkePEl HoudaiguiFMassartTJ.Coupled friction and roughness surface effects in shallow spherical nanoindentation. Wear. 2010;268(1–2):223–232.
15.
WalterCAntretterTDanielRFinite element simulation of the effect of surface roughness on nanoindentation of thin films with spherical indenters. Surf Coatings Technol. 2007;202(4–7):1103–1107.
16.
WeiYWangXZhaoM.Size effect measurement and characterization in nanoindentation test. J Mater Res. 2004;19(1):208–217.
17.
PelletierHGauthierCSchirrerR.Relationship between contact geometry and average plastic strain during scratch tests on amorphous polymers. Tribol Int. 2010;43(4):796–809.
18.
ZhangTYXuWHZhaoMH.The role of plastic deformation of rough surfaces in the size-dependent hardness. Acta Mater. 2004;52(1):57–68.
19.
ChuahHGTanWHChangBPThe influence of surface roughness on material dislocation of microindentation using bonded interface technique. Tribol - Mater Surf Interfaces. 2019;13(4):191–196.
20.
DurstKBackesBGökenM.Indentation size effect in metallic materials: correcting for the size of the plastic zone. Scr Mater. 2005;52(11):1093–1097.
21.
ZaafaraniNRaabeDSinghRNThree-dimensional investigation of the texture and microstructure below a nanoindent in a Cu single crystal using 3D EBSD and crystal plasticity finite element simulations. Acta Mater. 2006;54(7):1863–1876.
22.
WangYRaabeDKlüberCOrientation dependence of nanoindentation pile-up patterns and of nanoindentation microtextures in copper single crystals. Acta Mater. 2004;52(8):2229–2238.
23.
ResterMMotzCPippanR.Microstructural investigation of the volume beneath nanoindentations in copper. Acta Mater. 2007;55(19):6427–6435.
24.
HaysCKendallEG.An analysis of knoop microhardness. Metallography. 1973;6(4):275–282.
25.
CookRFPharrGM.Direct observation and analysis of indentation cracking in glasses and ceramics. J Am Ceram Soc. 1990;73(4):787–817.
26.
DoernerMFNixWD.A method for interpreting the data from depth-sensing indentation instruments.J Mater Res. 1986;1(4):601–609.
27.
LiHBradtRC.The microhardness indentation load/size effect in rutile and cassiterite single crystals. J Mater Sci. 1993;28(4):917–926.
28.
NyeJF.Some geometrical relations in dislocated crystals. Acta Metall. 1953;1(2):153–162.
29.
YangBVehoffH.Dependence of nanohardness upon indentation size and grain size - a local examination of the interaction between dislocations and grain boundaries. Acta Mater. 2007;55(3):849–856.
KartiniSEIsmailR Analysis of the contact area of smooth and rough surfaces in contact with sphere indenter using finite element method. 2016.
32.
GrilliNTarletonECocksACF.Coupling a discrete twin model with cohesive elements to understand twin-induced fracture. Int J Fract. 2021;227(2):173–192.
33.
ChuahHGRipinZM.Modeling of microindentation with consideration of the surface roughness. Metall Mater Trans A Phys Metall Mater Sci. 2013;44(13):5676–5687.
34.
Abu Al-RubRK.Prediction of micro and nanoindentation size effect from conical or pyramidal indentation. Mech Mater. 2007;39(8):787–802.
35.
GaoHHuangY.Geometrically necessary dislocation and size-dependent plasticity. Scr Mater. 2003;48(2):113–118.
36.
MuránskyOBaloghLTranMOn the measurement of dislocations and dislocation substructures using EBSD and HRSD techniques. Acta Mater. 2019;175:297–313.
37.
WangLYangLDongXDynamic constitutive distortional law of materials—micro mechanism based on dislocation dynamics. Dyn Mater. Elsevier. 2019: 221–272. https://doi.org/10.1016/B978-0-12-817321-3.00006-1.
38.
FleckNAMullerGMAshbyMFStrain gradient plasticity: theory and experiment. Acta Metall Mater. 1994;42(2):475–487.
39.
BeakeBDGoelS.Incipient plasticity in tungsten during nanoindentation: dependence on surface roughness, probe radius and crystal orientation. Int J Refract Met Hard Mater. 2018;75:63–69.
