Nanomechanical Response of Materials and Thin Film Systems: Finite Element Simulation
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FINITE ELEMENT MODEL In this study, simulations of the nanoindentation of a sample by a conical indenter were performed using the large strain elasto-plastic feature of the ABAQUS [10] finite element code, with yield stress and Young's modulus as input. In the FEM model shown in fig (1) the specimen and the indenter were modelled as bodies of revolution to take advantage of the axisymmetric elements and simplify the problem. The indenter was modelled as a + Ur=-O perfectly rigid conical indenter with half cone angle of 70.30 ( to have the same depth to area as the Berkovitch indenter). The semiinfinite elastoplastic specimen was discretized into 615 axisymmetric 4 Ur The node bilinear elements. _0 boundary conditions used for the simulation are shown in figure (1). -0I Contact between the indenter and the specimen surface was modelled Uz=0o,& as a sliding interface using Fig. 1.FEM model used for simulation in the (IRS21A) elements interfacial Abaqus code. To study the effect of residual stress in the film (500 nm thick) on nanoindentation response, a uniform biaxial stress ( a6r = ae, az=O, both compressive and tensile) was applied to the film. To simulate the indentation process the indenter was given a downward displacement, as the indenter moved downward into the specimen, the corresponding load determination was achieved by summing the reaction force at the contact node points on the indenter. After the prescribed displacement was reached the indenter was given an upward displacement to begin unloading until it was free of contact. The displacement and the total reaction force were obtained from the program. The constitutive model for the specimen material was that of an elasto-plastic Von-Mises material with linear strain hardening. The material property and the simulation conditions are given in table 1 [11]. Some trial runs were made to modify the mesh and the domain size so that the boundary is remote to the indentation.
-~1
TABLE 1 Material
Tungsten Copper Annealed copper Nickel Gold Silicon Aluminium
Poissons ratio
Indenter half cone angle 0
Friction coefficient
3080 330 54
Strain hardening slope, MPa 650 80 190
0.28 0.33 0.341
70.3 70.3 70.3
0 0 0
148 103 4140 120
319 0 0 110
0.31 0.35 0.278 0.3
70.3 70.3 70.3 & 45 70.3 & 45
0 0 0&I 0&1
E, Modulus, GPa 407 130 130
Yield stress Y, MPa
207 78 127 70
682
RESULT AND DISCUSSION The result of the load displacement simulation for annealed Cu using a conical indenter (half cone angle 70.30) with tip radii of 1 micron (The details of the tip radius calculation can be found in the reference[6] ) is shown in Fig (2.a) and is found to be in good agreement with the experimental result [121. This indicates that the model used is valid for simulation. b) a) 6
+
z E
5
-eFEM
*-*
FE-
Cone 70.3, p=O cone 45, pj=O
o-nCone 45,•j=1
xpExper..
4
z3 E
3 2
0
1 0
0
250 Displacement, nm
500
0
100 Displacement, nm
150
Fig. 2. FEM load-displacement result a) for Cu , b) for Si using two indenter geometries Increasing the coefficient of fri
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