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Surface roughness is a commonly used criterion for characterization of surface quality in a machining operation. In the study of micro-scale mechanical properties of machined surface and cutting tool using nanoindentation method, perfect surface finish on the specimen is often required for the reliable indentation result. However, the perfect surface finish is often difficult to obtain from the machining operation due to the dynamic behavior of the machining and the limitation of the cutting tool geometry. In the presented paper, the effect of surface roughness on the nanoindentation measurements is investigated by using finite element method. A 3D finite element model with seven levels of surface roughness is developed to simulate the load-displacement behavior in an indentation process with a Berkovich indenter. The material used in the simulation is AISI 316 L stainless steel, modeled as an elastic-plastic material. The mechanical properties were calculated by combining simulations with the Oliver-Pharr method. The hardness and reduced modulus from the simulation were found to decrease with an increase of roughness. The study showed that the scatter of the load-depth curves and the deviation of the hardness and the reduced modulus are significant affected by the variation of roughness. It was also found that the height of pile-up was little affected by the surface roughness from the simulation. The combined effect of indenter tip radius and surface roughness was also investigated. The study was complemented with experimental tests and the results from these tests support the results from the simulation.

It is well known that the mechanical properties at micro-scale level have significant impact on the performance of the machined component, such as fatigue, wear, corrosion resistance [_{proj}, see [

The effects of roughness on indentation, founded in previous investigations, were mostly focused on the spherical indenter [_{m}, of about 1 mm, for different shape of asperities both experimentally and numerically using spherical indenter. They found that the Young’s modulus, E_{IT}, and hardness, H, are sensitive to roughness. Furthermore a liner relationship between the effect of H and E_{IT} was also reported. In the study made by [_{IT}, in an elastic deformation material with a spherical indenter. Also [

Results from these previous investigation based on the FEM simulation indicated the significant effect of roughness on nanoindentation test. However, these models were only focused on the 2D axisymmetric model, the spherical indenter and full elastic material, in which the true scenario of the indentation measurement was significantly simplified. Moreover, the geometry effect was often ignored in the most research. This paper presents a fully 3D finite element model and Berkovich indenter is used to simulate the effect of roughness on nanoindentation test. The hardness and reduced modulus were determined from the simulation using the Oliver and Pharr method [

A 3D surface roughness with designed values was generated with Matlab program and then the roughness values were mapped into the Abaqus to create the FE roughness model. A flat surface was created with N × N nodes with Matlab, see [

R_{a} is the arithmetic average of absolute values, n is the amount nodes of the surface; y(i) is the distance between the peak or valley to the mean value; z(i) is the height of each node; R_{m} is the mean value of all nodes height; and z(i) is generated by a random function in Matlab software. The new surfaces were created with required surface roughness through the iterative calculations employing the numerical procedure for simulation of three-dimensional surfaces that has been developed by [_{a} = 2 nm, generated with the matrix of 100 × 100 points in the X-Y plane, is shown on

The model was generated in Abaqus CAE with initially flat surface. Then, Matlab code was written to find the top surface nodes, and change the height of top surface nodes to the requirement of the roughness profiles according to the procedure described above. Finally, the changed top surface nodes were put into the input file, a new surface was generated and simulations performed in Abaqus. In the generation of the surface with roughness, the maximum asperities of sample roughness was chosen to be 3 times smaller, than the minimum element size. Totally, surfaces with seven different levels of roughness were generated, 2 nm, 3 nm, 8 nm, 12 nm, 20 nm, 30 nm and 42 nm. The roughness of 2 nm, 20 nm and 42 nm models are shown in

The nanoindentation test on bulk materials with isotropic elastic-plastic properties was simulated using Abaqus/ Explicit 6.11 with uniaxial stress-strain data as an input. In this study, AISI316L was chosen as the reference material due to its single face simple structure. The material model used for the test specimen was Von Misses plasticity with isotropic hardening. The material parameters are specified as, [_{y} = 1.1 GPa and Poisson’s ratio ν_{S} = 0.28. A 3D Berkovich indenter was modelled in this study. The indenter was considered as a rigid body, since the elastic modulus of the indenter exceeds that of the specimen, and also due to the fact that this study do not focus on the deformation of the indenter. A modified 10-node second-order tetrahedral element (C3D10M) was applied in the model and the number of elements is 2313. The specimen was modeled with 321,632 continuum 3D, eight-node reduced integration elements (C3D8R). The model assembly, in its initial state is demonstrated in

The nanoindentation process was simulated both during the loading and unloading steps. In the loading pro- cess, the simulation was performed by applying a force of 5 mN in the vertical direction to a depth of 237 nm. During the process of unloading, the indenter tip returns to the original position. The contact constraint was defined by the master and slave surfaces. In the model, the indenter was the master surface and the specimen was the slave surface. A fix boundary condition was applied on the bottom of the specimen. The FE model was validated to experimental data for AISI316L. Simulation with an ideal surface was compared to experiments on a surface with roughness less than 1 nm, (see

The Young’s modulus E_{IT} and the hardness H can be calculated according to the Oliver and Pharr method described in details in [

with

In above expression η = 1.034 for a Berkovich indenter, ε = 0.72 and h is the total displacement from mea-

surement. _{max} is the maximum load in the test and

unloading stiffness at the depth of h. The properties of the indenter usedin the calculations are E_{i} = 1141 GPa, v_{i} = 0.07. The constant a_{0} and b_{0} are fitted to the experimental curves obtained from the area function for fused silica. The reduced modulus E_{r} represents the elastic deformation that occurs, without needing the Poisson’s ratio of the material. Therefore it was used in following.

The seven models with different level of roughness were used to study the roughness effect when performing a nanoindentation test with Berkovich indenter. For each roughness, fifteen simulations were conducted. The indentation position on specimen was randomly selected in the simulations. When the indenter is located on a peak the contact area is larger than the ideal case and when the indenter is located on a valley it is smaller. Since the force controlled method was applied in the simulation, the initial position of the indenter tip plays an important role. The zero point was set to the displacement when the load was over zero initially. In all simulation, the correction with the initial zero point selection was applied and the initial load was 0.03 mn. This results in different initial depths for the models with different roughness. For example for the roughness R_{a} = 2 nm the initial depth is between 80 - 120 nm for the R_{a} = 20 nm the initial depth between is 50 - 124 nm and for the R_{a} = 42 nm the initial depth is between 20 - 130 nm. The correction of the initial point will generate the different values when calculating the hardness modulus using the Oliver-Pharr method.

The initial load-displacement curves for three different roughness models were studied and the effect of roughness is clearly observed in

dention load of P = 5 mN. As expected, the data scatter is increasing with the increasing roughness. This scatter is due to high surface roughness and it is a frequently encountered problem when trying to characterize the mechanical properties at shallow nanoindentation depth.

The strain distribution at indentation loads of 1.5 and 5 mN is shown in _{a} = 42 nm, whereas for R_{a} = 2 nm the strain distribution becomes axisymmetric, as seen in

The deformation profiles for the three roughness models are seen in

The reduced modulus and hardness are calculated for different surface roughness using the Oliver-Pharr method described in [

In the ideal model, i.e. the model without roughness the reduced modulus was calculated to E_{r} = 190.6 GPa, and hardness to H = 2.56 GPa. As seen from _{a} = 2 nm, the results from the simulations are closely to the results from simulations onthe ideal surface. The mean values for each roughness are seen on

The indentation depth h in nanoindenation is affected by the roughness. To account for this dependence ratio h/Ra is interesting to study and the hardness and the reduced modulus were also plotted as a function of the ratio h/Ra in

Mechanical properties | Roughness R_{a} (nm) | ||||||||
---|---|---|---|---|---|---|---|---|---|

2 | 3 | 8 | 12 | 20 | 30 | 42 | |||

H | 2.15 | 2.17 | 2.32 | 2.24 | 2.38 | 2.33 | 2.9 | ||

Er | 212.3 | 214.2 | 225.4 | 222.1 | 233.5 | 233.5 | 222.3 | ||

values of about H = 2.25 GPa and E_{r} = 220 GPa.

The geometrical effects of the tip radius were studied in our previous work [

The nanoindentation tests of the Berkovich type were carried on the Nano-Test Vantage (Co. Micro material, UK), at room temperature, 20˚C. Several others environment factors as for example the vibration and humility, are controlled in the cabinet of the instrument. All indentations were performed in compliance with ISO 14577 and ASTM E2546-07. The material is AISI316L, which is a single phase stainless steel, the composition is 70 wt.% Fe, 18wt.%Cr, 11wt.% Ni, 1 wt.% Mo. The only phase present is austenite, and the grain size range is 13 um - 168 um. Five levels of surface roughness (1 nm, 2 nm, 3 nm, 8 nm and 42 nm) were generated with different polishing. At each load step the effect of roughness were studied statistically by performing a grid nanoindentation with the 10 by 10 matrix, resulting in a 100 different tests. The tip radius of the indenter in all experiments was 120 nm.

The reduced modulus and hardness were calculated for the five different surface roughness using the Oliver- Pharr method described in [_{r} = 220 GPa. This results support the finding from the simulation. However the mean values, presented on

The effects of surface roughness and indenter tip radius on nanoindentation measurement were simulated by developing a 3D FE roughness model loaded with Berkovich indenter. The 3D roughness surface was generated in Matlab and imported into Abaqus. Models with seven roughness levels were built and used to simulate the nanoindentation test. It was found that the elastic-plastic behavior is affected by the surface roughness and a scatter of the reduced modulus and the hardness was observed. The levels of the scatter increase with the rise of roughness level. It was found, that the increase of the surface roughness results in decreasing of reduced modulus and the hardness. The mean values of the hardness are increasing with an increased roughness. However, when studying the hardness and the reduced modulus as a function of the ratio h/Ra, it was observed that for decreasing roughness the values of both the hardness and the reduced modulus reach constant values. This was also supported from the experimental tests performed for five different roughness levels.

Little effect of roughness was found in height of pile-up during the indentation deformation profile. The results from the simulations of combined effect of tip radius and roughness indicate that the sensitive of radius in roughness is not obvious when considering the scatter of load-depth curve, and there is no significant effect on the hardness and the reduced modulus. The results from the simulations showed that the tip radius has little effect on the hardness and the reduced modulus, when roughness is introduced in the model. Finally roughness leads to underestimation of the hardness and reduced modulus in the nanoindentation test. For specimen with rougher surface, the larger indentation depth should be applied in order to reach more stable test values. The hardness and reduced modulus tend to be more stable when ratio of h and R_{a} value is over 100 for 316 L steel.

Mechanical properties | Roughness R_{a} (nm) | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 8 | 42 | |

H | 2.76 | 3.02 | 3.19 | 3.39 | 4.32 |

E_{r} | 196.64 | 201.69 | 221.26 | 229.82 | 198.53 |

This work is a part of the strategic research program under the Sustainable Production Initiative SPI. Authors would appreciate the help from Dr. V. Bushlya in sample preparation. The finite element simulations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at LUNARC.