3.4. Method to predict material properties from the Vickers and spherical indentation
3.4.1. Curvature of the indentation curve
As shown in Figures 3.3-5, the P-h curves for both Vickers and Spherical indentation obtained the following relationship:
C = P ℎ
I
⁄ 3.5
Where P and are the load and indentation depth on the loading curve respectively. C is the curvature coefficient with the curvature for the Vickers Indentation and spherical
indenter designated as ‡
¦
and ‡
§
respectively. The curvature is a function of the yields stress and the work hardening coefficient. This will provide a relationship which potential
allow the prediction of material parameters from continuous indentation tests. Figure 3.6 is a flow chart showing the main structure of the inverse modelling approach to
predict the material properties. In the first stage, systemic FE models were developed to form he simulation space covers the potential range of material properties. In the next
stage, the loading curves were used to develop an simulation space. The data will then be processed through three different approaches 3D mapping, dimensional analyse, and dual
indenter chart approach to predict the material parameters. Details of each approach and the results were presented in the next sections with discussion.
The three approaches have been comparative developed to assess their suitability to predict the materials properties based on the dual indenter approach. The second approach
is normalised dimensionless analysis in which the relationship is normalised than a dimensionless analysis is applied. In the third approach, the relationship between the
curvature for both the Vickers and spherical were developed then used a chart to predict all the material sets with the same curvature. The relationship is used to predict the
material sets have the sane indentation curvature. The key procedures of each approach and the typical results are detailed in the next three sections.
3.4.2. 3D- Mapping approach
In the 3D mapping approach, the curvature data were plotted against the materials properties, the an equation is developed base on either linear or nonlinear fitting, which
will give an equation between curvature and working hardening and yield stress. Variations of the curvature Cv and Cs with respect to
6
and n for Vickers indenter were
illustrated by the surface show Figure 3.7. The data for construction of these surfaces were obtained numerically through indentation finite element analysis encompassing a
domain of
6
from 100 to 190MPa and n varying from 0.01 to 0.5 It clearly showed that the curvature coefficients increased with
6
and n but with different gradients for different
regions.
The evaluation performed on surface plot 3D of loading curvature and properties material, this approach was started by setting the value of curvature and properties material as
mapping 3D. A linear fitting plane is shown in Figure 3.7a b. For each curvature value, there are an array of material property sets. These data were extracted and plotted in
Figure 3.7 c. The material property set at the intersection point between the data for the Vickers and Spherical indentation will represent the true material properties. The
accuracy of the approach has been assessed using a range of initial values, the results were listed din Table 3.1. Similar approach has been applied to the data using Nonlinear
Parabolic mapping and the results were shown in Figure 3.8 ab and the results of the accuracy test was listed in Table 3.2.
Evaluation of accuracy on the approach using 3D chat mapping carry out by taking input data which is characterized by randomize and represent the sample space. The selected
input data with 2 variations in the value n, namely n=0.15 and n=0.28 range 0.01 0.30 and
6
= 100, 140, 190 and 300. Accuracy study chat mapping 3D-Linier Table.3.1, known that on average value of different predictive of n into n-input as n=0.056
0.069 and average accuracy error ∆n n
⁄ is 0.1 both the prediction n on Vickers Indentation and on Spherical Indentation. This shows the selected predictors significantly
acceptable within the limit of level confidence less than 0.5 . While on an Accuracy study chat mapping 3D-Non Linier parabolic Table.3.2., known that on average value
of different predictive of n into n-input as n=0.059 0.061 and average accuracy error ∆n n
⁄ is 0.22 both the prediction n on Vickers Indentation and on Spherical Indentation. This shows the selected predictors significantly acceptable within the limit of
level confidence less than 0.5 . By Comparing the two approaches chat mapping 3D, known to have smaller average error by prediction using mapping 3D linear
∆n n ⁄ is
0.1 compared using the non linear parabolic ∆n n
⁄ is 0.22. This evaluation showed that the 3D chat mapping approach can serve as predictor value work hardening
coefficient n of both the prediction n on Vickers Indentation and on Spherical Indentation
3.4.3. Dimensional analysis and results
Kategori