Characterization Mechanical Properties Figure 41 shows a ser

Characterization, Mechanical Properties. Figure 4.1 shows a series of SPM images for residual Berkovich indents in a 320 nm thick TiW film deposited on a [100] Si substrate. Calculate and plot the hardness versus depth curve using the 6 indents. Is the hardness constant? Explain why or why not. List any assumptions.

Solution

solution:

1)here we are using berkovich indentor for which semi angle is 65.3 degree and effective cone angle is 76.9 degree

2)projected area of berkovich indentor is obtain from

A=24.56h^2

3)here hardness is given by

H=P/A

4)here for TiW plate depth of indentation for .5 MN and 300 Mn are 33 nm and 1297 nm

hence hardness are

H1=.5*10^6/24.56*(33*10^-6)^2

H1=18.69 GPa

for P=300 MN

H6=7.21 GPA

3)hence load dpth curve is given by

P=a(h2-h1)^b

4)hence it is observe that value of GPA or hardness is not constant for each load because pile up effect is more if

hmax>320nm

5)hence hardness not constant but close to around 13 GPA for given material