take SEM scan of the indentation and measure it

Thanks, Basavanna. But it's actually the contact force I'm trying to determine. I hope to work backward with a model.

Sorry for the confusion.

if you caluculate area by sem indentation (surface area), you can caluculate projecterd area, then knowing the property of a material(comressive strength and modulus) it is possible to find the load reponsible for indentation.

Thank you for the answer, Basavanna. Could you point me toward a reference of such method?

Dear Feng,

What is the target material? I can run Autodyn on my desktop computer for you if the elastic-plastic properties are available in the literature. . In fact, I have simulated similar problem few years ago to determine the Rockwell hardness of water-jet treated Al-alloy specimen. Yours, Ji.  

Dear Ji,

I appreciate very much for the help. I have a ruby ball of 0.3mm diameter pressed against a square brass piece with 10mm thickness(20mmx30mmx10mm). And the SEM shows a circular indentation with 55um diameter and 2.3 um depth (visualization of the site is attached). I need an estimated value for the 'pressing force'. If any more detail is needed, please feel free to let me know  or message me.

i think if you have some informations about Rockwell Hardness test method method you will find what you are looking for

regards

Draw a circle segment of 50micrometer and 2.3 micrometer depth. the projected area is  3.142x50x50=c/s area of 50 micrometer ircle. now use stress equation =load/area

KNOWING THE STRESS OF THE MATERIAL YOU CAN CALCULATE THE LOAD. IT IS APPROXIMATION METHOD.

Hi, again. I've checked your reply. 

use the theory of segment of radius r (r  radius of the pressed ball)

area of  the curved part = 1/2  r2 (Q-sinQ)

Q angle of the segment

Dear Feng,

Now I have the Johnson-Cook material model constants for brass in my hands.

Thank you Ji. Have you got all info to run the simulation now?

Dear Feng,

Now I have simulation result.  For the simulation, the Von Mises model was employed (Ref. Nsiampa et al., 23rd Int. Symp. Ballistics, 2007, Spain) for the brass. The ball material is assumed to be tungsten. Simulation results are as follows:

• Your physical experiment:   d = 50 um, h = 2.3 um
• Simulation w/  7.8 N:            d = 114 um, h = 2.9 um
• Simulation w/  3.9 N:            d = 80 um, h = 1.9 um

As you can see there is big difference in dent shape between experiment and simulation:  d / h ~ 40 in simulation while it is 22 in experiment.  At moment, the error source is not clear. Your dent depth measurement is reliable? Can you provide me the material properties of your brass specimen? Doubling the yield strength of the tungsten ball produced no difference. Attached please fined the simulation figure.Let me know if you need a different figure.   -JRC-

Hi!

Can you tell me about your current project in more detail? Regards, JRC.i

Now, I have result with the Johnson-Cook model: in summary,

• Your physical experiment :  d =   50 um, h = 2.3 um   -> d / h = 22
• Von Mises model (7.8 N) :  d = 114 um, h = 2.9 um   -> d / h = 39
• Von Mises model (3.9 N) :  d =   80 um, h = 1.9 um   -> d / h  = 42
• JC model (3.9 N)               :  d =   86 um, h = 2.0 um   -> d / h = 43

 Clearly, the mismatch of dent shape is not due to the material model adopted for simulation.  Assuming that your measurement is reliable, it is supposed that your brass specimen is not stress free but under residual stress.  regards, Ji.

Much appreciated, Ji. Apparently, the actual aspect ratio is deeper than all simulation results. I'm not sure what is the cause. But the brass is just a simple square block.

Did some quick calculation on the geometry, if I assume the brass surface to be perfectly soft and completely conforms to the ruby sphere, then a depth of 2.3 um would correspond to a diameter of ~52 um, which is close to measured profile.

In your simulations, all models predict a shallower dent. Is there any chance that in your simulation, the ball is 300 um in radius instead of diameter? Xiaobing

D was 1 mm in simulations. OK!  I'll check the ball-size effect. -Ji-