Over a decade ago I spent some time accumulating many journal papers on the use of the indentation test for purposes of deriving material models.  I came across an interesting paper by  John Clayton of ARL (attached in the zip file)

The material of interest in this paper is Ti-6Al-4V.  One thing I found really interesting was that in Appendix A, there was a complete Abaqus input file in three pages of text (containing 4900 elements).  Clayton's model,with some slight upgrades, is attached in the zip file. The .inp file uses this material model for Titanium:  unit of stress is MPa

The model attached runs in ~100 secs on 1 cpu on my laptop. It runs in ~73 secs on 2 cpus and in ~50 secs on 4 cpus. 

Clayton's paper does show some experimental data, for instance, in Figure 10.  Rather than try to digitize the Force-Disp curves, I have simply used the indentation model, with the material model above, to create some synthetic test data (U2, RF2).  Units of length in the .inp file is micro-m.  Output of Force is then micro-N.  The image below is the Force-Disp output of the attached .inp file, which matches Clayton's Figure 5. The waviness of the loading portion of the curve is directly related to the element side length as the element deforms to match the spherical indenter, and the nature of the elastic-plastic material.   

Here is the calibration model set up in the 3DEXPERIENCE Calibration App.  The test data was imported as positive values, in units of .   The calculation units are set to micron and kg.  The .inp file was imported in those units and 4 cpus used.  During the mapping process a  -1 scale factor was used to transform the U2 and RF2 output into positive values (just so the plot would look nice).  A single evaluation was performed and it took ~40 seconds. With the known answer entered, the R2 error norm is 1.0 out to 6 decimal places. 

The narrated video below shows how to set up this calibration

Once you can set up this calibration model, give calibration a try. The 3dxml file attached in the zip file below was used as a starting point to run a "brute-force" calibration.  That calibration took  17,480 seconds to complete.  (A smarter, or less "brute-force" approach is to refine the Elastic modulus, E, first before starting a calibration.)  At about 5,000 secs of calibration time:

At about 7,000 seconds of calibration time:

At about 15,000 seconds, the plot looks good, but the Johnson-Cook "A" parameter has gone down to 5.8 MPa.  Well, that is crazy, we know that "A" represents the initial yield and the initial yield stress of titanium is easily above 800 MPa.   We do see this behavior (driving "A" down towards zero) sometimes when we calibrate using a uniaxial stress-strain curve, but when using a uniaxial stress-strain it is fairly obvious how to set some bounds on "A". 

The calibration behavior, pushing "A" towards zero is disappointing to say the least.  While some people like to think that the indentation is easy to perform, it seems like a simple uniaxial tension test provides more information. 

The attached zip file contains 4 files:

1. The 2005 paper by John Clayton
2. The synthetic test data, in an Excel file
3. The Abaqus FE model input file.
4. A 3DEXPERIENCE 3dxml file.