I don't think so. You may need to check your machine again to ensure it is well calibrated as earlier highlighted. And also ensure the normal load is the actual load applied by the machine. 

COF is expected to increase with increasing frictional force or basically COF is a reflection of the friction force. 

Usually during tribological tests we get increasing frictional force accompanied increasing normal load, i.e. the higher normal load the higher frictional force. However, often the increase of frictional force is smaller comparing to the increase of normal load. So we get lower coefficient of friction with higher frictional force.

Increasing the load we get augmented friction force, and usually an increase of the friction coefficient. Check your machine first. Is the speed constant all the time?! Are there any run-out errors?! Are the sensors and the DAQ system well calibrated? Good luck! 

1st the graphite used is likely as nanoparticles. At similar normal force, oil with graphite would give lower COF compared to oil only. Tribofilm of graphite would form on contacting surfaces. This is a NPs lubrication mechanism to reduce COF & wear. If all test conditions are the same, then the environment and DAQ need re-checking. Lowered COF could not give higher friction force, except the normal increased. NPs lubrication mechanism is subject of current study. Your observation may steer closer look at emerging NPs in lubes, especially green lubes. 

I don't think so. You may need to check your machine again to ensure it is well calibrated as earlier highlighted. And also ensure the normal load is the actual load applied by the machine. 

COF is expected to increase with increasing frictional force or basically COF is a reflection of the friction force. 

I think you should find the answer in the following facts. Friction depends in any case on the material and the geometric properties of counter and basic body. Are you sure, that these properties where the same in both experiments? I have a lot of experimental results, where from a macroscopic viewpoint everything was the same, but microproperties and material properties of the micro surface zones where different. For example: If you have two plates, which you bring into contact caused by a normal load and you set up a differential speed and you take another two plates with same (macro) material and (macro) geometric properties, same oil, same ambient conditions and also same operating conditsions it is possible, that you get another COF. You can find the reason in waviness or roughness of the surface, which is for example influenced by the final manufacturing process. These properties influence the dimension of contour area and the real area of contact and also number of contacts (which influences the surface pressure and at the end the friction). But also material properties are influenced by final manufacturing process...think about...

According to,  friction force=F.A.t/W (F=force, A=contact true area, t= maximum shear stress and w=weight ), you can justify the issue.

That mean, graphite can decrease friction force due it is  removed from the asperities contact, resulting in a lower friction coefficient. Fore more detail you can find the article entitled " Development and application of tool wear: A review of the characterization of TiC-based cermets with different binders"

Can it be such that the lubricant reached its maximum load and the lubricant film broke. Due to the presence of graphite(macro particles) the lubricant flows was also restricted and thus higher wear occured.

which kind of shape are your contact bodies? ball contact or cylinder or plates?

Having a lower COF with oil containing graphit seems correct (the best COF with dry sliding contact). But if friction effect is amplified, it means that film lubrication is not verified. May be with cavitation effect (phenomenon depending on surface topography in micro scale and convergent/divergent surface in macro scale, normal load, relative velocity,...), the temperature of cavitated zone becomes heigher than lubricant evaporation limit and instead of having full film lubrication, a kind of mixed lubrication is occured but with the presence of porous media (nono particles of graphit).

Honestly, rare are studies modeling cavitation effect on such complex media.

 in short, there are two methods,  namely increasing the load or the contact area.

If you are using the same normal load for both tests, it would be rational that the friction coefficient increase as the frictional forces increase. I think if you find another results, it would be better if you check the machine, recalibrate the machine, check your calculating formulas. Finally, good luck

I used flat faced cylindrical pins of circular cross section area. Machine Used: Pin on disc tribometer

With lower loads the oil with graphite showed lesser coefficient of friction as well as lesser frictional force but as at 160N though the CoF was slightly lower but frictional force was much higher.

graphite is natural solid  lubrifiant its can be due to the reason to have a lower friction coefficient 

Shubrajit Bhaumik you can downold scientific article of Mouadji Youcef, who has a several experience on tribolgy of contact graphite 

Based on recent tribotest data analysis, I think the graphite (nanoparticles) additives may change sliding friction to rolling friction in the contact/interface. One nanoparticles lubrication mechanism is that of nano-bearing.

As you know, with the same normal load (force), the resisting tangential frictional force should be lower for oil and nanopaticles mixture. Thus, the COF with oil and graphite NPs would be lower than COF with oil only.