It is possible to obtain good joints between Cu and graphite. Many papers exist dealing with the problem of wetting graphite by Cu and on joining these two materials. Of course, in order to have a good joint you need to realize good wetting conditions between the two materials, This can be obtained by adopting specific filler alloys or by modifying the graphite surface by some specific coatings.
Have a look to the following papers (just as an example):
Asthana R, Singh M. Active Metal Brazing of Advanced Ceramic Composites to Metallic Systems, in:. Sekulic DP (Ed.). Adv. Brazing. Woodhead; 2013.
Eustathopoulos N. Curr Opin Solid State Mater Sci 2005;9:152.
Yang L, Shen P, Lin Q, Qiu F, Jiang Q. Appl Surf Sci 2011;257:6276.
Mao Y, Wang S, Peng L, Deng Q, Zhao P, Guo B, Zhang Y. J Mater Sci 2015;51:1671.
Zhang K, Xia L, Zhang F, He L. 2016;47:2162.
Yang L, Shen P, Lin Q, Qiu F, Jiang Q. Mater Chem Phys 2010;124:499.