Researchers at the US Department of Energy's Lawrence Berkeley National Laboratory have found that polycrystalline graphene has quite low toughness, or resistance to fracture, despite having very high strength. 

The researchers say that while the extremely high strength is impressive, it can't necessarily be utilized unless it has resistance to fracture. The senior scientist in the Materials Sciences Division of Berkeley Lab developed a statistical model for the toughness of polycrystalline graphene to better understand and predict failure in the material. This mathematical model found that the strength varies with the grain size up to a certain extent, but most importantly it defined graphene's fracture resistance. 

According to the research, a soccer ball can be placed on a single sheet of monocrystalline graphene without breaking it. But for polycrystalline graphene a soccer ball is much too heavy, and the material can support only a ping pong ball.