Bending induced interlayer shearing, rippling and kink buckling of multilayered graphene sheets

As one typical representative of van der Waals structures, multilayered graphene sheets (MLGSs) have attracted much attention in recent years due to their unusual properties and new phenomena. Due to the ultralow interlayer interaction, these materials may easily encounter mechanical failure and subsequently the malfunction of devices. It becomes essential to clarify failure modes and the beneath mechanism. Through an inverse blister test, bending induced failure (local buckling) of MLGSs is observed experimentally. Theoretical modeling and molecular dynamics simulations are then conducted to investigate the bending behavior of MLGSs without any edge constrain. We demonstrate three failure modes, including interlayer shearing, rippling and kink buckling/delamination. Compared with previous studies, we find the occurrence of failure is length and thickness dependent. Short sheets prefer to continuous interlayer shearing, long and thin/thick sheets prefer to snap-through sliding, while long and medium-thick sheets prefer to kink buckling. We propose failure criteria and draw a phase diagram to predict the failure modes. Furthermore, we analytically deduce the bending stiffness of MLGSs before the failure which is also found to be length dependent that below a critical length (∼9.7 nm), it decreases dramatically. Our results not only shed new light for understanding the bending behavior of MLGS, but also extend to other heterostructures, paving the way for potential implications of 2-dimensional materials.