Interfacial stress transfer in strain engineered wrinkled and folded graphene

Because of its large surface area and flexibility, graphene has been explored for various applications such as flexible electronics and energy storage. Topographical undulations are commonly generated in graphene artificially by pre-strain and annealing to allow more tunable properties in hierarchical patterns. It is also possible, however, that strain engineering may induce negative effects, such as inhomogeneous strain distribution and fracturing of graphene. However, the correlation between those negative defects and the interfacial stress transfer in graphene upon strain engineering is still not clear. This is practically crucial as the stress/strain state in graphene is one of the dominant factors in governing other properties such as conductivity and wettability etc. in flexible electronics. In this work, wrinkles/folds (i.e. without/with delamination) have been introduced into graphene by annealing and pre-straining. An interfacial stress transfer efficiency factor ηr, is proposed to quantify the effect of wrinkles/folds by comparing the area under the measured strain distribution curves with the ones calculated theoretically using the 'shear-lag' theory. It is found that the wrinkles, with small amplitudes, do not affect the value of ηr significantly due to good stress transfer being maintained by the graphene still conforming to the substrate, whereas the folds, with high amplitudes, reduce ηr remarkably as a result of the absence of stress transfer due to delamination. The effect of wrinkling can be predicted by a geometrical model that takes the amplitude and wavelength of the graphene wrinkling into account. The monitoring and evaluation of the interfacial stress transfer and the strain distribution of wrinkled and folded graphene provide insights into its interfacial instability, and will have wide impact and applications in the strain engineering of graphene and other 2D materials for flexible electronics and devices.