Fig. 1: Schematic of the on-chip mechanical testing set-up applied to single-layer graphene (SLG).

Both tensile-on-chip (TOC) and crack-on-chip (COC) configurations were combined to determine the critical flaw size that controls the failure of graphene membranes. The stress–strain response is given by TOC structures based on the displacement measured between movable and fixed cursors. The fracture toughness is determined using COC structures based on the measurement of the crack arrest length \({{a}}_{{arrest}}\) using a finite element model (FEM). The shaded blue sample represents SLG samples with defects, a_c is the defect size that leads to fracture. The critical flaw size leading to failure a_c can be estimated once the strength and fracture toughness are known from TOC and COC, respectively. The black arrows show that to determine ac, we need to use both data coming from TOC and COC. \({{E}}_{{{a}}}\) is the actuator Young’s modulus, \({{S}}_{{{{{{\rm{a}}}}}}}\) is the actuator area, S is the specimen area, u is the applied displacement, \({{L}}_{{{{{{\rm{a}}}}}}}\) is the actuator length, \({{L}}_{{{{{{\rm{s}}}}}}}\) is the specimen length, \({{\varepsilon }}_{{{a}}}^{{{mis}}}\) is the actuator mismatch, \({{\sigma }}_{{{{{{\rm{c}}}}}}}\) is the strength of the studied material, \({{a}}_{{{{{{\rm{c}}}}}}}\) is the critical flaw size, \({{\sigma }}_{{{a}}}^{{{int}}}\) is the residual stress of the actuator prior to release and \({{K}}_{{{Ic}}}\) is the fracture toughness.