Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene
Changgu Lee,1,2
Xiaoding Wei,1
Jeffrey W. Kysar,1,3
James Hone1,2,4*
We measured the elastic properties and intrinsic breaking strength of free-standing monolayer graphene membranes by nanoindentation in an atomic force microscope. The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and third-order elastic stiffnesses of 340 newtons per meter (N m–1) and –690 Nm–1, respectively. The breaking strength is 42 N m–1 and represents the intrinsic strength of a defect-free sheet. These quantities correspond to a Young's modulus of E = 1.0 terapascals, third-order elastic stiffness of D = –2.0 terapascals, and intrinsic strength of 
int = 130 gigapascals for bulk graphite. These experiments establish graphene as the strongest material ever measured, and show that atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.
1 Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA.
2 Defense Advanced Research Projects Agency Center for Integrated Micro/Nano-Electromechanical Transducers (iMINT), Columbia University, New York, NY 10027, USA.
3 Center for Nanostructured Materials, Columbia University, New York, NY 10027, USA.
4 Center for Electronic Transport in Molecular Nanostructures, Columbia University, New York, NY 10027, USA.
* To whom correspondence should be addressed. E-mail: jh2228{at}columbia.edu
