Length-scale-dependent cracking and buckling behaviors of nanostructured Cu/Cr multilayer films on compliant substrates

Cu/Cr nanostructured multilayer films (NMFs) with modulation periods (λ) ranging from 250 nm to 10 nm and modulation ratios (η) ranging from 0.1 to 2.0 were prepared on flexible polyimide substrates by using magnetron sputtering. Upon uniaxial tensile testing, the critical cracking strain (ε_c), critical buckling strain (ε_b), and fracture toughness (K_IC) of the NMFs were experimentally measured and all of the mechanical properties showed remarkable λ- and η-dependences. The cracking and buckling behaviors of the Cu/Cr NMFs were systematically investigated and both were found to depend strongly on the length scale. Based on an energy balance model, the interfacial adhesion energies (F) were determined using the measured buckle dimensions. Cracking maps and buckling maps were constructed from the experimental data to summarize the effects of λ and η on the cracking and buckling modes, respectively. In the cracking map, two regimes can be identified: one is brittle fracture with straight cracks and the other is ductile fracture with zigzag cracks. The ductile fracture regime is located in the region where λ ∼ 40 ± 20 nm and simultaneously η < ∼0.3, and the brittle-to-ductile transition is characterized by a fracture toughness criterion of ^KIC ∼ 12.5 MPa m^1/2. In the buckling map, four regimes are distinguished: cracked rectangular buckles, uncracked rectangular buckles, cracked triangular buckles, and uncracked triangular buckles. The effects of the length-scale-dependent deformation and adhesion energies on the buckling behaviors were discussed. A combined dimensionless parameter of K_IC/ (Formula presented.) (E_f: elastic modulus of the NMF) was proposed to assess the buckling behaviors, and the K_IC/ (Formula presented.) contours coincided well with the boundaries dividing the four buckling regimes.