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

Abstract 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 ( e c ), critical buckling strain ( e 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 ( Γ ) 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 K IC ∼ 12.5 MPa m1/2. 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 / E f Γ ( E f : elastic modulus of the NMF) was proposed to assess the buckling behaviors, and the K IC / E f Γ contours coincided well with the boundaries dividing the four buckling regimes.