Reverse analysis of film/substrate cohesion by indentation: A mesoscopic perspective

Abstract

Delamination remains a critical challenge in achieving robust cohesion between thin films and elastic substrates, particularly in electronic applications subjected to harsh operating conditions. Accurate assessment of the constitutive properties governing film/substrate cohesion is essential for addressing this delamination issue, yet in-situ measurement poses significant challenges. In this study, a numerical model is presented aimed at determining the mechanical properties of elastoplastic film materials adhered to an elastic substrate, leveraging the indentation response generated by a Berkovich indenter. To capture the interfacial damage effectively, cohesive elements are integrated into the finite element model to simulate the cohesive behavior between the elastoplastic film and the elastic substrate. The elastoplastic behavior of the film is characterized using a power-law constitutive model, while the tension-separation model is employed to describe interfacial cohesion. The constitutive parameters of thin film materials are deduced by treating the parameters of the substrate material, film material, and cohesion as dominant factors influencing the load–penetration depth curve. These parameters are combined dimensionlessly, offering an elegant method for solving the constitutive parameters of elastoplastic thin film materials. Evaluation of Young’s modulus, yield strength, and hardening exponent across different indentation depths reveals a highly consistent response in the applied load–penetration depth curve under varying parameter influences. Furthermore, the theoretical consideration of dislocation effects on the indentation process provides insight into the underlying failure mechanisms beneath the indenter. To refine the macroscale finite element model, the evolution of mesoscale dislocations during the indentation process is discussed based on plasticity gradient theory and reverse analysis. Finally, leveraging both macroscale finite element simulation and mesoscale theoretical models, a dimensionless equation is proposed for determining elastoplastic material parameters using the applied load–penetration depth curve. The proposed dimensionless equation demonstrates a fitting degree of up to 0.90, offering compelling evidence for its efficacy in employing indentation as a promising method for efficiently estimating constitutive properties of cohesion between the elastoplastic film and the elastic substrate by accounting for dislocations.