Influence of Hard Inclusion Embedment Depth on
Force-Displacement Behavior during AFM Using FEA

The presence of inclusions embedded within a polymer matrix significantly influences the macro- and nano-scale properties of the matrix. Characterizing the mechanical properties of such inclusion-embedded matrices is crucial for their diverse applications. Atomic force microscopy (AFM) has the unique ability to nondestructively characterize local modulus and height contours of nanocomposite surfaces. While previous studies have established a strong correlation between nanoparticle dispersion and the mechanical properties of nanocomposites, the combined influence of structural effects and material properties convolutes precise characterization. This study aims to deconvolute the effects of the nanoparticle’s embedment depth and damaged polymer on force-displacement curves using finite element analysis (FEA) to simulate the probe-matrix interactions in AFM. Validation of the FEA models was conducted using the Derjaguin-Muller-Toporov (DMT) and Hertzian contact mechanics models. Indentations were modeled for polymer matrices with inclusions embedded at varying depths and damaged polymer to analyze linear and nonlinear material, geometric, and contact mechanics effects. Nonlinear material behavior was characterized using a bilinear elastoplastic stress-strain curve and yield strength derived from Hertzian contact theory and Tresca’s yield criterion. Results revealed that inclusion depth and damaged polymer have distinct and measurable impacts on force-displacement curves retrace slopes, offering insights to identifiable patterns in mechanical behavior.