Physics-constrained inverse estimation of irradiation-induced strain in He–H ion-implanted 4H-SiC using nanoindentation and finite element modeling

Abstract

Nanoindentation is widely used to evaluate the mechanical properties of irradiated materials; however, its potential for quantifying irradiation-induced subsurface strain remains underexplored. In this work, an integrated experimental–numerical framework based on a physics-constrained inverse modeling approach is employed to estimate the magnitude of a depth-dependent irradiation-induced strain distribution in single-crystal 4H-SiC following sequential He and H ion implantation. The approach combines depth-sensing nanoindentation, finite element modeling (FEM), and a simplex-based inverse optimization routine to calibrate a physically motivated eigenstrain profile derived from ion-damage simulations. The strain field is assumed to follow a lognormal distribution consistent with independently determined damage profiles (stopping and range of ions in matter) and is implemented in the FEM model through a depth-dependent thermal expansion formulation. By minimizing the squared error between simulated and experimental force–displacement curves, the peak tensile strain is estimated to be ∼0.91%, accompanied by an effective Young's modulus of 310 GPa and a yield strength of 16.4 GPa. Independent validation by nano-beam precession electron diffraction confirms good agreement between the reconstructed and experimentally measured out-of-plane strain profiles in both magnitude and spatial distribution. The results demonstrate that nanoindentation, when combined with physics-based inverse modeling, can provide a practical tool for quantifying irradiation-induced strain and residual stress in nuclear ceramics. This methodology offers a complementary approach to diffraction-based techniques for assessing subsurface damage in ion-irradiated materials relevant to advanced nuclear systems.