COMPLAS 2025

Strain gradient crystal plasticity modeling on size effects in nanoindentation

  • Binh, Nguyen Xuan (Aalto University)
  • Demir, Eralp (University of Oxford)
  • Lian, Junhe (Aalto University)

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Nanoindentation is a standard and powerful experiment for studying mechanical behaviour at the microscale to nanoscale. This work presents a strain gradient crystal plasticity framework applied to nanoindentation, which aims to demonstrate the presence of geometrically necessary dislocations (GNDs) and their influence on indentation size effects (ISE). The experiment program involves conducting nanoindentation tests with indenters of four radiuses (1, 2, 5, 20 μm) on a cold-rolled ferritic stainless steel (AISI 439). For each indentation tip, three indentation strain of 0.2, 0.3 and 0.4 are conducted. Two grains are selected with crystallographic orientations close to [100] and [111] in the normal direction in the inverse pole figure. The output of the experiment program are the force-displacement curves, the pile-up curves, and the hardness values. Subsequently, two crystal plasticity (CP) models are used for the numerical study of indentation tests. Due to the anisotropy of crystal lattices, strain gradient crystal plasticity remains the most prominent theory to offer explanation for lattice anisotropy and ISE within several micrometres [1]. The first model used in this work is the conventional CP model that does not consider strain gradient formulation and GND calculation. As a result, this model requires different initial critical resolved shear stress for different indenter radius to fit the load-displacement and pile-up profiles, thereby capturing the ISE. The second CP model, as developed independently by the Tarleton’s group at Oxford University [2], can fit all experimental data with high accuracy under the same initial critical resolved shear stress. This work concludes that GNDs are the driving factor in the additional work hardening as the indenter tip becomes smaller. This insight is important as it aligns with previous existing studies on strain gradient formulation that attributes higher measured hardness at smaller indentation depth to GNDs to accommodate the shape of the indenter.