Experimental characterisation of microstructurally heterogeneous materials at small scales often generates significant variability in measured responses. TWI undertook a programme of multi-scale modelling to provide insight into these observed statistical variabilities and investigate the limitations of depth-sensing indentation testing to assess bulk material response.
Multiscale and micromechanics modelling is about how physics between diverse length-scales interact in a consistent manner. When understanding the fracture toughness of the heat-affected zone (HAZ) of a narrow weld, or the wear resistance of a nano-structured coating that prevents corrosion at high temperatures, it is important to understand the behaviour of material systems at small length-scales. To address these challenges, TWI generated finite element (FE) models of representative microstructures of electron beam welded steel samples and ultra-fine grain commercially pure aluminium samples. Over 6000 simulations of nano-indentation testing were analysed, each simulation featuring different individual grain orientations and micromechanical properties. The resulting hardness predictions were statistically analysed to develop relationships between uncertainty in responses as a function of the testing parameters. An example of a typical simulation is shown in Figure 2.
The simulations provided significant insight into the fundamental sources of uncertainty in characterising advanced material systems. Relationships between the coefficient of variation of hardness and normalised indentation depth (indentation depth to average grain size ratio) were developed as shown in Figure 3 (dashed curves).
The model predictions were then validated against over 300 different experimental measurements on multiple material systems (different-coloured data points in Figure 3).