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Micromechanics modelling techniques: a better understanding

TWI has been using micromechanical modelling techniques to better understand the links between a material’s microstructure and its macro-scale functional performance.

The lifecycle of industrial products and engineering components spans from design and manufacture to in-service use and ultimately disposal. Proper material performance is crucial at each stage, and material characterisation is routinely used to confirm that a product is fit for purpose.

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.

Micromechanical modelling

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).

Figure 1 (a) Nano-indentation equipment at TWI; (b) typical heterogeneous microstructure of a multi-phase structural steel; (C) nanoindentation load-depth measurements on a heterogeneous microstructure
Figure 1 (a) Nano-indentation equipment at TWI; (b) typical heterogeneous microstructure of a multi-phase structural steel; (C) nanoindentation load-depth measurements on a heterogeneous microstructure
Figure 2. FE material model including polycrystalline microstructure; (b) typical Von-Mises stresses contour for the simulated indentation of the multi-phase material
Figure 2. FE material model including polycrystalline microstructure; (b) typical Von-Mises stresses contour for the simulated indentation of the multi-phase material
Figure 3. COV upper and lower bound curves approach
Figure 3. COV upper and lower bound curves approach

Conclusions

The model predictions have provided TWI with valuable information about the limitations of depth-sensing indentation testing protocols. When the representative microstructural length-scale of a material to be characterised is known, these “look up” curves can be used to provide insight into the expected variability in measurements as well as target testing parameters than can be used to minimise variability.

For further information about Integrity Management, including micromechanics modelling, please email contactus@twi.co.uk