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After demonstrating that the crystal plasticity obtained at microscales could be used to predict the bulk’s compressive mechanical behaviour utilizing CPFE simulation (see Figure 5-8), a further step was taken to see if the current CPFE model could be used to mimic the deformation behaviour under tensile testing, given that most of the engineering components fail under tensile stress. A macro-mechanical CPFE model was constructed and used to simulate the tensile deformation behaviour of the ER5 and ER4 joints.

As shown in Figure 5-9a, the built model with dimensions of 1.75×0.4375×0.07 mm3 _is made of 157 grains with the grain size of 71 µm, as determined by the EBSD test. The different colours present different crystalline orientations abstracted from the EBSD test. The predicted stress-strain curves and the experimental curves are shown in Figure 5-9b. The good agreement between them is achieved, especially for the yield strength. The Von Mises stress distribution at 5% strain is shown in Figure 5-9c. The stress is not evenly distributed in the sample with some grains showing higher stress. The results of CPFE simulation of the ER4 joint are shown in Figure 5-10. Similarly, there is a good agreement between the simulation and the experiment, especially for the yield strength.

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Figure 5-9. (a) CPFE polycrystal model for tensile test of the ER5 joint, (b) tensile stress- strain curves from experiment and simulation with the yield stress showing in the image, (c) Von Mises stress distribution after 5% strain in CPFE simulation

Figure 5-10. (a) Tensile stress-strain curves from experiment and simulation with the yield stress shown in the image, (c) Von Mises stress distribution after 5% strain in CPFE simulation.

5.4 Discussion

As demonstrated in Figure 5-4 and Figure 5-6, the mechanical response at microscale of a SC in the FZ was reasonably well predicted by CPFE simulation, a finding which is similar to the published results [59, 196, 197]. However, the common problem for simulation is the

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discrepancy of the elastic period. The slope of the elastic period in the stress-strain curves from simulation results is greater than that of the experimental results (Figure 5-4a-c). In the simulation, Hooke’s law determined the slope. But in the experiment, the main factor influencing the slope was the misalignment between the tip and the pillar. The misalignment caused some areas to deform plastically before others, resulting in a smaller slope as demonstrated at the early stage of the deformation (see Figure 5-4a). Thus, the elastic period of the pillar is not reflective of pure elastic deformation, with some local plastic deformation is involved. Nevertheless, the plastic deformation is the focus during the simulation, and the results show that good agreement could be obtained through CPFE simulation.

The material parameters obtained by fitting the single crystal, as shown in Table 5-1 and Table 5-3, could be successfully used to predict the mechanical behaviour of polycrystals of the welded joint under compressive loading, as demonstrated by the results in Figure 5-8. The yield stress for both joints is accurately predicted by CPFE simulation. The strain hardening behaviour also shows a good agreement between the simulation and experiment. The results suggest that the microplasticity obtained by the micropillar compression test can be employed to predict the onset of plasticity of the welded joint precisely.

However, one aspect that needs to be taken into consideration is the size effect on the strength at microscale, as mentioned in Chapters 3 and 4. Generally, sample with smaller size had stronger strength. If the plasticity of smaller sized sample (e.g., 400nm-diameter pillar in this research) is used to predict the macroscale mechanical properties, much higher strength would be obtained. Thus, the choice of the size of the sample requires special care.

One of the drawbacks in this study is that porosity is not taken into consideration when simulating the mechanical properties of the welded joint. It is well known that porosity can reduce the elastic modulus of material [198, 199]. Since porosity is not included in the CPFE

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model, a direct outcome is mismatch of the elastic period in the stress-strain curves, as seen Figure 5-9b and Figure 5-10a. As this research focused on the mechanical properties under statistic loading, the residual stress, which is known to affect the fatigue strength of welded joints [200, 201], is not considered.

5.5 Conclusions

(1) A micromechanical CPFE model was successfully constructed and applied to simulate the compressive behaviour of single crystals of the FZ at microscale, and the material parameters used in the micromechanical model could be obtained from micropillar compression testing.

(2) A marco-mechanical CPFE model was proposed from the microplasticity and used to precisely mimic the deformation of ER4 joints under compressive loading, especially in the yield strength and hardening period; the onset of plasticity under tensile testing of the ER4 joint was also precisely predicted by CPFE simulation based on the microplasticity of the 2 µm-diameter pillar, with the predicted yield strength (223 MPa) very close to that found experimentally (230 MPa).

(3) Base on the microplasticity of pillars with the diameter of 6.8 µm, A marco- mechanical CPFE model could accurately predict the onset of plasticity of the ER5 joint, with the predicted yield strength (173 MPa) very close to that found experimentally (170 MPa).

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