Material modelling input into the FEM code (3)

Material modelling input into the FEM code

  • The NN material behaviour prediction is introduced into the FEM code according to the following procedure
  • The work hardening, temperature and strain rate effects on the flow stress must be computed, i.e. table(x), table(y) and table(z) are needed
  • These tables can be calculated by considering the stress as the product of a function of strain, a function of temperature and a function of strain rate and by neglecting the coupling effects
  • Thus, the flow stress is given by:
    • σeq = f(εeq) * g(T) * h(ε'eq)

 

The three terms on the right side of equation represent the work hardening, temperature and strain rate effects on the flow stress, respectively, that can be evaluated as follows. First, the temperature is set equal to room temperature and the strain rate is set equal to 10-6 s-1 (strain rate value for which the material begins to be sensitive to strain rate effects). Under these conditions, g(T) and h(ε'eq) in eq. are equal to 1, and the work hardening factor, , can be computed from the NN prediction. Then, the strain rate is again set equal to 10-6 s-1 and the strain is set equal to a constant value α (here α = 0.2). Under these conditions, the strain rate effect is null, g(ε'eq ) = 1, the work hardening factor is known and the temperature factor, g(T), can be calculated from the NN prediction. Finally, the strain is again set equal to the constant value α and the temperature is set equal to room temperature. Under these conditions, the work hardening factor, , is known, the temperature factor, g(T), is equal to 1, and the strain rate effect, h(ε'eq), can be computed from the NN prediction. The curves obtained are physically significant and, furthermore, they account for some phenomena that are usually ignored. Figure 7b clearly shows the thermal effect known as blue brittleness. When specimens are tested in tension at different temperatures they are found to be more brittle (low strain at fracture) at low temperature than at high temperatures. But in the vicinity of 560 °K (287 °C) steels show a higher yield stress and lower strain at fracture than at room temperature. This anomalous behaviour is due to migration of the interstitial C and N atoms to dislocations resulting in their immobilisation. On a first approximation basis, the blue brittleness anomaly is ignored and the yield stress is considered to decrease with increasing temperature. The existing literature dealing with FEM simulation of machining does not seem to account for this phenomenon, whereas the proposed NN approach is capable to consider this anomalous behaviour. Between strain rates 10-6 s-1 and 10-1 s-1, the strain rate sensitivity increases only by 7-8 %, with a very small slope. After strain rate 10-1 s-1, the curve slope increases notably, i.e. the material becomes more sensitive to the strain rate increase.

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