Neural network processing

• To model the work material response to different process conditions, 3-layered feed-forward back-propagation NN were trained and tested

• The inputs to the NN were chosen to be the parameters that define the physical meaning of the process

• Strain, strain-rate and temperature values for each experimental curve were always utilised as input features

• Also strain and strain-rate as logarithmic functions, ln(ε) and ln(ε'), temperature as inverse function, 1/T, and curve peak strain, ε_p, were employed as input features

• This allowed to take into account the analytical relationships among the considered process parameters and the influence of curve peak strain on the material behaviour modelling

Neural network processing

• The NN configurations had a number of nodes in the input layer equal to the number of features in the input vector

• NN configurations. ε = strain; ε' = strain-rate; T = temperature; ε_p = peak strain;  σ = flow stress.

'

 3-5-1 Neural Network results

• The first NN configuration had structure 3-3-1:
  - input layer with 3 nodes for ε, ε’ and T

  - hidden layer with 5 nodes

  - output layer with 1 node for flow stress s prediction

 

Desired and predicted flow stress vs. strain for test 28

4-5-1 Neural Network results

• The second NN configuration had structure 4-3-1:

• input layer with 4 nodes for ε, ε’, T and curve peak strain ε_p 
• hidden layer had 5 nodes
• output layer had 1 node for flow stress s prediction

 

Desired and predicted flow stress vs. strain for test 28

 

7-5-1 Neural Network results

•  The fourth NN configuration had structure 7-3-1:
• input layer with 7 nodes for each of  ε,  ε,’ and T, the logarithmic functions of ε and ε’, the inverse function of T, and curve peak strain εp 
• hidden layer had 5 nodes
• output layer had 1 node for flow stress σ prediction

  Desired and predicted flow stress vs. strain for test 28  

Material modelling input into the FEM code

• The rheological behaviour of a work material can be introduced into the FEM code in different ways

• An analytical model for the material rheological behaviour can be user selected from a list in the code (e.g. power law, rate power law, Johnson-Cook, Kumar, etc.). Then, the necessary coefficients are manually input by the user

• If this method is used, the stress value for each FEM model node is calculated during the simulation using the analytical model

• Alternatively, the user can enter three tables representing the work hardening (table(x)), temperature (table(y)) and strain rate (table(z)) effects on the flow stress. The data in the tables are typically obtained from experimental tests

Material modelling into the FEM code

• In this paper, the three tables representing the work hardening (table(x)), temperature (table(y)) and strain rate (table(z)) were used for material rheological behaviour input into the FEM code.

• However, these tables were compiled through the help of the learned NN for flow stress prediction

• The learned NN provides for the flow stress curves of the AISI 1010 C steel for any temperature and strain rate within the experimental range used for NN training set construction

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:
• σ_eq = f(ε_eq) * g(T) * h(ε'_eq)

 

Conclusions

• This work a part of a wider scope research on the thermo-mechanical coupled FEM simulation of AISI 1010 C steel machining
• The material rheological behaviour was modelled through a NN approach able to account for the real effects of strain hardening, strain rate and temperature dependencies of the workpiece material into the FEM analysis
• By utilizing a learned NN endowed with the knowledge on flow stress of the AISI 1010 C steel, the work material properties can be provided to the FEM code for each node of the workpiece mesh during the simulation
• The enormous potential of NN material modelling can be exploited in the simulation of processes, like metal cutting, where classical material description is unsatisfactory
• To achieve this results, a continuous information exchange between the learned NN and the FEM code during each iteration must be achieved