Multiscale simulation of metal deformation in deep drawing using machine learning Bachelor Integration Project Industrial Engineering & Management University of Groningen Author: F.M. Verwijs s3090345 Supervisors: Prof. dr. A. Vakis (First supervisor) Dr. ir. A.A. Geertsema (Second supervisor) Dr. S. Solhjoo (Daily supervisor) June 19th, 2019 Abstract Crystal plasticity modeling is a powerful and well-established computational materials science tool to investigate mechanical structure{property relations in crystalline materials. The mechanical behavior of crystalline matter is a multiscale problem, whereas the underlying deformation processes such as the slip of dislocations and their reactions and elastic interactions are microscopic problems, and the forming process itself is usually of a macroscopic nature. Information regarding the crystal plasticity of metals in deep drawing processes, can be obtained at microscale. However, for applicability, the larger scale is of importance. To transfer the crystal plasticity information to the larger scale, this information needs to be stored and arranged in a certain way. In this Integration Project, a novel method of integrating the simulations at microscale to larger scale is presented. Crystal plasticity information concerning the material behavior of deep drawing processes is obtained using the DAMASK simulation software, generating representative volume elements, based on various strain rates. An Artificial Neural Network shows the information generated from the crystal plasticity simulations in DAMASK and predicts new data points. The information that is arranged in this machine-learning neural network, will be loaded into a finite element analysis. Based on this information, simulations are performed in MSC.Marc. This ultimately yields the information at larger scale, desired in deep drawing processes. It was found that at the low strain rate used in this project, no significant differences show between the stress-strain behavior of unrolled and rolled materials. Additionally, it was concluded that the RVE representation after a certain value of strain rate does not show significant differences when a certain strain needs to be met. Furthermore, various methods of data storage were compared. It was found that for this project, the SCG-trained feedforward ANN with two hidden layers and five neurons per layer, performs best in terms of accuracy, simplicity, and computation times. Lastly, the methods of performing the integration and the selected parameters were validated. Moreover, it was found that the deep drawn sample shows mainly a strain rate deformation of 0:01s−1 and four ears are formed. This novel method significantly decreases computation times, while increasing accuracy and user simplicity. This makes this novel multiscale simulation method of the deep drawing process is very relevant in various applications. 2 Contents List of Tables 8 List of Figures 9 1 Introduction 11 2 State of the art 12 2.1 Crystal plasticity modeling . 12 2.2 Artificial Neural Network . 12 2.3 Finite element method . 13 2.4 Integration of crystal plasticity and FEM . 14 3 Problem analysis 15 3.1 Problem description . 15 3.2 Problem owner analysis . 15 3.3 Stakeholder analysis . 15 3.4 System description and scope . 16 3.5 Cycle selection . 16 3.6 Resources needed . 17 3.6.1 DAMASK . 17 3.6.2 MSC.Marc . 18 3.6.3 MATLAB . 18 3.6.4 FORTRAN and Visual Studio . 18 3.6.5 Literature about existing body of knowledge . 19 4 Goal 20 4.1 Main research question . 20 4.2 Sub questions . 20 5 DAMASK 21 5.1 Comparison to previous methods . 21 5.2 Process . 21 5.3 Parameter selection . 22 5.4 Results . 24 5.4.1 General remarks . 24 5.4.2 Representative Volume Elements . 24 5.4.3 Stress-strain curves . 25 5.4.4 Lankford coefficient . 26 5.5 Discussion . 27 6 Data storage 28 6.1 Methods . 28 6.1.1 Look-up table . 28 6.1.2 Fitted curve . 28 3 6.1.3 Artificial Neural Network . 29 6.2 Comparison to previous methods . 29 6.3 Process of LUT . 29 6.4 Process of ANN . 30 6.5 Parameter selection . 30 6.6 Results . 31 6.6.1 General description of network . 31 6.6.2 Training functions . 31 6.6.3 Error estimation . 32 6.6.4 Number of hidden layers and number of neurons per layer . 33 6.6.5 Transfer to MSC.Marc . 34 6.6.6 Requirements to the ANN by MSC.Marc . 35 6.6.7 Accuracy, based on error estimation . 35 6.6.8 Average training time . 35 6.6.9 User simplicity . 35 6.7 Discussion . 35 6.7.1 Data distribution . 35 6.7.2 Random selection of data within set . 36 6.7.3 Number of neurons optimization . 36 7 Finite Element Analysis using the ANN 37 7.1 Comparison to previous methods . 37 7.2 Process . 37 7.3 Parameter selection . 37 7.4 Results . 42 7.4.1 Comparison of data storage methods in FEM results . 42 7.4.2 Interpretation and simulation using the ANN . 42 7.4.3 Integration of the data storage method and MSC.Marc by means of the Fortran compiler . 43 7.4.4 Deep drawing simulation . 44 7.5 Discussion . 44 8 Finalized methodology 45 8.1 Comparison to previous methods . 45 8.2 Process . 45 8.3 Results . 46 8.3.1 Accuracy . 46 8.3.2 Decrease in computational times . 46 8.3.3 Simplicity for the user . 46 9 Validation 47 9.1 Crystal plasticity simulations in DAMASK . 47 9.2 Data storage using the ANN . 47 9.3 FE analysis in MSC.Marc . 47 9.4 Integration of these methods . 47 10 Conclusion 48 4 11 Discussion 50 Bibliography 51 A Theoretical background 57 A.1 Crystal plasticity and anisotropy . 57 A.2 DAMASK . 57 A.3 Plastic deformation behavior . 58 A.4 Stress-strain curves . 59 A.5 Representative volume elements . 59 A.6 Lankford coefficient . 59 A.7 Hill 1948 yield criterion . 60 A.8 Data storage methods . 60 A.8.1 Artificial neural network . 60 A.8.2 Lookup table . 61 A.8.3 Fitted function . 62 A.9 Finite Element Method . 62 A.9.1 MSC.Marc . 62 A.10 Strain rate dependence . 63 A.11 Deep drawing . 63 B Procedures 65 B.1 DAMASK . 67 B.1.1 Download the DAMASK software . 67 B.1.2 Determine the required strain rates and simulation times . 67 B.1.3 Generate the general seeds file . 67 B.1.4 Write the preprocessing code that will perform the simulation . 68 B.1.5 Visualize the RVEs generated in the simulation . 68 B.1.6 Write the postprocessing code to conclude the simulation . 69 B.1.7 Perform two more simulations under rolling angles 45◦ and 90◦ ..... 69 B.1.8 Determine stress-strain curves and the Lankford coefficient . 69 B.2 Artificial neural network . ..