1. Research at Welding Equipment and Engineering Department Speaker: Andrey Batranin, PhD. Student Tomsk Polytechnic University Non-destructive Testing Institute http://svarka.tpu.ru

2. Speaker: Andrey Batranin email: batranin@tpu.ru Contents Modeling of Processing Our Methods to Solve the Problems Mathematical Definition of the Problems Applications of the Methods Conclusions

3. Modeling of Processing Speaker: Andrey Batranin email: batranin@tpu.ru We focus on modeling of different kinds of processing: Welding Cutting Surface treatment Hardening Dynamic (shock) fracture

4. Speaker: Andrey Batranin email: batranin@tpu.ru Our Methods to Solve the Problems Primarily we use Finite Difference Method. Sometimes we use Variation-Difference Method and Smoothed Particle Hydrodynamics (SPH) Method Also we use state equations for complex materials such as mixtures and alloys.

5. Speaker: Andrey Batranin email: batranin@tpu.ru Mathematical Definition of the Problem С(Т) – heat capacity;  (Т) – density; Т – temperature; (Т) – heat conductivity; Q(x,y,z,t) – heat power in a point. To solve problems of welding we use Spatial Non-linear Dynamic Heat Transfer Equation

6. Speaker: Andrey Batranin email: batranin@tpu.ru Mathematical Definition of the Problem Initial and Boundary Conditions Initial condition: Common boundary condition: Melting and crystallization by Stephan’s equation

7. Speaker: Andrey Batranin email: batranin@tpu.ru Surface heat sources I – current, A; U – voltage, V; k – heat energy concentration coefficient, 1/m 2 ; r – distance between a point and the center of a heat spot, m. TIG-welding Electron beam treatment Е – accelerating voltage, V; k – beam concentration coefficient, 1/m 2 r 0 – beam acting radius, m. Mathematical Definition of the Problem

8. Speaker: Andrey Batranin email: batranin@tpu.ru Thermophysical properties of materials considerably depend on temperature. Mathematical Definition of the Problem

9. We use the Conservation Laws of Mass, Energy and Linear Momentum in partial differential equations. Additionally are used state equations for wide range of temperature and component concentration. Thus the models takes into account the following items: Non-linearity of physical properties (thermal dependences) Spatial geometry of a piece (3D form) Inhomogeneity: porosity, inclusions Phase transformations: melting, crystallization, etc. Complexity of heating: moving sources, preheating, etc. Speaker: Andrey Batranin email: batranin@tpu.ru Mathematical Definition of the Problem

10. Applications: software The “Model” Program Speaker: Andrey Batranin email: batranin@tpu.ru Problems were solved: Oxygen cutting TIG-welding Impulse TIG-welding

11. The “Meza” Program Speaker: Andrey Batranin email: batranin@tpu.ru Applications: software

12. The “Meza-cutting” Program Speaker: Andrey Batranin email: batranin@tpu.ru Applications: software Problems were solved: Oxygen cutting Electron beam treatment of titanium alloys

13. Applications: software Computing of stress and deformed states in welds Speaker: Andrey Batranin email: batranin@tpu.ru Problem was solved: Thermal-deformative process during and after welding in a weld joint t = 0.1 sect = 0.2 sec

14. Applications: software Speaker: Andrey Batranin email: batranin@tpu.ru Problem was solved: Plastic deformation in HAZ after welding Computing of stress and deformed states in welds

15. The “Virtual Workspace” Program (MATLAB) Speaker: Andrey Batranin email: batranin@tpu.ru Applications: software Trying to use: A modern software HPC possibilities Collaboration

16. Applications: developments Speaker: Andrey Batranin email: batranin@tpu.ru Furthermore the following researches are carrying out at our department: Stress computation of gradient materials Composition optimizing of coats Impulse control of arc welding Resistance welding of thin-walled pieces

17. Conclusions We model different technological processes: To determine behaviour of materials during and after a process To choose the optimal treatment among possible ones To obtain a material or surface or joint with properties we need To create a base for automation of processing Speaker: Andrey Batranin email: batranin@tpu.ru

18. Thank you! http://svarka.tpu.ru