Bruchmechanik grobkörniger Graphitkörper Experimentelle Untersuchung und FEM Modellierung

Transkript

1 Bruchmechanik grobkörniger Graphitkörper Experimentelle Untersuchung und FEM Modellierung Stefan Fischer, Oleg Benevolenski Frühjahrstagung des Arbeitskreises Kohlenstoffe 20. März 2013, Weimar 1

2 Outline Company Profile Motivation Conclusion 2

3 Outline Company Profile Motivation Conclusion 3

4 SGL Group Company Profile SGL Group is one of the world s largest manufacturers of carbon-based products Comprehensive portfolio ranging from carbon and graphite products to carbon fibers and composites Sales of ~ 1.5 bn in 2011 Head office in Wiesbaden/Germany Approx. 6,500 employees worldwide Listed on MDAX 46 production sites worldwide Service network covering more than 100 countries 4

5 Outline Company Profile Motivation Conclusion 5

6 Motivation Background: Graphite electrodes (GE) for electric arc furnaces (EAF) Extreme conditions ka T > 1800 C mechanical load (strand weight > 3 t, vibrations) Material failure Increased electrode consumption Target: Fracture mechanical characterization material improvement FEM analysis design for application 6

7 Outline Company Profile Motivation Conclusion 7

8 Determination of fracture mechanical properties - Setup 3 point bending test Scientifically well established Crack propagation starts at notch well defined Mode I H = 70 Samples Coarse grain graphite (< 2.5 cm) Notched (bandsaw) Dimensions are compromise btw. accuracy and material available Load B = 70 S = Partial unloading Compliance determination Displacement 8

9 Crack growth resistance and R-curves Crack growth resistance R: R = J + Φ P (elastic and plastic contribution) Typical R-curve behavior in synthetic graphite: Load U 1 U 2 Displacement U 1 J 1 = Bda U 2 Φ = Bda U 2 Φ = U Bda Bda partial unloading R = J + Φ R = J + Φ Crack growth resistance R growth of process zone constant crack growth sample size effect δa Crack length measurement crucial for data evaluation Conditions for crack growth: G < R: δa = 0; no crack growth (stable) G = R: δa = 0; quasi-static crack growth G > R: δa = 0; dynamic crack growth (unstable) 9

10 Crack length measurement methods Means to measure the crack propagation in graphite: Potential drop method Easy to measure Systematic errors due to crack bridging; needs calibration Acoustic Emission Volume analysis of crack position; additional information about areas of increased plastic energy dissipation Spatial resolution (?); hard to implement in standard lab test Compliance crack length No additional measurement necessary Significant systematic deviations Optical Microscopy method (travelling, long distance) Hard to introduce into standard lab method Digital Image Correlation 10

11 Crack length measurement with Digital Image Correlation (DIC) 1. Application of statistical pattern; Pictures taken after each unloading step 3. Compute displacement and raw strain 4. Define threshold for strain to assume crack propagation 2. Define grid, use digital image correlation to observe change in material Direct measurement of displacement Sufficient spatial resolution Can be implemented in standard lab setups Only surface information 11

12 FEM Approach Transversal crack near to socket bottom assumed Electric-Thermal-Structural simulations conducted Energy release rate calculated with help of the Virtual Crack Closure Technique 12

13 Outline Company Profile Motivation Conclusion 13

14 Crack length detection for different graphite recipes FILM crack length (mm) Formulation 1 Formulation ,5 1 1,5 displacement (mm) Crack development during deformation can be changed by material formulation and processing regarding onset and speed 14

15 Crack growth resistance Formulation 1 Formulation 2 specific energy (J/m²) R = J +Φ 0 R J Φ Crack growth elastic plastic resistance contribution contribution Reduced crack propagation of formulation 1 is reflected by a higher crack growth resistance, mainly based on increased plastic energy dissipation 15

16 Effect of the transversal crack on the electric and thermal fields Current density [A/m 2 ] Assumption: Conducting crack Crack is insulating Temperature [ C] crack increases current density by factor > 10 significantly increased temperature gradients 16

17 Effect of the crack length Energy release rate G (J/m²) ,1 0,2 0,3 Relative crack length a/r R (Formulation 1) R (Formulation 2) A stable growing crack turns into unstable growth when a certain crack length is passed Discontinuous material consumption can be reduced by improved crack growth resistance 17

18 Effect of the applied current Energy release rate G (J/m²) length a = 0.3 r, electrode diameter = 600 mm Electric current I [ka] R (Formulation 1) R (Formulation 2) On furnaces operated at higher electric currents unstable crack propagation may take place Higher productivity possible by improved crack growth resistance 18

19 Outline Company Profile Motivation Conclusion 19

20 Fracture mechanical analysis of coarse grain graphite Conclusions Fracture mechanical analysis method developed 3PB on notched samples + compliance method Crucial: crack length determination Digital Image Correlation is a valuable tool for crack length measurement Graphite grade development can directly aim at materials with improved crack growth resistance FEM modeling to simulate complex electrical and thermal conditions on furnace Improved crack growth resistance reduces discontinuous consumption and enables the steel shop to increase total current higher productivity Enhanced performance of graphite electrodes on EAF by on purpose improved fracture mechanical properties possible 20