1. 1. Elastic-plastic properties of Zr-Cu based BMG: indentation and numerical studies Gayan Abeygunawardane-Arachchige Vahid Nekouie Dr. Anish Roy Prof. Vadim Silberschmidt Wolfson School of Mechanical & Manufacturing Engineering, Loughborough University, UK Dr. Uta Khn IFW/Dresden, Germany 1 Mechanics of Advanced Materials Research Group MICROMECH 2014, Rzeszow, Poland, 8-11 July 2014
2. 2. What is a metallic glass? 2 TemperatureTmTg Crystal Glass Liquid > <
3. 3. Introduction & Motivation (Cont..) 3 Source Jan Schroers, Tranquoc Nguyen (2007) Source Oak Ridge National Laboratory Review Source Computer Desktop Encyclopaedia
4. 4. Introduction & Motivation Metallic glass shows unique mechanical properties Evidence of length scale effects Deformation mechanisms of metallic glass are unique plastic shear flow in the micro scale, but brittle fracture in macro scale No proper continuum model has been found yet to capture the behaviour of BMG in continuum scale. (free volume models only used for very small strain and 2-D analysis) Goal of this part of the research is to Experimental wise- introduce novel indentation technique to analyse shear bands underneath the indenter by uniform loading condition. Modelling wise introduce novel technique to determine initiation and propagation of damage parameter(D)through shear band, by Cohesive zone elements Ultimate goal of the research is to predict component deformation under macroscopically homogeneous loads. 4
5. 5. What is a Shear band? Localises large shear strains in relatively thin band (~20 nm). Forms long planes that closely approximate max. shear stress Cohesion is maintained across the planes and flow stress less than the bulk. The shear band propagation is inhomogeneous Propagation depends on loading conditions, sample imperfection. 5 Source nature materials
6. 6. Why shear bands are important in BMGs? The formation and evolution of shear bands controls the yielding and plasticity of all metallic glasses at room temperature. Most dominant shear band quickly leads to failure. The key is to fully understand shear bands, their initiation, propagation and evolution. 6
7. 7. Experiment BMG alloy manufactured at IFW/Dresden Zr48Cu36Al8Ag8 Samples: 70 mm 10 mm 2 mm ; 40 mm 30 mm 1.5 mm 7 Characterisation of the BMG alloy Macro scale X- ray diffraction, Transmission electron microscope Micro scale Wedge indentation
8. 8. 8NCRC Confidential & Privileged Information - Copyright, NCRC, 2007 Experiment Macro scale X-ray diffraction (XRD) Transmission Electron Microscopy XRD and TEM results show : The structure of the metallic glass is completely amorphous.
9. 9. Experiment Macro scale (Cont..) 3-point bending Test Elastic Modulus Poissons ratio E (GPa) y (MPa) In-house experiments 80 86 0.34 0.35
10. 10. 3mm TensionCompression 100 m Fracture surface (3 Point bending) 400 m 10 m
11. 11. 11 Experiment Micro scale: State of the art Technique use to analyse shear band underneath the indenter Bonded Interface Indentation Disadvantages of technique Not uniform perfect surface Formed shear band will be damaged due to cutting and pre-preparation activities. Property variation due to the temperature changes.. Cut the sample Re-joined ClampPolish Indentation
12. 12. 12 Instron 3345 Sample is cut Polished Zygo Talisurf Ra = 2 to 3 nm Wedge Indentation Max Load: 1 kN- 3 kN Deformation mode: Compression Displacement rate : 0.5 mm/min Indenter: High Speed Steel
13. 13. 13 Wedge indentation Wedge indenter Optical Microscope Bulk metallic glass Spring Fixture Spring Instron 3345
14. 14. Wedge indentation 60 m 1kN 22m 1-2kN 60 m 50m 1-2-3kN 60 m 85m 400 m 400 m 400 m 85m 130m 50m
15. 15. Wedge indentation: Load-Displacement Curve 22 m 50 m
16. 16. MODELLING OF WEDGE INDENTATION /Finite Element Modelling 16
17. 17. Microscale modelling Bulk material Drucker Prager : hydrostatic stress component is considered. Captures the rise of shear strength with the increase of hydrostatic pressure increase. Major cause for adoption. = 2 1 J2 second deviatoric stress invariant constant for a given material I1 first stress invariant hardening and softening function ABAQUS 6.12 is used to model Linear Drucker - Prager criterion is used: = Here: = and = To calculate, and : = 1 2 q 1 + 1 1 1 3 and = 1 1 3 = , = = 17
18. 18. Microscale modelling Shear band Cohesive Zone Elements with traction separation law. Shear band thickness lies in the ~nm scale. This fact prompt to employ traction separation laws. 18 Linear elastic behaviour = 0 , = 0 , = 0 Traction Separation response Damage initiation criterion 0 2 + 2 + 2 = 1 Nominator calculated by the solver, Denominator is user input dependent. Linear damage evolution = 0 0 effective displacement at complete failure, 0 effective displacement at damage initiation effective traction at damage initiation, maximum value of the effective displacement
19. 19. 19 Wedge Indenter Radius: 43 m FE Model Dimension: (2000 2000 ) m Displacement Given to Indenter: 4 m to 10 m Element type: Bulk Specimen and indenter CPE4R Shear bands COH2D4 Wedge Indenter: Deformable Body FE model 2D Plain Strain BC: bottom rigid
20. 20. 20 FE model Material Properties Drucker-Prager parameters Hardening Angle of friction() Flow stress ratio Dilation angle () 0.01 1 0.02 Shear damage parameters Yield stress (MPa) Plastic strain Fracture strain Shear stress ratio Strain rate ( s-1 ) 1900 0 0.05 1 0.016 1906.4 0.001 Material Properties for bulk metallic glass E (GPa) 86.0 0.35 Material Properties for deformable indenter (HSS) E (GPa) 231 0.30 Material properties for CZE were chosen by sensitivity analysis.
21. 21. 21 FE model: Results Damage initiation and propagation through the shear band
22. 22. 22 FE model: Results Effect of indenter deformability to damage initiation and propagation Rigid Indenter HSS Indenter Titanium Indenter
23. 23. Outlook Cohesive Zone Elements can be used to determined the initiation and propagation of the damage parameter(D) along the shear band. The approach could be used to analyse the afore mentioned advantage, for any shear band pattern. A gradient plasticity based approach is currently being developed to capture the nucleation and the effect of the local shear bands. 23NCRC Confidential & Privileged Information - Copyright, NCRC, 2007
24. 24. Thank You 24NCRC Confidential & Privileged Information - Copyright, NCRC, 2007