Fine adhesive particles A contact model including viscous damping CHoPS 2012 - Friedrichshafen 7 th International Conference for Conveying and Handling of Particulate Solids Friedrichshafen, 12 th September 2012 Prof. Dr.-Ing. habil. Jürgen Tomas
Content / Task 1) Motivation 2) Objectives 3) Model stiff particles with soft contacts 3.1) Reference particle systems 3.2) Normal loading 3.3) Sliding 3.4) Rolling 3.5) Twisting 4) Velocity-dependent viscous damping for normal loading 5) Experiments-determination of material data via nanoindentation 6) Conclusion/Outlook 2
1) Motivation Product design Conveying Process and handling problems of fine powders Flow properties Packing Transport Large adhesion potential F H0 F G Particle size d in µm Ratio F H0 / F G Evaluation 10 100 1 100 slightly adhesive 1 10 100 10 4 adhesive 0.01 1 10 4 10 8 very adhesive Adhesion intensification F H (F N ) FN FH(F N) F N FH(F N) Particle size d in µm Contact consolidation coefficient κ Evaluation 1 100 0.1 0.3 soft 0.1 1 0.3 0.8 very soft 0.01 0.1 > 0.8 extremly soft 3
2) Objectives (I) Central Aim: Understanding of the physical properties by Approach Contact Detachment Fine, dry and adhesive particles FN FN FN hk hk F N hk F N F N Approach Contact Detachment [1] Thornton, C., Interparticle sliding in the presence of adhesion, J. Phys. D: Appl. Phys. 24 (1991) 1942-1946 [2] Thornton, C., and Ning, Z., A theoretical model for the stick/bounce behaviour of adhesive, elastic-plastic spheres, Powder Technology 99 (1998) 154-162 4
2) Objectives (II) Modelling of force displacement and torsional moment angle functions of fine adhesive particles for van-der-waals forces Combination of the inelastic contact deformation and the intensification of the van-der-waals force within the flattened contact of fine particles Implementation of the velocity dependent viscous damping Normal loading Sliding Rolling Twisting FN(hK) F N F N F N hk FT FT(δ) δ MR(γ) MTo(φ) F N F N F N F N 5
3) Model Stiff particles with soft contacts External forces and short-range adhesion forces (near surface) generate directly a localized contact deformation Contact area is small in comparison to the sphere cross section Neglecting of the particle deformations outside of the contact Particle contact with variable adhesion Adhesive, elastic-plastic, viscoelastic and viscoelastic-plastic contact deformation Unloading and reloading hysteresis 6
3.1) Reference Particle Systems Correlation between the contact model and the physical material properties Glass particles ideal spheres Titania high adhesion potential o Ratio F H0 /F G : 1.3. 10³ > adhesive o Contact consolidation coefficient κ: 0.1 > soft o Ratio F H0 /F G : 2.5. 10 5 > very adhesive o Contact consolidation coefficient κ: 1.1 > extremly soft 7
3.1) Normal Loading 8
Characteristic Contact Normal Stress σ=f N /d² in kpa 3.1) Normal Loading Particle Comparison 45 35 25 15 5 Hertz Y Yield Limit Unloading Curve Glass Titania -0.005-5 0.005 A 0.015 0.025 0.035 Adhesion Relative Displacement Limit -15 ε=h K /d in % Contact Friction Coefficient µ i : Glass: 0.8 Titania: 0.64 Repulsion Coefficient κ p : Glass: 0.07 Titania: 0.44 Stiffness k: Glass: 2200 N/m Titania: 165 N/m Slope of the Yield Limit: dσ/dε Glass: 1074 kpa Titania: 74 kpa Micro Yield Strength p f : Glass: 300 MPa Titania: 400 MPa Yield Point: Glass: 4.5 kpa Titania: 5.8 kpa Characteristic Adhesion Force F H0 : Glass: 1.74 nn Titania: 0.54 nn U 9
3.3) Sliding F N FT FT(δ) δ F N [3] Mindlin, R.D., Deresiewicz, H. Elastic spheres in contact under varying oblique forces, Transactions of American Society Mechanical Engineers, Journal of Applied Mechanics, 20 (1953) 327-344 [4] Tomas, J., Adhesion of ultrafine particles Energy absorption at contact, Chemical Engineering Science 62 (2007), 5925 5939 Unloading and Reloading 10
Characteristic Shear Stress τ=f T /d² in kpa 3.3) Sliding Particle Comparison 20 15 COULOMB-Friction μ i. [F N +F H (F N )] 10 5 0-1.5-1 -0.5 0 0.5 1 1.5-5 Relative Displacement -10 δ/δ C,H σ M,st =15 kpa COULOMB-Friction -μ i. [F N +F H (F N )] -15-20 Glass Titania Coulomb Friction Limit Glass Titania Particle size d in µm 5.8 0.6 E-Modul in kn/mm 2 100 50 Shear Modulus in kn/mm 2 40 20 Micro Yield Strength in MPa 300 400 11
3.4) Rolling F N MR(γ) F N [5] Johnson, K.L., Contact Mechanics, Cambridge University Press 1985 Unloading and Reloading 12
Rolling Resistance Stress τ R =F R /d² in MPa 3.4) Rolling Particle Comparison 2 1.5 1 0.5 0-2 -1.5-1 -0.5-0.5 0 0.5 1 1.5 2-1 Relative Rolling Angle γ/γ C,H in 10-4 -1.5-2 Glass Titania Micro Yield Strength in MPa 300 400 Glass Titania Particle size d in µm 5.8 0.6 E-Modul in kn/mm 2 100 50 Shear Modulus in kn/mm 2 40 20 13
3.5) Twisting F N MTo(φ) F N [6] Deresiewicz, H. Contact of elastic spheres under an oscillating torsional couple. Transactions of American Society Mechanical Engineers, Journal of Applied Mechanics 21 (1954) 52-56 Unloading and Reloading 14
Torsional Moment M to in 10-15 Nm Torsional Moment M to in 10-17 Nm 3.5) Twisting Particle Comparison 40 30 20 10 0-2 -1-10 0 1 2 Relative Rotation -20 Angle -30 φ/φ C,H in 10-4 -40 Glass 10 8 6 4 2 0-2 -1-2 0 1 2-4 Relative Rotation Angle -6 φ/φ C,H in 10-4 -8-10 Titania Glass Titania Particle size d in µm 5.8 0.6 E-Modul in kn/mm 2 100 50 Shear Modulus in kn/mm 2 40 20 Micro Yield Strength in MPa 300 400 15
4) Viscous Damping (I) Task Combination of the velocity dependent viscous damping with the loading types 1. Normal Loading: Balance of Forces: F I F el F el pl F pl F d Inertia force Elastic, elasticplastic and plastic contact force Viscous damping force 16
4) Viscous Damping (II) Approach Contact Model Collision of two particles Analysis of a elastic, elastic-plastic and viscous contact Characterized by: Spring Dashpot Plasticity 17
4) Viscous Damping (III) Modelling Matlab Parameters of the reference particle systems Viscous damping approach: Tsuji [7] Parameter modification (damping coefficient, velocity) Bottom particle is fixed Upper particle falls down with a defined velocity h K v 0 m 2 m 1 [7] Tsuji, Tanaka, Ishida, Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe, Powder Technology, 71 (1992), 239-250 18
4) Viscous Damping Results Characteristic Contact Normal Stress σ= F N /d² in kpa Contact Stress-Strain-Relation (viscoelastic; α=1; v 0 =0.1 m/s) 70 60 50 40 30 20 Glass Titania 10 0 0.000-10 0.005 0.010 0.015 0.020 0.025-20 -30 Relative Displacement in % ε=h k /d 20
4) Viscous Damping Results Velocity in m/s Comparison of the Damping Coefficients of Glass; viscoelastic (v 0 =0.1 m/s) 0.15 0.10 0.05 alpha = 0 alpha = 0.2 alpha = 1 alpha = 2 0.00 0.0 0.5 1.0 1.5-0.05-0.10-0.15 Displacement in nm 21
4) Viscous Damping Results Acceleration in µm/s² 100 Acceleration versus material properties at impact (α=1; v 0 =0.1 m/s) 50 0-50 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4-100 -150-200 -250 viscoelastic viscous, elastic-plastic -300-350 Maximum Contact Flattening viscoplastic Time in ns 22
5) Experiments-determination of material data via nanoindentation Nanoindentation Surface imaging and tip-positioning Apply a load while measuring displacement of the tip Analyse the force vs. displacement data University of Siegen Additional options: Dynamic testing Tribological testing 23
5) Experiments-determination of material data via nanoindentation Sample preparation: Selection of the particle (size, shape, etc.) Preparation of the diamond tip with focused ion beam (FIB) Zeiss 24
5) Experiments-determination of material data via nanoindentation Normal Force in µn Wall-particle-wall contact (Indenter tip glass particle glass slide) Displacement controlled ( Max.: 31 nm) Determination of: Force-Displacement-Data (Glass d=20 µm) 850 750 650 550 450 350 250 150 50-30 -20-10 -50 0 10 20 30 40 Displacement in nm Effective modulus of elasticity E* Modulus of elasticity E Yield point Y Secant stiffness for elastic range k N,el,sec Micro-yield strength p f Contact stiffness for elastic-plastic range k N,el-pl Adhesion force F H0 Plastic repulsion coefficient κ p 25
5) Experiments-determination of material data via nanoindentation Force in µn Elastic Wall-Particle-Wall Contact Linearized force-displacement function of the elastic contact 800 700 600 500 Yield Point: F N,f = 46.4 µn h K,f =0.03 nm Effective E-modul: E*=80 kn/mm² 400 300 200 100 0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0-100 Displacement 3/2 in nm Particle E-modul: (Poisson number=0.25) E=38 kn/mm² Secant contact stiffness: k N,el,Sec =21 N/mm 26
5) Experiments-determination of material data via nanoindentation Normal Force in µn Elastic-plastic Wall-Particle-Wall Contact Force-Displacement-Data (Glass d=20 µm) 850 750 650 550 450 350 250 150 50 Elastic-plastic yield limit Adhesion force: F H0 = 136 µn Micro-yield strength: pf=377 MPa Contact stiffness: k N,el-pl =25 N/mm Plastic repulsion coefficient: κp=0.11-30 -20-10 -50 0 10 20 30 40 Displacement in nm 27
6) Conclusion/Outlook Derivation and calculation of the different loading with constant micro-yield strength p f Comparison and evaluation of the reference particle systems Implementation and modelling of the velocity dependent viscous damping for normal loading Evaluation of the results Determination of material data via nanoindentation for unmodified glass particles with the model stiff particles with soft contacts Next Steps: Viscous damping for sliding, rolling and twisting Modelling of the adhesive visco elastic contact in PFC (DEM) Derivation and calculation of the different loading with variable micro-yield strength p f Studying the influence of the surface modification and the relation to the adhesion force 28
Thank you for your attention!!! Contact: Otto-von-Guericke-University Magdeburg Institute of Process Engineering Mechanical Process Engineering Universitätsplatz 2 D-39106 Magdeburg Phone: +49 (0) 391 67 11866 The authors appreciate the financial support by the Deutsche Forschungsgemeinschaft. Email: katja.mader@ovgu.de 29