Characterisation Programme Polymer Multi-scale Properties Industrial Advisory Group 22 nd April 2008

Transcription

1 Characterisation Programme 6-9 Polymer Multi-scale Properties Industrial Advisory Group nd April 8 SE: Improved Design and Manufacture of Polymeric Coatings Through the Provision of Dynamic Nano-indentation Measurement Methods Nigel Jennett (Lead Scientist), Miguel Monclus, John Nunn Project Manager: Rob Brooks

2 Motivation for project Tuesday, May 8 Requirement for: Local polymer properties (bearings, gears, cams, composites (matrix and interfaces)) Properties of small volumes in part design (e.g. mico-mouldings, packaging, coatings). Nanoindentation has the resolution but polymers have time/rate dependent properties. Dynamic measurement methods are required!

3 Tuesday, May 8 Presentation outline Dynamic Nanoindentation: Loss and storage modulus from indentation amplitude and phase as a function of oscillation frequency Nanoindentation creep experiments to obtain modulus and viscoelasticity time constants 3

4 Tuesday, May 8 Measuring time dependent properties. Three methods: ) Indentation cycles much faster than viscoelastic time constant of sample. ) Oscillation of indenter/sample contact + measurement of relative amplitude and phase response (Dynamic Nanoindentation). 3) Indentation creep methods using step load followed by holding at constant force: the evolution of displacement creep is dependent upon the viscoelastic properties of the material. 4

5 Instrumented (Nano)indenter Schematic Tuesday, May 8 Current Source Oscillator Lock-in amplifier Displacement sensor Computer Magnet Coil Stage LOAD FRAME Suspension springs Capacitance Displacement Gauge Indenter Sample Quasi-static / Dynamic 5

6 Force (µn) / Displacement (nm) Spring and dashpot model K s h(t) S Phase Shift Amplitude F(t) m D i K f D s Time (milli-seconds) Displacement Load F h E = Storage modulus E = Loss modulus δ = Phase shift Tan δ = Damping coefficient tanδ = σ = K ωdeq mω eq ( E + ie )ε Tuesday, May 8 ( K m ) = ω Deq + ω eq 6

7 Tuesday, May 8 Dynamic contact mechanics δ E' E' ' = ωd S A( s π = Storage Modulus h c π A( h c ) ) Loss Modulus Damping Coefficient and Stiffness are a function of specimen and indenter geometry. Loss and storage modulus are material properties. 7

8 Tuesday, May 8 Sensitivity to primary calibration parameters Summary of findings: Dynamic calibrations are sensitive to static calibrations Output results of E and E are sensitive to dynamic calibration, particularly E. Dynamic calibration errors within reasonable tolerances do not significantly affect E results, (within the experimental uncertainty for tests on highly repeatable samples). 8

9 Tuesday, May 8 Materials Tested: Commercially Available Standard Polymers Quasi-static response: Load Vs. Depth Curves.5 PS - PS - 3 PS - 4 Load (mn) Depth (nm) 9

10 Dynamic Indentation on PS- at different frequencies (Berkovich) Tuesday, May 8 Elastic Modulus, E (GPa) Hz Hz Hz Vendor E =.5 GPa Displacement (nm)

11 Dynamic Indentation on PS-3 at different frequencies (Berkovich) Tuesday, May Hz Hz Hz Elastic Modulus, E (GPa) Displacement (nm) Vendor E =. GPa (More consistent with the loss modulus)

12 Tuesday, May 8 Testing at temperature : Force MicroMaterials NanoTest Hot stage sample temp 5 C Mapping the hardness of tribological coatings H(GPa) Heaters Harder phase to provide abrasive resistance Softer phase to provide toughness 5. micron Ion-beam Assisted Deposition (IBAD) Alumina; Stephen Abela, Unversity of Malta Depth sensor Scan

13 Tuesday, May 8 Preliminary measurements at different frequencies (NPL modified Nanotest) Need a solution that is compatible with future hot stage use Pendulum damping is adjustable Dynamic response should be similar to impact calibrations NPL system able to measure ~ frequencies per hour. (c.f. NanoII per day) 3

14 Nanotest Dynamic Compliance vs. Damping Tuesday, May 8 Dynamic Compliance (m/n) (mn) Dynamic Compliance (m/n) Dynamic Dynamic Dynamic Calibration Calibration curve curve curve - - No In - oil Deep In Oil Oil Data: Data_B Data: Data: Data_B Data_B Model: user Model: Model: user user Weighting: Weighting: W eighting: y No weighting y y No weighting No weighting Chi^/DoF = 5.396E-9 Chi^/DoF Chi^/DoF R^ = E = 7.457E- R^ R^ = = P ±.33 P P P ±.93 ±.44 ±.6 P P P ±.66 ±.74 ±.944 P3 P ±.66 ±.575 NanoTest NanoII Ks N/m m.36.7 Kg Di Ns/m.. -. Frequency Frequency of oscillation (rad/sec) (rad/sec) 4

15 Tuesday, May 8 Oscillation response when damped and in contact with PS- Oscillation amplitude vs. frequency on PS- 7 4 Oscillation Amplitude /[nm] Phase Fac = un Fac = un Fac = 5 un Phase /[deg] Frequency /[Hz] 5

16 Tuesday, May 8 Oscillation response when damped and in contact with PS-3 Oscillation amplitude vs. frequency on PS-3 Oscillation Amplitude /[nm] Phase Fac = un Fac = un Fac = 5 un Phase /[deg] Frequency /[Hz] 6

17 Next steps with Dynamic Nanoindentation Tuesday, May 8 Reduce amplitudes of oscillation (NanoTest) Validate calibration procedure Calculate modulus results from data Compare results with NanoII and DMA 7

18 Indentation Creep experiments Determination of modulus and viscosity from load and hold data.

19 Tuesday, May 8 Viscoelastic Indentation Analysis The current investigation builds on previous studies utilising spherical and conical indentation testing and integral analysis of polymer indentation data.* Analysis is based within the context of the Hertzian contact problem by Lee and Radock.** *M.L. Oyen, Phil. Mag. -7 (6) **J. Appl. Mech (96). 9

20 Tuesday, May 8 Viscoelastic Indentation Analysis Governing equations in force-displacement (P-h) variables: For indentation with conical/pyramidal indenter: h γ P γ t = h = J ( t u) π tanψ G π tanψ dp( u du ) du Integration takes place over applied loading conditions to obtain closed-form expressions for the load-displacement-time response for the creep function corresponding to a simplified model: η G G

21 Tuesday, May 8 Conical / Pyramidal Analysis For indentation with conical/pyramidal indenter: Resulting closed form expression for hold creep: Expression used for fitting mechanical data: + = c t G G t J τ exp ) ( G c η τ = G G η + = exp exp tan ) ( C C C t t G r G G rt t h τ τ τ ψ π γ ( ) C t C C t h τ = exp ) (

22 Tuesday, May 8 Materials Tested: Commercially Available Standard Polymers Quasi-static response: Load Vs. Depth Curves.5 PS - PS - 3 PS - 4 Load (mn) Depth (nm)

23 Dynamic Mechanical Analysis (DMA) Tuesday, May E ~. GPa Single cantilever bending mode Heating rate = 3 o C/min Frequency = 4 Hz E ~. GPa Single cantilever bending mode Heating rate = 3 o C/min Frequency = 4 Hz Storage Modulus (MPa) PS- Tan δ Loss Modulus (MPa) Storage Modulus (MPa) PS-3 Tan δ Loss Modulus (MPa) Temperature ( o C) Temperature ( o C) Vendor Nominal Values: Material Elastic Modulus, E (GPa) Poisson s ratio, ν PS PS-3..4 PS

24 Tuesday, May 8 Indentation Creep Experiments Load time input function: Indenter tips used: Pyramidal (Berkovich): P max Load, P t R Experiments included different combinations of peak load (P max ), t R and t hold. t hold + t R Conical: R =.6 µm R = 5 µm Time, t 4

25 Tuesday, May 8 Indentation Creep Experiments Load (mn) Rise time (s) Berks Con.6 µm Con 5 µm 8 5 (LL) 4 5 (LL) 5 / / 8 (LL) 6 / / 9 / 7 (LS) 9 / 7 (LS) 5 (LL).5 5 (LL).5 5 (LL).5 5 (LL).75 5 (LL) LL: Constant loading rate LS: Constant strain rate 5

26 Tuesday, May 8 Indentation Creep Experiments Conical / Pyramidal Analysis applied to the three indenters. h ( t) = C C exp ( t τ ) C R~. µm R~.6 µm Sample R~5 µm *Investigate effect of varying max. loads and rise times. 6

27 Tuesday, May 8 Maximum Indentation Force vs. Displacement Displacement (nm) Displacement (nm) Displacement at the end of loading curve Conical Indenter R =.6 microns PS- PS-3 spherical cap end Maximum Indentation Force (mn) Displacement at the end of loading curve Conical Indenter R = 5 microns PS- PS-3 spherical cap end Displacement (nm) Displacement at the end of loading curve Conical Indenter 8 R =.6 microns 7 PS- 6 PS spherical cap end Maximum Indentation Force (mn) Maximum Indentation Force (mn) 7

28 Tuesday, May 8 Conical Analysis: PS and PS3 Creep Response PS- PS-3 Scaled Displacement, h (m ).6E-.4E-.E-.E-.8E-.6E-.4E-.E-.E- 9.8E Scaled Displacement, h (m ).7E-5.6E-5.5E-5.4E-5.3E-5.E-5.E-5.E Time (seconds) Time (s) 8

29 Tuesday, May 8 Conical Analysis: Calculated Spring Constants (G and G ) Spring Coefficients, G (GPa) PS- G Conical Indenter R = 5 µm G Conical Indenter R = 5 µm G Conical Indenter R =.6 µm G Conical Indenter R =.6 µm G Berkovich Indenter G Berkovich Indenter η Maximum Load, L (mn) G G 9

30 Tuesday, May 8 Conical Analysis: Calculated Viscosity PS- η Conical Indenter R = 5 µm η Conical Indenter R =.6 µm η Berkovich Indenter Viscosity, η (GPa) η Maximum Load, L (mn) G G 3

31 Modulus E (GPa) Tuesday, May 8 Conical Analysis: Calculated Elastic Modulus (E and E inf ) PS- E Conical Indenter R = 5 µm E inf Conical Indenter R = 5 µm E Conical Indenter R =.6 µm E inf Conical Indenter R =.6 µm E Berkovich Indenter E inf Berkovich Indenter Maximum Load, L (mn) Modulus E (GPa) PS-3 E Conical Indenter R = 5 µm E inf Conical Indenter R = 5 µm E Conical Indenter R =.6 µm E inf Conical Indenter R =.6 µm E Berkovich Indenter E inf Berkovich Indenter Maximum Load, L (mn) J ( t) = G G + G t exp τ c η ( )[ ] G = lim J ( t) G = t ( )[ ] lim J ( t) = ( G + / G ) t = G E = G ( + υ) E = G ( + υ) G 3

32 Tuesday, May 8 Conical Analysis: Calculated E /E Ratio. PS-.6 PS-3.55 Modulus Ratio E inf / E o.8.6 Conical Indenter R =.6 µm Berkovich Indenter Modulus Ratio E inf / E o Conical Indenter R =.6 µm Berkovich Indenter Maximum Load, L (mn) Maximum Load, L (mn) E /E is a measure of polymer elasticity 3

33 Tuesday, May 8 Discussion / Conclusions Need better standards for testing mechanical behaviour of viscoelastic materials Vendor nominal DMA Dynamic Nano-Indentation E (GPa) E (GPa) E (GPa) E (GPa) E (GPa) PS PS Creep measurement techniques allow for measurements of short E and long E values in the same test. When stating E values, time frames of methodology employed must be specified. 33

34 Tuesday, May 8 Discussion / Conclusions Sharp indenters (i.e. Berkovich) are challenging due to additional time-independent plastic deformation under sharp contact. Obtained modulus values are smaller than true elastic modulus of the material : conical / pyramidal analysis still under investigation. Results from conical analysis are largely independent of max. applied force for Berkovich and Conical (R =.6 µm) indenter tests. Deviation of modulus values was observed at low loads where indenter geometry is spherical. 34

35 Tuesday, May 8 Next Steps: Apply spherical analysis to Creep indentation test + use spherical indenter with R > µm. Creep indentation tests vs. Greg/Louise predictions on modelled polymeric materials. Analyse creep data when applying a constant strain rate step load. (In collaboration with Cambridge University) Aim: Identify the agreement between methods as a route to validation of indentation derived viscoelastic property measurements. Draft ISO New Work Item 35