TSOM Webinar on Instrumented Indentation.. Dr. Ilja Hermann

Transcription

1 TSOM Webinar on Instrumented Indentation. Dr. Ilja Hermann

2 Outline Motivation Theory of instrumented-indentation Experimental aspects NanoForce Application examples

3 Motivation Why do we need mechanical properties? Wear Failure Analysis Virtual Tests Tribology Mechanical Properties Materials design Understand and prevent irreversible deformation November 19, 015 3

4 Motivation Fundamentals of mechanical properties Stress and Strain : Constitutive Equation : Normal Stress Normal Strain F σ = A l ε = l σ ij = Sijklε kl + Sijklmnε klε mn +... Shear Stress Shear Strain F τ = A tanγ = x h November 19, 015 4

5 Motivation Measuring mechanical properties Hooke: ε ν = ε 1 11 σ = ij Sijklε kl homogenious, isotropic: σ E = ε Test & specimen: Uniaxial tension/compression Bending Acoustic wave Properties: E, ν, K, G, Y 0, K I => Mechanical properties on macroscopic scale November 19, 015 5

6 Motivation Hardness test Concept: 1. Apply load.. Analysis of residual imprint after load removal VICKERS- Hardness number F HV = d [Applied load] = kgf [Diagonal] = mm Fracture- Toughness K I a = l 1 E H 3 c F 3 F Applied load (N) H Hardness (Gpa) E Young s Modulus (Gpa) c,a,l distances from img (m) Pros: Simple application Small specimen Easy to scale Cons: HV difficult co-relate to physical properties Scaling limited by imaging resolution No elastic properties November 19, 015 6

7 Motivation Instrumented indentation Concept: 1. Accurate measurement of compliance curve. Elastic analysis of tri-axial stress-state in contact Nano-indentation Elastic-plastic Typical load: ~10 mn Typical depth: ~100 nm Property access: E, H, Y, K I, σ Rep (ε Rep ) =>Mechanical properties on mesoscopic scale November 19, 015 7

8 Theory of Nano-indentation Fundamentals of contact mechanics Obtaining contact stress field and surface deformation p(r,φ) 1 ν u z = p( r, φ) drdφ πe σ, ε =? Superposition σ i, ε i Point-contact solution November 19, 015 8

9 Theory of Nano-indentation Elastic surface deformation Contact Geometry Pressure distribution Mean pressure Surface Deflection (r=0) Surface Deflection (r=a) Flat Punch 1 σ 1 z r = 1 ( 1 ν ) h = F p m a Era Sneddon: Sphere (Hertz) σ z p m 3 r = 1 a 1 p m = HB = 4E r a 3π R 3F h = 4 Er R 3 f (r) = Br n h e = ε F S with Cone 1 σ a π (Sneddon) ( 1 ν ) F = cosh h = p m z 1 r E r tanα m ε = m 1 1 Γ (m ) π m Γ (m 1) November 19, 015 9

10 Theory of Nano-indentation Hertzian contact stress Tensile stress Von Mises stress ( σ σ ) + ( σ σ ) + ( σ σ ) + 6* ( τ + τ τ )) 1 σ = von Mises xx yy zz yy xx zz xy xz + zy Principal stress σ 1 (a.u.) Von Mises Stress (a.u.) Related material failure modes Hertzian cone fracture Residual imprint by sub-surface plasticity November 19,

11 Theory of Nano-indentation Elastic-plastic indentation 0.07 a R = cos(α) > 0.5 Ideal cone/pyramid: elastic-plastic transition occurs instantly Stress field during unloading altered by elastic constraint plastic zone σ = σ i +σ R November 19,

12 Theory of instrumented-indentation Oliver & Pharr method Fitting unloading curve: Contact stiffness: Contact depth: Tip calibration: Reduced modulus: c S h c = df dh F = h max ε S c( hc ) = c+ a0h c + a1h c + ahc + a3h c a4hc A = A + E F = a(h h 0 ) m r F max π = β A = ma( h h0) c S m 1 Effective indenter Indentation modulus: Indentation hardness: h c = h max ε F S E p H = p = f(r)=br n r 1 ν p 1 1 ν i Er Ei F A c A i, m, a, h 0 fit parameters ; ε, β contact model parameters (Sneddon, Oliver&Pharr resp.) E i, ν i elastic indenter properties ν p..poisson ratio of specimen November 19, 015 1

13 Theory of instrumented-indentation Quasi-Static vs. Dynamic indentation Oliver&Pharr: Dynamic indentation m d u dt i σ x σ = ij j ij Sijklε kl F i = 0 d h( t) dh( t) iωt m D Kh( t) = F0 e dt dt i( h( t) = h e 0 ω t+φ ) Contact mechanics S = df dh Fmax h c = h max ε F S A c = A c (h c ) Oscillator theory Missing Contact mechanics! H = F A c E r π = β A c S H = F A c E ' = r E '' = r π F0 cos( φ) β A h c 0 β π Ac 0 F0 sin( φ) h November 19, 015

14 Experimental aspects Typical test setup Calibrations: Tip-shape Load frame compliance in-line tool offsets Specimen requirements: Roughness Flatness Mounting stiffness November 19,

15 Experimental aspects High-level corrections during raw-data post-processing Thermal drift h th = h t driftholdtime t First order estimate from drift during the unloading hold time. Validity assumes linear-elastic bahaviour, stationary drift, and a total drift << h max, h creep, h hystersis etc. Frame Compliance: h = frame F S i Treated as superposition of HOOKEian compliances for load frame deformation small compared to contact 1 S r 1 1 = S S i c Zero-Point correction: " h zero = h zero Depth at intersect of loading curve and abscissa. HERTZian contact fit with fit parameter A and the zero offset h zero F " " " " ( h ) = A( h hzero ) 3 Metrology chain corrections at a glance: Contact model h = h h F " " hzero hth hframe = h" t h zero t driftholdtime Si November 19,

16 November 19,

17 System overview Microscope for inspection pre- and pre- and post-test Actuator housing Thermal/Acoustic/ Seismic hood Coaxial optical lenses and AFM Quantitative property assessment: HIT, EIT, E, E, Y, K IC, σ Rep (ε Rep ), F Crit., topography Electromagnetic actuator (indentation loads between 0. un and 45 mn) Three-plate capacitor (indentation depth up to 40 um) Load control Depth- and strain-rate control by S/W feedback control Berkovich tip is included; misc. different indenter geometries optional; easy switch In-line microscope with coaxial turret optics and AFM are standard Automatic multi-specimen handling (magnetic, vacuum, mech. clamp mounting) Internal (3-plate) capacitance sensor housing November 19,

18 Experimental aspects Loading profile Controlled channels: Force (H/W) Displacement (S/W FBC) Strain (S/W FBC) Profile element types: Constant Increasing/decreasing Calculated (custom) Harmonic Full loading profile: Sequence of different element types & control modes November 19,

19 System data sheet Indentation head Load Resolution (un) Load noise floor PP (un) 0.05 max peak load (mn) 45 min peak load (mn) 0.01 min contact force (un) 0. Displacement Resolution (nm) noise floor rms (nm) 0.1 max displacement (um) 40 Dynamics Minimum Force amplitude (un) 0.05 Maximum Force amplitude (un) 1900 Bandwidth (Hz) Natural frequency oscillator air (Hz) 10 Drift System in contact (ppm/k) 1.54 Pre-test drift threshold (nm/s) 0.01 Indenter options misc., including Berkovich, Cube corner, Vickers, Conical, Flat punch Specimen holder Automatic ally handled up to 4 max. diameter (mm) 5.4 max. height (mm) 10 min. lateral dimension (mm) max diameter on Vacuum chuck (mm) 00 Platform Max. stage travel X (mm) 154 Max. stage travel Y (mm) 110 Max. stage travel X, useable (mm) 64 Max. stage travel Y, useable (mm) 65 Stage resolution XY (um) 0.1 Max. stage travel Z (mm) 3 Max. stage travel Z, useable (mm) 7 Stage resolution Z (nm) 34.6 Frame stiffness (10^6 N/m) 17.9 Imaging Optical objective magnifications.5x, 8x, 0x, max FOV (um) 41 min FOV (um) 8 Color Yes Screen Magnification max (x) 717 Illumination Bright-field std.; Dark-filed optional NanoLens objective (AFM) standard, topographical imaging Z range (um) XY range (um) 110 Environment Thermal-, acoustic- and seismic insulation hood included November 19,

20 Typcial Nanoindentation test AFM & Optical View (for test positioning ; here post-imaging of surface with 9 indents at different surface locations) Indentations Force-Displacement curves (Indentations at 9 different surface locations) Cube corner into Si (100) Berkovich into HPFS 1.5 um 1.7mm 1. Test positioning. Applying the test method (running indent-loading profile and analysis) 3. Post inspection of tested surface area November 19, 015 0

21 How small the testing object can be (indenter tip not to miss target spot )? Experiment: AFM 10-times Indent After indent #1 After indent #10 Timeline Target Even after subsequently adding 9 more indents, all tests remain <0.5 um away from target position Video: ftp://tmtftp.bruker-nano.com/tmt/outgoing/nanoforce/nano-dart.m4v => Nanoforce can perform NI experiments on specimen under 1 um lateral size

22 Instrument calibration

23 h Model, Hertz= 3F Er R 4 = h Frame Compliance S i Extraction of Load-Frame stiffness from HERTZian contact modeling 3 Experiment With: Tip radius R from AFM (calculations with radius as function of depth (R(h)) Best Fit for 3 reference materials (Fused Silica, Sapphire (0001) and Si (100)) F S i This is what we are after here Best fit: Frame stiffness ~.5 N/um (good agreement with. N/um from elasticplastic indentation by load-over-stiffness-square method (F/S )) November 19, 015 3

24 Example: modified Berkovich tip Tip Area-function A c The perfect one ( α ) tan A ( h) = 3 h = 4.49h γ tan With: α: included face-angle to axis of symmetry : 65.7 o γ: included angle between pyramid base-lines: 60 o h: height of pyramid apex above base Reality check: Direct tip characterization by NanoLens AFM Tip apex radius ~40 nm (Note: that is comparable with a typical indentation depths and cannot be neglected) Conclusion: Direct tip characterization if possible with NF. However, there is a quicker, and more accurate way quantify A c.

25 Indirect method: Tip Area-function A c Indentation into material with well-known properties, then reverse contact contact modeling Typical results dynamic indentation A ( h ) c c π βer S( h ) = c This is corrected for S i already E(h c ) if were calculated with ideal A c Modulus F/S Hardness Force-Displacement curve (corrected raw-data) November 19, 015 5

26 Tip Area-function A c Typical results - quasi-static indentation: E(h c ) if were calculated with ideal A c Modulus Force-Displacement curve (corrected raw-data) Hardness November 19, 015 6

27 Results on other typical reference materials Hardness- and Modulus-measurements on for instrument verification and calibration. BK7 BK7 HPFS HPFS Not any material makes a suitable reference material. Some key requirements : homogenous, isotropic, linear-elastic (with well-known elastic constants), surface w/o contamination ; low roughness November 19, 015 7

28 Surface Roughness measurement Topographical surface pre-inspection with AFM HPFS (Fused Silica), Contact, 56pts/ln Result: RMS ~0.9 nm Impact on experimental design: => Indentations must be deeper than ~0 nm (>0 x h) to neglect surface micro-structure in contact model November 19, 015 8

29 Thin film applications

30 Traditional approaches to measure thin-film Hardness Example: Hardness by Indentation into 100 nm DLC Oliver&Pharr: 10 % rule [1] Film hardness if data within: h c <0.1d S = df dh Fmax h c = h max ε F S A c = A c (h c ) F H = A Film hardness from Interpolation []: H f ' = H s H H f s 1 h D 1+ B d Compound Hardness! [1] H. Buckle, Metallurgical Reviews 4, London, Institute of Metals, (1959) 49 [] X.Z. Hu and B.R. Lawn: A simple indentation stress strain relation for contacts with spheres on bilayer structures. Thin Solid Films 3, 5 (1998). November 19, 015

31 Cyclic (quasi-static) measurements of thermal-sio on Silicon Strain-rate controlled indentation with Berkovich tip and 30 partial unloading cycles, applied to SiO of different thickness on Si (100) substrate: 50 nm Bulk Si: ~164 GPa 100 nm 300 nm Bulk Bulk SiO :~7 GPa Note: Noisy data; property-depth-profile recognize-/quantify- able. Modulus shows strong gradient even for the thickest film Effective ~50 nm depth: 137 Gpa, 110 Gpa, 83 Gpa, 71.8 Gpa (thin=>bulk) November 19,

32 Dynamic measurements of thermal-sio film on Silicon Strain-rate controlled indentation with Berkovich tip and superimposed nm harmonic excitation 10 Hz on various thickness SIO on Si (100) on substrate: 50 nm 100 nm 300 nm Bulk Si: ~164 GPa Bulk Bulk SiO :~7 GPa Note: Dynamic test data are much less noisy! Modulus- and hardness- gradients exhibit clear trend Effective 50 nm depth is still disclosing significant substrate-effect November 19, 015 3

33 Cube Corner β A = ( α ) tan 3 h γ tan With: α: included face-angle to axis of symmetry : 35.6 o β: included angle between ribs: 90 o γ: included angle between pyramid base-lines: 60 o β α = a sin tan γ tan h: height of pyramid apex above base November 19,

34 Dynamic measurements of thermal-sio film on Silicon Strain-rate controlled indentation with Cube corner tip and superimposed nm harmonic excitation 10 Hz on various thickness on Si (100) on substrate: 50 nm Bulk Si: ~164 GPa 100 nm 300 nm Depth-profile converges when substrate-effect becomes negligible Bulk Bulk SiO :~7 GPa Note: With dynamics and sharper (Cube corner) tip the Young s modulus of SiO films can be measured practically independent on thickness down to 50 nm film thickness. November 19,

35 Quasi-static measurements with Cube Corner of thermal-sio film on Silicon Strain-rate controlled indentation with Berkovich tip and 30 partial unloading cycles, applied to SiO of different thickness on Si (100) substrate: Modulus 50 nm 100 nm 300 nm Bulk Si: ~164 GPa Hardness Bulk Bulk SiO :~7 GPa Depth-profile converges when substrate-effect becomes negligible Hardness-/Modulus coincidence at shallowest depths with sharper tip is independent on the loading dynamics (completely different models used) November 19,

36 Cube corner What happens when we change the tip angle? Berkovich Indentation strain goes up for CC Cube corner: sharper tip angle => pile-up, radial fracture due to buildup of stress-intensity November 19,

37 Static vs. instrumented Hardness on metals Example: Hardness standard reference block 74HV1 Static : HV = ( 75.0 ±11.4) mm H = 7.11± 0.11 Instrumented : H = 9.8 ± 0.17 ( )GPa ( )GPa Poor agreement with traceable Hardness -standard! Topographical pile-up analysis -V +V - A c Apply correction to Vickers imprint into 74 HV1 Correction: A c,afm = 1+ A C A C A c,op A C A C 6% Static Instrumented Accurate traditional instrumented tests require correction of pile-up! November 19, 015

38 Role of pile-up for a 50 nm Cube corner indent on var. coating thickness Film thickness Volume analysis of pile-up 50 nm 100 nm 300 nm Pile-up volume scales approx. inversely-proportional with film thickness. While quasi-static measurements would become erroneous, dynamic measurements help to minimize this impact from measuring thin-film properties November 19, 015

39 Summary thin films Accuracy improvement for measurements on a sub-100 nm coatings possible with: Noise surpression by superimposed dynamics and low-pass filtering Dynamics to take in account for pile-up Cube corner tip to reduce the apex radius November 19,

40 Brittle material characterization November 19,

41 Nano-indentation results Fracture toughness Step 1: Measure Hardness and Young s modulus of the specimen Step : Produce a series of indentations at different loads and surface locations Step 3: Image indents to find critical load for fully developed set of lead corner radial cracks Step 4: Calculate Fracture toughness : Cube Corner [1]: Berkovich []: Method inputs: E Young s modulus H hardness P test load a, c, l.distances from image [1] D. S. Harding, W. C. Oliver and G. M. Pharr: Mat. Res. Soc. Symp. Proc., 356, 1995, 663. [] R. Dukino and M.V. Swain, J. Am. Ceram. Soc. 75 1, 199, 399 November 19,

42 Nano-indentation results Fracture toughness BK7 HPFS Cube Corner: Method Inputs: E Young s modulus H hardness P test load c.distance from image BK7 glass is ~ twice as tough as synthetic Silica November 19, 015 4

43 Characterization of metallic single crystals November 19,

44 Quasi-static indentation with multiple-partial unloading Modified Berkovich tip on Aluminum (110) single crystal F krit Initial elastic-plastic transition can be observed at ~0uN Perfect elastic partial unloading cycles (no hysteresis) Pop-ins appear associated to the beginning / end of a partial unloading cycle November 19,

45 Dynamic indentation on single crystals: Cube Corner tip on Copper (110) and (111) orientations F crit Cu (110) Cu (111) The (111) orientation appears stiffer than the (110) orientation The (111) orientation exhibits pop-in events at approx. 10 un load November 19,

46 Indentation Creep November 19,

47 Quasi-static indentation with multiple-partial unloading and CREEP Cube corner on Aluminum (110) single crystal OM AFM P max Indentation Creep found to be CIT~6% constant load Most significant contributor to depth-increase during peak-load-hold time are pop-in events (Plastic flow/ dislocation mobility) November 19,

48 (Soft) Polymers November 19,

49 (soft) Polymers Quasi-static indentation on PDMS with cube corner tip ( very sharp on very soft ) EIT=( ) Mpa HIT=( ) Mpa EIT=( ) Mpa HIT=( ) Mpa CIT=(5+-9) % CIT=( ) % Repeatable raw-data due to precise load-control below 10 un Both PDMS-blends clearly distiguished at hand of raw-curves (F(h), h(t)) Resultant YOUNG s modulus is in line with expectations (3.5 Mpa &.5 MPa resp. for PeakForce QNM) Indentation creep exceeds 30% November 19,

50 Adhesion November 19,

51 Adhesion Quasi-static indentation on PDMS with 50 um conical tip Nano-Indenter gives insights into new more complex contact physics: Contact model with stiction (DMT) 4 3 P indenter = Er Rd + P 3 Adhesion R=50um R=5 um Obtain quantitative data : DMT modulus, ~1 Mpa Adhesion Energy dissipation Surface deformation R=.5 um Tip-stiction forces was approach (and pull-off) down to.5 um radius November 19,

52 Scratch November 19, 015 5

53 Scratch Mixed loading profile: Dynamic indentation combined with Creep and scratch => Conical tip R=.5 um on AR glass coating on float glass 50 x OM (50 x opt & 5 x digital) F crit ~4mN 50 x OM Note: Coating starts chipping here PreIMG PostIMG 0 x OM Single test method run tests to measure E, E, H, CIT and Scratch resistance

54 Other misc. applications November 19,

55 Precision of head mount and Indenter tip mounting NanoForce tip shape options: mod. Berkovich Cube Corner Vickers Conical R=Var Flat Punch R=Var Requires remove/reinstall tip Experiment: Measure remaining pos. accuracy after tip change Cube Corner tip => Berkovich tip Pos error ~7 um and re-calibrate inline offset Berkovich Tip => Conical tip Pos error ~5 um Quiz: What if re-cal is skipped?: Answer: No big problem: pos accuracy remain better 10 um! ( and is this is not enough best accuracy is just s fe clicks away (no new indent required) November 19,

56 Optical Microscope.5x 5x 8x Silicon or smooth, reflective surfaces in Bright-field optional Skin or rough, absorbing surfaces: Dark-field BF.5x 10x 0x 50x AFM Vs. dark-field DF.5x Standard FOV All pixels Resolution ~500nm opt; ~1.6 nm AFM scanner >3000x total magnification + digital zoom Bright-field illumination; Optional: Extra objectives & Dark-field November 19,

57 Hardness measurement with Sharp (cone/pyramid) - the traditional way Static Concept: 1. Apply load. Analysis of residual imprint after load removal Apply static concept with NanoForce 1. Apply loading profile + (static load) Calculate number F HV = d (OM image) Direct method. -difficult to co-relate to physical properties -No elastic properties [Applied load] = kgf [Diagonal] = mm. Direct measurement of actual- or projected contact area A c by AFM 3. Calculate Hardness 4. Convert to other hardness scales. November 19,