DIC to Stud Deformations * Jajam, Tippur, Int. J. Solids/Structures, Strains from DIC
Sub image Size Effect a) b) c) d) Contours of displacement from piel sub-images (a, b) indicate nois data, while piel sub-images (c, d) indicate over-smoothing of raw data. The former shows the crack tip location more precisel compared to the latter. * Bedsole, Tippur, ASME J. Eng. Materials, 3 Digital Gradient Sensing (DGS): A New Method for Static and Dnamic Deformation Measurement 4
Transmission DGS Eperimental setup Digital camera B Transparent specimen L F O Q speckled target P L >> L >> ROI (paraial appro.) z * Periasam, Tippur, Applied Optics, 6 3
B A C O R Working Principle Unit vector along OQ, dˆ iˆ ˆjkˆ S S ˆ d iˆ ˆjkˆ Optical path change in the specimen*, deformation*, S, B n zz d z B B n d z B Q D Refractive inde change, n, D zz E P z Normal strain zz : zz zz ( ) E * Periasam, Tippur, Applied Optics, 7 or, Governing equations zz S BD n D dz B E degree of plane strain for plane stress, D D n E D n E S (, ) CB C D E n The unit vector along OQ can also be written as*, S S ˆ d iˆ ˆjkˆ negligible thickness average elasto-optic material constant * Periasam, Tippur, Applied Optics, 8 4
Governing equations Now, S S dˆ iˆ ˆ jkˆ. Recall, dˆ iˆ ˆj kˆ and S (, ) CB Therefore, CB CB * Periasam, Tippur, Applied Optics, 9 Governing equations A B C For small angular deflections and plane stress appro*, O R D P Q E CB CB where, z C D E n * Periasam, Tippur, Applied Optics,
transmission DGS: Advantages t-dgs takes advantage of optical transparenc of the material; No need to decorate samples with speckles; measurements are digital. Not all transparent materials are birefringent; measurements are analog. Measurement sensitivit can be easil controlled (increased) b changing and without changing (decreasing) the ROI. Possible to amplif the signal using the optical arm if stiff materials (glass, spinel) have to be studied. In-plane rigid bod translations do not contribute to the gradient field. Stresses can be estimated b numericall integrating DGS data. In fracture problems, locating the crack tip is easier due to the nature of the mechanical field measured (r -3/ variation). Line load on the edge of an elastic sheet 6
Loading configuration and results (r, ) F 8 mm 7 mm 3 Angular deflection contours F = 77 N F = N F F = 77 N mm mm F = N (r, ) F mm mm Contour interval = -3 radians 4 7
Angular deflection fields: Flamant s solution (r, ) F cos rr B r,, r F 8 mm C B C B Angular deflection field equations: F cos CB B r F sin CB B r., 7 mm Stresses from stress gradients Resultant angular deflection, F CB Br Also recall, Therefore, (r, ) F cos rr B r rr r cos CB F = N - - -8 6 8
Dnamic Crack Growth Long-bar Speckle Target Putt Specimen Long-bar Tip Flash Lamps Camera Lens Thickness = 8.6 mm = mm, fps * Sundaram, Tippur, Eperimental Mechanics, 7 Measured Crack Tip Fields t = 3 s t = 6 s t = 9 s mm t = 3 s t = 6 s t = 9s t = corresponds to crack initiation at the original notch tip; crack speed 3 m/sec 8 9
Fracture of Laered Materials interface t = 3 s t = 6 s t = 8 s t = 3 s mm t = 3 s t = 6 s t = 8 s t = 3 s t = corresponds to crack initiation at the original notch tip 9 Reflection DGS
Working principle specimen specimen O w t O (,) camera L beam splitter r i i n r target plate target plate P Q (, ) z Camera is focused on the target plane via the reflective specimen and through the beam splitter Incident and reflected ras make angle = i + r w Therefore, surface slope, tan tan * Periasam, Tippur, Measurements Science and Technolog, 3 Surface slopes of a silicon wafer Si wafer glued to steel washer (inner dia =.7 mm) using epo silicon wafer = 66 mm beam splitter (4 ) Reference image recorded Central deflection, w = 3 m applied using micrometer micrometer steel washer L target plate Perturbed speckle pattern (deformed image) recorded Obtain and, and hence w, and w, camera * Periasam, Tippur, Measurements Science and Technolog, 3
Surface slope contours w 4( ; ) w Analtical epressions: log ; R R w 7.. 3 7.. 3 w 3. 7. 7.. 3 mm mm Contour levels: -4 radians 3 Topograph: Applied Displacement µm b a w d b a w d * Jain, Tippur, Optics & Lasers in Engineering, () 4
DGS for Transient Impact Studies Specimen Flash lamps Steel ball impactor Target plate High speed camera Beam Splitter Specimen holder Beam Splitter holder Specimen holder PMMA disk specimen Beam splitter Target plate tilt stage * Jain, Tippur, Optics & Lasers in Engineering, () High speed Speckle Images t = sec t = µsec t = 4 µsec t = 36 µsec t = 48 µsec t = 6 µsec 3 dia disk 3
Time resolved Surface Slopes t = sec -3 3 t= µsec t=4 µsec r w contours mm - - -3 t=36 µsec t=48 µsec t=6 µsec Contour increments 3 4 rad Time resolved Surface Slopes t = sec 3-3 t= µsec t=4 µsec r w contours mm - - -3 t=36 µsec t=48 µsec t=6 µsec Contour increments 3 4 rad 4
Transient Surface Slopes -3 t= µsec 4. t= µsec t=4 µsec 4 r w w mm 3. 3... t=36 µsec t=48 µsec t=6 µsec Contour increments 3 4 rad Transient Surface Topograph 4 8 Displacement(µm) 6 4 radius(mm) µs 4µs 36µs 48µs 6µs Solid lines are from FEA and smbols are from r DGS