Damage evaluation and measurement via correlation techniques

Transcription

1 Damage evaluation and measurement via correlation techniques (Schadensbewertung und Messung mit Korrelationstechniken) François HILD & Eikology team

2 2 Damage / Fracture Challenges Need for reliable kinematic fields Robust and validated models Outline Evaluation of damage via DIC and DVC Design of discriminating experiments (e.g., concrete) Summary and perspectives

3 3 Damage / Fracture Challenges Need for reliable kinematic fields Robust and validated models Outline Evaluation of damage via DIC and DVC Design of discriminating experiments (e.g., concrete) Summary and perspectives

4 4 Digital Image Correlation Measurement of optical flow I0( x) I t ( x u( x)) Local approach u I ( x) I ( x u) 2 c 0 t ZOI ( I0 t 0 t u ZOI I )( u) I ( x) I ( x ) 2 Fluid mechanics : PIV [Barker et al., 1977 ; Grousson et al., 1977 ; Dudderar and Simpkins, 1977] Solid mechanics : DIC [Kanade et al., 1981 ; Burt et al., 1982 ; Sutton et al., 1983]

5 5 Local Approach u y (µm) Cloud of points

6 6 Standard Practice in Commercial Codes

7 7 Global Approach Measurement of optical flow I0( x) I t ( x u( x)) Global approach (FE bases*) u x N (x) m a i i ROI a I 0( x) ( x um( x)) 2 c I t i 2 *[Besnard et al., 2006, Exp. Mech. 46 pp ]

8 8 Local Approach u y (µm) Cloud of points

9 9 Global Approach u y (µm) Dense and continuous field [Leclerc et al., 2009, in LNCS 5496 pp ]

10 10 Mechanical Regularization Gray level conservation 2 a I ( x) ( x u ( x)) Internal equilibrium 2 EQ t t a a K K a Boundary regularization 2 t t a a L L 2 tot 0 m c I t EP a a a w a w a c ROI EQ EQ EP 2 EP [Réthoré et al., 2009, Europ. J. Comput. Mech. 18 pp ] [Tomičević et al., 2013, J. Strain Anal. 48 pp ]

11 11 New Length Scale(s) Choice: plane wave for v(x) = v 0 e ik x 2 c ( v) k EG ( v) k and EP ( v) k Weights w reg proportional to 4 reg 4 log(2 tot ) Regularization DVC Cross-over scale reg log( k )

12 12 Global Approach u y (µm) Dense and continuous field [Leclerc et al., 2009, in LNCS 5496 pp ]

13 13 Reguralized Approach (mechanical filter) u y (µm) Dense, continuous and filtered field

14 14 Cracks?

15 15 Reguralized Approach (w/ Crack) u y (µm) ( x) I0( x) ( x u ( x)) I t m

16 16 Reguralized Approach (w/ Crack) u y (µm) ( x) I0( x) ( x u ( x)) I t m

17 17 Mechanical Regularization w/ Damage Gray level conservation Internal equilibrium with 2 tot a I ( x) ( x u ( x)) m 2 c 0 I t ROI ~ ~ t a a K K a 2 EQ ~ [ K e ] [ K e ](1 D a a w a w a c EQ e t ) EQ D e D EP 2 1 exp EP e 1 0 m *[HF et al., 2015, Int. J. Fracture 191(1-2) pp ]

18 18 Reguralized Approach (w/ Crack) u y (µm)

19 19 Reguralized Approach w/ Damage u y (µm)

20 20 Reguralized Approach w/ Damage u y (µm)

21 21 Reguralized Approach w/ Damage 1

22 22 Cracks in 3D?

23 23 X-Ray Imaging 3 rd generation synchrotron facilities Lab tomograph

24 24 X-Ray Computed Tomography X-Ray tube Sample Detector Rotating stage Radiographs 3D rendering after 1000 projections reconstruction

25 25 Digital Volume Correlation Local approach* I I )( u) I ( x) I ( x ) ( 0 t 0 t u ZOI Global approach** a I 0( x) ( x um( x)) 2 c I t ROI Regularized approach*** 2 tot a a w a w a c EQ EQ EP EP 2 ***[Bay et al., 1999, Exp. Mech. 39(3) pp ] ***[Roux et al., 2008 Compos. Part A 39(8) ] ***[Leclerc et al., 2011, Exp. Mech. 51(4) pp ]

26 26 3-Point Flexural Test on Plaster 1 voxel 25 µm

27 27 3-Point Flexural Test on Plaster Crack visualization?

28 28 3-Point Flexural Test on Plaster Maximum principal strains? Elastic strains?

29 30 Quantified Cracking 8voxels m b 60 voxels

30 31 Quantified Cracking 8voxels m b 60 voxels

31 34 Quantified Cracking 8voxels m 4 b 60 voxels w/ damage

32 36 Multiple Cracking? 1 voxel 50 µm l = 12 voxels l m = l b = 30 voxels [Bouterf, 2014, PhD thesis, ENS Cachan]

33 37 Multiple Cracking 1 voxel 50 µm l = 12 voxels l m = l b = 30 voxels COD (voxel) [Bouterf, 2014, PhD thesis, ENS Cachan]

34 38 Interim Summary 2D & 3D imaging: very powerful (qualitative) tool! DIC and DVC: quantitative tools Damage quantification in brittle materials

35 39 3D imaging: big data 4D extensions DVC: Outlook big and fast calculations multiscale analyses robust when localization or damage set in Quantitative assessments of damage Model identification and validation

36 40 Smart Testing with DIC Loaded sample or structure Measurement Quantity of interest: Displacement, crack tip, SIF Experiment Boundary conditions Model Hexapod kinematics Crack path: manual control (interactive procedure) real time (hybrid procedure)

37 41 Hexapod

38 42 YES NO convergence DIC-Controlled Hexapod DOF com L V computation PID L Veq 20Hz I-DIC GPUs Cam(1) solver Cam(i) Cam(n) [Le Flohic et al., 2014, Exp. Mech. 54(5) ]

39 43 DIC All Over The Place U shaped BC RBM Plates z y x

40 D Simulations Driven by Measured BCs [Carpiuc et al., 2017, Cem. Concr. Res. 100 pp ]

41 45 P (kn) P s (kn) Macroscopic Validation? Longitudinal Response Transverse Response d (mm) Experimental test Damage model d s (mm) Experimental test Damage model

42 46 Nonlocal Damage Model

43 47 Cracking Pattern Back Face Front Face Couloir

44 U [mm] R [rad] Interactive Test X comm X LVDT Y comm Y LVDT Y DIC Loading steps: Time [s] x x Z comm Z LVDT Z DIC Rx comm Rx LVDT 0. Elastic load-unload 1. Rotation & shear + 2. Shear 3. Rotation 4. Shear + 5. Rotation 6. Shear 7. Traction z y Rx DIC Ry comm z y Ry LVDT Rz comm 5 Rz LVDT Time [s] x 10 4 [Carpiuc et al., 2017, Eng. Fract. Mech. 176 pp. 1-22] z y 3

45 49 Fy [kn] Shear force [kn] Rotation + Shear Time [s] x 10 4

46 50 Fy [kn] Shear force [kn] Shear Time [s] x 10 4

47 51 Fy [kn] Shear force [kn] Rotation Time [s] x 10 4

48 52 Fy [kn] Shear force [kn] Shear Time [s] x 10 4

49 53 Fy [kn] Shear force [kn] Rotation Time [s] x 10 4

50 54 Fy [kn] Shear force [kn] Shear Time [s] x 10 4

51 55 Shear Fy force [kn] [kn] Tension Time [s] x 10 4

52 56 Hybrid Test Control - LEFM u z u x Desired crack path K I /K II u z =1 u y =1 Geometry update Bifurcation angle Crack tip Sensitivity matrix Inverse problem U Z /U Y Williams fields Measurement Mechanical loading

53 57 Hybrid Test

54 58 Virtual Hybrid Test* *[Jailin et al., 2017, J. Mech. Phys. Solids 102 pp ]

55 59 Virtual Hybrid Test

56 60 Hybrid Test z y U Z [px] IDIC 0.55 [px] Crack tip detection IDIC: Williams [1957] fields (LEFM) [Roux et al., 2006] for straight cracks [Réthoré, 2015] for curved cracks [Carpiuc, 2015, PhD thesis ENS Cachan]

57 61 Hybrid Test U Z [px]

58 62 Hybrid Test

59 63 Summary Evaluation of damage in brittle materials via DIC and DVC Design of discriminating experiments (e.g., concrete) DIC benchmark DIC-driven tests optimized tests

60 64 Vielen Dank für Ihre Aufmerksamkeit!