Hoefnagels, J.P.M.

Vermeij, Tijmen

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 Integrated DIC based HR-EBSD: High accuracy androbustnessCitation for published version (APA):Vermeij, T., & Hoefnagels, J. P. M. (2018). Integrated DIC based HR-EBSD: High accuracy and robustness.Poster session presented at EBSD 2018, Plymouth, United Kingdom.https://doi.org/10.13140/RG.2.2.18834.96962DOI:10.13140/RG.2.2.18834.96962Document status and date:Published: 01/04/2018Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 04. Oct. 2023See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/325105548Integrated DIC based HR-EBSD: High accuracy and robustnessPoster · April 2018DOI: 10.13140/RG.2.2.18834.96962CITATIONS0READS172 authors:Some of the authors of this publication are also working on these related projects:Size-effects in time-dependent anelasticity of thin metal films View projectAdvancing High angular Resolution EBSD (HR-EBSD) through full-field Integrated Digital Image Correlation (IDIC) View projectTijmen VermeijTechnische Universiteit Eindhoven8 PUBLICATIONS   4 CITATIONS   SEE PROFILEJohan HoefnagelsTechnische Universiteit Eindhoven127 PUBLICATIONS   1,229 CITATIONS   SEE PROFILEAll content following this page was uploaded by Tijmen Vermeij on 12 May 2018.The user has requested enhancement of the downloaded file.Integrated DIC based HR-EBSDPart I: High accuracyand robustnessTijmen Vermeij&Johan Hoefnagelsj.p.m.hoefnagels@tue.nlEindhoven University of Technology, Department of Mechanical Engineering, Den Dolech 2, 5612 AZ Eindhoven, The NetherlandsMechanics of Materials Groupfg⇤ ~xpc0⇤ ~xpc~x0⇤ ~xpc0⇤ ~xpc~x00~x0~x~u~ex~ey~ezSample	surfaceIncident	e-beam⇤ ~xpc0⇤ ~xpc0pcpc0~x00~x000dddd0Phosphor	screen~x00~x0~ex~ey~ezFr0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-40 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4E11 = 3 · 10 4E12 = 1.5 · 10 4E22 = 2 · 10 4E33 =  2.1 · 10 4E11 = 1.2 · 10 3E12 = 5 · 10 4E22 =  8 · 10 4E33 =  1.7 · 10 4E11 =  7.5 · 10 3E12 = 0E22 = 3 · 10 3E33 = 1.9 · 10 30 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq✏E✏✓qSmall	strainEeq = 5 · 10 4Eeq = 2 · 10 3Eeq = 1 · 10 2Medium	strainLarge	strain0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq  1201p2x✓q y✓q z✓q1p21p2 01p2  121p2Quaternion	axes:EBSD 2018 Plymouth Generic full-field Integrated DIC framework for HR-EBSDStarting point: brightness conservation HR-EBSD geometry• Plane stress assumption for hydrostatic expansion coefficient• Optional contrast/brightness relaxation for remedying inaccurate background subtractionConvergence and Robustness-0.015-0.01-0.0050.0100.0050.010.0150-0.01 0.010-0.01200 400 600 800 1000 1200 1400200400600800100012001400200 400 600 800 1000 1200 1400200400600800100012001400200 40 60 80 100 12 140200400600800100012001400200 400 600 800 100 120 1400200400600800100012001400(g)0 1 2 3 4 5iterations10-610-410-2100mean(|r|)||b||F11F12F13F21F22F23F31F320 1 2 3 4 5iterations10-610-410-2100mean(|r|)||b||F11F12F13F21F22F23F31F320 1 2 3 4 5iterations10-610-410-2100mean(|r|)||b||F11F12F13F21F22F23F31F320 1 2 3 4 5iterations10-610-410-2100mean(|r|)||b||F11F12F13F21F22F23F31F32(-1°)(1°)(-1°)(1°)-0.0100.010.010.0100-0.01 -0.01Initial guessAfter convergencefReference	gROIDeformed	gROIInitial	guess	residual;	mean(|r|) =	24.4Converged	residual;	mean(|r|)	=	2.610-5-101110-510-50 10-1 -110-1 100 101 102Noise level [%]10-510-410-3E[-]050100150200No. of iterationsENo. of iterations✏✓z✏✓y✏✓xiteratiomean(|r|)||b||Reference pattern Deformed and rotated patternResidual at initial guess (zero strain & 1º rotation error)All for “medium deformation” and 10º misorientationConvergence behaviour Residual after convergence Robustness to initial guess errorRobustness and accuracy with noise AccuracyAbsolute ErrorValidation on dynamically simulated patterns (generated using Bruker’s Esprit DynamicS)• One-step correlation of full field-of-view of EBSPs without filtering or remapping.• High strain accuracy (~110-5) for large rotations up to 10º, rivaling state-of-the-art HR-EBSD.• High robustness & rapid convergence from 1º misorientations with noise up to 20% / 5%.Conclusions{ } = Argmin Z⌦[r( ~x0, { })]2 d~xr( ~x0, { }) = f( ~x0)  g( ~x0 + ~u( ~x0, { }))One-step minimization of EBSP image residual w.r.t. DOFs:~u( ~x0, { }) =dd~ez · Fr · (dd0 ~ez + ~x0   ~x0pc)⇣Fr · (dd0 ~ez + ~x0   ~x0pc)  ~ez · Fr · (dd0 ~ez + ~x0   ~x0pc) ~ez⌘+ ~xpc   ~x0In-detector-plane displacement field, with !" components as DOFs:T. Vermeij, J.P.M. Hoefnagels, A consistent full-field integrated DIC framework for HR-EBSD, Submitted to Ultramicroscopy (2018)Digital Image Correlation(High angular Resolution Electron Backscatter Diffraction)(Degrees of freedom)(Deformation Gradient Tensor)View publication stats

Integrated DIC based HR-EBSD: High accuracy and robustness

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 Integrated DIC based HR-EBSD: High accuracy androbustnessCitation for published version (APA):Vermeij, T., & Hoefnagels, J. P. M. (2018). Integrated DIC based HR-EBSD: High accuracy and robustness.Poster session presented at EBSD 2018, Plymouth, United Kingdom.https://doi.org/10.13140/RG.2.2.18834.96962DOI:10.13140/RG.2.2.18834.96962Document status and date:Published: 01/04/2018Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 17. Nov. 2023See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/325105548Integrated DIC based HR-EBSD: High accuracy and robustnessPoster · April 2018DOI: 10.13140/RG.2.2.18834.96962CITATIONS0READS172 authors:Some of the authors of this publication are also working on these related projects:Size-effects in time-dependent anelasticity of thin metal films View projectAdvancing High angular Resolution EBSD (HR-EBSD) through full-field Integrated Digital Image Correlation (IDIC) View projectTijmen VermeijTechnische Universiteit Eindhoven8 PUBLICATIONS   4 CITATIONS   SEE PROFILEJohan HoefnagelsTechnische Universiteit Eindhoven127 PUBLICATIONS   1,229 CITATIONS   SEE PROFILEAll content following this page was uploaded by Tijmen Vermeij on 12 May 2018.The user has requested enhancement of the downloaded file.Integrated DIC based HR-EBSDPart I: High accuracyand robustnessTijmen Vermeij&Johan Hoefnagelsj.p.m.hoefnagels@tue.nlEindhoven University of Technology, Department of Mechanical Engineering, Den Dolech 2, 5612 AZ Eindhoven, The NetherlandsMechanics of Materials Groupfg⇤ ~xpc0⇤ ~xpc~x0⇤ ~xpc0⇤ ~xpc~x00~x0~x~u~ex~ey~ezSample	surfaceIncident	e-beam⇤ ~xpc0⇤ ~xpc0pcpc0~x00~x000dddd0Phosphor	screen~x00~x0~ex~ey~ezFr0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-40 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4E11 = 3 · 10 4E12 = 1.5 · 10 4E22 = 2 · 10 4E33 =  2.1 · 10 4E11 = 1.2 · 10 3E12 = 5 · 10 4E22 =  8 · 10 4E33 =  1.7 · 10 4E11 =  7.5 · 10 3E12 = 0E22 = 3 · 10 3E33 = 1.9 · 10 30 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq✏E✏✓qSmall	strainEeq = 5 · 10 4Eeq = 2 · 10 3Eeq = 1 · 10 2Medium	strainLarge	strain0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq0 1 2 3 4 5 6 7 8 9 10q [°]10-610-510-4Eq  1201p2x✓q y✓q z✓q1p21p2 01p2  121p2Quaternion	axes:EBSD 2018 Plymouth Generic full-field Integrated DIC framework for HR-EBSDStarting point: brightness conservation HR-EBSD geometry• Plane stress assumption for hydrostatic expansion coefficient• Optional contrast/brightness relaxation for remedying inaccurate background subtractionConvergence and Robustness-0.015-0.01-0.0050.0100.0050.010.0150-0.01 0.010-0.01200 400 600 800 1000 1200 1400200400600800100012001400200 400 600 800 1000 1200 1400200400600800100012001400200 40 60 80 100 12 140200400600800100012001400200 400 600 800 100 120 1400200400600800100012001400(g)0 1 2 3 4 5iterations10-610-410-2100mean(|r|)||b||F11F12F13F21F22F23F31F320 1 2 3 4 5iterations10-610-410-2100mean(|r|)||b||F11F12F13F21F22F23F31F320 1 2 3 4 5iterations10-610-410-2100mean(|r|)||b||F11F12F13F21F22F23F31F320 1 2 3 4 5iterations10-610-410-2100mean(|r|)||b||F11F12F13F21F22F23F31F32(-1°)(1°)(-1°)(1°)-0.0100.010.010.0100-0.01 -0.01Initial guessAfter convergencefReference	gROIDeformed	gROIInitial	guess	residual;	mean(|r|) =	24.4Converged	residual;	mean(|r|)	=	2.610-5-101110-510-50 10-1 -110-1 100 101 102Noise level [%]10-510-410-3E[-]050100150200No. of iterationsENo. of iterations✏✓z✏✓y✏✓xiteratiomean(|r|)||b||Reference pattern Deformed and rotated patternResidual at initial guess (zero strain & 1º rotation error)All for “medium deformation” and 10º misorientationConvergence behaviour Residual after convergence Robustness to initial guess errorRobustness and accuracy with noise AccuracyAbsolute ErrorValidation on dynamically simulated patterns (generated using Bruker’s Esprit DynamicS)• One-step correlation of full field-of-view of EBSPs without filtering or remapping.• High strain accuracy (~110-5) for large rotations up to 10º, rivaling state-of-the-art HR-EBSD.• High robustness & rapid convergence from 1º misorientations with noise up to 20% / 5%.Conclusions{ } = Argmin Z⌦[r( ~x0, { })]2 d~xr( ~x0, { }) = f( ~x0)  g( ~x0 + ~u( ~x0, { }))One-step minimization of EBSP image residual w.r.t. DOFs:~u( ~x0, { }) =dd~ez · Fr · (dd0 ~ez + ~x0   ~x0pc)⇣Fr · (dd0 ~ez + ~x0   ~x0pc)  ~ez · Fr · (dd0 ~ez + ~x0   ~x0pc) ~ez⌘+ ~xpc   ~x0In-detector-plane displacement field, with !" components as DOFs:T. Vermeij, J.P.M. Hoefnagels, A consistent full-field integrated DIC framework for HR-EBSD, Submitted to Ultramicroscopy (2018)Digital Image Correlation(High angular Resolution Electron Backscatter Diffraction)(Degrees of freedom)(Deformation Gradient Tensor)View publication stats

Integrated DIC based HR-EBSD: High accuracy and robustness

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