{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/50624"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/50624","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Determination of grain-level strain and proposing a new method of strain determination for three dimensional x-ray diffraction (3DXRD)","abstract":"A new approach for lattice strain determination is proposed for analysis of three dimensional x-ray diffraction (3DXRD) data. Our objective is to establish a correspondence between lattice strain and change of diffraction spot position in $\\omega$ ($\\omega$ is the rotation angle about the loading axis for 3DXRD experiment), using far-field configuration. The final goal is to apply the same concept to extract subgrain level strain from near-field data (near-field has less resolution in 2$\\theta$. $\\theta$ is the scattering angle for diffraction). The method is developed using the far-field 3DXRD data obtained from an \\textit{in-situ} experiment of a Ti-7Al alloy sample. The experiment is conducted at beamline- 1 ID of the Advanced Photon Source at Argonne National Laboratory. A high-resolution monochromator is used to get high strain resolution. The specimen is subjected to combined bending and uniaxial tensile loads up to yield at highest local stress points. Far-field images are collected in two ways- (a) at each $0.5^o$ rotation about the loading axis from $-180^o$ to $180^o$ (coarse scan),(b) at each $0.05^o$ rotation about the loading axis from $-180^o$ to $0^o$ (fine scan). A near-field data collection is carried out simultaneously. A study of the stress gradient developed in the Ti-7Al sample is performed using lattice strain determination algorithm taking care of the grain precession. A map of grain orientation in the cross-section of the sample is determined through use of the near-field technique. A state of bending with superposed tension is revealed through correlation of the near-field grain map with the far-field strain and center of mass (COM) result. Lattice strain induced changes of $\\omega$ are found for all scattering vectors of individual grains. It is plotted against the final $\\omega$ positions of the scattering vectors. Such plots are generated for every individual grain indexed by \\textit{GrainSpotter}. The theoretically determined values of change of $\\omega$ ($\\Delta\\omega_{model}$) follow a sinusoidal pattern when plotted against the final $\\omega$ positions (the effect of grain precession on lattice strain is taken care of in the theoretical calculations). The experimentally found values of change of $\\omega$ ($\\Delta\\omega_{meas}$ or $\\Delta\\omega_{log}$) may or may not show the similar coorespondence depending on the lattice orientation and lattice strain. The magnitude of the $\\Delta\\omega_{model}$ is found to be lower than the magnitude of the $\\Delta\\omega_{meas}$ or $\\Delta\\omega_{log}$. The fine scan proves to be more informative than the coarse scan for study of shift of $\\omega$ position of a diffraction spot with change of load.","abstract_html":"A new approach for lattice strain determination is proposed for analysis of three dimensional x-ray diffraction (3DXRD) data. Our objective is to establish a correspondence between lattice strain and change of diffraction spot position in ω (ω is the rotation angle about the loading axis for 3DXRD experiment), using far-field configuration. The final goal is to apply the same concept to extract subgrain level strain from near-field data (near-field has less resolution in 2θ. θ is the scattering angle for diffraction). The method is developed using the far-field 3DXRD data obtained from an \\textit{in-situ} experiment of a Ti-7Al alloy sample. The experiment is conducted at beamline- 1 ID of the Advanced Photon Source at Argonne National Laboratory. A high-resolution monochromator is used to get high strain resolution. The specimen is subjected to combined bending and uniaxial tensile loads up to yield at highest local stress points. Far-field images are collected in two ways- (a) at each 0.5o rotation about the loading axis from -180o to 180o (coarse scan),(b) at each 0.05o rotation about the loading axis from -180o to 0o (fine scan). A near-field data collection is carried out simultaneously. A study of the stress gradient developed in the Ti-7Al sample is performed using lattice strain determination algorithm taking care of the grain precession. A map of grain orientation in the cross-section of the sample is determined through use of the near-field technique. A state of bending with superposed tension is revealed through correlation of the near-field grain map with the far-field strain and center of mass (COM) result. Lattice strain induced changes of ω are found for all scattering vectors of individual grains. It is plotted against the final ω positions of the scattering vectors. Such plots are generated for every individual grain indexed by \\textit{GrainSpotter}. The theoretically determined values of change of ω (\\Deltaωmodel) follow a sinusoidal pattern when plotted against the final ω positions (the effect of grain precession on lattice strain is taken care of in the theoretical calculations). The experimentally found values of change of ω (\\Deltaωmeas or \\Deltaωlog) may or may not show the similar coorespondence depending on the lattice orientation and lattice strain. The magnitude of the \\Deltaωmodel is found to be lower than the magnitude of the \\Deltaωmeas or \\Deltaωlog. The fine scan proves to be more informative than the coarse scan for study of shift of ω position of a diffraction spot with change of load.","abstract_has_math":true,"creators":["Chatterjee, Kamalika"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Beaudoin, Armand J."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-09-16T17:24:28Z","date_published":"2014-09-16T17:24:28Z","updated_at":"2026-07-22T22:25:40Z","subjects":["x-ray diffraction","far-field","near-field","high resolution monochromator","lattice strain","center of mass","grain map","diffraction spot position","bending trend"],"languages":["en"],"rights":["Copyright 2014 Kamalika Chatterjee"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/50624","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Beaudoin, Armand J."]},{"key":"dc:creator","label":"Author","values":["Chatterjee, Kamalika"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-09-16T17:24:28Z","2014-08","2014-09-16"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["x-ray diffraction","far-field","near-field","high resolution monochromator","lattice strain","center of mass","grain map","diffraction spot position","bending trend"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2014 Kamalika Chatterjee"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/50624"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A new approach for lattice strain determination is proposed for analysis of three dimensional x-ray diffraction (3DXRD) data. Our objective is to establish a correspondence between lattice strain and change of diffraction spot position in $\\omega$ ($\\omega$ is the rotation angle about the loading axis for 3DXRD experiment), using far-field configuration. The final goal is to apply the same concept to extract subgrain level strain from near-field data (near-field has less resolution in 2$\\theta$. $\\theta$ is the scattering angle for diffraction). The method is developed using the far-field 3DXRD data obtained from an \\textit{in-situ} experiment of a Ti-7Al alloy sample. The experiment is conducted at beamline- 1 ID of the Advanced Photon Source at Argonne National Laboratory. A high-resolution monochromator is used to get high strain resolution. The specimen is subjected to combined bending and uniaxial tensile loads up to yield at highest local stress points. Far-field images are collected in two ways- (a) at each $0.5^o$ rotation about the loading axis from $-180^o$ to $180^o$ (coarse scan),(b) at each $0.05^o$ rotation about the loading axis from $-180^o$ to $0^o$ (fine scan). A near-field data collection is carried out simultaneously. A study of the stress gradient developed in the Ti-7Al sample is performed using lattice strain determination algorithm taking care of the grain precession. A map of grain orientation in the cross-section of the sample is determined through use of the near-field technique. A state of bending with superposed tension is revealed through correlation of the near-field grain map with the far-field strain and center of mass (COM) result. Lattice strain induced changes of $\\omega$ are found for all scattering vectors of individual grains. It is plotted against the final $\\omega$ positions of the scattering vectors. Such plots are generated for every individual grain indexed by \\textit{GrainSpotter}. The theoretically determined values of change of $\\omega$ ($\\Delta\\omega_{model}$) follow a sinusoidal pattern when plotted against the final $\\omega$ positions (the effect of grain precession on lattice strain is taken care of in the theoretical calculations). The experimentally found values of change of $\\omega$ ($\\Delta\\omega_{meas}$ or $\\Delta\\omega_{log}$) may or may not show the similar coorespondence depending on the lattice orientation and lattice strain. The magnitude of the $\\Delta\\omega_{model}$ is found to be lower than the magnitude of the $\\Delta\\omega_{meas}$ or $\\Delta\\omega_{log}$. The fine scan proves to be more informative than the coarse scan for study of shift of $\\omega$ position of a diffraction spot with change of load.","Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-07-18T16:33:59Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Chatterjee_Kamalika.pdf: 16339065 bytes, checksum: 9f4d8ad2edc123d6c938068bc0f57938 (MD5)","Made available in DSpace on 2014-09-16T17:24:28Z (GMT). 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The final goal is to apply the same concept to extract subgrain level strain from near-field data (near-field has less resolution in 2$\\theta$. $\\theta$ is the scattering angle for diffraction). The method is developed using the far-field 3DXRD data obtained from an \\textit{in-situ} experiment of a Ti-7Al alloy sample. The experiment is conducted at beamline- 1 ID of the Advanced Photon Source at Argonne National Laboratory. A high-resolution monochromator is used to get high strain resolution. The specimen is subjected to combined bending and uniaxial tensile loads up to yield at highest local stress points. Far-field images are collected in two ways- (a) at each $0.5^o$ rotation about the loading axis from $-180^o$ to $180^o$ (coarse scan),(b) at each $0.05^o$ rotation about the loading axis from $-180^o$ to $0^o$ (fine scan). A near-field data collection is carried out simultaneously. A study of the stress gradient developed in the Ti-7Al sample is performed using lattice strain determination algorithm taking care of the grain precession. A map of grain orientation in the cross-section of the sample is determined through use of the near-field technique. A state of bending with superposed tension is revealed through correlation of the near-field grain map with the far-field strain and center of mass (COM) result. Lattice strain induced changes of $\\omega$ are found for all scattering vectors of individual grains. It is plotted against the final $\\omega$ positions of the scattering vectors. Such plots are generated for every individual grain indexed by \\textit{GrainSpotter}. The theoretically determined values of change of $\\omega$ ($\\Delta\\omega_{model}$) follow a sinusoidal pattern when plotted against the final $\\omega$ positions (the effect of grain precession on lattice strain is taken care of in the theoretical calculations). The experimentally found values of change of $\\omega$ ($\\Delta\\omega_{meas}$ or $\\Delta\\omega_{log}$) may or may not show the similar coorespondence depending on the lattice orientation and lattice strain. The magnitude of the $\\Delta\\omega_{model}$ is found to be lower than the magnitude of the $\\Delta\\omega_{meas}$ or $\\Delta\\omega_{log}$. The fine scan proves to be more informative than the coarse scan for study of shift of $\\omega$ position of a diffraction spot with change of load.","Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-07-18T16:33:59Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Chatterjee_Kamalika.pdf: 16339065 bytes, checksum: 9f4d8ad2edc123d6c938068bc0f57938 (MD5)","Made available in DSpace on 2014-09-16T17:24:28Z (GMT). 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