Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Methodology for Determining the Variance of the Taylor Factor: Application in Fe-3%Si J. Eng. Mater. Technol. 2006;129(1):82-93. doi:10.1115/1.2400268 Figure Legend: Definition of material space. The ith sample is shown cut out of the parent material. The various mathematical constructs used in the derivation of the statistical variance relationship are indicated.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Methodology for Determining the Variance of the Taylor Factor: Application in Fe-3%Si J. Eng. Mater. Technol. 2006;129(1):82-93. doi:10.1115/1.2400268 Figure Legend: The local state space as defined by the complete set all physically distinctive orientations for cubic sample symmetry known as the fundamental zone or SO(3)∕G. This space is three-dimensional and parametrized by the Euler angles φ1, Φ, and φ2. An orientation g in the tessellated space, SO(3)∕G, is shown within the tessera hj.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Methodology for Determining the Variance of the Taylor Factor: Application in Fe-3%Si J. Eng. Mater. Technol. 2006;129(1):82-93. doi:10.1115/1.2400268 Figure Legend: The volume of overlap of two equal rectangular regions (each defined by Ω) whose centers are separated by r⃗

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Methodology for Determining the Variance of the Taylor Factor: Application in Fe-3%Si J. Eng. Mater. Technol. 2006;129(1):82-93. doi:10.1115/1.2400268 Figure Legend: Coordinate system used to define the R-value in terms of a tensile sample where F is the applied force and w and t are the width and thickness of the tensile sample, respectively

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Methodology for Determining the Variance of the Taylor Factor: Application in Fe-3%Si J. Eng. Mater. Technol. 2006;129(1):82-93. doi:10.1115/1.2400268 Figure Legend: Six principal directions defined by the hexagonal scanning grid that was used for the OIM measurements. (The negative directions are shown but not labeled.)

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Methodology for Determining the Variance of the Taylor Factor: Application in Fe-3%Si J. Eng. Mater. Technol. 2006;129(1):82-93. doi:10.1115/1.2400268 Figure Legend: OIM scan of the surface of Fe-3%Si with grain orientation indicated by different false shades of gray. The window, Ω, placed in the scan defines the area in which the two-point statistics are sampled. Each material point in Ω (that was sampled in OIM to determine lattice orientation) is sampled by r⃗. The tail of the sampled vectors, r⃗, is allowed to fall outside Ω but the head is not as shown by the arbitrarily placed vector r⃗ in the figure. (The dimensions of the OIM scan must at least twice that of Ω so the statistics sampled by r⃗ are equally weighted for all lengths of r⃗.)

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Methodology for Determining the Variance of the Taylor Factor: Application in Fe-3%Si J. Eng. Mater. Technol. 2006;129(1):82-93. doi:10.1115/1.2400268 Figure Legend: The tensile samples cut from Fe-3%Si with the circle grid etched onto the surface. The base and height of the rectangles defined by Ω1 and Ω1 were determined by taking the average of the measurements taken at each indicated corner.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Methodology for Determining the Variance of the Taylor Factor: Application in Fe-3%Si J. Eng. Mater. Technol. 2006;129(1):82-93. doi:10.1115/1.2400268 Figure Legend: The effective Taylor factors are compared for 0<λ<1 as calculated according to Eq. . For this calculation the fundamental zone of orientations (SO(3)∕G) was tessellated using 512, 1728, and 4096 tesserae. The complete continuous (nondiscretized) dataset obtained from the OIM scan was also included for comparison.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Methodology for Determining the Variance of the Taylor Factor: Application in Fe-3%Si J. Eng. Mater. Technol. 2006;129(1):82-93. doi:10.1115/1.2400268 Figure Legend: Standard deviation of the effective Taylor factor over Ω=2.2×2.2mm

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Methodology for Determining the Variance of the Taylor Factor: Application in Fe-3%Si J. Eng. Mater. Technol. 2006;129(1):82-93. doi:10.1115/1.2400268 Figure Legend: Standard deviation of the effective Taylor factor over Ω=4.7752×9.5504mm. The terms λl=0.00 and λl=0.93 define the range of possible contractile strain ratios within the variation of M¯(λ).

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Methodology for Determining the Variance of the Taylor Factor: Application in Fe-3%Si J. Eng. Mater. Technol. 2006;129(1):82-93. doi:10.1115/1.2400268 Figure Legend: Standard deviation of the effective Taylor factor over Ω=9.5504×9.5504mm. The terms λl=0.02 and λl=0.87 define the range of possible contractile strain ratios within the variation of M¯(λ).