Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Application of the Continuous and Discontinuous Fields of Plastic Deformations to the Evaluation of the Initial Thickness of Bent Tubes J. Eng. Mater. Technol. 2016;139(1):011009-011009-10. doi:10.1115/1.4034944 Figure Legend: Scheme of a tube bending machine with a rotating template and a mandrel, (1) mandrel, (2) clamp bolt, (3) rotating template, (4) sliding slat, (5) planisher, (6) bed of sliding slat, (7) bending pipe, and (8) mandrels rod

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Application of the Continuous and Discontinuous Fields of Plastic Deformations to the Evaluation of the Initial Thickness of Bent Tubes J. Eng. Mater. Technol. 2016;139(1):011009-011009-10. doi:10.1115/1.4034944 Figure Legend: Scheme of the connection of a elbow and a straight section of a pipe when their internal and external diameters are equal, then (g1min  < gt), where gt is the thickness of the tube, rtm is the radius of the template, and m is the straight section of the elbow

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Application of the Continuous and Discontinuous Fields of Plastic Deformations to the Evaluation of the Initial Thickness of Bent Tubes J. Eng. Mater. Technol. 2016;139(1):011009-011009-10. doi:10.1115/1.4034944 Figure Legend: (a) and (b) The schemes of connections of elbows with straight sections of pipelines: (a) for the case when centering isdone on the external pipe side (both dext are equal), (b) forthe case when centering is done based on the internal pipe side (both dint are equal). In both cases, it should be, that (g0 > g1min > gt). Remaining parameters as on Fig. 2.

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Application of the Continuous and Discontinuous Fields of Plastic Deformations to the Evaluation of the Initial Thickness of Bent Tubes J. Eng. Mater. Technol. 2016;139(1):011009-011009-10. doi:10.1115/1.4034944 Figure Legend: Geometrical and dimensional quantities pertaining to tube-bending processes

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Application of the Continuous and Discontinuous Fields of Plastic Deformations to the Evaluation of the Initial Thickness of Bent Tubes J. Eng. Mater. Technol. 2016;139(1):011009-011009-10. doi:10.1115/1.4034944 Figure Legend: Schematic picture of the elbow cross section and its characteristic parameters

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Application of the Continuous and Discontinuous Fields of Plastic Deformations to the Evaluation of the Initial Thickness of Bent Tubes J. Eng. Mater. Technol. 2016;139(1):011009-011009-10. doi:10.1115/1.4034944 Figure Legend: Variation of the initial thickness versus R for four calculation methods, for α=β=0 deg, kαb=180 deg and (g0=g0ext max,g0′=g0ext max′,g0″=g0ext max″,g0‴=g0ext max‴)

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Application of the Continuous and Discontinuous Fields of Plastic Deformations to the Evaluation of the Initial Thickness of Bent Tubes J. Eng. Mater. Technol. 2016;139(1):011009-011009-10. doi:10.1115/1.4034944 Figure Legend: Variation of the maximum initial thickness (g0ext′=g0ext max′,g0int′=g0int max′) of the wall of a tube subjected to bending, calculated according to a simplification of the first order and in measures of logarithmic strains, versus the bending radius R, when the required minimum wall thickness of the bent elbow is g1 = 4.5 mm and (α=β=0 deg, kαb=180 deg)

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Application of the Continuous and Discontinuous Fields of Plastic Deformations to the Evaluation of the Initial Thickness of Bent Tubes J. Eng. Mater. Technol. 2016;139(1):011009-011009-10. doi:10.1115/1.4034944 Figure Legend: Exemplary calculations of longitudinal deformations φ1, depending on the neutral axis displacement y0, where (dz ≡ dext)

Date of download: 10/26/2017 Copyright © ASME. All rights reserved. From: Application of the Continuous and Discontinuous Fields of Plastic Deformations to the Evaluation of the Initial Thickness of Bent Tubes J. Eng. Mater. Technol. 2016;139(1):011009-011009-10. doi:10.1115/1.4034944 Figure Legend: Exemplary calculations of the wall thickness distribution g1, depending on the neutral axis displacement y0, where (dz≡dext)