On the formability limits of thin-walled tube inversion using different die fillet radii

Tube Expansion by Single Point Incremental Forming: An Experimental and Numerical Investigation

“…The first part of this section summarizes the methods and procedures that were utilized to determine the material flow curve and the formability limits by necking (FLC) and by fracture under tension (FFL) using conventional tube forming processes. The data provided in the figures were retrieved from previous publications of the authors [9][10][11][12].…”

“…Figure 2 shows the formability limits of the aluminum AA6063-T6 tubes by necking (FLC) and by fracture under tension (FFL) in principal strain space. Determination of the FLC required measuring the strain paths of conventional tube expansion, inversion and bulging by means of digital image correlation (DIC) and combining these results with time-dependent and force-dependent methodologies that were specifically developed by the authors for tube materials [11,12]. Determination of the FFL required measuring the wall thickness of the tube cracked regions by optical microscopy (D software version 5.11.01, NIS-Elements, Tokyo, Japan)to obtain the "gauge length" strains at fracture.…”

“…The corresponding effective strain at fracture ̅ = 1.17 was obtained from Equation (4) and defines a dashed ellipse of constant effective strain values in principal strain space (refer to both Figures 8 and 9). The comparison of the results obtained for incremental tube expansion against those obtained for conventional tube expansion with a rigid tapered conical punch [9][10][11][12] allowed identifying two main differences regarding material flow and cracking. First, incremental tube expansion is performed under biaxial stretching conditions, whereas conventional tube expansion subjects the material to near pure tension.…”

“…No 2 of 18 methodologies for characterizing the crack opening modes and determining the fracture forming lines were proposed until 2016, when Centeno et al [9] utilized CGA to plot the FLC and the FFL corresponding to tube cracking by tension. Subsequent research work combining numerical methods, digital image correlation (DIC) and making use of a broader range of tube forming processes comprising expansion [10], inversion [11] and bulging [12] allowed obtaining the FLC and the FFL of tube materials for a wider range of strain paths running from uniaxial tension up to equal biaxial stretching (e.g., from strain ratios β = dε 2 /dε 1 ranging between −1/2 to 1). These efforts were recently complemented by the work of Magrinho et al [13], who proposed an experimental procedure to determine the SFFL of tube materials (i.e., the fracture forming limit line corresponding to tube cracking by in-plane shear).…”

On the effect of anisotropy on the performance and simulation of shrinking tubes used as energy absorbers for railway vehicles

“…Numerous numerical models have been developed to assess the strain fields, which demonstrate high correlation against test data. These include those based on force balance of membranes [19], balance of forces [21] [22], energy balance [23] [24] [25], circle grid analysis [26] [27] [28], and eccentric compression [29], with consideration also made for shear effects [30]. Whilst primarily based on expanding steel, models have also been developed for use with aluminium [31].…”