A hybrid method for detecting the onset of local n

Authors: Bertrand Galpin Vincent Grolleau Arnaud Penin Gérard Rio

Publish Date: 2015/02/10

Volume: 9, Issue: 2, Pages: 161-173

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Abstract

Strainbased Forming Limit Diagrams FLD which are typically obtained under linear or quasilinear loading conditions describe the limiting strains in terms of the major and minor inplane strains before the onset of necking or the final failure FFD These strains can be detected by analysing the strain field in the vicinity of necking or cracking defects It has generally been agreed that the loading versus time signal is not suitable for detecting necking processes A novel hybrid method of detecting the onset of necking based on the experimental and simulated bulging load is presented in this paper This method consists mainly in comparing the experimental forming load ie a load showing plastic instability with the numerical predictions obtained by performing finite element simulation The simulation of the bulging process does not include any damage or failure criteria A homogeneous forming load can therefore be simulated without requiring any information about the localization This method was applied to detecting the onset of local necking in circular and elliptic quasistatic bulge tests on sheet material with a diameter of 200 mm Two materials were tested a 08 mm thick DP450 Dual Phase steel sheet and a 1 mm thick AA6016T4 aluminium sheet The onset of necking observed with our method was compared with the results obtained by performing Hogström’s analysis based on the measured strain field over time and similar necking strains were obtained Beside the Bressian Williams Hill BWH shear criterion was identified for each test from experimental results A slight scattering of the shear stress values was observedγFh was calculated in two stages In the first stage the ratio Rh was calculated with various values of h The values of Fexpe and Fsimu pertaining in the case of identical displacements were not available Interpolations were therefore performed on the cloud of dots corresponding to the experimental loads which were simulated using fourthorder polynomials in the windows width L centred on the value h of the displacement at which it was intended to calculate Rh Fexpeh and Fsimuh could then be calculated Rh + ∆h was determined by sliding the overlapping interpolation window We took ∆h = 002 L The value of the function Rh was therefore known only at some values of h Secondly we again interpolated the dots in Rh into the window L using an order 3 polynomial where the coefficients ai Rh=a0+a1h+a2h2+a3h3 were identified It was then possible to explicitly determine the second derivative of Rh γFh = 2a2 + 6a3h It sufficed to slide the overlapping interpolation window in order to calculate γFh+∆h in the same way taking ∆h = 001 LThe sensitivity of the width of the window was then studied Decreasing L was found to result in changes in the value of Rh and hence in that of γFh These values stabilised in a range of L values before becoming sensitive to changes in L The influence of L observed here was probably attributable to the small number of dots available in the window for defining the polynomial satisfactorily It was therefore decided to select the size of L in the range in which Rh was stabilised

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