Hardening laws, surface roughness and biaxial tensile limit strains of sheet aluminium alloys

The roles of hardening laws and surface roughness have been assessed in the prediction of biaxial tensile limit strains of two Al alloy sheet materials with different strain hardening characteristics namely AA6111-T4 and AA5754-O, utilizing the surface roughness model proposed by Parmar, Mellor and Chakrabarty [6]. In the work of Parmar et al., the predictions of limit strains were based on the Marciniak-Kuczynski inhomogeneity analysis and utilized the commonly used power hardening law (Hollomon equation) to describe the stress-strain behavior of the material. In the present work, (i) the suitability of a Voce hardening law, (ii) the effect of surface roughness parameters and (iii) the effect of grain size parameters on the prediction of biaxial limit strains has been studied. The biaxial limit strains based on Voce equation were obtained by modifying the set of equations of Parmar et al, and utilizing the experimentally measured surface roughness in 3-D, grain size parameters and stress-strain curves from uniaxial tensile and hydraulic bulge tests for the two Al sheet materials. The predictions from Voce and Hollomon equations have been compared with the experimental forming limits determined by hemispherical punch stretching of gridded blanks. The discrepancy between predictions from Holloman equation and experiments is small for the low strain hardening AA6111-T4 material but is quite significant for the high strain hardening AA5754-O material. Further, the predictions are also strongly dependent upon the measure of surface roughness and the grain size utilized in the calculations. The results indicate good predictions of limit strains for the two alloys when (i) stress-strain data from tensile or hydraulic bulge tests are fitted to a Voce equation and (ii) half of the maximum peaks-to-valley height and grain thickness are utilized as a measure of surface roughness and grain size respectively. The results are discussed in the context of the characteristics of the hardening laws, assumptions of surface roughness model and surface and grain characteristics of the alloys studied.