Partially coupled anisotropic fracture model for aluminum sheets

Abstract The objective of the present paper is to incorporate the effect of plastic anisotropy on the fracture modeling of aluminum alloy 6061-T 6 sheets. Six different types of tests were performed to fracture, including tensile tests on classical dog-bone specimens, flat specimens with cutouts, plane strain grooved specimens, and punch indentation tests on circular blanks. A limited number of shear/tension tests on butterfly specimens were performed on a dual-actuator loading frame. Plastic properties were determined from the dog-bone tensile tests, and were verified by the remaining tests. It was found that the sheets exhibited little planar anisotropy but substantial out-of-plane anisotropy, characterized by the Lankford parameter, r. A comprehensive numerical analysis of the experiments revealed that the Hill 1948 quadratic anisotropic yield model is able to describe, with good accuracy, the plastic response of all five types of tests. Fracture surface strains were measured using a digital image correlation system. Average fracture strains were determined by measuring post-fracture thickness reduction. Local fracture strains were determined by means of an inverse engineering method involving matching the displacement to fracture from numerical simulations to those measured. Possible discrepancies between the magnitudes of the fracture strain in the three above methods are discussed. Based on the previous experience of the investigating team, the experimental fracture data were analyzed within the realm of the three-parameter Modified Mohr–Coulomb fracture model. Using the plane stress anisotropic plasticity equations, the calibrated fracture model was then transformed to the space of the equivalent strain to fracture and stress triaxiality. An alternative representation of the fracture locus in the space of principal strains was also constructed. Other important factors influencing the form of the fracture locus, such as mesh-size effect and solid versus shell representation, were also investigated.

[1]  Yuanli Bai,et al.  Application of extended Mohr–Coulomb criterion to ductile fracture , 2009 .

[2]  A. Atkins,et al.  Upsetting of Cylinders: A Comparison of Two Different Damage Indicators , 2001 .

[3]  F. Barlat,et al.  Yield function development for aluminum alloy sheets , 1997 .

[4]  R. Hill.  Constitutive modelling of orthotropic plasticity in sheet metals , 1990 .

[5]  Frédéric Barlat,et al.  Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions , 1989 .

[6]  D. Mohr,et al.  Large deformation of anisotropic austenitic stainless steel sheets at room temperature: Multi-axial experiments and phenomenological modeling , 2008 .

[7]  A. P. Karafillis,et al.  A general anisotropic yield criterion using bounds and a transformation weighting tensor , 1993 .

[8]  Stephen F. Corbin,et al.  The influence of iron content on the plane strain fracture behaviour of AA 5754 Al–Mg sheet alloys , 2002 .

[9]  F. Barlat,et al.  Plane stress yield function for aluminum alloy sheets—part 1: theory , 2003 .

[10]  Toshihiko Kuwabara,et al.  Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations , 2007 .

[11]  T. Wierzbicki,et al.  A new model of metal plasticity and fracture with pressure and Lode dependence , 2008 .

[12]  Xiaosheng Gao,et al.  Effects of the stress state on plasticity and ductile failure of an aluminum 5083 alloy , 2009 .

[13]  Tomasz Wierzbicki,et al.  Prediction of plane strain fracture of AHSS sheets with post-initiation softening , 2010 .

[14]  D. Mohr,et al.  A New Experimental Technique for the Multi-axial Testing of Advanced High Strength Steel Sheets , 2008 .

[15]  Imad Barsoum,et al.  Rupture mechanisms in combined tension and shear : Experiments , 2007 .

[16]  Glenn J. Grant,et al.  Formability Investigation of Aluminum Extrusions under Hydroforming Conditions , 2000 .

[17]  R. E. Dick,et al.  Plane stress yield functions for aluminum alloy sheets , 2002 .

[18]  Mitsutoshi Kuroda,et al.  Path-dependence of the forming limit stresses in a sheet metal , 2007 .

[19]  Otmar Kolednik,et al.  A note on calibration of ductile failure damage indicators , 1995 .

[20]  Ted Belytschko,et al.  A local space-time discontinuous finite element method , 2006 .

[21]  Stelios Kyriakides,et al.  Inflation and burst of anisotropic aluminum tubes for hydroforming applications , 2008 .

[22]  W. Hosford.  A Generalized Isotropic Yield Criterion , 1972 .

[23]  Dirk Mohr,et al.  Calibration of Stress-triaxiality Dependent Crack Formation Criteria: A New Hybrid Experimental–Numerical Method , 2007 .

[24]  A. H. van den Boogaard,et al.  A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states , 2006 .

[25]  R. Hill.  A theory of the yielding and plastic flow of anisotropic metals , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.