Given the current trends of globalization and active competition, the reduction of the lead time in transfer of new alloys and design is critical. Virtual testing and design using finite element (FE) analyses may contribute to this reduction. Indeed, FE analysis has been applied extensively to compare design options, understand the influence of process conditions on both formability and structural performance and to reduce the trial and error in the development of tools for optimum performance. However, for realistic simulations the use of improved constitutive models for the description of the mechanical behaviour and accurate prediction of formability are essential. Key is the use of well-posed yield functions which are applicable to any type of loadings and a correct and efficient implementation in the FE framework. As discussed in the first part of this talk, for general three-dimensional (3-D) loadings, the onset of irreversible plastic deformation in fully dense metallic materials is defined in terms of fifth-dimensional yield surfaces. Given that the fabrication process induces plastic anisotropy, formulation of well posed yield surfaces is a great challenge. An argument that is widely used for justifying the use of 2-D yield criteria  for simulation of complex engineering problems is related to the fact that well-posed 3-D orthotropic yield criteria contain at least six anisotropy coefficients and as such there are increased uncertainties related to parameter identification . Indeed, the larger number of parameters involved in 3-D yield criteria is one of the reasons for the popularity of yield functions termed as plane-stress. In this talk are presented new mathematical results concerning widely used orthotropic plane stress yield surfaces. It is shown that the manner in which the material’s anisotropy is introduced in these formulations leads to inconsistencies in terms of predicted mechanical behavior. Discussions concerning the calibration procedures for these yield functions and the manner in which Lankford coefficients are calculated using these 2-D formulations are provided. Inconsistencies in the mathematical derivations are put into evidence. Next, the numerical schemes presently used to implement these 2-D orthotropic yield functions are analyzed and examples of sheet forming applications are presented. Next, possible corrections of the mathematical formulations and robust numerical algorithms are discussed. Examples and comparisons with published FE results and data obtained in cup drawing experiments on textured aluminum alloys are provided.

 

References:

Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Lege, D.J., Pourboghrat, F., Choi, S.H. and Chu, E., 2003. Plane stress yield function for aluminum alloy sheets—part 1: Theory. Int J Plast, 19(9), 1297-1319.

Yoon, J.W., Barlat, F., Dick, R.E., Chung, K. and Kang, T.J., 2004. Plane stress yield function for aluminum alloy sheets—part II: FE formulation and its implementation. Int J Plast, 20(3), 495-522.

 

 


New Representations of Anisotropic Yield Functions and Implications in Terms of Calibration and Predictive Capabilities (Part II)

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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