On the calculation of plastic strain by simple method under non-associated flow rule

- Simple method and full method for non-AFR are comprehensively compared.
- A restriction in calculating parameters in plastic potential function by simple method is clarified.
- The conditions in applying simple method for non-AFR are investigated.
- An effective approach is introduced to improve the applicability of simple method.

The non-associated flow rule (non-AFR), which has been proved with advantages in accurately predicting yield stress components and Lankford coefficients, has different definitions for yield function and plastic potential function. Currently, there are two typical approaches to determine the plastic strain for non-AFR, one is called simple method which still uses the equivalent plastic strain (EPS) to calculate the plastic strain tensor, while the other is called full method which adopts the plastic compliance factor. Many researchers prefer to adopt the simple method in calculating the plastic strain due to its higher computation efficiency and its acceptable accuracy like the full method for some materials. However, the limitation and application condition of the simple method are still ambiguous. In the present work, a restriction for calculating the parameters in plastic potential function for the simple method is clarified and the limitation of the simple method has also been investigated. It is found that if the relative error of the difference between the yield function value and that of plastic potential function is within ±5% and hardening exponent is in the range of 0.1-0.3, the maximum absolute value of the relative error of the stress predicted by the simple method can be controlled less than 1.6%. Besides, an effective approach is introduced to reduce the error of the stress predicted by these two methods, which can improve the applicability of the simple method for those materials with the relative error of the difference between the value of yield function and that of plastic potential function is less than 10%. In order to have deeper understanding about their applicability, the two methods are compared under uniaxial tension along different orientations for AA2090-T3 and AA2008-T4 with the fully implicit return-mapping scheme. Fracture simulations of AA2090-T3 have also been conducted by introducing different methods. The results show that during the loading in transverse direction, the difference of EPSs predicted by these two methods is very small for AA2008-T4, while for AA2090-T3, the EPS predicted by the simple method is almost twice of that calculated by the full method. This further indicates that the applicability of the simple method mainly depends on the characteristics of materials.