PSI - Issue 13

Fuhui Shen et al. / Procedia Structural Integrity 13 (2018) 1312–1317 Author name / Structural Integrity Procedia 00 (2018) 000–000

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1. Introduction Advanced high strength steels with improved mechanical properties have been widely applied to various industries. In the meanwhile, the ductile damage and fracture behaviors of these advanced materials are more complicated due to their complex microstructures. A variety of damage mechanics models have been proposed to describe the degradation and failure (Bai and Wierzbicki (2008, 2010); Lou et al. (2014); Mohr and Marcadet (2015)), which can be classified into coupled and uncoupled groups according to Besson (2009). In the recent development of damage mechanics, the effects of the Lode parameter, which is related to the third invariant of the stress tensor, have attracted increasing interest of researcher, like Bai and Wierzbicki (2010); Lou et al. (2014); Mohr and Marcadet (2015). In the uncoupled models, fracture is assumed to be triggered once the critical value of a specific variable is reached, which is taken as a weighted function of the stress state (Bai and Wierzbicki (2008, 2010); Lou et al. (2014); Mohr and Marcadet (2015)). For the coupled approach, the damage induced softening is taken into account from the beginning of plastic deformation such as in the continuum damage mechanics (CDM) models (Lemaitre (1985)) and the micromechanical GTN type models (Gurson (1977)). Lian et al. (2013) have integrated the Bai–Wierzbicki (BW) uncoupled fracture model into the continuum damage mechanics framework to formulate the MBW model, which is a hybrid approach to consider the stress state effects on the plasticity, damage initiation, damage evolution and fracture behaviors of advanced high strength steels. This model has been applied to describe various deformation properties with high accuracy. It has been extended to consider the loading history effects by Wu et al. (2017) and cleavage fracture behavior by He et al. (2017) recently. However, one important feature of plastic deformation in terms of anisotropy has not been included so far. Due to the previous forming process, such as rolling, strong anisotropy effects on the mechanical properties of metallic materials could be induced. Many constitutive models have been proposed to capture the anisotropic plasticity behaviors, such as the simple quadratic Hill48 model (Hill (1948)) and those advanced non-quadratic ones (Barlat et al. (2005); Barlat et al. (2003)). The conventional Hill48 model cannot describe the stress and r-value directionality simultaneously. The advanced non-quadratic ones have their drawbacks due to the complicated materials parameter calibration procedure and the related implementation difficulties for complex forming simulations. Therefore, the non associated flow rule-based Hill48 model has been proposed by Stoughton (2002), in which both the stress and r-value directionality can be well captured simultaneously. It has been also noted that these anisotropic features are changing during the deformation process. In order to well describe the evolving features of anisotropic deformation, an evolving non-associated Hill48 model (enHill48) has been formulated by Lian et al. (2017b). It has been successfully applied to predicting the forming limit curves of a strong anisotropic material with a very good agreement with experimental results (Lian et al. (2017a); Lian et al. (2017b); Lian et al. (2018); Shen et al. (2018)). The aim of this research is to couple the enHill48 plasticity model with the MBW damage mechanics model and then apply this coupled anisotropic damage mechanics model to investigating the ductile damage and fracture behavior of a high strength steel plate. 2. Materials and Experiments The material used in this investigation is a X70 pipeline steel that has been produced after the thermal mechanical control process (TMCP). A 2 mm thick sheet has been manufactured from the 1/3 position of the heavy plate and various types of flat specimens have been produced from the sheet. Typical smooth dog bone specimens have been used to perform uniaxial tensile tests at room temperature and under quasi-static condition (strain rate of 1×10 -4 s -1 ) according to the European standard EN 10002-1 to characterize the flow behaviors of this material. Tensile tests have been performed along seven different loading directions (15° as an interval) with respect to the rolling direction to investigate the in-plane anisotropic plasticity behaviors of the material. Three parallel tests have been performed for each angle and during the experiments both the stresses and the Lankford coefficients (r-value) along different loading directions are determined. The true stress-strain curves and the r-values along three directions are determined until the uniform elongation point as shown in Fig. 1. The experimental results show that the anisotropic flow behaviors of this material are quite obvious. The flow stress along the transverse direction is the highest and that is the lowest along the diagonal direction. The r-value along the diagonal direction is higher than the other two directions. It is also obvious that the r-values are not constant during the deformation process.