PSI - Issue 13

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

1315

4

(a)

(b)

Fig. 3. (a) The dependence of shear fraction over temperature from the DWTT specimens along three loading directions; (b) The fracture surfaces of the DWTT specimens at -10 °C along three loading directions. 3. Models In order to describe the degradation induced by damage, a damage variable D has been incorporated into the yield criterion f and flow potential g based on the small strain theory. Detailed descriptions about the enHill48 plasticity model and the MBW damage mechanics model are given in Lian et al. (2017b) and Lian et al. (2013), respectively. Only some key equations are briefly summarized here. � � �� , � � , � , � , � , � , � � � �� � � ∙ � � ̅ � � � � (1) � � �� , � � , � , � , � , � , � � � �� � � ∙ � � ̅ � � � � (2) � is the equivalent stress, is the stress tensor and � is the flow stress as a function of plastic strain ̅ � in the reference direction. F , G , H , L , M and N are anisotropic parameters which can be determined by different ways. In the enHill48 model based on the non-associated flow rule, anisotropic parameters in the yield criterion are determined by flow stresses while those in the flow potential are determined by r-values. These anisotropic parameters are also dependent on the equivalent plastic strain (PEEQ). According to the non-associated flow rule, the flow direction can be determined as: � � � � � � � (3) � is the plastic multiplier. In the phenomenological hybrid damage mechanics model, the softening induced by damage starts once the local damage initiation criterion is reached. The criterion is described by a critical damage initiation plastic strain ̅ �� , which is a weighted function of local stress state, the stress triaxiality and the normalized Lode angle parameter ̅ . In this extended version, the material parameters � ~ � in the damage initiation criterion are dependent on the loading direction angle with respect to the rolling direction. ̅ �� � � � �� ∙ �� �� ∙� � �� ∙ �� �� ∙� � ∙ ̅ � � �� ∙ �� �� ∙� (4) After the damage initiation, damage accumulation is controlled as a linear and isotropic function of the equivalent plastic strain rate. �� is the flow stress at the onset of damage initiation and � is a material parameter that controls the energy dissipation rate. ̅ �� � is the equivalent plastic strain at the fracture moment under a given stress state. Once the critical value of the damage variable �� under a certain stress state is reached, the final ductile fracture is triggered. � � � �� � � ∙ ̅ � � (5) �� � � � � �� � � �� � ̅ � (6)