PSI - Issue 28

J. Xue et al. / Procedia Structural Integrity 28 (2020) 1047–1054 Author name / Structural Integrity Procedia 00 (2019) 000–000

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2. Finite element model 2.1. Material model

Recently, a round-robin investigation on the influence of constraint on fracture initiation for an X80 pipeline steel was conducted by Wilkowski et al. (2019). Although the round-robin considered only fracture initiation, a damage model that considered both initiation and propagation was explored by Xue et al. (2019). The model developed in this round-robin to describe the fracture initiation response of X80 was used in the current work to study the influence of biaxial stress states. In the model, the flow stress, � , of the material was described according to the true stress versus strain response for X80 in Wilkowski et al. (2019) given by � � ������������ � ̅ � � ���� (1) where ̅ � is the effective plastic strain. Isotropic (von Mises) deformation was assumed. The MMC model detailed by Bai et al. (2010) was used to model damage initiation. In this model, the strain to initiate fracture, � , depends on stress triaxiliaty, , and Lode angle, � . The initiation strain is given by, � � � � � � � � � �� √ √ � � �� � � � � � � � � � � � ��� �� ��� � � � � � � � � � � � � � � � � � � � � ���� � ��� (2) where � , � , � , , and n are material constants specific to a single temperature and strain rate. The damage is given by, � � � � � � � � � � (3) To calibrate the MMC damage initiation parameters, Paredes et al. performed a number of mechanical tests on X65 in Paredes et al. (2018) a, X70 in Paredes et al. (2016), and TC128 steel in Paredes et al. (2018) b, which included tensile tests, tests on notched round bars, biaxial tests, shear tests, and tests on flat specimens with circular cut-outs. These tests were required to produce a range of triaxiality and Lode angles for accurate model calibration. In additional to mechanical testing, several FEA simulations were carried out to calculate parameters such as stress triaxiality and Lode angle for the various specimen geometries. An optimization process was used to minimize the error between simulation and experiment during model calibration. In the current work, the MMC surface was described using the damage initiation routines available in Abaqus. In the work of Paredes et al., the softening of the element was described using a non-linear relationship which was also dependent on triaxiality and Lode angle. In the current work, the built-in damage evolution law in Abauqs was used to control the softening of damaged elements and was based on a linear softening for which stability was maintained with the implicit solver In determining the damage initiation coefficients for the X80 model, it was ensured that the same trend with stress triaxiality and Lode angle as determined by Paredes et al. for X65, X70 and TC128 was maintained. The coefficients were adjusted to obtain agreement between X80 experiments and simulations based on compact tension, single-edge notched tension, and pipe specimen geometries (Wilkowski et al. and Xue et al.). The coefficients used for X80 in Equation 2 were C1 =0.12, C2 =598.44, C3 =0.9, A =1094.9, and n =0.16. The damage initiation surface for X80 is shown in Fig. 1.