PSI - Issue 28

Theodosios Stergiou et al. / Procedia Structural Integrity 28 (2020) 1258–1266 T. Stergiou et al. / Structural Integrity Procedia 00 (2019) 000–000

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A modelling approach for polyurea coating follows the framework presented by Bergström and Boyce (1998) and Boyce et al. (1988, 1989, 2000), where the total resistance to motion is the sum of the contributions of the soft and hard segments. In this work, a four-branch Parallel Network framework is implemented to account for intermolecular (1) and network (2) contributions to resistance in hard (A) and soft (B) segments; a schematic of the model is provided in Fig. 1b. This model was incorporated into ABAQUS Explicit (2018) as a user-defined material subroutine (VUMAT). The Cauchy stress tensor was calculated at each material point for each time increment, through the addition of the stresses from the four model branches. In branches A1 and B2, containing viscoplastic contributors, a numerical integration scheme was implemented. The increment of the viscous deformation gradient ( ), for the next time increment, was calculated based on numerical integration of deformations at times and � � , through � and ���� . The values of material-model parameters are provided in Table 1, together with the respective formulations of the model components-intermolecular and network, for the hard and soft segments. The true stress-true strain response predicted by the proposed model are compared in Fig. 1a to the experimental results of Choi et al. (2012). Six strain rates were compared in compressions denoted in the legend with the letter C, followed by the strain rate, and two in tension denoted with letter T. The figure demonstrates the high predictability of the proposed model, with a coefficient of determination of 0.85.

Table 1. Parameter values for the polyurea four-branch parallel model INTERMOLECULAR COMPONENT Formulation

Hard component � ���� ��� � � ��� ��� � � ������ � � ����� ̂ � ���� ��� � � ���� � � ���� ̂ � ������ �/� � ��� Hard component � ����� ��� � � ���� � � ��� ���

Soft component � ���� ��� � � ��� ���

� � dev� ∗ � � �� � �� � � � � � � � �� � ∙ � � ̂ � � ��� ��� � � � � � � � ∙ e ��/� � � � � � �/� � �� � �� NETWORK COMPONENT Formulation

Soft component � ���� ��� � � ���� � � ��� ��� � � � � � ����� ̂ � ���� ��� � ����� � � ����

� � ∗ � Λ �� � ∗ � / � � Λ �� ��/ � � dev� ∗ � � �� � �� γ� � � � � � � �� � ∙ � f � τ� � �

� � ��� ����� � � � �� � � � FRACTURE Formulation � � � � � � �� �� e ��� �

Parameters � � �� � �� ��� � � ���� � � ����