PSI - Issue 60

Rajagurunathan M et al. / Procedia Structural Integrity 60 (2024) 517–524 Rajagurunathan and Prakash./ Structural Integrity Procedia 00 (2024) 000–000

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a) c) Fig. 1. a) Material property degradation models for composite laminates; b) Equivalent Stress; c) Damage variable vs Equivalent Displacement [Yang et al. (2021)]. 2.1.1. Intra ‑ Laminar Damage Initiation Criterion Hashin failure criterion that is built-in ABAQUS® is adopted in this simulation to predict the failure initiation of matrix and fiber. The 2-D Hashin failure criterion works only with continuum shell elements (SC8R). According to this criterion, four different failure modes such as fiber and matrix damages due to tension and compression are found. The failure index equations are given in Table. 1. [Liu et al. (2016), Zhou et al. (2019)] Table 1: The damage initiation criteria of the composite laminates [Sellitto et al. (2019), Anuse et al. (2022)] Failure mode Initiation Criteria Fiber tension failure mode, � ≥0 � � =� � � � � + � �� � � � ≥1 (1) Fiber compression failure mode, � ≤0 � � =� � � � � ≥1 (2) Matrix tension failure mode, � ≥0 �� =� � � � � +� �� � � � ≥1 (3) Matrix compression failure mode, � ≤0 �� =� � � ��� � 2 � � � −1�+� � 2 � � � +� �� � � � ≥1 (4) Here, X T and X C denote the tensile and compressive strength along fibre direction. Y T , Y C , S L and S T are strengths of transverse tensile, transverse compressive, longitudinal shear and transverse shear loads respectively. � , � �� are the normal stress tensors in fiber direction, transverse direction and shear tensor, respectively. is the shear failure coefficient. The value of failure index varies from 0 to 1 (f < 1 for no damage and f = 1 for damage). 2.1.2. Intra ‑ Laminar Damage Evolution The intra-laminar damage is described using a bilinear degradation law. According to this linear softening behavior, the stress is reduced progressively when either the displacement or strain increases. Once damage initiates, [ ] is replaced with the elasticity matrix [ � ] which represents the damage state and is defined as { } = [ � ]{ } . The damage evolution formula is linear and progressive. [Liu et al. (2016), Zhou et al. (2019)] [ � ]= 1 � �1− � � � �1− � �(1− � ) �� � 0 �1− � �(1− � ) �� � (1− � ) � 0 0 0 (1− � ) �� � (5) Here, �1 − � �(1− � ) �� �� and � , � , � are the current values of damage variables of fiber damage, matrix damage and shear damage respectively. � and � are elastic modulus along longitudinal and transverse directions. �� and �� are the major and minor poisson’s ratios and �� is the in-plane shear modulus. Damage variables for different failure modes are derived from the damage parameters of fiber ( �� , �� ) and matrix ( �� , �� ) as follows: b)