PSI - Issue 60

Rajagurunathan and Prakash./ Structural Integrity Procedia 00 (2024) 000–000

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

520

� =� �� , � ≥0 �� , � <0 �

� =� �� , � ≥0 �� , � <0 �

(6, 7)

� =1−(1− �� )(1− �� )(1− �� )(1− �� ) (8) The damage variable ( � ) indicates the loss in stiffness at the failure mode after damage initiation ( �,�� ≥ � �,�� ) . � = � � ,�� ( �,�� − � � ,�� ) �,�� ( � � ,�� − � � ,�� ) ( � ∈ [0,1], = , , , ) (9) Here � � ,�� and � � ,�� represent the equivalent displacement at damage initiation and final failure respectively. In this work, a cohesive surface-based damage model in ABAQUS®/Explicit was used to study the progression of delamination. The elasticity matrix provides uncoupled behavior of the traction vector and separation vector. � , � , � denote the penalty stiffnesses. According to the quadratic nominal stress function, delamination happens when the contact stress ratios approach a value of one. � � � � �= � � 0 0 0 � 0 0 0 � �� � � � � (10) The equation of delamination initiation can be written as follows: � ( ) � +� ( ) � +� ( ) � = (11) Where , are normal (n) and shear tractions (s, t) respectively. The inter-laminar strength along normal and shear directions are represented as , , . 2.2.2. Inter ‐ Laminar Damage Evolution A bi-linear traction-separation law is used to calculate the degradation of the cohesive surface characteristics when the delamination between each ply begins. When a delamination initiation criterion is satisfied, delamination evolution must be considered because the stiffness of the interface will degrade with continued loading. Delamination will occur if the following damage variable reaches one. = ( − ) ( − ) (12) Where is the effective displacement at damage initiation. , denote the maximum displacement and displacement at complete failure of mixed-mode loading, respectively. The total mixed-mode displacement (normal, sliding and tearing) is represented as =� + + (13) According to Benzeggagh and Kenane (B-K) fracture criterion, when the energy release rate is higher than the critical energy release rate, the failure under mixed-mode loading occurs. = +( − )� + + � (14) Where � � , � � � , � � �� are normal and shear critical fracture energies. The BK power law coefficient ( η ) value is considered as 1.45 [Zhang et al. (2021)]. 3. Numerical Simulations of low-velocity impact tests The low velocity impact on a composite laminate is a highly nonlinear contact process which takes place in a short duration. Therefore, it is necessary to develop a finite element model to predict different failure mechanisms 2.2. Damage model of Delamination 2.2.1. Inter ‐ Laminar Damage Initiation