PSI - Issue 52

Satrio Wicaksono et al. / Procedia Structural Integrity 52 (2024) 438–454 Satrio Wicaksono et al./ Structural Integrity Procedia 00 (2023) 000 – 000

442

5

Stiffness in tangential direction, Ett [MPa]

2240 21.63 17.9 17.9 0.43

Normal stress [MPa]

Stress in 1 st Direction (MPa) Stress in 2 nd Direction (MPa)

Normal Mode Fracture Energy (J/mm 2 ) Shear Mode Fracture Energy (1 st Direction) (J/mm 2 ) Shear Mode Fracture Energy (2 nd Direction) (J/mm 2 )

4.7 4.7

2.1. Failure Modelling

2.1.1. Traction-separation In this research, the adhesive layer is modeled by introducing cohesive elements with traction-separation law. The cohesive element method has been widely used to successfully model the delamination by other researchers. The traction-separation model in ABAQUS/CAE assumes a linear-elastic initial behavior followed by damage initiation and damage evolution. The elastic behavior is written in the form of an elastic constitutive matrix that relates the nominal stress to the nominal strain at the interface. The nominal stress is the component of the force divided by the initial area at each point, while the nominal strain is the separation divided by the unit thickness. The constitutive thickness ( 0 ) used for the traction-separation response is usually the thickness defined as the thickness of the cohesive element (not necessarily the thickness of the geometric model because the zero-thickness method can be used). The nominal traction stress vector ( t ) consists of three components, two components in the two-dimensional case t n and t s , and one in the three-dimensional case, t t , which represent the normal direction and two shear tractions. Separation is denoted by δ n , δ s , and δ t . For the original thickness of the cohesive element, the nominal strain can be defined as: = 0 , = 0 , = 0 The elastic behavior of the traction stress ( t ) can be written as: = { }= [ 0 0 0 0 0 0 ]{ } = The elasticity matrix provides un-coupled behavior between all components of the traction vector and separation vector, and can depend on temperature and/or field variables. In addition, for uncoupled-traction behavior, a compression factor can be specified. 2.1.2. Crushable foam In modeling foam materials, the crushable foam model was use to capture the plastic and hardening behaviors of foam due to densification. The crushable foam model has the advantage to model the non-spontaneous deformation as the reaction of compressive loading. In addition, this model is capable of describing different yield strength in compression, shear and also tension, hence, called pressure-dependent plasticity. a. Yield Surface In the isotropic hardening model, the yield surface is defined as: = √ 2 − 2 2 − =0