PSI - Issue 80

Yichen Zhang et al. / Procedia Structural Integrity 80 (2026) 289–298 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Fibre-reinforced polymers (FRPs) have attracted considerable attention because of their high strength-to-weight ratios, corrosion resistance, and design flexibility [1]. These properties allow the manufacture of lightweight yet strong composite structures, making FRPs indispensable for applications such as aerospace, automotive, and wind energy [1,2]. However, accurately simulating FRP damage under complex stress states can be challenging. Although ABAQUS provides a two-dimensional progressive damage model (2D PDM) based on the Hashin criterion for continuum shell elements, it neglects through-thickness stresses. This deficiency reduces its accuracy in fully three-dimensional scenarios that require consideration of out-of-plane stress components. In addition, the 2D PDM does not handle non monotonic loading conditions effectively, thereby further limiting its applicability. To overcome these shortcomings, this study presents a torsional loading study using an enhanced 3D progressive damage model (3D PDM), specifically designed for reduced elements, described and validated by the authors in [3], implemented within the ABAQUS/Explicit ™ framework using a VUMAT subroutine. This 3D model fully incorporates the Hashin failure criterion [4], which is expressed mathematically as follow: (1) Fibre tension mode ( 11 ≥0 ): =( 11 ) 2 + ( 12 12 ) 2 + ( 13 13 ) 2 ( =1) (1) (2) Fibre compression mode ( 11 ≤0 ): = − 11 (2) (3) Matrix tension mode ( 22 + 33 ≥0 ): =( σ 22 +σ 33 ) 2 + σ 22 3 −σ 22 σ 33 2 2 3 +( σ 12 12 ) 2 +( σ 13 13 ) 2 (3) (4) Matrix compression mode ( 22 + 33 ≤0 ): = 1 (( 2 23 ) 2 −1)(σ 22 +σ 33 )+ (σ 22 +σ 33 ) 2 4 2 2 3 + σ 22 3 −σ 22 σ 33 2 2 3 +( σ 12 12 ) 2 +( σ 13 13 ) 2 (4) In torsional analyses of FRP tubes, this enhanced 3D PDM predicts realistic crack paths and enables element deletion along the actual fibre direction. In contrast, using the 2D built-in PDM available in Abaqus can lead to incorrect fracture patterns and crack propagations. Through the parametric study conducted in this paper for FRP cylindrical tubes under torsional loading, the 3D PDM is shown to more accurately capture their damage progression. In contrast, the 2D PDM may yield incorrect fracture patterns . These findings highlight the 3D PDM’s superior capability for predicting crack propagation under torsional loading, thereby further confirming its advantages. 2. Numerical model establishment The FRP cylindrical tube model features an outer diameter of 100 mm, inner diameter of 98 mm, and wall thickness of 1 mm (Figure 1). The boundary conditions are shown in Fig. 2, which are implemented with complete constraint of the 6 degrees of freedom (DOF) at the stationary side, while the rotation side is coupled to a reference point (RP) through kinematic coupling. A rotational displacement about the longitudinal axis (Z-direction) is applied at the RP, with constrained rotations in the transverse directions (UR X =0, UR Y =0). The E-glass/Polyester composite material properties of the cylindrical tubes are detailed in Table 1.