PSI - Issue 77

Tianyu Wang et al. / Procedia Structural Integrity 77 (2026) 512–520 Wang et al./ Structural Integrity Procedia 00 (2026) 000 – 000

515

4

3. Failure analysis and validation of the model To validate the analytical model, the finite element model was developed. FEM employed a 20-node quadratic brick element with reduced integration (C3D20R), selected for its superior performance in capturing through thickness stress gradients whilst avoiding shear locking phenomena common in lower-order elements. The mesh density was carefully selected through a convergence study, ensuring that further refinement produced stress changes of less than 1%. The loading implementation deserves particular attention: axial loads were directly applied to the pipe ends as distributed forces; torsional loads were applied through reference points at the ends, kinematically coupled with the end surface motion to ensure proper load distribution; internal pressure loads were directly applied to the inner surface as follower forces; and bending loads were implemented by applying rotation to reference points located at the centres of both ends. The total rotation angle in radians was / , where is the pipe length and is the bending radius, ensuring consistency with the curvature parameter in the analytical model. The FE model was constructed to precisely replicate the geometry, material properties, and loading conditions of the problem, assuming perfect bonding between layers — an assumption consistent with high-quality manufacturing processes. For the validation a four-layer pipe made from AS4/APC-2 carbon/PEEK (Table 1, [8, 9]) was considered. The composite pipe had an inner diameter of 53.5 mm and a composite layer thickness of 2.5 mm. The pipe had a stacking sequence of [+0°/−0°/+90°/−90°] and was subjected to a combined load case consisting of internal pressure (10 MPa), compressive force (10 kN), torque (10 kN·m), and bending (10 degrees/100 ft). The comparison revealed excellent, near-identical agreement between the analytical (TLM) and finite element (FEM) methods for the three principal stresses in the outermost composite layer — hoop, axial, and shear stresses across the full circumference (see Fig. 2). The maximum deviation between the results was less than 3% for all stress components, well within the uncertainty bounds of material property characterisation. This close correlation serves as powerful validation of the mathematical formulation and implementation of the two-level analytical model, confirming its capability to accurately predict complex three-dimensional stress states in thick-walled composite pipes whilst requiring only a fraction of the computational resources.

1 2 = 3 12 = 13 23 = = 23 12 = 13

Properties

Values 141.72

(GPa)

(GPa)

9.57 5.97 0.37 0.33 2068 1196 177 3.6 79

(GPa)

(GPa) 12 = 13 23 (MPa) (MPa)

(MPa)

(MPa)

91

(MPa)

(MPa) 185 Table 1. Properties of AS4/APC-2 carbon/PEEK plies at 25 ℃

Fig. 2. Stress distribution, TLM vs. FEM

To assess the structural integrity of the composite pipe under the computed stress states, a failure analysis framework was employed. The selection of multiple failure criteria reflects the complex failure modes possible in composite materials and the ongoing debate in the composites community regarding the most appropriate failure theory for different loading conditions. This framework utilises three distinct and widely recognised failure criteria to provide a robust evaluation of potential failure mechanisms: the Maximum Stress criterion, the modified Tsai-Hill criterion, and the Hashin criterion [5, 14, 15]. The application of multiple criteria serves a dual purpose: it provides bounds on the failure prediction (with Maximum Stress typically being most conservative and Tsai-Hill least conservative) and offers insight into the failure mechanism (with Hashin providing mode identification). This multi criteria approach ensures a thorough and reliable assessment of the pipe ’ s failure behaviour, acknowledging the inherent uncertainties in composite failure prediction.