A Robust Numerical Methodology for Fatigue Damage Evolution Simulation in Composites

Abstract

Composite materials, like metals, are subject to fatigue effects, representing one of the main causes for component collapse in carbon fiber-reinforced polymers. Indeed, when subject to low stress cyclic loading, carbon fiber-reinforced polymers exhibit gradual degradation of the mechanical properties. The numerical simulation of this phenomenon, which can strongly reduce time and costs to market, can be extremely expensive in terms of computational effort since a very high number of static analyses need to be run to take into account the real damage propagation due the fatigue effects. In this paper, a novel cycle jump strategy, named Smart Cycle strategy, is introduced in the numerical model to avoid the simulation of every single cycle and save computational resources. This cycle jump strategy can be seen as an enhancement of the empirical model proposed by Shokrieh and Lessard for the evaluation of the fatigue-induced strength and stiffness degradation. Indeed, the Smart Cycle allows quickly obtaining a preliminary assessment of the fatigue behavior of composite structures. It is based on the hypothesis that the stress redistribution, due to the fatigue-induced gradual degradation of the material properties, can be neglected until sudden fiber and/or matrix damage is verified at element/lamina level. The numerical procedure has been implemented in the commercial finite element code ANSYS MECHANICAL, by means of Ansys Parametric Design Languages (APDL). Briefly, the Smart Cycle routine is able to predict cycles where fatigue failure criteria are likely to be satisfied and to limit the numerical simulation to these cycles where a consistent damage propagation in terms of fiber and matrix breakage is expected. The proposed numerical strategy was preliminarily validated, in the frame of this research study, on 30° fiber-oriented unidirectional coupons subjected to tensile-tensile fatigue loading conditions. The numerical results were compared with literature experimental data in terms of number of cycles at failure for different percentage of the static strength. Lastly, in order to assess its potential in terms of computational time saving on more complex structures and different loading conditions, the proposed numerical approach was used to investigate the fatigue behavior of a cross-ply open-hole composite panel under tension-tension fatigue loading conditions.

Keywords: fatigue; open-hole specimen; residual stiffness cycle jump strategy; residual strength.

Figure 1

Schematic representation of the strength degradation under variable stress conditions.

Figure 2

Constant-amplitude loading pattern.

Figure 3

Flowchart of the numerical procedure.

Figure 4

Flowchart of the numerical procedure with the introduction of the Smart Cycle strategy.

Figure 5

Off-axis tensile specimen: (a) numerical model; (b) Finite Elements model.

Figure 6

Off-axis tensile specimen: Boundary conditions.

Figure 7

Off-axis tensile specimen: S–N curves.

Figure 8

Off-axis tensile specimen: stiffness vs. number of cycles.

Figure 9

Off-axis tensile specimen: damaged area vs. number of cycles.

Figure 10

Off-axis tensile specimen: comparison of the final damage state obtained with the Smart Cycle strategy and with constant δn = 100 cycle intervals.

Figure 11

Off-axis tensile specimen: damage status at cycles number (a) 1343, (b) 1488, (c) 1658 (d) 2255, (e) 2257, and (f) 2259 at 80% of the static load using the Smart Cycle strategy.

Figure 12

Off-axis tensile specimen with gradual degradation of material properties using the Smart Cycle strategy: (a) shear modulus (MPa), (b) longitudinal modulus (MPa), (c) transversal modulus (MPa), (d) longitudinal tensile strength (MPa), (e) transversal tensile strength (MPa), (f) longitudinal compressive strength (MPa), and (g) transversal compressive strength (MPa).

Figure 13

Off-axis tensile specimen: (a) simulation time bar chart, (b) simulation time vs load percentage.

Figure 14

Off-axis tensile specimen: (a) hard disk memory allocation bar chart; (b) hard disk memory allocation vs. load percentage.

Figure 15

Cross-ply open-hole specimen: (a) geometrical model; (b) FEM model.

Figure 16

Cross-ply open-hole specimen: (a) numerical maximum principal strain; (b) final damage status obtained by considering constant cycle increments δn = 100; (c) final damage status obtained by using the Smart Cycle strategy.

Figure 17

Cross-ply open-hole specimen: maximum first principal strain at 1000 and 5000 cycles.

Figure 18

Cross-ply open-hole specimen: XY shear strain at 1000 and 5000 cycles.

Figure 19

Cross-ply open-hole specimen: strain vs. number of cycles.

Figure 20

Cross-ply open-hole specimen: damage status at cycle numbers (a) 1, (b) 4500, (c) 10,200, and (d) 30,000.

Figure 21

Cross-ply open-hole specimen: comparison between the final damage state obtained with the Smart Cycle strategy and δn = 100 cycles.

Figure 22

Cross-ply open-hole specimen—comparison between Smart Cycle and standard procedure: (a) numerically predicted stiffness vs. number of cycles; (b) numerically predicted damaged area vs. number of cycles.

Figure 23

Cross-ply open-hole specimen—comparison between Smart Cycle and standard procedure: shear modulus E₁₂ vs. number of cycles.

Figure 24

Cross-ply open-hole specimen—comparison between Smart Cycle and standard procedure: simulation time and memory allocation.