Fig. 1.
Global and local elements in S-version FEM
Fig. 2.
Concept of VCCM. VCCM, virtual crack closure method
Fig. 3.
Comparison between Monte Carlo and Bootstrap concepts
Fig. 4.
Surface crack at the centre of the model
Table 1.
Input distribution for the four-point bending model aluminium alloy (Al 7075-T6)
| Variable | Distribution | Mean | Standard deviation |
|---|---|---|---|
| Initial crack length (ci) | Lognormal | 8.00 mm | 0.1 |
| Initial crack depth (ai) | Lognormal | 4.50 mm | 0.1 |
| Young’s modulus (E) | Lognormal | 71.7 GPa | 0.01 |
| PR | Deterministic | 0.33 | 0 |
| Tensile strength (yield) | Deterministic | 503 MPa | 0 |
| Fatigue power parameter (n) | Lognormal | 2.88 | 0.1 |
| Paris coefficient (C) | Lognormal | 2.29 × 10–10 | 4.01 × 10–10 |
| Critical SIF (KIC) | Deterministic | 29 MPa. | 0 |
Fig. 5.
Experimental process
Fig. 6.
Crack length and depth measurement using Baty Vision System
Table 2.
Classification of the tension model
| Tension model | Crack shape aspect ratio (a/c) | Crack size aspect ratio (a/t) | Model width Aspect ratio (c/b) | Tension load (KN) |
|---|---|---|---|---|
| A | 1.00 | 0.8 | 0.5 | 45 |
Fig. 7.
Surface crack at the centre of tension model
Fig. 8.
Normalised SIFs along the crack front for tension. SIFs, stress intensity factors
Fig. 9.
SIFs by (A) deterministic, (B) Monte Carlo and (C) bootstrap. SIF, stress intensity factor
Fig. 10.
Geometry model for four-point bending with mode I loading
Fig. 11.
Global mesh with boundary conditions and overlaid local mesh in a wireframe view of the four-point bending model
Fig. 12.
Beach marks at the surface crack growth for the four-point bending model
Fig. 13.
Comparison of surface crack growth between the experimental and probabilistic S-version FEM approaches including 95% bounds for third and sixth beach marks
Fig. 14.
Comparison of fatigue crack growth between the experimental, deterministic and developed probabilistic S-version FEM approaches
Fig. 15.
Comparison between the experimental and probabilistic S-version FEM by deterministic, Monte Carlo and bootstrap approaches