Tools for Assessing the Damage Tolerance of Primary Structural Components

Abstract

Fatigue considerations play a major role in the design of optimised flight vehicles, and the ability to accurately design against the possibility of fatigue failure is paramount. However, recent studies have shown that, in the Paris Region, cracking in high-strength aerospace quality steels and Mil Annealed Ti–6AL–4 V titanium is essentially R ratio independent. As a result, the crack closure and Willenborg algorithm’s available within commercial crack growth codes are inappropriate for predicting/assessing cracking under operational loading in these materials. To help overcome this shortcoming, this chapter presents an alternative engineering approach that can be used to predict the growth of small near-micron-size defects under representative operational load spectra and reveal how it is linked to a prior law developed by the Boeing Commercial Aircraft Company. A simple method for estimating the S–N response of 7050-T7451 aluminium is then presented.

Appendix: Formulae for Computing the Crack Opening Stress

Newman [31] defined an opening load, which he denoted as S₀, as:

$${{S }}_0{{/S}}_{{max}}={\textrm{A}}_0 + {\textrm{A}}_1{{R}} + {\textrm{A}}_2{{R}}^2 + {\textrm{A}}_{\textrm{3}} {{R}}^{\textrm{3}}\ {\textrm{for}}\ {R}\ \geq 0$$

((2.14))

and

$${{S}}_0 {{/S}}_{{max}}={\textrm{A}}_0+{\textrm{A}}_1=\ {{R}}\ {\textrm{for}}\ {R}< 0 $$

((2.15))

for $S_{\max}< 0.8\sigma_{0},S_{\min}>-\sigma_{0}$, where S_max and S_min are the maximum minimum stress in the cycle and σ ₀ is the yield stress. If $S_{0}/S_{\max}$ is less than R then $S_0 = {\textrm{S}}_{\min}$, whilst if $S_0/S_{\max}$ is negative then $S_0/S_{\max} = 0.0$.

The A coefficients in Equations (2.14) and (2.15) are functions of α, the constraint factor, and $S_{\max}/\sigma_0$ and are given in [31] as:

$${\textrm{A}}_{\textrm{o}}=(0.825-0.34\alpha+0.05\alpha^{2})[{\textrm{COS}}(\pi{\textrm{S}}_{\max}{\textrm{F}}/2\sigma_{0}]^{1/\alpha}\\$$

$${\textrm{A}}_{1}=(0.415-0.071\alpha){\textrm{S}_{\max}}{\textrm{F}/\sigma_0}\\$$

$${\textrm{A}}_{2}={1-}{\textrm{A}}_0-{\textrm{A}}_{1}{-A3}$$

$${\textrm{A}}_3=2{\textrm{A}}_0+A_{1}-1$$

((2.16))

for α = 1 to 3.

The boundary correction factor, F, accounts for the influence of finite width on the stresses required to propagate the crack. For 3D small 3D surface cracks we can approximate F as F ∼ 2 × 1.12/π.