On the Growth of Fatigue Cracks from Material and Manufacturing Discontinuities Under Variable Amplitude Loading

Abstract

This paper focuses on problems associated with aircraft sustainment-related issues and illustrates how cracks, that grow from small naturally occurring material and manufacturing discontinuities in operational aircraft, behave. It also explains how, in accordance with the US Damage Tolerant Design Handbook, the size of the initiating flaw is mandated, e.g. a 1.27-mm-deep semi-circular surface crack for a crack emanating from a cut out in a thick structure, a 3.175-mm-deep semi-circular surface crack in thick structure, etc. It is subsequently shown that, for cracks in (two) full-scale aircraft tests that arose from either small manufacturing defects or etch pits, the use of da/dN versus ∆K data obtained from ASTM E647 tests on long cracks to determine the number of cycles to failure from the mandated initial crack size can lead to the life being significantly under-estimated and therefore to an unnecessarily significant increase in the number of inspections, and, hence, a significant cost burden and an unnecessary reduction in aircraft availability. In contrast it is shown that, for the examples analysed, the use of the Hartman–Schijve crack growth equation representation of the small crack da/dN versus ∆K data results in computed crack depth versus flight loads histories that are in good agreement with measured data. It is also shown that, for the examples considered, crack growth from corrosion pits and the associated scatter can also be captured by the Hartman–Schijve crack growth equation.

Appendix: The Hartman–Schijve Variant of the Nasgro Crack Growth Equation

The NASGRO equation36 can be written in the form:

$$ {\text{d}}a/{\text{d}}N \, = \, D \, \left[ {\left( {1 - f} \right)/\left( {1 - R} \right)} \right]^{m} \Delta K^{(m - p)} \left( {\Delta K \, - \, \Delta K_{\text{thr}} } \right)^{p} /\left( {1 - K_{\hbox{max} } /A} \right)^{q} = \, D \, \Delta K_{eff}^{(m - p)} \left( {\Delta K_{\text{eff}} - \, \Delta K_{{{\text{eff, th}}r}} } \right)^{p} /\left( {1 - {\rm K}_{\hbox{max} } /A} \right)^{q} $$

(5)

where D, m, p and q are constants, f = K _op/K _max, K _op is the value of the stress intensity factor at which the crack first opens, ΔK _eff = K _max – K _op and the terms ΔK _thr and A are best interpreted as parameters chosen so as to fit the measured da/dN versus ΔK data. The NASGRO equation36 contains the Hartman–Schijve crack growth equation,7 viz:

$$ {\text{d}}a/{\text{d}}N \, = \, D \, \left( {\Delta K_{\text{eff}} - \, \Delta K_{\text{eff,thr}} } \right)^{p} /\left( {1{-}K_{\hbox{max} } /A} \right)^{p/2} $$

(6)

as a special case, i.e. m = p and q = p/2. (Here, ΔK _eff,thr is the associated effective threshold value of ΔK _thr.)

As explained in Ref. 7 and Appendix X3 of ASTM E647-13a, there is little R ratio and hence little crack closure effects associated with cracks that grow from small naturally occurring material discontinuities. In such cases for cracks that grow from small naturally occurring material discontinuities, the function f asymptotes to R and ΔK _eff can be approximated by ΔK so that Eqs. 5 and 6 become

$$ {\text{d}}a/{\text{d}}N \, = \, D\Delta K^{(m - p)} (\Delta K{-}\Delta K_{\text{thr}} )^{p} /(1{-}K_{\hbox{max} } /A)^{q} $$

(7)

and

$$ {\text{d}}a/{\text{d}}N \, = \, D \, \left( {\Delta K \, {-} \, \Delta K_{\text{thr}} } \right)^{p} /\left( {1{-}K_{\hbox{max} } /A} \right)^{p/2} $$

(8)

respectively.