PSI - Issue 76

Mehmet F. Yaren et al. / Procedia Structural Integrity 76 (2026) 99–106

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Fig. 3. Illustration of the transformation from a plain material with uniformly distributed voids (a) to an equivalent homogenized cracked continuum material (b); process zone (c) and fictitious linear-elastic local stress fields (e) to estimate fatigue lifetime of notched components (d) of AM PLA

and equals 1. Additionally, the structures shown in Figs. 3a and b are assumed to exhibit the same fatigue strength in the case of 100% in-fill and absence of any cracks. To achieve identical fatigue lives ( N f ) under cyclic loading with a maximum stress of σ max for both the plate containing a central through-thickness crack and the un-notched plate with internal voids, a relationship between the equivalent half-crack length ( a eq ) and the internal void size ( d v ) must be established. In Eq. (1), the function f( d v ) transforms the AM plate with internal voids (Fig. 3a) into an equivalent homogeneous, isotropic, linear-elastic plate containing a central crack, as depicted in Fig. 3b. a eq = f ( d v ) (1) The Theory of Critical Distances (TCD), as given in Eqs. (2) and (3), is used to evaluate the fatigue strength of an infinite plate with a through-thickness crack under cyclic tensile loading. ∆ σ 0 n =∆ σ o  1 −    a a + L 2    2 (2) ∆ σ 0 n =∆ σ o  L a + L (3) By replacing the a in Eqs. (2) and (3) with the a eq and using the critical distance L M ( N f ), the PM and LM can be directly expressed as follows for PM (Eq. 4) and LM (Eq. 5). For a detailed definition of critical distance for fatigue loading L M ( N f ), readers are referred to the paper by Susmel and Taylor (2007). σ max =        σ max , 0 ·  N Ref N f  k        100% ·  1 −    a eq a eq + | L M ( N f ) | 100% 2    2 (4) σ max =        σ max , 0 ·  N Ref N f  k        100%     L M ( N f )    100% a eq +    L M ( N f )    100% (5) In Eqs. (4) and (5), σ max , 0 represents the endurance limit at N Ref cycles, and k is the negative inverse slope of the fatigue curve obtained from specimens manufactured with 100% in-fill. Notably, these equations are expressed