PSI - Issue 76

D. Kaschube et al. / Procedia Structural Integrity 76 (2026) 19–26

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To describe the relationship between strain amplitude and number of cycles to failure, the Co ffi n-Manson descrip tion has proven useful and is also applied here, Co ffi n (1954); Manson (1965): (1) where ε a is the total strain amplitude, ε a , el is the elastic part of the total strain amplitude, ε a , pl is the plastic part of the strain amplitude, σ ′ f is the fatigue strength coe ffi cient, E is the Young’s modulus, N f is the number of cycles to failure, b is the fatigue strength exponent, ε ′ f is the fatigue ductility coe ffi cient, and c is the fatigue ductility exponent. The following mean strain theories are applied: Morrow relationship : modifies the classic strain-life relationship by incorporating the mean stress σ m into the fatigue strength coe ffi cient term of the Co ffi n-Manson equation, Morrow (1968). The commonly used form is: (2) SWT-parameter : The Smith, Watson and Topper (SWT) parameter is a widely used fatigue damage parameter, originally developed to estimate the fatigue life of metallic materials under cyclic (tension–compression) loading with non-zero mean stresses. It is particularly relevant for analysing fatigue crack initiation in metals, especially under low cycle fatigue conditions where both stress and strain are significant factors. It combines stress and strain information from a loading cycle, linking the maximum tensile stress σ max and the accompanying strain amplitude. It increases as either the peak stress or the amplitude of strain increases, making it sensitive to both loading severity and material deformation, Smith, RN and Watson, P and Topper, TH (1970). This is expressed by: σ max ε a E =  σ ′ f  2  2 N f  2 b + σ ′ f ε ′ f E  2 N f  b + c (3) Ince-Glinka relationship , Ince and Glinka (2011): Ince and Glinka’s approach is to apply the changes proposed by Smith, Watson and Topper only to the elastic part of the equation in order to compensate for the disadvantages of the previous models. ε a = ε a , el + ε a , pl = σ ′ f E (2 N f ) b + ε ′ f (2 N f ) c ε a = σ ′ f − σ m E (2 N ) b + ε ′ f (2 N ) c

σ ′ f E

σ max σ ′ f

(2 N ) 2 b

+ ε ′ f (2 N ) c

(4)

+ ε a , p =

ε a , e

Walker relationship , Walker (1970): Its key feature is the inclusion of a material-dependent exponent γ that allows fine-tuning to di ff erent materials’ sensitivity to mean strain e ff ects.

b    b

+ ε ′ f  

b    c

σ ′ f E  

 2 N f 

 2 N f 

2 

2 

1 − γ

1 − γ

1 − R

1 − R

(5)

ε a =

with

σ min σ max

R = (6) There are several ways to calculate the Walker parameter γ . Method one is a method originally proposed for steels. Here, γ is calculated using this equation, Dowling (2009): γ = − 0 . 0002 · σ u + 0 . 8818 (7) with σ u being the ultimate tensile stress. Another way to calculate γ is also given by Dowling et al, Dowling (2009). Here, the completely reversed stress amplitude σ ar is used together with the equivalent formulation of the Walker equation to apply a multiple linear regression using the values of fully reversed and data with mean strain. Modified SWT-parameter , Lv et al. (2016): Lv et al. proposed combining the advantages of the SWT model with those of the Walker model and therefore integrate the material parameter γ into the SWT parameter, although using a di ff erent equation to calculate the mean strain influence.

2

( σ ′ f )

(2 N ) 2 b

b + c

+ ε ′ f σ ′ f (2 N )

2 γσ max ε a =

(8)

E

σ u − σ y σ u + σ y

γ = 0 . 5 ±

(9)