PSI - Issue 19

Asma Manai et al. / Procedia Structural Integrity 19 (2019) 12–18

14

Asma Manai / Structural Integrity Procedia 00 (2019) 000–000

3

Fig. 2. stress-time curve with specification of loading peaks

The expression of mean stress at the current time as function of the peaks (numbers and values) of the corresponding time segment is presented in eqatuion (1).

t current j = t start

1 t current − t strart

σ m ( t current ) =

σ ( t j )

(1)

with

• t i : a peak loading • t start : start time (start peak) • t current : current time (current peak) Based on equation (2) the determination of the stress amplitude at the current time (which considers the e ff ect of the load history within the corresponding time segment [ t start , t current ]) can be computed. σ a ( t current ) = σ ( t current ) − σ m ( t current ) = σ ( t current ) − 1 t current − t strart t current j = t start σ ( t j ) (2)

Equation (3) gives thus the stress range at the current time. ∆ σ ( t current ) = 2 σ ( t current ) − σ m ( t current )

(3)

A mean stress correction of the new computed stresses (mean stress and stress range) with any mean stress correction law leads to determine the stress range at the current time with zero mean stress. For example, equation (4) shows Morrow law.

σ a ( t current ) σ ar ( t current )

σ m ( t current ) σ f B

= 1

(4)

+

With

• σ a ( t current ): the stress amplitude at the current time • σ ar ( t current ): the stress amplitude to be determined (i.e. with zero mean stress)

• σ m ( t current ): the mean stress at the current time • σ f B : the true fracture strength of the material.