PSI - Issue 78

Yangwen Zhang et al. / Procedia Structural Integrity 78 (2026) 1008–1015

1010

Manson (1953)). By incorporating the elastic strain amplitude, the relationship between the total strain amplitude ε a and the fatigue life, i.e., the number of cycles to failure ( N f ), can be extended to the Basquin-Co ffi n-Manson form, which can be expressed as below:

σ ′ f

∆ ε p 2

∆ ε e 2

b

+ ε ′ f · (2 N f ) c

(2 N f )

(1)

E ·

ε a =

+

=

Where ∆ ε e ∆ ε p 2 are the elastic and plastic strain amplitude, and the fatigue parameters σ ′ f , ε ′ f , b , and c are the fatigue strength coe ffi cient, fatigue ductility coe ffi cient, fatigue strength exponent, and fatigue ductility exponent, respectively. 2 N f is the number of reversals to failure, which is twice the number of cycles to failure. In this study, a steel material comparable to AISI 1015 is used for the investigated SHARK ® hysteretic damper. Therefore, the strain-life curve of AISI 1015, as shown in Fig.2, is applied for the fatigue analysis (SAE (2002)). 2 and

Fig. 2. Applied strain life curve: Reversals vs Strain amplitude.

2.2. Strain amplitude based on FEM

The strain amplitude can be calculated as:

ε max − ε min 2

∆ ε 2

(2)

ε a =

=

where ε max and ε min are the total maximum and minimum principal strains obtained from the FEM simulation. According to the simulation results, under 100% of the design displacement d bd , the investigated SHARK ® hysteretic damper exhibits a total maximum principal strain (in tension) of 0.0402, and a total minimum principal strain (in compression) of -0.0332. As shown in Fig.3, both the maximum and minimum principal strains are concentrated in the lamellae of the dissipative core. In the SHARK ® hysteretic damper investigated, both dissipative cores are identical, rather than consisting of a major and a minor core as seen in adaptive design (see in Fig.1 (b)). This symmetrical configuration increases the overall stroke capacity. As observed, at 100% of the design displacement d bd , the total maximum principal strain occurs in the tensile zone of the lamella, while the total minimum principal strain occurs in the compressive zone. Under cyclic loading, these tensile and compressive regions alternate within the same area of the lamella. The cycle limit corresponding to 25% d bd , 50% d bd , and100% d bd can then be determined from the strain life curve, as shown in Fig.4.