PSI - Issue 68

M. Mahatab et al. / Procedia Structural Integrity 68 (2025) 815–821 M. Mahatab and R. Ranjan / Structural Integrity Procedia 00 (2025) 000–000

817

3

Where Y(a) is a correction factor accounting for the crack shape, the free surface of one side of the crack, and the finite thickness of the plate. Where ε(a) is the local inelastic strain at the deepest and surface point at each crack depth a and a o accounts for the small crack growth behaviour. Using the Paris crack growth law, fatigue life is estimated by integrating the following expression until the crack reaches a critical crack size.

!

!

" ( ( .

"# "*

# ) +

$ * ,

• ••

• % % C''

••

$ = %

&  

(3)

()

& -

The stress non-uniformity along the crack path is considered by modifying the local elastic stress field due to applied load and residual stress distribution using the weight function approach given by Shen and Glinka (1991).

• • • • • • ! " # $ # % &# ! = " #

(4)

Where σ(x) is non-uniform local elastic stress and m(x,t) is the weight function coefficient. For each closed cycle of load history, the local inelastic strain and crack opening strains are calculated at the surface, and the deepest point of the crack and strain-based fracture mechanics analysis is performed. Finally, the cycle to failure is estimated by numerical integration of crack growth law. A detailed description of the SBFM modal can be found in Ghahremani et al. (2016), Walbridge (2008), and Ranjan and Walbridge (2021). 3. SBFM prediction for S550MC steel grade The SBFM prediction for the S550MC steel grade cruciform welded joint has been carried out for three loading conditions in as-welded and impact-treated conditions. The input parameters and the fatigue analysis are discussed in the following sections. 3.1. Input parameter for SBFM model The input parameters required for the fatigue analysis by the SBFM model are related to component geometry, material properties, stress concentration factor ( SCF ) variation, residual stress distribution, crack geometry, and loading history. A cruciform welded joint with a thickness of 10 mm and width of 40 mm (rectangular cross-section) made of high-strength steel grade S550MC, as shown in Figure 1(a), was used in fatigue analysis. The material properties related to static and cyclic material tests (Elastic modulus E, yield strength σ y , Ultimate strength σ u ) and crack growth parameters (Paris Erdogan law constant C , m , Threshold stress intensity factor range Δ K th ) were adopted from existing literature. The input parameters for crack growth and fatigue analysis are summarised in Table 1.

Table 1: Input parameters for the SBFM model Ref Variable

Value 9.5 mm

Ref

Variable

Value

-

Specimen Thickness, t

Mikkola et al. (2016), Ranjan and Walbridge (2021) Mikkola et al. (2016), Ranjan and Walbridge (2021) Ranjan and Walbridge (2021) Ranjan and Walbridge (2021) Lindqvist (2002)

R-O cyclic material model parameter, K’ R-O cyclic material model parameter, n’

775.29 MPa

Ellerbeck (2023)

Elastic Modulus, E

210 GPa

0.0757

Ellerbeck (2023)

Yield strength, σ y

598 MPa

Initial crack size, a i

0.15

Ellerbeck (2023)

Ultimate strength, σ u

667 MPa

Crack closure parameter

0.002

Lindqvist (2002) Lindqvist (2002)

Paris constant LN( C )

-28.3

Paris law constant, m

3

Threshold SIF, Δ K th

120 MPa. m^0.5