PSI - Issue 42

Tuncay Yalçinkaya et al. / Procedia Structural Integrity 42 (2022) 1651–1659 Tuncay Yalc¸inkaya et al. / Structural Integrity Procedia 00 (2019) 000–000

1654

4

a (GPa)

C 0 0.7

q

b (GPa)

n m

33

1.45

360

120

Table 2: Parameter set used for martensite flow curves.

3. Failure Modeling

3.1. Martensite Failure

Failure on martensite grains is attributed to high stress and a failure criterion based on Bao and Wierzbicki (2004) is employed to model the damage evolution. This criterion assumes equivalent plastic strain to fracture ¯ ε f is dependent on the stress triaxiality η = σ m / ¯ σ , where σ m is the mean stress and ¯ σ is the Von Mises equivalent stress. It is verified that when stress triaxiality, η is kept constant, the fracture locus can be described by a piece-wise function in the form: ¯ ε f =   C 1 1 + 3 η for − 1 3 ≤ η ≤ 0 C 2 + ( C 2 − C 1 )(3 η − 1) for 0 ≤ η ≤ 1 3 C 2 exp − α η − 1 3 for η ≥ 1 3 (8) is the equivalent plastic strain to fracture in uniaxial tension and α is the fitting parameter used for large triaxiality values. Matsuno et al. (2015) proposed and verified by experiments that for martensite grains these parameters can be taken as C 1 = 0 . 02, C 2 = 0 . 02 and α = 3 . 0 which will also be used throughout this study. Further, damage accumulation is calculated by considering the following integral: D ( ¯ ε p ) = ¯ ε p 0 1 ¯ ε f d¯ ε p . (9) Clearly, since ¯ ε f is always positive, damage only increases. This damage model is incorporated by a means of a user-defined field subroutine to quantify the damage initiation and accumulation in the martensite phase. The generalized potential-based cohesive constitutive model is applied here for the mixed-mode fracture to simulate the decohesion of grain boundaries in three dimensional framework (see Cerrone et al. (2014), Park et al. (2009)). In this model, complete cohesive normal failure occurs when the normal separation, ∆ n , reaches the normal final crack opening width, δ n , or the effective sliding displacement, ∆ t , reaches the tangential conjugate final crack opening width, ¯ δ t , moreover, complete cohesive tangential failure occurs when the effective sliding displacement reaches the tangential final crack opening width, δ t , or normal separation reaches the normal conjugate final crack opening width, ¯ δ n . The model is defined through the potential function, Ψ , as Ψ ( ∆ n , ∆ t ) = min ( φ n , φ t ) +   Γ n   1 − ∆ n δ n   α   m α + ∆ n δ n   m + φ n − φ t   ×   Γ t   1 − | ∆ t | δ t   β   n β + | ∆ t | δ t   n + φ t − φ n   . (10) Here, m , n are non-dimensional exponents, Γ n , Γ t are energy constants, α , β are shape parameters which concern with the shape of the softening curves, δ n , δ t are the normal and tangential final crack opening widths, ∆ n is the normal separation and ∆ t is the effective sliding displacement which is given by ∆ t = ∆ 2 t 1 + ∆ 2 t 2 where ∆ t 1 ∆ t 2 are the two tangential sliding displacements and φ n , φ t are fracture energies that corresponds to the area under the traction-separation curves for ∆ t = 0 and ∆ n = 0, respectively. where C 1 = ¯ ε S S f is the equivalent plastic strain to fracture in pure shear, C 2 = ¯ ε UT f 3.2. Ferrite-Martensite Decohesion Through Cohesive Zone Framework