PSI - Issue 19

J. Srnec Novak et al. / Procedia Structural Integrity 19 (2019) 548–555 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

552

5

A combined nonlinear kinematic and isotropic material model ( “ reference model ” ) is used for simulating the cyclic behavior of all three materials (base metal, weld metal and HAZ) in the welded joint. Material parameters are summarized in Table 1. In the under-matched weld under study, the weld metal has a lower strength than base metal. By contrast, the HAZ has an initial yields stress that is 20% higher than base metal, whereas it has same kinematic and isotropic parameters as base metal.

Table 1. Material parameters taken from Hanji et al. (2011) and Saiprasertkit et al. (2012). Material E (GPa) σ 0 (MPa) C (MPa) γ R ∞ (MPa)

b 4 4 1

Base metal SBHS500-2

200 200 200

452 542 328

190 190 215

36 36 92

143 143 113

HAZ

Weld metal

An elasto-plastic FE analysis is performed according to the load history shown in Fig. 1(c). The calculation is carried out up to material stabilization is reached. As proposed in Saiprasertkit et al. (2012), the critical point is that experiencing the maximum value of the equivalent total strain range Δ ε eq,notch , which is used as the effective notch strain range Δ ε eff . The equivalent total strain range is the summation of the elastic and plastic components:





eq

(5)

eff    





 



eq, notch

pl, eq

E



  2 zx

  2 6



  2

  2

2 1

2 xy

2 yz

                           



(6)

eq

x

y

y

z

z

x

 

  

  

 

 

3 1

2 3

                 2 p,zx 2 p,yz 2 p,xy 2 p,x p,z 2 p,z p,y 2 p,y p,x         

2

  pl, eq 

(7)

where Δ σ is the normal stress range, Δ τ is the shear stress range, Δ ε p is the plastic strain range, Δ γ p is the shear plastic strain range, Δ σ eq is the equivalent stress range, Δ ε pl,eq is the equivalent plastic strain range.

3.2. Reference case: cyclic behavior up to stabilization

The results of the reference case (i.e. not-accelerated material model) are considered first. Simulation shows that the maximum stress is always located at the weld toe and increases over cycles, see Fig. 3. At the first loading, plasticization occurs only in a localized area between the weld root and toe. As the number of applied cycles increases, a significant stress redistribution takes place while the plasticization area enlarges (see Fig. 4), similarly to the study presented in Hanji et al. (2011).

N =757

N =1

σ vM (MPa)

a)

b)

Fig. 3. Von Mises stress distribution: (a) first cycle; (b) stabilized cycle.