PSI - Issue 17

J.P. Pascon et al. / Procedia Structural Integrity 17 (2019) 411–418 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

414

4

strain relation, where σ is the stress tensor, ε and ε p are the total and plastic strain tensors; equation (2) describes the yield criterion, where ϕ is the yield surface ( ϕ < 0 denotes elastic behavior) and σ κ is the yield stress limit; equation (3) provides the plastic flow rule; equation (4) is the Swift isotropic hardening model, where K , ε 0 and n are the material coefficients and κ is the equivalent plastic strain, given by equation (5).

(

) p

: = − σ C ε ε

(1)

2 0 3   

σ

dev



=

−

(2)

g g

  

0   g

ε

=

, (

)

(3)

p

σ



n

(

)

0 K     = +

(4)

g

2 3 p ε g

 =

(5)

In order to enrich the numerical approximation, the finite element mesh adopted is more refined around the crack region, according to Figure 3. The crack front is straight. Two layers (along the z -direction) of solid tetrahedral finite elements are employed, resulting in a mesh with 5019 nodes and 2424 elements of quadratic order. Further details regarding the finite element and the numerical algorithm employed can be found in Pascon and Coda (2012). At the end of each loading cycle, the values of the nodal displacements as well as the plastic strain components at each numerical integration point are determined and stored. With these values, the stress components and the equivalent plastic strain can be determined at any point of the mesh.

Fig. 3. Finite element mesh employed: general view and zoom at the crack region. The circles at the left and the right denote, respectively, the initial ( 2a = 11 mm) and the final ( 2a = 15 mm) crack lengths.