PSI - Issue 2_A

Benjamin Werner et al. / Procedia Structural Integrity 2 (2016) 2054–2067 Author name / Structural Integrity Procedia 00 (2016) 000–000

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Fig. 11. Location of crack initiation (white) at the weld joints and the following crack path through the fillet welds (gray) in the numerical analysis of experiment (a) K3 and (b) K4

fixture, the crack grows in longitudinal direction of the weld joint. The initial crack appears on the opposite side of the central bearings (blue in Fig. 8d). The location of the initial crack is highlighted using white elements in Fig. 11b. Due to the load direction of the specimen, the crack grows from the location of initiation to the other side of the specimen. It is illustrated in an initial state using gray elements in Fig. 11b. The stress state at the location of crack initiation is almost identical to the results of the numerical investigation of the experiment K1 (Fig. 7b). The stress triaxiality increases up to T = 2.17, while the plastic strain reaches ε = 3.6% at failure. 4.2. Gurson The damage model according to Gurson (1977) is used often and in various ways to predict failure in porous materials through nucleation and growth of voids (Dunand and Mohr (2011), Xue et al. (2010), Xue et al. (2013), Nègre et al. (2004), Nielsen and Tvergaard (2010) and Zhou et al. (2014)). The porosity of a material is described by an approach based on continuum mechanics through the effective void volume fraction. Whereby the yield condition

* 3 2 cosh q f   1

  

2 q





2

1  

3 q f

vM   

*2

(4)

2

m

Y 

Y 



of the Gurson damage model depends on * f , the von Mises equivalent stress σ vM , and the hydrostatic stress state σ m . Tvergaard (1981) introduced the parameters q 1 , q 2 , and q 3 into the yield condition and showed that, in numerical investigations, the values of q 1 = 1.5, q 2 = 1, and q 3 = q 1 2 reproduce the hardening behavior more accurately than the original yield condition by Gurson, wherein q 1 = q 2 = q 3 = 1. The function of the effective void volume fraction

f



f f

f f

for for

 

(5)

f

1 q f  

 

c

*

 





f

f f 

1

c

 

c

c

f

f



c

f

c

is subdivided into the range for values less than or equal to the critical void volume fraction f c and for the range of values f > f c modified by Tvergaard and Needleman (1984). Apart from f c , the yield condition parameter q 1 and the void volume fraction at fracture f f are included. On reaching the critical void volume fraction f c , the load capacity of the material declines, till it vanishes entirely when * f = f f . The increment of the void volume