PSI - Issue 33

R.V.F. Faria et al. / Procedia Structural Integrity 33 (2021) 673–684 Faria et al. / Structural Integrity Procedia 00 (2019) 000 – 000

676

4

Table 1. Araldite ® 2015 properties (Campilho et al. 2011, Campilho et al. 2013). Property Araldite ® 2015 Young’s mo dulus, E [GPa] 1.85±0.21 Poisson’s ratio,  0.33 a Tensile yield stress,  e [MPa] 12.63±0.61 Tensile strength,  f [MPa] 21.63±1.61 Tensile failure strain,  f [%] 4.77±0.15 Shear modulus, G [GPa] 0.70 b Shear yield stress,  e [MPa] 14.6±1.3 Shear strength,  f [MPa] 17.9±1.8 Shear failure strain,  f [%] 43.9±3.4 Fracture toughness in tension, G IC [N/mm] 0.43±0.02 Fracture toughness in shear, G IIC [N/mm] 4.70±0.34 a manufacturer’s data b obtained using Hooke’s law ( E and ν )

The fabrication process (bonded and hybrid joints) began by grit blasting the surfaces with aluminum oxide grains, followed by removing contaminants with a solvent. To assure t A =0.2 mm (spacing between adherends), two 0.2 mm thick strips were placed in the gap between adherends, along the bond length. The adhesive was then applied to one of the bonding surfaces, and both adherends were set in position in the jig. Then, the adherends were pressured to expel the excess adhesive and t A was achieved. For the weld-bonded joints, the weld-through method was used, i.e., welding after bonding. As a result, the adherends deformed locally during the welding process around the weld location. At the same time, a small portion of adhesive near to the weld-nugget was degraded, as a consequence of the applied heat, whose post-failure analysis showed to have a thickness of about 1 mm. Both joint types were cured over one week. Each joint type was replicated in five specimens, tested in a Shimadzu AG-X 100 (Shimadzu, Kyoto, Japan) testing machine using a 100 kN load cell, and a 1 mm/min testing speed.

3. Numerical modelling 3.1. XFEM formulation

The XFEM principle consists of including enrichment functions in FEM modelling (Pike and Oskay 2015), which simulate the separation of crack faces taking place during crack growth. The XFEM module of Abaqus ® implies either that the user creates a pre-crack, or it may automatically initiate cracks when continuum mechanics damage initiation criteria are met in a given element. This work uses the second approach. Thus, damage onset and resulting propagation take place at the locations at which either stresses or strains become higher than those considered as the maximum allowable. Abaqus ® has six available initiation criteria. The maximum principal stress (MAXPS) and maximum principal strain (MAXPE) initiation criteria are respectively defined by the expressions

    

 

    

    

 

    

max

max

or

f

f

,

(1)

=

=

0

0

max

max

where σ max and σ 0 max are the current and maximum principal strains. 〈 〉 prevent compressive stresses to induce damage. The software defines the crack propagation direction for these criteria as being perpendicular to the maximum principal stress/strains. Under mixed mode loading, these criteria result in crack growth entering into the adherends. Thus, in these criteria, P m is obtained, by approximated, when adhesive layer cracking is first detected in the model. Mathematical representation of the maximum nominal stress (MAXS) and maximum nominal strain (MAXE) criteria is given by, respectively max are the current and maximum principal stresses and ε max and ε 0

t t

   

    

    

n     s 0 0 ,

    

t

n

s

max , 

or

max

f

f

,

(2)

=

=

0

0

t

n

s

n

s