PSI - Issue 5

Behzad V. Farahani et al. / Procedia Structural Integrity 5 (2017) 468–475 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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3. FE analysis An explicit FEM model was considered in which a 3D deformable shell model was simulated in ABAQUS©. The geometric characteristics was considered as presented in Fig. 1. The material properties were used as: Density = 2.7 −9 ( 3 ⁄ ) ; Young’s modulus = 69 3 ( ) ; Poisson’s ratio = 0.33 and yield stress = 297.6 ( ) . 3-node linear triangular elements (S3) were used to form a FE mesh, in which the element size was limited to 0.5 and 1.0 ( mm ) with a total number of 7046 and 3739 elements and nodes, respectively, see Fig. 2-a. More refined elements were considered on the central section of the specimen. Concerning the essential boundary condition, the points located on the upper specimen edge was clamped to satisfy experimental circumstances. A uniform displacement enforcement with a magnitude of ̅ = −0.3 ( ) was vertically imposed on the points coupled with the bottom edge, as Fig. 2-a demonstrates. Considering intended points 1 and 2 (with the same properties as DIC analysis), the force response was correlated with the displacement variation 21 , see Fig. 3-b. 4. NNRPIM study In NNRPIM analysis, the bi-failure specimen was considered as seen in Fig. 1. A regular nodal distribution was used consisting of a total number of 3735 and 25055 nodes and integration points, respectively, as Fig. 2-b shows. The material properties were used the same as FE analysis while the tangential modulus was defined as 0 = %0.1 × = 69 ( ) . As shown in Fig. 2-b, a uniformly distributed displacement imposition was vertically enforced in the bottom side of the specimen as ̅ = −0.3 ( ) . The points located on the upper side of the specimen was clamped to follow experimental conditions. Taking into account of the plane stress deformation theory, the non-linear Newtown-Raphson algorithm ( 0 ) was therefore used to acquire the non-linear solution with a tolerance of 1 −4 and a maximum increment number of 30 (referring to Box 1). The reaction force/displacement variation on two pre defined points was obtained and mapped in Fig. 3-b.

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Fig. 2. Numerical characterization; (a) FEM model and (b) NNRPIM model.

5. Conclusions

This preliminary study focused on the elastoplastic analysis of a bi-failure specimen with a material property of an aluminum alloy AA6061-T6 under uniaxial tensile test. The experimental results were acquired using DIC analysis and the force/displacement variation was obtained. In addition, the model was numerically solved using FEM formulation in ABAQUS© to assess the performance of FE analysis in the presence of the isotropic elastoplastic behavior of the material. The reaction force in terms of the intended displacement field was thereby attained having a good agreement with the DIC solution. Moreover, the problem was resolved using an advanced discretization meshless method NNRPIM to access the performance of the proposed supporting elastoplastic algorithm. The NNRPIM plane stress formulation was thus extended to the non-linear elastoplastic theory. Due to the non-linearity, the non-linear incremental Newton-Raphson algorithm relied on 0 was therefore handled and the variation of force in terms of the vertical displacement was achieved. Comparing all results, it infers that the FEM produced reasonable results very close to the DIC solution. Regarding the NNRPIM analysis, the non-linear solution algorithm was successfully