PSI - Issue 34

Sigfrid-Laurin Sindinger et al. / Procedia Structural Integrity 34 (2021) 78–86 S.-L. Sindinger et al. / Structural Integrity Procedia 00 (2019) 000–000

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tween 0.05 and 0.25%. Poisson’s ratios ν i j were evaluated in the same range using a stereo digital image correlation (DIC) system (Vic-3D 9, Correlated Solutions Inc., Irmo, SC, USA) that allows the contactless derivation of strains on the coupon surface. Additionally, ultimate strength values σ ∗ i were acquired by recording the maximum apparent stress before coupon fracture for all orientations and thicknesses. While the material parameters along the orthotropic axes can be obtained directly in the uni-axial tensile tests of coupons in corresponding orientations, shear moduli and ultimate shear stress were derived of the 45 ◦ o ff -axis tensile coupons. The approximation approaches were originally proposed for classical fiber-reinforced composites (Chamis and Sinclair, 1977; Morozov and Vasiliev, 2003) and to date, are also used in context of AM (Laghi et al., 2021) as more complex test setups are thereby omitted. Considering a plane stress condition in the tensile tests, the shear modulus G i j and ultimate shear stress τ ∗ i j are transformed for an o ff -axis angle θ via Eqs. 1

cos 2 θ sin 2 θ

τ ∗ i j = σ ∗ i j ,θ cos θ sin θ

and

(1)

G i j =

2 θ

2 ν i j cos 2 θ sin

sin 4 θ E j

cos 4 θ

1 E i j ,θ −

E i −

+

E i

whereby θ in the present case is equal to 45 ◦ and E i j ,θ and σ ∗ i j ,θ are the Young’s modulus and ultimate strength measured at the corresponding o ff -axis coupon orientations, respectively. Potential e ff ects of the clamping condition and extension shear coupling are not taken into account. The experimental procedure for the thin-walled ribbed beams involved displacement-controlled loading the parts at a rate of 5 mm / min until initial fracture. The setup consisted of a servo-hydraulic cylinder (ZwickRoell,LH,10) in conjunction with a three-point bending fixture (MTS 642.01A-02, MTS Systems Corp., Eden Prairie, MN, USA), as detailed elsewhere (Sindinger et al., 2021b).

2.3. Finite Element Model Setup

Fig. 2a depicts the experimental three-point bending setup replicated as FE model by use of the pre-processor HyperMesh ® 2020 (Altair Engineering, Inc., Troy, USA). The thin-walled ribs were represented using first order quadrilateral shell elements (CQUAD4), whereby the element size was chosen based on a mesh convergence study (Sindinger et al., 2021b). The thickness information from the initial solid geometry is in the meshing process auto matically assigned to each element. The bulky region at the top, where seven ribs meet, as well as the rollers of the bending fixture, were meshed using 3D eight-node hexahedral elements (CHEXA). Boundary conditions were realized via multi-point constraints (RBE2), with all degrees of freedom fixed for the supports and with an enforced displacement in vertical direction at the indenter. The displacement was introduced in 50 steps at 0.03 mm increments. Between the part and the polished steel rollers sliding contacts were defined, since frictional forces were deemed negligibly small. The numeric simulation was setup as static geometric non-linear analysis using the Optistruct ™ solver template.

(a)

(b)

Fig. 2: ( a ) FE model with and without thickness representation, multi-point constraints at load introduction 1 and supports 2 as well as contact regions 3 . ( b ) Shell element rotated out of global material coordinate system by angle θ . Adapted from Sindinger et al. (2021b).