PSI - Issue 64

Saim Raza et al. / Procedia Structural Integrity 64 (2024) 1200–1207 Raza / Structural Integrity Procedia 00 (2024) 000 – 000

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mm. The left segment is prescribed as the hinge support while the right segment is defined as the roller. Given the material properties in Table 1, the stress field starting from the outermost bottom edge of the prism, named as a corrugated tip in corrugated candidates, extending up to 2 mm is plotted for different scenarios.

Density [ kg/m 3 ] 2400.0

Table 1: Material properties selected for the concrete prism

Elastic modulus [GPa]

Poisson's ratio

Tensile strength [MPa]

20.0 3.00 As this study focuses on stress concentration in the local region surrounding the corrugated tip, analyzing mesh sensitivity becomes essential. To do so, we have plotted the normal stress field 33 ahead of the corrugated tip of the real prism with the sharp notch for three different meshes, corresponding to a specific load applied by the moving head; these three mesh sizes are as follows: I) coarse mesh: 0.4 mm II) normal mesh: 0.2 mm III) fine mesh: 0.1 mm. As shown in Fig. 6, starting from the mesh size of 0.2 mm, the stress field 33 becomes independent of the mesh size in regions separated by the dashed orange margin from the so-called mesh-dependent region, as shown in Bärnkopf et al. (2023). As expected the intrinsic singularity of the sharp notch impedes the mesh sensitivity analysis from converging in regions closer than 0.1 mm to the corrugated tip. In reality, an inelastic softening region ahead of the crack tip may develop, its size determined by a fraction of the Irwin material's length scale that bridges fracture toughness and material strength, as discussed in Sakha 2023. While this study does not explicitly define the extent of this inelastic region, we assume that it fully develops within the boundaries of the singular-dominated, mesh dependent region. It should be noted that following ABAQUS user's manual, a second-order fully integrated element type should be employed in stress-concentrated regions to accurately capture the severe gradients of stress distributions (Simulia, 2006). Therefore, in this study, we use element type C3D20 for the stress concentration regions. 0.2

Mesh-independent region

Fig. 6. Variation of the stress field ahead of the corrugated tip of the real prism for different mesh sizes

5.2. Implications of Stress Concentration in 3DPC on Flexural Cracking Loads Fig. 7a depicts the stress distribution 33 ahead of the outermost bottom edge of the prism across different architectures at a specific load of 210N. To ensure clarity, the contour plot's range remains consistent for all these candidates. As expected, stress concentration persists in all corrugated architectures. However, the degree of this concentration is most pronounced in the real prism with the sharp notch compared to its corrugated counterparts. Given this concentration effect, our focus now shifts to determining the cracking load for each candidate, defined as the load at which the normal stress 33 reaches the prism's tensile strength (as given in Table 1). This is shown in Fig. 7b, where the stress distribution for each scenario at the cracking load is plotted. Considering the extent of mesh-dependent region, the cracking load for corrugated architectures is calculated within the mesh-independent region, which is not applicable to the simple prism. As shown in Fig. 7b, the simple prism is