PSI - Issue 68

6

N.T. Nguyen et al. / Structural Integrity Procedia 00 (2025) 000–000

Nhan T. Nguyen et al. / Procedia Structural Integrity 68 (2025) 91–98

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Fig. 1. (a) The uniaxial tension behaviour of quasi-brittle material under different settings for dissipation ratio produced by rate-independent model; (b) The effect of Perzyna viscosity variation on the uniaxial tension response; (c) Rate-effect captured by Perzyna enhancement model. The rate-effect investigation was then carried out through a simulation of the three-point bending test using the numerical Smoothed Particle Hydrodynamics (SPH) via the GeoXPM software (Bui et al., 2023). The simulation setup including the SPH parameters and test geometry follows the work by Wang et al. (2019). Fig. 2a illustrates the simulation result with Damage contour development, while the location for investigating the horizontal strain rate, ̇ Y , is located at 4 mm away from the tip of the notch, given that the beam height is 80 mm and the notch depth is 8 mm. Fig. 2b shows the effect of varying the damage dissipation levels on the beam response in term of load-displacement denoted as − . The beam response reveals that increased damage dissipation correlates with a higher peak load. This relationship suggests that as damage dissipation rises, indicating higher material brittleness, the material more likely facilitates crack growth, promoting faster fracture progression. Consequently, higher damage dissipation may implicitly link to strain rate, as an elevated strain rate within the FPZ is anticipated to contribute to a higher peak load.

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Fig. 2. (a) Damage contour in three-point bending simulation; (b) The effect of damage energy dissipation on beam response.

The strain rate associated with fracture opening was analysed by examining the strain rate of the SPH particles located at the notch tip, as illustrated in Fig. 2a. According to Lian et al. (2023), the quasi-static range falls between 10 /Z to 10 /X /! , yet, the opening strain rate within the fracture process zone (FPZ) was considerably higher, around 10 /% /! or even higher, and increased with the loading rate in all three cases, as shown in Fig. 3c. The rate independent simulation failed to reflect any change in the macro response (Fig. 3a). By contrast, simulations run with