13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- 1, the element is assumed to have failed and removed from the model instantly [7]. 2.1.4. Equation of state When a ductile material is impacted by erodent particles at a considerably high speed, the Grüneisen equation of state (EOS) [7] is used to simulate the shockwave effects for ductile material. The shockwave velocity υୱ is much higher than the elastic-plastic wave or material velocity. Across the shock wave, a discontinuity takes place in material properties. The cubic shock velocity υୱ and material particle velocity υ୮ obey the following relation: υୱ ൌC Sυ୮ (5) Table 1. Material constants of Ti-6Al-4V Material properties Symbol Ti–6Al–4V Density (kg/m3) 4428 Elastic modulus E (GPa) 113.8 Poisson’s ratio 0.31 J-C yield strength A (MPa) 1098 J-C hardening coefficient B (MPa) 1092 J-C strain hardening exponent n 0.93 J-C strain rate constant C 0.014 J-C softening exponent m 1.1 Melting temperature Tm (K) 1878 J-C damage constant d1 0.09 J-C damage constant d2 0.27 J-C damage constant d3 0.48 J-C damage constant d4 0.014 J-C damage constant d5 3.87 Elastic bulk wave velocity C0 (km/s) 5.13 Slope in ߭ ௦ vs. ߭ diagram S 1.028 Grüneisen coefficient ߛ 1.23 where ܥ is the elastic bulk wave velocity. For compressed materials ( ߤ 0), the pressure is defined as follows: ܲ ൌబబమఓൣ ଵାሺଵି ఊబ/ଶሻఓି ሺ/ଶሻఓమ൧ ሾଵି ሺௌି ଵሻఓሿమ ߛ ܧ, (6) For expanded materials ( ߤ ൏0), the pressure is defined as follows: ܲ ൌ ߩ ܥ ଶ ߤ ሺ ߛ ܽ ߤ ሻE (7) where ߛ is the Grüneisen gamma, ܽ is the first-order volume correction to ߛ , and ߤ ൌ ߩ/ߩ െ 1, ߩ is for current density, and ߩ is initial density. The material constants for Ti-6Al-4V are listed in Table 1.Table 1 [6]. 2.2. FE model The erosion wear process is simulated using a commercial finite element solver, ABAQUS/Explicit (Version 6.11-2). The analysis is performed using Lagrangian formulation. In previous study,
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