13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- Figure 4 shows cumulative mass loss of the substrate material after 5 sphere particle impacts. It is seen that the material removal is very small after the first impact and then increases with the number of impacts. In some cases, impact particles are able to penetrate into the substrate, which is not included in the cumulative mass loss. 0 1 2 3 4 5 6 0.0 0.1 0.2 0.3 0.4 Cumulative mass loss of substrate (10-6 kg) Impact particles 70m/s 80m/s 90m/s 100m/s 110m/s 120m/s 130m/s Figure 4. Variation of cumulative substrate mass loss As defined in the above section, erosion rate is the ratio of the cumulative mass loss of the substrate and the weight of impact particles. The relationship between erosion rate and impact velocity was proposed following a power law function from publications [13 - 16], that is, ݁ ݎ ݅ݏ ݊ ݁ݐ ܽݎ ∝ ܸ (9) However, the exponent value n differs with different literatures. Finnie [13] proposed the exponent of 2 and Hashish [14] gave a value of 2.5, respectively. Scheldon et al. [15] experimentally obtained an exponent value in the range of 2-3, while Yerramareddy et al. [16] reported a value of 2.35 for Ti-6Al-4V. In general, the exponent value n is in the range of 2.0 - 2.7. For metallic material, the value is in the range of 2.0 - 2.5 [6, 7]. Figure 5 shows the relation of erosion rate with the impact velocities in log - log scale. The slope of linear fitting curve gives an exponent value ݊ equal to 2.22 for Ti-6Al-4V, which is in accordance with the range reported by other researchers [13-16]. In addition, ElTobgy et al. [6] explained the reason for the relation between velocity and erosion rate in terms of energy aspect. 1.90 1.95 2.00 2.05 2.10 2.15 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 Original data point Linear Fitting curve Log(Erosion rate) Log (Velocity) y=2.22*x-4.35 Figure 5. Erosion rate vs. velocity in log-log scale Similarly, the relations between erosion rate and impact velocity have also been analyzed with irregular non-spherical particles. Figure 6 shows erosion rate and velocity relationship in log-log scale. The exponent value provided by the slope of linear fitting curve is 2.40, which is also in the
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