Material hardness at strain rates beyond 106 s−1 via high velocity microparticle impact indentation

The combined effect of size, inertia and porosity on the indentation response of ductile materials

“…Shu and Fleck (1998)). The greater indentation speeds are similar to the velocities used in the dynamic experiments performed by Sundararajan and Tirupataiah (2006) and Hassani et al (2020), among others. For all indentation speeds, the H − h curves display a concave-upwards shape, with decreasing hardness as the indentation depth increases (as in Fig.…”

“…In this section we present the results obtained with the cavity expansion model developed in Section 3, for indentation velocitiesḣ ranging from 10 −4 m/s to ≈ 400 m/s. We compare the theoretical predictions with the experimental results of Poole et al (1996), McElhaney et al (1998, Lim and Chaudhri (1999) and Hassani et al (2020) to demonstrate the predictive capabilities of our analytical model. In addition, we perform parametric analyses to bring out the effects that inertia, size effect and initial porosity have on the material hardness and the elasto-plastic fields that develop near the indenter during the indentation process.…”

“…The dynamic spherical cavity expansion model used to analyze dynamic indentation is developed in Section 3. Section 4 compares the results of the theoretical model with experimental results of Poole et al (1996), McElhaney et al (1998, Lim and Chaudhri (1999) and Hassani et al (2020) for annealed OFHC copper, showing that the cavity expansion model developed herein very well captures the increase in material hardness with decreasing indentation depth and increasing strain rate. The results of parametric analyses elucidating the specific roles of indentation speed, size effect and initial porosity, on the material hardness and cavitation fields that develop during the indentation process are also presented in Section 4.…”

“…In these experiments, the measured indentation depth and load were used to estimate the strain rate sensitivity of OFHC copper, and the results obtained were shown to be in agreement with the data obtained with Kolsky bar experiments. More recently, Hassani et al (2020) have developed an experimental setup to perform microparticle impact indentation to determine material hardness at strain rates beyond 10 6 s −1 (these are probably the first measurements of hardness at such high strain rates). These authors employed laser ablation to impact ceramic alumina microparticles of 14 µm diameter (as indenter) onto copper and iron targets, and obtained time-resolved measurements of the impact and rebound velocities together with post-impact measurements of the volume of the indent.…”

“…These authors employed laser ablation to impact ceramic alumina microparticles of 14 µm diameter (as indenter) onto copper and iron targets, and obtained time-resolved measurements of the impact and rebound velocities together with post-impact measurements of the volume of the indent. Similarly to Tirupataiah and Sundararajan (1991), Hassani et al (2020) calculated the dynamic hardness of the target material as the ratio of the plastic work to the indentation volume, and showed that, for strain rates greater than 10 6 s −1 , the hardness of the material increases up to 4 − 5 GPa, i.e. it becomes one order of magnitude greater than under quasi-static loading conditions.…”