Distribution of breakage events in random packings of rodlike particles

Uniaxial compaction and breakage of rodlike particle packing has been studied using a discrete element method simulation. A scaling relationship between the applied stress, the number of breakage events, and the number-mean particle length has been derived and compared with computational experiments. Based on results for a wide range of intrinsic particle strengths and initial particle lengths, it seems that a single universal relation can be used to describe the incidence of breakage events during compaction of rodlike particle layers.

Figure 1

Rodlike particle packing before compression with random $\lambda =0$ (a) and uniaxial $\lambda =1$ (b) orientation.

Figure 2

Illustration of progress of breakage events during a single numerical experiment.

Figure 3

Correction to account for the breakage due to its own weight of the particle layer. The closed unconnected symbols represent uncorrected data ($\sigma /{\sigma }_{\mathrm{mat}}$), while open connected symbols represent data with correction [$(\sigma +w)/{\sigma }_{\mathrm{mat}}$]. It can be seen that the correction is significant for particles with small ${\sigma }_{\mathrm{mat}}$ only.

Figure 4

Double-logarithmic plot showing the dependence of the reciprocal number-mean particle length $1/L=M/\left(M_0{L}_0\right)$ on the effective stress $\widehat{\sigma }=(\sigma +w)/{\sigma }_{\mathrm{mat}}$. Data are annotated according to (a) the initial particle length $L_0$ or to (b) the particle strength ${\sigma }_{\mathrm{mat}}$. The two solid lines have slopes 0.37 and 3/5.

Figure 5

(a) Number of breakage events $M-M_0$ and (b) particle aspect ratio $L/2$ dependence on the effective compression stress $\widehat{\sigma }=(\sigma +w)/{\sigma }_{\mathrm{mat}}$ for random packings of various particle strengths ${\sigma }_{\mathrm{mat}}$ and initial particle length $L_0=21$. The solid lines in (a) correspond to the sigmoidal function defined by Eq. (7).

Figure 6

Dependence of the number of breakage events $M-M_0$ on the stress $\sigma$ for packings of various degrees of particle orientation $\lambda$.