In the paper, we propose a new nucleation rate function, which combines grain size, and models for nucleation and growth of voids in a ductile polycrystalline metal. The proposed model is used to analyse the effects of grain size on the dynamic tensile damage of high purity Cu samples with different grain sizes. Numerical results show that pull-back minima and void number decrease with grain size increasing, slope after pull-back and average void diameter increase with grain size increasing. The computed results are in qualitative agreement with experimental results.