The cross sections of fragments produced in the 140 A MeV 40,48Ca+9Be and 58,64Ni+9Be reactions have been calculated by the statistical abrasion-ablation model. The calculated cross sections of fragments are compared to the experimental results. Adopting the free space nucleus-nucleus cross sections in the calculations, the cross sections of fragments produced in the non-central collisions are well reproduced, but the cross sections of fragments produced in the central collisions are overestimated. If adopting the saturate density related nucleus-nucleus cross sections in the calculation, the cross sections of fragments produced in the non-peripheral collisions are well reproduced, but the cross sections of fragments produced in the peripheral collision are underestimated. It's suggested that the cross sections of fragments will be better reproduced by the SAA model if the nucleus-nucleus cross sections are related to the density distributions of projectile and target nuclei precisely.