In this work, interaction forces between two silica nanospheres after contact including the van der Waals (vdW) attraction, Born repulsion and mechanical contact forces are studied by molecular dynamics (MD) simulations. The effects of interaction path (approach or departure), initial relative velocity and relative orientations of two nanospheres are first examined. The results show that the interparticle forces are, to a large degree, independent of these variables. Then, emphasis is given to other important variables. At a small contact deformation, the size dependence of the vdW attraction and Born repulsion qualitatively agrees with the prediction based on the conventional theories, but this becomes vague upon further deformation due to the gradually flattened shape of deformed particles. An alternative approach is provided to calculate the interparticle vdW attraction and Born repulsion forces. Moreover, the MD simulations show that the Hertz model still holds to describe the mechanical contact force at low compression, which is obtained by subtracting the vdW attraction and Born repulsion forces from the total normal force. Comparisons with the Johnson-Kendall-Roberts (JKR) and Derjaguin-Muller-Toporov (DMT) models in terms of force-displacement relationships and contact radius show that the two models can be used to provide the first approximation, but there is some deviation from the MD simulated results. The origins of the quantitative difference are analyzed. New equations are formulated to estimate the interaction forces between silica nanospheres, which should be useful in the dynamic simulation of silica nanoparticle systems.