You should not add a diffuse or specular contribution if the dot product between the normal and the direction to the light is negative (you have "fabs" in there, which creates the artifact in the middle part of the sphere on the first picture).

EDIT: Wikipediaseems to agree:

Although the above formulation is the common way of presenting the Phong reflection model, each term should only be included if the term's dot product is positive. (Additionally, the specular term should only be included if the dot product of the diffuse term is positive.)

You should not add a diffuse or specular contribution if the dot product between the normal and the direction to the light is negative (you have "fabs" in there, which creates the artifact in the middle part of the sphere on the first picture).