The carbon added to the iron matrix sits in atomic sites that are not normally occupied. These are the "interstitial" sites of the body centered cubic crystal structure of iron. This is illustrated below for a stainless steel which also contains substitutional chromium that replaces iron on the normal lattice sites. The bcc crystal structure of iron is also shown.

The addition of these alloying elements to the crystal structure causes local distortions of the lattice and it is these distortions that make the lattice plastic deformation more difficult. Because the alloying elements are dilute, they do not much change the atom-atom interaction in the material and the elastic behavior is, therefore, little changed implying that Young's modulus will remain the same.

From: McMahon and Graham, :"The Bicycle and the Walkman," Merion (1992)