Am I authorized a overseas service bar for my deployment to Afghanistan from July 15, 2013 to December 18, 2013?

LTC Paul Labrador is correct in stating one day in combat zone equals one month. Time in combat zone is cumulative, so if you have three two month tours that would give you six months in combat and one strip. I believe you were looking at DA PAM 670-1. In AR 670-1 date 10 April 2015 Para 21-29 a (12)-(16) address the time periods since 9/11 to present for overseas service bars. Para 21-29 a (12) address your dates specially "One overseas service bar is authorized for each 6–month period of active Federal service as a member of a U.S. Service participating in Operation Enduring Freedom, in the CENTCOM area of operations, and under the control of the Combatant Commander, CENTCOM, between 19 September 2001 and 31 December 2014; or Operation Enduring Freedom-Philippines, between 19 September 2001 and a date to be determined."

OSB's are awarded for 6 month's deployed duty in a designated area. Unless things have changed, a "month" was counted as a full month if you were in theater and drew combat pay any time during that month. It could have literally been one day and you would have been credited the whole month for purposes of the OSB. So if you are asking if the partial months will still qualify you, they should.

Edited comment. I misread the topic and thought you were asking about the OSR and not the OSB.