I processed a Membership Expiration smart field and it does not show on the Smart Field tab of the constituent record. It does show in my query's results.
The Membership expiration smart field calculates values for membership expiration dates based on criteria you set. Based on your selection in the Value to return field, the smart field returns the number of days, weeks, months, quarters, or years until the membership is set to expire.
This smart field's value must be used within a query and will not show on the constituent record.