A method of making a composite downhole article is disclosed. The method include forming at least one corrodible core member comprising a first material that is corrodible in a wellbore fluid at a first corrosion rate; and disposing at least one outer member on the core member, the outer member comprising a second material that is corrodible in the wellbore fluid at a second corrosion rate, wherein the corrodible core member has a composition gradient or a density gradient, or a combination thereof, and wherein the first corrosion rate is substantially greater than the second corrosion rate. A method of using a composite downhole article is also disclosed. The method includes forming a composite downhole article as described above; using the article to perform a first wellbore operation; exposing the article to the wellbore fluid; and selectively corroding the second corrodible member.