A multi-piece projectile for a small arms cartridge includes a metal cup that has a bore, a plastic sheath having a through hole and a high-density core. The cup is a cylindrical metal structure having a bore. The sheath is a cylindrical end and a conical end and a through hole. The core is a cylindrical structure having conical end and a blunt end. The projectile is assembled by placing the core in the through hole of the sheath and then pressing the sheath into the bore of the cup. The assembled projectile is attached to the cartridge by crimping the cup to the orifice in the end of the cartridge casing after it is filled with the propellant. When the projectile is fired all of the components remain coupled together but break apart upon impact with a target. Because the core has a higher mass than the other components the components separate very easily, the majority of the kinetic energy remains in the core. Once separated from the other components, the core is able to penetrate through various protective materials.