Many bathtubs are made from acrylic coatings, which consist of acrylic polymers and an acrylic paint covered with sealants. This helps these bathtubs stay affordable while still protecting against moisture damage and providing resistance to impact damage. The acrylic surface of your bathtub is not designed to hold any other materials, including tile and tile components like grout.
Acrylic Surface Adhesion
The main problem with your acrylic tub surface is adhesion. Tile uses strong adhesives so that the tiles can be bonded to the subfloor and stay bonded permanently. No tile can be placed over sealants or paints of the sort that acrylic tubs have. The tile simply will not be able to bond with the surface, and will soon fall off.
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Another reason that tile cannot be used with acrylic tubs is the subfloor issue. An acrylic tub is not a true subfloor. Even if the coatings were removed and a rough fiberglass, metal or porcelain surface was left, the tub was still not made to function as a strong, level subfloor to support the tile. With the weak acrylic subfloor, the vibration and warping alone would cause the tile to fall off, even if there were no problems with the adhesive bond.
Tile requires a mortar bed or cement fiberboard, preferably a combination of the two, for a good tub subfloor. The mortar bed is created from different layers of concrete, which are often slanted toward a drain so that the tub will not experience standing water problems. The fiber cement board helps add a moisture-resistant, even layer for the tile to adhere to.
Surrounds and Other Alternatives
While you may not be able to install tile on your acrylic tub, you can certainly install tile around it. This is a common type of bathtub remodeling, in which a tile surrounding is installed in front of the tub. It adds tile accents that you may be wanting to use, but avoids the cost of replacing the tub entirely so you can tile properly.