A composite frac plug (12) is formed of composite polymer materials, except for shear pins (52) and anchor cleats (96, 112) which are formed of metal. The frac plug (12) has an elastomeric ball seat (44) which sealing engages with a frac ball (18). A ratchet lock assembly (26) has a split ratchet ring (82) which moves over the mandrel (22) in a downward direction only, and prevents movement of the mandrel (22) downward within the ratchet ring (92). An anchor assembly (28) has slip bodies (92, 108) which are segmented and separately urge anchor cleats (96, 112) into the interior surface of a well casing (136).