Abstract: A coated part intended to be mounted in a turbomachine, includes a substrate of composite material with a matrix at least partially of ceramic, and an environmental barrier on the substrate and including (i) a bond coat layer including silicon present on a surface of the substrate, and (ii) an environmental barrier layer covering the bond coat layer, the environmental barrier layer including an inner region of barrier to oxidizing and corrosive species which is not cracked and located on the bond coat layer side, and an outer region, opposite the bond coat layer and covering the inner region, having a network of thermomechanical adaptation cracks having a distance between adjacent cracks included between 10 ?m and 50 ?m and having cracks extending over a depth included between 50% and 95% of the thickness of the environmental barrier layer.