It depends on how much sun "semi-shade" involves. Panicum amarum and some Arundo cultivars will work in 1/2-2/3 sun. They won't be as tall or vigorous as in full sun, but they'll survive and bloom. P. amarum 'Dewey Blue' should hit 4' with enough water. Arundo donax will easily hit 6' with enough water. 'Peppermint Stick' is my favorite cultivar...so far.

Helictotrichon sempervirens gets 2 feet tall and has upright blue foliage that stays real neat and is clumping. It will take part shade, if its not too much shade.

Most often what I see under trees where grass will not grow is a lack of enough organic matter to help the grass grow. The soil will be very compacted and the tree itself will suck any moisture from the soil leaving none for any grass, although lack of sunlight can also inhibit many grasses from growing. Contact the people at your counties University Of Illinois Cooperative Extension Service and ask about 1) having a good, reliable soil test done, and 2) which Fescues would grow well in shady areas. Then dig in with these simple soil tests, Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top. 2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up. 3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart. 4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell. 5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy. to see what that soil might need to grow a good turf.

The two are not very compatible. If its not deep shade, you can use a Bermuda type that has some shade tolerance. 'Blackjack' is such a variety.