Look at some of the Sedges, Genus Carex. Many of them love semi-shade and wet soil, but it would be a big help if you could do some amending to provide drainage. Lacking that, how about piling good soil on top of the wet clay, and building a raised bed?

Well I've tried amending by adding manure compost and straw(not all at the same time) but it had no effect. Couldn't really do a raised bed as the ground slopes towards the house and when it rains well, we get a lot of rain! The back part of the bed is the edge of the lawn and is raised some but the front edge is flush with the ground. I don't have a lot of money and don't want to do any major work as we may be moving in a few years,would just like something there other than bare soil.

Amending clay soil can take years....so you might want to give up if it is as low draining as you say....

Definitely wouldn't add soil on top...the drainage would really be the same and it would be a waste of money...

Keep adding OM, but also add some Gypsum pellets...very cheap, but you need to add quite a bit when amending.

To be honest you'd need a JCB excavator on this stuff to even make a dent. Even the weeds struggle! I like the round of carex and rushes,even tho they're not grasses they are rather cool

"Definitely wouldn't add soil on top...the drainage would really be the same and it would be a waste of money..."

Think about it a bit. We regularly grow grasses in containers on patios and walks, which are no different from a berm of well draining soil on top of something which doesn't drain. I've grown them in raised beds built on concrete slabs. As long as the growing medium drains, the plants will grow.

Larry..a word of caution. Look for varieties which will grow in standing water. When you dig a planting hole in your clay, you are effectively creating a bucket, into which you will place your plant's root ball. When it rains, that 'bucket' will fill with water which will take a long time to drain away. Depending upon how deep the clay is, you can alleviate this to an extent by drilling holes in the bottom of the planting hole. Use a piece of rebar, and drive it in a ways with a hand sledge. Then force it back and forth to widen the hole. Keep doing this as deep as you can. When you have the rebar hole drilled, fill it with pea gravel or coarse sand. Do a few of these, and you'll improve the drainage in the planting hole.

When you dig a planting hole in your clay, you are effectively creating a bucket, into which you will place your plant's root ball. When it rains, that 'bucket' will fill with water which will take a long time to drain away.
Yea donn thats exactly how it is out the front,which is why I thought of grasses and sedges etc.

Have you tried digging land drains? You will need to dig right through the clay and then fill the trench with stone, covered with subsoil and then topsoil.

You will need to allow for the ground sinking as it settles

Here is a link that might be useful: Turf

If you don't want to amend all the soil (I would advise lots of coarse concrete grade sand which is real cheap) here are some grasses to try. The first one will tolerate less full sun and you might have enough sun for the second two. If you amend just parts, you might be able to do a mixed grass planting by adding the carex types, choosing a nice color combination.

1. Leymus arenarius "Blue Dune". This very pretty grass will take anything and is a powder blue. Its a spreader however and can be invasive in wet soil. You might want to contain it with some kind of barrier. It prefers exactly what you have, heavy clay and wet. There is another type Leymus arenarius "Blue Lyme Grass" that gets about 4 ft. tall. Same tolerance but a bit less decorative.

2.Andropogon glomeratus. Has very pretty plumes and good golden winter color.

3.Sorgastum nutans "Indian Steel" Very upright, blue form.

Also, look at the types of Juncus. They like it wet and some tolerate part shade.

Karl Forster will grow in clay soil. Being a reed grass it handles moisture well.

So does Panicum. Lots of nice cultivars. I'm going to hate trimming mine down this spring when the new growth starts.

I started a perennial/Ornamental grass bed last year in a very heavy clay area that is also wet. I started out doing a hybrid Inter Bay/Lasagna mulching process (see Soil and Compost forum) on this area in Nov and then planted in the following March. I then had worms and better soil and it will be better this coming year. It does take time.

I also experimented with different planting holes and mixes and found that deep holes accumulated water with no where for it to go resulting in dead plants. The best holes were very shallow wide holes like a plate (not a bowl) with the plant raised on top of that. Then there was no where for the water to accumulate.

I had a lot more problems with the perennials that were not grasses. The grass did best but I have yet to go through a wet winter yet (which I am having) so the final verdict is still out until spring. As mentioned above, Karl Forester seemed to do well in clay.