I have a nice book "Waffen Enzyklopädie" (the english version has the title "Weapons - An international encyklopedia 5000 B. C. to 2000 A. D."), and it has a nice chapter about the effects of a nuclear detonation. Following effects are important in the first seconds of a detonation: air pressure and his effect on the buildings and the heat wave.
For the heat wave there are 7 categorys:
A - metal evaporates, B - metal melts, C - rubber is melting, D - wood is burning, E - burn of the skin, 3d degree, F - burn of the skin, 2nd degree and G - burn of the skin, first degree.
Effect of the air pressure on the buildings:
0-1 -> total destruction, 1-2 -> massive buildings are destroyed, 2-3 -> smaller objects are destroyed, 3-4 -> high buildings are damaged, 4-5 -> fabrics are destroyed, 5-6 -> dwellings are destroyed, 6-7 -> vehicles fallen, 7-8 brick houses are damaged, 8-9 wooden houses are damaged.
So now the interesting part the radius of each zone depending on how strong the warhead is:
200 kt:
A -> 0 - 1,7 km; B -> 1,4 - 2,5 km; C -> 2,4 - 5 km; D -> 3,7 - 5,8 km; E -> 5,3 - 7,6 km; F -> 6,7 - 10,5 km; G -> 9 - 15,3 km

1 -> <1,3 km; 2 -> <1,6 km; 3 -> <1,7 km; 4 -> <2,2 km; 5 -> <2,8 km; 6 -> <3,5 km; 7 -> <4,5 km; 8 -> <5,4 km 9 -> <9,4 km

There are also radii for a 1 Mt and even a 10 Mt warhead but i think its enough to answer the question could the battery survive an explosion of a small (compared to the mentioned above 200 kt warhead) 15 kt warhead at 40 km distance...
Edit: The overpressure in kPa left and the speed of the air in km/h right:
1: 21000 - 1078; 2: 14000 - 766; 3: 10500 - 611; 4: 7000 - 466; 5: 4900 - 362; 6: 3500 - 257; 7: 2100 - 186; 8: 1400 - 112; 9: 700 - 77