Invading causes an immediate drop of 5% for attacks 75% and greater of your land size. For hits below 75%, the following formula is used as well:
((Range - 0.40) * 100 / 7) - 5
You cannot invade if your morale is below 80%.
Exploring is not limited by morale.
Morale is a multiplicative bonus.
Bonus * Morale Penalty
Morale refreshes by 6% per hour when under 80% and by 3% when 80% or higher.