Hello.
I am not all knowing, and do not know the truth about prophet Muhammad's life to the fullest. God Allmighty knows best.
First, I have to say one thing: the Qur'anic principle requires that one restrains himself from his/her urges and acts as morally as possible. In order to have sexual relations with someone, a Muslim must be married to the person. The person to be married (woman) must agree to the man be he a king, a prophet or a slave.
With that being said, as a leader of a Muslim community and the Seal of the Prophets (the Last Prophet pbuh) Muhammad savs would never, in my personal opinion backed by the Qur'anic verses and teachings, rape a woman.
In the ancient times, all the way going to the Abraham pbuh and Moses pbuh, it was practiced according to the Holy Bible that the women captured in war be taken to wives. The same was ordered in the Holy Qur'an as a rule of warfare, I believe.
When you look at the Holy Bible, it is said that Sarah r.a. suggested to Abraham pbuh to take Hagar r.a. to have her give birth to a child. In our age this would sound to be against Hagar's will, but in their time it was acceptable.
The time of the Prophet Muhammad savs was different from ours. He grew up in a place where female infanticide was practiced, women were slaves and had no rights at all. Islam gave many rights to the women. I know that it is difficult, but we often scrutinize Prophet Muhammad's life through the modernized eyes. One thing that is overlooked about his life is the fact that he was married to only one wife for 25 years of his life. The majority of women he married later were widows and he lived up to the Qur'anic teaching to protect and respect women. Despite the freedom of Islam that was brought to the female population of his time, the women I am sure still were in danger as well. I mean, look at our time. 1400 years later after the Revelation of the HOly Qur'an, we still see some unislamic practices in the Middle East: 'honor killings,' stoning and throwing acid at women who refuse to marry certain men. All three are examples of grave sins, go totally against the Qur'anic laws and are the attack on basic human rights.