if a husband and wife after 20 years of marriage and in their mid fifties,have discord because the husband verbally abuses her and physically threatens her and has hit her.finally after a serious act of violence when he hit her hard on the head and kicked her, she still kept quiet and talks only when necessary. is this sinful.? He is very quick tempered ,he refuses to discuss matters and has told her not to involve any outsiders.He is a TV addict and does not like to engage in working, from the early days. she helped throughout to run an islamic girls school,and he handled the finances. most of the issues can be sorted out if he talks.but he refuses to , and curses her,. she has strong reason to believe he indulges in porn. he suffers from erectile dysfunction, for the past 10 years.he uses bad language, . he makes salat and talks islaam! she remains this way because she has only him for a mahrem. her only brother has apostated!will it be sinful if she finally decides to divorce. she has a daughter who is unmarried.she is prepared to forgive him but he still is unrepentant and once said,"i should have murdered you", when she tried to reason with him. she too prays, wears hijab etc:

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

If the situation is as mentioned in the question that the husband abuses his wife physically and threatens to beat her, kicks her and abuses her verbally using obscene words and other details which you mentioned, then this is a clear injustice and his behavior contradicts the order of Allaah to the husbands to treat their wives honorably. Allaah Says (what means): {And live with them in kindness.}[Quran 4:19]

In fact, each of the above misbehavior of the husband allows the wife to ask for divorce but we do not advise her to hasten to ask for divorce unless she performs the Istikhaarah prayer and seeks the advice of wise people from her relatives because it might be more beneficial for her to be patient with her husband. For more benefit on the cases when a wife is permitted to ask for divorce, please refer to Fatwa 88408.

However, we advise the spouse to have mutual understanding and both of them should know the rights of each other and fulfill them as much as they can. Allaah Says (what means): {And due to the wives is similar to what is expected of them, according to what is reasonable.}[Quran 2:228] For more benefit on the rights of the spouses towards each other, please refer to Fataawa 85308 and 83157.

Finally, the two following matters should be mentioned:

1-    It is not permissible for the wife to accuse her husband of watching pornographic films without clear evidence. This is a bad assumption (suspicion) and this is forbidden.

2-    It is an obligation to advise the brother of this wife who apostated from Islam and remind him about the seriousness of this matter hoping that he will take heed and re-embrace Islam. For more benefit, please refer to Fatwa 87672.

Allaah Knows best.