The HTTP basic authentication protocol has no support for any notion of "logout". The most one can do is some client/browser-specific action to get the client to stop using the set of credentials it has cached for a given host and realm and optionally start using another set of credentials. As others have noted, such client-specific actions exist in various browsers for those who find them useful.
If you need a true sense of "logout", i.e. one that is understood by the server and that truly ends a login session, then you'll need to use a different authentication scheme, e.g. form-based authentication using cookies. This is supported as of Windchill 10.1 M010, but requires that you select a form-based authentication mechanism you wish to use. In general such mechanisms also tend to impose an idle timeout on login sessions, which can be a source of annoyance for end users. If you enable form-based authentication in 10.1 M010 or higher you will get a "logout" action in the Windchill UI.