Recently I encountered this problem with kubuntu 16.04 SDDM login screen hangs. The issue occurred after I installed kubuntu 16.04 on an Intel i7-7700k with Intel 630 HD graphics and then updated to the latest packages.
I was able to login using the workaround of using Ctrl+Alt+F1 to get to a text console and then Ctrl+Alt+F7 to get back to X and the logged in session.
I stumbled upon a fix to the login hang while I was working to get rid of a screen tearing problem. The fix involves changing the compositor rendering backend from XRender to OpenGL.
More specifically to address the hang on login and problem with screen
tearing I did the following:
FIX SCREEN TEARING AND LOGIN HANGING
A) Start K -> Settings -> System Settings
Under Hardware section
Double-click Display and Monitor
Choose Compositor on LHS
Enable compositor on startup: Checked # was checked
Rendering backend: OpenGL 3.1 # was XRender
OpenGL interface: GLX
Tearing prevention ("vsync"): Full screen repaints # was Automatic
Ignore message "Full screen repaints" can cause performance problems.
Bug 321589 - Automatic VSync strategy causes tearing
Screen Tearing on Kubuntu 16.04 with Intel Drivers?
B) Set KWIN variables.
Edit /etc/environment and add the top and bottom line:
Listed as also working with NVidia.
I hope the above steps help others get rid of the login hang and screen tearing problems.