Hi, dfwaters.
Thank you for visiting Apple Support Communities.
I understand Safari unexpectedly closes when using the search function. I would recommend clearing your history and cookies from Safari. Once this is done test using the search function of Safari again.
To clear your history and cookies from Safari in iOS 8 or later, tap Settings > Safari > Clear History and Website Data. In iOS 7 or earlier, tap Clear History and tap Clear Cookies and Data.
To clear other stored information from Safari, tap Settings > Safari > Advanced > Website Data > Remove All Website Data.
Clearing your history, cookies, and browsing data from Safari won't change your AutoFill information.
To visit sites without leaving a history, learn how to turn private browsing on or off.
Safari web settings on your iPhone, iPad, and iPod touch
Cheers