Automatically applying a pre_get_posts filter for child categories only

Try this:

EDIT: added short circuit return statements to avoid running unnecessary code on admin pages or other queries (e.g. nav menu items)

// Custom query for research sub-categories
function custom_query_for_research_subcategories($query) {
    if (is_admin() || !$query->is_main_query()) {
        return $query;
    }
    $qobj = get_queried_object();
    if (isset($qobj->taxonomy) && 'category' == $qobj->taxonomy ) {
        $term = get_term($qobj->term_id);
        if (!is_wp_error($term) && $term->parent === '45') { // replace 45 with whatever the research parent category is
            $query->set('orderby', 'title');
            $query->set('order', 'asc');
        }
    }
}
add_filter( 'pre_get_posts', 'custom_query_for_research_subcategories' );