Select posts with a custom taxonomy as a custom field

I am using woocommerce, so I have the product category taxonomy (product_cat). On a product category page, I would like to display the posts that are in that (product) category. That will be the announcements for that product category.

So I add a custom taxonomy field named 'related_category' to the posts and select the product_cat as the taxonomy. Here are my settings:

On the product category page, here is what I do:

$currentId = get_the_ID();
//Get terms
$terms = get_the_terms( $currentId, 'product_cat', 'string');
//Pluck out the IDs to get an array of IDS
$term_ids = wp_list_pluck($terms,'term_id');

At this point I have an array of id's. Then I build a query:

$r = new WP_Query( apply_filters( 'widget_posts_args', array(

  'post_type' => 'post',
  'tax_query' => array(
    array(
      'taxonomy' => 'related_category',
      'field' => 'id',
      'terms' => $term_ids,
      'operator'=> 'IN'
    ))

) ) );

And I get no results. I check the database and see that the posts have the right values in their custom fields:

I am suspecting that there is some mistake in my query. Any ideas how to form the query?