Filter custom post with custom taxonomies with AJAX

For several hours I have been searching for the solution to my problem, I have created a custom post 'work' with an 'expertise' taxonomy and I want to display my posts and add a filter by taxonomy. The code below works well but instead of loading in the same page the result of the filter it opens me each time a new page. I have tried several ways to achieve this result but I still have this problem so I come to wonder if the problem is not elsewhere, my file to display my custom posts maybe?

archive-work.php

<?php
/**
 * Template Name: Work List
 *
 */
get_header();

the_post();
?>


<section class="headerpage">
    <div class="head" >
        <div class="container">
            <div class="col-md-7">
                <h1><?php echo get_the_title( 14 ); ?></h1>

                <?php echo '<p class="subtitle">'. get_secondary_title( 14 ) .'</p>';?>
            </div>
        </div>

    </div>
</section>
<div class="container filters-projects-wrap">
    <div>
        <span class="small-text">FILTER BY</span>
    </div>
    <div>
        <ul class="filters-projects-ul">
            <li><a href="<?php echo esc_url( home_url( '/projects/' ) ); ?>">ALL</a></li>
        <?php $categories = get_categories('taxonomy=expertises&post_type=work'); ?>
                <?php foreach ($categories as $category) : ?>
                        <li><a class="projects-filter" href="<?php echo get_term_link($category->cat_ID); ?>"><?php echo $category->name; ?></a></li>
        <?php endforeach; ?>
        </ul>
    </div>
</div>



<div class="projects-results">
        <?php $res = my_get_posts();
                echo $res['response'];
        ?>
</div>

<?php get_footer(); ?>

functions.php

function ajax_filter_posts_scripts() {
  // Enqueue script
  wp_register_script('afp_script', get_template_directory_uri() . '/assets/js/work.js', false, null, false);
  wp_enqueue_script('afp_script');

  wp_localize_script( 'afp_script', 'afp_vars', array(
        'afp_nonce' => wp_create_nonce( 'afp_nonce' ), // Create nonce which we later will use to verify AJAX request
        'afp_ajax_url' => admin_url( 'admin-ajax.php' ),
      )
  );
}
add_action('wp_enqueue_scripts', 'ajax_filter_posts_scripts', 100);


function ajax_filter_get_posts( $taxonomyproject ) {

  // Verify nonce
  if( !isset( $_POST['afp_nonce'] ) ||
      !wp_verify_nonce( $_POST['afp_nonce'], 'afp_nonce' ))
    die('Permission denied');

     $taxonomyproject = $_POST['expertises'];
     $result = json_encode(my_get_posts($taxonomyproject, true));
     echo $result;

     die();

}

function my_get_posts($taxonomyproject = '', $ajax = false){

// WP Query
$args = array(
    'post_type' => 'work',
    'posts_per_page' => -1,
    'tax_query' => array(
        array(
            'taxonomy' => 'expertises',
        )
    )
);

  // If taxonomy is not set, remove key from array and get all posts
  if( !$taxonomyproject ) {
    unset( $args['tax_query'] );
  }

  $query = new WP_Query( $args );
  $html = '';
  $items = array();

  if ( $query->have_posts() ) :
       while ( $query->have_posts() ) :
       $query->the_post();

       $res = '<div class="col-lg-4">'.
                  '<a href="'.get_permalink().'">'.
                      '<article class="panel panel-default" id="post-'.get_the_id().'">'.
                          '<div class="panel-body">'.
                              get_the_post_thumbnail().
                              '<div class="panel-cover">'.
                                  '<h3>'.get_the_title().'</h3>'.
                                      get_the_content().
                              '</div>'.
                          '</div>'.
                      '</article>'.
                  '</a>' .
              '</div>';


       $ajax ? $items[] = $res : $html .= $res;


   endwhile;

   $result['response'] = $ajax ? $items : $html;
   $result['status'] = 'success';

   else:
       $result['response'] = '<h2>No posts found</h2>';
       $result['status']   = '404';
   endif;
wp_reset_postdata();
return $result;
}

work.js

data = {
            action: 'filter_posts', // function to execute
            afp_nonce: afp_vars.afp_nonce, // wp_nonce
            post_type: "work", // selected tag
            };

        $.ajax({
            type: "post",
            dataType: "json",
            url: afp_vars.afp_ajax_url,
            data: data,
            success: function(data, textStatus, XMLHttpRequest) {
                console.log(data);
                // Restore div visibility
                $('.projects-results').fadeOut()
                    .queue(function(n) {
                            $(this).html(data.response);
                            n();
                }).fadeIn();
            },
            error: function( XMLHttpRequest, textStatus, errorThrown ) {
                /*console.log( MLHttpRequest );
                console.log( textStatus );
                console.log( errorThrown );*/
                $('.projects-results').fadeOut()
                    .queue(function(n) {
                            $(this).html("No items found. ");
                            n();
                }).fadeIn();
            }
        });
    });

});