i have a very simple ajax call, just so i can test first:
<script  src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
<script type="text/javascript">
function validateLogIn()
{
  var username  = $("#username").val();     
  console.log(username,password,login,remember);
  //alert('Given data is not correct' + username + "   " + password);
  $.ajax({     
    url: 'validate.html'                         
    type: 'POST', // POST/GET
    data: { 'username' : username } //for now just pass username
    }).done(function(response){  //Attach a succes handler
    alert(response); //my complete code in validate.html
                     // displays in this alert!
    }); 
  }); 
}
 </head>
 <body>
   <form action="crud.html" method="post" name="form_submit" onsubmit="return validateLogIn()">
      <input required placeholder="Username" type="text" name="username" id="username"/>
      <input required placeholder="Password" type="password" name="password" id="password"/>
      <label for="remember">Remember Me:</label>
    <input type="checkbox" name="remember" value="yes" id="remember" />
    <br />
    <br />
    <input type="submit" name="login" value="login" id="login"/>
</form>
in validate.html: none of this gets executed
 <?php
  echo htmlspecialchars($_POST['username'], ENT_QUOTES, 'UTF-8');
  echo $username = $_POST['username']; 
  <script type='text/javascript'>alert('$username');</script>
 
    