PHP's strlen() function returns the number of ASCII characters.
strlen('borsc') -> 5 (bytes)
strlen('boršč') -> 7 (bytes)
$limit_in_kBytes = 20000;
$pointer = 0;
while(strlen($your_string) > (($pointer + 1) * $limit_in_kBytes)){
    $str_to_handle = substr($your_string, ($pointer * $limit_in_kBytes ), $limit_in_kBytes);
    // here you can handle (0 - n) parts of string
    $pointer++;
}
$str_to_handle = substr($your_string, ($pointer * $limit_in_kBytes), $limit_in_kBytes);
// here you can handle last part of string
.. or you can use a function like this:
function parseStrToArr($string, $limit_in_kBytes){
    $ret = array();
    $pointer = 0;
    while(strlen($string) > (($pointer + 1) * $limit_in_kBytes)){
        $ret[] = substr($string, ($pointer * $limit_in_kBytes ), $limit_in_kBytes);
        $pointer++;
    }
    $ret[] = substr($string, ($pointer * $limit_in_kBytes), $limit_in_kBytes);
    return $ret;
}
$arr = parseStrToArr($your_string, $limit_in_kBytes = 20000);