OpenGraph descriptions not showing when using WordPress SEO (Yoast)

Okay, now I’ll try to answer your question, but first a quote from the Yoast SEO Guide:

Some plugins, most specifically the All in One SEO plugin, use so
called “automated descriptions”. They use the first sentence of a post
to fill the meta description by default. That’s not very smart. That
first sentence might be an introductory sentence which has hardly
anything to do with the subject.

Thus, the only well written description is a hand written one, and if
you’re thinking of auto generating the meta description, you might as
well not do anything and let the search engine control the snippet… If
you don’t use the meta description, the search engine will find the
keyword searched for in your document, and automatically pick a string
around that, which gives you a bolded word or two in the results page.

But perhaps you can specify at least a default custom template for your meta descriptions: Go to SEO › Title & Metas and set up an Meta description template. You’ll find a lot of variables like %%sitedesc%% or %%excerpt%% within the Help tab.

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As I know, your aim is to display the description on Google+ and Facebook. You can also specify these descriptions in detail (recommended) within the Yoast WordPress SEO Widget:

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UPDATE: Check the class-opengraph.php file within the frontend folder of the plugin. What you’ll need is something like this:

if ( $ogdesc && $ogdesc != '' ) { // check if there is a custom description
    if ( $echo !== false )
        echo "<meta property='og:description' content="" . esc_attr( $ogdesc ) . ""/>\n";
    else
        return $ogdesc;
} else { // take the excerpt as fallback description
    echo "<meta property='og:description' content="" . esc_attr( strip_tags( get_the_excerpt() ) )  . ""/>\n";
}

UPDATE 2: Simply add the following filter at the bottom of your function.php (so you’ll be able to update the plugin):

function add_yoast_opengraph_description( $str ) {
    if ( $str == '' )
        return strip_tags( get_the_excerpt() );

    return $str;
}
add_filter( 'wpseo_opengraph_desc', 'add_yoast_opengraph_description' );

FYI: I noticed that it will take some time (sometimes) till meta descriptions will show up within social networks.