Can I buy a apple care after I bought the iPhone for half year？

Nothing. You'll have to pay the out of warranty repair fee to get the screen fixed.

See here for details:

iPhone Screen Repair & Replacement - Official Apple Support

Apple Care + is a preemptive measure. You cannot buy Apple Care + after the device has been damaged anyway.

海玮from北海 wrote:

I did that，my phone is iPhoneX without apple care，do I only have to pay 418 dollars for screen cracked？because I bought the phone 4 months a go

Sorry. Doesn't matter how long ago.

Crack screen is not part of a warranty.

Apple Care Plus will lower the fees for 2 incidents if you have Apple Care Plus within 60 days before the accident.

海玮from北海 wrote:

So I can not add the apple care to my iphone after I bought it for 60 days？

That's correct.

Note: Even if you broke the screen in just a few day after the purchased date, you won't be able to get Apple Care Plus.

Apple will check the iPhone for any damages before you can get Apple Care Plus

You have 60 days from date of purchase of the iPhone to get Apple Care+.

After that, you cannot get Apple Care+.

And if you were to break the screen during those 60 days you would not be able to get Apple Care+ either.

Apple Care+ needs to be bought while the iPhone is in perfect working order, less than 60 days old.

The screen repair cost for an iPhone X is $279 U.S. Price may change if you are somewhere other than the U.S.

海玮from北海 wrote:

I did not buy an apple care，but I screen cracked，what can I do now

Where are you located (I'm translating your username as being from Beihai, Guangxi, China) and where was the phone purchased (was it an Apple Store or authorized retailer)? There are a lot of little things that might matter as to whether or not you can have it fixed locally. If it was gray-marketed (originally for sale in another country) then Apple is well known for not servicing iPhones unless they're brought back to the country where they were supposed to be sold.

The issue with the iPhone X is that the glass is fused to the OLED display, so the cost of glass replacement includes the entire display assembly.

At this point (it's too late anyways) you're not going to be able to buy AppleCare after damaging it.

deggie wrote:

The display has been one piece since the first Retina display. You cannot change just the glass on any iPhone since then.

Most of the unauthorized repairs only involve the glass, which can be removed from the LCD. However, I heard about one company claiming that they can reuse the OLED from an iPhone X by removing it and re-fusing it in an oven.

y_p_w wrote:

Most of the unauthorized repairs only involve the glass, which can be removed from the LCD. However, I heard about one company claiming that they can reuse the OLED from an iPhone X by removing it and re-fusing it in an oven.

Which is COMPLETELY IRRELEVANT. Why are you even bringing it up? No responsible member here would recommend anyone take their phone for a repair by an unauthorized 'chop shop' unless the chance of having the device serviced by Apple had already been forfeited by a previous unauthorized repair.

You just proved the point I made regarding your posts in my last posting here.

Contradictory, uninformed, and irrelevant.

They don't involve replacing only the glass unless it is an iPhone 3GS or older. As I said before after the introduction of the Retina display (not the OLED) Apple displays were one piece units. I don't know of any 3rd party repair people who replace only the glass on the display. And you "hearing" about some company is just a useless hearsay.

deggie wrote:

They don't involve replacing only the glass unless it is an iPhone 3GS or older. As I said before after the introduction of the Retina display (not the OLED) Apple displays were one piece units. I don't know of any 3rd party repair people who replace only the glass on the display. And you "hearing" about some company is just a useless hearsay.

I wouldn't recommend it, but there are glass-only aftermarket replacement parts for various iPhones. When a mall kiosk charges $75 they're not replacing the LCD. I'd recommend going with Apple, but a lot of people are cheap and go aftermarket.

If a mall kiosk is charging $75 for just the glass they are ripping people off. A decent non-Apple display goes for around $75USD. I've seen a few glass replacements available for much older iPhones (Apple 2G, 3G, 3GS) but other than that I've not see any just glass available.

Too late. You would have had to purchase AppleCare within 60 days of purchasing the phone.

Click Support at the top of this page, then iPhone, then repair options to see your options.

Out of warranty screen replacement on iPhone X is $279 which is what is listed in the link Phil provided above.

Schedule an appointment at your Apple Store Genius Bar and that's what they'll charge.