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Apple can replace the device with a new one, if you are willing to pay the Out-of-Warranty-Service fee:

Out-of-warranty repair service

If your repair isn’t covered by Apple’s One Year Limited Warranty, AppleCare+, or AppleCare Protection Plan, your iPhone might be eligible for out-of-warranty service. For example, liquid damage isn’t covered by warranty but might be eligible for out-of-warranty service. Some damage isn’t eligible at all, for example if your device has been broken into multiple pieces. See Apple’s Repair Terms and Conditions for complete details.
Read Apple’s Repair Terms and Conditions

Model	Out-of-warranty service fee	Battery service*
iPhone 6s Plus, iPhone 6 Plus	$329	$79 *available only if battery fails Apple’s diagnostic test
iPhone 6s, iPhone 6	$299
iPhone 5s, iPhone 5c, iPhone 5	$269
iPhone 4s	$199
iPhone 4, iPhone 3GS, iPhone 3G	$149

Plus a $6.95 shipping fee, if required. Fees are in USD and exclude local tax. Pricing is for service through Apple. The final service fee we charge will be determined during testing and may be less than the service fee listed above. Pricing and terms vary for service through an Apple Authorized Service Provider.

Out-of-warranty pricing varies for Apple accessories such as adapters and Apple iPhone cases. Contact your carrier, Apple, or an Apple Authorized Service Provider for more information.

copied from Service Answer Center - iPhone