How to repair corrupted external hard disk

TestDisk, Data Recovery
TestDisk is powerful free data recovery software! It was primarily designed to help recover lost partitions and/or make non-booting disks bootable again when these symptoms are caused by faulty software, certain types of viruses or human error (such as accidentally deleting a Partition Table). Partition table recovery using TestDisk is really easy.

TestDisk Step By Step to recover lost partitions and repair damaged FAT/NTFS boot sector
Recover deleted files from NTFS partition

NOTE If seeked lost file are still missing, give PhotoRec a try. PhotoRec is a signature based file recovery utility and may be able to recover your data where other methods failed.

PhotoRec is file data recovery software designed to recover lost files including video, documents and archives from hard disks, CD-ROMs, and lost pictures (thus the Photo Recovery name) from digital camera memory. PhotoRec ignores the file system and goes after the underlying data, so it will still work even if your media's file system has been severely damaged or reformatted.

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The corrupted hard drive can be damaged in two ways: physical damage or logical damage. The logical damage still can be fixed by formatting. However, the physical damage can be irrecoverable.
Therefore, you could firstly try a free hard drive recovery tool to take a chance and format it afterwards. (This freeware has helped my friend recover his inaccessible data from his corrupted drive successfully.)
If this can not make a difference, you'd better ask a specialist or data recovery company for help.
Tips:
1. Stop writing anything new on the same drive to avoid original data overwritten by new data, which can make your data gone permanently.
2. Save your recovered data on a different drive in case of recovery failure.
3. Not forget to format this drive to see whether it could work.
4. Back up your data regularly in the future.