When a computer need to be replaced, I remove the hard disk. However it seems a hell of a job to physically destroy the hard disk without heavy tools, which i don't have.
What is a safe way to destroy all a hard disk?
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I drive a 4" nail through the casing, near the motor. With a hammer and a bit of wood under the drive, it's easy. No need to open the case.
If you have a nail gun, it is perfectly capable of driving nails into a hard drive platter (source).
TL;DR probably you don't need to, unless you want visual, physical proof of data loss.
Chances are that what you really want to do is "be sure it cannot be read".
Now you've probably heard that deleting files or formatting the disk is not enough to prevent data recovery. You may even have heard that there are techniques capable of reading the content of a completely overwritten disk.
The first is true: deletion and formatting is almost always just a "marking of the space as available", but the contents is not immediately lost, and can be "undeleted", or recovered almost in its entirety as long as nothing else was written over that suddenly "available" space.
Recovering overwritten data on the other hand, while theoretically possible due to the physical HDD characteristics, requires significant means, a long time, and costs lots of money. It's also highly likely that it would not work (or cost even more) on modern hard disks where data is more tightly packed, redundancy is lower, and microscopic examination proportionally more difficult. Also, a modern hard disk is several orders of magnitude larger (in data size) than the first models where tunnel microscopy recovery was demonstrated feasible, which makes data recovery a seek for a much stealthier needle inside a much larger haystack.
It would only be conceivable for government-level operations (think San Bernardino iPhone unlocking). Is this really a plausible threat scenario for you?
If it is not, then simple overwriting should be enough. Just grab a DiskEraser boot CD, or SafeDelete, Darik's Boot And Nuke (DBAN), or any of several such utilities. You plug the CD in the drive, boot from it, answer a couple of questions (or even none) and let the utility chug along, overwriting some hundred gigabytes per hour or more depending on disk and CPU.
Pros: while the disk is obviously not "as new", it is possibly still useable - sellable, even. Any replaced obsoleted PC is still in working condition. Both the PC and the hard disk can be used for something else (if the disk has still a reasonable life expectancy, it can e.g. be placed in an external USB enclosure and used for backups). There are several charities that will accept in donation, or "purchase" the unit for a symbolic price, avoiding you all the hassle of electronic waste disposal (which would still be needed if you sandblasted, drilled or smashed the platters).
Cons: much slower than e.g. driving a large iron spike through the magnetic data platters. But if you have several PCs to get rid of, you can let them go in parallel. Two minutes to boot each, two hours erasure, and in three hours you have zapped twelve machines, which works up to a quarter hour per machine; more or less the same time it takes to physically extract each hard disk and subject it to the Van Helsing decommissioning.
NOTE: I've been advised that the Van Helsing decommissioning is NOT RELIABLE against those same techniques that allow recovering data from overwritten media. Those methods do not require an intact surface, which is why "ultra-safe deletion" does not simply shred the magnetic platters but has them burnt to ash.
So the situation is like this:
Overwriting Spiking Incineration Average opposition ENOUGH ENOUGH ENOUGH Three-Letter Agencies MAYBE NOT ENOUGH ENOUGH Three-Letter Agencies w/time and LOTS of money NOT ENOUGH NOT ENOUGH ENOUGH
On the other hand, a spiked hard disk is immediately recognizable as "decommissioned", which gives a certain additional procedural safety; it is much less likely to happen that hard disk is accidentally left undecommissioned.
An alternative to the "Van Helsing decommissioning" could be, since you need to disassemble all the platters if you want to safely spike them through, put them in a microwave oven, separately. The conductive surface will be thoroughly demagnetized (and stray currents will actually burn it through in several places). The platters will be mechanically intact (with visible burn marks), no splinters or cutty bits exposed, and the data on them will be even more unrecoverable than if you had drilled a hole through them (the smoke is probably unsafe to inhale).
There are a few reasonable ways to do this.
Destroying the platters
Hard drives work by using magnetized platters. The easiest way to destroy these would be to simply open the hard drive casing (often doable with nearby screwdrivers) and pour something like sand into the case. Often, just opening the case and getting dust on the platters will ruin them, but I assume you want to be extra sure. You could also use sandpaper to fully destroy the platter.
Destroying the data
Alternatively, you can destroy the data by using something like Darik's Boot 'n Nuke, this will repeatedly write over each byte to the point where data cannot be recovered, but the drive is still usable. This is my preferred method, but be very careful with DBAN - If you accidentally nuke the wrong drive, that data is gone. I would advise dedicating a machine to nuking disks so every disk attached can be safely destroyed.
There are powerful rare-earth magnets in most disk drives, so simply unscrew the case and salvage the magnets. Merely removing or even touching the platter will probably make it unreadable, due to contamination from dust and hands, but if you want to ensure a thorough job, pass one of those magnets along the surface. The platter also makes a decent first-surface mirror.
Simpler than some of the other methods, but more secure and reliable than the simpler methods, is to disassemble the drive (as explained in other answers), then use abrasives, i.e. sandpaper or similar, to remove the magnetic coating from the platters. The material of the platters themselves, whether glass, ceramic, or aluminum, is non-magnetic (it has to be, or it would interfere with data storage in the coating). So, no coating, no data. Done!
If you don't want to burn it, or don't have a fireplace that can contain a fire. Another way of rendering it useless is using acid. Hydrofluoric acid can burn through glass, some ceramics, and reacts with metals, so it should do the trick to destroy it, however it is extremely dangerous to handle, as it is a "contact-poison that causes deep, initially painless burns which result in permanent tissue death. It also interferes with calcium metabolism, which means that exposure to it can and does cause cardiac arrest (heart attack) and death. Contact with as little as 160 square centimeters (25 square inches) of skin can kill – that’s about the area of the palm of your hand" (source).
Hard disks/drives have platters inside of them on which data is stored. Destroying these platters is all you need to do to make the data unrecoverable. These platters are generally made from aluminum, ceramic or glass. Shattering them by smashing them with a hammer, or throwing them against the wall will do the trick most of the time, but the FBI has been known to recover data by painstakingly rebuilding the disks and piecing together data they can extract from it, so if you really want to be sure of it being gone, make a nice hot fire and toss the hard drive into it to melt the platters into something completely unsalvageable.
Note: when burning stuff, especially stuff not generally meant to be burned, you should be extremely careful that nothing explodes, and that the fire does not spread to places you do not want the fire going.
You are not supposed to throw away those computer parts, you should recycle them just like how you would recycle your batteries. Find recycling places in your city that takes computers and electronics. Wipe/Format your hard drive so it doesn't have your information on there and send it away to be recycled.
You mentioned you don't have any heavy tools around. However, if you have a sidewalk or other un-damagaible solid surface in your area, you could put the drive in a bag of some kind (to contain pieces) and drop it as hard as possible on the surface several times.
Also, in the area where I live, there are services that will destroy it for you (but obviously, if you want it done free, it's best to do it yourself).
Once you have done that, you should take it some place that can recycle the contents of the drive.