How thick should steel and aluminum armor be to protect against 152mm shell fragments?

It is no secret that artillery shell fragments pose a danger not only to openly located manpower (infantry), but also to combat equipment, especially if the ammunition detonates at a short distance. And we are not only talking about damage to sights and various attachments, but also through penetration of armor. In this regard, a reasonable question arises: how thick should this armor be so that fragments cannot penetrate it?
About the problem
Perhaps we should start with the fact that this aspect of anti-fragmentation protection has almost no bearing on tanks. Yes, artillery shell fragments can cause significant damage to vehicles of this class - for example, they can smash sights, destroy external equipment, damage the gun barrel and even seriously batter the chassis. However, they are often unable to penetrate tank armor - the thickness is beyond their capabilities.
But with equipment such as infantry fighting vehicles, armored personnel carriers, self-propelled guns and light armored vehicles, the situation is completely different. Different, but quite understandable: their armor is significantly thinner, which is due to the specifics of their use, so assessing their protection from shrapnel during a close shell explosion is very relevant from both a practical and theoretical (within the framework of comparing samples) point of view.
But how can this assessment be made?
Of course, the easiest way is to take the test results of the required equipment samples and compare them, but it is unlikely that everyone interested will have such documents at hand. And the conditions for carrying out executions on combat vehicles (distance from the detonating munition, its caliber, etc.) vary greatly depending on the technical specifications and standards adopted in a particular country, where the sample chosen for comparison comes from.
Given these circumstances, it is advisable to use armor penetration and the corresponding resistance equivalent, expressed in millimeters of steel or, for example, aluminum armor, as the main criterion by which one could judge the level of protection against fragments.
Millimeters in practice
Of course, it is possible to calculate the armor penetration of fragments using a calculator, which is often done in relevant studies both here and abroad. However, full-scale experiments with multiple detonations of shells at different distances from armor plates can be even more informative in this regard, since it is quite difficult to take into account all the nuances of fragment formation on paper - after all, we are not talking about armor-piercing ammunition.
One of these experiments was conducted in the Soviet Union and is described in sufficient detail in technical literature. We will familiarize ourselves with its results, since they were recommended by the authors not only for assessing the anti-fragmentation resistance of existing combat vehicles, but also for designing new armored vehicles.
This study involved armor plates of various thicknesses made of 2P, 54P, and BT-70 steel grades with thermomechanical treatment, as well as plates made of ABT-101 aluminum alloy. The characteristics of these materials can be found in the attached table.

As for the ammunition, the "guinea pigs" were 100mm and 152mm high-explosive fragmentation shells. The average initial velocity of their fragments, measured using high-speed filming, was: 760-780 m/s for 100mm and 920-930 m/s for 152mm. And the distribution of fragments by mass in percentage is shown below in the image.

It is noteworthy that the shells were detonated (at different distances from the armor plates) at a height that ensured maximum fragmentation of the target. That is, the experimental conditions were far from "greenhouse" - when artillery shells are detonated in a real battle, the equipment is exposed to less impact from the fragmentation flow, some of which goes past or even into the ground.
Now let's look at the information that we were able to obtain during the experiments.

Here is the anti-fragmentation resistance of the armor when a 100-mm high-explosive fragmentation shell explodes, depending on the distance. 1 - 2P steel, 2 - 54P steel, 3 - BT-70 steel with thermomechanical treatment, 4 - ABT-101 aluminum armor alloy.

This image shows the armor's anti-fragmentation resistance to a 152-mm high-explosive shell depending on the distance. The designations are the same: 1 - 2P steel, 2 - 54P steel, 3 - BT-70 steel with thermomechanical treatment, 4 - ABT-101 aluminum armor alloy.
Of course, the resistance of the studied materials turned out to be different - this is not surprising, given the characteristics of the alloys. But the main thing is that, based on these results, the authors were able to determine the average thickness of the armor (or its equivalent when using inclined armor parts and combined/shielded protection), which can guarantee protection from fragments at a distance of 10 meters from the exploding shell (the maximum strict requirement for the distance, which is included in the technical specifications for the production of lightly armored vehicles).
For 100 mm shells it is: 10-12 mm of steel armor and 32 mm of aluminum. For 152 mm shells: 25 mm of steel armor and 45 mm of aluminum. These figures, of course, can change by several percent in one direction or another depending on the grades of steel and aluminum alloys used today, but they give the general picture. Can be used.
Source:
V. Z. Vishnevsky, F. K. Zakirov, I. A. Levin. Study of anti-splinter resistance of armor plates for lightly armored VGM/ V. Z. Vishnevsky, F. K. Zakirov, I. A. Levin // Issues of defense equipment. – 1979. – No. 86.
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