The scaling effect is caused by several factors:

1. The fact that the crystals in the steel do not change their size, so the proportion of surface area sticking them together versus the forces within the crystals (usually much stronger) change. The smaller the plate, the bigger the crystals are in proportion and the less surface between them (down to the point of a microscopic plate made up of one crystal!). This crystal-caused effect is rather small for the large plates used in real vehicles and ships, but is evident in all armors, homogeneous and ductile (can bend and tear) or hard and brittle (break suddenly). For this reason, the armor has to be made progressively softer (and, thus weaker, since hardness and strength track rather closely as long as the plate is not breaking in a brittle manner) as the scale increases to keep it from getting too brittle under projectile impact (cracks through too easily), which gradually causes the heavier armor to lose some resistance.
2. The fact that the brittle materials crack along surfaces (once a crack starts in such a material it tends to self-propagate unless somehow the tip of the crack is locked up). This lockup can be due to reducing stress points (curves instead of corners at edges, using nickel in the steel to replace iron at many points in the crystals, so that the sudden change in metal acts like a piece of cloth in a zipper and jams the crack tip, and so forth) or changing the metal properties so that the material that the crack tip enters is ductile and soft (relatively) and spreads the force on the crack tip, stopping it (an extreme example is that Jello does not crack!). Since a face-hardened plate has the face very hard and rigid, it does not resist cracking too well and the force from a sudden impact can cause the hard face to crack unless there is somewhere for the energy to go. The back layer, if properly made, will allow the shock-wave from the impact to move into it with no sudden changes that can start cracks, only failing if the energy is great enough to begin tearing out the back surface as it reflects back into the plate there (there is no place for most of the shock-wave to go at that point but back into the plate moving toward the face again). This takes a lot more shock energy than the hard face would require to split it open. This problem is compounded by the fact that the energy goes up in step with the weight of the projectile - that is, with the cube of the increasing dimensions for exactly scaled tests - but the surfaces that are cracking can only increase in size with the increase in surface area of the impact site - that is, with the square of the increasing dimensions - so the larger tests simply pour more energy into the cracks at the same rate (same speed of impact), causing the cracks to go farther before they can be slowed or stopped. The thicker the hard, brittle face layer in a face-hardened plate in proportion to it total thickness (the deeper the "chill"), the more this cracking can grow before the ductile back layer can disperse the remaining energy. This means that the thicker the face, the worse the plate resistance becomes for scaled tests with large projectiles hitting scaled-up plates. Conversely, with smaller scales, this works in reverse and can make thick-faced plates stronger against small projectiles which have much less weight and, thus, energy at a given striking velocity.
3. The method of plate failure is crucially important. For hard materials struck in their face with enough energy to punch through, the entire face will be punched out a roughly cylindrical plug like a cork from a wine bottle, tearing out the back layer in a cone shape (usually) in a thick-faced face-hardened plate as the face acts like a billiard cue ball hit by the player, with the backing layer acting like the numbered billiard ball. However, in this case, the cue ball and the numbered ball fuse together and exit the plate back at a reduced velocity (due to the increased weight of this one large mass), though it may break apart as it exits the plate back, of course. The continued force of the projectile on the face ensures that nothing (except some surface flakes, perhaps) can move in that direction, focusing this cork effect into a narrow cone or cylinder directly in front of the projectile nose, at least a low obliquity (near right angles). While this cork effect puts a very large stress on the projectile nose tip, which must essentially stop cold as its energy is transferred to the face layer and, eventually, the entire plug of face plus back layer - increasing the chance of the projectile nose shattering into pieces or suffering some other drastic damage, which usually reduces the ability of the projectile to continue trying to penetrate - this cork is also a surface failure and follows the square-cube law mentioned above, so it actually takes less energy to make happen than if the projectile had to tear open the entire thickness of the plate made of a soft, ductile material before it could go through. Thus, the formation of a plug indicates that the plate is good at breaking up a projectile's nose (shatter into small pieces before the shell can penetrate more than a tiny distance being the most effective form of damage), but it also indicates that the plate is rather brittle and takes less energy than a similar softer plate that does no form such plugs (assuming the same strength for this solid all-the-way-through-softer armor ("homogeneous") to the back layer of the hardfaced plate). For small-scale tests, the energy that the projectile has due to its weight is going down faster than the needed energy to plug the plate, so if the scale is small enough, plugging does not hurt resistance and can even help it, again assuming similar soft-portion strength to all of the armors involved in the comparison. Note that if the face layer is very thin, as in Harvey armor in the thicker plates, the punching out of the face does not go very deep before the tough, ductile steel in the rest of the plate stops it, after which the projectile must push through more-or-less like a ductile, homogeneous plate, but if the nose tip of the shell is shattered, this becomes much more difficult, causing the projectile to crush itself between its base moving forward at full speed (at least initially) and the broken nose trying to move forward at slow speed (relatively) through the steel armor. A shattered, weakened, flattened nose doesn't penetrate thick armor very well at right angles!

Soft AP caps work because they give the projectile nose its own "shock-absorber" that works just like the tough back of the face-hardened plate. The energy that passes through the plate face into its back layer does not break the face as long as there is no spot in the face that causes a crack to start prematurely. Similarly, the shock of impact into the projectile nose can be resisted as long as there is somewhere to hand off the energy fast enough to keep it from bouncing around in the nose and starting cracks. The shockwave moving directly down the projectile's length has to go all the way to the base (most of it, except for some that reflects off of the upper end of the explosive cavity) before it can reflect and go back into the nose; by that time, the armor impact is already decided one way or the other as to penetration. The energy going sideways in the nose has no such long delay; in fact, it has no real delay at all before it hits the sides of the nose and reflects, cracking the nose if the impact is of high-enough energy (which it almost always is against a good face-hardened armor). If you add a tightly-fitting thick ring of steel to the sides of the nose (the deeper the hard face of the plate, the larger the needed absorption ring), the shockwave can be handed off to that ring and it exits the nose. If the ring is too small to stay in one piece under the impact blow, it literally explodes outward as the shockwave reaches its outer boundary, absorbing the energy and making the projectile nose much less liable to be damaged. Thus, a soft AP cap merely has to flatten out evenly and in a ductile manner as it is squeezed between the plate and projectile nose tip, forming a tight-fitting cup surrounding the nose. This requirement restricts the obliquity angle that this kind of cap will work, however, since as the obliquity goes over about 15 degrees, the sides of the cap fold and leave air gaps, which are places where the impact shock is not absorbed and shatter can start. By 20 degrees obliquity, soft AP caps are virtually useless and very rarely work. On top of this, later extra-tough facehardened armors could remain uncracked at any impact angle even after the soft cap had been destroyed, forcing the hard nose tip and hard face layer into a "Sumo"-style pushing contest which the projectile nose tip almost always loses, since the plate is so much bigger and can resist more in such a relatively slow-motion brute-force contest. (Hard caps, introduced later, gouge a pit into the plate face as they are crushed, so they work much like a center-punch with a drill (the nose), destroying much of the hard face layer and seating the projectile nose into the pit to concentrate its impact force. Hard caps are much better and work at almost every angle of impact.)

In the KC tests given below, I give two or more computations where I adjust the thickness of face for the armor - change the percent of unhardened back, UB in the program, which is UB = 100 - (face layer thickness percentage) - and I also throw in a test of a similar Harvey Nickel-Steel plate (as computed using the Harvey test data given above to calibrate FACEHARD). The usual KC a/A armor of the period, as actually applied by Krupp to warships starting in the mid-1890's, had a roughly 35% face, though this varied quite a bit from manufacturer to manufacturer and time to time as the they tried to find the "sweet spot" of maximum resistance against various projectiles at different scales. I think that Krupp did a lot of experimenting with this face depth before coming up with the 35% as the best all-round compromise. The results below seem to indicate this. The projectiles are all the rather brittle uncapped steel AP shot of the late 1890s, which fail much more easily than the later improved steel projectile introduced during the 20th Century - those Midvale AP projectiles demonstrate how much of an improvement was made, once the ability to stiffen up the tough projectiles to reduce the rather extreme upset (compression lengthwise) effects they suffered from. The results are interesting.

FACEHARD "6.8" is my current modified FACEHARD version with more debugging and with Harveyized Nickel-Steel and Harveyized Mild Steel (estimated) added into the plate quality database. It was modified to handle the data from this and other sources concerning old AP shot and shell versus Harveyized Ni-Steel Armor Plate, which FACEHARD 5.8, the version used in the initial analysis, did not handle very accurately. The success of this upgrade is given in this revised analysis of the extensive data in the Cleland Davis PROCEEDINGS article described below. FACEHARD when doing damage effects, uses NONE, SHATTER ONLY ("perfect" uncapped projectile), MAX DAMAGE w/o SHATTER (typical damage effects on the projectile due to this impact if the shell does not shatter), and MAX DAMAGE w/SHATTER (all remaining applicable damage effects when shatter occurs first - shatter replaces many other kinds of damage, precluding them from ever happening). Damage effects, including those of shatter, vary from impact to impact, forming a "blur" of results through which I drew a line in the middle of to get my estimates in the FINAL RESULTS output (I tried to round the curve toward the worst damage results when doing this to give a better "feel" of the spread of effects in the output, unless they were very rare). Thus, for example, if the MAX DAMAGE w/SHATTER and SHATTER ONLY detailed results bracket the actual results, this indicates that the projectile is within the expected blurry-results range for shatter and, if shatter is indicated in the FINAL RESULTS for that impact, the program is working properly.

These results in my revised FACEHARD 6.8 are derived from:

1. When all estimated damage, but not shatter, is used, these old AP/APC shells have an average Q(Projectile-DAMAGE) = PDAM = 0.7 (compared to the best US Navy WWII AP projectiles with Q(Projectile) = 1.00). The projectile is penetrating in this damaged condition, bent, compressed, and/or broken in some manner, which requires a significantly higher velocity to accomplish. This is used for determining the kind of damage and the EBL, not the HBL or NBL (see definitions below). When shatter occurs, this is ignored and damage is determined by the various versions of shatter (nose-only or complete).
2. When no penetration-modifying damage occurs when going through the plate or when shatter occurs with weak-bodied shells, the value used for the HBL and NBL for these shells is Q(projectile-BALLISTIC LIMIT) = PLIM = 0.795 (based on tests against Krupp KC armor of the period ("KC a/A" or KC Old Type, as Krupp later called it)). When no damage occurs, this non-1.00 projectile quality is due to the fact that when hitting at a velocity less than that using this value in the formulae, the projectile deforms or breaks up instead of penetrating - if shatter also occurs, you get the sum of both this damage and shatter damage degrading penetration. That is, there is an "extra" velocity that must be added to allow the impact shock to the plate to be great enough that it breaks before the projectile does from this kind of damage and, at oblique impact, that the projectile is deflected less from its original path, reducing the twisting forces that can damage the middle and lower body.

M79APCLC is a program developed to incorporate a medium-long-nose (tangent ogive with radius of 1.667 calibers) pointed projectile of any size manufactured with high quality (resistance to damage from impacts) into WWII homogeneous armor steel penetration logic. It is based on extensive data developed during and after WWII at the US Naval Proving Ground, Dahlgren, Virginia, under Dr. Allen V. Hershey. Added to it was data concerning low- ductility plates from German Krupp Corporation WWII Wh-armor tests and penetration curves (the Percent Elongation logic). It is a complete, far superior replacement to the 1890 French DeMarre Nickel-Steel Armor Penetration Program good for undamaged uncapped AP projectiles to up to 80 degrees obliquity, plates up to 2 caliber thick, and striking velocities up to 3000 ft/sec, whichever of those three reaches its maximum first. The standard plate type is US Navy WWII Special Treatment Steel (STS) or Class "B" armor of 225 Brinell Hardness, 115,000 psi ultimate tensile strength, 95,000 psi yield strength, and 25% Elongation - this is rather low for US Army tank Rolled Homogeneous Armor (RHA), which is designed for small-size-projectile, very-high-velocity impacts, unlike ironclad naval armor. The DeMarre Formula has a plate/projectile combined quality modifier call the "DeMarre Coefficient" - given as "C" - to divide the actual striking velocity to give the expected complete penetration striking velocity (= US Navy NBL) for the plate and projectile used in a given test. This formula was only good at normal (right angles) impact; any other angle gives very poor results unless a complex adjustment for C is employed (rarely used). For example, C = 1.21 gives a value for the NBL very close to my M79APCLC program when the Ni-steel plate thickness is one-caliber - T = D - at normal obliquity, which is equivalent to Q(Armor) = 0.76 in M79APCLC when an uncapped projectile suffers no damage due to the impact with an 1890 Ni-steel plate. M79APCLC as-is and the DeMarre Formula using C = 1.21 give rather close results to one-another for the entire most-probable naval plate thickness range of 0.2-1.1 caliber at normal obliquity, which is to be expected, since DeMarre did a rather good job in his analysis work!

To do an actual analysis, one should adjust the striking velocity up and down from the actual one by 2.5% and also the impact obliquity up and down by 2.5% (0 degrees minimum, of course, and above the maximum allowed obliquity value for that impact - 70-80 degrees - would mean no penetration possible for that adjustment). This gives the blurry results "box" about the actual impact. Only if ALL adjusted value combinations give the same results (COMPLETE PENETRATION or NO PENETRATION with the same projectile damage in all cases, for example), is that result probably solid for all such impacts in that blurry region. Otherwise, you can "roll a die" to get which result will happen in any given impact.

On top of that, when shatter occurs, an additional factor is that the range is somewhat wider when there is a range of results between the no-non-shatter damage applied and the full non-shatter damage applied cases, here with another die roll, but being more like with two dice, going from rolling a 7 for full non-shatter damage applied down to a 2 for the no non-shatter damaged applied (ignoring rolls above 7), linearly stepping the HBL and NBL down by (DIE ROLL/6) times the difference between the two velocities as one gets the intermediate die rolls, if you want a simple way to do this. FACEHARD gives the various HBL and NBL values for all cases on its last optional screen, indicating the ones it used in its output screen, but also showing those it calculated, but skipped over, too.

Ensign Davis used the above tests to match "best-fit" curves for (soft) capped (APC) & uncapped (AP) Armor-Piercing projectiles, resulting in the above two formulae. His results were presented in the US Naval Institute PROCEEDINGS, Volume XXIII, Number 2, of 1897, Pages 284-299 + 8 pages of the raw test result data referenced in the text, in an article entitled "On the Perforation of Face-Hardened Armor".

Interestingly, the capped formula above is the same as the formula used by Krupp in WWII for armor-piercing capped (APC) projectiles versus nickel-chromium-steel face-hardened Krupp Cemented "New Type" (KC n/A) and homogeneous "Wotan Härte" (Wh, "Odin Hard") naval armors, though the Krupp formula changed to metric units, the constant 0.000085822 was replaced with another value, and the striking velocity was divided by a variable "C" - exactly equivalent to the "DeMarre Coefficient" used in that 1890 French homogeneous Ni-steel armor penetration formula of that name to adjust the test results for each set of test conditions (plate type, plate thickness, projectile type, projectile diameter, obliquity, and the striking velocity that gave the desired limit condition estimated by averaging several results under similar conditions) to match the formula as well as possible, smoothed into a curve of average C values versus obliquity for each projectile/armor combination. The Krupp version of this formula thus create tables of C values to adjust the results to match test results for normal and oblique impact up to 70 degrees from normal. This was for complete penetration for KC and Wh armors and, for KC armor only, for holing (caliber-size, I think) entirely through the plate, each projectile having its own set of C-value tables.

• ^This projectile acts like it was capped and the cap worked at 21 degrees (1 degree beyond regular soft cap functioning range with a KC plate). Thin face may allow cap to work since it only needs to work for a very short time before thin cemented surface is cracked around the nose tip, so cap pull-off occurs AFTER cap has performed its function for these plates. Even so, I would not expect a soft cap to work much over 20 degrees against this armor.
• ^6" is barely thin enough so that the back would not have cracked open when it bulged; no thinner.
• ^3.13.2These projectiles are the beginning of the development that led to the 1916 'MIDVALE UNBREAKABLE' shells.
• ^This projectile acts like it was capped and the cap worked at 21 degrees (1 degree beyond regular soft cap functioning range with a KC plate). Thin face may allow cap to work since it only needs to work for a very short time before thin cemented surface is cracked around the nose tip, so cap pull-off occurs after cap has performed its function for these plates. Even so, I would not expect a soft cap to work much over 20 degrees.
• ^This projectile did not have a chilled (hardened) nose and it had a large cavity (~4-6% filler weight).
• ^6.16.2These projectiles are the beginning of the development that led to the 1916 'MIDVALE UNBREAKABLE' shells. Deformed MIDVALE 10" AP acts like broken non-Midvale APC here; neither shatter.

This article is copyrighted 2017 by Nathan Okun and is reproduced on NavWeaps.com with permission.

11 October 2008

Revised, and added detailed KC test analysis.

11 January 2011

Revised using Facehard 6.8, and Q(Armor) = 0.76 for Ni-steel in M79APCLC.