Thermal–chemical–mechanical gun bore erosion of an advanced artillery system part one: theories and mechanisms

Wear 258 (2005) 659–670

Thermal–chemical–mechanical gun bore erosion of an advanced artillery system part one: theories and mechanisms S. Sopoka,∗ , C. Rickarda , S. Dunnb a

Army Armament RD&E Center, Ben´et Laboratories, Watervliet, NY 12189, USA b Software and Engineering Associates, Carson City, NV, USA Received 22 December 2003 Available online 28 October 2004

Abstract Thermal–chemical–mechanical gun bore erosion theories and mechanisms are described for an advanced artillery system and its associated laboratory-firing simulator system. Both high and low contractile chromium electroplated-coating types are examined. These theories and mechanisms are based on bore erosion measurements and characterizations for each of the coating types used in this live fired system and its simulator. This artillery system consists of a cannon, charge, projectile, and additives. Its simulator consists of a vented combustor, charge, and additives. Gun bores typically have an erosion barrier of 0.05–0.50 mm high or low contractile chromium electroplated coating on a nickel–chromium–molybdenum–vanadium high strength gun steel substrate. Gun system firing rates, zones, coating types, and coating thickness vary. The main types of measurements and characterizations are of gun system components, firing conditions, gas–wall kinetic thresholds from simulators, during-life erosion metallography and depth, and end-of-life erosion metallography, depth and chemistry. The initial gun bore erosion theories and mechanisms consist of combustion gases traveling down very fine radial cracks in the chromium coating and degrading the substrate steel. These fine cracks result from the plating process. This thermal, diffusion, and chemical degradation weaken the coating–substrate interface. Coating platelets eventually depart forming micro-pits that grow into gun tube condemning macro-pits. These erosion theories and mechanisms are subsequently used to develop erosion models, predictions, and mitigation efforts for each of the coating types used in this advanced artillery system and its simulator. © 2004 Elsevier B.V. All rights reserved. Keywords: Gun systems; Bore erosion; Bore coatings; Bore substrates; Erosion theories; Erosion mechanisms

1. Introduction Two major research efforts were undertaken by the US Defense Department to understand and control gun bore erosion. The first National Defense Research Committee effort resulted in a final report, “Hypervelocity Guns and the Control of Gun Erosion”, published in 1946 that provided the first notable description and theories of gun bore erosion [1]. The second effort resulted in numerous final reports, “Gun Tube Erosion and Control”, published in 1970, 1977, 1982, and 1988 volumes that provided the first comprehen∗

Corresponding author. Tel.: +1 518 266 4952. E-mail addresses: [email protected], [email protected] (S. Sopok). 0043-1648/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2004.09.031

sive description and theories of steel bore and chromium plated gun bore erosion [2]. This second effort, of which we participated, provided the detailed description and theories of gun bore erosion that we still use today based on the dominant degradation from thermal, interstitial diffusion, and gas–wall reaction effects leading to erosion. This second effort was summarized in a 1988 book chapter entitled “The Problem of Gun Bore Erosion: An Overview” by Ahmad [3]. More recent achievements were summarized at the 1996 Sagamore Workshop on Gun Barrel Wear and Erosion [4]. New insights provide additional details to our previous thermal–chemical–mechanical gun bore erosion characterizations, theories, mechanisms, models, and predictions for non-coated and coated cannons [5,6]. This erosion model was

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comprehensively extended for advanced direct fire refractory metal-coated gun bores with steel substrates in the latter reference. This paper extends this previous work by providing gun bore erosion characterizations, theories, and mechanisms for advanced artillery systems. These characterizations, theories, and mechanisms can be used to develop subsequent associated erosion models and predictions for these advanced indirect fire systems. Substantial gun system firing data and laboratory analyses of fired specimens are required to develop subsequent erosion models and predictions. These include non-destructive and/or destructive pressure gauge, radar, thermocouple, metallographic, kinetic rate, microscopic materials, and microscopic chemical data from live and simulated gun tube firings. These also include substrate exposure, coating loss, cracks, pits, interfaces, voids, surfaces, crack/pit frequency, crack/pit width, coating platelet width, wall layers, residues, reactions, diffused species, and phase changes as a function of position, time, and round history. Each specific gun system has its own mix of degradation effects that lead to its own erosion rate and pattern. The specific mix of degradation effects includes the heat-affected zone (HAZ), chemical diffusion-affected zone (CDAZ), and chemical reaction-affected zone (CRAZ) as a function of the axial position of the non-coated steel, coated steel, and exposed steel that was once coated. A specific gun system as defined here includes its cannon, charge, projectile, and additives. The peak bore temperature of a gun may reach up to 1800 K a few milliseconds after it is fired. The bore temperature is approximately halved its peak a few milliseconds later. These extreme temperatures and heating rates typically requires 0.05–0.50 mm high or low contractile chromium plated coating to protect the underlying steel from these high wall temperatures. Peak gas pressure may reach up to 700 MPa in tank guns and 400 MPa in artillery guns. Propellant flame temperature reaches 3500 K for tank guns and 3000 K for artillery guns. With additional firing, this chromium coating tends to form heat checking crack defined platelets, substrate voids at the base of the heat checking cracks, micro-cracks within platelets, substrate micro-voids at the base of the microcracks, eventual individual platelet spalling (micro-pitting), and finally combined adjacent platelet spalling (pitting) due to thermal–chemical–mechanical interfacial degradation. Substrate gun steel not exposed to the combustion gases that exceeds approximately 1000 K becomes hard and brittle and is called the heat-affected zone. Exposed substrate gun steel that exceeds approximately 1000 K has diffusion of carbon, hydrogen, oxygen and nitrogen species into its exposed surfaces becoming a hard and brittle chemical diffusionaffected zone (CDAZ). Exposed substrate gun steel that exceeds approximately 1000 K may further react (oxidize, carburize, sufidize) with the exposed surfaces becoming a weaker, brittle, cracked, and non-metallic chemical reactionaffected zone (CRAZ).

Key gun system details include the 155 mm 56 caliber rifled XM297 cannon with a 0.023 m3 (1400 in.3 ) chamber, zone six combustible case-type modular artillery charge (maximum propelling charge), triple-base propellant, an approximately 100-pound M549-like projectile, its nominal obturator, maximum chamber pressure of approximately 379 MPa (55 kpsi), ambient temperature conditioning, no in-wall barrel cooling, decoppering and flash additives, and no wear additives. HC-Cr plated guns had 0.127 mm (0.0050 in.) HC-Cr plated on the gun steel bore lands, 0.114 mm (0.0045 in.) HC-Cr plated on the gun steel bore origin grooves, and 0.089 mm (0.0035 in.) HC-Cr plated on the non-origin bore grooves. LC-Cr plated guns had 0.191 mm (0.0075 in.) thick LC-Cr plated on the gun steel bore lands and 0.064 mm (0.0025 in.) thick LC-Cr plated on the gun steel bore grooves. Key charge details were discussed, confirmed, and cleared with the charge designers [7]. The thicker 0.114 mm HC-Cr plate at the origin grooves compared to the thinner 0.089 mm HC-Cr plate at the non-origin grooves can possibly be attributed to the effects of the up-bore taper on plating rates at the origin. We are not sure if this phenomenon applies to LC-Cr plate until we cut up a LC-Cr plated gun tube. This gun system can be condemned on erosion due to loss of velocity, fuse malfunction, rotating band wear, excessive body engraving, and loss of accuracy. A provisional diametric origin erosion limit of 2.54 mm (0.100 in.), usually at 12:00 to 6:00 peak, applies in the absence of these condemning effects as measured by pullover or star gauges. The departure of on coating platelet forms a “micro-pit” on the bore surface. The departure of numerous adjacent coating platelets around this micro-pit forms a “macro-pit” on the bore surface if this pit is visible to the unaided eye. The “erosion condemnation” of this gun tube by the provisional diametric origin erosion limit criteria results from the erosion and enlargement of these macro-pits to the diametric limit producing a hazardous condition. Fig. 1 shows a labeled 10× magnifying borescope micrograph of this gun tube’s high contraction chromium (HC-Cr) plated gun steel bore origin area. One of each of the 48 lands and 48 grooves are labeled. The lands are 3.2 mm wide and the grooves are 6.4 mm wide. The gun bore origin is about 1190 mm from the rear of the gun and occurs at the onset of the lands. Gun steel degradation from these various affected zones occurs at much lower wall temperatures than the melting point of the steel, is gun system dependent, is not as durable to the gun system transient gradients as the steel, and determines the rate and extent of wear and erosion. Gun bore wear and erosion occurs at the origin in artillery guns and somewhat down bore of the origin in smoothbore guns. This wear and erosion due to gas leakage between the projectile and eroded bore affects projectile operation and reduces accuracy, precision, muzzle velocity, and range. Wear and erosion is gradual in non-coated steel bores and rapid after coating failure in coated bores.

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erosion mechanism determinations to address these concerns and enable erosion mitigation. The gun system’s erosion life is compared for plated high contraction chromium (HC-Cr) and low contraction chromium (LC-Cr).

2. Actual and simulated gun system data: introduction

Fig. 1. Labeled 10× magnifying borescope micrograph of HC-Cr plated gun steel bore origin area. One of each of the 48 lands and 48 grooves are labeled. The lands are 3.18 mm wide and the grooves are 6.35 mm wide. The gun bore origin is 1194 mm from the rear of the gun and occurs at the onset of the lands.

A number of complications increase the difficulty of determining erosion mechanisms including: only a small number of cannons have been fired, these cannons are less than half way through their erosion life, there is a mix of charges and zones fired, firing was conducted with a mix of round conditioning temperatures, firing was conducted with a mix of projectiles, and firing was conducted with a mix of firing rate scenarios. For a given advanced prototype gun system, firing, inspection, characterization, and experimental data are used to develop our erosion models. A zone is a modular increment of propelling charge filled with propellant. A zone six charge is a gun chamber filled with the maximum number of six modular increments of propelling charge. The term “zone six charge” will be used extensively throughout the report and represents the maximum modular propelling charge that will fit in this gun chamber consisting of six increments. The origin of this gun system is at the full commencement of rifling which occurs at about 1190 mm (47.0 in.) from the rear face of the tube and at 7485 mm (294.7 in.) from the front face of the muzzle. This prototype charge consisted of an ambient temperature conditioned combustible case-type modular artillery charge with triple-base propellant that produced a chamber pressure of approximately 379 MPa (55 kpsi) and had decoppering and flash additives but no wear additives. This projectile had a nominal obturator. Never before seen rapid firing-induced groove erosion caused an early prototype of this gun system to erode to condemnation in less than a tenth of its expected life. A pullover gauge is used in the field to measure cannon origin erosion. A pullover gauge misses this origin groove erosion since it occurred in the near absence of origin land erosion. In addition, never before seen deep origin groove pits caused serious fatigue concerns for the artillery community. We conducted

The following data types are used to calibrate any subsequent thermal and erosion wall calculations: measured gas–wall kinetic rate function input data, measured thermocouple input data, measured destructive/non-destructive microscopic coating and substrate loss input data (cracks, pits, interfaces, surfaces), and measured destructive phase change/diffusion/reaction degradation layer input data (cracks, pits, interfaces, surfaces). Different input data are required for both cannons having fired only recurring single rounds and cannons having fired recurring rapid-fired rounds.

3. Actual and simulated gun system data: chemical kinetics We measure the achievement of and level above these reaction thresholds as a function of position, time, and round history using non-destructive and destructive laboratory microscopic materials/chemical analyses of fired cannon specimens. This bore coating erosion model requires measurable gas–wall bore coating and steel substrate reactivity data as functions of pressure, temperature, and velocity. These data are from the literature and in-house measurements for each gun system material-configuration using specialized gas–wall kinetic rate testers. Experimentally measured chemical gas–wall kinetic rate function data are used to calibrate the thermochemical calculation and transform this chemical equilibrium calculation into a partial chemical kinetic calculation. Various techniques are used to chemically characterize and further guide this gas–wall kinetics calibration including wall layer (crack, pit, interface, surface) analyses for phase change degradation (carburized white layer, heat-affected zones), chemical reaction degradation of the steel substrate under the chromium plate (oxidation, sulfidation), subsurface void residues, and surface residues. Thermocouple and metallographic data are used to calibrate the wall thermal profile calculation.

4. Actual and simulated gun system data: non-destructive bore characterization Fig. 2 gives magnifying borescope measured HC-Cr/1 rounds per hour (rph)/zone six charge-related land substrate exposure versus selected axial positions near the 12:00 bore origin at 1, 50, 80, and 100% equivalent HC-Cr life. Fig. 3 gives magnifying borescope measured HC-Cr/8 rounds per

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Fig. 2. Magnifying borescope measured HC-Cr/1 rph/zone six chargerelated land substrate exposure vs. selected axial positions near the 12:00 bore origin at 1, 50, 80, and 100% equivalent HC-Cr life.

Fig. 3. Magnifying borescope measured HC-Cr/8 rpm/zone six chargerelated groove substrate exposure vs. selected axial positions near the 12:00 bore origin at 1, 50, 80, and 100% equivalent HC-Cr life.

minute (rpm)/zone six charge-related groove substrate exposure versus selected axial positions near the 12:00 bore origin at 1, 50, 80, and 100% equivalent HC-Cr life. Fig. 4 gives magnifying borescope measured LC-Cr/1 rph/zone six charge-related land substrate exposure versus selected ax-

Fig. 4. Magnifying borescope measured LC-Cr/1 rph/zone six chargerelated land substrate exposure vs. selected axial positions near the 12:00 bore origin at 1, 50, 80, and 100% equivalent HC-Cr and LC-Cr life.

Fig. 5. Magnifying borescope measured LC-Cr/8 rpm/zone six chargerelated groove substrate exposure vs. selected axial positions near the 12:00 bore origin at 1, 50, 80, and 100% equivalent HC-Cr and LC-Cr life.

ial positions near the 12:00 bore origin at 1, 50, 80, and 100% equivalent HC-Cr and LC-Cr life. Fig. 5 gives magnifying borescope measured LC-Cr/8 rpm/zone six chargerelated groove substrate exposure versus selected axial positions near the 12:00 bore origin at 1, 50, 80, and 100% equivalent HC-Cr and LC-Cr life. The selected axial positions in Figs. 2–5 include the 1194 (bore origin), 1270, and 1346 mm (47, 50, and 53 in.) positions from the rear face of the tube (RFT). These four figures are based on the latest non-destructive and destructive cannon steel substrate exposure inspection and characterization data for this gun system. The cannon data in these four figures were measured at 1% (non-destructively measured at post-proofing), 50% (exponentially estimated from nondestructive measurements), 80% (exponentially estimated from non-destructive measurements), and 100% (exponentially estimated from non-destructive measurements) of this equivalent ambient conditioned zone six charge erosion life. In addition, the HC-Cr tubes were also destructively measured and characterized near the end of their service life. In these last four figures, HC-Cr related groove erosion dominated over land erosion for this gun system’s 8 rpm firing rate, based on the rate of groove erosion in tubes 8, 9 and 12, and 13. Similarly, LC-Cr related groove erosion dominated over land erosion for this gun system’s 8 rpm firing rate based on the rate of groove erosion in tubes OPM-4 and -13. HC-Cr related land erosion dominated over groove erosion for this gun system’s 1 rph firing rate, based on the rate of land erosion in tubes 2, 7, and a number of other tubes that experienced this low firing rate. Similarly, LC-Cr related land erosion dominated over groove erosion for this gun system’s 1 rph firing rate based on the rate of land erosion in tube OPM3 and a few other tubes during their low firing rate phase. Substrate exposure for the lands would have been a much higher percentages if they were only for the driving edge and not averaged over the whole land. For this gun system, these data are from a small sampling of both low and high rate of fire chromium plated cannons that have typical cracking, pitting, chromium plate loss,

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Fig. 6. Typical magnifying borescope micrograph of HC-Cr/1 rph/zone six charge-related midlife land erosion at the 12:00 bore origin. Related LCCr/1 rph/zone 6 micrographs are similar but not shown.

and erosion. A 70× magnifying borescope with a calibrated scale, a video borescope, and an erosion gauge performed non-destructive substrate exposure measurements. Erosion depth was performed by a pullover and star gauge. These non-destructive measurements are based on the verified assumption that substrate exposure is approximately equal at the surface and interface. No non-destructive or destructive erosion depth measurements were made for the LC-Cr plated gun tubes in the latter part of their service life since none were condemned and cut up to date. Figs. 6 and 7 show related land and groove micrographic examples of non-destructive substrate exposure measurements taken by a 70× magnifying borescope with a calibrated scale. Using this technique, these and similar micrographs illustrate the progression of this gun system’s erosion at a low and high rate of fire. Fig. 6 shows typical magnify-

Fig. 7. Typical magnifying borescope micrograph of HC-Cr/8 rpm/zone six charge-related midlife groove erosion at the 12:00 bore origin. Related LCCr/8 rpm/zone six charge micrographs are similar but not shown.

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Fig. 8. Typical 10× magnifying borescope micrograph of HC-Cr/1 rph/zone six charge-related near-end-of-life land and groove erosion at the 12:00 bore origin. Land erosion far exceeds groove erosion. LC-Cr/1 rph/zone six charge related micrographs are similar but not shown.

ing borescope micrograph of HC-Cr/1 rph/zone six chargerelated midlife driving edge land erosion for the 12:00 bore origin. Related LC-Cr/1 rph/zone six charge micrographs are similar but not shown. In the figure, coppering is evident, HCCr loss is about 50%, and gas washing has produced moderately deep measured pits. Fig. 7 shows typical magnifying borescope micrograph of HC-Cr/8 rpm/zone six chargerelated midlife groove erosion for the 12:00 bore origin. Related LC-Cr/8 rpm/zone six charge micrographs are similar but not shown. In this figure, mean HC-Cr loss is about 50% in this area compared to 20% in LC-Cr and gas washing has produced moderately deep measured pits. As we have seen in previous work [5,6], the high velocity reacting gases progressively wash and widen the interconnected canyons and form extending voids in the dead-end areas. At the midlife stage, the unsupported chromium plate breaks off where it is unsupported. Chromium platelets are smaller on the land driving edge at the minimum 1 rph firing rate than they are in the grooves at the maximum 8 rpm firing rate. Figs. 8–10 show various macrographs of coating spalling and substrate erosion. Fig. 8 shows typical 10× magnifying borescope micrograph of HC-Cr/1 rph/zone six chargerelated near-end-of-life land and groove erosion at the 12:00 bore origin. Related LC-Cr/1 rph/zone six charge micrographs are similar but not shown. HC-Cr tube 2 (Fig. 8) and LC-Cr tube OPM3 (not shown, near-end-of-life) have significant land erosion and minimal groove erosion. Fig. 9 shows typical 10× magnifying borescope micrograph of HC-Cr/8 rpm/zone six charge-related near-end-oflife land and groove erosion at the 12:00 bore origin. Related LC-Cr/8 rpm/zone six charge micrographs are similar but not shown. HC-Cr tube 8 (Fig. 9) and LC-Cr tube OPM4 (not shown, second quarter erosion life) have significant groove erosion and minimal land erosion.

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origin from 1194 to 1346 mm (47–53 in.) from RFT. Related HC-Cr/1 rph/zone six charge micrographs are similar but not shown. HC-Cr tube 2 (not shown, near-end of erosion life) and LC-Cr tube OPM3 (not shown, near-end of erosion life) have significant 10:00–2:00 o’clock land erosion and minimal 10:00–2:00 o’clock groove erosion.

5. Actual and simulated gun system data: destructive bore characterization

Fig. 10 shows typical 360◦ magnifying borescope micrograph of LC-Cr/8 rpm/zone six charge-related secondquarter-life land and groove erosion near the bore origin from 1194 to 1346 mm (47–53 in.) from RFT. Related HCCr/8 rpm/zone six charge micrographs are similar but not shown. HC-Cr tube 8 (not shown, near-end of erosion life) and LC-Cr tube OPM4 (Fig. 10) have significant 10:00–2:00 o’clock groove erosion and minimal 10:00–2:00 o’clock land erosion. Other micrographs show typical 360◦ magnifying borescope micrograph of LC-Cr/1 rph/zone six chargerelated near-end of life land and groove erosion near the bore

For condemned cannons, erosion characterizations were destructively conducted on surfaces and cross-sections of sectioned cannons by a metallograph and scanning electron microscope. Peak erosion is at the origin and diminishes completely 6 in. down-bore of the origin. Bore positiondependent and equivalent erosion life-dependent substrate exposure measurements of specimens from fired cannons include axial and circumferential crack/pit frequency, axial and circumferential crack/pit width, and axial and circumferential platelet width. Fig. 11 shows a typical scanning electron microscope (SEM) cross-sectional micrograph of HC-Cr/zone six charge related of land and groove substrate erosion through a microcrack at the 12:00 bore origin. Related LC-Cr/zone six charge micrographs are similar but not shown. Similar destructive characterizations were made by a metallograph. This and other cross-sections were taken away from origin groove pits and land pits at middle tube life at about 2000×. The inverted triangles in the steel substrate are typical at the base of the fine chromium platelet crack for both land and groove erosion. The rate of erosion varied with the zone six charge firing rate. The damage to this steel substrate is caused by high-pressure combustion gas filling from each round. To put

Fig. 10. Typical 360◦ magnifying borescope micrograph of LCCr/8 rpm/zone six charge-related second-quarter-life land and groove erosion near the bore origin from 1194 to 1346 mm from RFT. Groove erosion far exceeds land erosion. HC-Cr/8 rpm/zone six charge-related micrographs are similar but not shown.

Fig. 11. Typical SEM cross-sectional micrograph of HC-Cr/zone six chargerelated of land and groove substrate erosion through a micro-crack at the 12:00 bore origin. Related LC-Cr/zone six charge micrographs are similar but not shown.

Fig. 9. Typical 10× magnifying borescope micrograph of HCCr/8 rpm/zone six charge-related near-end-of-life land and groove erosion at the 12:00 bore origin. Groove erosion far exceeds land erosion. LC-Cr/8 rpm/zone six charge-related micrographs are similar but not shown.

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into perspective the small size of the inverted triangles and crack width, the HC-Cr plate thickness is 0.089–0.127 mm (0.0035–0.0050 in.). In addition, typical land and groove interface degradation and voids are present in this figure to the right of the inverted triangle. This figure shows the initiation of erosion that progresses and accelerates with HC-Cr crack widening, substrate steel interfacial damage, HC-Cr platelet spalling, micro-pitting enlargement to macro-pitting, and substrate steel gas washing to condemnation. There are no cross-sectional metallographic micrographs of steel substrate erosion for these LC-Cr plated tubes since none of these tubes have been condemned and destructively characterized. There are numerous cross-sectional scanning electron microscope micrographs of steel substrate erosion through a fine crack from a previous and similar LC-Cr plated 155 mm tube. They were also taken away from groove pits and land pits at the origin position. These previous characterizations showed that substrate steel damage is almost universally present at the base of the LC-Cr heat checking and micro-cracks and their adjacent coating–substrate interface for both land and groove erosion. Their rate of erosion varied with zone six charge firing rate. The initiation, progression, acceleration, and condemnation of erosion damage are similar to HC-Cr above. The LC-Cr plate thickness on the bore lands is about 190 ␮m (0.0075 in.) and on the bore grooves is about 64 ␮m (0.0025 in.). Using coupled chemical analysis techniques, characterizations of these and other similar surface and crosssectional micrographic areas show a number of types of degradation. Phase change degradation is diffusion-induced carburized white layer damage and heat-affected zone damage on/into exposed gun steel. Chromium recrystallization is present. Chemical reaction degradation of the gun steel substrate under the chromium plate at crack and interfacial walls/wall layers is also present. Oxygen and sulfur oxidation of exposed gun steel forms semi-metallic to non-metallic layers. The exact degradation and erosion mechanism for these LC-Cr plated tubes will not be known until a few of these tubes are condemned and destructively characterized. In the interim, we will assume that this gun system’s degradation and erosion mechanisms are similar to previous LC-Cr 155 mm artillery systems with an adjustment for differing charges and firing rates. Although degradation and erosion of these LC-Cr plated tubes proceeded at a faster rate than their earlier 155 mm counterparts, we used non-destructive bore subsurface exposure data like those in the figures above for calibration.

6. Erosion theories and mechanisms: introduction This gun system’s erosion mechanism onset and progression has many components. Fig. 12 gives a schematic of the general thermal–chemical–mechanical erosion mechanisms. Reacting flow, heating, thermal gradient, thermal

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Fig. 12. General schematic of the thermal–chemical–mechanical erosion mechanisms. Reacting flow, heating, thermal gradient, thermal stress cracks, radiation, gas–wall reactions, surface melting, ablation products, and mechanical removal are shown for a transient gun firing.

stress cracks, radiation, gas–wall reactions, surface melting, ablation products, and mechanical removal are shown for a transient gun firing. Crack-related firing damage leading to erosion includes major chromium plate heat checking cracks, smaller microcracks within chromium platelets, and major/minor steel substrate cracks. Thermal related firing damage leading to erosion includes grain growth near chromium plate surface, 1322 K (1920 ◦ F) recrystallization deeper in chromium plate, and 1000 K (1340 ◦ F) substrate steel transformations and a heat-affected zone near the steel interface. Thermochemicalrelated firing damage leading to erosion includes corrosion and scale damage very near the steel interface in the form of an oxidation layer and white layer. We have detailed all of these erosion mechanisms and components in previous work we conducted on other rifled artillery, smoothbore tank, and rifled medium caliber cannons [5,6]. The following discusses specific erosion mechanisms for this gun system although it has many similarities to our previously detailed artillery, tank, and medium caliber cannons.

7. Erosion theories and mechanisms: heat and crack-affected zones There is a transformation onset of the steel substrate at about 1000 K causes a heat-affected zone. This steel substrate HAZ also requires more volume then the non-transformed steel and applies an upward force on chromium platelet that assists spalling. These effects cause chromium radial cracking, heat checking, and formation of a semi-porous crack network within the platelets. The crack-affected zone includes manufacturing-induced bore micro-cracks and firing-induced crack widening of some of these micro-cracks. Gun bore chromium plate has a network of electroplating and associated heat treatment-induced radial micro-cracks that usually do not all extend into the

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steel substrate and LC-Cr are fewer in frequency than HCCr plate. With limited firing, some of these radial microcracks widen and extend to/beyond the steel interface forming well-defined platelets in the chromium coating known as heat checking cracks. More of these radial micro-cracks are within the platelets and they do not widening but instead form a semi-porous micro-crack network that extends to the steel interface. Continued firing produces LC-Cr plate contraction or shrinkage that causes radial heat checking cracks to permanently widen but not nearly as much as HC-Cr plate. Firing pressure dilation initially opens these major radial cracks wider but about a millisecond later thermal expansion of the coating re-closes these cracks. Radial heat checking cracks and micro-cracks within platelets are less frequent in LC-Cr than HC-Cr plate that tends to extend erosion life. When heated between 200 and 600 ◦ C, HC-Cr plate contracts near irreversibly while LC-Cr plate contracts near reversibly [8]. Numerous reasons explain this permanent widening of chromium radial heat checking cracks. Chromium plate radial heat checking cracks widen due to thermally-induced outgassing of non-metallics out of the exposed coating surfaces and through the semi-porous micro-crack network within platelets. Outgassing is controlled by time above a various temperature thresholds. This outgassing is less prevalent in LC-Cr plate than HC-Cr plate due to a much-reduced micro-crack network within LC-Cr platelets. Chromium plate radial heat checking cracks also widen due to radial crack wall yielding due to thermally-induced expansion forces on the brittle yielding sidewalls of chromium platelets. This yielding is much less for the more ductile LC-Cr plate than its HC-Cr plate counterpart. Chromium plate radial heat checking cracks also widen due to thermally-induced platelet sidewall transition from a less efficiently packed non-equilibrium state to a more efficient packing equilibrium state (not a transformation volume change) controlled by time above various temperature thresholds. These heat checking cracks form interconnecting canyons with degraded steel substrate walls at the canyon bases. Each round fired provides a high velocity flow of these turbulent degrading combustion gases (gas wash flow) across the exposed interfacial steel substrate surfaces at the base of these canyons that continuously refreshes and further degrades the exposed interfacial steel surface. Polished bore cross-sections of heat checking cracks and thermochemically damaged steel substrate voids at the base of these cracks typically require 100× magnification.

8. Erosion theories and mechanisms: chemical-affected zones Wear and erosion rate depends on the depth of the HAZ but the depth of both the chemical diffusion-affected zone and chemical reaction-affected zone which comprise the chemically-altered zones tends to accelerate wear and ero-

sion. Carbon monoxide and hydrogen tend to be more erosive to steel than carbon dioxide, water, and nitrogen. New propellants are being developed that oxidize the carbon monoxide and hydrogen and maintain both propellant flame temperature and peak bore temperature by increasing nitrogen content. Increased nitrogen content may increase nitriding of the steel bore that tends to inhibit carbon monoxide-steel reactions at the bore surface. There are varying numbers and amounts of other transient and equilibrium molecular combustion gas species from the propellant, primer, igniter, additives, ablatives, flash suppressants, decoppering agents, and gun system components that contribute to varied steel erosivity. The exposure of the interfacial steel substrate to thermochemically degrading combustion gases contributes to erosion. With limited firing, the chromium plate’s radial heats checking cracks progressively widened increasing the combustion gas path and quickly extend to the steel interface forming substrate voids. Also, the semi-porous radial microcracks in the platelets extend to the entire cross-sectional area of the platelet-steel interface forming many substrate micro-voids. The combustion gases chemically degrade the substrate producing a semi-metallic to non-metallic interfacial oxidization layer in these voids and micro-voids. Although there is little convective heating in these narrow cracks, the substrate steel at the base of these heat checking cracks and micro-cracks reacts with the high pressure combustion gases for as long as the substrate steel temperature is above a given reaction threshold. HC-Cr plate’s semi-porous radial micro-crack network within each platelet extends to the steel interface with limited firing. There are about 500–1500 micro-cracks extending to the substrate per platelet or about 20–40 microcracks per cross-sectional platelet face extending to the interface. This micro-crack network provides a somewhat larger cross-sectional path for thermochemical degrading combustion gases to form approximately 500–1500 micro-voids per platelet in their exposed steel interface at the base of these micro-cracks. Similarly, but much less frequently, LC-Cr plate’s semiporous radial micro-crack network within each platelet extends to the steel interface with limited firing. These are about 10–15 micro-cracks extending to the substrate per platelet or about 3–4 micro-cracks per cross-sectional platelet face extending to the interface. The micro-crack network provides an even larger cross-sectional path for thermochemical degrading combustion gases to form approximately 10–15 microvoids per platelet in their exposed steel interface at the base of these micro-cracks. LC-Cr platelets are typically wider than HC-Cr platelets. Wider platelets require more cross-sectional interface degradation for platelet spalling.

9. Erosion theories and mechanisms: CRAZ These micro-voids are filled with a semi-metallic to non-metallic interfacial oxidization layers. Spalling of a

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chromium platelet produces a micro-pit that accelerates adjacent platelet spalling and eventually produces a larger pit. Although there is nearly no convective heating in these very narrow cracks, the substrate steel at the base of these microcracks reacts with the high pressure combustion gases for as long as the substrate steel temperature is above a given reaction threshold. These interfacial micro-voids (extensive for HC-Cr, fewer for LC-Cr) reduce platelet–substrate adhesion across the entire cross-sectional area of the platelet–substrate interface. These oxidation layer filled micro-voids at the base of a platelet’s micro-crack network partially detach the chromium platelet from the steel substrate at each crosssectional interfacial locations (500–1500 per HC-Cr platelet, 10–15 per LC-Cr platelet) and it does not matter whether these micro-void thickness are each a thousand, million, or billon atoms thick since the adhesion is still zero at any atomic thickness. We have often measured the oxygen and sulfur percentages in these oxidized layers and found that they are similar for advanced artillery, tank, and medium caliber gun systems. We also found that white layer and the steel substrate HAZ are much lower in oxygen and sulfur content since oxygen and sulfur diffuse poorly into these regions. Typical oxidized steel layers consist of approximately 10–50% oxygen as iron oxides and may also consist of approximately 1–10% sulfur as iron sulfides. As exposed substrate steel surfaces are degraded, iron atoms migrate to the surface from within leaving a defect laden metal matrix under the oxide layers. Erosion accelerates if the iron oxides or iron sulfides in these oxidation layers melt. If the substrate at the base of a radial chromium crack or pit is above a particular oxidation threshold then a gas–wall chemical reaction occurs until the exposed substrate wall temperature drops below the threshold. This forms a semimetallic to non-metallic ceramic-like oxidization layer on the exposed steel. The oxide layer cracks with thermal expansion, contraction, expansive flaking oxidation, and firing shock. During the next firing and filling of combustion gases, the gas passes through the cracked oxide layer to the exposed steel surface. Exposed interfacial steel preferentially oxidize due to their higher energy state of the interface bonds at the substrate base of heat checking cracks, at the substrate base of the micro-crack network within a platelet, and at the substrate base of pits. At about 1000 K (1340 ◦ F), there is an accelerated expansive flaking scale-type oxidation onset of iron by oxygen. Gases oxidize (oxidation, sulfidation) the exposed interface steel as long as the substrate wall temperature is above this required threshold. This oxide layer takes up more volume than when it was a metal forming a non-metallic void in the steel at the interface. This void is filled with a poorly attached semi-metallic to non-metallic interfacial oxidization layer between the steel and the chromium that push up on the chromium platelets. Exposed interfacial steel substrate provides a path for oxidizing combustion gas products to travel down chromium

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plate micro-cracks, cracks, micro-pits, and pits to the exposed substrate steel. Semi-metallic to non-metallic oxidation layers form on the exposed interfacial substrate on top of the iron carbide white layer eutectoid from diffusion and thermo-chemical damage leading to micro-void and void formation. These interfacial oxide layers in the voids and microvoids take up more volume then when they were metal, reducing platelet–substrate adhesion, pushing up the chromium platelets, and assisting spalling. The oxide layer cracks with thermal expansion, contraction, expansive flaking oxidation, and firing shock. During the next firing and filling of combustion gases, the gas passes through the cracked oxide layer to the exposed steel surface. Exposed interfacial steel preferentially oxidizes due to their higher energy state of the substrate–platelet interface bonds.

10. Erosion theories and mechanisms: CDAZ The exposed interfacial steel substrate is also exposed to carburizing combustion gas products that travel down chromium plate micro-cracks, cracks, micro-pits, and pits to the exposed substrate steel. On top of the steel substrate, HAZ is a white layer consisting of an iron carbide white layer eutectoid. This white layer is metallic steel substrate with thermal and diffusion damage. We have often measured the above carbon percentages in these white layers, steel substrate HAZ, and virgin steel below the HAZ and found that they are similar for artillery, tank, and medium caliber gun systems. Hardening at the steel surface or steel substrate surface is the process of heating the steel to a temperature sufficient to produce a fully austenitic condition followed by cooling at a rate fast enough to prevent transformation to any product other than martensite. The transient bore heating associated with gun firing may produce a heat affect zone consisting of untempered martensite which is very hard, brittle, and contains high internal residual stresses [9]. We also found that the formation of untempered martensite from martensite produces a steel substrate HAZ that enhances carbon diffusion into this region. The virgin steel substrate contains roughly a third of a percent of carbon. Typical steel white layers consist of approximately 10% carbon as iron carbide eutectoid. Typical steel substrate HAZ consists of less than 1% to almost 10% carbon. Exposed steel is highly degraded at surface and a decreasing carbon diffusion gradient damages the steel below the surface. Erosion accelerates if the iron carbide eutectoid in the white layer melts.

11. Erosion theories and mechanisms: origin blow-by bore heating During the first 6 in. of travel, obturator blow-by and accelerated groove erosion produce reduced erosion life due to the higher rate of fire scenarios. Never before seen rapid

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firing-induced groove erosion apparently caused erosion condemnation in less than a tenth of expected life for this gun system’s high-rate-of-fire cannons. The reduced erosion life at higher rate of fire is due to obturator blow-by that causes accelerated groove erosion during the first 6 in. of travel. Our finite element analysis studies of this gun system during top zone rapid firing indicate that high pressure-induced tube dilation reduces the nominal obturator’s ability to reach and seal to the bottom of the grooves during the first 6 in. of travel. Similar studies of this gun system during top zone lower rate of firing indicate that high pressure-induced tube dilation is lower and this increases the nominal obturator’s ability to reach and seal to the bottom of the grooves during the first 6 in. of travel. These studies indicate that it takes less than 1 in. to up to 6 in. of travel for the obturator to fully seal the bottom of the grooves due to obturator high pressure deformation and thermal softening depending on the firing rate-induced tube dilation. These studies are based on interior ballistic core flow, properties of the nominal obturator, and measured dilation data. Our non-destructive magnifying borescope studies and destructive metallographic studies indicate near origin groove heating significantly exceeds the heating that results from the non-blow-by full obturation condition and can easily equal the heating that would result from the blow-by less-than-full obturation condition. These studies are based on micro-crack widths, heat checking crack widths, substrate degradation, and chromium loss.

12. Erosion theories and mechanisms: coating adhesion loss and spalling Recent work by Underwood [10] includes a much-needed quantitative thermal–mechanical erosion model where different width radial heat checking cracks are on opposite sides of a fully adhered chromium platelet attached to the steel substrate. This model predicts the interfacial forces required to shear this platelet from the substrate based on the thermally-induced expansion forces on the yielding sidewalls of chromium platelets that widen these radial heat-checking cracks. This shearing model predicts the extreme upper limit of forces (excellent adhesion) required to shear a chromiumplated platelet from its fully adhered metal–metal bonded steel substrate. This shearing model also predicts the extreme lower limit of forces (very poor adhesion) required to shear a chromium-plated platelet from its non-adhered physically attached steel substrate. Our thermal–chemical–mechanical erosion model addresses the substantial reduction of thermo-mechanical forces required to spall a platelet due to interfacial degradation. We have previously said that degradation of the platelet–substrate interface plus mild thermo-mechanical forces and interfacial shearing forces are typical in gun systems [5,6]. Thermo-mechanical forces and interfacial shearing forces alone are not enough to take chromium platelets

off the steel substrate. Underwood’s model sets much needed boundaries on these shearing forces enabling us to better compute reduced shearing forces due to interfacial degradation. All else equal, LC-Cr platelets are wider than HC-Cr platelets requiring more cross-sectional interfacial degradation for platelet spalling. The oxidation layer filled voids at the base of heat checking cracks partially detach the chromium platelet edges from the steel substrate reducing platelet–substrate adhesion around the interfacial edges of the platelet–substrate interface. Also, the interfacial micro-voids occur at the base of most extended micro-cracks, are extensive, and reduce platelet–substrate adhesion across the entire cross-sectional area of the platelet–substrate interface. Both heat checking cracks and micro-cracks provide paths for these oxidizing and carburizing combustion gases to chemically degrade the exposed steel interface at the substrate bases of these two types of cracks forming layers. Each round fired provides a fresh volume of thermochemical degrading high-pressure gases to fill each of these two types of cracks extending to the steel substrate interface. It does not matter whether the substrate void or micro-void thickness is a thousand, million, or billon atoms thick since the adhesion is still zero at any atomic thickness. Interfacial void link-up around the edges of the platelets and micro-void link-up across the platelet–substrate interface both accelerate the loss of platelet–substrate adhesion leading to platelet spalling. Interfacial void link-up around the edges of the platelets and micro-void link-up across the platelet–substrate interface accelerate the loss of platelet–substrate adhesion leading to platelet spalling. These combustion gas paths include the entire cross-sectional area of the platelets. Each round fired provides a fresh volume of thermochemical degrading highpressure gases to fill each radial micro-crack extending to the steel interface within these platelets. Polished bore crosssections of networks of radial micro-cracks within platelets and thermochemically damaged steel substrate micro-voids at the base of these micro-cracks typically require 1000× magnification. When voids at the substrate base of a heat checking cracks are filled with a semi-metallic to non-metallic interfacial oxidization layer then it reduces platelet–substrate adhesion around the interfacial edges of the platelet–substrate interface and applies an upward force on the platelet that assists spalling. When micro-voids at the substrate base of a microcrack network within a platelet are filled with semi-metallic to non-metallic interfacial oxidization layers then it reduces platelet–substrate adhesion across the entire cross-sectional area of the platelet–substrate interface and applies an upward force on the platelet that assists spalling. The shear stress generated by the projectile-bore contact and the high velocity gases assist in removing poorly adhered platelets and cracked/brittle degraded non-metallic layers on the steel. Spalling of a chromium platelet produces a micro-pit that accelerates adjacent platelet spalling and eventually produces

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a larger pit. Combustion gas degradation forms voids in the exposed substrate steel that progressively enlarge with extended firing. Overhanging portions of chromium platelets above these widened canyon voids crack and break off since the unsupported overhanging portion of a chromium platelet is somewhat brittle and the supported non-overhanging portion of the chromium platelet is still attached to the substrate. There is slightly reduced projectile obturation near the origin in the canyons of these widened cracks, thus allowing combustion gases to briefly reach high velocities in these canyons as the projectile passes. Progressive thermochemical degradation and gas washing (removal) of the exposed interfacial steel substrate surfaces in these canyons of the widened cracks result in the removal of unsupported chromium directly above these canyons. The chromium gets somewhat brittle with aging, and its unsupported pieces above the widened canyons and the adjacent degraded steel walls of the canyons result in the breaking away of unsupported chromium pieces from any chromium pieces that still have partially non-degraded steel interfaces. Forces, such as high velocity flow and constrained thermal bore expansion of the chromium platelets, assist in the brittle failure-removal of unsupported chromium pieces above these canyons and their adjacent degraded walls. This results in further widening of the canyons, an increase in interfacial convective heating, and an acceleration of the erosion process. This acceleration of the erosion process eventually leads to the complete degradation of the interfacial steel substrate under a chromium platelet. The spallation of a chromium platelet results in a micro-pit. Micro-pitting onset sets the stage for progressively wider and deeper pit growth. This pit growth is due to an exponential increase in interfacial convective heating and steel gas washing and results in a rapid acceleration of the erosion process. For this gun system, this thermo-chemical mechanism is the same for lands and grooves for firing rates up to 8 rpm. For this HC-Cr coating/8 rpm-firing rate, the rate of groove erosion far exceeds the rate of land erosion as shown in tubes 8, 9, and 12. Conversely, for this HC-Cr coating/1 rph-firing rate, the rate of land erosion far exceeds the rate of groove erosion as shown in tubes 2, 7, and other tubes that experienced this slow firing rate. For this LC-Cr coating/8 rpm-firing rate, the rate of groove erosion far exceeds the rate of land erosion as shown in tubes OPM-4 and -13. Conversely, for this LC-Cr coating/1 rph-firing rate, the rate of land erosion far exceeds the rate of groove erosion as shown in tubes OPM-3 and a few other tubes during their low firing rate phase. In addition, there is a mechanical wear mechanism component to driving edge land erosion that is semi-quantitatively addressed in this effort. With extended firing, chromium pits form due to platelet spalling providing a massive cross-sectional path for thermal and thermochemical degrading combustion gases to reach the exposed steel interface. Each round fired provides a high velocity flow of these turbulent degrading combustion gases

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(gas wash flow) across the substrate steel at the base of these pits that continuously refreshes the exposed interfacial surface.

13. Erosion theories and mechanisms: erosion reduction On of the most important reasons for developing erosion theories and mechanisms are to enable the development of erosion mitigation efforts. Numerous concepts are being tried to reduce zone six charge rapid firing related origin erosion. Improved obturators are being developed that should fully seal the bottom of the grooves in less than 1 in. during zone six charge, rapid firing thus minimizing near-origin groove erosion. Improved bore coating material are being developed that should resist near-origin groove erosion longer during zone six charge, rapid firing. Cooling the bore with a water–glycol mixture is 4 s late for reducing the maximum origin wall temperature that determines the erosion rate but this bore cooling does allow more high rate of fire rounds to be fired before the charge cook-off temperature is reached. Current modular artillery charge ablatives are not very effective at reducing the maximum origin wall temperature that determines the erosion rate. Rear notched ablative obturators are being developed that should reduce the maximum origin wall temperature that determines the erosion rate by deploying ablative at the origin where it is needed and not from the chamber. We have previously determined ablative mechanisms, erosion models and erosion predictions for a number of advanced artillery, tank, and medium caliber gun systems [5,6].

14. Conclusions Thermal–chemical–mechanical gun bore erosion theories and mechanisms are described for an advanced artillery system and its associated laboratory-firing simulator system. These erosion theories and mechanisms are subsequently used to develop erosion models, predictions, and mitigation efforts for each of the coating types used in this advanced artillery system and its simulator. A number of key findings resulted from this coating– substrate inspection and characterization data shown in Figs. 2–11 and similar data. Each finding partially explains the more than double erosion life of LC-Cr tubes compared to their HC-Cr counterparts. The rate of HC-Cr plate related subsurface exposure was at least twice that of its LC-Cr counterpart for a given axial position at each firing rate. The LC-Cr plate has platelet widths, heat-checking crack spacing (frequency), and micropit widths that are at least twice that of its HC-Cr counterpart for a given axial position at each firing rate. The LC-Cr plate has a larger cross-sectional substrate interface to degrade under a typical platelet that is at least four times that of its HC-Cr

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counterpart for a given axial position at each firing rate. The LC-Cr plate heat checking crack widths are at least half that of its HC-Cr counterpart for a given axial position at each firing rate. The LC-Cr plate micro-cracks reaching a typical platelet’s cross-sectional substrate interface is less than a factor of ten of that of its HC-Cr counterpart for a given axial position at each firing rate. The accelerated turbulent heating of the exposed substrate in micro-pits and pits raised the exposed substrate wall temperature much higher than it would reach for the unexposed substrate for a given axial position at each firing rate. The higher firing rates had much higher obturator blow-by than their lower firing rate counterparts due to variations in pressure dilation and wall temperatures producing accelerated groove erosion in the origin area. The actual number of “effective full charges fired at zone six charge” (EFCs) it took these key peak eroded LC-Cr plated tubes to get to an arbitrary 2.54 mm (0.100 in.) origin erosion depth on both 12:00 wall and 12:00 to 6:00 diameter is more than twice that of their HC-Cr counterparts at the same firing rate. The thinner/softer LC-Cr grooves had at least double the erosion life of their thicker/harder HCCr counterparts for a given axial position at each firing rate. The thicker/softer LC-Cr lands had at least double the erosion life and mechanical wear of their thinner/harder HC-Cr counterparts for a given axial position at each firing rate. Extensive cannon firing, inspection, characterization, and experimental data in Figs. 2–11 and similar data can be subsequently used to develop thermal–chemical–mechanical erosion models and predictions. Most key HC-Cr plated cannons were near this provisional diametric erosion limit and were destructively characterized resulting in moderately high confidence erosion mechanism determinations. Most key LC-Cr plated cannons were from 40 to 80% of this provisional diametric erosion limit and were only non-destructively characterized and not destructively characterized resulting in moderate confidence erosion mechanism determinations. It appears from actual firings that these key peak eroded LC-Cr and HC-Cr plated tubes fired at the lowest firing rate outperformed by more than a factor of two their counterparts fired at the highest firing rate. These predictions are based on an arbitrary 2.54 mm (0.100 in.) erosion depth for both the 12:00 wall and the 12:00 to 6:00 diameter for a given axial position. It also appears from actual firings that these key peak eroded LC-Cr tubes (0.191 mm/0.0075 in. LC-Cr plated on the bore lands, 0.064 mm/0.0025 in. LC-Cr plated on the bore grooves) outperformed by more than a factor of two the key peak eroded standard HC-Cr tubes (0.127 mm/0.0050 in. HC-Cr plated on the origin lands, 0.114 mm/0.0045 in. HCCr plated on the origin grooves, 0.089 mm/0.0035 in. HC-Cr plated on the non-origin bore grooves) for a given axial position at each firing rate. These standard HC-Cr tubes are at their chromium plate thickness limit with little erosion life improvement expected. By any measure, it appears that these key peak eroded LC-

Cr tubes in this study outperformed by more than a factor of two the standard key peak eroded HC-Cr tubes for a given axial position at each firing rate. Similar untested LC-Cr with approximately 0.45 mm (0.018 in.) LC-Cr plated on the bore lands and 0.15 mm (0.006 in.) LC-Cr plated on the bore grooves should further outperform these tested LC-Cr plated tubes in this study for a given axial position at each firing rate.

Acknowledgements The authors are pleased to acknowledge the help of numerous colleagues for their technical guidance in many phases of this work including: E. Hyland, S. VanDyke-Resitifo, A. Wakulenko, and J. Underwood of Benet Labs; S. Coladonato of Applied Ordnance Technology (Waldorf, MD); B. Anderson of United Defense L.P. (Minneapolis, Minnesota); J. Rutkowski and T. Grieg of the previous PM-Crusader Office; and T. Sterlacci of the FCS-NLOS Office. The authors are also pleased to acknowledge the preliminary modeling efforts of M. Witherell, G. Pflegl, and P. O’Hara of Benet Labs as well as the non-destructive testing efforts of D. Le of the Army Test Center (Yuma Proving Ground, AZ).

References [1] J.S. Burlew (Ed.), Hypervelocity Guns and The Control Of Gun Erosion, Summary Technical Report of the National Defense Research Committee, Division I, Office of Scientific Research and Development, Washington, DC, 1946, also available from the US Government Chemical Propulsion Information Agency, Columbia, MD. [2] I. Ahmad, J.P. Picard (Eds.), Gun Tube Erosion And Control, Proceedings of the Tri-Service Gun Tube Wear and Erosion Symposium US Army Armament Research and Development Center, Dover, NJ, 1970, 1977, 1982, and 1988, also available from the US Government Chemical Propulsion Information Agency, Columbia, MD. [3] I. Ahmad, The problem of gun bore erosion: an overview, in: L. Stiefel (Ed.), Gun Propulsion Technology, Progress in Astronautics and Aeronautics, vol. 109, AIAA, Washington, DC, 1988, pp. 311–355. [4] R.J. Dowding, J.S. Montgomery (Eds.), Proceedings of the Sagamore Workshop on Gun Barrel Wear and Erosion, Wilmington, DE, 29–31 July, 1996, also available from the US Army Research Laboratory, Aberdeen, MD. [5] S. Dunn, S. Sopok, D. Coats, P. O’Hara, G. Nickerson, G. Pflegl, Unified computer model for predicting thermochemical erosion in gun barrels, in: Proceedings of 31st AIAA Joint Propulsion Conference, San Diego, CA, July, 1995; also AIAA J. Propul. Power 15 (4) 601–612. [6] S. Sopok, Cannon coating erosion model with updated M829E3 example, in: Proceedings of the 36th AIAA Joint Propulsion Conference, Huntsville, AL, 2000. [7] J. Rutkowski, Private Communication on the Propelling Charge, US Army ARDEC, Dover, NJ, 2002. [8] E. Chen, et al., J. Appl. Electrochem. 17 (1987) 315–321. [9] P. Thorton, V. Colangelo, Fundamentals of Engineering Materials, Prentice-Hall, Englewood Cliffs, NJ, 1985. [10] J. Underwood, A. Parker, G. Vigilante, P. Cote, Thermal damage, cracking, and rapid erosion of cannon bore coatings, in: Proceedings of the Gun Tubes Conference 2002, Keble College, Oxford, UK, 2002.