Some problems related to thermophysical properties of selected barrel steels

The paper discusses selected issues related to the thermophysical properties of selected barrel steels, which the authors have been dealing with over the last few years, i.e. 38HMJ (1.8509), 30HN2MFA, X37CrMoV5-l hot-work tool steel (1.2343), DUPLEX (1.4462) and MARAGING 350 (1.6355). In some of them, i.e. in the X37CrMoV5-1 hot work tool steel, 38HMJ, 30HN2MFA, a ferrite-austenite phase transition occurs, which causes shrinkage of the material. During a series of shots, multiple shrinkage of material degrades the barrel channel and deteriorates the ballistic parameters of the cannon barrel. Another problem concerns the apparent specific heat that we get from the DSC measurement and the dependence of the specific heat on temperature in the form that we use for the numerical simulations. The point is that the phase transition effect should not be taken into account twice, i.e. in the thermal diffusivity characteristics and in the specific heat characteristics. For all selected steels the thermophysical properties, i.e. thermal diffusivity, thermal conductivity, specific heat and thermal expansion, were obtained in a wide range of temperature, so they can be used as input data for numerical simulations.


Introduction
In classical barrel weapons the shooting effect lasts from a few to a few dozen milliseconds, and temperature of gaseous combustion products reaches the values of a few thousand degrees, at pressure of a few hundred MPa.At such extreme conditions the barrel, and especially its internal surface, is a part of weapon exposed in greatest degree to wearing.After the mechanical processing, the barrels are subjected to electrolytic coating of the bore by chromium protecting against corrosion against damage of the barrel internal surface by powder gases.The thermal fatigue of barrels is connected with structural transformations of steel, mainly with the transition ferrite-austenite, at barrel heating and cooling cycles [1][2][3].Despite plating the internal surfaces of barrels by chromium they are damaged due to cyclical volumetric changes of the steel background effecting the breaking and crumbling of its chromium layer.The way to increase the durability of barrels is to change the steel grade to one in which there is no ferrite-austenite structural change, or the temperature of the structural transformation is as high as possible.Tests of the thermophysical properties of selected barrel steels, i.e. 30HN2MFA, 38HMJ (1.8509) and DUPLEX 2205, showed that the lowest ferrite-austenite phase transition temperature occurs for 30HN2MFA steel at a temperature of approximately 730℃.For 38HMJ steel, the temperature of this transformation takes place at 790℃, while for DUPLEX 2205 steel such a change does not occur [1,4].Therefore, 38HMJ steel is better than 30HN2MFA steel.Another problem is the correct preparation of the thermal characteristics of thermal conductivity and specific heat as inputs to the numerical simulation of heat transfer issues in the cannon barrel.Thermal diffusivity a, thermal conductivity k, specific heat cp and density ρ are related to the expression  = /( •   ).Each of these thermophysical parameters can be determined on separate measuring setups or, for example, the thermal conductivity can be calculated from the expression  =  •  •   .The phase transformation is visible in each thermophysical parameter.Thus, when calculating the thermal conductivity k in the phase transition region from formula  =  •  •   , this effect is taken into account both in thermal diffusivity and in specific heat.This means that the phase change effect and the associated enthalpy are taken into account twice.
The paper discusses the thermal characteristics of the thermophysical properties, i.e. a, k, cp and ρ of selected barrel steels, i.e. 38HMJ (1.8509), 30HN2MFA, X37CrMoV5-1 hot-work tool steel (1.2343), DUPLEX (1.4462) and MARAGING 350 (1.6355) in the temperature range from room temperature (RT) to 1000℃, which were measured by the authors [1,[4][5][6].Another problem raised in the paper concerns the apparent specific heat that we get from the DSC measurement and the dependence of the specific heat on temperature in the form that we use for the numerical simulations of heat transfer in cannon barrels.

Materials
The subject of analysis were 5 types of barrel steels: 38HMJ with a density of 7.65 g/cm 3 at RT, 30HN2MFA with a density of 7.75 g/cm 3 at RT, X37CrMoV5-1 hot-work tool steel with a density of 7.75 g/cm 3 at RT, DUPLEX 2205 with a density of 7.72 g/cm 3 at RT and Maraging 350 with a density of 8.05 g/cm 3 at RT.The chemical composition of these steels is given in table 1 [4][5][6].38HMJ steel is an alloy steel that, thanks to the nitriding process, obtains increased surface hardness and corrosion resistance without the need for additional heat or electrochemical treatment.This steel is currently used as a barrel material [4].30HN2MFA steel is an alloy steel characterized by high impact strength.This parameter is particularly significant in small-caliber weapon barrels due to the loads typical of the firing phenomenon.Due to the lack of alloy additives protecting against corrosion, the inner surface of the barrel made of this steel must be plated with chrome [4].DUPLEX 2205 steel is a high-alloy steel which, thanks to alloy additions (22% Cr, 5% NI), obtains a two-phase structure and high resistance to pitting and intergranular corrosion.The ferritic-austenitic structure provides much higher strength compared to typical austenitic steels.It has twice the tensile strength of this steel grade.The higher hardness of DUPLEX steel is related to the high strength of this steel.It is now used as steel for hunting gun barrels [6].X37CrMoV5-1 hot-work tool steel is highly alloyed steel, designed to work at elevated temperatures [5].MARAGING 350 is a low-carbon iron-nickel martensitic steel hardened by precipitations of intermetallic phases [5].The last two steels, i.e.X37CrMoV5-1 and MARAGING 350 have not yet been used as barrel steels, but are proposed by military experts and armament factories for such use.

Experimental procedures
Thermal diffusivity measurements of the 5 selected steels applying the NETZSCH LFA 427 laser flash apparatus were made in the temperature range from RT to 1000℃.A standard Cape-Lehman model of heat transfer with pulse correction was applied.For thermal diffusivity testing, cylindrical samples with a diameter of 12.70 mm and a thickness of 1.99 mm were cut from a rod.The samples were covered with a thin layer (2-3 µm) of graphite (GRAPHIT 33 Kontakt Chemie) to increase the absorption of the thermal energy.The apparent specific heat of the barrel steels was measured by continuous scanning DSC using a NETZSCH DSC 404 F1 Pegasus instrument.In the classic DSC method, the temperature characteristics of the specific heat capacity were calculated using the Cp coefficient method based on 3-DSC curves (baseline, sapphire line and line of the tested sample).The samples for DSC tests were cylinder with diameter 6.0 mm and were placed into a Al2O3 crucible, which in turn was inside a platinum crucible with a platinum lid (volume of Pt crucible: 85 µL).The weights of the steels were 347.The density of the tested steel samples at room temperature was measured using the Archimedes method.SARTORIUS MSA125-1CE-DA analytical balance and distilled water were used.

Discussion
The paper summarizes the thermophysical properties of five barrel steels, i.e. 30HN2MFA, 38HMJ, X37CrMoV5-1, DUPLEX 2205 and MARAGING 350, which were recommended by Polish arms factories.The first three, i.e. 30HN2MFA, 38HMJ, X37CrMoV5-1, are characterized by medium carbon content and the occurrence of ferrite-austenite transformation at high temperatures.This means that 30HN2MFA steel shrinks at a temperature of 735.7℃ (ONSET), 38HMJ steel at a temperature of 797.6℃, and X37CrMoV5-1 steel at a temperature of 853.8℃.In the other two steels, i.e.DUPLEX 2205 and MARAGING 350 with low carbon content, the ferrite-austenite transformation effect does not occur.The maximum allowable barrel temperature depends on the number of shots.Only in the case of steel from the second group, the number of shots does not matter much.The thermophysical properties as a function of temperature of steel with medium carbon content are similar in nature.In the case of thermal diffusivity, we observe a decrease in the diffusivity value in the range from RT to the Curie point temperature, i.e. 742.5℃ for X37CrMoV5-1 steel, 741.0℃ for 30HN2MFA and 743.3℃ for 38HMJ, and then a slight increase.Temperature characteristics of thermal diffusivity for the steels are shown in figure 1.These tests revealed the existence of two peaks.According to the Ehrenfest classification, the transition of iron from the ferromagnetic to the paramagnetic state at the Curie point is a phase transition of the second kind, i.e. the heat of the phase transition is zero [7].The situation is completely different in the case of the shrinkage effect, which is a phase transition of the first kind, i.e. it requires the supply of heat.For steel with medium carbon content, the first peak corresponds to the Curie temperature, while the second one is related to the ferrite-austenite phase transition (-Fe) and material shrinkage.For 30HN2MFA steel, the Curie temperature is 748.2℃, while for 38HMJ and X37CrMoV5-1 steel -758.9℃.It should be added that in the case of 30HN2MFA steel, the Curie temperature coincides with the material shrinkage temperature.In the case of 38HMJ steel, the shrinkage temperature is 804.8℃, and for X37CrMoV5-1 steel -871.8℃.Additionally should be added, due to the method of measuring thermal diffusivity, which requires thermostating the sample at each temperature measurement point, the effect of steel shrinkage is not reflected in the thermal characteristics of thermal diffusivity of the tested steels -figure 1. Temperature characteristics of CLTE and density as a function of temperature for the steels are shown in figure 3 and 4. The ONSET value reveals the beginning of the shrinkage effect in selected medium carbon steels, i.e.: 735.7℃ for 30HN2MFA steel, 797.6℃ for 38HMJ steel, 853.8℃ for X37CrMoV5-1 steel.As input to the numerical simulation of heat transfer in the barrel, we use only the specific heat in the form of approximation presented in figure 5.
Figure 5. Temperature characteristics of apparent specific heat for the X37CrMoV5-1 hot-work tool steel (black line) and approximation (dashed green line) as input data for numerical simulation of heat transfer in the gun barrel [6].
The proposed approximation of the specific heat capacity formula for the X37CrMoV5-1 hot-work tool steel has the following form [5,8]: The values of coefficient   are given in table 2.
In the case of low-carbon steels (DUPLEX 2205 and MARAGING 350), diffusivity and thermal conductivity as a function of temperature are quasilinear over the entire temperature range from about 4 mm 2 /s to about 5 mm 2 /s.The apparent specific heat as a function of temperature for these steels shows small peak values: for DUPLEX steel, at a temperature of approximately 530.1℃, chromiumrich ferrite, i.e. the ' phase, dissolves and a peak appears, for MARAGING 350 steel, at least four appear peaks: 470.4℃, 547.5℃, 697.6℃, 734.9℃, the nature of which is explained in [5,6].A separate problem is the method of calculating the thermophysical properties of barrel steels in order to obtain input data for the simulations of heat transfer in the barrel wall [8].As a rule, we consider the phase transition effect only in thermal conductivity characteristics -figure 6.In the formula  =  •  •   , the specific heat is treated as a polynomial (1).Sometimes this effect is taken into account twice, both in thermal diffusivity and in specific heat.This way of calculating thermal conductivity should be considered incorrect.

Conclusion
The results of the discussion of selected issues related to the thermophysical properties of selected barrel steels are summarized as follows: a) in the first group of the investigated steels, i.e. in medium carbon steels, the chromium content determines the shrinkage temperature.The highest temperature, i.e. 860.9℃, occurs in X37CrMoV5-1 steel with a chromium content of 5.52%, the lowest, i.e. 749.7℃, in 30HN2MFA steel with a chromium content of 0.65%; b) in the second group of the steels, i.e. in DUPLEX 2205 and MARAGING 350 there is no effect of material shrinkage at high temperature; c) in heat transfer calculations, we take into account the thermal characteristics of specific heat in the form of a polynomial, and the effect of phase transitions only in the thermal characteristics of thermal conductivity.

Figure 1 .
Figure 1.Thermal diffusivity as a function of temperature for the chosen steels obtained from the first heating runs on LFA 427 [1, 6].

Figure 2 .
Figure 2. Temperature characteristics of apparent specific heat for the chosen steels obtained from the first heating runs on DSC 404 F1 Pegasus [1, 6].

Figure 3 .
Figure 3. CLTE as a function of temperature for the chosen steels obtained from the first heating runs on DIL 402 C [1, 6].

Figure 4 .
Figure 4. Density as a function of temperature for the chosen steels obtained from the first heating runs on DIL 402 C [1, 6].

Figure 6 .
Figure 6.Thermal conductivity as a function of temperature for the chosen steels obtained from the first heating runs on LFA 427 [1, 6].
3 mg for 38HMJ, 335.41 mg for 30HN2MFA, 219.13 mg for X37CrMoV5-1, 383.39 mg for DUPLEX 2205 and 236.25 mg for MARAGING 350.The thermal expansion of selected steels was measured with a NETZSCH DIL 402 C pushrod dilatometer in the range from RT to 1000 °C.Measurements of coefficient of linear expansion (CLTE) were carried out in the same temperature range as in the case of LFA 427 and DSC 404 F1 Pegasus.The samples for DIL tests had the shape of a cylinder with a length of 26 mm and a diameter of 5 mm, cut from a bar by a water-cooled cutting disc.

Table 2 .
Coefficient for calculating specific heat capacity of X37CrMoV5-1 hot-work tool steel on equation (1):