Study of Effect of Interface Pressure on the Stress Analysis of Ceramic Lined Pressure Vessels

The present work deals with the effect of interface pressure on the stress and fracture analysis of carbon-epoxy dual jacketed pressure vessels at elevated temperatures. Pre-stress and firing stress is determined for an init ial residual interface p ressure applied between liner and jacket. The effect o f a unifo rm 100°C temperature rises above ambient had mixed results for a carbon-epoxy jacketed vessel, due to the differential thermal expansion. While jacket stresses increased moderately and further exceeded typical material strengths, liner stresses decreased significantly and improved structural integrity. The effect of a temperature rise for a steel jacketed vessel was deleterious. Jacket stresses decreased, but with no effect on structural integrity, while liner stresses increased, to the detriment of integrity.


Introduction
Ceramic -lined cannons have gained attention in recent years [1] due to increased and more sustained combustion gas temperatures used to attain imp roved cannon performance. Thermal damage of the electroplated chro miu m used on a cannon bore has become a significant erosion failu re mode for today's gun barrels [2]. The higher elevated-temperature strength of ceramics provides significantly imp roved resistance to thermal damage in the severe thermomechanical environ ment of cannon firing [3].
Methods of analysis will be generally similar to those described recently by Parker et al. [4], where various combinations of autofrettage and external tension wrapping of steel-lined, carbon-fiber jacketed tubes were studied. Here, the liner-jacket analysis will be for t wo types of ceramic liner, Si 3 N 4 and SiC, and two types of jacket, A723 p ressure vessel steel and carbon-epoxy laminate. Emphasis is on composite jacket inner radius stresses that can exceed typical failu re strengths and on ceramic liner inner radius stresses that can result in alarmingly s mall critical crack sizes for britt le fracture. The analysis is for a representative initial residual interface pressure between liner and jacket that would be expected for either shrink fitting or tension wrapping of a liner-jacket vessel.
The wo rk of Malino ws ki and M agnu ki [5] emp loyed p arametric d is cret e opt imizat io n techn iq ues to d es ign internal rein forcements of pressure vessels by minimizing the reinforcement mass considering stress constraints. Following an analytical approach, Banichuk et al. [6] used variational calculus to find the head meridian profile optimal curve in order to maximize the rat io between head volu me and mass subjected to stress constraints.
A follow up of this wo rk was provided by Du and Olhoff [7] and Zheng et al. [8], who extended the investigation to three-dimensional structures. However, they considered as objective function the minimizat ion of mean co mpliance without stress constraints, which is not realistic for pressure vessel design. In fact, the solution of topology optimization considering stress constraints is still an open problem [9][10][11].
Recently, Blachut and Magnuki [12] published an extensive review about modeling and optimization of pressure vessels where they mention that, in the optimization field, there are still few p ieces of work related to pressure vessel design. This work provides a contribution along those lines by presenting an integrated approach in wh ich the entire vessel is considered in the optimization process.

Fracture Analysis
Fracture analysis is done to calculate the fracture thickness values at the inner radius of the ceramic lined vessel can be calculated using the formu la given below.

Effect of J acket
Ic Ic θ π Stresses were calculated for a Silicon-nitride lined vessel with dual jacket is listed in Table 1. Figure 1 shows the results for the C-epoxy jacket, including prestress, firing and total stresses versus radial position, r/a. The prestress is due to the interface pressure at the junction, already discussed. The pressure applied to the vessel inner radius was 500 MPa, based on the 400-700 M Pa pressures used in modern cannons. Note that, although the radial prestress does not exceed the C-epo xy comp ressive strength, when the firing stresses are added, both radial and hoop stresses exceed the respective strength values for C-epo xy.
The total radial stress at the interface is 2300 MPa, compared with 120 MPa co mpressive strength, and the total jacket hoop stress is 770 MPa, co mpared with the 600 M Pa tensile strength. The problems under consideration are a composite pressure vessel shell which has a liner and a single jacket or a dual jacket. Stress analysis is to be done for the single jacket vessel and dual jacket vessel and the stress variations are to be studied. The wear and erosion is also high in gun barrels. So suitable materials are to be chosen for this application. The different materials taken for this purpose are ceramic materials like Si 3 N 4 and SiC for liner, and C-epo xy and A723 Steel for Jacket.

Effect of Temperature
The effect of moderately elevated temperature on total stresses in a ceramic lined vessel is of interest for cannons and some other applications. Figures 4 and 5 show results for C-epo xy or steel jacked, Si3N4 lined vessels, respectively, at 25°C ambient temperature and after a uniform rise to 125°C. First, note that the ambient results ~25°C; solid lines! are nearly identical for the two vessel ~Fig. 4! the jacket stresses at 125°C are slightly increased, adding to the problem of exceeding the material strength, discussed earlier. However, the liner integrity is improved with the increase in temperature.
The stresses are decreased due to the favorable differential expansion between C-epo xy jacket and ceramic liner. This differential expansion was modeled by an increased 0.13 mm interference between jacket and liner at 125°C, co mpared with 0.10 mm at 25°C.The effect of temperature on total stresses with a steel liner in Fig. 5 shows that jacket stresses are slightly reduced, but to no advantage in structural integrity because of the adequate strength of steel. Ho wever the liner integrity suffers at high temperature, because differential expansion decreases the interference.

Fracture Analysis
The fracture analysis is performed fo r the t wo ceramic materials for single and dual jacketed vessels and tabulated in Table4. It is observed that silicon carbide materials are prone to less crack thickness than silicon nitride materials.

Summary & Conclusions
The type of jacket had no significant effect on liner or jacket stresses, because the elastic modulus of the carbon-epoxy considered was close to that of steel. However, the total prestress, firing radial and hoop stresses at the inner radius of the carbon epo xy jack et exceeded typical material strengths in these directions. The result of the fracture analysis is that a ceramic lined pressure vessel with a thin, low modulus, high toughness ceramic liner and a dual-steel interference-fitted jacket would have the best structural integrity of the cases considered. However, it is emphasized that the very small crit ical crack size for brittle fracture that is inherent in the use of ceramics demands the utmost care in pressure vessel design.