Structural response analysis of a solid rocket motor charge under temperature and internal pressure loads

To study the structural integrity of a solid rocket motor under low temperature load, internal pressure load, and two combined loads, based on the linear viscoelastic model, the structural response of a solid rocket motor under low temperature load, internal pressure load and two combined loads were analyzed by ANSYS finite element software, and the temperature field and strain field of charge loading were obtained. The Von Mises strain distribution of the solid rocket motor along the axial characteristic line is obtained. The results are: Under the combined action of low temperature load, internal pressure load, and two kinds of loads, the maximum Von Mises strain appears at the transition position between the blade joint and the barrel section, which is the most dangerous position for charging.


Introduction
Compared with a liquid rocket engine and other chemical energy rocket engines, a solid rocket engine has the advantages of simple structure, reliable operation, easy operation, safe use, and long-term storage, so it is widely used as the power device of various military rockets and tactical missiles [1] .In the design of a solid rocket motor charge (SRM), we should consider the requirements of tactical and technical performance and the structural integrity of the charge.In the life cycle of SRM, it is affected by loads such as temperature, storage, transportation, vibration, and ignition pressure.The structural integrity analysis of the charge ensures that the charge column does not break (cracks, interface debonding, large deformation) under these loads [2,3] .
On the issue of structure completeness of SRM load, domestic and foreign researchers have carried out a large amount of research.Yang et al. [4] performed structural simplification of the wing-column type charge.They studied the structural deformation law of the charge under the conditions of solidification cooling and working internal pressure.Birkan et al. [5] and colleagues analysed the threedimensional stresses of a rocket engine under a cyclic temperature load.The propellant composition model considers the effects of viscoelasticity, deformation, temperature, pressure, and softening under monotonous and cyclic loading.Deng et al. [6] made the butyl hydroxyl composite propellant charge as the object of study, linear viscoelastic constitutive equation and the maximum strain energy, and other theories based on the use of three-dimensional modeling and Ansys Workbench software on the charge in the low-temperature ignition process numerical calculations, the results show that low-temperature ignition of the engine working conditions is the worst.Wang et al. [7] studied the effect of two kinds of loads, temperature and pressure, on the structural integrity of the charge.By comparing the lowtemperature load alone and the low-temperature ignition and boosting of the joint action, the corresponding strain values were calculated by using the uncoupling property, and it was concluded that the equivalent strain of the pillars under the action of the ignition and boosting loads still meets the requirements of structural integrity.
Based on the linear viscoelastic finite element method, the document analyses the structural response of a solid motor under low temperature load, internal load, and combined low temperature load and internal pressure.The results can provide a reference for the design of the solid motor.
2 Finite element computational model

Geometric model
This paper studies the SRM for the wall casting form of charge due to the symmetry of the pillar structure, using 1/18 of the charge to analyze.The model includes three parts: shell, adiabatic layer, and pillars, and the mesh is encrypted in the wing groove part to ensure the calculation accuracy.The solid rocket motor finite element model is divided into 53, 321 hexahedral cells and 220, 893 nodes, as shown in Figure 1.

Physical property parameters of materials
The study envelope material is metallic, the insulation layer material is ethylene rubber, and HTPB propellant, the parameters for each material are given in Table 1.
Table 1.Material property parameters.
Propellant Heat insulating layer Metal shell Density/kg•m -3 1.76×10 0.55 0.3 38.92 Propellers are typical viscoelastic materials whose mechanical properties are strongly correlated with time and temperature [8] , and the propellant satisfies the WLF equation: is the temperature shift factor, t is the test temperature, and the selection reference temperature TS is 293.15K.
The relaxation modulus E(t) of fuel is generally described in the following Prony series form:

Boundary condition
When the solid rocket motor charge is solidified and cooled, the curing temperature is about 50°C, and the zero stress temperature is 58°C [9] .The outer surface of the grain, the inner surface of the insulation layer, the outer surface of the cladding layer, and the inner surface of the shell are completely bonded and fixed.The inner hole surface is a free surface to consider the symmetry of the model.Symmetric boundary conditions are applied on the symmetrical surface of the engine to constrain the normal displacement of the nodes on the symmetrical surface.At the same time, the axial displacement of the end face nodes of the engine shell is constrained to eliminate the rigid body motion.

Evaluation criterion of charge structure integrity
In practical engineering applications, the failure of the interface debonding type is usually judged according to the stress criterion, and the failure of the grain is judged based on the strain criterion.The Von strain criterion under temperature load is often used as a criterion for the analysis of the structural integrity of solid motion grains [10] .The Von Mises strain ε v is expressed as:

Computation
To facilitate the analysis, two characteristic lines were taken along the inner grain surface, as shown in Figure 2, and the distribution law of grain deformation along the two characteristic lines was studied under load.

Strain analysis of charge under low temperature (−40°C) load
The Von Mises deformation of the SRM at a low temperature of -40°C is illustrated in Figure 3.The maximum Von Mises deformation occurs at the transition position between the blade slot and the cylinder section, at 16.65%.

Figure 3.
Von Mises strain cloud diagram.Figure 4 shows the Von Mises strain along the axis (from left to right).The concentration of surface deformation within the visible load is more obvious.The strain value of characteristic line A gradually increases along the axial direction of the charge.It reaches the maximum at the transition position between the wing groove and the cylindrical section.In addition, the strain value of the characteristic line A at the wing groove is higher than that of the characteristic line B, and the Von Mises strain of the two characteristic lines in the cylindrical section is not much different.This shows that the wing groove structure obviously influences the strain of the charge, and the strain concentration phenomenon is more likely to occur at this position under low-temperature conditions.Therefore, in the design of the wing groove charge, the strain value of the transition position between the wing groove and the cylindrical section should be focused on.

Strain analysis of charge under internal pressure (10 MPa) load
The internal pressure load is the main grain filling structural integrity analysis load.In the analysis process, the pressure is increased from 0 MPa to 10 MPa within 1 s to simulate the actual ignition and pressurization process of the solid rocket motor.Figure 5 shows the Von Mises strain cloud diagram of the charge under 10 MPa internal pressure load, and Figure 6 shows the distribution of the Von Mises strain of the grain along the axial direction (from left to right).It can be seen from Figure 5 that the maximum Von Mises strain of the charge is 20.725 %.Greater Von Mises strain also occurs in the transition positions of the slot and the cylindrical section under the internal pressure load, as in the case of low temperature loads.The same applies to the Von Mises distortion of the character lines in Figure 6.Engineering practice shows that during the SRM solid rocket engine low temperature ignition test, the low temperature load and the internal pressure load are present simultaneously.Therefore, the response analysis of the charge structure under the combined action of the two loads is carried out in this section.
Figure 7 shows the Von Mises deformation cloud for laxatives under low temperatures and internal load combined.And see in figure 8. Figure 8.The Von mises strain of the charge is distributed along two characteristic lines (-40℃+10 MPa).As you can see in Figure 3 and Figure 5, the maximum strain of low-temperature, internal load charge filling Von Mises is 16.653% and 20.725%, respectively, and the maximum strain of particle filling Von Mises under the two combined loads is 37.378%.It is known that the maximum deformation of the Von put load under the joint action of the low temperature, and the internal load is the sum of the deformation of the load under the action of two separate loads.This shows that the maximum Von Mises strain caused by low temperature and internal pressure is superimposed on each other.In addition, it can also be seen from the diagram that under the combined action of the two loads, the transition position between the wing groove and the cylindrical section is still the most dangerous part of the charge.

Conclusion
In this paper, the structural integrity of a solid rocket motor under the action of low temperature, internal pressure, and the combination of two loads is simulated and calculated.The following conclusions are obtained: (1) Under the separate action of the charges at low temperature and internal pressure, as well as the combination of the two charges, the maximum Von Mises strain for charge filling appears in the transition position between the slot and the cylindrical surface, which is the most dangerous part of the internal surface of the charge filling.
(2) The maximum Von Mises strain on the inner surface of the charge caused by low temperature and internal pressure loads is superimposed on each other.The maximum Von Mises strain of the charge under the combined action of the two loads is the sum of the maximum Von Mises strain caused by the two loads alone.(3) According to the strain distribution on the characteristic line, it can be seen that there are two maximum values of Von Mises strain on the inner surface of the charge, which are located at the transition position between the wing groove and the cylindrical section and the front 1/3 position of the cylindrical section, indicating that there is also strain concentration in the cylindrical section.

Figure 2 .
Figure 2. Characteristic line identification diagram of a solid rocket motor.

Figure 4 .
Figure 4.The distribution law of Von Mises strain of low temperature (−40°C) charge along two characteristic lines.

Figure 5 .
Figure 5. Von Mises strain cloud diagram.It can be seen from Figure5that the maximum Von Mises strain of the charge is 20.725 %.Greater Von Mises strain also occurs in the transition positions of the slot and the cylindrical section under the internal pressure load, as in the case of low temperature loads.The same applies to the Von Mises distortion of the character lines in Figure6.

Figure 6 . 5 3. 3
Figure 6.The Von Mises strain distribution of the grain under internal pressure (10 MPa) along three characteristic lines.