# The Mesoscopic Numerical Simulation of GAP/CL20/AP Composite Solid Propellant Based on MPM and FEM
## 4 Simulation Results and Discussion
### Debonding Process of AP Grains and CL20 Grains  
A numerical simulation of the uniaxial tension of the meso-model was carried out using the commercial finite element software Abaqus, and Figure 7 shows the stress nephograms corresponding to propellant strains of 30%, 60% and 80%.  
In this paper, the model was established according to the true composition and grain arrangement morphology of the propellant. As shown in Figure 7, during the initial stage of the uniaxial tensile nominal strain reaching 30%, the bonding interface between grain substrates was well bonded. Because the modulus of the grains was much higher than  
Figure 6: Stress–strain curve of GAP/CL20/AP propellant.  
that of the matrix, stress concentration mainly occurs in the interior of the grains and in the matrix of adjacent grains. As the nominal strain reaches 60%, debonding occurs first in the vicinity of large grains and then in dense grain areas. The reason for this is that the strain of the matrix is large near large grains and dense grain areas, which become weak links in the propellant, and these areas are prone to interfacial debonding. As the nominal strain reached 80%, at this time, much interfacial debonding occurred, which led to the gradual convergence of micro-cracks, which eventually tore the matrix and caused the macro-destruction of the propellant. This was consistent with the conclusions in Reference [56].  
Figure 8 shows the engineering stress-strain curve of the composite propellant at a 100 mm/s tensile rate, wherein the black curve is the curve obtained by numerical simulation, and the curves of the other three colors were obtained from experiments. As shown in Figure 8, when the strain is small (\(\epsilon<30\%\)), the propellant is in the linear elastic region, and the stress increases linearly with the increase in strain. When the strain reaches 60%, the interfacial adhesion strength becomes weak, and the stress-strain curve begins to appear nonlinear. When the load continues to increase to a strain of 80%, there is more debonding at the particle interfaces, and the stress hardly increases with the increase in strain. Comparing the simulation curve of the meso-model in Figure 8 with the macro-experimental curve of this propellant, it can be seen that after inversion analysis, the simulation curve is basically consistent with the real experimental curve, the value of  
Figure 7: The stress nephogram of propellant under different strains: (**a**) At a strain value of \(3\times 10^{-2}\); (**b**) At a strain value of \(6\times 10^{-2}\); (**c**) At a strain value of \(8\times 10^{-2}\); (**d**) The scanning electron microscope of the propellant before tensile fracture [7].  
the objective interpolation function min\(R\) in Equation (20) is 0.05078%, and the degree of coincidence is very high in the strain range of 20-80%, so it can be considered that the simulation results can reflect a real experiment.  
We thought the reasons for the gap were as follows: (1) The micro-simulation of the propellant in this paper was based on two-dimensional plane strain, which had some deviation from the three-dimensional one; (2) the initial microscopic defects such as micropores, microcracks, and incomplete grain wrapping were not considered when establishing the microscopic model. The initial microscopic defects will lead to a decrease in the initial modulus.