Method for predicting thermal shock resistance of polymer bonded explosive considering structure effect

Abstract

The application discloses a kind of high polymer bonded explosive heat shock resistance performance prediction method considering structural effect, obtains the PBX explosive basic force thermal parameter required according to test calibration / direct test, determines the characteristic size of structure, determines shape factor, finally obtains the expression of prediction method;The prediction method considers the influence of material physical property, structural effect and material nonlinearity on heat shock resistance performance, and can be used for the heat shock resistance performance prediction of typical high polymer bonded explosive structures such as PBX cylinder, PBX hemispherical shell, and the prediction effect is good;The prediction method does not need simulation, and the prediction process is rapid and convenient.

Description

Technical Field

[0001] This invention relates to the field of energetic materials technology, and in particular to a method for predicting the thermal shock resistance of polymer-bonded explosives considering structural effects. Background Technology

[0002] Polymer-bonded explosives (PBX) are composite materials composed of explosive crystals and soft polymer binders, widely used in defense and military fields. During storage, transportation, assembly, and use, PBX may be subjected to various types of temperature loads, including temperature cycling, temperature gradients, and temperature shocks. Due to the typical low-strength, high-linear-expansion characteristics of PBX explosives, they are prone to cracking under temperature differences, making them a weak point in environmental adaptability. Currently, thermal shock testing is mainly used to determine the thermal shock resistance of explosive materials; however, this method is time-consuming and costly. Especially in the early stages of explosive formulation development, experimental methods are unsuitable for determining the thermal shock resistance of explosives. How to quickly evaluate the thermal shock resistance of PBX is a key factor affecting the progress of formulation development, necessitating the development of a rapid evaluation method for the thermal shock resistance of PBX explosives.

[0003] To rapidly evaluate thermal shock resistance, the ceramics field has defined several thermal shock resistance parameters based on the fundamental physical properties of materials. These include a first thermal shock resistance parameter reflecting the influence of mechanical properties on thermal shock resistance, and a second thermal shock resistance parameter reflecting the influence of both mechanical properties and thermal conductivity. However, these parameters only consider the influence of material-level mechanical and thermal characteristics, neglecting structural effects (structural dimensions, shape, etc.). Furthermore, these parameters employ linear elastic constitutive models to convert thermal strain into thermal stress and determine the critical temperature difference the material can withstand based on stress failure criteria. While this approach is suitable for ceramic materials, it leads to significant deviations for materials like PBX explosives, which exhibit marked nonlinearity. Therefore, a comprehensive method for predicting the thermal shock resistance of PBX explosives that considers material properties, structural effects, and material nonlinearity is still lacking. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the thermal shock resistance of polymer-bonded explosives that considers structural effects in order to solve the above-mentioned problems. This invention targets typical PBX explosive components such as PBX cylinders and PBX hemispherical shells for assessing thermal shock resistance, and comprehensively considers the influence of material properties, structural effects, and material nonlinearity on thermal shock resistance. It can be used to predict the thermal shock resistance of typical polymer-bonded explosive structures such as PBX cylinders and PBX hemispherical shells.

[0005] The present invention achieves the above objectives through the following technical solutions:

[0006] A method for predicting the thermal shock resistance of polymer-bonded explosives considering structural effects includes the following steps:

[0007] Currently, the thermal shock resistance of PBX explosives is generally determined by rapid cooling thermal shock tests on PBX cylindrical and hemispherical shell components. The experimental procedure involves placing the explosive sample in a temperature chamber and then slowly heating it to a certain initial temperature (T0) at a quasi-static rate, maintaining this temperature until thermal equilibrium is reached. The ambient temperature inside the chamber is then rapidly reduced until the sample fails. The difference between the initial temperature (T0) and the surface temperature at failure (T1) is used to characterize the thermal shock resistance. This loading method approximates instantaneous environmental temperature changes.

[0008] In a quasi-static loading scenario (where temperature does not change over time), the thermal deformation caused by temperature changes is as follows:

[0009] ε T =αΔT (9)

[0010] Where α is the coefficient of linear expansion, and ΔT = T0 - T1 is the temperature difference.

[0011] If a stress failure criterion is used, similar to the first thermal shock resistance parameter, a constitutive model is needed to convert thermal strain into thermal stress. However, PBX explosives exhibit significant nonlinearity, making linear elastic constitutive models unsuitable. Furthermore, the construction of nonlinear constitutive models may differ for different PBX types. Therefore, this method uses a strain failure criterion to determine the critical temperature difference the material can withstand. This not only solves the problem of nonlinear constitutive properties but also allows for direct measurement of strain in thermal shock experiments, where stress data is difficult to obtain. Therefore, in a quasi-static scenario, the critical temperature difference that PBX explosives can withstand is:

[0012]

[0013] Where, ε f The tensile strain at which the material fails is denoted as .

[0014] Based on this, in order to accurately predict the material's ability to resist thermal stress, and further considering the influence of structural shape, the temperature difference it can withstand is corrected as follows:

[0015]

[0016] Where S is the form factor. Due to their different shapes, structural components will experience different stress concentrations within the structure; therefore, the form factor is essentially the reciprocal of the stress concentration factor. According to the strain failure criterion, the structure will fail when the maximum strain reaches the failure strain. Therefore, the form factor that needs to be determined is the form factor of the failure hazard point. The hazard point may have various geometric features such as curved surfaces and holes; therefore, the form factor is:

[0017] S = S 几何特征1 ×S 几何特征2 ×...S 几何特征n (12)

[0018] For transient temperature shock scenarios such as rapid cooling thermal shock experiments, the maximum thermal stress value and its occurrence time are related to the Biot number. A higher Biot number indicates a larger proportion of surface heat transfer and thus greater thermal stress; a lower Biot number indicates a larger proportion of heat conduction and thus less thermal stress. The Biot number β is:

[0019]

[0020] Where, r m λ is the characteristic dimension of the structural component, λ is the thermal conductivity (characterizing the ability of internal heat conduction), and h is the convective heat transfer coefficient (characterizing the ability of the surface to exchange heat).

[0021] Due to the combined effects of internal heat transfer and surface heat exchange, the temperature distribution on the structural component exhibits a nonlinear pattern when the Biot number is finite. To account for the influence of this nonlinear temperature distribution, a temperature correction formula f(β) is introduced, drawing on the method of Kingey et al. The tolerable temperature difference is then further corrected as follows:

[0022]

[0023] Where f(β) = 1 + C / β, C = 0.8 (calibrated based on an existing set of PBX propellant charge temperature surge tests). The characteristic dimensions of the component are: λ is the thermal conductivity (characterizing the internal heat conduction capacity), and h is the convective heat transfer coefficient (characterizing the surface heat exchange capacity).

[0024] In summary, considering all material properties (α, λ, h, ε) f ), structural effects (r m The expression for the prediction method of thermal shock resistance of PBX explosives based on S) and material nonlinearity is:

[0025]

[0026] In specific calculations, the required basic mechanical and thermal parameters of the PBX explosive are first obtained based on experimental calibration / direct testing, including the coefficient of linear expansion α, thermal conductivity λ, convective heat transfer coefficient h, and tensile failure strain ε. f ;

[0027] Secondly, determine the characteristic dimensions of the structure. The characteristic dimension of the PBX cylinder is the cylinder radius, and the characteristic dimension of the PBX hemispherical shell is the shell thickness.

[0028] Next, the shape factor is determined by consulting stress concentration factor handbooks or calculating using elasticity theory based on the geometric characteristics of the structure. This method mainly targets PBX cylindrical and PBX hemispherical shell components, and considers two typical local geometric features: holes and foci.

[0029] For a simple cylindrical PBX configuration, the shape factor is set to 1 according to the stress concentration factor handbook.

[0030] For a PBX hemispherical shell, according to the bending theory of curved rods, the stress concentration factors of the inner and outer surfaces of the shell are respectively:

[0031]

[0032] in, a and b are the inner and outer diameters of the spherical shell.

[0033] For the hole, according to Lamé's formula, the stress concentration factor at the edge of the hole is 2, therefore the shape factor is S. 孔 =1 / 2.

[0034] For the ball-and-socket joint, calculations based on elasticity theory show that the stress concentration factor is greatest at the top of the joint, at 2.086. Therefore, S 球窝 =1 / 2.086.

[0035] The beneficial effects of this invention are as follows:

[0036] This invention discloses a method for predicting the thermal shock resistance of polymer-bonded explosives considering structural effects. Based on experimental calibration / direct testing to obtain the required basic mechanical and thermal parameters of the PBX explosive, the characteristic dimensions of the structure are determined, the shape factor is determined, and finally, a prediction method expression is derived. This prediction method considers the influence of material properties, structural effects, and material nonlinearity on thermal shock resistance, and can be used to predict the thermal shock resistance of typical polymer-bonded explosive structures such as PBX cylinders and PBX hemispherical shells, with good prediction results. This prediction method does not require simulation, and the prediction process is rapid and convenient. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a schematic diagram of the PBX cylindrical temperature stamping experiment of the present invention.

[0039] Figure 2 This is a schematic diagram of the external punching experiment of the perforated PBX hemispherical shell of the present invention.

[0040] Figure 3 This is a schematic diagram of the internal punching experiment of the perforated PBX hemispherical shell of the present invention.

[0041] Figure 4 This is a schematic diagram of the external impact test of the PBX hemispherical shell with a ball socket according to the present invention. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be described in detail below. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0043] In any embodiment, such as Figure 1-4 As shown, the present invention provides a method for predicting the thermal shock resistance of polymer-bonded explosives considering structural effects, comprising:

[0044] 1) Temperature shock test loading method

[0045] The selected PBX components are a PBX cylinder, a PBX hemispherical shell with a hole, and a PBX hemispherical shell with a spherical socket. The following four types of experiments were carried out.

[0046] ①PBX cylindrical warm stamping

[0047] like Figure 1 As shown, a PBX cylindrical sample is placed in a temperature chamber and subjected to temperature shock by rapidly cooling the sample with air. When the thermal strain exceeds the material failure strain, the sample fractures, causing a sudden change in the strain on the sample surface and generating an elastic wave. The acoustic emission signal caused by the elastic wave is detected by an acoustic emission sensor and a thermocouple attached to the sample surface, and the crack initiation time and corresponding temperature are determined accordingly.

[0048] ② Perforated PBX hemispherical shell external punch

[0049] like Figure 2 As shown, a perforated PBX hemispherical explosive component and an insulating base plate are placed in the middle of an ambient temperature chamber. The insulating base plate is used to slow down the heat exchange between the inner surface of the explosive component and the ambient air, thereby achieving the purpose of thermal stress loading on the outer spherical shell. The temperature of the ambient temperature chamber is slowly raised to a certain high temperature. After the temperature of the inner and outer surfaces of the explosive component is consistent with the ambient temperature, the temperature of the inner spherical surface is kept constant, and the temperature of the temperature chamber is rapidly reduced. A transient internal and external temperature difference and thermal strain are formed between the inner and outer surfaces of the explosive component. When the transient internal and external temperature difference increases to the point where the explosive component cracks, the time of crack initiation and the temperature at the time of crack initiation are determined by temperature and acoustic emission.

[0050] ③ Perforated PBX hemispherical shell internal punch

[0051] like Figure 3 As shown, the perforated PBX hemispherical explosive component and the heat insulation sleeve are placed in the middle position inside the ambient temperature chamber. The heat insulation sleeve is used to slow down the heat exchange between the outer surface of the explosive component and the ambient air, thereby achieving the purpose of temperature-loaded inner spherical shell. The remaining experimental conditions are the same as those for the perforated PBX hemispherical shell external impact.

[0052] ④ PBX hemispherical shell with ball socket

[0053] like Figure 4 As shown, the PBX hemispherical explosive with a spherical socket and the heat-insulating base plate were placed in the middle position inside the ambient temperature chamber, and the other experimental conditions were the same as those for the PBX hemispherical explosive with a hole.

[0054] 2) Basic mechanical and thermal parameters of PBX explosives

[0055] The selected PBX explosive materials are an HMX-based explosive (denoted as PBX-1) and a TATB-based explosive (denoted as PBX-2). Based on material-level experimental testing, the mechanical and thermal parameters of these two PBXs are determined as shown in the table below.

[0056]

[0057] 3) Feature size and shape factor

[0058] The PBX cylinder has dimensions of Φ100mm × 110mm, therefore its characteristic dimension is 50mm. For this simple configuration of the PBX cylinder, according to the stress concentration factor handbook, the form factor is set to 1.

[0059] The perforated PBX hemispherical shell has an inner diameter a = 100 mm and an outer diameter b = 150 mm. Therefore, the characteristic dimension is 50 mm, and the shape factors for the perforated outer spherical surface and the perforated inner spherical surface are respectively:

[0060]

[0061] The PBX hemispherical shell with a notch has an inner diameter a = 100 mm and an outer diameter b = 160 mm. Therefore, the characteristic dimension is 60 mm, and the shape factor of the outer spherical surface with the notch is:

[0062]

[0063] 4) Prediction and experimental verification of thermal shock resistance

[0064] By incorporating the basic mechanical and thermal parameters, characteristic dimensions, and shape factor into the expression for predicting the thermal shock resistance of PBX explosives, the predicted results of thermal shock resistance for different explosives and different experiments were obtained. The calculated results showed good agreement with the experimental results.

[0065]

[0066] This invention has been successfully applied to different types of PBX explosive materials and explosive components with different configurations at the Institute of Chemical Materials, China Academy of Engineering Physics, achieving accurate prediction of the thermal shock resistance of PBX explosives and obtaining excellent application results.

[0067] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims. It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not describe the various possible combinations separately. Furthermore, various different embodiments of the present invention can also be arbitrarily combined, as long as they do not violate the spirit of the present invention, they should also be considered as the content disclosed in the present invention.

Claims

1. A method for predicting the thermal shock resistance of polymer-bonded explosives considering structural effects, characterized in that, Includes the following steps: Step 1: Place the explosive sample in a temperature chamber, and then heat the sample to the initial temperature T0 in a quasi-static manner at a slow heating rate and keep the temperature constant so that the sample reaches thermal equilibrium at T0; then rapidly reduce the ambient temperature in the temperature chamber until the sample is destroyed. The difference between the initial temperature T0 and the surface temperature T1 when the explosive is destroyed is used to characterize the thermal shock resistance. In a quasi-static loading scenario, the thermal deformation caused by temperature changes is as follows: e T =αΔT (1) Where α is the coefficient of linear expansion, and ΔT = T0 - T1 is the temperature difference; Step 2: The critical temperature difference that the material can withstand is determined using the strain failure criterion. Under quasi-static conditions, the critical temperature difference that the PBX explosive can withstand is: Where, ε f The tensile strain at which the material fails. Step 3, considering the influence of structural shape, the temperature difference it can withstand is corrected as follows: Where S is the shape factor; when the maximum strain in the structure reaches the failure strain, the structure will fail, so the shape factor that needs to be determined is the shape factor of the failure hazard point; the failure hazard point has multiple geometric features, therefore the shape factor is: S=S 几何特征1 ×S 几何特征2 ×...S 几何特征n (4) Step 4: For transient temperature shock scenarios such as rapid cooling thermal shock experiments, the maximum thermal stress value and the time of occurrence are related to the Biot number, β, which is: Where, r m Let λ be the characteristic dimension of the structural component, λ be the thermal conductivity, and h be the convective heat transfer coefficient. Step 5: Due to the combined effects of internal heat transfer and surface heat exchange, when the Biot number is finite, the temperature distribution on the structural component is non-linear. A temperature correction formula f(β) is introduced, and the tolerable temperature difference is corrected as follows: Where f(β)=1+C / β, C=0.8 is the characteristic dimension of the component, λ is the thermal conductivity, and h is the convective heat transfer coefficient; Step 6, comprehensively consider the material properties (α, λ, h, ε) f ), structural effects (r m The expression for the prediction method of thermal shock resistance of PBX explosives based on S) and material nonlinearity is:

2. The method for predicting the thermal shock resistance of polymer-bonded explosives considering structural effects as described in claim 1, characterized in that, In step 3, the shape factor is determined. Based on the geometric characteristics of the structure, it is obtained by consulting a stress concentration factor handbook or calculating using elasticity theory. The following are methods for determining the shape factor for PBX cylindrical and PBX hemispherical shell components, considering two typical local geometric features: holes and spherical sockets. For a simple cylindrical PBX configuration, according to the stress concentration factor handbook, the form factor is set to 1. For a PBX hemispherical shell, according to the bending theory of curved rods, the stress concentration factors of the inner and outer surfaces of the shell are respectively: in, a and b are the inner and outer diameters of the spherical shell; For the hole, according to Lamé's formula, the stress concentration factor at the edge of the hole is 2, therefore the shape factor is S. 孔 =1 / 2 For the ball-and-socket joint, calculations based on elasticity theory show that the stress concentration factor is greatest at the top of the joint, at 2.

086. Therefore, S 球窝 =1 / 2.086.

Images