CN108828008B - Explosive internal explosion power evaluation method based on shock wave overpressure and quasi-static pressure - Google Patents

Explosive internal explosion power evaluation method based on shock wave overpressure and quasi-static pressure Download PDF

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CN108828008B
CN108828008B CN201810354892.3A CN201810354892A CN108828008B CN 108828008 B CN108828008 B CN 108828008B CN 201810354892 A CN201810354892 A CN 201810354892A CN 108828008 B CN108828008 B CN 108828008B
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张玉磊
苏健军
李芝绒
蒋海燕
袁建飞
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Xian Modern Chemistry Research Institute
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Abstract

The invention discloses an explosive internal explosion power evaluation method based on shock wave overpressure and quasi-static pressure, which adopts the same mass of explosive to be evaluated and TNT to carry out an explosive internal explosion power evaluation test, determines the types of power evaluation parameters, a measuring point arrangement method and a data processing method according to the explosive internal explosion characteristics, and establishes a power equivalent TNT equivalent calculation method based on shock wave overpressure and quasi-static pressure. The method breaks through the single index of explosive power of shock wave overpressure, can comprehensively reflect the explosive power characteristics in the explosive, has more scientific and reasonable evaluation result, and can be used for explosive formula selection and explosive power evaluation.

Description

Explosive internal explosion power evaluation method based on shock wave overpressure and quasi-static pressure
The invention belongs to the technical field of explosive explosion power test and evaluation, and particularly relates to a power evaluation method, in particular to an explosive internal explosion power evaluation method based on shock wave overpressure and quasi-static pressure.
Background
For the damage of the target with a cavity structure of ships, buildings and the like, internal explosion is the most common damage means, and the pressure effect under the working conditions is divided into shock wave overpressure and quasi-static pressure. The quasi-static pressure is formed by the fact that high-temperature and high-pressure gas products generated by explosion expand outwards and are restrained by a closed space, the quasi-static pressure rises relatively slowly and is stabilized to a certain lower pressure, and the peak value is far smaller than the overpressure peak value of the shock wave. After the ammunition explodes, the closed space structure is firstly affected by high-frequency shock waves to generate pre-damage such as cracks, throwing, tearing and the like, then low-frequency quasi-static pressure continuously acts on a target to cause more serious damage such as structure disintegration, flying and the like, the final damage effect of the target is closely related to the action strength of the shock wave overpressure and the quasi-static pressure, particularly, the vulnerability of the target is obviously reduced after the shock wave action, and the subsequent quasi-static pressure can even be a determining factor of the target damage effect.
At present, researchers at home and abroad carry out a great deal of research on the explosive effect in explosives. Foreign scholars predict the distribution of the internal explosion shock wave load based on tests, establish a simplified triangular load model, and domestic scholars develop numerical research on the evolution of shock wave systems in an explosion container and develop internal explosion shock wave overpressure and quasi-static pressure characteristic research of TNT-based explosives under sealed conditions by using a sealed tank. With the popularization and application of non-ideal explosive with remarkable post-combustion effect such as warm-pressed explosive, the quasi-static pressure effect of the explosive after the explosive is imploded is remarkable, and the quasi-static pressure power is concerned more widely. The American naval Water surface weapon center has used quasi-static pressure as one of ammunition charging power assessment indexes.
Although a large number of internal explosion pressure effects and power researches have been carried out at home and abroad, the researches generally only consider the overpressure power of the shock wave and hardly relate to the quasi-static pressure power of explosive internal explosion, and an evaluation system is not comprehensive in the department of science. In addition, most explosive internal explosion power evaluation methods are power parameter lists or direct comparison, and no explosive internal explosion power evaluation method adopting an explosion power equivalent TNT equivalent is seen, so that the evaluation standards are not uniform, and the evaluation results are not visual.
Disclosure of Invention
In order to overcome the defects and shortcomings of the prior art, the invention provides an explosive internal explosion power evaluation method based on shock wave overpressure and quasi-static pressure. The method determines the type, the acquisition method, the measuring point arrangement method and the data processing method of the power evaluation parameters according to the explosion characteristics of the explosive in the closed space, establishes the equivalent TNT equivalent calculation method of the explosive internal explosion power based on the overpressure and the quasi-static pressure of the shock wave, solves the problems of incomplete and non-uniform evaluation indexes of the current internal explosion power, and can be used for explosive formula selection, explosion power evaluation and damage power estimation of explosive ammunition.
TNT equivalent weight is initially defined as the ratio of the detonation heat per mass of a given explosive to the detonation heat of TNT. However, explosives with high explosive heat have not necessarily high explosive shock wave overpressure power, and especially after the explosive containing metal fuel explodes, part of energy is released in a combustion mode, so that the explosive heat TNT equivalent is not suitable for explosive power evaluation. The invention relates to a power equivalent TNT equivalent method, which is characterized in that a TNT explosion power model is established by TNT field explosion power data, an explosion power experimental result obtained under the same explosive charging condition to be evaluated is substituted into the TNT model, and TN (total nitrogen) reaching the same explosion power is solvedT equivalent charge meAnd taking the ratio of the equivalent loading of the TNT of the explosive to be evaluated and the loading of the TNT as the equivalent weight of the TNT. The power equivalent TNT equivalent method is based on the explosion power parameter as evaluation basis and reflects the damage capacity of explosion to the target really.
In order to solve the problems, the invention adopts the following technical solutions:
a method for evaluating explosive internal explosion power based on shock wave overpressure and quasi-static pressure comprises the following steps:
the method comprises the following steps: method for determining internal explosion power parameter and obtaining internal explosion power parameter
The explosive power parameters in the explosive comprise an explosion shock wave overpressure peak value and a quasi-static pressure peak value. The overpressure peak value of the explosion shock wave is obtained through a high-frequency shock wave pressure sensor, and the quasi-static pressure peak value is obtained through a low-frequency quasi-static pressure sensor.
Step two: test method for determining internal explosion power parameter
The explosive internal explosion power test environment is a closed space, such as a simulated or real internal explosion environment of an explosion tank, an explosion tower, a closed cabin, underground works and the like. The test samples are TNT explosive charges and explosive charges to be evaluated with the same mass, and if the test samples are not arranged at the appointed installation position, the test samples are installed at the center of the closed space.
The shock wave pressure sensor and the quasi-static pressure sensor are arranged on the wall surface of the closed space, wherein at least 6 shock wave pressure sensors are arranged, and the sensitive surface of the sensor is just opposite to the center of burst to ensure that the shock wave is in normal incidence; the number of the quasi-static pressure sensors is not less than 2. The internal explosion test under the same conditions was repeated three times and the average value was taken as the test result.
Step three: model for determining overpressure force of TNT explosion shock wave
After the explosive explodes in the closed space, the incident shock wave acts on the sensitive surface of the shock wave pressure sensor to generate positive reflection, and the shock wave pressures obtained in the table 1 are positive reflection pressures. If the overpressure peak value measured by the shock wave pressure sensor is prCalculating the incident pressure p of the blast shock wave from the formula (1)i
Figure BDA0001634328790000031
In the formula: p is a radical ofiThe incident shock wave overpressure is MPa; p is a radical of0Taking the pressure as atmospheric pressure, and taking the pressure of 0.101 MPa; p is a radical ofrThe positive reflection pressure is MPa.
And (3) substituting the shock wave incident pressure, the TNT charge quality and the measured point detonation center distance which are obtained by calculation of the formula (1) into a formula (2), and obtaining coefficients a, b and c in the formula (2) by adopting a least square method.
Figure BDA0001634328790000032
In the formula: m isTTNT charge, kg; r is the distance between the two blast centers, m; a. b and c are undetermined coefficients.
Step four: determining TNT explosion quasi-static pressure power model
The formation of the internal explosion quasi-static pressure can be divided into two parts: pressure rise p caused by diffusion of gas generated by explosion into enclosed space1Pressure rise p caused by temperature rise in the sealed space due to explosion energy release2The quasi-static pressure p can be known by ideal gas equationqsClosely related to the test drug quantity-closed space volume ratio m/V. The post-combustion reaction process between detonation reaction products, air and products under a closed condition is very complex, no better theoretical model exists at present, and a quasi-static pressure engineering calculation model obtained by an applicant on the basis of a large number of tests and data analysis is
Figure BDA0001634328790000041
In the formula: p is a radical ofqsQuasi-static pressure peak value, MPa; m isTTNT charge, kg; v is the volume of the enclosed space, m3(ii) a Alpha is a undetermined coefficient. Substituting the actual measurement result of the quasi-static pressure of the explosion in the TNT explosive charging, the TNT charging amount and the closed space volume V into formula (1), and fitting to obtain alpha.
Step five: calculating the equivalent TNT equivalent of the overpressure force of the explosion shock wave in the explosive to be evaluated
Substituting the test results of each shock wave pressure test point of the explosive charge to be evaluated in the table 1 into formula (1) to obtain the incident shock wave pressure p of the explosive charge to be evaluated at each test pointi(ii) a Measuring point burst center distance r and incident shock wave pressure piSubstituting the obtained value into a formula (2) with determined coefficients to obtain the TNT equivalent explosive loading m which generates the same incident shock wave pressure as the explosive to be evaluated at different measuring pointseShock wave overpressure force equivalent TNT equivalent of explosive to be evaluated
Figure BDA0001634328790000042
In the formula: q. q.sPunching machineThe equivalent TNT equivalent of the overpressure force of the shock wave is dimensionless; n is the number of effective results of the shock wave pressure test; m iseiTNT equivalent load at test point i (i ═ 1, 2, … …, n), kg; m isaKg for explosive charge to be evaluated.
Step six: calculating equivalent TNT equivalent of quasi-static pressure power equivalent of explosion in explosive to be evaluated
The test result p of each quasi-static pressure test point of explosive charge to be evaluated in the table 1 is measuredqsSubstituting the volume V of the closed space into a formula (3) with a determined coefficient to obtain the TNT equivalent charge m 'generating the quasi-static pressure peak value same as the explosion of the explosive to be evaluated'eiThen the quasi-static pressure power equivalent TNT equivalent of the explosive to be evaluated
Figure BDA0001634328790000051
In the formula: q. q.sQuietThe equivalent TNT equivalent of the quasi-static pressure power is dimensionless; n' is the number of effective results of the quasi-static pressure test; m'eiTNT equivalent load at test point j (j ═ 1, 2, … …, n'), kg; m isaKg for explosive charge to be evaluated.
Step seven: calculating the equivalent TNT equivalent of the explosive comprehensive power equivalent to be evaluated
And (3) calculating the equivalent TNT of the explosive internal explosion comprehensive power according to the formula (6):
qTNT=k1qpunching machine+k2qQuiet (6)
In the formula: q. q.sTNTThe equivalent TNT equivalent of explosive comprehensive power in the explosive to be evaluated is free of dimension; q. q.sPunching machineThe equivalent TNT equivalent of the overpressure force of the shock wave is dimensionless; q. q.sQuietThe equivalent TNT equivalent of the quasi-static pressure power is dimensionless; k is a radical of1、k2For weighting coefficients, the method of averaging weights when weights are not agreed, i.e. k1=k2=0.5。
The beneficial effects of the invention are shown in the following aspects:
(1) according to the explosive implosion power evaluation method based on the shock wave overpressure and the quasi-static pressure, provided by the invention, the shock wave overpressure power and the quasi-static pressure power of explosive implosion are comprehensively considered, an evaluation system taking the shock wave overpressure as a single index is broken through, and the power evaluation result is more scientific, comprehensive and accurate;
(2) the evaluation result of the method adopts the equivalent TNT equivalent of power, the internal explosion power of different types of explosives to be evaluated is converted into equivalent TNT charge, the evaluation standard is unified, the evaluation result is visual, and the method can be widely used for power evaluation and power comparison of the internal explosion explosives.
Drawings
FIG. 1 is a flow chart of a method for evaluating the explosive detonation power in an explosive based on shock wave overpressure and quasi-static pressure;
FIG. 2 is a curve of explosive shock wave overpressure in 2kg of a certain temperature and pressure explosive and TNT explosive;
FIG. 3 is a quasi-static pressure curve of 2kg of a thermal pressure explosive and TNT explosive.
Detailed Description
The invention will be further described in the following with reference to the drawings and preferred embodiments.
A method for evaluating explosive internal explosion power based on shock wave overpressure and quasi-static pressure comprises the following steps:
the method comprises the following steps: method for determining internal explosion power parameter and obtaining internal explosion power parameter
The explosive power parameters in the explosive comprise an explosion shock wave overpressure peak value and a quasi-static pressure peak value. The overpressure peak value of the explosion shock wave is obtained through a high-frequency shock wave pressure sensor, and the quasi-static pressure peak value is obtained through a low-frequency quasi-static pressure sensor.
Step two: test method for determining internal explosion power parameter
The explosive internal explosion power test environment is a closed space, such as a simulated or real internal explosion environment of an explosion tank, an explosion tower, a closed cabin, underground works and the like. The test samples are TNT explosive charges and explosive charges to be evaluated with the same mass, and if the test samples are not arranged at the appointed installation position, the test samples are installed at the center of the closed space.
The shock wave pressure sensor and the quasi-static pressure sensor are arranged on the wall surface of the closed space, wherein at least 6 shock wave pressure sensors are arranged, and the sensitive surface of the sensor is just opposite to the center of burst to ensure that the shock wave is in normal incidence; the number of the quasi-static pressure sensors is not less than 2. The internal explosion test under the same conditions was repeated three times and the average was taken as the final result.
Step three: model for determining overpressure force of TNT explosion shock wave
After the explosive explodes in the closed space, the incident shock wave acts on the sensitive surface of the shock wave pressure sensor to generate positive reflection, and the shock wave pressures obtained in the table 1 are positive reflection pressures. If the overpressure peak value measured by the shock wave pressure sensor is prCalculating the incident pressure p of the blast shock wave from the formula (1)i
Figure BDA0001634328790000061
In the formula: p is a radical ofiThe incident shock wave overpressure is MPa; p is a radical of0Taking the pressure as atmospheric pressure, and taking the pressure of 0.101 MPa; p is a radical ofrThe positive reflection pressure is MPa. And (3) substituting the shock wave pressure test result in the table 1 into the formula (1) to calculate to obtain the shock wave incident pressure, substituting the shock wave incident pressure into the TNT explosion shock wave overpressure power formula (2) together with the TNT charge quality and the measured point centre-of-burst distance, and obtaining coefficients a, b and c in the formula (2) by adopting a least square method.
Figure BDA0001634328790000071
In the formula: m isTTNT charge, kg; r is the distance between the two blast centers, m; a. b and c are undetermined coefficients.
Step four: determining TNT explosion quasi-static pressure power model
The power model for calculating the quasi-static pressure of the explosion in the TNT explosive charging is
Figure BDA0001634328790000072
In the formula: p is a radical ofqsQuasi-static pressure peak value, MPa; m isTTNT charge, kg; v is the volume of the enclosed space, m3(ii) a Alpha is a undetermined coefficient. Substituting the actual measurement result of the quasi-static pressure of the explosion in the TNT explosive charging, the TNT charging amount and the closed space volume V into formula (1), and fitting to obtain alpha.
Step five: calculating the equivalent TNT equivalent of the overpressure force of the explosion shock wave in the explosive to be evaluated
Substituting the test results of each shock wave pressure test point of the explosive charge to be evaluated in the table 1 into formula (1) to obtain the incident shock wave pressure p of the explosive charge to be evaluated at each test pointi(ii) a Measuring point burst center distance r and incident shock wave pressure piSubstituting the obtained value into a formula (2) with determined coefficients to obtain the TNT equivalent explosive loading m which generates the same incident shock wave pressure as the explosive to be evaluated at different measuring pointseShock wave overpressure force equivalent TNT equivalent of explosive to be evaluated
Figure BDA0001634328790000073
In the formula: q. q.sPunching machineThe equivalent TNT equivalent of the overpressure force of the shock wave is dimensionless; n is the number of effective results of the shock wave pressure test; m iseiTNT equivalent load at test point i (i ═ 1, 2, … …, n), kg; m isaKg for explosive charge to be evaluated.
Step six: calculating equivalent TNT equivalent of quasi-static pressure power equivalent of explosion in explosive to be evaluated
The test result p of each quasi-static pressure test point of explosive charge to be evaluated in the table 1 is measuredqsSubstituting the volume V of the closed space into a formula (3) with a determined coefficient to obtain the TNT equivalent charge m 'generating the quasi-static pressure peak value same as the explosion of the explosive to be evaluated'eiThen the quasi-static pressure power equivalent TNT equivalent of the explosive to be evaluated
Figure BDA0001634328790000081
In the formula: q. q.sQuietThe equivalent TNT equivalent of the quasi-static pressure power is dimensionless; n' is the number of effective results of the quasi-static pressure test; m'eiTNT equivalent load at test point j (j ═ 1, 2, … …, n'), kg; m isaKg for explosive charge to be evaluated.
Step seven: calculating the equivalent TNT equivalent of the explosive comprehensive power equivalent to be evaluated
And (3) calculating the equivalent TNT of the explosive internal explosion comprehensive power according to the formula (6):
qTNT=k1qpunching machine+k2qQuiet (6)
In the formula: q. q.sTNTThe equivalent TNT equivalent of explosive comprehensive power in the explosive to be evaluated is free of dimension; q. q.sPunching machineThe equivalent TNT equivalent of the overpressure force of the shock wave is dimensionless; q. q.sQuietThe equivalent TNT equivalent of the quasi-static pressure power is dimensionless; k is a radical of1、k2For weighting coefficients, the method of averaging weights when weights are not agreed, i.e. k1=k2=0.5。
The following are specific examples given by the inventors.
In this example, the evaluation of the explosive power in a certain temperature-pressure explosive is carried out, the test explosive amount is 2kg, the closed container is a capsule type explosive can, and the volume is 26m3. And 6 pressure sensors and 2 quasi-static pressure sensors are arranged on the inner wall surface of the explosion tank, the test result is shown in table 1, a typical shock wave pressure curve is shown in fig. 2, and a typical quasi-static pressure curve is shown in fig. 3.
TABLE 1 test results of internal explosion power of explosive under certain temperature and pressure
Figure BDA0001634328790000082
Figure BDA0001634328790000091
The shock wave pressure test results in table 1 were substituted for formula (1), and the resulting explosion incident shock wave pressure values are shown in table 2.
TABLE 2 incident shock wave pressure calculation results
Figure BDA0001634328790000092
Substituting the TNT internal explosion incident pressure in the table 2 into the formula (2) to obtain an internal explosion incident shock wave overpressure force model of the TNT
Figure BDA0001634328790000093
Substituting the TNT internal explosion quasi-static pressure in the table 1 into the formula (3) to obtain the TNT internal explosion quasi-static pressure power model of
Figure BDA0001634328790000094
Substituting the internal explosion incident pressure of the temperature and pressure explosive in the table 2 into a formula (7), obtaining the overpressure force equivalent TNT equivalent of the explosion shock wave in the temperature and pressure explosive at each measuring point according to a formula (4), and calculating the average value; substituting the quasi-static pressure of the temperature-pressure explosive in the table 1 into a formula (8), obtaining the equivalent TNT equivalent of the quasi-static pressure power of the explosion in the temperature-pressure explosive at each measuring point according to a formula (5), and calculating the average value. The results of the calculations are shown in Table 3.
TABLE 3 incident shock wave pressure calculation results
Figure BDA0001634328790000095
Figure BDA0001634328790000101
Obtaining the equivalent of the TNT equivalent of the comprehensive explosive inner explosion power equivalent q according to the formula (6)TNT=k11.18+k21.975, if the weight-sharing method is adopted, the comprehensive power equivalent TNT equivalent is 1.58.

Claims (1)

1. A method for evaluating explosive internal explosion power based on shock wave overpressure and quasi-static pressure is characterized by comprising the following steps:
the method comprises the following steps: method for determining internal explosion power parameter and obtaining internal explosion power parameter
The explosive internal explosion power parameters comprise an explosion shock wave overpressure peak value and a quasi-static pressure peak value; the overpressure peak value of the explosion shock wave is obtained through a high-frequency shock wave pressure sensor, and the quasi-static pressure peak value is obtained through a low-frequency quasi-static pressure sensor;
step two: test method for determining internal explosion power parameter
The explosive internal explosion power test environment is a closed space, the test samples are TNT explosive charges and explosive charges to be evaluated with the same mass, and if no appointed installation position exists, the test samples are installed at the center of the closed space;
the high-frequency shock wave pressure sensors and the low-frequency quasi-static pressure sensors are arranged on the wall surface of the closed space, wherein the number of the high-frequency shock wave pressure sensors is not less than 6, and the sensitive surface of each sensor is over against the center of explosion to ensure that shock waves are normally incident; at least 2 low-frequency quasi-static pressure sensors are arranged; repeating the internal explosion test for three times under the same condition and taking an average value;
step three: model for determining overpressure force of TNT explosion shock wave
After the explosive explodes in the closed space, the incident shock wave acts on the sensitive surface of the high-frequency shock wave pressure sensor to generate positive reflection, and the obtained shock wave pressure is positive reflection pressure; if the overpressure peak value measured by the high-frequency shock wave pressure sensor isp r Calculating the blast shock wave incidence from equation (1)Press and pressp i
Figure DEST_PATH_IMAGE002
(1)
In the formula:p i the incident shock wave overpressure is MPa;p 0 taking the pressure as atmospheric pressure, and taking the pressure of 0.101 MPa;p r is the positive reflection pressure, MPa; substituting the TNT explosion shock wave pressure test result into formula (1) to obtain shock wave incident pressure, substituting the TNT explosive loading and the measuring point explosion center distance into a TNT explosion shock wave overpressure force formula (2), and obtaining the coefficient in formula (2) by adopting a least square methodabc
Figure DEST_PATH_IMAGE004
(2)
In the formula:m T TNT charge, kg;ris the distance between the two fulcrums, m;abcis the undetermined coefficient;
step four: determining TNT explosion quasi-static pressure power model
The power model for calculating the quasi-static pressure of the explosion in the TNT explosive charging is
Figure DEST_PATH_IMAGE006
(3)
In the formula:p qsquasi-static pressure peak value, MPa;m T TNT charge, kg;Vis a closed space volume, m3
Figure DEST_PATH_IMAGE008
Is the undetermined coefficient; the actual measurement result of the quasi-static pressure of the explosion in the TNT explosive charging, the TNT charging amount and the closed space volumeVSubstituting the formula (3) to obtain
Figure DEST_PATH_IMAGE008A
Step five: calculating the equivalent TNT equivalent of the overpressure force of the explosion shock wave in the explosive to be evaluated
Substituting the test results of each shock wave pressure test point of the explosive charge to be evaluated into formula (1) to obtain the incident shock wave pressure of the explosive charge to be evaluated at each test pointp i (ii) a Distance between centers of detonation of measured pointsrPressure of incident shock wavep i Substituting the obtained value into a formula (2) with determined coefficients to obtain the TNT equivalent explosive loading quantity which generates the same incident shock wave pressure with the explosion of the explosive to be evaluated at different measuring pointsm eShock wave overpressure force equivalent TNT equivalent of explosive to be evaluated
Figure DEST_PATH_IMAGE011
(4)
In the formula:q punching machineThe equivalent TNT equivalent of the overpressure force of the shock wave is dimensionless;nnumber of valid results for shock wave pressure test;m ei is as followsii=1,2,……,nTNT equivalent loading in kg at the measuring point;m a kg for explosive charge to be evaluated;
step six: calculating equivalent TNT equivalent of quasi-static pressure power equivalent of explosion in explosive to be evaluated
Testing results of quasi-static pressure measuring points for explosive loading to be evaluatedp qsVolume of the closed spaceVSubstituting the obtained value into a formula (3) with determined coefficients to obtain the TNT equivalent explosive loading amount which generates the same quasi-static pressure peak value with the explosive explosion to be evaluated
Figure DEST_PATH_IMAGE013
Then the quasi-static pressure power equivalent TNT equivalent of the explosive to be evaluated
Figure DEST_PATH_IMAGE015
(5)
In the formula:q quietThe equivalent TNT equivalent of the quasi-static pressure power is dimensionless;
Figure DEST_PATH_IMAGE017
the number of valid results is the number of quasi-static pressure tests;
Figure DEST_PATH_IMAGE013A
is as followsjj=1,2,……,
Figure DEST_PATH_IMAGE017A
TNT equivalent loading in kg at the measuring point;m a kg for explosive charge to be evaluated;
step seven: calculating the equivalent TNT equivalent of the explosive comprehensive power equivalent to be evaluated
And (3) calculating the equivalent TNT of the explosive internal explosion comprehensive power according to the formula (6):
Figure DEST_PATH_IMAGE021
(6)
in the formula:q TNTthe equivalent TNT equivalent of explosive comprehensive power in the explosive to be evaluated is free of dimension;q punching machineThe equivalent TNT equivalent of the overpressure force of the shock wave is dimensionless;q quietThe equivalent TNT equivalent of the quasi-static pressure power is dimensionless;k 1k 2for weighting coefficients, the method of averaging weights when weights are not agreed, i.e.k 1=k 2=0.5。
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