CN111191345A - Method for predicting ballistic limit speed of laminated plate under impact of ball head bullet - Google Patents

Method for predicting ballistic limit speed of laminated plate under impact of ball head bullet Download PDF

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CN111191345A
CN111191345A CN201911259060.4A CN201911259060A CN111191345A CN 111191345 A CN111191345 A CN 111191345A CN 201911259060 A CN201911259060 A CN 201911259060A CN 111191345 A CN111191345 A CN 111191345A
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laminated plate
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吴乔国
程长征
王宝珍
潘建华
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Hefei University of Technology
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Abstract

The invention discloses a method for predicting ballistic limit speed of a laminated plate under ball bullet impact, which is used for calculating a conversion critical condition value T between an overall response failure mode and a localized failure mode of the laminated platec(ii) a Calculating the ratio H/d of the thickness of the laminated plate to the diameter of the ball bullet body, and if H/d is more than or equal to TcThen solving ballistic limit velocity V based on laminate localized failure modeb(ii) a If H/d < TcThen by calculating the laminate contact stiffness KcBending stiffness KbFilm stiffness KmShear stiffness KsBending shear equivalent stiffness KbsMaximum transverse deformation W of the laminateofMaximum local penetration αfQuasi-static through total energy consumption E of laminated plateTDynamic through total energy consumption EPSolving ballistic limit velocity V of the overall response failure mode of the laminateb. The invention provides a method for predicting the ballistic limit speed of a local failure mode and an overall response failure mode of a laminated plate, realizes effective judgment of the failure mode of the laminated plate and accurate prediction of the ballistic limit speed, and has the characteristics of simplicity, high efficiency and wide application range.

Description

Method for predicting ballistic limit speed of laminated plate under impact of ball head bullet
Technical Field
The invention relates to the technical field of damage and protection, in particular to a method for predicting ballistic limit speed of a laminated plate under impact of a ball head bullet.
Background
The fiber reinforced composite material laminated plate has the advantages of high specific strength, high specific stiffness, flexible structural design and the like, and is widely applied to the fields of aerospace, transportation, national defense and military industry and the like. However, the fiber reinforced composite material laminate is sensitive to impact damage, and after a transverse impact by an elastomer (foreign object), damages such as fiber fracture and delamination are easily formed, which leads to strength reduction and even through destruction.
Ballistic limit velocity is a critical parameter in determining whether a projectile (foreign object) can penetrate a laminate. When the initial impact velocity of the projectile is above the ballistic limit velocity, the projectile is able to penetrate the laminate; when the initial impact velocity of the projectile is below the ballistic limit velocity, the projectile cannot penetrate the laminate. Thus, effective prediction and evaluation of ballistic limit velocity is critical to the design of laminate protective structures.
At present, the ballistic limit prediction and evaluation of the fiber reinforced composite material laminated plate under the impact of a ball head bullet mainly adopts a test or numerical simulation method, and a large amount of manpower, material resources and computing resources are consumed. In the aspect of theoretical prediction, as the response process of the fiber reinforced composite laminated plate under the ball-head bullet impact is complex, the laminated plate has different thicknesses, the failure mode generally has two forms of overall response failure and local failure, and the theoretical prediction method of ballistic limit speed comprehensively considering different failure modes and conversion critical conditions of the laminated plate at present is still lack of research. The situation brings difficulty to the high-efficiency and accurate prediction of the ballistic limit speed of the fiber reinforced composite material laminated plate under the impact of a ball head bullet.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a method for predicting the ballistic limit speed of a laminated plate under the impact of a ball bullet, which can efficiently and accurately predict the ballistic limit speed of a fiber reinforced composite laminated plate under the impact of the ball bullet.
In order to achieve the purpose, the invention adopts the following technical scheme that:
a method for predicting the ballistic limit speed of a laminated plate under the impact of a ball head bullet comprises the following steps:
s1, constructing a conversion critical condition expression of the laminated plate between the overall response failure mode and the localized failure mode under the impact of the ball bullet according to the parameters of the ball bullet and the laminated plate, and calculating to obtain a conversion critical condition value T between the overall response failure mode and the localized failure modec；
S2, calculating the ratio of the thickness H of the laminated plate to the diameter d of the ball bullet, namely H/d, and converting the ratio H/d to a critical condition value TcComparing, judging the failure mode of the laminated plate, if H/d is more than or equal to TcThe laminate undergoes localized failure and, in a localized failure mode, the laminate's ballistic limit velocity VbThe calculation is performed by the following step S3; if H/d < TcThe laminate undergoes an overall responsive failure and in the overall responsive failure mode, the laminate's ballistic limit velocity VbThe calculation is performed by the following step S4;
s3, ballistic limit velocity V of the laminate in localized failure modebThe calculation of (c) is shown as follows:
Figure BDA0002311107330000021
in the formula, σeThe quasi-static compression line elastic limit strength in the thickness direction of the laminated plate; ρ t is the laminate density; d is the diameter of the ball head bullet body; h is the thickness of the laminated plate; m is the ball head bullet mass;
s4, ballistic limit velocity V of the laminate in the overall response failure modebThe calculation of (c) is shown as follows:
Figure BDA0002311107330000022
in the formula, M is the mass of the ball head bullet; epThe total energy consumption of the laminated plate under dynamic impact of the ball head bullet is reduced;
in step S4, the total energy consumption E of the laminated board penetrating under dynamic impact of the ball head bulletpThe calculation of (c) is shown as follows:
EP＝ΦET；
in the formula, ETThe total energy consumption of the laminated plate under the quasi-static penetration of the ball head bullet is achieved;
phi is a dynamic enhancement factor, and the value mode of phi is shown as the following formula:
Figure BDA0002311107330000023
b is an empirical constant, and the value of the empirical constant B is related to the material of the laminated plate;
Vcis the Von Karman critical impact velocity, VcThe value of (A) is shown as follows:
Figure BDA0002311107330000031
εfis the in-plane tensile strain at break of the laminate; rhotA laminate density; e1Is the in-plane modulus of elasticity of the laminate;
ballistic limit velocity V of the laminate in the overall response failure modebThe calculation method of (1) is as follows:
Figure BDA0002311107330000032
total energy consumption E of laminated plate under ball head elastic quasi-static penetrationTThe calculation of (c) is shown as follows:
ET＝Ect+Ebm+Efrac+Edel；
in the formula, EctEnergy consumption for contact of ball stud locally pressed into laminate, EbmEnergy consumption for integral deformation of ball stud partially pressed into laminated plate, EfracEnergy consumption for local destruction of ball stud locally pressed into laminate, EdelThe energy consumption of the ball bullet is layered when the ball bullet is locally pressed into the laminated plate.
Total energy consumption E of laminated plate under ball head elastic quasi-static penetrationTThe calculation process specifically comprises the following steps:
s401, calculating the contact rigidity K between the laminated plate and the ball head bulletcThe calculation method is shown as the following formula:
Figure BDA0002311107330000033
Figure BDA0002311107330000034
Figure BDA0002311107330000035
in the formula, K1、K2、A11、A22、A12Are all intermediate variables;
rHthe radius of the ball head bullet body; v. ofHThe Poisson ratio of the ball bullet material; eHThe elastic modulus of the ball bullet material; g31Is the laminate shear modulus; e1Is the in-plane modulus of elasticity of the laminate; e3The elastic modulus in the thickness direction of the laminate; v. of11、v31Is the Poisson ratio of the laminated plate;
s402, respectively calculating the bending stiffness K of the laminated platebFilm stiffness K of the laminatemShear stiffness K of the laminatesAnd a laminate flexural shear equivalent stiffness KbsThe calculation formulas are respectively shown as follows:
Figure BDA0002311107330000041
Figure BDA0002311107330000042
Figure BDA0002311107330000043
Figure BDA0002311107330000044
in the above formula, v12、v13Is the Poisson ratio of the laminated plate; s is the laminate span;
Rcthe radius of the contact area between the ball stud and the laminated plate,
Figure BDA0002311107330000045
p is the contact force of the ball pressed into the laminate, according to the tensile failure criteria of the laminate under bending deformation:
Figure BDA0002311107330000046
σuin-plane tensile ultimate strength, σ, of the laminateu＝E1×εf，E1Is the in-plane elastic modulus of the laminate, epsilonfIs the in-plane tensile strain at break of the laminate;
F1is an empirical coefficient, F1＝2ln(2S/πrH)+0.669，rHThe radius of the ball head bullet body is set, and S is the span of the laminated plate;
s403, respectively calculating the maximum transverse deformation Wo of the laminated plate when the ball head is pressed in a quasi-static statefMaximum local pressed-in amount α of ball bullet to laminated platef；
Maximum transverse deformation WofMaximum local penetration αfSolving according to the tensile fracture failure criterion of the lower laminate plate under bending deformation, wherein the tensile fracture failure criterion of the lower laminate plate under bending deformation is
Figure BDA0002311107330000047
Namely:
Figure BDA0002311107330000048
Figure BDA0002311107330000049
s404, respectively calculating the contact energy consumption E of the ball bullet locally pressed into the laminated platectIntegral deformation energy consumption E of laminated platebmLocal destruction energy consumption of laminated plate EfracLaminated plate layering energy consumption EdelObtaining the total energy consumption E of the laminated plate under the ball head elastic quasi-static penetrationT，ET＝Ect+Ebm+Efrac+Edel；
Contact energy consumption E of ball bullet locally pressed into laminated platectThe calculation of (c) is shown as follows:
Figure BDA0002311107330000051
integral deformation energy consumption E of laminated platebmThe calculation of (c) is shown as follows:
Figure BDA0002311107330000052
local destruction energy consumption of laminated plate EfracThe calculation of (c) is shown as follows:
Figure BDA0002311107330000053
in the formula, etTensile failure energy density for the laminate;
laminated plate layering energy consumption EdelThe calculation of (c) is shown as follows:
Figure BDA0002311107330000054
in the formula, τIRSSIs interlaminar shear strength; gIICIs between layersFracture toughness; pdIs the critical load at which delamination damage occurs to the laminate,
Figure BDA0002311107330000055
in step S1, the parameters of the ball stud and the laminated board include: tensile strain at break epsilon in laminate facef(ii) a In-plane elastic modulus E of laminate1(ii) a Quasi-static compression line elastic limit strength sigma in thickness direction of laminated platee(ii) a Ball head bullet density rhop(ii) a Laminate density ρt(ii) a The diameter d of the ball head bullet body; equivalent length L of ball head bulleteffAnd L iseff＝4M/(πd2·ρp)；
The critical condition expression for the transition between the overall response failure mode and the localized failure mode of the constructed laminate at ball-bullet impact is given by:
Figure BDA0002311107330000056
where f (-) is the conversion critical condition expression function.
In step S1, a critical condition expression function f (-) for the transition between the overall response failure mode and the localized failure mode of the laminate under ball-bullet impact is shown as follows:
Figure BDA0002311107330000057
in step S1, the laminate in-plane tensile strain to break εfIn-plane elastic modulus E of laminated sheet1Quasi-static compressive line proof of elasticity σ in the thickness direction of the laminateeDensity of laminated board ρtAll can be obtained by material performance tests.
In step S4, the laminate has a thickness-direction elastic modulus E3Poisson ratio v of laminated plate11、v12、v13、v14Shear modulus G of laminated sheet31In-plane tensile ultimate Strength σ of the laminateuLaminated ofElastic limit strength sigma of quasi-static compression line in plate thickness directioneTensile failure energy density e of the laminatetInterlaminar fracture toughness G of the laminateIICInterlaminar shear strength τ of laminated sheetIRSSAll can be obtained by material performance tests.
The laminated plate is a fiber reinforced resin-based composite material laminated plate.
The empirical constant B of the carbon fiber reinforced composite material laminate is 0, and the empirical constant B of the glass fiber reinforced composite material laminate is 1.64.
The invention has the advantages that:
(1) the method comprehensively considers the ballistic terminal velocity prediction method of the local failure mode and the overall response failure mode of the laminated plate, and realizes effective discrimination of the failure mode of the laminated plate and accurate prediction of the ballistic terminal velocity.
(2) The method makes up the defect that a large amount of manpower, material resources and computing resources are required to be consumed in a test or numerical simulation analysis method, and has the characteristics of simplicity, high efficiency and wide application range.
Drawings
FIG. 1 is a schematic flow diagram of the present invention.
Fig. 2 is a schematic view of the ball-end bullet quasi-static press-in carbon fiber reinforced composite material laminate of the present embodiment.
FIG. 3 is a diagram showing the comparison between the predicted result and the experimental result of this example.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the embodiment, aiming at the condition that the ball-head bullet impacts a certain carbon fiber reinforced composite material laminated plate, the method provided by the invention is adopted to carry out carbon fiber reinforced compositeMaterial laminated plate ballistic limit velocity VbAnd (6) performing calculation.
As shown in FIG. 1, the carbon fiber reinforced composite material laminate has a ballistic limit velocity V under impact of a ball bulletbThe calculation method comprises the following steps:
s1, constructing a conversion critical condition expression of the laminated plate between the overall response failure mode and the localized failure mode under the impact of the ball bullet according to the parameters of the ball bullet and the laminated plate, and calculating to obtain a conversion critical condition value T between the overall response failure mode and the localized failure modec。
Converting the critical condition expression as shown in the following formula (1):
Figure BDA0002311107330000071
in the formula (1), the reaction mixture is,
εfis the in-plane tensile strain at break, ε, of the laminatef＝0.0138；
E1Is the in-plane modulus of elasticity, E, of the laminate1＝53.7GPa；
σeThe quasi-static compressive linear elastic limit strength, σ, in the thickness direction of the laminatee＝85MPa；
ρtAs the density of the laminate, pt＝1550kg/m3；
ρpIs the ball bullet density, rhop＝7850kg/m3；
d is the diameter of the ball head bullet body, and d is 6 mm;
Leffis the equivalent length of the ball head bullet, Leff＝4M/(πd2·ρp) M is the ball head bullet mass, and M is 0.88g, and then L is obtainedeff＝4M/(πd2·ρp)＝4mm；
After the parameters of the ball bullet and the laminated plate are substituted into the formula (1), the critical condition value T for conversion between the overall response failure mode and the local failure mode is obtainedc＝0.132。
S2, calculating the thickness H of the laminated plate and the diameter d of the ball head bulletIs H/d, and the ratio H/d is compared with the conversion critical condition value TcComparing, judging the failure mode of the laminated plate, if H/d is more than or equal to TcThe laminate undergoes localized failure and, in a localized failure mode, the laminate's ballistic limit velocity VbThe calculation is performed by the following step S3; if H/d < TcThe laminate undergoes an overall responsive failure and in the overall responsive failure mode, the laminate's ballistic limit velocity VbThe calculation is performed by the following step S4;
in this embodiment, the used laminated plate is a clamped circular plate, and the plate thicknesses H of the laminated plate are 0.5mm, 1.0mm and 2.0mm, respectively; the ratio H/d of the thickness H of the laminated plate to the diameter d of the ball bullet body is respectively 0.083, 0.167 and 0.333, and the ratio H/d of the thickness H of the laminated plate to the diameter d of the ball bullet body and the conversion critical condition value T are sequentially carried outcAnd (3) comparison:
the laminated board has a thickness H of 0.5mm, a ratio H/d of 0.083, and H/d < TcThe laminate undergoes an overall responsive failure and in the overall responsive failure mode the laminate has a ballistic limit velocity VbThe calculation is performed by the following step S4;
the thickness H of the laminated board is 1.0mm, the ratio H/d is 0.167, H/d > TcThe laminate undergoes localized failure and, in a localized failure mode, the laminate's ballistic limit velocity VbThe calculation is performed by the following step S3;
the laminated board has a thickness H of 2.0mm, a ratio H/d of 0.333, H/d > TcThe laminate undergoes localized failure and, in a localized failure mode, the laminate's ballistic limit velocity VbThe calculation is performed by step S3 described below.
S3, ballistic limit velocity V of the laminate in localized failure modebThe calculation method of (2) is as shown in the following formula:
Figure BDA0002311107330000081
the thickness H of the laminate was 1.0mm and 2.0mm, respectively, and the ballistic limit velocity V of the laminate was calculated by substituting the thickness H into the formula (2)b，
The thickness H of the laminate was determined to be 1.0mm, and the ballistic limit velocity V of the laminate in the localized failure mode was determinedb：
Figure BDA0002311107330000082
The thickness H of the laminate was determined to be 2.0mm, and the ballistic limit velocity V of the laminate was calculated in a localized failure modeb：
Figure BDA0002311107330000083
S4, sheet thickness H of 0.5mm, ballistic limit velocity V of the laminate in the overall response failure modebThe calculation method comprises the following steps:
s401, calculating the contact rigidity K between the laminated plate and the ball head bulletcThe calculation method is shown in the following formula (3):
Figure BDA0002311107330000084
Figure BDA0002311107330000091
Figure BDA0002311107330000092
in the formula (3), K1、K2、A11、A22、A12All are intermediate variables, with no physical meaning;
rHis the radius of the ball head bullet body rH＝3mm；
vHPoisson's ratio, v, of ball-end projectile materialH＝0.33；
EHIs the modulus of elasticity of the material of the ball bullet, EH＝210GPa；
E3Is a thickness-direction elastic modulus of the laminate, E3＝11.7GPa；
E1Is the in-plane modulus of elasticity, E, of the laminate1＝53.7Gpa；
G31Is a laminate shear modulus, G31＝4.0GPa；
v11、v31Is a laminated board Poisson ratio, v11＝0.31，v31＝0.072；
Substituting the specific values into the formula (3) to obtain the contact rigidity K between the laminated plate and the ball head bulletc＝8.642×108N/m。
S402, respectively calculating the bending stiffness K of the laminated platebFilm stiffness K of the laminatemShear stiffness K of the laminatesAnd a laminate flexural shear equivalent stiffness KbsThe calculation methods are shown in the following formulas (4), (5), (6) and (7), respectively:
Figure BDA0002311107330000093
Figure BDA0002311107330000094
Figure BDA0002311107330000095
Figure BDA0002311107330000096
in the above-mentioned formula, the compound of formula,
v12、v13is a laminated board Poisson ratio, v12＝0.31，v13＝0.33；
S is the laminate span, S is 120 mm;
h is the thickness of the laminated plate, and H is 0.5 mm;
Rcthe radius of the contact area between the ball stud and the laminated plate,
Figure BDA0002311107330000101
p is the contact force of the ball pressed into the laminate, according to the tensile failure criteria of the laminate under bending deformation:
Figure BDA0002311107330000102
σuin-plane tensile ultimate strength, σ, of the laminateu＝E1×εf，E1Is the in-plane modulus of elasticity, E, of the laminate1＝53.7Gpa，εfIs the in-plane tensile strain at break, ε, of the laminatef＝0.0138；
F1Is an empirical coefficient, F1＝2ln(2S/πrH)+0.669＝2ln(2×120/3π)＝7.144；
The specific values are respectively substituted into the formulas (4), (5), (6) and (7) to obtain the bending rigidity K of the laminated plateb8537.4N/m; laminate film stiffness Km＝6.879×109N/m; shear stiffness K of laminated sheets＝2.452×106N/m; flexural shear equivalent stiffness K of laminated platebs＝8507.8N/m。
S403, respectively calculating the maximum transverse deformation Wo of the laminated plate when the ball head is pressed in a quasi-static statefMaximum local pressed-in amount α of ball bullet to laminated platef；
The schematic diagram of the ball-end bullet quasi-static pressing-in of the carbon fiber reinforced composite laminated plate is shown in fig. 2, and the transverse deformation of the laminated plate in the ball-end bullet pressing-in process is WoThe local pressing amount of the ball head bullet to the laminated plate is α, P is the contact force of the ball head bullet pressing into the laminated plate, and P and W areoThe relationships of α are shown in the following formulas (8) and (9), respectively:
P＝KbsWo+KmWo 3； (8)
P＝Kcα3/2； (9)
maximum transverse deflection WofMaximum local penetration αfAccording to the tensile fracture failure criterion of the lower laminate plate under bending deformation, the tensile fracture failure criterion of the lower laminate plate under bending deformation is
Figure BDA0002311107330000103
Obtained by solving the following equations (10), (11):
Figure BDA0002311107330000104
Figure BDA0002311107330000105
in the above-mentioned formula, the compound of formula,
σuin-plane tensile ultimate strength, σ, of the laminateu＝E1×εf，E1Is the in-plane modulus of elasticity, E, of the laminate1＝53.7Gpa，εfIs the in-plane tensile strain at break, ε, of the laminatef＝0.0138；
F1Is an empirical coefficient, F1＝2ln(2S/πrH)+0.669＝2ln(2×120/3π)＝7.144；
The specific values are respectively substituted into the formulas (10) and (11) to obtain the maximum transverse deformation W of the laminated plate when the ball head is pressed in a quasi-static stateof0.18mm, maximum local penetration α of ball bullet to laminatef＝0.02mm。
S404, calculating the total energy consumption E of the laminated plate under the ball head elastic quasi-static penetrationTContact energy consumption E including ball stud partially pressed into laminatectIntegral deformation energy consumption E of laminated platebmLocal destruction energy consumption of laminated plate EfracLaminated plate layering energy consumption Edel；
Contact energy consumption E of ball bullet locally pressed into laminated platectIntegral deformation energy consumption E of laminated platebmAccording to the contact force P and the transverse deformation W of the ball-end bullet pressed into the laminated plateoAnd the local indentation α are obtained by integral calculation in the following formulas (12) and (13), respectively:
Figure BDA0002311107330000111
Figure BDA0002311107330000112
calculating to obtain the contact energy consumption E of the ball head bullet locally pressed into the laminated platect＝3.39×10-4J; integral deformation energy consumption E of laminated platebm＝0.0307J。
Local destruction energy consumption of laminated plate EfracThe calculation of (c) is shown in the following formula (14):
Figure BDA0002311107330000113
in the formula (14), etEnergy density for tensile failure of the laminate, et＝5.1MJ/m3；
Calculating to obtain local damage energy consumption E of the laminated platefrac＝1.269J。
Laminated plate layering energy consumption EdelThe calculation method of (2) is shown in the following formula (15):
Figure BDA0002311107330000114
in the formula (15), the reaction mixture is,
τIRSSis the interlaminar shear strength, τIRSS＝50Mpa；
GIICIs interlaminar fracture toughness, GIIC＝0.8kJ/m3；
PdIs the critical load at which delamination damage occurs to the laminate,
Figure BDA0002311107330000115
calculating to obtain the laminated plate layering energy consumption Edel＝0.012J。
Total energy consumption E of laminated plate under ball head elastic quasi-static penetrationTThe calculation of (2) is shown in the following formula (16):
ET＝Ect+Ebm+Efrac+Edel； (16)
calculating to obtain a layerTotal energy consumption E of plywood under quasi-static penetration of ball head bulletT＝1.312J。
S405, calculating total energy consumption E of the laminated plate penetrating under dynamic impact of the ball head bulletpThe calculation method is shown in the following formula (17):
EP＝ΦET； (17)
in the formula (17), Φ is a dynamic enhancement factor, and the value of Φ is represented by the following formula (18):
Figure BDA0002311107330000121
in the formula (18), B is an empirical constant, and values of the empirical constants of different composite material laminated plates are different, such as: the carbon fiber reinforced composite material laminated plate is taken as 0, and the glass fiber reinforced composite material laminated plate is taken as 1.64; this example is a carbon fiber reinforced composite material laminate, B ═ 0;
Vcis the Von Karman critical impact velocity, VcIs as shown in the following formula (19):
Figure BDA0002311107330000122
calculated, the Von Karman critical impact velocity Vc＝81.2m/s；
S406, calculating the ballistic limit speed V of the laminate under the overall response failure modebThe calculation is shown in the following formula (20):
Figure BDA0002311107330000123
by combining the formulas (17) and (18), the formula (20) can be rewritten as:
Figure BDA0002311107330000124
calculating ballistic limit velocity V of laminate under total response failure mode using equation (21)bWhen it is needed, the default V is firstbGreater than VcUsing the formula
Figure BDA0002311107330000125
Find out VbAfter the value of (3), the obtained V is judgedbWhether or not it is greater than or equal to VcIf V isbGreater than or equal to VcThen V isbThe value of (a) is the ballistic limit speed of the laminate under the final overall response failure mode; if VbLess than VcThen reuse the formula
Figure BDA0002311107330000131
Find a new VbAs the ballistic limit velocity of the laminate in the final overall response failure mode;
the laminate thickness H was calculated to be 0.5mm, and the ultimate ballistic limit velocity V of the laminate in the overall response failure modeb54.6 m/s. In addition, VbLess than VcDynamic enhancement factor
Figure BDA0002311107330000132
Total energy consumption E of laminated plate penetrating under dynamic impact of ball head bulletp＝1.312J。
The ballistic limit speed V of the carbon fiber reinforced composite material laminated plate with the plate thickness H of 0.5mm, 1.0mm and 2.0mm under the impact of a ball bullet in the embodiment is calculated and obtained according to the method of the inventionbRespectively 54.6mm, 93.6m/s and 145.1 m/s.
In the present invention, the in-plane tensile strain at break ε of the laminatefIn-plane elastic modulus E of laminated sheet1Quasi-static compressive line proof of elasticity σ in the thickness direction of the laminateeDensity of laminated board ρtElastic modulus E in the thickness direction of the laminate3Poisson ratio v of laminated plate11、v12、v13、v31Shear modulus G of laminated sheet31In-plane tensile ultimate Strength σ of the laminateuTensile failure energy density e of the laminatetInterlaminar fracture toughness G of the laminateIICInterlaminar shear strength τ of laminated sheetIRSSAll can be obtained by material performance tests.
In the present invention, the laminate has a Poisson's ratio v11、v12、v13、v31Respectively showing the poisson's ratio of the laminated plate in different directions, wherein the directions are schematically shown in fig. 2, the directions 1 and 2 are two directions which are mutually orthogonal in the plane of the laminated plate, and the direction 3 is the thickness direction of the laminated plate; poisson ratio v of laminated plateijIn the formula, subscript i represents that the Poisson ratio is in a plane parallel to the direction i in the normal direction, and subscript j represents that the Poisson ratio direction is parallel to the direction j; poisson ratio v of laminated plateiiIndicating that the poisson's ratio direction is parallel to the i-direction.
As shown in FIG. 3, when the predicted results of the present example were compared with the experimental results, the sheet thickness H was 0.5mm, and the corresponding ratio H/d was smaller than the transition critical condition value TcBelonging to the overall response failure mode, the plate thicknesses H are 1.0mm and 2.0mm, and the corresponding ratios H/d are both larger than the conversion critical condition value TcAll belong to a localized failure mode, and the plate thicknesses H of the carbon fiber reinforced composite material laminated plates are respectively 0.5mm, 1.0mm and 2.0mmbThe predicted results of all the tests are consistent with the experimental results.
The invention is not to be considered as limited to the specific embodiments shown and described, but is to be understood to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.

Claims (10)

1. A method for predicting the ballistic limit speed of a laminated plate under the impact of a ball head bullet is characterized by comprising the following steps:
s1, constructing a conversion critical condition expression of the laminated plate between the overall response failure mode and the localized failure mode under the impact of the ball bullet according to the parameters of the ball bullet and the laminated plate, and calculating to obtain a conversion critical condition value T between the overall response failure mode and the localized failure modec；
S2, calculating the ratio of the thickness H of the laminated plate to the diameter d of the ball bullet, namely H/d, and converting the ratio H/d to a critical condition value TcComparing, judging the failure mode of the laminated plate, if H/d is more than or equal to TcThe laminate undergoes localized failure and, in a localized failure mode, the laminate's ballistic limit velocity VbThe calculation is performed by the following step S3; if H/d < TcThe laminate undergoes an overall responsive failure and in the overall responsive failure mode, the laminate's ballistic limit velocity VbThe calculation is performed by the following step S4;
s3, ballistic limit velocity V of the laminate in localized failure modebThe calculation of (c) is shown as follows:
Figure FDA0002311107320000011
in the formula, σeThe quasi-static compression line elastic limit strength in the thickness direction of the laminated plate; rhotA laminate density; d is the diameter of the ball head bullet body; h is the thickness of the laminated plate; m is the ball head bullet mass;
s4, ballistic limit velocity V of the laminate in the overall response failure modebThe calculation of (c) is shown as follows:
Figure FDA0002311107320000012
in the formula, M is the mass of the ball head bullet; epThe total energy consumption of the laminated plate under dynamic impact of the ball head bullet is reduced.
2. The method of claim 1, wherein in step S4, the total energy E consumed by the laminated board under dynamic impact of a ball bullet is EpThe calculation of (c) is shown as follows:
EP＝ΦET；
in the formula, ETThe total energy consumption of the laminated plate under the quasi-static penetration of the ball head bullet is achieved;
phi is a dynamic enhancement factor, and the value mode of phi is shown as the following formula:
Figure FDA0002311107320000021
b is an empirical constant, and the value of the empirical constant B is related to the material of the laminated plate;
Vcis the Von Karman critical impact velocity, VcThe value of (A) is shown as follows:
Figure FDA0002311107320000022
εfis the in-plane tensile strain at break of the laminate; rhotA laminate density; e1Is the in-plane modulus of elasticity of the laminate;
ballistic limit velocity V of the laminate in the overall response failure modebThe calculation method of (1) is as follows:
Figure FDA0002311107320000023
3. the method of claim 2, wherein the total energy consumption E of the laminated board under quasi-static penetration of the ball bullet isTThe calculation of (c) is shown as follows:
ET＝Ect+Ebm+Efrac+Edel；
in the formula, EctEnergy consumption for contact of ball stud locally pressed into laminate, EbmEnergy consumption for integral deformation of ball stud partially pressed into laminated plate, EfracEnergy consumption for local destruction of ball stud locally pressed into laminate, EdelThe energy consumption of the ball bullet is layered when the ball bullet is locally pressed into the laminated plate.
4. The method of claim 3, wherein the total energy consumption E of the laminated board under quasi-static penetration of the ball bullet isTThe calculation process specifically comprises the following steps:
s401, calculating the contact rigidity K between the laminated plate and the ball head bulletcThe calculation method is shown as the following formula:
Figure FDA0002311107320000024
Figure FDA0002311107320000025
Figure FDA0002311107320000031
in the formula, K1、K2、A11、A22、A12Are all intermediate variables;
rHthe radius of the ball head bullet body; v. ofHThe Poisson ratio of the ball bullet material; eHThe elastic modulus of the ball bullet material; g31Is the laminate shear modulus; e1Is the in-plane modulus of elasticity of the laminate; e3The elastic modulus in the thickness direction of the laminate; v. of11、v31Is the Poisson ratio of the laminated plate;
s402, respectively calculating the bending stiffness K of the laminated platebFilm stiffness K of the laminatemShear stiffness K of the laminatesAnd a laminate flexural shear equivalent stiffness KbsThe calculation formulas are respectively shown as follows:
Figure FDA0002311107320000032
Figure FDA0002311107320000033
Figure FDA0002311107320000034
Figure FDA0002311107320000035
in the above formula, v12、v13Is the Poisson ratio of the laminated plate; s is the laminate span;
Rcthe radius of the contact area between the ball stud and the laminated plate,
Figure FDA0002311107320000036
p is the contact force of the ball pressed into the laminate, according to the tensile failure criteria of the laminate under bending deformation:
Figure FDA0002311107320000037
σuin-plane tensile ultimate strength, σ, of the laminateu＝E1×εf，E1Is the in-plane elastic modulus of the laminate, epsilonfIs the in-plane tensile strain at break of the laminate;
F1is an empirical coefficient, F1＝2ln(2S/πrH)+0.669；
S403, respectively calculating the maximum transverse deformation W of the laminated plate when the ball head is pressed in a quasi-static stateofMaximum local pressed-in amount α of ball bullet to laminated platef；
Maximum transverse deflection WofMaximum local penetration αfSolving according to the tensile fracture failure criterion of the lower laminate plate under bending deformation, wherein the tensile fracture failure criterion of the lower laminate plate under bending deformation is
Figure FDA0002311107320000041
Namely:
Figure FDA0002311107320000042
Figure FDA0002311107320000043
s404, respectively calculating the contact energy consumption E of the ball bullet locally pressed into the laminated platectIntegral deformation energy consumption E of laminated platebmLocal destruction energy consumption of laminated plate EfracLaminated plate layering energy consumption EdelObtaining the total energy consumption E of the laminated plate under the ball head elastic quasi-static penetrationT，ET＝Ect+Ebm+Efrac+Edel；
Contact energy consumption E of ball bullet locally pressed into laminated platectThe calculation of (c) is shown as follows:
Figure FDA0002311107320000044
integral deformation energy consumption E of laminated platebmThe calculation of (c) is shown as follows:
Figure FDA0002311107320000045
local destruction energy consumption of laminated plate EfracThe calculation of (c) is shown as follows:
Figure FDA0002311107320000046
in the formula, etTensile failure energy density for the laminate;
laminated plate layering energy consumption EdelThe calculation of (c) is shown as follows:
Figure FDA0002311107320000047
in the formula, τIRSSIs interlaminar shear strength; gIICInterlaminar fracture toughness; pdIs the critical load at which delamination damage occurs to the laminate,
Figure FDA0002311107320000048
5. the method of claim 1, wherein the step S1 is based on parameters of the ball bullet and the laminate including: tensile strain at break epsilon in laminate facef(ii) a In-plane elastic modulus E of laminate1(ii) a Quasi-static compression line elastic limit strength sigma in thickness direction of laminated platee(ii) a Ball head bullet density rhop(ii) a Laminate density ρt(ii) a The diameter d of the ball head bullet body; equivalent length L of ball head bulleteffAnd L iseff＝4M/(πd2·ρp)；
The critical condition expression for the transition between the overall response failure mode and the localized failure mode of the constructed laminate at ball-bullet impact is given by:
Figure FDA0002311107320000051
where f (-) is the conversion critical condition expression function.
6. The method for predicting ballistic limit velocity of a laminated panel under ball-bullet impact according to claim 5, wherein in step S1, the critical condition expression function f (-) of the laminated panel for transition between the overall response failure mode and the localized failure mode under ball-bullet impact is expressed by the following formula:
Figure FDA0002311107320000052
7. the method for predicting ballistic limit velocity of a laminate under ball-bullet impact according to claim 5, wherein in step S1, the in-plane tensile strain at break ε isfIn-plane elastic modulus E of laminated sheet1Quasi-static compressive line proof of elasticity σ in the thickness direction of the laminateeDensity of laminated board ρtAll can be obtained by material performance tests.
8. The method for predicting ballistic limit velocity of a laminated panel under ball-end bullet impact according to claim 4, wherein in step S4, the thickness direction elastic modulus E of the laminated panel3Poisson ratio v of laminated plate11、v12、v13、v31Shear modulus G of laminated sheet31In-plane tensile ultimate Strength σ of the laminateuQuasi-static compressive line proof of elasticity σ in the thickness direction of the laminateeTensile failure energy density e of the laminatetInterlaminar fracture toughness G of the laminateIICInterlaminar shear strength τ of laminated sheetIRSSAll can be obtained by material performance tests.
9. The method for predicting the ballistic limit speed of a laminated plate under the impact of a ball head bullet according to any one of claims 1 to 6, wherein the laminated plate is a fiber reinforced resin-based composite material laminated plate.
10. The method for predicting the ballistic limit velocity of a laminate under the impact of a ball-nose bullet as claimed in claim 2, wherein the empirical constant B of the carbon fiber reinforced composite material laminate is 0, and the empirical constant B of the glass fiber reinforced composite material laminate is 1.64.
CN201911259060.4A 2019-12-10 2019-12-10 Method for predicting ballistic limit speed of laminated plate under impact of ball head bullet Pending CN111191345A (en)

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