CN113607772A - Method and system for determining damage of toughened composite material during curing molding - Google Patents
Method and system for determining damage of toughened composite material during curing molding Download PDFInfo
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Abstract
The invention discloses a method and a system for determining damage of toughened composite material curing molding. The method comprises the following steps: according to the parameters of the Z-pin toughened resin-based composite material, calculating the curing degree of the Z-pin toughened resin-based composite material by using a curing temperature field model; the curing temperature field model is a heat conduction model established according to Fourier heat conduction law and energy balance theorem; respectively calculating the current curing residual stress of the resin area and the current curing residual stress of the pin needle area by using a microscopic scale model according to the curing degree; determining the current curing residual stress of the resin-pin needle interface area by utilizing a cohesion model according to the current curing residual stress of the resin area and the current curing residual stress of the pin needle area; and determining the damage state of the resin-pin needle interface area according to the current curing residual stress of the resin-pin needle interface area. According to the invention, by establishing the curing reaction model, the curing residual stress of the pin interface in the curing reaction process can be calculated, and the damage condition of the pin interface can be accurately determined.
Description
Technical Field
The invention relates to the field of composite material curing and forming, in particular to a method and a system for determining damage of a toughened composite material during curing and forming.
Background
The resin-based composite material laminated plate is easy to generate the damage phenomenon of layering failure in the actual bearing process due to the extremely strong in-plane mechanical property and the poor interlayer mechanical property. As the only interlaminar reinforcement technology suitable for prepreg forming at present, the Z-pin toughening technology is widely applied to actual production by the characteristics of simple and convenient process and low cost, namely, high-strength and high-modulus pin needles are implanted into a prepreg paving layer along the thickness direction (Z direction) of a material and then are put into a hot-pressing tank together to complete co-curing reaction, and finally, the Z-direction reinforced resin matrix composite material laminated plate is obtained. In the co-curing reaction process, the Z-pin toughened resin-based composite material has different material properties of each component, so that the Z-pin toughened resin-based composite material shows larger performance differences of thermal, chemical, mechanical and the like in a set high-temperature and high-pressure environment, a large amount of non-uniform current curing residual stress is gathered in the material, particularly in a resin-pin interface area, and the resin-pin interface area is damaged and cracked when the current curing residual stress is accumulated excessively, so that the bridging effect, the service performance and the like of the toughened resin-based composite material are influenced insignificantly.
At present, research work aiming at curing and forming of Z-pin toughened resin-based composite materials mainly focuses on exploring the mechanical properties of the materials in a test detection mode, and quantitative simulation of the curing and forming process of the Z-pin toughened resin-based composite materials is rarely researched, so that the damage condition of the interface region of the material resin-pin cannot be predicted, the curing damage evolution mechanism is difficult to master, and further the service performance of the materials cannot be accurately evaluated. Therefore, how to effectively predict the damage condition of the resin-pin interface area in the curing and forming process of the Z-pin toughened resin-based composite material is a key factor for mastering the service performance and expanding the application range of the toughened resin-based composite material, and is one of the core problems to be solved in the field at present.
Disclosure of Invention
The invention aims to provide a method and a system for determining damage of a toughened composite material during curing molding, which can calculate the curing residual stress of a resin-pin interface of a Z-pin toughened resin-based composite material in a curing reaction process, and further accurately determine the damage condition of the resin-pin interface.
In order to achieve the purpose, the invention provides the following scheme:
a damage determination method for curing and forming of a toughened composite material comprises the following steps:
acquiring parameters of the Z-pin toughened resin-based composite material;
according to the parameters of the Z-pin toughened resin-based composite material, calculating the curing degree of the Z-pin toughened resin-based composite material by using a curing temperature field model; the curing temperature field model is a heat conduction model established according to Fourier heat conduction law and energy balance theorem;
respectively calculating the current curing residual stress of the resin area and the current curing residual stress of the pin needle area by using a microscopic scale model according to the curing degree;
determining the current curing residual stress of the resin-pin interface area by utilizing a cohesion model according to the current curing residual stress of the resin area and the current curing residual stress of the pin area;
and determining the damage state of the resin-pin needle interface area according to the current curing residual stress of the resin-pin needle interface area.
Optionally, the curing temperature field model is:
in the formula, λxx、λyy、λzzThe heat conduction coefficients of the Z-pin toughened resin matrix composite material along the x axis, the y axis and the Z axis respectively, T is the temperature of the curing reaction at the current moment,
an exothermic endogenous term for the resin during the curing reaction,ρcdensity, C, of Z-pin toughened resin-based composite materialscSpecific heat capacity, rho, for Z-pin toughened resin-based compositesrFor Z-pin toughening of the density, V, of the resin material in the resin-based compositefIs the volume fraction H of the fiber material in the Z-pin toughened resin-based composite materialrThe total heat, K, released when the resin material in the Z-pin toughening resin-based composite material is subjected to curing reaction1(T) is the first reaction rate constant, K2(T) is a second reaction rate constant, α is the degree of cure, n1For the first stage of the curing reaction, n2M is the third stage of the curing reaction.
Optionally, the respectively calculating the current curing residual stress of the resin region and the current curing residual stress of the pin needle region by using a mesoscale model according to the curing degree specifically includes:
according to the solidification degree, using a formula
Determining the elastic modulus of the Z-pin toughened resin-based composite material;
determining a resin rigidity matrix and a pin rigidity matrix of the Z-pin toughened resin-based composite material according to the elastic modulus;
according to the resin rigidity matrix and the pin rigidity matrix, utilizing a formula sigmar＝[Cr]·εelAnd formula σpin＝[Cpin]·εelRespectively calculating the current curing residual stress of the resin area and the current curing residual stress of the pin area;
in the formula, alphamodAs a function of the degree of cure,
αgeldegree of curing at the time of gel point of the resin, ErIs the modulus of elasticity of the resin,
is elasticity of the resin when uncuredThe modulus of the polymer is as follows,
the modulus of elasticity, σ, of the resin after curingrFor the current curing residual stress of the resin region, [ Cr]Is a resin stiffness matrix, σpinFor the current curing residual stress of the pin area, [ C ]pin]Is a pin stiffness matrix, epsilonelIs an elastic strain.
Optionally, the resin stiffness matrix is;
in the formula, vrIs the poisson's ratio for the resin to cure.
Optionally, the pin stiffness matrix is:
in the formula, E11、E22、E33Modulus of elasticity, G, of the pin in the direction of the materials 1, 2, 3, respectively12、G13、G23Shear modulus, v, of the pin in the direction of the materials 1, 2, 3, respectively12、v13、v23Respectively the Poisson's ratio of the pin needle along the direction of the materials 1, 2 and 3, and the lambda is a middle variable,
optionally, the determining, according to the current curing residual stress of the resin region and the current curing residual stress of the pin region, the current curing residual stress of the resin-pin interface region by using a cohesion model specifically includes:
transmitting the current curing residual stress of the resin area and the current curing residual stress of the pin area to the resin-pin interface area in a mode of common node, and calculating to obtain the current curing residual stress of the resin-pin interface area by using the cohesion model, wherein the cohesion model is as follows:
in the formula, σn、σs、σtThe current curing residual stress, K, of the resin-pin needle interface area along the vertical direction and two tangential directions of the interfacenn、Kss、KttThe material stiffness, delta, in the resin-pin needle interface region in the direction perpendicular to the interface and in the two tangential directions, respectivelyn、δs、δtThe current traction displacement of the resin-pin needle interface area along the interface vertical direction and the two tangential directions is respectively.
Optionally, the determining the damage state of the resin-pin needle interface region according to the current curing residual stress of the resin-pin needle interface region specifically includes:
according to the current curing residual stress of the resin-pin needle interface area, utilizing a formula
Calculating a damage value of the resin-pin needle interface;
judging whether the damage value is larger than a threshold value of the initial damage or not to obtain a first judgment result;
if the first judgment result is yes, determining that the damage state of the resin-pin needle interface is the beginning of damage;
if the first judgment result is negative, determining that the damage state of the resin-pin needle interface is not damaged;
wherein H is an initial damage value,
initial curing residual stress, sigma, of the resin-pin interface in the direction perpendicular to the interface and in the two tangential directionsn、σs、σtRespectively resin-pin needle boundaryThe current curing residual stress of the face in the direction perpendicular to the interface, in both tangential directions.
Optionally, after determining that the damage state of the resin-pin needle interface is that damage starts to occur, the method further includes:
according to the current curing residual stress, using a formula
And formula
Calculating the total energy release rate of the resin-pin needle interface;
judging whether the total energy release rate is greater than an energy release rate threshold value or not to obtain a second judgment result;
if the second judgment result is yes, determining that the damage state of the resin-pin needle interface is damage termination;
if the second judgment result is negative, determining that the damage state of the resin-pin needle interface is not terminated;
in the formula, GCIs the total energy release rate of the resin-pin needle interface,
the critical energy release rates, G, of the resin-pin interface in the direction perpendicular to the interface and in the two tangential directionsI、GII、GIIIThe current energy release rate, eta, of the resin-pin interface in the vertical direction and two tangential directions along the interfaceBKIs the damage constant.
A damage-determination system for curing a shaped toughened composite material, comprising:
the parameter acquisition module is used for acquiring parameters of the Z-pin toughened resin-based composite material;
the curing degree calculation module is used for calculating the curing degree of the Z-pin toughened resin-based composite material by utilizing a curing temperature field model according to the parameters of the Z-pin toughened resin-based composite material; the curing temperature field model is a heat conduction model established according to Fourier heat conduction law and energy balance theorem;
the curing residual stress calculation module of the current resin area and the pin needle area is used for calculating the current curing residual stress of the resin area and the current curing residual stress of the pin needle area respectively by utilizing a microscopic scale model according to the curing degree;
the resin-pin needle interface area solidification residual stress calculation module is used for calculating the current solidification residual stress of the resin-pin needle interface area by utilizing a cohesion model according to the current solidification residual stress of the resin area and the current solidification residual stress of the pin needle area;
and the damage state determining module is used for determining the damage state of the resin-pin needle interface according to the current curing residual stress of the resin-pin needle interface area.
Optionally, the curing temperature field model is:
in the formula, λxx、λyy、λzzThe heat conduction coefficients of the Z-pin toughened resin matrix composite material along the x axis, the y axis and the Z axis respectively, T is the temperature of the curing reaction at the current moment,
internal heat-releasing term, rho, for the resin during the curing reactioncDensity, C, of Z-pin toughened resin-based composite materialscSpecific heat capacity, rho, for Z-pin toughened resin-based compositesrFor Z-pin toughening of the density, V, of the resin material in the resin-based compositefIs the volume fraction H of the fiber material in the Z-pin toughened resin-based composite materialrThe total heat, K, released when the resin material in the Z-pin toughening resin-based composite material is subjected to curing reaction1(T) is the first reaction rate constant, K2(T) is a second reaction rate constant, α is the degree of cure, n1For the first stage of the curing reaction, n2Second order of curing reaction, mThe third stage is the curing reaction.
Optionally, the module for calculating the curing residual stress of the current resin region and the pin needle region specifically includes:
an elastic modulus calculation unit for using a formula according to the degree of cure
Determining the elastic modulus of the Z-pin toughened resin-based composite material;
the resin rigidity matrix and pin needle rigidity matrix determining unit is used for determining a resin rigidity matrix and a pin needle rigidity matrix of the Z-pin toughened resin-based composite material according to the elastic modulus;
a current resin area and pin needle area curing residual stress calculation unit for using formula sigma according to the resin stiffness matrix and pin needle stiffness matrixr＝[Cr]·εelAnd formula σpin＝[Cpin]·εelRespectively calculating the current curing residual stress of the resin area and the current curing residual stress of the pin area;
in the formula, alphamodAs a function of the degree of cure,
αgeldegree of curing at the time of gel point of the resin, ErIs the modulus of elasticity of the resin,
is the modulus of elasticity of the resin when it is uncured,
the modulus of elasticity, σ, of the resin after curingrFor the current curing residual stress of the resin region, [ Cr]Is a resin stiffness matrix, σpinFor the current curing residual stress of the pin area, [ C ]pin]Is a pin stiffness matrix, epsilonelIs an elastic strain.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a method and a system for determining damage of toughened composite material curing molding, wherein the method comprises the following steps: acquiring parameters of the Z-pin toughened resin-based composite material; according to the parameters of the Z-pin toughened resin-based composite material, calculating the curing degree of the Z-pin toughened resin-based composite material by using a curing temperature field model; the curing temperature field model is a heat conduction model established according to Fourier heat conduction law and energy balance theorem; respectively calculating the current curing residual stress of the resin area and the current curing residual stress of the pin needle area by using a microscopic scale model according to the curing degree; determining the current curing residual stress of the resin-pin interface area by utilizing a cohesion model according to the current curing residual stress of the resin area and the current curing residual stress of the pin area; and determining the damage state of the resin-pin needle interface area according to the current curing residual stress of the resin-pin needle interface area. According to the invention, by establishing the curing reaction model, the curing residual stress of the resin-pin interface in the curing reaction process can be calculated, so that the damage condition of the resin-pin interface can be accurately determined.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flowchart of a damage determination method for curing and molding a toughened composite material according to an embodiment of the present invention;
FIG. 2 is a schematic view of a microscopic scale model of a Z-pin toughened resin-based composite material according to an embodiment of the present invention;
FIG. 3 is a graph illustrating the temperature and curing degree of the cured resin according to the curing time on a microscopic scale model according to an embodiment of the present invention;
FIG. 4 is a graph showing the predicted residual stress distribution for curing according to the present invention, wherein (a) is a-45 ° ply, (b) is a 90 ° ply, (c) is a 45 ° ply, and (d) is a 0 ° ply;
FIG. 5 is a graph showing the result of damage of the resin-pin interface in curing molding predicted by the present invention, wherein (a) indicates the start of damage and (b) indicates the end of damage.
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.
The invention aims to provide a method and a system for determining damage of a toughened composite material during curing molding, which can calculate the curing residual stress of a resin-pin interface of a Z-pin toughened resin-based composite material in a curing reaction process, and further accurately determine the damage condition of the resin-pin interface.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
As shown in fig. 1, the damage determination method for curing and molding of the toughened composite material provided by the invention comprises the following steps:
step 101: and acquiring parameters of the Z-pin toughened resin-based composite material.
Step 102: according to the parameters of the Z-pin toughened resin-based composite material, calculating the curing degree of the Z-pin toughened resin-based composite material by using a curing temperature field model; the curing temperature field model is a heat conduction model established according to Fourier heat conduction law and energy balance theorem.
The curing temperature field model is:
in the formula, λxx、λyy、λzzThe heat conduction coefficients of the Z-pin toughened resin matrix composite material along the x axis, the y axis and the Z axis respectively, T is the temperature of the curing reaction at the current moment,
internal heat-releasing term, rho, for the resin during the curing reactioncDensity, C, of Z-pin toughened resin-based composite materialscSpecific heat capacity, rho, for Z-pin toughened resin-based compositesrFor Z-pin toughening of the density, V, of the resin material in the resin-based compositefIs the volume fraction H of the fiber material in the Z-pin toughened resin-based composite materialrThe total heat, K, released when the resin material in the Z-pin toughening resin-based composite material is subjected to curing reaction1(T) is the first reaction rate constant, K2(T) is a second reaction rate constant, α is the degree of cure, n1For the first stage of the curing reaction, n2M is the third stage of the curing reaction.
Step 103: and respectively calculating the current curing residual stress of the resin region and the current curing residual stress of the pin needle region by using a microscopic scale model according to the curing degree.
According to the solidification degree, using a formula
Determining the elastic modulus of the Z-pin toughened resin-based composite material;
determining a resin rigidity matrix and a pin rigidity matrix of the Z-pin toughened resin-based composite material according to the elastic modulus;
according to the resin rigidity matrix and the pin rigidity matrix, utilizing a formula sigmar＝[Cr]·εelAnd formula σpin＝[Cpin]·εelRespectively calculating the current curing residual stress of the resin area and the current curing residual stress of the pin area;
in the formula, alphamodAs a function of the degree of cure,
αgeldegree of curing at the time of gel point of the resin, ErIs the modulus of elasticity of the resin,
is the modulus of elasticity of the resin when it is uncured,
the modulus of elasticity, σ, of the resin after curingrFor the current curing residual stress of the resin region, [ Cr]Is a resin stiffness matrix, σpinFor the current curing residual stress of the pin area, [ C ]pin]Is a pin stiffness matrix, epsilonelIs an elastic strain.
The resin stiffness matrix is:
in the formula, vrPoisson's ratio for resin curing;
the pin stiffness matrix is as follows:
in the formula, E11、E22、E33Modulus of elasticity, G, of the pin in the direction of the materials 1, 2, 3, respectively12、G13、G23Shear modulus, v, of the pin in the direction of the materials 1, 2, 3, respectively12、v13、v23Respectively the Poisson's ratio of the pin needle along the direction of the materials 1, 2 and 3, and the lambda is a middle variable,
step 104: and determining the current curing residual stress of the resin-pin needle interface area by utilizing a cohesion model according to the current curing residual stress of the resin area and the current curing residual stress of the pin needle area.
Transmitting the current curing residual stress of the resin area and the current curing residual stress of the pin area to the resin-pin interface area in a mode of common node, and calculating to obtain the current curing residual stress of the resin-pin interface area by using the cohesion model, wherein the cohesion model is as follows:
in the formula, σn、σs、σtThe current curing residual stress, K, of the resin-pin needle interface area along the vertical direction and two tangential directions of the interfacenn、Kss、KttThe material stiffness, delta, in the resin-pin needle interface region in the direction perpendicular to the interface and in the two tangential directions, respectivelyn、δs、δtThe current traction displacement of the resin-pin needle interface area along the interface vertical direction and the two tangential directions is respectively.
Step 105: and determining the damage state of the resin-pin needle interface area according to the current curing residual stress of the resin-pin needle interface area.
According to the current curing residual stress of the resin-pin needle interface area, utilizing a formula
Calculating a damage value of the resin-pin needle interface;
judging whether the damage value is larger than a threshold value of the initial damage or not to obtain a first judgment result;
if the first judgment result is yes, determining that the damage state of the resin-pin needle interface is the beginning of damage;
if the first judgment result is negative, determining that the damage state of the resin-pin needle interface is not damaged;
in the formula (I), the compound is shown in the specification,h is the initial damage value of the glass fiber,
initial curing residual stress, sigma, of the resin-pin interface in the direction perpendicular to the interface and in the two tangential directionsn、σs、σtThe current curing residual stress of the resin-pin interface along the vertical direction of the interface and two tangential directions are respectively.
After determining the damage state of the resin-pin needle interface as the damage starting to occur, the method further comprises the following steps:
according to the current curing residual stress, using a formula
And formula
Calculating the total energy release rate of the resin-pin needle interface;
judging whether the total energy release rate is greater than an energy release rate threshold value or not to obtain a second judgment result;
if the second judgment result is yes, determining that the damage state of the resin-pin needle interface is damage termination;
if the second judgment result is negative, determining that the damage state of the resin-pin needle interface is not terminated;
in the formula, GCIs the total energy release rate of the resin-pin needle interface,
the critical energy release rates, G, of the resin-pin interface in the direction perpendicular to the interface and in the two tangential directionsI、GII、GIIIThe current energy release rate, eta, of the resin-pin interface in the vertical direction and two tangential directions along the interfaceBKIs the damage constant.
The principles of the present invention are described in detail below:
(1) and establishing a Z-pin toughened resin-based composite material meso-scale model according to the meso-morphology characteristics of the unidirectional resin-based composite material implanted in the Z direction of the pin needle, and calculating to obtain the curing degree by utilizing a curing temperature field model.
The curing temperature field model specifically comprises a heat conduction model and a modified Kamal curing kinetic model.
The heat conduction model is established based on Fourier heat conduction law and energy balance theorem, and the expression is as follows:
in the formula, λxx、λyy、λzzThe heat conduction coefficients of the Z-pin toughened resin-based composite material along the x axis, the y axis and the Z axis respectively, T is the temperature of the curing reaction at the current moment, CcSpecific heat capacity, rho, for Z-pin toughened resin-based compositescThe density of the Z-pin toughened resin-based composite material is expressed as follows:
ρc＝Vfρf+(1-Vf)ρr
in the formula, VfIs the fiber volume fraction of the material, pfIs the density of the fiber, prIs the density of the resin.
Is an internal term of resin heat release during the curing reaction, and the expression is as follows:
in the formula, HrThe method is characterized in that the total heat released by a resin material in a Z-pin toughening resin-based composite material during a curing reaction is adopted, d alpha/dt is a curing reaction rate, and is established by a modified Kamal curing kinetic model based on an autocatalysis model and an n-grade reaction model, and the expression is as follows:
wherein α is a degree of curing, n1For the first stage of the curing reaction, n2A second stage of curing reaction, m a third stage of curing reaction, K1(T) is the first reaction rate constant, K2(T) is a second reaction rate constant, which is determined by the Arrhenius equation, expressed as follows:
Ki(T)＝Aiexp(-ΔEi/RT) (i＝1,2)
in the formula, AiIs a frequency factor, Δ EiIs the reaction activation energy, and R is the universal gas constant.
(2) And inputting the curing degree data into a microscopic scale model, and calculating the curing residual stress of each component material by introducing the thermal-chemical-force coupling effect of each component material in the curing reaction process.
The thermal-chemical-force coupling effect of each component material in the curing reaction process is established based on a thermal-chemical-force coupling strain increment model, and the expression is as follows:
Δε＝Δεel+Δεth+Δεch
wherein Δ ε is the total strain increment per time increment step, Δ εelIs the elastic mechanical strain increment, Delta epsilonthIs the thermal strain increase,. DELTA.. epsilonchIs the chemical strain increment.
The curing residual stress is established based on a linear elastic stress increment model, and the expression of the curing residual stress is as follows:
σ＝∑{Δσ}＝∑[C]·{Δεel}
where σ is a total curing residual stress, Δ σ is a total stress increment at each time increment step, and [ C ] is a rigidity matrix of the material, which is determined by the elastic modulus, where the rigidity matrix of the resin matrix is expressed by:
the rigidity matrix expression of the unidirectional composite material is as follows:
the material parameters of the resin matrix in the curing reaction process can change along with the curing degree, and the expression is as follows:
in the formula, ErIs the modulus of elasticity of the resin,
the modulus of elasticity of the resin when it is not cured,
is the modulus of elasticity, alpha, of the resin after curingmodIs a curing degree function, and the expression thereof is as follows:
in the formula, alphagelThe degree of curing at the time of gel point of the resin.
The uncured elastic modulus of the resin is calculated by the following expression:
in the formula, Kr 0And Kr ∞The bulk modulus, G, of the uncured and cured resins, respectivelyr 0And Gr ∞The shear modulus, v, of the uncured and cured resin, respectivelyr 0Is the uncured poisson's ratio of the resin.
The mechanical property of the unidirectional composite material is formed by resin and fiber under microscopic scale, and the expression is as follows:
in the formula, E11、E22、E33The modulus of elasticity, G, of the material in the 1, 2, 3 directions, respectively12、G13、G23Shear modulus, v, of the material in the 1, 2, and 3 directions, respectively12、v13、v23Respectively, the poisson's ratio of the material in the 1, 2, 3 directions, the subscripts r, f represent resin and fiber, respectively, and K is the bulk modulus of the material.
The thermal strain increment of the material is calculated by the following expression:
Δεth＝ΔT×β
in the formula: Δ T is the temperature difference and β is the coefficient of thermal expansion. The thermal expansion coefficient of the resin is calculated by the following expression:
βr＝(1-α)βr r+αβr g
in the formula, betar rAnd betar gAre the coefficients of thermal expansion of the material in the rubbery and glassy states, respectively.
The coefficient of thermal expansion of the unidirectional composite is calculated by the following expression:
in the formula, betac1，βc2，βc3The coefficients of thermal expansion of the material in the 1, 2, 3 directions, respectively.
The chemical strain increment of the material is calculated by the following expression:
Δεch＝Δα×γ
wherein Δ α is a difference in degree of curing and γ is a chemical shrinkage coefficient.
The chemical shrinkage coefficient of the unidirectional composite material is calculated by the following expression:
in the formula, gammac1，γc2，γc3The chemical shrinkage coefficients of the material in the 1, 2 and 3 directions, respectively.
(3) And applying the curing residual stress as a predefined field on the microscopic scale model, setting an interface damage initial criterion and an interface damage evolution criterion, establishing a curing damage judgment model, and calculating the curing molding damage.
The cohesion model is used for specifically characterizing the elastic mechanical behavior of the material in the resin-pin needle interface area, and the expression is as follows:
in the formula, σn、σs、σtThe current curing residual stress, K, of the resin-pin needle interface area along the vertical direction and two tangential directions of the interfacenn、Kss、KttThe material stiffness, delta, in the resin-pin needle interface region in the direction perpendicular to the interface and in the two tangential directions, respectivelyn、δs、δtThe current traction displacement of the resin-pin needle interface area along the interface vertical direction and the two tangential directions is respectively.
(4) And setting a damage criterion of the resin-pin needle interface according to the current curing residual stress of the resin-pin needle interface area, and determining the damage state of the resin-pin needle interface area. The initial criterion of the resin-pin needle interface damage adopts a secondary stress criterion as a judgment basis, and the expression is as follows:
in the formula, σ0 n、σ0 s、σ0 tInitial curing residual stress, σ, of the interface in the direction perpendicular to the interface and in the two tangential directions, respectivelyn、σs、σtThe current curing residual stress of the resin-pin needle interface area along the interface vertical direction and the two tangential directions are respectively.
The B-K evolution criterion is adopted as a judgment basis by the resin-pin interface damage evolution criterion, and the expression is as follows:
in the formula, GCIs the total energy release rate of the resin-pin needle interface,
the critical energy release rates, G, of the resin-pin interface in the direction perpendicular to the interface and in the two tangential directionsI、GII、GIIIThe current energy release rate, eta, of the resin-pin interface in the vertical direction and two tangential directions along the interfaceBKIs the damage constant.
Simulation analysis of the whole curing, loading and damage process is realized through finite element software ABAQUS.
The specific embodiment is as follows:
step 1: establishing a mesoscale model shown in FIG. 2, and applying a bilinear cohesion model in a resin-pin needle interface area by adopting a resin-based composite material layering mode of [0/45/90/-45] s;
step 2: applying a curing molding load condition on the microscopic scale model, and solving the curing degree and the residual stress of the model, wherein the results are respectively shown in fig. 3 and fig. 4;
and step 3: and applying the obtained curing residual stress as a predefined field on the microscopic scale model again, setting a resin-pin needle interface damage criterion, and solving the damage of the resin-pin needle interface curing molding, wherein the result is shown in fig. 5.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
(1) according to the method, a numerical simulation analysis method is adopted, a Z-pin toughened resin matrix composite material microscopic scale model, a curing temperature field model, a residual stress calculation model and a curing damage judgment model are respectively established, the curing molding damage is predicted from the perspective of quantitative simulation, a theoretical basis is provided for researching the evolution mechanism of the curing damage of the toughened resin matrix composite material, the method has independent innovation, a large amount of time and cost are saved, and a new way is opened up for researching the technical field of the curing molding damage of the toughened composite material;
(2) the thermal-chemical-mechanical coupling effect of each component material of the toughened composite material is fully considered, and the thermal expansion phenomenon and the chemical shrinkage phenomenon of the material in the curing reaction process are quantified, so that a more accurate curing residual stress simulation result is obtained through calculation;
(3) according to the method, a cohesion model is adopted to specifically represent the special material properties of the resin-pin needle interface area, a secondary stress criterion and a B-K damage evolution criterion are combined and applied, and an interface damage starting behavior standard and a damage evolution behavior standard are specified, so that a damage evolution process of the interface area in the curing and forming process is systematically constructed.
The invention also provides a damage determination system for the curing molding of the toughened composite material, which comprises the following components:
the parameter acquisition module is used for acquiring parameters of the Z-pin toughened resin-based composite material;
the curing degree calculation module is used for calculating the curing degree of a pin interface of the Z-pin toughened resin-based composite material by using a curing temperature field model according to the parameters of the Z-pin toughened resin-based composite material; the curing temperature field model is a heat conduction model established according to Fourier heat conduction law and energy balance theorem;
the curing residual stress calculation module of the current resin area and the pin needle area is used for calculating the current curing residual stress of the resin area and the current curing residual stress of the pin needle area respectively by utilizing a microscopic scale model according to the curing degree;
the resin-pin needle interface area solidification residual stress calculation module is used for calculating the current solidification residual stress of the resin-pin needle interface area by utilizing a cohesion model according to the current solidification residual stress of the resin area and the current solidification residual stress of the pin needle area;
and the damage state determining module is used for determining the damage state of the resin-pin needle interface according to the current curing residual stress of the resin-pin needle interface area.
Wherein, the solidification residual stress calculation module in current resin region and pin needle region specifically includes:
an elastic modulus calculation unit for using a formula according to the degree of cure
Determining the elastic modulus of the Z-pin toughened resin-based composite material;
the resin rigidity matrix and pin needle rigidity matrix determining unit is used for determining a resin rigidity matrix and a pin needle rigidity matrix of the Z-pin toughened resin-based composite material according to the elastic modulus;
a current resin area and pin needle area curing residual stress calculation unit for using formula sigma according to the resin stiffness matrix and pin needle stiffness matrixr＝[Cr]·εelAnd formula σpin＝[Cpin]·εelRespectively calculating the current curing residual stress of the resin area and the current curing residual stress of the pin area;
in the formula, alphamodAs a function of the degree of cure,
αgeldegree of curing at the time of gel point of the resin, ErIs the modulus of elasticity of the resin,
is the modulus of elasticity of the resin when it is uncured,
the modulus of elasticity, σ, of the resin after curingrFor the current curing residual stress of the resin region, [ Cr]Is a resin stiffness matrix, σpinFor the current curing residual stress of the pin area, [ C ]pin]Is a pin stiffness matrix, epsilonelIs an elastic strain.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A method for determining damage of a toughened composite material during curing molding is characterized by comprising the following steps:
acquiring parameters of the Z-pin toughened resin-based composite material;
according to the parameters of the Z-pin toughened resin-based composite material, calculating the curing degree of the Z-pin toughened resin-based composite material by using a curing temperature field model; the curing temperature field model is a heat conduction model established according to Fourier heat conduction law and energy balance theorem;
respectively calculating the current curing residual stress of the resin area and the current curing residual stress of the pin needle area by using a microscopic scale model according to the curing degree;
determining the current curing residual stress of the resin-pin interface area by utilizing a cohesion model according to the current curing residual stress of the resin area and the current curing residual stress of the pin area;
and determining the damage state of the resin-pin needle interface area according to the current curing residual stress of the resin-pin needle interface area.
2. The method for determining damage of the toughened composite material during curing molding according to claim 1, wherein the curing temperature field model is:
in the formula, λxx、λyy、λzzThe heat conduction coefficients of the Z-pin toughened resin matrix composite material along the x axis, the y axis and the Z axis respectively, T is the temperature of the curing reaction at the current moment,
internal heat-releasing term, rho, for the resin during the curing reactioncDensity, C, of Z-pin toughened resin-based composite materialscSpecific heat capacity, rho, for Z-pin toughened resin-based compositesrFor Z-pin toughening of the density, V, of the resin material in the resin-based compositefVolume fraction of fiber material in resin-based composite material for toughening Z-pin，HrThe total heat, K, released when the resin material in the Z-pin toughening resin-based composite material is subjected to curing reaction1(T) is the first reaction rate constant, K2(T) is a second reaction rate constant, α is the degree of cure, n1For the first stage of the curing reaction, n2M is the third stage of the curing reaction.
3. The method for determining damage to the cured and molded toughened composite material according to claim 2, wherein the step of calculating the current curing residual stress of the resin region and the current curing residual stress of the pin region by using a microscopic scale model according to the curing degree comprises:
according to the solidification degree, using a formula
Determining the elastic modulus of the Z-pin toughened resin-based composite material;
determining a resin rigidity matrix and a pin rigidity matrix of the Z-pin toughened resin-based composite material according to the elastic modulus;
according to the resin rigidity matrix and the pin rigidity matrix, utilizing a formula sigmar＝[Cr]·εelAnd formula σpin＝[Cpin]·εelRespectively calculating the current curing residual stress of the resin area and the current curing residual stress of the pin area;
in the formula (I), the compound is shown in the specification,αmodas a function of the degree of cure,
αgeldegree of curing at the time of gel point of the resin, ErIs the modulus of elasticity of the resin,
is the modulus of elasticity of the resin when it is uncured,
the modulus of elasticity, σ, of the resin after curingrFor the current curing residual stress of the resin region, [ Cr]Is a resin stiffness matrix, σpinFor the current curing residual stress of the pin area, [ C ]pin]Is a pin stiffness matrix, epsilonelIs an elastic strain.
4. The method for determining damage to the cured and molded toughened composite material according to claim 3, wherein said resin stiffness matrix is:
in the formula, vrPoisson's ratio for resin curing;
the pin stiffness matrix is as follows:
in the formula, E11、E22、E33Modulus of elasticity, G, of the pin in the direction of the materials 1, 2, 3, respectively12、G13、G23Shear modulus, v, of the pin in the direction of the materials 1, 2, 3, respectively12、v13、v23Respectively the Poisson's ratio of the pin needle along the direction of the materials 1, 2 and 3, and the lambda is a middle variable,
5. the method for determining damage to the cured and molded toughened composite material according to claim 1, wherein the determining the current curing residual stress of the resin-pin interface region by using a cohesion model according to the current curing residual stress of the resin region and the current curing residual stress of the pin region specifically comprises:
transmitting the current curing residual stress of the resin area and the current curing residual stress of the pin area to the resin-pin interface area in a mode of common node, and calculating to obtain the current curing residual stress of the resin-pin interface area by using the cohesion model, wherein the cohesion model is as follows:
in the formula, σn、σs、σtThe current curing residual stress, K, of the resin-pin needle interface area along the vertical direction and two tangential directions of the interfacenn、Kss、KttThe material stiffness, delta, in the resin-pin needle interface region in the direction perpendicular to the interface and in the two tangential directions, respectivelyn,、δs,、δtThe current traction displacement of the resin-pin needle interface area along the interface vertical direction and the two tangential directions is respectively.
6. The method for determining damage to the cured and molded toughened composite material according to claim 1, wherein the determining the damage state of the resin-pin interface region according to the current residual stress of curing of the resin-pin interface region specifically comprises:
according to the current curing residual stress of the resin-pin needle interface area, utilizing a formula
Calculating a damage value of the resin-pin needle interface;
judging whether the damage value is larger than a threshold value of the initial damage or not to obtain a first judgment result;
if the first judgment result is yes, determining that the damage state of the resin-pin needle interface is the beginning of damage;
if the first judgment result is negative, determining that the damage state of the resin-pin needle interface is not damaged;
wherein H is an initial damage value,
initial curing residual stress, sigma, of the resin-pin interface in the direction perpendicular to the interface and in the two tangential directionsn、σs、σtThe current curing residual stress of the resin-pin interface along the vertical direction of the interface and two tangential directions are respectively.
7. The method for determining damage of the toughened composite material cured and molded according to claim 6, further comprising, after determining that the damage state of the resin-pin interface is that damage starts to occur:
according to the current curing residual stress, using a formula
And formula
Calculating the total energy release rate of the resin-pin needle interface;
judging whether the total energy release rate is greater than an energy release rate threshold value or not to obtain a second judgment result;
if the second judgment result is yes, determining that the damage state of the resin-pin needle interface is damage termination;
if the second judgment result is negative, determining that the damage state of the resin-pin needle interface is not terminated;
in the formula, GCIs the total energy release rate of the resin-pin needle interface,
the critical energy release rates, G, of the resin-pin interface in the direction perpendicular to the interface and in the two tangential directionsI、GII、GIIIRespectively resin-pin interface at the edge of the interfaceCurrent energy release rate, eta, in a straight direction, two tangential directionsBKIs the damage constant.
8. A damage-determination system for curing a shaped toughened composite material, the system comprising:
the parameter acquisition module is used for acquiring parameters of the Z-pin toughened resin-based composite material;
the curing degree calculation module is used for calculating the curing degree of the Z-pin toughened resin-based composite material by utilizing a curing temperature field model according to the parameters of the Z-pin toughened resin-based composite material; the curing temperature field model is a heat conduction model established according to Fourier heat conduction law and energy balance theorem;
the curing residual stress calculation module of the current resin area and the pin needle area is used for calculating the current curing residual stress of the resin area and the current curing residual stress of the pin needle area respectively by utilizing a microscopic scale model according to the curing degree;
the resin-pin needle interface area solidification residual stress calculation module is used for calculating the current solidification residual stress of the resin-pin needle interface area by utilizing a cohesion model according to the current solidification residual stress of the resin area and the current solidification residual stress of the pin needle area;
and the damage state determining module is used for determining the damage state of the resin-pin needle interface according to the current curing residual stress of the resin-pin needle interface area.
9. The system for determining damage to cured and molded toughened composite material according to claim 8, wherein said curing temperature field model is:
in the formula, λxx、λyy、λzzThe heat conduction coefficients of the Z-pin toughened resin-based composite material along the x axis, the y axis and the Z axis respectively, and T is curingReflecting the temperature at the present moment of time,
internal heat-releasing term, rho, for the resin during the curing reactioncDensity, C, of Z-pin toughened resin-based composite materialscSpecific heat capacity, rho, for Z-pin toughened resin-based compositesrFor Z-pin toughening of the density, V, of the resin material in the resin-based compositefIs the volume fraction H of the fiber material in the Z-pin toughened resin-based composite materialrThe total heat, K, released when the resin material in the Z-pin toughening resin-based composite material is subjected to curing reaction1(T) is the first reaction rate constant, K2(T) is a second reaction rate constant, α is the degree of cure, n1For the first stage of the curing reaction, n2M is the third stage of the curing reaction.
10. The system for determining damage to toughened composite material during curing and molding according to claim 9, wherein the module for calculating the curing residual stress of the current resin region and the pin region specifically comprises:
an elastic modulus calculation unit for using a formula according to the degree of cure
Determining the elastic modulus of the Z-pin toughened resin-based composite material;
the resin rigidity matrix and pin needle rigidity matrix determining unit is used for determining a resin rigidity matrix and a pin needle rigidity matrix of the Z-pin toughened resin-based composite material according to the elastic modulus;
a current resin area and pin needle area curing residual stress calculation unit for using formula sigma according to the resin stiffness matrix and pin needle stiffness matrixr＝[Cr]·εelAnd formula σpin＝[Cpin]·εelRespectively calculating the current curing residual stress of the resin area and the current curing residual stress of the pin area;
in the formula, alphamodAs a function of the degree of cure,
αgeldegree of curing at the time of gel point of the resin, ErIs the modulus of elasticity of the resin,
is the modulus of elasticity of the resin when it is uncured,
the modulus of elasticity, σ, of the resin after curingrFor the current curing residual stress of the resin region, [ Cr]Is a resin stiffness matrix, σpinFor the current curing residual stress of the pin area, [ C ]pin]Is a pin stiffness matrix, epsilonelIs an elastic strain.
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