CN112329297A - Composite material strength detection method and system considering curing residual stress - Google Patents

Composite material strength detection method and system considering curing residual stress Download PDF

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CN112329297A
CN112329297A CN202011188544.7A CN202011188544A CN112329297A CN 112329297 A CN112329297 A CN 112329297A CN 202011188544 A CN202011188544 A CN 202011188544A CN 112329297 A CN112329297 A CN 112329297A
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许英杰
惠新育
张卫红
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Northwestern Polytechnical University
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Abstract

The invention discloses a method and a system for detecting the strength of a composite material by considering curing residual stress, which firstly solve the problem of three-dimensional heat transfer by considering the heat released by a curing reaction through a macro-scale model, and calculate and obtain the temperature and the curing degree of the composite material in the curing process through thermochemical coupling analysis; secondly, establishing a microscopic scale model, introducing the temperature and the curing degree into the model as input parameters, and considering the interaction between materials of different components to obtain the residual stress under the microscopic scale; and finally, taking the predicted residual stress as a predefined stress field in a subsequent loading process, and finally obtaining the loaded damage response and strength value.

Description

Composite material strength detection method and system considering curing residual stress
Technical Field
The invention relates to the field of composite thermosetting resin-based composite materials, in particular to a method and a system for detecting the strength of a composite material by considering curing residual stress.
Background
Thermosetting resin-based composite materials are increasingly widely applied in the industrial fields of aviation, aerospace, transportation, energy and the like by virtue of excellent and stable mechanical properties, and strength prediction of the composite materials through finite element analysis is a hot point of research. The forming of the thermosetting resin-based composite material cannot leave the curing process of the resin matrix in the composite material, and in the process, different materials are easy to cause inevitable non-uniform stress, namely residual stress, in the composite material due to mismatching of properties such as heat, force, chemistry and the like under designed temperature and pressure, and the stress can also have certain influence on the strength performance of the composite material in a later service period. At present, the calculation of the residual stress and the prediction of the strength properties of thermosetting resin-based composite materials are separately studied, and the research capable of coupling the influence of the residual stress to the prediction of the strength properties is relatively few, and mainly focuses on the following documents:
in document 1 "L.ZHao, N.Warrior, A.Long, A thermo-visco elastic analysis of process-induced residual stress in fibrous formed polymer-matrix composites, Materials Science and Engineering: A452-453(2007) 483-498", the authors investigated the curing residual stress of thermosetting resin-based composites and its effect on transverse damage, found that the introduction of residual stress has a significant effect on the initiation and evolution of damage, and whether the residual stress is favorable for the strength of the composite is related to the loading conditions. However, the finite element modeling was simulated using representative volume elements containing only individual fibers, ignoring the fact that the fibers are randomly distributed in the composite.
In document 2 "L.Yang, Y.Yan, J.Ma, B.Liu, Effects of inter-fiber space and thermal stress on transformed polymer-matrix composites, and synthetic Materials Science 68(2013) 255-262", the authors constructed a representative volume cell model containing multiple fibers and randomly distributed to study the Effects of fiber volume fraction and fiber spacing on the curing residual stress. Furthermore, the influence of residual stress on the failure behavior of the composite material is further explored, wherein the residual stress can significantly change the damage initial position and damage evolution path of the composite material. However, the description of the curing process in the literature is simple, and the guiding effect of the curing kinetic model on the resin performance is neglected.
In document 3 "f.danzi, d.fantia, e.patenetieri, m.mancino, a digital micro-mechanical study on data induced by the curing process in carbon/epoxy unidirectional materials, Composite Structures 210(2019) 755-. However, only the design temperature is considered in the curing stage, and the coupling influence of resin curing heat release and mold heat transfer on the resin temperature is not considered.
In conclusion, the existing resin model frames have different defects, and a complete numerical model is rarely considered to realize accurate prediction of residual stress so as to further research the strength performance of the resin matrix composite material.
Disclosure of Invention
The invention aims to provide a method and a system for detecting the strength of a composite material by considering curing residual stress, which firstly solve the problem of three-dimensional heat transfer by considering the heat released by a curing reaction through a macro-scale model and calculate the temperature and the curing degree of the composite material in the curing process through thermochemical coupling analysis; secondly, establishing a microscopic scale model, introducing the temperature and the curing degree into the model as input parameters, and considering the interaction between materials of different components to obtain the residual stress under the microscopic scale; and finally, taking the predicted residual stress as a predefined stress field in a subsequent loading process, and finally obtaining the loaded damage response and strength value.
In order to achieve the purpose, the invention provides the following scheme:
a method for detecting the strength of a composite material by considering curing residual stress comprises the following steps:
calculating the temperature and the curing degree of the composite material through a macro scale model; the macroscopic model is a heat transfer model;
inputting the temperature and the curing degree data into a microscopic model to calculate residual stress; the mesoscopic model is a linear elastic incremental model;
and performing transverse tensile loading analysis on the mesoscopic model by taking the calculated residual stress as an initial predefined field to obtain the stress and the strain of the composite material, and completing the strength detection of the composite material.
Optionally, a heat transfer model is established based on Fourier heat conduction law and energy balance principle, and the expression of the heat transfer model is as follows:
Figure BDA0002752110800000031
wherein rho is the density of the composite material, C is the specific heat capacity of the composite material, T is the temperature at the current moment of the curing reaction, and lambdaiiI-x, y, z represents the thermal conductivity of the anisotropic material in three directions,
Figure BDA0002752110800000032
the term "internal heat source" in the curing reaction means the amount of heat given off by the resin when the curing reaction occurs.
Optionally, the expression of the incremental linear elastic model is as follows:
Figure BDA0002752110800000033
Figure BDA0002752110800000034
wherein, { Δ σ }i、{Δε}iFor the stress increment and strain increment at each time step i, σ is the total residual stress, ε is the total residual strain, and C is the stiffness matrix of the resin matrix.
Optionally, when the mesoscopic model is subjected to transverse tensile loading analysis by using the calculated residual stress as an initial predefined field, the fibers in the composite material are not damaged, so that a damage model is not introduced, and different failure criteria are introduced for the interface and the resin matrix respectively.
Alternatively, Drucker-Prager is used to describe the plastic behavior for the resin matrix, the expression is as follows:
F＝t-ptanβ-d＝0
wherein F represents a yield function, p is hydrostatic stress, beta is a friction angle, d is a cohesion parameter, and t is yield stress.
Optionally, a bilinear softening cohesion model is used for describing the elastic behavior of the interface, and the expression is as follows:
Figure BDA0002752110800000035
where d denotes the stress tensor, and δ denotes the displacement tensor, K is the stiffness matrix, and n and s are the principal radial and shear directions.
The invention also provides a composite material strength detection system considering curing residual stress, which comprises:
the temperature and curing degree calculating module is used for calculating the temperature and curing degree of the composite material through the macro scale model; the macroscopic model is a heat transfer model;
the residual stress calculation module is used for inputting the temperature and the curing degree data into a mesoscopic model to calculate the residual stress; the mesoscopic model is a linear elastic incremental model;
and the strength detection module is used for carrying out transverse tensile loading analysis on the mesoscopic model by taking the calculated residual stress as an initial predefined field to obtain the stress and the strain of the composite material and finish the strength detection of the composite material.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention discloses a method and a system for detecting the strength of a composite material by considering curing residual stress, which firstly solve the problem of three-dimensional heat transfer by considering the heat released by a curing reaction through a macro-scale model, and calculate and obtain the temperature and the curing degree of the composite material in the curing process through thermochemical coupling analysis; secondly, establishing a microscopic scale model, introducing the temperature and the curing degree into the model as input parameters, and considering the interaction between materials of different components to obtain the residual stress under the microscopic scale; and finally, taking the predicted residual stress as a predefined stress field in a subsequent loading process, and finally obtaining the loaded damage response and strength value. The invention considers the influence of resin curing heat release and heat transfer on a mesoscopic resin-based composite material model on the basis of the existing research, simultaneously considers the thermal deformation and the chemical shrinkage deformation of a matrix in the curing process and considers the different damage modes of the matrix and an interface in the loading process, establishes an integrated model of the material in the whole forming and loading process and is used for calculating the final strength response analysis of a finite element model.
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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 flow chart of a method for testing the strength of a composite material in consideration of residual stress during curing according to an embodiment of the present invention;
FIG. 2 is a flowchart illustrating the overall analysis of a method for testing the strength of a composite material in consideration of residual stress during curing according to an embodiment of the present invention;
FIG. 3 is a graph of temperature and degree of cure as a function of cure time calculated from a macroscopic model in accordance with an embodiment of the present invention, wherein (a) is the temperature and (b) is the degree of cure;
FIG. 4 is a graph of residual stress distribution under a mesoscopic model predicted by the present invention, wherein (a) the graph is a Missels equivalent stress graph, (b) the graph is a stress graph along a loading direction, and (c) the graph is a stress graph in an in-plane direction;
FIG. 5 is a graph of stress strain with and without residual stress being taken into account as predicted by the present invention;
FIG. 6 is a graph of the final damage distribution during loading predicted by the present invention, wherein (a) is a damage crack initiation graph, (b) is a crack propagation graph, and (c) is a final failure graph;
fig. 7 is a block diagram of a composite strength detection system considering curing residual stress according to an embodiment of the present invention.
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 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. 1-2, a method for detecting the strength of a composite material considering curing residual stress includes:
step 101: calculating the temperature and the curing degree of the composite material through a macro scale model; the macroscopic model shown is a heat transfer model. The degree of cure and temperature data required for subsequent analysis from the macroscopic model analysis is shown in figure 3.
Step 102: inputting the temperature and the curing degree data into a microscopic model to calculate residual stress; the mesoscopic model is a linear elastic incremental model. The residual stress distribution was solved by substituting the temperature and cure data into the microscopic model as shown in fig. 3.
Step 103: and performing transverse tensile loading analysis on the mesoscopic model by taking the calculated residual stress as an initial predefined field to obtain the stress and the strain of the composite material, and completing the strength detection of the composite material. The experimental curve is given in fig. 4 in comparison with the stress-strain curve without taking into account the curing residual stress, and it was found that the stress-strain curve with taking into account the curing residual stress fits better to the experimental curve. FIG. 5 shows a graph of lesion extension during loading.
The following steps are described in detail:
step 101: the temperature and degree of cure are first calculated by a macro scale model. Based on the Fourier heat conduction law and the energy balance principle, a heat transfer model is established, and the expression is as follows:
Figure BDA0002752110800000061
wherein rho is the density of the composite material, C is the specific heat capacity of the composite material, T is the temperature at the current moment of the curing reaction, and lambdaii(i ═ x, y, z) represents the thermal conductivity in three directions of the anisotropic material,
Figure BDA0002752110800000062
the term of internal heat source in the curing reaction represents the heat quantity released by the resin when the curing reaction occurs, and the expression is as follows:
Figure BDA0002752110800000063
in the formula (I), the compound is shown in the specification,
Figure BDA0002752110800000064
for the internal heat source term in the curing reaction, prRepresents the resin density, VfRepresents the fiber volume fraction, HrRepresenting the total resin exotherm, alpha is the degree of cure,
Figure BDA0002752110800000065
is the instantaneous cure rate and is defined by the formula:
Figure BDA0002752110800000066
in the formula, A1And A2Is a frequency factor, E1And E2For model activation energy, R is the ideal gas constant, m, n1And n2Are fitting coefficients. Compound medicineThe specific heat and thermal conductivity parameters of the composite are defined by the following formulas:
Figure BDA0002752110800000067
λ(α,T)＝(1-α)λ(0,T)+αλ(1,T) (5)
wherein (0, T) and (1, T) represent uncured prepreg and fully cured composite respectively and vary with temperature, C is specific heat capacity, lambda is thermal conductivity, and T isgRepresents the glass transition temperature and is linear with the degree of cure:
Figure BDA0002752110800000071
in the formula, Tg(0) Represents the glass transition temperature, g, of the uncured prepreg1And g2Are fitting parameters.
Step 102: and substituting the temperature and curing data obtained by the macroscopic model into the microscopic model to solve the residual stress. The curing behavior of the resin is expressed by a linear elastic incremental model:
Figure BDA0002752110800000072
Figure BDA0002752110800000073
in the formula, { Δ σ }i、{Δε}iFor the stress increment and strain increment at each time step i, σ is the total residual stress, ε is the total residual strain, C is the stiffness matrix of the resin matrix, ε is the total strain and is calculated by the following equation:
ε＝εe+εth+εch (9)
in the formula, epsiloneFor mechanical strain,. epsilonthFor thermal strain,. epsilonchIs the chemical shrinkage strain. C may be represented by the modulus of elasticity E and is represented byThe following formula is calculated:
Figure BDA0002752110800000074
wherein E is the modulus of elasticity, E0And E∞Respectively representing the modulus of elasticity, alpha, at uncured and at cured completiongelDegree of curing at gel Point, αmodAs a function of the degree of cure and is defined by the formula:
Figure BDA0002752110800000075
Figure BDA0002752110800000076
calculated by the following formula:
Figure BDA0002752110800000077
in the formula, K0And K∞Represents the bulk modulus at uncured and fully cured states, G0And G∞Denotes the shear modulus at uncured and fully cured, respectively, v0Is the poisson ratio.
Thermal strain epsilonthAnd chemical shrinkage strain εchCalculated by the following equation:
Figure BDA0002752110800000081
wherein gamma is a thermal expansion coefficient and beta is a chemical contraction coefficient.
Step 103: and (3) taking the calculated residual stress as an initial predefined field, and performing damage analysis of subsequent loading, wherein for transverse loading, fibers in the composite material are generally not damaged and are not introduced into a damage model, and different failure criteria are introduced into an interface and a resin matrix respectively.
Wherein the elastic behavior is described for the resin matrix using Drucker-Prager:
F＝t-ptanβ-d＝0 (14)
wherein p is the hydrostatic stress, β is the angle of friction, d is the cohesion parameter, and t is the yield stress and is defined by the formula:
Figure BDA0002752110800000082
wherein q is the Misses equivalent stress, k is the axial stress ratio, and r is the third stress deflection number.
The damage behavior of the resin matrix is described by Ductile, and the introduced damage factor
Figure BDA00027521108000000811
Is defined by the formula:
Figure BDA0002752110800000083
wherein L is the characteristic length of the unit,
Figure BDA0002752110800000084
and
Figure BDA0002752110800000085
equivalent plastic strain and equivalent plastic displacement, respectively. Prior to the initiation of the lesion(s),
Figure BDA0002752110800000086
is 0, and after the initiation of the injury,
Figure BDA0002752110800000087
Figure BDA0002752110800000088
is the equivalent displacement at material failure and
Figure BDA0002752110800000089
wherein sigmay0Yield stress of the material just to meet the failure criterion, GfIs the energy to break of the material.
The fracture energy, which is a determining parameter for determining whether the resin matrix meets the failure criterion, is defined by the following formula:
Figure BDA00027521108000000810
in the formula (I), the compound is shown in the specification,
Figure BDA0002752110800000091
and
Figure BDA0002752110800000092
the equivalent plastic strain at the time of the onset of damage (at which the damage factor D is 0) and the equivalent plastic strain at the time of ultimate failure (at which the damage factor D is 1) were respectively identified.
The elastic behavior of the interface using a bilinear softened cohesion model can be represented by the following equation:
Figure BDA0002752110800000093
where d denotes the stress tensor, and δ denotes the displacement tensor, K is the stiffness matrix, and the indices n and s are the principal radial and shear directions.
The loss criterion expression is as follows:
Figure BDA0002752110800000094
in the formula (I), the compound is shown in the specification,
Figure BDA0002752110800000095
and
Figure BDA0002752110800000096
critical failure strength representing the principal and shear directions;
by giving matrix and interface correspondence criteria in step 103, in finite element softThe damage analysis is realized in the ABAQUS, and the integral stress of the composite material is obtained by a homogenization method in each analysis step
Figure BDA0002752110800000097
And strain
Figure BDA0002752110800000098
Figure BDA0002752110800000099
Where V is the finite element model volume, σ (i) is the stress in the i-direction of each element in the finite element model, and ε (i) is the strain in the i-direction of each element in the finite element model.
The simulation of the whole curing and loading process is realized by finite element software ABAQUS.
The specific embodiment is as follows:
step 1: the analysis route determined according to fig. 2 is that the data of the degree of solidification and temperature required for the subsequent analysis are obtained from the macro model by analysis as shown in fig. 3.
Step 2: the residual stress distribution was solved by substituting the temperature and cure data into the microscopic model as shown in fig. 4.
And step 3: and taking the obtained residual stress as an initial predefined field to continuously perform transverse tensile loading analysis on the microscopic model to obtain a stress-strain curve, and comparing an experimental curve with the stress-strain curve without considering the curing residual stress in the graph shown in FIG. 5, so that the stress-strain curve with considering the curing residual stress is better fitted with the experimental curve.
And 4, step 4: FIG. 6 shows a graph of lesion extension during loading.
As shown in fig. 7, the present invention also provides a composite strength detection system considering curing residual stress, including:
a temperature and curing degree calculation module 701, configured to calculate a temperature and a curing degree of the composite material through the macro scale model; the macroscopic model shown is a heat transfer model.
A residual stress calculation module 702, configured to input the temperature and the curing degree data into a mesoscopic model to calculate residual stress; the mesoscopic model is a linear elastic incremental model.
And the strength detection module 703 is configured to perform transverse tensile loading analysis on the mesoscopic model by using the calculated residual stress as an initial predefined field to obtain stress and strain of the composite material, and complete strength detection of the composite material.
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 (7)

1. A method for detecting the strength of a composite material considering curing residual stress is characterized by comprising the following steps:
calculating the temperature and the curing degree of the composite material through a macro scale model; the macroscopic model is a heat transfer model;
inputting the temperature and the curing degree data into a microscopic model to calculate residual stress; the mesoscopic model is a linear elastic incremental model;
and performing transverse tensile loading analysis on the mesoscopic model by taking the calculated residual stress as an initial predefined field to obtain the stress and the strain of the composite material, and completing the strength detection of the composite material.
2. The method for detecting the strength of the composite material considering the curing residual stress as claimed in claim 1, wherein a heat transfer model is established based on Fourier heat conduction law and energy balance principle, and the expression of the heat transfer model is as follows:
Figure FDA0002752110790000011
wherein rho is the density of the composite material, C is the specific heat capacity of the composite material, T is the temperature at the current moment of the curing reaction, and lambdaiiI-x, y, z represents the thermal conductivity of the anisotropic material in three directions,
Figure FDA0002752110790000012
the term "internal heat source" in the curing reaction means the amount of heat given off by the resin when the curing reaction occurs.
3. The method for detecting the strength of the composite material considering the curing residual stress as claimed in claim 1, wherein the expression of the linear elastic incremental model is as follows:
Figure FDA0002752110790000013
Figure FDA0002752110790000014
wherein, { Δ σ }i、{Δε}iFor the stress increment and strain increment at each time step i, σ is the total residual stress, ε is the total residual strain, and C is the stiffness matrix of the resin matrix.
4. The method for detecting the strength of the composite material considering the curing residual stress as claimed in claim 1, wherein when the microscopic model is subjected to transverse tensile loading analysis by using the calculated residual stress as an initial predefined field, the fibers in the composite material are not damaged, so that a damage model is not introduced, and different failure criteria are introduced for the interface and the resin matrix respectively.
5. The method for detecting the strength of the composite material considering the curing residual stress as claimed in claim 4, wherein Drucker-Prager is used for describing the plastic behavior of the resin matrix, and the expression is as follows:
F＝t-p tanβ-d＝0
wherein F represents a yield function, p is hydrostatic stress, beta is a friction angle, d is a cohesion parameter, and t is yield stress.
6. The method for detecting the strength of the composite material considering the curing residual stress as claimed in claim 4, wherein a bilinear softening cohesion model is adopted for the interface to describe the elastic behavior, and the expression is as follows:
Figure FDA0002752110790000021
where d denotes the stress tensor, and δ denotes the displacement tensor, K is the stiffness matrix, and n and s are the principal radial and shear directions.
7. A composite strength detection system that accounts for curing residual stresses, comprising:
the temperature and curing degree calculating module is used for calculating the temperature and curing degree of the composite material through the macro scale model; the macroscopic model is a heat transfer model;
the residual stress calculation module is used for inputting the temperature and the curing degree data into a mesoscopic model to calculate the residual stress; the mesoscopic model is a linear elastic incremental model;
and the strength detection module is used for carrying out transverse tensile loading analysis on the mesoscopic model by taking the calculated residual stress as an initial predefined field to obtain the stress and the strain of the composite material and finish the strength detection of the composite material.
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CN114970170A (en) * 2022-05-31 2022-08-30 西北工业大学 Z-pin toughening composite material strength prediction method considering curing defects
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