CN112487557A - Method for predicting interface failure and microscopic crack propagation of composite material under hydraulic permeation load - Google Patents

Method for predicting interface failure and microscopic crack propagation of composite material under hydraulic permeation load Download PDF

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CN112487557A
CN112487557A CN202011393937.1A CN202011393937A CN112487557A CN 112487557 A CN112487557 A CN 112487557A CN 202011393937 A CN202011393937 A CN 202011393937A CN 112487557 A CN112487557 A CN 112487557A
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张律文
田坤
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Abstract

The invention discloses a prediction method of interfacial failure and microscopic crack propagation under a hydraulic osmotic load of a composite material, which uses a fracture phase field and an interfacial phase field to represent the fracture state and the interfacial distribution of a model; in the simulation prediction process, a phase field method is combined with a Biot pore elastic medium theory, the displacement field and the liquid pressure field distribution of the model under the hydraulic load are calculated, and the influence of the displacement field on a fracture phase field is calculated, so that the crack growth simulation of the composite material under the mesoscale is realized when the composite material is subjected to the hydraulic load. The invention considers the normal and tangential rigidity of the interface in the inner focusing force interface model. According to the phase field method model, the growth and the bifurcation of the microscopic crack of the composite material can be accurately simulated.

Description

Method for predicting interface failure and microscopic crack propagation of composite material under hydraulic permeation load
Technical Field
The invention relates to the technical field of composite materials, in particular to a method for predicting interface failure and microscopic crack propagation under hydraulic permeation load of a composite material.
Background
The cryogenic tank is a complete structure in the rocket. The material selection of the storage tank is closely related to the bearing mode and the development level of the manufacturing process. With the development of composite material technology, the combination of metal and non-metal materials (composite materials) is also applied in the manufacturing process of the storage tank, and the composite material without a metal lining layer is usually selected as the new generation storage tank material. With the continuous research and development of composite materials with excellent cold and hot cycle mechanical properties, a full-composite material storage tank without a metal lining layer becomes a main development direction for light weight of a spacecraft.
Composite components are susceptible to microcracking within the composite component under hydraulic loading, and the propagation of these microcracks under load can lead to failure of the structure. With the increase of the service time, microcracks in the composite material expand, and then defects such as pores, cracks, delamination and the like are generated. When each layer in the composite material structure layer has transverse cracks and interlaminar cracks, a leakage path along the thickness direction is formed, so that the influence of the comprehensive mechanical property of the composite material under the low-temperature condition on the quality of the storage tank is very important. To reduce design manufacturing costs, it is desirable to simulate the composite tank during the design process.
A composite tank is a pressure vessel that is subjected to hydraulic loading within it. The problem of fracture and damage of the existing composite material pressure container is mainly solved by means of a traditional laminated plate theory and a stress factor method, but the method cannot well predict the generation and development of cracks under a microscopic scale. The reason is that the method is a geometric description method, cracks are based on grid expansion, such as a unit deletion method (unit failure method), an interface unit method and the like, the simplest method is the unit deletion method, the stress of a unit is only required to be set to zero when conditions are met, but the unit deletion method has defects in calculating crack bifurcation. The interface cell method is the simplest method for calculating the crack score, the crack can be randomly expanded at the cell boundary by inserting a cohesive force cell at the cell boundary, and when the cell boundary reaches the criterion of fracture, the interface cell can fail, but has dependence on a grid and numerical instability.
The phase field method is characterized in that a dispersed phase boundary is used for describing a sharp boundary actually, a fracture model can be described by using a continuous function by introducing parameters, a tracking crack surface is not displayed during simulation, and a crack path and a crack position are obtained through automatic evolution of the parameters.
The Biot pore elasticity theory establishes the relation between a liquid component and a pore medium, the deformation of a solid is coupled with the change of the pressure of the liquid, and the liquid in a solid crack is considered as Poisea laminar flow.
Disclosure of Invention
The invention aims to provide a method for predicting the interface failure and the microscopic crack propagation of a composite material under hydraulic osmotic load according to the defects of the prior art, and the method realizes the crack growth simulation prediction of the composite material through a phase field method model, a cohesion interface model and a Biot pore elastic medium theory.
The invention is realized by the following technical scheme:
a prediction method for interfacial failure and microscopic crack propagation under hydraulic infiltration load of a composite material is characterized in that a fracture phase field and an interfacial phase field are used for representing the fracture state and the interfacial distribution of a model; in the simulation prediction process, a phase field method is combined with a Biot pore elastic medium theory, the displacement field and the liquid pressure field distribution of the model under the hydraulic load are calculated, and the influence of the displacement field on a fracture phase field is calculated, so that the crack growth simulation of the composite material under the mesoscale is realized when the composite material is subjected to the hydraulic load.
The invention is further improved in that: and preprocessing the model at the beginning of the simulation prediction process, wherein the preprocessing process comprises the step of determining the geometric parameters and the mechanical property parameters of the model.
The invention is further improved in that:
the geometric parameters comprise the length and height of the whole model and the position and diameter of the fiber;
the mechanical property parameters comprise the elastic modulus of the matrix, the Poisson ratio, the critical stress, the Biot modulus, the Biot coefficient, the permeability coefficient, the elastic modulus of the reinforced material, the Poisson ratio, the critical stress, the Biot modulus, the Biot coefficient, and the normal fracture energy and the tangential fracture energy of the interface; the viscosity of the liquid.
The invention is further improved in that: the fracture phase field is a scalar field, 0 represents no damage, and 1 represents complete fracture; the interfacial phase field is a scalar field.
The invention is further improved in that: dividing the simulated prediction process into a plurality of time steps; at each time step:
(S21) obtaining a stress state from the displacement field of the previous time step, and obtaining a phase field driving force from the stress state; calculating a fracture phase field according to the phase field driving force;
(S22) according to the obtained fracture phase field, weakening the rigidity of the fracture part of the model, and obtaining a new displacement field and a new liquid pressure field.
The invention is further improved in that: and initializing the model in a first time step, and calculating an initial value of a displacement field, an initial value of a liquid intensity field and an interface phase field in the initialization process.
The invention is further improved in that: in step (S21), the calculation of the phase-breaking field from the phase-field driving force takes the expression:
Figure BDA0002813884980000031
wherein: beta is the interface phase field, phi is the fracture phase field, HφIs the phase field driving force,/0Is a characteristic size parameter of the crack in the phase field method,
the invention is further improved in that: in step (S22), the new displacement field and liquid pressure field are obtained by the following expressions:
Ru=∫Ωeff-bpI)·εe(δu)dV+fΩγβt·w dV
Figure BDA0002813884980000032
wherein: sigmaeffRepresenting the stress of the solid component of the model, b is the Biot coefficient, p is the fluid pressure field at the current time step, I is the unit second order tensor, t is the traction of the cohesion model, γβIs a function of interfacial surface density, equal to
Figure BDA0002813884980000033
β is the interphase field; p is a radical ofnIs the fluid pressure field at the previous time step, u is the displacement field at the current time step, u is the fluid pressure field at the previous time stepnIs the displacement field of the previous time step, M is the Biot modulus;
Figure BDA0002813884980000034
is the tensor of seepage expressed as
Figure BDA0002813884980000035
Figure BDA0002813884980000036
KhomoIs the permeability coefficient of the solid, η is the liquid viscosity; kcrackIs the anisotropy tensor of the liquid flow in the fracture, which conforms to the poisson law:
Figure BDA0002813884980000037
wnis the crack opening displacement, and n is the normal vector of the crack surface; epsiloneIs an elastic strain expressed as
Figure BDA0002813884980000038
Figure BDA0002813884980000039
ni,njIs the interface normal vector component; τ is the time step.
The invention is further improved in that: and after the simulation prediction process is finished, post-processing the simulation result, and obtaining a displacement response cloud picture, a stress distribution cloud picture, a pressure distribution cloud picture and a fracture phase field distribution cloud picture of the model in the post-processing process.
Compared with the prior art, the method considers the normal stiffness and the tangential stiffness of the interface in the inner focusing force interface model. According to the phase field method model, the growth and the bifurcation of the microscopic crack of the composite material can be accurately simulated.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic structural diagram of a model of the present invention;
FIG. 3 is a cloud diagram illustrating the phase-splitting field distribution of a simulation prediction process interruption. .
Detailed Description
The embodiment shown in fig. 1 and 2 relates to a method for simulating crack propagation of a composite material under the pressure of liquid, which comprises the following steps:
the model is preprocessed at the beginning stage of the simulation prediction process, the preprocessing process comprises the steps of determining the geometric parameters and the mechanical property parameters of the model, a rectangular grid is divided through software, and the boundaries of a matrix of the model and a reinforcing material are approximated by the direct boundaries of the grid. The geometric parameters of the model comprise the length and the height of the whole model and the position and the diameter of the fiber; the mechanical property parameters comprise the elastic modulus of the matrix, the Poisson ratio, the critical stress, the Biot modulus, the Biot coefficient, the permeability coefficient, the elastic modulus of the reinforced material, the Poisson ratio, the critical stress, the Biot modulus, the Biot coefficient, and the normal fracture energy and the tangential fracture energy of the interface; the viscosity of the liquid.
In the pretreatment process, initial conditions are set, and an interface phase field is obtained. In the calculation process, u is a displacement field, p is a liquid pressure field, phi is a fracture phase field, the fracture phase field is a scalar field, the value at the crack is 1, the position far away from the crack is 0, the distribution of the rest positions is calculated by a phase field control process, beta is an interface phase field, the interface phase field is a scalar field, the value at the interface is 1, the position far away from the interface is 0, the values of other regions are obtained by continuous function interpolation, and the distribution of the interface phase field beta does not change along with time. The interface phase field beta is used for representing the interface distribution of the matrix and the reinforcement of the composite material, the matrix and the reinforcement have certain adhesion at the interface, and the matrix and the reinforcement are just like being stuck together, and one of the damage forms of the composite material is interface debonding.
In the method of the embodiment, a mechanical equilibrium equation, a Biot pore hydraulic control equation and a phase field control equation are adopted in the simulation prediction process, and the expressions of the equations are respectively as follows:
Figure BDA0002813884980000041
Figure BDA0002813884980000042
Figure BDA0002813884980000043
wherein sigmaeffRepresenting the stress of the solid components of the model, I is the unit second order tensor, b is the Biot coefficient, M is the Biot modulus,
Figure BDA0002813884980000044
is the tensor of seepage, which can be expressed as
Figure BDA0002813884980000045
KhomPermeability coefficient of solids,. eta.is liquid viscosity,. KcrackIs the anisotropy tensor of the flow of liquid in the fracture of the model, which can be assumed to comply with the poisson law.
Figure BDA0002813884980000046
wnIs the crack opening displacement (jump displacement) and n is the normal to the crack surface. l0Is a characteristic size parameter of the crack in the phase field method, HφIs the phase field driving force, which can be found from the stress state of the model, and the phase field driving force does not decrease with time, so that the crack is not recoverable in the simulation prediction process.
In the above equations, the mechanical equilibrium equation of equation (1) and the Biot pore hydraulic control equation of equation (2) describe the model of the solid and the movement process of the liquid applying the hydraulic load. Equation (3) is used to describe the phase field driving force and the split phase field of the model. The above formula is difficult to be directly used for numerical solution, and for numerical solution, the above formula is transformed as follows:
by time-discretizing equation (2), we can obtain:
Figure BDA0002813884980000051
where p is the fluid pressure field at the current time step, pnIs the fluid pressure field at the previous time step, u is the displacement field at the current time step, u is the fluid pressure field at the previous time stepnIs the displacement field of the previous time step, the index n of the pressure and the displacement represents the previous time step, and τ is the time step.
To describe the fracture at the interface of the matrix and the reinforcement of the model, a cohesive force model was introduced in this example. Under the cohesive force model, the potential energy generated by the interfacial failure is as follows:
W=∫γβt·wdV (5)
where t is the traction force of the cohesion model, γβIs a function of interfacial surface density, equal to
Figure BDA0002813884980000052
Figure BDA0002813884980000053
Equation (5) is introduced and the weak form of equations (1), (3), (4) is found as:
Ru=∫Ωeff-bpI)·εe(δu)dV+fΩγβt·w dV (6)
Figure BDA0002813884980000054
Figure BDA0002813884980000055
εeis an elastic strain expressed as
Figure BDA0002813884980000056
ni,njIs the interface normal vector component. In the formulae (6), (7) and (8), Ru,RpAnd RφRespectively representing the residue after volume integrationValue (residual). dV denotes volume infinitesimal.
The equations (6), (7) and (8) are spatially discretized using a two-dimensional four-node element, and the integral in the weak form is found by a gaussian integration algorithm. In the simulation prediction process, the discrete equation is solved numerically, the process is divided into a plurality of time steps, and each time step comprises the following steps:
1) by the last time step tnThe obtained displacement field obtains the stress state of the model, and the phase field driving force H is obtained through the stress stateφ. Solving equation (8) by using a Newton method iteration method according to the phase field driving force to obtain a time step tn+1The fracture phase field distribution. Calculating the phase field driving force from the stress state is a prior art in the phase field method. For the first time step, it uses the initial value u of the field shift0Initial value p of the pressure field0The interface phase field β is determined from the equations (6) to (8) and the parameters in the initialization process.
2) According to time step tn+1The fracture phase field distribution weakens the rigidity of the model so as to simulate the influence of the fracture on the rigidity of the model. After the rigidity is weakened, equations (6) and (7) are solved simultaneously through a Newton iteration method to obtain tn+1And (3) a displacement field and a pressure field of a time step, and storing the stress numerical value of each Gaussian integration point for calculating the phase field driving force at the next time step.
3) Let tn=tn+1And repeating the steps 1) to 3) until the end point of the solution time is reached.
And after the simulation prediction process is finished, carrying out post-processing on the simulation result. In the post-processing process, the displacement field, the liquid pressure field and the stress of the model are smoothed by a difference method, and a cloud picture of each field is obtained. And (4) making a cloud picture of a fracture phase field, and simulating the propagation mode of the crack in the material. In the process, a displacement response cloud picture is obtained according to the displacement field, a stress distribution cloud picture is obtained according to the stress numerical value of each Gaussian integration point in the simulation process, a pressure distribution cloud picture is obtained according to the pressure field distribution, and a fracture phase field distribution cloud picture is obtained according to the fracture phase field.
The phase field method adopted in the invention is a simulation method with non-geometric description, and the method is characterized in that crack simulation does not depend on a grid and can be expanded in the grid. The expansion finite element method adds degree of freedom at nodes, and the main idea is to add the characteristics of displacement places into a variation function space and a trial function space by using an expansion shape function, wherein the expansion shape function implicitly expresses the discontinuity of cracks, and the discontinuity is irrelevant to grids. The core idea of the phase field method is to introduce an additional scalar function, namely a phase field, to describe the fracture state of the material, construct a dirac function by using a phase field variable to disperse sharp crack boundaries in a solving area, and obtain the evolution, path and position of cracks according to the distribution of the phase field without explicitly tracking crack surfaces during simulation.
Example calculation:
the model of this example is shown in FIG. 2, and the geometric dimensions of the model are 50 mm. times.50 mm. The grid is a square grid with the size of 0.125 mm. The elastic modulus E of the matrix is 16GPa, the Poisson ratio v is 0.2, and the critical stress sigma isc0.45MPa and, Biot modulus M12.5 GPa, Biot coefficient b 0.79, permeability coefficient Khomo=2×10-14m2The elastic modulus E of the reinforcing material is 52GPa, the Poisson ratio v is 0.2, and the critical stress sigma isc1.8MPa, and, Biot modulus M12.5 GPa, Biot coefficient b 0, permeability coefficient Khom=2×10-20m2(ii) a Normal energy to fracture of interface
Figure BDA0002813884980000061
And energy of fracture in tangential direction
Figure BDA0002813884980000062
Viscosity η of liquid 1 × 10-3kg/(m.s). After the simulation process is finished, the fracture phase field distribution cloud pictures at different time steps shown in fig. 3 can be obtained.
Compared with the prior art, the performance index of the method is improved as follows: deformation in both the normal direction and the tangential direction is considered in the cohesive force interface model; in addition, the method can successfully simulate and predict the crack propagation mode of the composite material under the hydraulic load.
At present, the research on the damage and the service life of the composite material storage tank is focused on experiments, but the work in the aspect of simulation and prediction is less, and the applied method is mainly the traditional mesoscopic composite material mechanics, such as a bridging theory. There has been no study of the problems of composite leakage and fracture failure involving fluid-solid coupling. The working plan applies the processing mode of the fluid-solid coupling problem in the hydraulic fracturing problem to the fiber reinforced composite material, and applies the phase field method to process the crack generation, the bifurcation and the expansion of the material in the continuous medium mechanics, thereby realizing the simulation prediction of the damage of the hydrogen storage tank. The method can make up the blank of numerical simulation and prediction of the crack propagation of the composite material storage tank under the condition of considering the fluid-solid coupling problem, and explore the leakage failure mechanism of the storage tank structure.
The foregoing embodiments may be modified in many different ways by those skilled in the art without departing from the spirit and scope of the invention, which is defined by the appended claims and all changes that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

Claims (9)

1. A method for predicting interfacial failure and microscopic crack propagation under a hydraulic infiltration load of a composite material is characterized by comprising the following steps: representing the fracture state and the interface distribution of the model by using a fracture phase field and an interface phase field; in the simulation prediction process, a phase field method is combined with a Biot pore elastic medium theory, the displacement field and the liquid pressure field distribution of the model under the hydraulic load are calculated, and the influence of the displacement field on a fracture phase field is calculated, so that the crack growth simulation of the composite material under the mesoscale is realized when the composite material is subjected to the hydraulic load.
2. The method for predicting the interfacial failure and the microscopic crack propagation under the hydraulic infiltration load of the composite material according to claim 1, wherein the method comprises the following steps: and preprocessing the model at the beginning of the simulation prediction process, wherein the preprocessing process comprises the step of determining the geometric parameters and the mechanical property parameters of the model.
3. The method for predicting the interfacial failure and the microscopic crack propagation under the hydraulic infiltration load of the composite material according to claim 2, wherein the method comprises the following steps:
the geometric parameters comprise the length and height of the whole model and the position and diameter of the fiber;
the mechanical property parameters comprise the elastic modulus of the matrix, the Poisson ratio, the critical stress, the Biot modulus, the Biot coefficient, the permeability coefficient, the elastic modulus of the reinforced material, the Poisson ratio, the critical stress, the Biot modulus, the Biot coefficient, and the normal fracture energy and the tangential fracture energy of the interface; the viscosity of the liquid.
4. The method for predicting the interfacial failure and the microscopic crack propagation under the hydraulic infiltration load of the composite material according to claim 1 or 2, wherein the method comprises the following steps: the fracture phase field is a scalar field, 0 represents no damage, and 1 represents complete fracture; the interfacial phase field is a scalar field.
5. The method for predicting the interfacial failure and the microscopic crack propagation under the hydraulic infiltration load of the composite material according to claim 1, wherein the method comprises the following steps: dividing the simulated prediction process into a plurality of time steps; at each time step:
(S21) obtaining a stress state from the displacement field of the previous time step, and obtaining a phase field driving force from the stress state; calculating a fracture phase field according to the phase field driving force;
(S22) according to the obtained fracture phase field, weakening the rigidity of the fracture part of the model, and obtaining a new displacement field and a new liquid pressure field.
6. The method for predicting the interfacial failure and the microscopic crack propagation under the hydraulic infiltration load of the composite material according to claim 5, wherein the method comprises the following steps: and initializing the model in a first time step, and calculating an initial value of a displacement field, an initial value of a liquid intensity field and an interface phase field in the initialization process.
7. The method for predicting the interfacial failure and the microscopic crack propagation under the hydraulic infiltration load of the composite material according to claim 6, wherein in the step (S21), the expression used for calculating the fracture phase field according to the phase field driving force is as follows:
Figure FDA0002813884970000021
wherein: beta is the interface phase field, phi is the fracture phase field, HφIs the phase field driving force,/0Is a characteristic size parameter of the crack in the phase field method.
8. The method for predicting interfacial failure and microscopic crack propagation under hydraulic infiltration load of composite material according to claim 6, wherein in the step (S22), the new displacement field and liquid pressure field are obtained by the following expressions:
Ru=∫Ωeff-bpI)·εe(δu)dV+fΩγβt·wdV
Figure FDA0002813884970000022
wherein: sigmaeffRepresenting the stress of the solid component of the model, b is the Biot coefficient, p is the fluid pressure field at the current time step, I is the unit second order tensor, t is the traction of the cohesion model, γβIs a function of interfacial surface density, equal to
Figure FDA0002813884970000023
Figure FDA0002813884970000024
β is the interphase field; p is a radical ofnIs the fluid pressure field at the previous time step, u is the displacement field at the current time step, u is the fluid pressure field at the previous time stepnIs the displacement field of the previous time step, M is the Biot modulus;
Figure FDA0002813884970000025
is the tensor of seepage expressed as
Figure FDA0002813884970000026
Figure FDA0002813884970000027
KhomoIs the permeability coefficient of the solid, η is the liquid viscosity; kcrackIs the anisotropy tensor of the liquid flow in the fracture, which conforms to the poisson law:
Figure FDA0002813884970000028
wnis the crack opening displacement, and n is the normal vector of the crack surface; epsiloneIs an elastic strain expressed as
Figure FDA0002813884970000029
Figure FDA00028138849700000210
ni,njIs the interface normal vector component; τ is the time step.
9. The method for predicting the interfacial failure and the microscopic crack propagation under the hydraulic infiltration load of the composite material according to claim 1, wherein the method comprises the following steps: and after the simulation prediction process is finished, post-processing the simulation result, and obtaining a displacement response cloud picture, a stress distribution cloud picture, a pressure distribution cloud picture and a fracture phase field distribution cloud picture of the model in the post-processing process.
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