CN112560315B - Method for constructing lightweight refractory material random heterogeneous continuous model - Google Patents
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Abstract
The invention provides a method for constructing a random heterogeneous continuous model of a lightweight refractory material. By defining and inputting basic parameters, generating random coordinates of aggregate central points in the effective size of the model by using a pseudo-random number generator, and establishing a finite element model with randomly distributed spherical aggregates under the condition of no intersection among the aggregates; and determining the content of each component in the aggregate element group by utilizing double-parameter Weber distribution according to the characteristics of high porosity and high heterogeneity of the lightweight refractory aggregate, and realizing the heterogeneity of the aggregate element group by circulating feeding, thereby establishing a random heterogeneous continuous finite element model. Through the mode, the random heterogeneous continuous model established by the method can meet the requirement of generating randomness of the aggregate, and better accords with the real microscopic structure of the lightweight aggregate, so that a basis is provided for service life prediction and material design optimization of the refractory material, and the method has higher application value.
Description
Technical Field
The invention relates to the technical field of refractory material numerical simulation, in particular to a method for constructing a lightweight refractory material random heterogeneous continuous model.
Background
Energy conservation and emission reduction are the keys of sustainable and healthy development of national economy in China, and the energy consumption of high-temperature industry accounts for about 50% of the total energy consumption and is listed as the national key energy-saving field. In the measures of energy conservation and emission reduction aiming at the high-temperature industry, the light-weight refractory material is used for replacing a compact refractory material as a lining material of the high-temperature industrial kiln, so that the heat dissipation of a high-temperature furnace body can be reduced by reducing the heat conductivity coefficient, the volume density of the material can be reduced, the consumption of refractory material resources and power in the thermal engineering process can be reduced, and better effects of energy conservation and emission reduction can be achieved.
However, the lightweight refractory material is used in a high-temperature environment with fluctuating temperature, the influences of microstructures such as composition, content, pore size distribution and interface of a physical phase in the lightweight aggregate on thermal stress distribution and material properties (such as thermal conductivity, mechanical properties and the like) are complex, and the traditional experimental method is difficult to characterize the microscopic-scale service behavior. And a proper calculation model is established for finite element simulation, so that the damage behavior of the lightweight refractory material in the service process can be intuitively and accurately predicted and evaluated, and the relationship between the microscopic structure and the macroscopic performance is established, so that the method has important significance for developing a new generation of lightweight refractory material and continuously meeting the requirements of energy conservation and emission reduction of high-temperature industry.
At present, scholars at home and abroad successfully apply a finite element simulation method to the design of a metallurgical furnace lining and the design of a compact refractory material, but the numerical simulation work aiming at the lightweight refractory material is not carried out yet. In the prior finite element model, the compact refractory material is generally simply homogenized, or the model is simplified into a single component of compact aggregate which is randomly dispersed in a homogeneous matrix, and the aggregate participates in the fracture only as an unbreakable reinforcing structure. However, the lightweight refractory is a more complex cross-scale, multi-phase, heterogeneous composite material, and the simple homogenization method is not suitable for numerical simulation of the lightweight refractory.
In view of the above, there is a need to develop a finite element model conforming to the microscopic structural features of lightweight refractory material to truly simulate the service performance thereof, so as to solve the above problems.
Disclosure of Invention
In view of the above-mentioned drawbacks of the prior art, an object of the present invention is to provide a method for constructing a lightweight refractory random heterogeneous continuous model. Establishing a finite element model of random distribution of spherical aggregates according to the distribution characteristics of the aggregates in the matrix; and determining the property and content of the component phase according to the high porosity and high heterogeneity microstructure characteristics of the lightweight aggregate, and establishing a random heterogeneous continuous finite element model to meet the requirement of generating randomness of the aggregate, so that the constructed model and the real microscopic structure of the lightweight aggregate are more consistent, the model and the real microscopic structure are conveniently used for simulating the service performance of the lightweight refractory material and the relationship between the microscopic structure and the macroscopic performance, and a basis is provided for service life prediction and material design optimization of the refractory material.
In order to achieve the aim, the invention provides a method for constructing a lightweight refractory random heterogeneous continuous model, which comprises the following steps:
s1, establishing a finite element model of random distribution of spherical aggregates according to the distribution characteristics of the aggregates in a matrix;
and S2, determining the performance and the content of each heterogeneous component phase in the element group in the spherical aggregate random distribution finite element model obtained in the step S1 according to the microstructure characteristics of the lightweight aggregate, and establishing a random heterogeneous continuous finite element model.
As a further improvement of the invention, in step S1, the distribution characteristics of the aggregate in the matrix conform to an Alfred particle size distribution curve and belong to a closest packing mode, and the particle size distribution condition of the aggregate in the matrix satisfies the following formula:
wherein d is any particle size value of the aggregate, R is the content of the aggregate with the diameter exceeding d,
the diameter of the aggregate is the maximum diameter,
is the minimum aggregate diameter, and n is the packing constant.
As a further improvement of the present invention, in step S1, the establishing a finite element model with randomly distributed spherical aggregates specifically includes the following steps:
s11, defining an array for storing parameters and inputting the parameters;
s12, generating random coordinates of the center points of the aggregates and the sizes of the aggregates, and setting limiting conditions;
s13, generating an aggregate part of the model for the aggregates meeting the limiting conditions set in the step S12; projecting the aggregate part into a two-dimensional geometrical structure, and removing the area overlapped with the aggregate part to generate a matrix part of the model; and assembling the aggregate part and the matrix part to obtain the finite element model with the spherical aggregate randomly distributed.
As a further improvement of the present invention, in step S11, the parameters include, but are not limited to, one or more of model size, aggregate content, aggregate maximum particle size, alfred particle size distribution factor, and gridding density.
As a further improvement of the present invention, in step S12, the constraint is that any pair of spherical aggregates does not intersect, and any spherical aggregate does not exceed the boundary of the model.
As a further improvement of the present invention, in step S12, the random coordinates of the center points of the aggregates and the sizes of the aggregates are generated by a pseudo random number generator.
As a further improvement of the present invention, in step S2, the element group is the aggregate part in the spherical aggregate random distribution finite element model.
As a further improvement of the present invention, in step S2, the random heterogeneous continuous finite element model is established by circularly defining each heterogeneous component phase and putting a random seed.
As a further improvement of the present invention, in step S2, the content of each non-homogeneous component phase satisfies a two-parameter weber distribution, and the functional formula is:
wherein x is a variable, λ is a proportional parameter, and k is a shape parameter.
As a further improvement of the present invention, in step S2, the properties of each of the heterogeneous component phases include mechanical properties, which follow a double-fold strain-softening curve.
The beneficial effects of the invention are:
(1) The invention provides a method for constructing a random heterogeneous continuous model of a lightweight refractory material, which comprises the steps of defining and inputting basic parameters such as model size, aggregate content, alfred particle size distribution factor and the like, then utilizing a pseudo-random number generator to generate random coordinates of aggregate central points in the effective size of the model, and establishing a finite element model with spherical aggregates randomly distributed under the condition of non-intersection among the aggregates; on the basis, according to the characteristics of high porosity and high heterogeneity of lightweight refractory aggregate, the content of each component in the aggregate element group is determined by utilizing two-parameter Weber distribution, and the heterogeneous of the aggregate element group is realized by circulating feeding, so that a random heterogeneous continuous finite element model is established. Based on the method provided by the invention, the random heterogeneous continuous finite element model established by the method can meet the requirement of generating randomness of the aggregate, so that the established model and the real mesoscopic structure of the lightweight aggregate are more consistent, the method is convenient for simulating the service performance of the lightweight refractory material and the relation between the mesoscopic structure and the macroscopic performance, and provides a basis for predicting the service life of the refractory material and optimizing the material design.
(2) The random heterogeneous continuous finite element model established by the invention can meet the requirement of generating randomness of the aggregate and accords with the real aggregate stacking rule; the constructed mesoscopic calculation model containing the high porosity and the high heterogeneity of the aggregate is more consistent with the real lightweight aggregate mesoscopic structure. Meanwhile, the model established by the invention eliminates the interface barrier, accords with the phenomenon of interface compatibility improvement observed by experiments, allows the crack to be expanded in the aggregate and makes great progress compared with the existing model. In addition, the method provided by the invention can adopt different heterogeneous strategies, grid division, assignment and the like for different parts in the model, the controllability is strong, and the numerical calculation of the established finite element model is favorable for establishing the relationship between the microscopic structure and the macroscopic performance. In addition, based on the construction method of the random heterogeneous continuous model provided by the invention, the corresponding model can be established only by inputting corresponding parameters, and the microscopic structure of the model can be adjusted by changing the input parameters, so that the method is favorable for freely designing the model and popularizing the model to other systems such as multiphase materials, porous media and the like, and has wide application range.
Drawings
Fig. 1 is a schematic flow chart of a method for constructing a lightweight refractory random heterogeneous continuous model provided by the invention.
FIG. 2 is a structural diagram of a finite element model with spherical aggregates randomly distributed.
FIG. 3 is a graph showing the relationship between the properties and the content of a heterogeneous component phase.
FIG. 4 is a random heterogeneous continuous finite element model of lightweight aggregate containing two phases.
FIG. 5 is a random heterogeneous continuous finite element model of lightweight aggregate containing three phases.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
It should be noted that, in order to avoid obscuring the present invention with unnecessary details, only the structures and/or processing steps closely related to the aspects of the present invention are shown in the drawings, and other details not closely related to the present invention are omitted.
In addition, it is also to be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
The invention provides a method for constructing a lightweight refractory random heterogeneous continuous model, which has a flow diagram shown in figure 1 and specifically comprises the following steps:
s1, establishing a finite element model of random distribution of spherical aggregates according to the distribution characteristics of the aggregates in a matrix.
The most basic structure of a refractory material consists of a granular aggregate and a fine powder matrix, wherein aggregates of different particle sizes act as a skeleton and are randomly dispersed in the matrix. The particle size distribution of the aggregate conforms to an Alfred particle size distribution curve and belongs to a closest packing mode, and the particle size distribution condition of the aggregate in the matrix meets the following formula:
wherein d is any particle size value of the aggregate, R is the content of the aggregate with the diameter exceeding d,
is the maximum diameter of the aggregate, and is,
n is the packing constant for the minimum aggregate diameter.
Based on the distribution characteristics of the aggregate in the matrix, firstly defining an array for storing parameters, and interactively acquiring input parameters with finite element software through a getInput statement; corresponding parameters can be input randomly in the interface as required, and the universality and the flexibility of the self-compiling program are effectively improved. In some embodiments of the invention, the parameters include one or more of model size, aggregate content, aggregate maximum particle size, alfred particle size distribution factor, and gridding density, and in other embodiments of the invention, the parameters may be self-defined and input as desired.
Then, generating random coordinates of the center point of the aggregates and the corresponding sizes of the aggregates by using a pseudo-random number generator; based on the coordinates and the size, any pair of spherical aggregates do not intersect, and any spherical aggregate does not exceed the boundary of the model as a limiting condition, namely the aggregates and the boundaries of the model do not intersect, and the coordinates and the size of the aggregates meeting the limiting condition are output to serve as the aggregate part of the model.
Finally, projecting the aggregate part into a two-dimensional geometrical structure, and removing the area which is overlapped with the aggregate part to generate a matrix part of the model; and assembling the aggregate part and the matrix part, thereby establishing a finite element model with the spherical aggregates distributed randomly.
According to the invention, the aggregate part and the matrix part of the model are respectively generated and then assembled into the spherical aggregate random distribution finite element model, so that the aggregate-matrix interface performance setting, the definition of material performances of different parts and the subsequent treatment process are facilitated.
In one embodiment of the invention, the particle size distribution of the aggregate with the maximum particle size of 5mm and the minimum particle size of 1 mm-5 mm conforms to an Alfred particle size distribution curve, and the packing constant n is 0.37 so as to simulate closest packing; aggregate accounting for 60 percent of the total components is randomly put into an effective space of 30mm multiplied by 30mm, and the size of a grid is 0.2mm. By inputting the parameters on the finite element interactive interface, a finite element model with the required size and the random distribution of spherical aggregates can be efficiently and quickly established, and the structural schematic diagram is shown in FIG. 2. In FIG. 2, (a) is a finite element model in which spherical aggregates are randomly distributed, (b) is an aggregate portion, and (c) is a matrix portion.
S2, determining the performance and the content of each heterogeneous component phase in the element group in the spherical aggregate random distribution finite element model obtained in the step S1 according to the microstructure characteristics of the lightweight aggregate, and establishing a random heterogeneous continuous finite element model.
The most important microstructural features of lightweight refractory materials compared to traditional refractory materials are the high porosity and high heterogeneity of the aggregate. The probability of each non-homogeneous component in the aggregate occurring within a given area can be expressed by a particular mathematical distribution function.
According to the microstructure characteristics of the lightweight aggregate, the aggregate part in the finite element model with the spherical aggregate randomly distributed in the step S1 is named as a Grains element group, and the performance and the content of each non-homogeneous component phase in the element group are defined.
Specifically, the content of each component phase is distributed by adopting double-parameter Weber distribution, and the component phases are assigned. The functional formula of the two-parameter weber distribution is as follows:
wherein x is a variable, λ is a proportional parameter, and k is a shape parameter.
In an embodiment of the present invention, there are five types of heterogeneous components, the content of each type of component satisfies the two-parameter weber distribution, the mechanical properties thereof follow the double-fold strain softening curve, and the schematic diagram of the relationship between the corresponding properties and the content is shown in fig. 3. In order to make the macroscopic properties conform to the actual or optimal microstructure form, the macroscopic properties of the material are generally taken as an objective function, the contents of the components are taken as variables, and the optimal distribution function is obtained by inverse fitting.
In another embodiment of the invention, the probability distribution of each component can be determined by a scanning electron microscope according to the developed material type.
After the performance and the content of each heterogeneous component phase are determined, continuous non-homogenization of the Grains element group is realized by circularly defining each heterogeneous component phase and putting random seeds, so that a random heterogeneous continuous finite element model is established.
In one embodiment of the present invention, two phases are contained in the lightweight aggregate, the aggregate is defined as two-phase heterogeneous material on the basis of the finite element model with the spherical aggregate randomly distributed according to the method provided in step S1 (input parameters include size: 30mm × 30mm, aggregate volume content: 60%, maximum aggregate particle size: 5 mm), and the random heterogeneous continuous finite element model established according to the method provided in step S2 is shown in fig. 4. In fig. 4, the black area is a component phase with a volume fraction of 45% of the aggregate volume, which is used to represent the pore phase, the dark gray portion is the aggregate component phase, and the two heterogeneous elements are randomly distributed.
In another embodiment of the invention, the lightweight refractory material is a lightweight periclase-magnesium aluminate spinel refractory material, the matrix of which comprises two phases of pores and periclase, and the lightweight aggregate comprises three phases of pores, periclase and magnesium aluminate spinel. According to the characterization results of the microstructure and the porosity, the following parameters are input:
the size is 30mm multiplied by 30mm, and the volume content of the aggregate is 63 percent; the volume fraction of the pore phase in the matrix is 37 percent, and the volume fraction of the periclase phase is 63 percent; the volume fraction of the pore phase in the aggregate is 21%, the volume fraction of the periclase phase is 51%, and the volume fraction of the magnesia-alumina spinel phase is 28%.
And according to the method provided by the step S2, realizing the non-homogenization of the aggregate element group and the matrix element group through the circular feeding, and obtaining a random non-homogeneous continuous finite element model as shown in figure 5. In fig. 5, (a) is an integral model obtained by non-homogenizing only the aggregate element group, the aggregate contains three phases, the matrix is homogenized, and the interface between the aggregate and the matrix is clear; (b) The aggregate contains three phases, the matrix contains two phases, and the degree of engagement between the aggregate and the interface is high; (c) The method is a local amplification model of an interface position, wherein black areas are used for representing gas pores, dark grey represents a periclase phase, light grey represents a magnesium aluminate spinel phase, and heterogeneous elements of all phases are randomly distributed. Meanwhile, different gridding matrixes are adopted for the matrix and the aggregate part, so that the characteristic of small aperture of the aggregate is favorably embodied, and the aggregate is more fit with an actual structure.
Based on the method, the lightweight refractory material random heterogeneous model established by the invention is a continuous model, the subsequent numerical calculation time cannot be greatly increased due to the complex structure, and the calculation efficiency is ensured to a limited extent. Meanwhile, according to the technical principle and implementation steps described above, only by changing input parameters, the method can construct a finite element model of a heterogeneous material with any geometric structure and size, and can also be widely applied to finite element modeling of heterogeneous material systems other than lightweight refractory materials, especially to the heterogeneous material (such as concrete) containing an aggregate structure, and the application range is wide.
In conclusion, the invention provides a method for constructing a lightweight refractory random heterogeneous continuous model. By defining and inputting basic parameters, generating random coordinates of aggregate central points in the effective size of the model by using a pseudo-random number generator, and establishing a finite element model with randomly distributed spherical aggregates under the condition of no intersection among the aggregates; and determining the content of each component in the aggregate element group by utilizing two-parameter Weber distribution according to the characteristics of high porosity and high heterogeneity of the lightweight refractory aggregate, and realizing the heterogeneity of the aggregate element group by circulating feeding, thereby establishing a random heterogeneous continuous finite element model. Through the mode, the random heterogeneous continuous model established by the method can meet the requirement of generating randomness of the aggregate, and better accords with the real microscopic structure of the lightweight aggregate, so that a basis is provided for service life prediction and material design optimization of the refractory material, and the method has higher application value.
Although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the spirit and scope of the present invention.
Claims (9)
1. A method for constructing a lightweight refractory random heterogeneous continuous model is characterized by comprising the following steps:
s1, generating an aggregate part of a model according to the distribution characteristics of aggregates in a matrix; projecting the aggregate part into a two-dimensional geometrical structure, and removing the area overlapped with the aggregate part to generate a matrix part of the model; assembling the aggregate part and the matrix part to obtain a finite element model with randomly distributed spherical aggregates;
s2, determining the performance and the content of each heterogeneous component phase in the element group in the spherical aggregate random distribution finite element model obtained in the step S1 according to the microstructure characteristics of the lightweight aggregate, and establishing a random heterogeneous continuous finite element model by circularly defining each heterogeneous component phase and putting random seeds.
2. The method for constructing the random heterogeneous continuous model of the lightweight refractory material as claimed in claim 1, wherein the method comprises the following steps: in step S1, the distribution characteristics of the aggregates in the matrix conform to an Alfred particle size distribution curve and belong to a closest packing mode, and the particle size distribution condition of the aggregates in the matrix satisfies the following formula:
wherein d is any particle size value of the aggregate, R is the content of the aggregate with the diameter exceeding d,
the diameter of the aggregate is the maximum diameter,
n is the packing constant for the minimum aggregate diameter.
3. The method for constructing the random heterogeneous continuous model of lightweight refractory according to claim 1, wherein the method comprises the following steps: in step S1, the step of generating the aggregate part of the model specifically includes the steps of:
s11, defining an array for storing parameters and inputting the parameters;
s12, generating random coordinates of the center points of the aggregates and the sizes of the aggregates, and setting limiting conditions;
and S13, generating an aggregate part of the model for the aggregates meeting the limiting conditions set in the step S12.
4. The method for constructing the random heterogeneous continuous model of lightweight refractory according to claim 3, wherein the method comprises the following steps: in step S11, the parameters include, but are not limited to, one or more of model size, aggregate content, aggregate maximum particle size, particle size distribution factor, and gridded density.
5. The method for constructing the random heterogeneous continuous model of lightweight refractory according to claim 3, wherein the method comprises the following steps: in step S12, the limiting condition is that any pair of spherical aggregates do not intersect, and any spherical aggregate does not exceed the boundary of the model.
6. The method for constructing the random heterogeneous continuous model of lightweight refractory according to claim 3, wherein the method comprises the following steps: in step S12, the random coordinates of the center point of the aggregates and the size of each aggregate are generated by a pseudo random number generator.
7. The method for constructing the random heterogeneous continuous model of lightweight refractory according to claim 3, wherein the method comprises the following steps: in step S2, the element group is the aggregate part in the spherical aggregate random distribution finite element model.
8. The method for constructing the random heterogeneous continuous model of lightweight refractory according to claim 1, wherein the method comprises the following steps: in step S2, the content of each non-homogeneous component phase satisfies a two-parameter weber distribution, and the functional formula is:
wherein x is a variable, λ is a proportional parameter, and k is a shape parameter.
9. The method for constructing the random heterogeneous continuous model of the lightweight refractory material as claimed in claim 1, wherein the method comprises the following steps: in step S2, the properties of each of the heterogeneous component phases include mechanical properties that follow a birefringence strain softening curve.
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