JP2973190B2 - Design method of materials and structures by combined analysis of molecular simulation method and homogenization method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for designing a material and a structure by a combined analysis of a molecular simulation method and a homogenization method. For example, destruction due to heat or joining with a foreign material becomes a problem. Design and manufacture of the following products using new ceramic materials: ceramic base for high-speed computers, ceramic electrodes for molten fuel cells, heat-resistant tiles for spacecraft, electronic circuit products made from polycrystalline thin-film electronic materials, metals and Applied to ceramic coating tools and ceramic engines with ceramics joined. Further, the present invention, CO ₂ measures and the design and manufacture of ultra-fine ceramic filter turbine or the like for the purpose of high energy efficiency, the design and manufacture of conductor-superconductor material, magnetic material, a radiation having a new function, steel Design and manufacture of structures using polycrystalline materials consisting of single minerals such as aluminum and aluminum; design and manufacture of structures using polycrystalline materials consisting of various minerals such as granite; Design and manufacture of structures using a mixture of various types of minerals and substances that fill gaps, quality evaluation of agricultural land, industrial production of soil with new functions, drugs and useful biological varieties with new functions, It is applied to the development of microorganisms and genes.

[0002]

2. Description of the Related Art Most materials, such as steel, concrete, and rocks, as well as composite materials, contain various types of substances at the micro level or have a single substance but countless crystals (polycrystalline). Has microheterogeneity. When building mechanical structures such as automobiles or civil structures such as bridges using such materials, at present, in many cases, using macro-level specimens with micro-level non-homogeneity is not a problem. The macro phenomenological dynamics method of experimentally determining the material properties of the material and using it for structural design calculations has been adopted. At this time, it is said that a test piece having a size 10 times or more the size of the microstructure formed by assembling the micro components is required, but there is no firm basis. Also, from the viewpoint of time factors, the material properties obtained as an experimental result must be used within the range of the experiment time, but materials in an environment where the experiment is impossible, for example, Characteristics of shields (vitrified materials, iron containers, bentonite clay, surrounding rocks, etc.) in the geological disposal problem of high-level radioactive waste that must isolate radioactive materials from human society for more than 10,000 years A method for assessing has not been developed to date.

In the molecular simulation method, a physical system composed of a large number of particles such as atoms and molecules expressing positions and velocities numerically is given a physicochemical law such as a law of interaction between particles and a law of motion. Simulations are performed inside the system to determine the spatial coordinates of all particles under the laws of physicochemistry, and apply statistical thermodynamics to the results to apply various physicochemical properties (crystal structure properties, density And physical properties such as mechanical properties of materials, thermodynamic properties, etc.). (See Kawamura 1990). The physicochemical properties determined above are the macroscopic properties of the whole particles obtained through statistical thermodynamics.

[0004] The molecular simulation method includes the following three methods. Monte Carlo Method (MC) Molecular Mechanics Method (MM) Molecular Dynamics Method (Molecular Dynamics Method) The Monte Carlo method estimates the equilibrium distribution of particles using random numbers and uses the results. Is a method of statistically and thermodynamically determining the physicochemical properties of a material system, as described in Metropolis et al. (195
Developed by 3). The molecular mechanics method is usually applied to molecules composed of a finite number of atoms, and the structure and energy are optimized to estimate the equilibrium state of the particle system, and the results are used to estimate the physical This is a method of determining chemical properties by statistical thermodynamics, and is mainly used in the field of organic matter-related chemistry (Wiberg 1965; Boyd 1968). These two methods do not describe the time history motion of a material system composed of particles. On the other hand, molecular dynamics method
For a material system consisting of particles such as molecules, the force acting on each particle is determined by the law of interaction between particles, and under this acting force, the equation of motion of all particles is solved to determine the position and velocity of the particles at each time. It is a method for statistically and thermodynamically determining various macrophysical properties of material systems using the results (Alder and Wainwright 1957; Rahman 1964; Rahman
man and Stillinger 1972). The outline of each method is shown in FIG.

It is not possible to design by directly analyzing the behavior of mechanical structures such as automobiles and civil structures such as bridges using these molecular simulation methods. that is,
This is because structures of the size we usually use contain too many atoms and molecules. For example, only one mole of a substance (equivalent to a mass of 12 g with carbon ¹² C) is 6.022136
It is composed of 7 × 10 ²³ molecules. Ability current computer has is only molecular dynamics simulations of particle system also ¹⁰⁶ orders a using state-of-the-art parallel supercomputer is possible in the near future, the ability of computers dramatically Even if it is increased, it is unlikely that molecular design will allow direct design of structures.

[0006] The homogenization method is a mathematical theory expressing an object having a periodic repeating structure at a micro level by connecting a micro behavior and a macro behavior by introducing a perturbation method. -Pal
encia 1980) and Russia (Bakhvalov and Panasenko 1984)
(Fig. 2). Note that a single microstructure is called a unit cell. Here, the perturbation method is one method for obtaining an approximate solution of a nonlinear problem. In the perturbation method, the solution is usually exponentially expanded with a small parameter ε, and ε = 0
Based on the solution (standard system) at, an approximate solution is constructed by adding a small fluctuating solution for ε around it.

The outline of the homogenization method will be described for the simplest one-dimensional static elasticity problem. The problem is the differential equation

(Equation 1) Is represented by Here, u (ε, x) represents a displacement accompanied by a microscopic large fluctuation, E is an elastic coefficient, and f is a body force per unit volume. Note that the value of E varies significantly from place to place at the micro level. Now, assuming that the size of the microstructure is εY, the macro coordinate system x and the micro coordinate system y are connected to y = x / ε by the parameter ε (see FIG. 2), and a displacement u (ε, x) Perturbation expansion

(Equation 2) Is introduced. Here, u ₀ (x, y), u ₁ (x, y), u ₂ (x, y) are periodic conditions u _i (x, y + Y) = u _i (x, y) (i = 0 , 1,2). When such expansion in the two coordinate systems x and y is performed, the derivative with respect to x becomes

(Equation 3) Substituting the above perturbation approximation into the original differential equation, and assuming that each power term of ε is zero, the following relationship is obtained. First, for the ε ^-2 term,

(Equation 4) It is. This means that the first approximation term u ₀ is a function only in the macro coordinate system x, that is, u ₀ = u ₀ (x). Next, for the ε ^-1 term,

(Equation 5) It is. This equation is a differential equation in the micro coordinate system y for determining the second approximation term u ₁ ,

(Equation 6) Introduces the differential equation of the microproblem for the characteristic function N (y) in the unit cell

(Equation 7) Is obtained. Finally, for the ε ₀ term,

(Equation 8) It is. Integral averaging of this formula by the unit cell and dividing by the unit cell volume gives the function u _i (x, y)
Is a periodic function, so the second term on the left and right sides disappears, and the differential equation of the macro problem

(Equation 9) Is obtained. here,

(Equation 10) As the integral average operator

[Equation 11] And put it. This E ^* is called the homogenized elastic modulus. Thus, the microproblem is solved under the periodic condition, and the solution N (y)
Is used to determine the homogenized elastic modulus, and solving a macro problem having the same form as the original differential equation yields u ₀ . This u ₀
Since the N (y) u ₁ is determined from by substituting the equation epsilon ⁰ Section u
Ask for ₂ . However, the effect of the ε ² u ₂ (x, y) term is considered to be small.

(Equation 12) In many cases, the search for u ₂ is stopped. At this time,
The strain is

(Equation 13) Therefore, the stress of the object having the micro-periodic structure becomes

[Equation 14] It is determined. In addition, for the actual engineering problem, both the micro problem and the macro problem are solved by a numerical analysis method (mainly a finite element method) using a computer.

[0008]

The molecular simulation method and the homogenization method have been developed as completely independent fields, both with the background of the development of computers, and there has been no mutual interaction between the two methods. The problem with applying the homogenization method to micro-heterogeneous materials and structures made from such materials is how to determine the physical properties of each material (micro-component system) that constitutes the microstructure. is there. In other words, it is difficult to estimate the physicochemical properties (physical properties such as crystal structure properties, density and material mechanical properties, thermodynamic properties, etc.) of individual microscopically dispersed materials in a micro heterogeneous material. In many cases, the behavior of structures made from such materials could not be properly evaluated by the homogenization method. On the other hand, from the viewpoint of the molecular simulation method, it is impossible to apply this method to an object having a size that is technically significant. As described above, the molecular simulation method and the homogenization method have problems that cannot be solved by themselves. An object of the present invention is to compensate for the disadvantages of each of the molecular simulation method and the homogenization method, and to accurately estimate the behavior of a microheterogeneous material and a structure made from the material, thereby enabling a microheterogeneous method. It is to provide a means for designing various industrial products using materials.

[0009]

Means for solving the problems The method of designing materials and structures based on the combined analysis of the molecular simulation method and the homogenization method according to the present invention, which has been made to achieve the above object, has been developed on a micro level. The method is applied to an object made of a microheterogeneous material in which substances are mixed, and includes the following processes (A) to (D): (A) An object made of a microheterogeneous material is converted based on a predetermined coordinate system. Each material system that forms the microstructure, that is,
It is divided into micro component systems, and the physicochemical properties of each micro component system are determined as predetermined physical property values by a molecular simulation method. (B) The physical property values of the micro component system obtained by the molecular simulation method are introduced into the homogenization method, and the amounts of fields such as displacement, temperature, and stress generated in the object are calculated. (C) By comparing the amount of the field of the object obtained by the homogenization analysis with a predetermined reference value, it is predicted whether or not a problem such as destruction occurs in the object. (D) When a problem such as destruction is expected to occur in the object, the material or structure of the object is changed and
The process of (C) is repeated. Was implemented. That is, as shown in FIG. 3, the present invention applies a molecular simulation method to each material constituting a single microstructure for a microheterogeneous material and a structure made from the material. Determine various physicochemical properties (physical properties such as crystal structure properties, density and material mechanical properties, thermodynamic properties, etc.) of the system and apply the physicochemical properties of each material obtained to the homogenization method. In addition to determining the characteristics of the microheterogeneous material, the behavior of the structure made from the microheterogeneous material is analyzed and provided for the design. The amount of the field (stress, temperature, etc.) is changed by the homogenization method. When the environmental conditions of the molecular simulation method change, the gist is to conduct the molecular simulation analysis and the subsequent homogenization analysis again.

[0010]

According to the design method of materials and structures based on the combined analysis method of the molecular simulation method and the homogenization method of the present invention, a micro-heterogeneous material in which the geometrical shape of the micro-structure is determined, The molecular simulation method is applied to each micro component system to determine the physicochemical properties of the material system. Next, the homogenization method is applied by applying the physicochemical properties obtained by the molecular simulation method to each micro component system constituting the single micro structure. This action enables the properties of microheterogeneous materials to be determined and the behavior of structures made from microheterogeneous materials to be analyzed, allowing structures made from microheterogeneous materials to be rationally designed. You.

[0011]

Embodiments of the present invention will be described below with reference to the drawings. As a method of molecular simulation, a molecular dynamics method is used. The molecular dynamics method was applied to quartz and mica, which are the rock forming minerals of granite, to determine their elastic properties, and the results of molecular dynamics were applied to the mechanical properties of the rock forming minerals of granite whose shape was determined by microscopic observation And perform homogenization analysis.

In the molecular dynamics method, a material system composed of many particles is considered, a force acting on each particle is determined using a given interaction potential between particles, and all particles are simultaneously determined by a difference approximation equation of a motion equation. To obtain information such as the position and velocity of the particles over time. Further, various physical property values are estimated from the results obtained by applying the statistical thermodynamic relationship. FIG. 4 shows a series of calculation procedures of the molecular dynamics method.

As the interatomic potential for the rock mineral, a partial ionic two-body potential model is used.
This potential model is represented by Coul
omb interaction term, proximity repulsion interaction term, dipole-dipole interaction term in dispersion force (electric quadrupole potential term), intermolecular force / covalent potential term (Morse
Term) is added, and is represented by the following equation.

(Equation 15) Here, the following symbols were used. U _ij (r _ij ): represents a partial ionic two-body potential acting between the particle at position r _i and the particle at r _j . Note that r _ij is a distance between two particles, and r ^* _ij is a distance between equilibrium atoms of an ion pair in an ion molecule in vacuum. z _i , z _j : valences of i, j ions when the elementary charge is e. f ₀ : Material constant for unit matching. f ₀ = 1 [kca
1 / (molÅ)]. _{a i, b i, c i} , a j, b j, c j: is a constant unique to the ion species. It is determined so as to stably maintain the crystal structure at room temperature. D _ij : a constant representing the depth of the potential function. β _ij : a constant that determines the shape. Table 1 lists constants for quartz (SiO ₂ ) and Table 2 lists constants for muscovite (KAl ₂ [Si ₃ Al] O ₁₀ (OH) ₂ ). However, in the table, subscripts such as z _i and a _i are omitted. In the table, [] indicates a unit.

[Table 1]

[Table 2]

In the molecular dynamics method, the motion of a particle i is represented by the equation of motion.

(Equation 16) Is obtained by solving Where _mi is the mass of particle i, v
_i = dr _i / dt is the speed. Further, the force F _i is obtained from the action force F _ij = − ▽ U _ij between the particles i and j obtained by differentiating the potential U _ij.

[Equation 17] Is obtained. Here, ▽ represents a gradient operator. Since the details of the molecular dynamics calculation method are described in Kawamura 1990, they will not be described here. In this calculation, the NPT ensemble molecular dynamics method in which the number of particles N, the pressure P, and the temperature T are constant is applied. The basic cell shape was changed by applying a tensile or shearing force at predetermined time steps as boundary conditions. Note that the calculation was performed under the following conditions. Quartz: (x, y, z) = (5.147630, 8.
96122, 5.7808) [Å] A rectangular parallelepiped cell in which five basic cells were stacked in the x direction, three in the y direction, and four in the z direction was used. The total number of quartz molecules is set to 360, and the temperature is set to be constant at 300 ° K. Note that the target quartz crystal is a trigonal crystal. Muscovite: (x, y, z) = (5.158653,
8.954407, 20.05636) A cell in which six basic cells in [x] were stacked in the x direction, three in the y direction, and one in the z direction was used. The total number of molecules of muscovite is 72, and the temperature is set to be constant at 300 ° K. The target muscovite crystals are monoclinic.

The macro physicochemical properties of a material system are as follows:
Determined by applying statistical thermodynamics to the output results of molecular dynamics calculations (see Kawamura 1990). In this calculation, as described above,
The basic cell shape was changed by applying a tensile or shear force as a boundary condition, and the relationship between stress and strain as a macro response was obtained from the output results. The obtained elastic modulus
Table 3 shows the values of E and Poisson's ratio ν in comparison with the experimental results (Ahrens 1995).

[Table 3]

Calculation of a two-dimensional plane stress state uniaxial compression test in the longitudinal direction of the granite specimen shown in FIG.
Find the relationship between macro stress and strain. The dynamic model is shown in FIG. According to the microscopic observation, the microstructure of the granite has a shape represented by FIG. 6 (b). FIG.
The properties in Table 3 determined by molecular dynamics method are applied to the properties of each mineral in (b). However, the mechanical properties of biotite are the same as muscovite, and the properties of feldspar are determined from Ahrens (1995) as elastic modulus E = 69.70 [GPa] and Poisson's ratio ν = 0.301. As shown in FIG. 6 (a), as a boundary condition of the macro problem, 1,000 [kgf / c
m ² ]. As a result of the homogenization analysis, the distribution of micro stress was obtained as shown in FIG.

The process of designing a material by the proposed method will be described below. The most severe load was set, and Fig. 6 (a)
The homogenization analysis is performed under a simple load condition as shown in. Micro-stress distribution by homogenization analysis, for example,
It is obtained as shown in FIG. The safety at the micro level is evaluated by comparing the value of the micro stress of each constituent material with the strength of each constituent material obtained by the molecular simulation method. If the predetermined safety factor is ensured, the design process ends. If the specified safety factor is not ensured, change the molecular components of the constituent substances to determine the physical properties of the substance considered to be stronger by molecular simulation, and perform the homogenization analysis again, or The recalculation is performed by either changing the geometrical shape of the constituent material or repeating the calculation until a predetermined safety factor for each constituent material is secured.

The process of designing a structure by the proposed method will be described, taking as an example the case of designing an underground structure such as a tunnel or a power plant cavity in a granite bedrock. It is assumed that a horseshoe-shaped cross section was assumed in the initial design as shown in FIG. It is assumed that the microstructure system is determined in consideration of the influence of discontinuous surfaces such as joints included in the bedrock, and the physical properties of the substances such as minerals constituting the microstructure system have been determined by the molecular simulation method. When the homogenization analysis is performed, a micro stress distribution as shown in FIG. 7 is obtained at an arbitrary place.
In general, failure of the entire structure is caused by local stress exceeding the strength of the material and causing total failure. For example, FIG.
If part of the micro-stress at point A in (a) exceeds the strength of the constituent material, the shape of the structure is reexamined on the condition that the stress does not exceed the strength and that the macro-stress does not cause the total failure However, it is necessary to design as shown in FIG.

A method of designing a microheterogeneous material composed of a material exhibiting a time-dependent viscoelastic behavior and a structure made from the microheterogeneous material will be described. Determining the physical properties of each constituent material by the molecular simulation method is similar to the elasticity problem. However, if the substance is 2 as shown in FIG.
In the case of a Maxwell-type viscoelastic element, the elasticity coefficient E is calculated by applying statistical thermodynamics to the output result of the molecular dynamics calculation.
And the viscosity coefficient η must be determined. The one-dimensional static viscoelastic problem for this two-element Maxwell-type viscoelastic body is

(Equation 18) Therefore, the homogenization method is derived through a process similar to the elasticity problem. As a result of the homogenization analysis, a micro stress distribution as shown in FIG. 7 is obtained at each time step. Therefore, the micro stress and the macro stress are evaluated at each time, and the micro stress is produced from the micro heterogeneous material and the micro heterogeneous material. Evaluate the safety of structures and implement safe and rational design of their materials and structures.

An example of applying the proposed method to a new ceramic material and its structure will be described. The microstructure as shown in FIG. 6 (b) is found in many new ceramic materials. For example, a polycrystalline thin film electronic material has such a microstructure, and when an integrated circuit or the like is manufactured using the thin film material, locally excessive heat stress due to the microstructure during energization is caused. May occur, leading to total destruction. To solve this problem, the properties of each crystalline material forming the microstructure are determined by molecular simulation, and then the homogenization analysis is applied assuming the internal force due to heat instead of the external force shown in FIG. 6 (a). Evaluate the safety of new ceramic materials and their structures from micro stress distribution and macro stress distribution. In a ceramic coating tool (FIG. 10 (a)) in which metal and ceramics are joined, the ceramics coated on the surface form a microstructure as shown in FIG. 10 (b). However, there are problems in the state of stress generated during use, the presence or absence of breakage, and the like. To solve such problems, the characteristics of the coated ceramic material are determined by molecular simulation, and the deformation and fracture behavior of the structure in which the tool body, which is a metal material, is integrated is determined by homogenization analysis, and the micro stress Evaluate the safety of the whole structure from the distribution and macro stress distribution.

[0021] The destruction of the entire structure usually causes a total destruction when the local stress exceeds the strength of the material. Therefore, accurately predicting the distribution of micro stress is indispensable in designing a structure safely and economically. In the past, since it was not possible to accurately predict the distribution of stress due to such a microstructure, a high safety factor was set and a long-lasting design was required.

As described above, according to the material and structure design method based on the combined analysis of the molecular simulation method and the homogenization method of the present embodiment, the behavior of the microheterogeneous material and the structure made from the material can be precisely determined. It is possible to estimate
Means are provided for rational design of various industrial products using microheterogeneous materials.

[0023]

As described in detail above, the method of designing materials and structures based on the combined analysis of the molecular simulation method and the homogenization method according to the present invention has a problem that destruction due to heat or bonding with a foreign material is a problem. Design and manufacture of the following products using new ceramic materials: ceramic base for high-speed computers, ceramic electrodes for molten fuel cells, heat-resistant tiles for spacecraft, electronic circuit products made of polycrystalline thin-film electronic materials, metals ceramic coating tool formed by joining ceramics and ceramic engines and, CO ₂ measures and the design and manufacture of ultra-fine ceramic filter turbine or the like for the purpose of high energy efficiency, conductor-superconductor material, magnetic material, a radiation having a new function Designing and manufacturing bodies, designing structures using polycrystalline materials consisting of single minerals such as steel and aluminum Design and manufacture of structures using polycrystalline materials composed of various minerals such as artificial and granite in the limit state, structures using materials mixed with various minerals such as clay and concrete and materials that fill gaps Micro-heterogeneous materials, such as the design and manufacture of agricultural products, the evaluation of agricultural land quality, the industrial manufacture of soils with new functions, the development of drugs, useful biological varieties, microorganisms and genes with new functions, etc., and structures made from such materials Applying molecular simulation method to each material constituting a single microstructure for various physical and chemical properties (physical properties such as crystal structure properties, density and material mechanical properties, thermal properties, etc.) Mechanical properties,
Other) and apply the obtained physicochemical properties of each material to the homogenization method to determine the characteristics of the microheterogeneous material and analyze the behavior of the structure made from the microheterogeneous material. By providing for design, socially important microheterogeneous materials and structures made from microheterogeneous materials can be efficiently and economically designed and manufactured.

[References] 1) BJ Alder and TF Wainwright (1957): "Phase T
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[Brief description of the drawings]

FIG. 1 is an explanatory diagram of each method of molecular simulation.

FIG. 2 is an explanatory diagram of an object having a micro periodic structure.

FIG. 3 is an explanatory diagram of a combined solution method of a molecular simulation method and a homogenization method according to the present invention.

FIG. 4 is an explanatory diagram showing a flow of a procedure of molecular dynamics calculation.

FIG. 5 shows a specimen of a uniaxial compression test of granite,
(a) is an overall view, and (b) is a plan view.

FIG. 6 shows a granite microstructure (unit cell), (a) is an overall view, and (b) is a partially enlarged view.

FIG. 7 is a characteristic diagram showing a micro stress distribution obtained by homogenization analysis of a uniaxial compression test of granite.

FIG. 8 is a schematic cross-sectional view showing a process of evaluating a micro stress of an underground hollow structure excavated in a rock to design a safe structure.

FIG. 9 is a schematic view showing a two-element Maxwell-type viscoelastic body.

10A and 10B show a ceramic coating tool, wherein FIG. 10A is an overall view and FIG. 10B is a partially enlarged view.

Claims (1)

(57) [Claims] The present invention is applied to an object made of a micro-heterogeneous material in which various kinds of substances are mixed at a micro-level, and includes the following processes (A) to (D): (A) a micro-heterogeneous material Each substance system that forms a microstructure on the basis of a predetermined coordinate system for an object consisting of
It is divided into micro component systems, and the physicochemical properties of each micro component system are determined as predetermined physical property values by a molecular simulation method. (B) The physical property values of the micro component system obtained by the molecular simulation method are introduced into the homogenization method, and the amounts of fields such as displacement, temperature, and stress generated in the object are calculated. (C) By comparing the amount of the field of the object obtained by the homogenization analysis with a predetermined reference value, it is predicted whether or not a problem such as destruction occurs in the object. (D) When a problem such as destruction is expected to occur in the object, the material or structure of the object is changed and
The process of (C) is repeated. A material and structure design method based on a combined analysis of a molecular simulation method and a homogenization method, characterized in that the method is performed.