JP2020060850A - Method of analyzing composite material and computer program for analyzing composite material - Google Patents

Abstract

To provide a composite material analysis method configured to predict fracture of a composite material, and a computer program for analyzing composite materials.SOLUTION: A composite material analysis method, which is a method of analyzing composite materials based on molecular dynamics using a computer includes: a first step of preparing, by the computer, an analysis model for a composite material including a composite material model generated by modeling the composite material; a second step of setting a threshold to an interparticle distance between at least a pair of particles belonging to the composite material model to be analyzed in the analysis model and bonded by interparticle bond; a third step of executing first numerical analysis of the analysis model by breaking the interparticle bond when the interparticle distance is equal to or larger than the threshold; a fourth step of setting conditions different from those applied in the second step and executing second numerical analysis of the analysis model; and a fifth step of calculating fracture characteristics of the composite material on the basis of at least the first numerical analysis and the second numerical analysis.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a composite material analysis method and a composite material analysis computer program, for example, a composite material analysis method and a composite material analysis computer program containing two or more substances.

  Conventionally, a method for simulating a composite material using molecular dynamics has been proposed (see, for example, Patent Document 1). In the composite material simulation method described in Patent Document 1, after a polymer model and a filler model are created in the model creation region, the polymer model is bonded to the bonding position on the surface of the filler model. Accordingly, the composite material analysis method described in Patent Document 1 makes it possible to analyze the influence of the bonding state of the polymer particles on the filler surface on the material characteristics of the composite material.

JP, 2005-064242, A

  By the way, in order to accelerate the development of rubber materials that improve the wear resistance of tires, it is helpful to clarify the mechanism of destruction of the nanostructure due to the deformation of the rubber material. By analyzing the fracture of the nanostructure of the rubber material before and after deformation, it is possible to accelerate the development of materials for improving the fracture strength of the filler-filled rubber used in actual tires.

  However, in the conventional numerical analysis using molecular dynamics, in order to analyze the destruction of the nanostructure due to the deformation of the rubber material, it is necessary to break and erase the interparticle bond of the polymer particles in the rubber material. Therefore, even if the polymer model after fracture is analyzed, the interparticle bond has already disappeared, so it is not possible to identify the fracture site, and it is difficult to analyze the mechanism of destruction of the nanostructure of the rubber material. It was Further, even if the breakage point could be specified, it was difficult to predict the breakage of the rubber material.

  The present invention has been made in view of such circumstances, and an object thereof is to provide a composite material analysis method and a composite material analysis computer program capable of predicting fracture of the composite material.

  A method for analyzing a composite material according to the present invention is a method for analyzing a composite material by a molecular dynamics method using a computer, wherein the computer includes a composite material model in which the composite material is modeled And a second step of setting a threshold value for the interparticle distance of at least a pair of particles that belong to the analysis target composite material model in the analysis model and are bonded by interparticle bonding, When the inter-particle distance is equal to or more than the threshold value, the third step of performing the first numerical analysis of the analysis model by breaking the inter-particle bond and the condition different from the condition given in the second step are set. The fracture characteristics of the composite material are set based on the fourth step of setting and executing the second numerical analysis of the analysis model, and at least the first numerical analysis and the second numerical analysis. A fifth step of leaving, characterized in that it comprises a.

  According to the composite material analysis method of the present invention, it is possible to perform numerical analysis under a plurality of different conditions. Therefore, the composite material analysis method according to the present invention can calculate the fracture characteristics based on a plurality of numerical analyses. As a result, the method for analyzing a composite material according to the present invention can calculate fracture characteristics more accurately. Since the breaking process can be performed in a pseudo manner, it is possible to numerically analyze the analysis model even if the interparticle distance is equal to or larger than the threshold value, because the interparticle bond is not erased by the break. Accordingly, the method for analyzing a specific substance can prevent physical disappearance of interparticle bonds due to breakage, so that pseudo breakage of interparticle bonds can be reproduced.

  In the method for analyzing a composite material according to the present invention, it is preferable that the first numerical analysis and the second numerical analysis perform different molecular dynamics methods. By this method, numerical analysis under different conditions can be executed in the same analysis model. As a result, since a plurality of numerical analyzes can be executed, the fracture characteristics can be calculated with higher accuracy.

  In the composite material analysis method of the present invention, it is preferable that the computer creates a plurality of the analysis models in the first step. By this method, it is possible to create a plurality of analytical models with different conditions. As a result, it is possible to evaluate the nanostructure of the composite material and the influence of the deformation conditions on the judgment of the composite material.

  In the composite material analysis method of the present invention, it is preferable that the computer creates the analysis model for executing the finite element method in the first step. By this method, in addition to the analytical model for executing the molecular dynamics method, an analytical model for executing the finite element method can be created. As a result, it becomes possible to perform numerical analysis in a number of different ways.

  In the composite material analysis method of the present invention, it is preferable that the computer executes the molecular dynamics method and the finite element method in the fourth step. This method makes it possible to compare the results of different numerical analyses. As a result, the fracture characteristics can be calculated with higher accuracy.

  In the composite material analysis method of the present invention, it is preferable that the computer reflects the result of the numerical analysis by the molecular dynamics method and creates the analysis model for executing the finite element method. By this method, the result of the numerical analysis of the molecular dynamics method can be included in the analytical model of the finite element method, which is different in scale from the analytical model of the molecular dynamics method. As a result, the fracture characteristics can be calculated with higher accuracy.

  In the composite material analysis method of the present invention, it is preferable that in the fourth step, the computer calculates the fracture characteristics based on a result of numerical analysis of the plurality of analysis models. With this method, the fracture characteristics can be calculated based on a plurality of analytical models. As a result, it is possible to eliminate the influence of variations caused by the analysis model. As a result, the fracture characteristics can be calculated with higher accuracy.

  In the composite material analysis method of the present invention, it is preferable that the computer compares the results of the numerical analysis of a plurality of the analysis models. As a result, it becomes possible to compare the results of a plurality of numerical analyzes under different conditions. This makes it possible to evaluate the nanostructure of the composite material and the influence of deformation conditions. As a result, the fracture characteristics can be calculated more accurately.

  In the composite material analysis method of the present invention, it is preferable that, in the fourth step, the computer execute an operation based on a result of the numerical analysis and calculate the fracture characteristics based on the operation result. By this method, the fracture characteristics of the composite material can be analyzed using the results of the numerical analysis. As a result, the fracture characteristics can be calculated with higher accuracy.

  In the composite material analysis method of the present invention, in the third step, the computer calculates a progress until the inter-particle bond accompanying the breaking process is broken, and in the fourth step, the inter-particle bond is calculated. It is preferable to calculate the characteristic value regarding the fracture of the composite material based on the progress until the fracture. By this method, the breaking characteristics can be calculated without breaking the interparticle bond. As a result, the amount of calculation can be reduced, and the fracture characteristics can be efficiently calculated.

  A computer program for analyzing a composite material of the present invention is characterized by causing a computer to execute the above-described method for analyzing a composite material.

  According to the computer program for analyzing a composite material of the present invention, it is possible to execute numerical analysis under a plurality of different conditions. Therefore, the composite material analysis method according to the present invention can calculate the fracture characteristics based on a plurality of numerical analyses. As a result, the method for analyzing a composite material according to the present invention can calculate fracture characteristics more accurately. Since the breaking process can be performed in a pseudo manner, it is possible to numerically analyze the analysis model even if the interparticle distance is equal to or larger than the threshold value, because the interparticle bond is not erased by the break. Accordingly, the method for analyzing a specific substance can prevent physical disappearance of interparticle bonds due to breakage, so that pseudo breakage of interparticle bonds can be reproduced.

  According to the present invention, a composite material analysis method and a composite material analysis computer program capable of predicting fracture of a composite material can be realized.

FIG. 1 is a flowchart showing an outline of an example of a method for analyzing a composite material according to an embodiment of the present invention. FIG. 2 is a conceptual diagram showing an example of an analytical model of a composite material according to an embodiment of the present invention. FIG. 3 is a conceptual diagram showing an example of a composite material analysis model according to an embodiment of the present invention. FIG. 4 is a conceptual diagram showing an example of an analytical model of a composite material according to an embodiment of the present invention. FIG. 5 is a partial cross-sectional view showing a part of the meridional cross section of the tire model shown in FIG. FIG. 6 is a conceptual diagram of a method of creating the analysis model shown in FIG. FIG. 7A is an explanatory diagram of fracture positions of interparticle bonds in the model creation region. FIG. 7B is an explanatory diagram of fracture positions of interparticle bonds in the model creation region. FIG. 7C is an explanatory diagram of fracture positions of interparticle bonds in the model creation region. FIG. 8 is a flowchart showing a flow of processing of the first numerical analysis according to the embodiment of the present invention. FIG. 9 is a flowchart showing a flow of processing of the second numerical analysis according to the embodiment of the present invention. FIG. 10 is a flowchart showing a flow of processing for calculating a fracture characteristic value according to the embodiment of the present invention. FIG. 11 is a diagram for explaining a method of calculating a fracture characteristic value according to the embodiment of the present invention. FIG. 12 is a functional block diagram of a composite material analysis method and an analysis apparatus that executes the composite material analysis method according to the present embodiment. FIG. 13 is a diagram for explaining the result of the numerical analysis according to the example of the present invention. FIG. 14 is a diagram for explaining the result of the numerical analysis according to the example of the present invention.

  Hereinafter, each embodiment of the present invention will be described in detail with reference to the accompanying drawings. It should be noted that the present invention is not limited to each of the following embodiments and can be implemented by appropriately changing it. In addition, although an example in which the composite material to be analyzed includes a polymer and a filler is described below, the present invention is also applicable to a composite material containing two or more kinds of substances. The present invention is also applicable to composite materials containing substances other than fillers and polymers.

  FIG. 1 is a flowchart showing an outline of a method for analyzing a composite material according to this embodiment. As shown in FIG. 1, the composite material analysis method according to the present embodiment includes a first step ST11, a second step ST12, a third step ST13, a fourth step ST14, and a fifth step ST15. , A method for analyzing composite materials by a molecular dynamics method using a computer.

  In the first step ST11, the computer creates, for example, an analytical model of a composite material including a polymer model that models a polymer and a filler model that models a filler.

  In the second step ST12, the computer sets a threshold value for the interparticle distance of at least a pair of particles that belong to the first substance model or the second substance model that is an analysis target and are coupled by interparticle coupling.

  In the third step ST13, the computer executes the first numerical analysis of the analysis model by breaking the interparticle bond when the interparticle distance is equal to or greater than the threshold value.

  In the fourth step ST14, the computer sets conditions different from the conditions set in the second step ST12 in the analysis model. In the fourth step ST14, the second numerical analysis is executed according to the set conditions.

  In the fifth step ST15, the computer at least based on the results of the first numerical analysis executed in the third step ST13 and the second numerical analysis executed in the fourth step ST14, the fracture characteristics of the composite material. To calculate.

  FIG. 2 is a conceptual diagram showing an example of the first analysis model 1-1 of the composite material according to the present embodiment. As shown in FIG. 2, the first analysis model 1-1 is modeled in a model creation area A, which is a virtual space of a substantially cubic shape with one side having a distance L, for example. The model creating area A is a three-dimensional space extending in the X-axis, Y-axis, and Z-axis directions that are orthogonal to each other. The first analysis model 1-1 includes four filler models 11A-1, 11B-1, 11C-1, 11D-1 in which a plurality of filler particles 11a-1 are modeled, and a plurality of polymer particles 21a-1. And four polymer models 21-1 in which the binding chain 21b-1 was modeled. Hereinafter, the four filler models 11A-1, 11B-1, 11C-1, 11D-1 may be simply referred to as the filler model 11-1 unless distinction is required. In the example shown in FIG. 2, the first analysis model 1-1 is an example in which four filler models 11A-1, 11B-1, 11C-1, 11D are modeled, but the first analysis model 1-1 is modeled. There is no limit to the number of filler models that can be used. The first analysis model 1-1 may include less than four filler models 11-1 and may include more than four filler models 11-1. Further, in FIG. 2, only four polymer models 21-1 are shown, but in the first analysis model 1-1, a plurality of polymer models 21 exist over the entire area of the model creation area A. There is. Further, in the example shown in FIG. 2, the model creating area A is an example of a virtual space having a substantially rectangular parallelepiped shape, but may have any shape such as a spherical shape, an elliptical shape, a rectangular parallelepiped shape, or a polyhedral shape.

  The filler model 11-1 is modeled in a state where a plurality of filler particles 11a-1 are gathered in a substantially spherical body. Further, the filler models 11-1 are arranged in a state of being separated from each other by a predetermined distance. The outer edge portions of the filler model 11-1 and the filler model 11-1 may be covalently linked to each other in a state of being aggregated with each other.

  Examples of the filler include carbon black, silica, alumina and the like. The filler particles 11a are modeled by gathering a plurality of filler atoms. In addition, the filler particles 11a-1 constitute a filler particle group in which a plurality of filler particles 11a-1 are aggregated. The relative position of the filler particles 11a-1 is specified by the bonding chains (not shown) between the plurality of filler particles 11a-1. This bond chain (not shown) has a function as a spring in which the equilibrium length, which is the bond distance between the filler particles 11a-1, and the spring constant are defined, and binds between the filler particles 11a-1. . The bond chain is a bond in which the relative position of the filler particles 11a-1 and the potential at which a force is generated by twisting, bending, etc. are defined. The filler model 11-1 is numerical data including the mass, volume, diameter and initial coordinates of the filler particles 11a-1 for handling the filler by molecular dynamics. Numerical data of the filler model 11-1 is input to the computer.

  Examples of the polymer include rubber, resin, and elastomer. The polymer particles 21a-1 are modeled by gathering a plurality of polymer atoms. Further, the polymer particles 21a-1 form a polymer particle group by assembling a plurality of polymer particles 21a-1. A modifier, which enhances the affinity with the filler, is added to the polymer as needed. Examples of the modifier include a hydroxyl group, a carbonyl group, and a functional group of an atomic group. The polymer model 21-1 is modeled by packing a plurality of polymer atoms and polymer particles 21a-1 which are an aggregate of a plurality of polymer atoms in a model creating region A at a predetermined density. The polymer particles 21a-1 are linked by the linking chains 21b-1 between the plurality of polymer particles 21a-1, and the relative position is specified. The bonding chain 21b-1 has a function as a spring in which an equilibrium length, which is a bonding distance between the polymer particles 21a-1, and a spring constant are defined, and binds between the polymer particles 21a-1. The bonding chain 21b-1 is a bond in which the relative position of the polymer particle 21a-1 and the potential at which a force is generated due to twisting, bending, etc. are defined. Further, the binding chain 21b-1 is also bonded as a cross-linking bond (not shown) between the polymer models 21-1 in which a plurality of polymer particles 21a are connected in series. This polymer model 21-1 is numerical data (including mass, volume, diameter, initial coordinates, etc. of the polymer particles 21a-1) for handling the polymer by molecular dynamics. Numerical data of the polymer model 21-1 is input to the computer.

  In the first analysis model 1-1, various physical quantities are acquired by numerical analysis by the molecular dynamics method. Examples of numerical analysis include deformation analysis such as extension analysis and shear analysis, and motion analysis such as relaxation analysis. As the physical quantity acquired by these motion analysis, a value such as a displacement obtained as a result of the motion analysis may be used, or a strain obtained by executing a predetermined calculation process may be used. Among these, as the motion analysis, the deformation analysis is preferable from the viewpoint that the mechanical properties of the compound of the composite material can be analyzed.

  In the present embodiment, in order to calculate the fracture characteristics, in addition to the first analysis model 1-1, a second analysis model 1-2 different from the first analysis model 1-1 is created. FIG. 3 is a conceptual diagram showing the second analysis model 1-2.

  As shown in FIG. 3, the second analytical model 1-2 includes filler models 11A-2, 11B-2, 11C-2, 11D-2, a plurality of polymer particles 21a-2, and a bonding chain 21b-2. And four polymer models 21-2 modeled. The four filler models 11A-2, 11B-2, 11C-2, 11D-2 may be simply referred to as the filler model 11-2. The filler model 11-2 is modeled in a state where a plurality of filler particles 11a-2 are aggregated into a substantially spherical body. In this case, each element included in the second analysis model 1-2 is created under the same condition as each element included in the first analysis model 1-1, for example. In the present embodiment, different numerical analyzes are performed on the first analysis model 1-1 and the second analysis model 1-2. Then, in the present embodiment, the fracture characteristics of the composite material are calculated based on the result of the numerical analysis for the first analysis model 1-1 and the result of the numerical analysis for the second analysis model 1-2.

  In the following, a case of comparing the results of two analysis models will be described, but this is an example and does not limit the present invention. In the present invention, for example, the numerical analysis may be executed using three or more analytical models, and the fracture of the composite material may be predicted based on the result of the numerical analysis.

  3 shows a model for executing the molecular dynamics method as the second analysis model 1-2, but this is an example and does not limit the present invention. Specifically, the second analysis model 1-2 may be a model for executing a continuum simulation. More specifically, the second analysis model 1-2 may be, for example, a model for executing a finite element method (FEM). Hereinafter, a tire model will be described as the second analysis model 1-2, but this does not limit the composite material of the present invention by way of example.

  FIG. 4 is a conceptual diagram showing an example of the second analysis model 1-2A. FIG. 5 is a partial cross-sectional view showing a part of the meridional cross section of the tire model as the second analysis model 1-2A. As shown in FIG. 4, the second analysis model 1-2A according to the present embodiment is, for example, a three-dimensionally modeled first analysis model 1-1 including the shape of a tire as a composite material. It is a model for analysis of a relatively large composite material. In other words, the second analysis model 1-2A is an analysis model having a different scale from that of the first analysis model 1-1. The second analysis model 1-2A is a model that can be analyzed by a computer (analysis model) that is used to create a basic tire model by performing eigenvalue analysis using a numerical analysis method such as a finite element method and a finite difference method. Is. The second analysis model 1-2A includes a mathematical model and a mathematical discretized model. In this embodiment, the finite element method is used as the analysis method used when creating the tire model. Since the finite element method is an analysis method suitable for structural analysis, it can be suitably applied especially to a structure such as a tire.

  In the second analysis model 1-2A, the tire is divided into a finite number of elements composed of a plurality of nodes, and the basic tire model shown in FIGS. 4 and 5 is created. In the finite element method used for analysis, a tire for evaluating tire performance (for example, wear resistance performance and uneven wear resistance performance) is divided into a finite number of elements E1, E2, ... A second analysis model 1-2 as a model is created. Each element E is composed of a plurality of nodes N1. For example, when the element E is a quadrilateral element in a two-dimensional analysis model, one element E is composed of four nodes N1. Further, when the element E is a hexahedral element in the three-dimensional analysis model, one element E is composed of eight nodes N1. The model creating unit 52 a (see FIG. 12) stores the created second analysis model 1-2 in the storage unit 54.

  FIG. 6 is a conceptual diagram of a method for creating an analysis model of a composite material according to the embodiment of the present invention. In the second analysis model 1-2A, the first analysis model 1-1 obtained by the molecular dynamics method is divided into a plurality of meshes in the model creation area A. For example, the second analysis model 1-2 is a model in which five filler models 11-2 are dispersed in the model creation area B. Here, the parameter of each element / region of the second analysis model 1-2A which is the continuum model is set from the result of the numerical analysis of the molecular dynamics of the first analysis model 1-1.

  Next, the method of analyzing the composite material according to this embodiment will be described in detail. In the first step ST11, a filler material 11 in which a plurality of filler particles 11a are aggregated and modeled, and a composite material including a polymer model 21 in which a plurality of polymer particles 21a are connected via a bonding chain 21b and modeled A first analysis model 1-1 is created. In addition, when creating a model for executing molecular dynamics as the second analysis model 1-2, the description is omitted because it is the same as the method of creating the first analysis model 1-1.

  In the first step ST11, the interaction is set between the created filler model 11-1 and polymer model 21-1. Examples of the interaction between the filler model 11-1 and the polymer model 21-1 include chemical interaction such as intermolecular force and attractive force such as hydrogen bond and repulsive force, and physical interaction such as covalent bond. The action is included. It should be noted that the interaction between the filler model 11-1 and the polymer model 21-1 is caused by the filler particles 11a-1, between the polymer particles 21a-1, and between the filler particles 11a-1 and the polymer particles 21a-1. It is set as needed. Therefore, not all the filler particles 11a-1 and the polymer particles 21a-1 are necessarily set. Further, when the polymer model 21-1 is composed of a plurality of types of polymer particles 21a-1, the interactions may be set to each of the plurality of types of polymer particles 21a-1. Further, the interaction between each of the plurality of types of polymer particles 21a-1 and the filler model 11-1 may be the same or different. For example, the interaction between the polymer particles A and the filler particles 11a-1 and the interaction between the polymer particles B and the filler particles 11a-1 may be set differently.

  Next, in the second step ST12, a predetermined threshold value is set for the interparticle distance of the polymer particles 21-1a. As the interparticle distance, the length of the binding chain 21b-1 connecting the polymer particles 21a-1 may be used, or the linear distance between the pair of polymer particles 21a-1 may be used. Note that, in the present embodiment, an example in which a predetermined threshold is set for the interparticle distance of the pair of polymer particles 21a-1 to be analyzed in the second step ST12 will be described, but the present invention is not limited to this. . The threshold value of the interparticle distance may be set to the interparticle distance between the pair of filler particles 11a-1 according to the composite material to be analyzed.

  Next, in the third step ST13, the interparticle bond is calculated using the fracture bond calculation function that reduces at least one of the bond energy and the bond force of the interparticle bond of the polymer particles 21a, and the first numerical analysis is executed. .

  Next, in the fourth step ST14, conditions different from those in the third step ST13 are given to the first analysis model 1-1. In the fourth step ST14, the second numerical analysis is executed according to the set conditions. For example, the second numerical analysis is a simulation for evaluating the growth of voids in the first analysis model 1-1.

  Next, in the fifth step ST15, the fracture characteristics are calculated based on at least two analysis results. In the present embodiment, for example, the fracture characteristics are calculated based on the results of the first numerical analysis and the second numerical analysis.

  Specifically, in the present embodiment, a predetermined threshold is set for the interparticle distance between the pair of polymer particles 21a-1, and when the interparticle distance is equal to or greater than the threshold, the interparticle distance is less than the threshold S. On the other hand, the interparticle bond is calculated by using the breaking bond calculation function that reduces the bond energy and the bond force of the interparticle bond. Examples of the breakage bond calculation function include those shown in the following formula (1). By using this breaking bond calculation function, when the inter-polymer particle distance is less than a predetermined threshold value, the binding energy and the binding force are increased or decreased according to the inter-particle distance between the pair of polymer particles 21a-1. When the distance is equal to or greater than the predetermined threshold value S, the binding energy and the binding force are zero. In addition, about the following formula (1), it can be changed as appropriate within the range in which the effect of the present invention is exhibited. In the following, an example in which the binding energy is reduced will be described, but the same can be applied to the case where the binding force is reduced.

  As described above, according to the above-described embodiment, in the region where the interparticle distance is equal to or more than the threshold value, at least one of the binding energy and the binding force of the interparticle bond decreases, and thus the first analysis without breaking the interparticle bond. It becomes possible to continue the numerical analysis of the application model 1-1. As a result, it is possible to prevent the physical disappearance of the interparticle bond due to the breakage, and it is possible to reproduce the pseudo disconnection without physically extinguishing the interparticle bond. Therefore, it is possible to realize a method for analyzing a composite material, which makes it possible to specify the fractured portion of the interparticle bond that has fractured during numerical analysis.

  Further, in the above-described embodiment, an example in which the interparticle bond is calculated by applying a predetermined breaking bond calculation function when the interparticle distance of the polymer particles 21a-1 is equal to or greater than the threshold value has been described, but the present invention is not limited thereto. Not a thing. For example, when the time average value of the interparticle distance is equal to or more than the threshold value, the numerical analysis of the first analysis model 1-1 is performed using the fracture bond calculation function that reduces the bond energy and the bond force of the interparticle bond. You may execute. As a result, for example, a breakage bond calculation function that reduces the bond energy and bond force of the interparticle bond in the pair of polymer particles 21a-1 whose interparticle distance has temporarily become equal to or greater than the threshold due to Brownian motion or the like is used. Operations can be excluded. As a result, it becomes possible to accurately reproduce the breakage of the interparticle bond in the actual composite material.

  By the way, when there are a plurality of pairs of polymer particles 21a-1 connected by interparticle bonds, after the numerical analysis of the first analysis model 1-1, the interparticle distances of the plurality of pairs of polymer particles 21a-1. Sequentially becomes the threshold value S or more. Then, at least one of the binding energy and the binding force of the interparticle bond is sequentially lowered. In this case, even if each of the coordinates of the polymer model 21-1 in which at least one of the binding energy and the binding force of the interparticle bond is lowered is specified, it may not always be possible to sufficiently evaluate each accurate break position. .

  Therefore, in the above embodiment, the coordinates of the interparticle bond at the time when the interparticle distance becomes equal to or larger than the threshold value may be specified and evaluated as the fracture position. 7A to 7C are explanatory diagrams of fracture positions of interparticle bonds in the model creation region A. Note that FIG. 7A shows the state of the first analysis time T1, FIG. 7B shows the state of the second analysis time T2, and FIG. 7C shows the state of the third analysis time T3.

In the present embodiment, the positions of the interparticle bonds where the binding energy and the binding force of the interparticle bonds have decreased are specified for each of a plurality of analysis times. In the example illustrated in FIG. 7A, at the first analysis time T1, the polymer model 21A-1 has a fracture bond chain 21bx in which the interparticle distance in the vicinity of the filler model 11-1 is the threshold value S or more and the binding energy or the binding force is decreased. -1 has occurred. In the polymer models 21B-1 and 21C-1 existing in the vicinity of the filler model 11, the interparticle distance of the polymer particles 21a-1 is less than the threshold value S, and the binding chain 21b-1 remains. At the first analysis time T1, the coordinates of the polymer model 21A-1 are specified as the break coordinates X ₁ .

Next, at the second analysis time T2 after the lapse of a predetermined time, in the polymer model 21B-1, the interparticle distance in the vicinity of the filler model 11-1 becomes the threshold value S or more, and the bond energy or the bond strength is decreased. 21bx-1 has occurred. In the polymer model 21C-1 existing in the vicinity of the filler model 11-1, the interparticle distance of the polymer particles 21a-1 is less than the threshold value S, and the binding chain 21b-1 remains. On the other hand, in the polymer model 21A-1 separated from the filler model 11-1 by the movement, the broken bond chain 21bx-1 in which the bond energy or the bond strength is reduced is maintained. In the second analysis time T2, to identify the model polymer 21B-1 of the coordinates as the new fracture coordinates _{X 2,} the current coordinates of the model polymer 21A-1 already has broken tether 21Bx-1 generated in the first analysis time T1 Is not newly specified as a break coordinate.

  Further, at the third analysis time T3 after the lapse of a predetermined time, in the polymer model 21C-1, the interparticle distance in the vicinity of the filler model 11-1 becomes the threshold value S or more, and the binding energy or the binding force is reduced. -1 has occurred. In the polymer models 21A-1 and 21B-1 separated from the surface of the filler model 11-1 by the movement, the interparticle bond of the polymer particles 21a-1 becomes the threshold value S or more and the broken bond chain 21bx-1 is maintained. At the third analysis time T3, the coordinates of the polymer model 21C-1 are newly specified as the break coordinates X3. The current coordinates of the polymer model 21A in which the broken bond chain 21bx-1 has already been generated at the first analysis time T1 and the current coordinates of the polymer model 21B-1 in which the broken bond chain 21bx-1 has already been generated at the second analysis time T2 are Not specified as break coordinates.

In this way, for example, the filler model 11-1 is obtained by sequentially specifying the fracture coordinates X _{1 to} X ₃ in which the interparticle distance becomes the threshold value S or more during the continuous first analysis time T1 to third analysis time T3. The distance from the surface and the coordinate distribution of the break coordinates are obtained. Thereby, in the numerical analysis of the first analysis model 1-1 shown in FIGS. 7A to 7C, the coordinate distribution of the fracture coordinates X _{1 to} X ₃ increases as the distance from the filler model 11-1 becomes shorter. I understand. From this result, the place where the interparticle bond is likely to be broken can be evaluated, so that the relationship between the distance from the surface of the filler model 11-1 and the breaking probability can be evaluated.

  In the example shown in FIGS. 7A to 7C, a representative point may be set in the interparticle bond to specify the breakage position (breakage coordinate). For example, in the example shown in FIG. 7A, the center of gravity (middle point) with the pair of polymer particles 21a-1 in the bonding chain 21b-1 which is an interparticle bond, or the end point overlapping the coordinates of the polymer particles 21a-1 is a representative point. Is specified as the fracture position. This makes it possible to evaluate the coordinates of the representative point of the interparticle bond having the increased length as the fracture position, which facilitates the assessment of the fracture position.

Further, in the example shown in FIGS. 7A to 7C, the inter-particle bond in which the inter-particle distance becomes a predetermined value or more may be visualized. Accordingly, since it is possible to visually confirm the broken bond chain 21bx-1 which is the interparticle bond between the pair of pseudo-broken polymer particles 21a-1, it is possible to confirm the broken portion of the broken interparticle bond during the numerical analysis. Identification becomes easy. Similarly, the breaking coordinates X _{1 to} X _{3 in} which the interparticle bond is broken and the broken bond chain 21bx-1 is generated may be visualized. This makes it possible to visually evaluate the locations where the breakage is likely to occur, and thus facilitate the evaluation of the locations where the breakage is likely to occur. Also, the representative points may be visualized. As a result, the representative point is visualized without visualizing the whole interparticle bond having the increased length, so that the broken interparticle bond can be easily confirmed. The visualization of the interparticle bond may be performed by, for example, hiding the bonding chains 21b other than the breaking bonding chain 21bx-1, increasing the transparency of the bonding chain 21b-1, and determining the color and the thickness of the breaking bonding chain 21bx-1. The length may be changed to the binding chain 21b-1 and displayed. As a result, the broken bond chain 21bx-1 can be emphasized and can be easily confirmed visually.

  A method of calculating a characteristic value using the first analysis model 1-1 according to this embodiment will be described with reference to FIG. 8. FIG. 8 is a flowchart showing an example of a process of calculating a characteristic value using the first analysis model 1-1.

  First, in the present embodiment, the first analysis model 1-1 for executing the numerical analysis is created (step ST21). Then, the present embodiment proceeds to step ST22.

  Next, the present embodiment sets the first analysis condition for executing the numerical analysis on the first analysis model 1-1 (step ST22). Here, a plurality of analysis conditions for carrying out a plurality of numerical analyzes with the first analysis model 1-1 may be set. Then, the present embodiment proceeds to step ST23.

  Next, in the present embodiment, the first numerical analysis is performed according to the set first analysis condition (step ST23). Here, when a plurality of analysis conditions are set in step ST22, a plurality of numerical analyzes may be performed. Then, the present embodiment proceeds to step ST24.

  Then, the present embodiment calculates the first characteristic value based on the analysis result of the first numerical analysis (step ST24). Then, in this embodiment, the process of FIG. 5 ends.

  A method of calculating the characteristic value using the second analysis model 1-2 according to this embodiment will be described with reference to FIG. 9. FIG. 9 is a flowchart showing an example of a process of calculating a characteristic value using the first analysis model 1-1.

  First, in the present embodiment, the second analysis model 1-2 for executing the numerical analysis is created (step ST31). Here, the second analysis model 1-2 is created under conditions different from those of the first analysis model 1-1. In addition, when the second analysis model 1-2 is, for example, an analysis model for executing the finite element method, the second analysis model 1-2 is based on the result of the first numerical analysis illustrated in FIG. It is preferable to create the model 1-2. Thereby, the result of the numerical analysis of the molecular dynamics method can be included in the analysis model of the finite element method. As a result, the fracture characteristics can be calculated with higher accuracy. Then, the present embodiment proceeds to step ST32.

  Next, in the present embodiment, the second analysis model 1-2 is set with the second analysis condition for executing the numerical analysis (step ST32). Here, the second analysis condition may be the same as or different from the first analysis condition. Further, a plurality of analysis conditions may be set in order to carry out a plurality of numerical analyzes with the second analysis model 1-2. Then, the present embodiment proceeds to step ST33.

  Next, in the present embodiment, the second numerical analysis is performed according to the set second analysis condition (step ST33). Here, when a plurality of analysis conditions are set in step S32, a plurality of numerical analyzes may be performed. Then, the present embodiment proceeds to step ST34.

  Then, in the present embodiment, the second characteristic value is calculated based on the analysis result of the second numerical analysis (step ST34). Then, in the present embodiment, the processing of FIG. 9 ends.

  Next, the process of calculating the fracture characteristic value will be described with reference to FIG. FIG. 10 is a flowchart showing the flow of processing for calculating the fracture characteristic value.

  First, in the present embodiment, the first characteristic value and the second characteristic value are acquired (step ST41). Specifically, the present embodiment acquires the first characteristic value calculated by the first analysis model 1-1 and the second characteristic value calculated by the second analysis model 1-2. Then, the present embodiment proceeds to step ST42.

  Next, in the present embodiment, the fracture characteristic value is calculated based on the first characteristic value and the second characteristic value acquired in step ST41 (step ST42). Then, in this embodiment, the processing of FIG. 7 ends.

  A method of calculating the fracture characteristic value will be described with reference to FIG. FIG. 11 is a schematic diagram for explaining the method of calculating the fracture characteristic value.

  FIG. 11 shows the results of executing the numerical analysis A and the numerical analysis B on the first analysis model 1-1 and the second analysis model 1-2. In FIG. 11, the results of each numerical analysis are shown by numbers, and it is assumed here that the smaller the numerical value is, the more difficult it is to break, but this is an example and does not limit the present invention. In the present invention, for example, those having relatively good fracture characteristics may be evaluated by symbols such as “◯”, and those having relatively poor fracture characteristics may be evaluated by symbols such as “×”. Although FIG. 11 shows a case where two numerical analyzes are executed for each analysis model, three or more numerical analyzes may be executed for each analysis model.

  Specifically, the result of executing the numerical analysis A on the first analysis model 1-1 is 100. The result of executing the numerical analysis B on the first analysis model 1-1 is 100. The present embodiment is modeled as the first analysis model 1-1 by performing calculation on the results of each numerical analysis such as (result of numerical analysis A + result of numerical analysis B) / 2. Calculate the macro fracture characteristics of the composite material. In the case of the example shown in FIG. 11, the present embodiment calculates the judgment characteristic of the composite material as (100 + 100) / 2 = 100.

  The result of executing the numerical analysis A on the second analysis model 1-2 is 90. The result of executing the numerical analysis B on the second analysis model 1-2 is 80. In this case, the present embodiment calculates the macro fracture properties of the modeled composite material as (90 + 80) / 2 = 85.

  In FIG. 11, the result of each numerical analysis is used as it is, but this is an example and does not limit the present invention. In the present embodiment, the fracture characteristics may be calculated by weighting the results of each numerical analysis.

  Further, in FIG. 11, the average value of the results of each numerical analysis is described as the fracture characteristic of the analysis model, but this is an example and does not limit the present invention. In the present embodiment, for example, the median value or the mode value of the results of each numerical analysis may be calculated as the fracture characteristic. In this case, the number of types of numerical analysis is preferably three or more.

  Furthermore, the present embodiment may compare the results of each numerical analysis of each analysis model created under different conditions. In the case of the example shown in FIG. 11, the result of the numerical analysis A of the first analysis model 1-1 may be compared with the result of the numerical analysis A of the second analysis model 1-2. Further, the result of the numerical analysis B of the first analysis model 1-1 and the result of the numerical analysis B of the second analysis model 1-2 may be compared. This makes it possible to evaluate the nanostructure of the composite material and the effect of deformation conditions on fracture. Differences in the analytical model include crosslink density, crosslink distribution, crosslink, presence / absence of filler, morphology of filler, volume fraction of filler, and filler diameter. Further, differences in the analytical model include interaction between the filler and the polymer, polymer species (elongation, twist, dihedral angle energy, etc.), polymer structure (length, etc.), blend polymer, and the like. The analytical models for comparison given here are examples and do not limit the present invention. The present invention may compare other different analytical models.

  Next, the composite material analysis method, the composite material analysis model creation computer program, the composite material analysis method, and the composite material analysis computer program according to the present embodiment will be described in more detail. FIG. 12 is a functional block diagram of a composite material analysis method and an analysis apparatus that executes the composite material analysis method according to the present embodiment.

  As shown in FIG. 12, the analysis method of the composite material according to the present embodiment is realized by the analysis device 50 which is a computer including the processing unit 52 and the storage unit 54. The analysis device 50 is electrically connected to an input / output device 51 having an input means 53. The input unit 53 processes various physical property values of a polymer and a filler that are targets for creating an analysis model of a composite material, an actual measurement result of an extension test result using a composite material containing the polymer and the filler, and boundary conditions in the analysis. Input to the unit 52 or the storage unit 54. As the input unit 53, for example, an input device such as a keyboard or a mouse is used.

  The processing unit 52 includes, for example, a central processing unit (CPU: Central Processing Unit) and a memory. The processing unit 52 reads the computer program from the storage unit 54 and expands it in the memory when executing various processes. The computer program loaded in the memory executes various processes. For example, the processing unit 52 expands the data relating to various processes stored in advance from the storage unit 54 into the area allocated to itself on the memory as needed. Then, the processing unit 52 executes various processes related to the creation of the composite material analysis model based on the developed data and the analysis of the composite material using the composite material analysis model.

  The processing unit 52 includes a model creating unit 52a, a condition setting unit 52b, and an analyzing unit 52c. The model creation unit 52a, based on the data stored in the storage unit 54 in advance, the number of particles of the composite material such as the filler and the polymer when creating the first analysis model 1-1 of the composite material by the molecular dynamics method, Arrangement and setting of the number of molecules, molecular weight, molecular chain length, number of molecular chains, branching, shape, size, reaction time, reaction conditions and the target number of molecules, which is the number of molecules included in the analytical model to be created, and setting. Set the coarse-grained model such as the number of calculation steps. The model creation unit 52a also sets initial conditions of various calculation parameters such as interactions between the filler particles 11a, between the polymer particles 21a, and hydrogen bonds between the filler / polymer particles, intermolecular forces, and the like. Further, the model creating unit 52a may create a cross-linking analysis such as creation of cross-linking by cross-linking the polymer model 21 as necessary.

  As the calculation parameters for adjusting the interaction between the filler particles 11a and the interaction between the polymer particles 21a, σ and ε of the Leonard-Jones potential represented by the following formula (2) are used, and these are adjusted. By increasing the upper limit distance (cutoff distance) for calculating the potential, it is possible to adjust the attractive force and repulsive force that have worked to a long distance. It is preferable that the parameters of the interaction between the filler particles 11a and the interaction between the polymer particles 21a be successively decreased until the interaction between the filler particles 11a and the interaction between the polymer particles 21a reach a constant value. By gradually bringing the σ and ε of the Leonard-Jones potential from large values to the original values, particles can be approached at a moderate speed that does not lead the molecule to an unnatural state. Further, the attractive force and the repulsive force can be adjusted within an appropriate range by gradually reducing the cutoff distance.

  The condition setting unit 52b sets various numerical analysis conditions such as numerical analysis such as temperature change analysis and voltage transformation analysis, deformation analysis such as extension analysis and shear analysis, and motion analysis such as relaxation analysis.

  The analysis unit 52c executes various numerical analyzes of the first analysis model 1-1 based on the analysis conditions set by the condition setting unit 52b. Further, the analysis unit 52c uses the first analysis model 1-1 of the composite material created by the model creation unit 52a to perform a numerical analysis by the molecular dynamics method to acquire a physical quantity. Here, the analysis unit 52c executes, as numerical analysis, deformation analysis such as extension analysis and shear analysis, and motion analysis such as relaxation analysis. In addition, the analysis unit 52c acquires a value such as a displacement obtained as a result of the numerical analysis or a physical amount such as a distortion obtained by performing a predetermined calculation process on the obtained value.

  Further, the analysis unit 52c acquires various physical quantities such as a movement displacement obtained as a result of the movement analysis by numerical analysis and a nominal stress or a nominal strain obtained by calculating the movement displacement. By such numerical analysis and kinetic analysis, the segment such as physical length such as bond length and polymer particle velocity of polymer molecule of the whole analysis model, velocity or bond length between cross-linking points and free ends, orientation, etc., which changes with analysis time It is possible to evaluate the relationship between the numerical value that represents the state change and distortion. In addition, it is possible to evaluate the relationship between the pressure or the analysis time and the numerical value indicating the change in the state of the segment such as the bond length of the polymer molecule and the polymer particle velocity, which changes with each analysis time. Furthermore, it is possible to evaluate the relationship between the numerical value indicating the state change of the segment such as the bond length of the polymer molecule and the polymer particle velocity, which changes with each analysis time, and the temperature or the analysis time. This enables a more detailed analysis of local molecular state changes of polymer molecules.

  Further, the analysis unit 52c identifies the break coordinates of the polymer model 21 obtained by the numerical analysis, and evaluates the specified break coordinates. Here, the analysis unit 52c may visualize and evaluate the fractured interparticle bonds, or may visualize and evaluate the fracture coordinates. Furthermore, the analysis unit 52c may aggregate and evaluate the fracture coordinates generated around the plurality of filler models 11, and aggregate the fracture coordinates generated around the plurality of filler models 11 into one representative filler model. You may evaluate it. In addition, the analysis unit 52c may aggregate and evaluate the analysis results separately analyzed using the plurality of first analysis models 1-1. The analysis unit 52c stores the analysis result of the analyzed composite material in the storage unit 54.

  The storage unit 54 includes a nonvolatile memory, which is a read-only recording medium such as a hard disk device, a magneto-optical disk device, a flash memory, and a CD-ROM, and a read / write device such as a RAM (Random Access Memory). A volatile memory that is a possible recording medium is appropriately combined.

  In the storage unit 54, data of a filler such as rubber carbon black, silica, and alumina, which is data for creating an analysis model of a composite material to be analyzed via the input unit 53, rubber, resin, and elastomer. Stores data such as polymer data. Further, the storage unit 54 stores a stress-strain curve that is a preset physical quantity history, a composite material analysis method according to the present embodiment, a computer program for realizing the composite material analysis method, and the like. This computer program may be one that can realize the composite material analysis method according to the present embodiment in combination with a computer program already recorded in a computer or a computer system. The “computer system” here includes an OS (Operating System) and hardware such as peripheral devices.

  The display unit 55 is, for example, a display device such as a liquid crystal display device. The storage unit 54 may be included in another device such as a database server. For example, the analysis device 50 may access the processing unit 52 and the storage unit 54 by communication from a terminal device including the input / output device 51.

[First embodiment]
As a first example using the present invention, an analysis model of pure rubber and filler-filled rubber filled with a filler is created, and the ease of occurrence of voids and the ease of propagation of cracks are numerically analyzed. It was calculated. Then, the macro rupture characteristics of the pure rubber and the filler-filled rubber were calculated based on the easiness of generation of voids and the easiness of crack propagation. FIG. 13 is a table showing the results of the first example.

  As shown in FIG. 13, the easiness of generating voids of pure rubber is 60. Further, the crack easiness of pure rubber is 100. For macro rupture properties, the ease of crack propagation has a greater effect on macro rupture properties than the likelihood of occurrence of voids, so the ease of crack propagation is weighted, Calculate the macro fracture properties. As a result, the macro rupture property of pure rubber is calculated as 100, which is the value of the crack growth.

  The ease of occurrence of voids in the filler-filled rubber is 100. Further, the easiness of crack growth of the filler-filled rubber is 20. In this case, in the filler-filled rubber, voids are likely to occur, but cracks are less likely to propagate, so the macro fracture property is calculated to be 50.

  In addition, in the first embodiment, the easiness of generating voids of pure rubber and the easiness of generating voids of filler-filled rubber may be compared. This makes it possible to evaluate the ease with which voids are generated due to the difference in models. Specifically, it is possible to evaluate the influence of the filling of the filler on the easiness of generating voids. Similarly, the easiness of crack growth of pure rubber and the easiness of crack growth of filler-filled rubber may be compared. This makes it possible to evaluate the effect of the filler filling on the ease of crack growth.

[Second embodiment]
As a second embodiment used in the present invention, an analytical model of a single polymer and a blended polymer was created, and the ease of void generation and the ease of crack propagation were calculated by numerical analysis. Then, the macro rupture property was calculated based on the easiness of void generation and the easiness of crack propagation. FIG. 14 is a table showing the results of the second embodiment.

  As shown in FIG. 14, the likelihood of occurrence of voids in a single polymer is 100. Further, the crack easiness of the single polymer is 100. In this case, the macro-rupture property of the single polymer is calculated as 100.

  The easiness of generation of voids in the blend polymer is 80. The easiness of crack growth of the blend polymer is 90. The macro rupture property is calculated to be 88, because the easiness of crack propagation has a greater effect on the macro rupture property than the easiness of generating voids.

  In addition, in the second embodiment, the easiness of generating voids of a single polymer and the easiness of generating voids of a blend polymer may be compared. This makes it possible to evaluate the influence of the structure of the polymer on the occurrence of voids. Similarly, crack growth of a single polymer may be compared with that of a blend polymer. This makes it possible to evaluate the influence of the polymer structure on the easiness of crack growth.

1-1 First analysis model 1-2 Second analysis model 11-1, 11-2 Filler model 11a-1, 11a-2 Filler particles 21-1, 21-2 Polymer model 21a-1, 21a-2 Polymer particles 21b-1, 21b-2 Bonded chain 21bx-1 Broken bonded chain 50 Analysis device 51 Input / output device 52 Processing part 52a Model creation part 52b Condition setting part 52c Analysis part 53 Input means 54 Storage part 55 Display means A Model creation Area X1, X2, X3 Break coordinates

Claims (11)

A method for analyzing a composite material by a molecular dynamics method using a computer,
The computer is
A first step of creating a model for analysis of a composite material including a composite material model modeling the composite material;
A second step of belonging to a composite material model to be analyzed in the analysis model, and setting a threshold value for an interparticle distance of at least a pair of particles bonded by interparticle bonding;
A third step of performing a first numerical analysis of the analysis model by performing a breaking process on the interparticle bond when the interparticle distance is equal to or greater than the threshold value,
A fourth step of setting a condition different from the condition given in the second step and executing a second numerical analysis of the analysis model;
A fifth step of calculating fracture characteristics of the composite material based on at least the first numerical analysis and the second numerical analysis;
A method for analyzing a composite material, comprising: The computer executes the different molecular dynamics methods in the first numerical analysis and the second numerical analysis,
The method for analyzing a composite material according to claim 1. The computer creates a plurality of the analysis models in the first step,
The method for analyzing a composite material according to claim 1 or 2. The computer creates the analysis model for executing the finite element method in the first step,
The method for analyzing a composite material according to claim 3. In the fourth step, the computer executes the molecular dynamics method and the finite element method,
The method for analyzing a composite material according to claim 4. The computer reflects the result of the numerical analysis by the molecular dynamics method to create the analytical model for executing the finite element method,
The method for analyzing a composite material according to claim 4 or 5. In the fourth step, the computer calculates the fracture characteristics based on a result of numerical analysis of the plurality of analysis models.
The method for analyzing the composite material according to claim 3. The computer compares the results of the numerical analysis of a plurality of the analytical models,
The method for analyzing a composite material according to claim 7. In the fourth step, the computer executes a calculation based on the result of the numerical analysis, and calculates the fracture characteristic based on the calculation result.
The method for analyzing the composite material according to claim 1. The computer is
In the third step, the progress until the interparticle bond is broken due to the breaking treatment is calculated,
In the fourth step, a characteristic value regarding fracture of the composite material is calculated based on the progress until the interparticle bond is fractured.
The method for analyzing the composite material according to claim 1.   A computer program for analyzing a composite material, which causes a computer to execute the method for analyzing a composite material according to any one of claims 1 to 10.