Thermal stress analysis method and thermal dependency evaluation method

Abstract

To propose a technique for easily improving accuracy of thermal stress analysis by taking into account physical properties relating to irreversible expansion and constriction with temperature dependency, and reversible physical properties.SOLUTION: A thermal stress analysis method conducts stress analysis of a material, according to an analysis model with a temperature dependent term that is a term relating to expansion and constriction including a product of a thermal expansion coefficient of an object material and temperature as a variable. In the thermal stress analysis method, the object is a material having a first property being a property relating to irreversible expansion and constriction with temperature dependency, and an amount of change according to the first physical property with temperature as a variable is obtained as a physical property value of the first physical property, and the analysis model in which the temperature dependent term has been corrected with the obtained physical property value of the first physical property is used.SELECTED DRAWING: None

Description

[Technical Field]

[0001] The present invention relates to the thermal analysis of a material having a first property of irreversible reaction that is temperature-dependent and a second property of reversible reaction that is temperature-dependent. The present invention also relates to a thermal stress analysis method for analyzing such a material (including an article made of the material; the same applies hereinafter) using an analytical model, and a thermal dependency evaluation method using the analysis method.

[0002] Suitable materials to which the present invention can be applied include, for example, refractories, concrete, and other materials that undergo sintering or other chemical reactions when heated.The present invention can be applied to, for example, evaluating the heat resistance of fire-resistant walls made of these materials during use, and analyzing thermal stresses that occur due to thermal changes in the usage environment.

[0003] The second physical property is, for example, the coefficient of thermal expansion (also called the thermal expansion coefficient). The first physical property is, for example, the linear change rate of an irreversible reaction caused by heat. In refractories, for example, an irreversible reaction occurs in which the volume expands and contracts nonlinearly due to a sintering reaction (chemical reaction) caused by heating.

[0004] The value of the second physical property is, for example, the value of the thermal expansion coefficient determined by the material itself or the amount of change according to the thermal expansion coefficient, and the value of the first physical property is the value of the first physical property itself or the amount of change of the material according to the first physical property. [Background technology]

[0005] Patent Document 1 describes a method of inputting expansion energy due to a chemical reaction and calculating the amount of strain from the amount of energy. Furthermore, Patent Document 2 describes a method for calculating the amount of strain that occurs when concrete dries using the humidity inside the concrete. Furthermore, Patent Document 3 proposes a simulation method that takes into consideration changes in constraint conditions due to temperature changes. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Patent No. 6240721 [Patent Document 2] Patent No. 6986323 [Patent Document 3] Japanese Patent Application Laid-Open No. 2010-52019 Summary of the Invention [Problem to be solved by the invention]

[0007] However, the inventors have found that the conventional analysis methods described in Patent Documents 1 to 3 provide poor accuracy in evaluation results (analysis results) for some materials. That is, the conventional analysis methods do not perform thermal stress analysis to evaluate materials that have a first physical property, which is an irreversible property that is temperature-dependent, and a second physical property, which is a reversible property that is temperature-dependent, by taking both the first physical property and the second physical property into consideration. For this reason, the inventors have found that the conventional analysis methods provide poor accuracy in evaluation results (analysis results) for materials that have both the first physical property and the second physical property.

[0008] The present invention has been made with the above points in mind, and aims to propose a technology that can easily improve the accuracy of thermal stress analysis by taking into account temperature-dependent irreversible and reversible physical properties. [Means for solving the problem]

[0009] To solve the problem, one aspect of the present invention is a thermal stress analysis method for performing stress analysis on a material using an analytical model having a temperature-dependent term, which is a term related to expansion / contraction that is the product of the thermal expansion coefficient of the material and temperature as a variable, in which the material has a first physical property, which is a physical property related to irreversible expansion / contraction that is temperature-dependent, and the amount of change due to the first physical property, which is a variable of temperature, is determined as the physical property value of the first physical property, and the analytical model is used in which the temperature-dependent term is corrected by the determined physical property value of the first physical property.

[0010] Here, the temperature-dependent term, which is a term related to expansion and contraction that is the product of the thermal expansion coefficient of the material and temperature as a variable, is a term in the analytical model formula that expresses the amount of change due to temperature-dependent reversible physical properties using temperature as a variable. [Effects of the Invention]

[0011] According to an aspect of the present invention, as an analysis condition of an analytical model for analyzing thermal stress, a condition of a temperature-dependent reversible second physical property is corrected by a temperature-dependent irreversible first physical property. As a result, according to an aspect of the present invention, it is possible to improve the accuracy of the analysis results (evaluation results) by the analytical model for a material having a temperature-dependent irreversible first physical property and a reversible second physical property. [Brief explanation of the drawings]

[0012] [Figure 1] FIG. 2 is a diagram illustrating a processing flow according to an embodiment of the present invention. [Figure 2] FIG. 3 is a graph showing the relationship between the linear change rate, which is a first physical property value, and temperature. [Figure 3] FIG. 3 is a diagram showing the relationship between the thermal expansion coefficient, which is a first physical property value, and temperature. [Figure 4] 1 is an example of a time series of thermal changes to be evaluated. DETAILED DESCRIPTION OF THE INVENTION

[0013] Next, an embodiment of the present invention will be described with reference to the drawings. In this embodiment, a refractory material will be described as an example of a material to be analyzed. However, the present invention is not limited to refractories. The present invention is applicable to any material (including articles made of such a material) that has a first property, which is an irreversible property that is temperature-dependent, and a second property, which is a reversible property that is temperature-dependent. However, it is preferable to select a material in which the property that changes due to heat of the first property is the same as the property that changes due to heat of the second property.

[0014] In this embodiment, the second physical property, which is a temperature-dependent, reversible physical property, is the thermal expansion coefficient α defined by the material itself. The quantity expressed based on the product (calculation) of the thermal expansion coefficient α and the temperature t as a variable is the physical property value of the second physical property with temperature as a variable. The physical property value of this second physical property defines the temperature-dependent term in the analytical model formula. Alternatively, the value of the thermal expansion coefficient α itself may be used as the physical property value of the second physical property.

[0015] As the first physical property, a physical property having the property of expanding and contracting due to heat is used. Here, the first physical property, which is a physical property related to irreversible expansion and contraction that is temperature-dependent, is not, for example, a temperature-dependent physical property defined by the material itself. The first physical property is, for example, a rate of change that occurs due to a chemical reaction that occurs in the material based on a temperature change. The amount of change in volume that occurs due to the first physical property becomes the physical property value of the first physical property. The value of the rate of change (linear rate of change in this embodiment) that indicates the first physical property may itself be the physical property value of the first physical property.

[0016] In this embodiment, the first physical property is a physical property (linear change rate) of volume change mainly due to a sintering reaction (chemical reaction) caused by heating. Here, the sintering reaction of the refractory causes an irreversible reaction that reduces the volume nonlinearly.

[0017] In this embodiment, the relationship between the linear change rate and temperature is calculated as a value of the first physical property with the temperature as a variable, as shown in FIG. The thermal expansion coefficient as the first physical property is generally set to a constant value regardless of temperature changes, as shown in FIG.

[0018] (Method of thermal stress analysis) The thermal stress analysis method will be explained according to the flow shown in Figure 1.

[0019] <Creating an analysis model 10> In this embodiment, a reference thermal stress analysis model is created for the target refractory. As a condition of thermal dependence, the model formula of the analytical model has a temperature-dependent term having the product of temperature as a variable and the thermal expansion coefficient α as a second physical property.

[0020] The conditions and model formula of the reference thermal stress analysis model to be created here are set by a conventionally known method. In the model, a temperature-dependent term having the product of the temperature as the variable and the thermal expansion coefficient α as the second physical property is set as a heat-dependent condition by a conventionally known method. For example, one method is to combine the first and second physical properties, create a function at each temperature, and give it as a single parameter. Another method is to reflect the volume change caused by the first physical property in the model used for thermal stress analysis, and give only the second physical property. This analysis model is a model for determining, for example, the stress and tensile strength generated in a material under set heating conditions (thermal change conditions), for example, conditions under which a thermal change to be evaluated is applied to the material.

[0021] <Heat Transfer Analysis 20> A heat transfer analysis is performed on the target refractory (material) under the heating conditions (thermal change conditions) set above, and the temperature distribution occurring in the refractory is obtained as the analysis temperature. Here, as a heating condition, when a refractory material is heated to produce the refractory material, it is not heated at a constant temperature, but is heated with a non-steady temperature trend (time series of temperature change) having temperature changes, as shown in Figure 4.

[0022] In contrast, in this embodiment, the set time series of temperature change (heating) is divided into multiple sections according to the elapsed time of heating. For ease of understanding, FIG. 4 shows a case where the number of sections is limited to four sections. In reality, the sections are divided into more sections. The greater the number of sections, the higher the analysis accuracy tends to be. Then, a representative analytical temperature for each section is determined by heat transfer analysis. Here, if the set heating temperature is a constant temperature, it is not necessary to divide the temperature into multiple sections as described above. If an unsteady thermal change occurs, it is preferable to divide the temperature into multiple sections.

[0023] In this embodiment, the maximum temperature in each section is taken as the analysis temperature for that section. Here, the sintering reaction changes depending on the maximum temperature experienced by the object. Therefore, the maximum temperature reached before the analysis is used in the calculation. The analysis temperature for a section is not limited to the maximum temperature, and may be the average temperature within the section, the heating temperature at the very end of the time within the section, or the like.

[0024] <Linear change rate calculation 30> A heating experiment is actually carried out to heat the target material. Through this experiment, a nonlinear relationship between the linear change rate (first physical property) and temperature is obtained, as shown in Figure 2. In this embodiment, the first physical property is a physical property that expands and contracts nonlinearly due to a chemical reaction caused by a thermal change. The relationship between the thermal expansion coefficient α as the second physical property and the temperature is, for example, as shown in FIG.

[0025] <Calculation of the first physical property value 40> The physical property value g(t) of the first physical property in each section is calculated based on the analysis temperature for each section calculated by the heat transfer analysis 20 and the linear change rate for the temperature calculated by the linear change rate calculation 30. t represents temperature as a variable (parameter).

[0026] The physical property value g(t) is, for example, the volume change amount set for each compartment, calculated by multiplying the linear change rate at the maximum temperature in each compartment by the volume. Note that if the linear change rate or volume decreases, g(t) is a negative value. In this embodiment, the physical property value g(t) is calculated as a constant for each compartment. If the value of the second property is the thermal expansion coefficient itself with temperature as a variable, the value of the first property is the linear change rate with temperature as a variable. In this case, the value of the first property is the linear change rate (constant) at the analysis temperature of the target section for each section.

[0027] <Analysis model update 50> In this embodiment, the temperature-dependent term in the model formula set based on the thermal expansion coefficient α as the second physical property is corrected by a physical property value corresponding to the value of the first physical property at the analysis temperature obtained by heat transfer analysis. Here, the function representing the temperature-dependent term before correction is expressed as f(t), where t represents the temperature as a variable (parameter).

[0028] Furthermore, if the equation for the temperature-dependent term in the analytical model is F(t), the corrected (updated) temperature-dependent term F(t) is expressed as in equation (1). Note that the temperature-dependent term F(t) before the model update is expressed as in equation (2).

[0029] F(t) = f(t) + g(t) (1) F(t) = f(t) (2)

[0030] Here, f(t) is written as, for example, "α·t·V", where V represents the volume of the material. Alternatively, f(t) may be the thermal expansion coefficient α itself with temperature as a variable, and g(t) may be the linear change rate itself. In this case, the thermal expansion coefficient α itself is corrected by the physical property value of the first physical property. Also, g(t) may be multiplied by a conversion coefficient that optimizes the amount of correction.

[0031] <Thermal Stress Analysis (Evaluation) 60> Then, using the updated analytical model, a thermal stress analysis of the target refractory (material) is performed. Specifically, the changes in thermal stress and tensile strength that occur in the target refractory (material) when the material is heated with the thermal change to be evaluated are calculated. Then, an evaluation is performed to see if the obtained thermal stress and tensile strength are within an allowable range.

[0032] Here, let us assume that the thermal stress and tensile strength were evaluated to be within the allowable range when the analysis was performed using the analysis model before updating, depending on the heating conditions (thermal change conditions) to be evaluated. When the refractory was actually heated under the above heating conditions (thermal change conditions), cracked refractory was found.

[0033] When a thermal stress analysis was performed using the updated analytical model under the analytical conditions for this cracked refractory, it was found that the thermal stress and tensile strength obtained in the analysis were greater than the allowable range.

[0034] In this manner, in this embodiment, by using an analytical model that reflects the temperature-dependent irreversible first property value and the temperature-dependent reversible second property value during thermal stress analysis, it becomes possible to perform thermal stress analysis of the target material with high accuracy, thereby enabling the appropriate evaluation of thermal stress in the target material, such as a refractory. Furthermore, by reflecting the physical property value of the first physical property as a constant, the model formula can be easily updated.

[0035] In conventional analysis methods, thermal stress is calculated by providing the results of heat transfer analysis with physical property values ​​such as the thermal expansion coefficient and Young's modulus. Therefore, with conventional analysis methods, it is difficult to perform accurate thermal stress analysis for materials that have both a reversible second physical property and an irreversible first physical property that is temperature dependent.

[0036] For example, in addition to the volume change due to heating that is determined by the thermal expansion coefficient, refractories also undergo volume expansion and contraction depending on the heating temperature due to chemical reactions in response to thermal changes such as sintering reactions. Therefore, unless the thermal dependency term in the analytical model is corrected using the physical property value corresponding to the first physical property, it is not possible to perform an accurate analysis using the analytical model.

[0037] In contrast, in this embodiment, a heat transfer calculation is first performed to obtain the temperature distribution in the thermal stress analysis model. Then, the amount of change due to the physical property value related to irreversible expansion and contraction is calculated from the temperature distribution, and the amount of change based on the first physical property is reflected in the amount of change in the temperature-dependent reversible physical property of the thermal stress analysis model, as shown in equation (1).

[0038] By performing a thermal stress analysis using such an updated analysis model, it becomes possible to easily perform an analysis that takes into account the effects of the first physical property, improving the accuracy of the analysis results. Note that the expansion and contraction due to the first physical property also includes the expansion and contraction due to the thermal expansion coefficient, but it was confirmed that accuracy improves when correction based on the first physical property is performed. This is presumably because the amount of change in expansion and contraction due to chemical reactions is greater. For this reason, it is acceptable to only reflect the property value of the first physical property when it is equal to or greater than a predetermined threshold. When the tensile strength or the like has temperature dependency, the tensile strength is corrected based on the temperature distribution inside the model when the analysis is performed, and then the thermal stress analysis is performed.

[0039] As described above, the analysis method of this embodiment can consider both temperature-dependent irreversible expansion and contraction-related physical properties and temperature-dependent reversible physical properties, thereby improving the accuracy of the analysis. This improved analytical accuracy can be utilized when designing facilities and equipment that use temperature-dependent materials such as refractories.

[0040] (Example) A thermal stress analysis of a refractory was carried out using the analysis method of this embodiment. Refractories have a first physical property (linear change) that causes irreversible changes in volume depending on the maximum temperature experienced, and a second physical property (thermal expansion coefficient) that is temperature-dependent. A typical analytical model includes a term for the temperature change due to the second physical property (temperature-dependent term).

[0041] In contrast to this, in the analytical model based on the present invention, the amount of change based on the first physical property is added as a correction amount to the term for the amount of temperature change (temperature-dependent term). Here, the environment in which the refractory is used is assumed to be a heating furnace, etc. The internal temperature of the refractory was calculated by heat transfer analysis, with the high temperature part being approximately 1300°C and the low temperature part being approximately 50°C.

[0042] When performing a non-steady state analysis, the temperature applied to the material may rise or fall, as shown in Figure 4. In each section of Figure 4, the temperature assigned to the irreversible physical properties is given by taking the highest temperature in the period up to the time of analysis and applying it based on the temperature trend (time series of temperature change) during the analysis, as shown below.

[0043] Here, the analysis temperatures for each section were set as follows: Section 1: Temperature at the time of analysis Section 2: Temperature A Section 3: Temperature at analysis timing Section 4: Temperature B

[0044] Since refractory is used as the material, the temperature for linear change, a physical property related to temperature-dependent irreversible expansion and contraction, is selected under the above conditions. The volume change is then calculated based on the linear change rate generated by sintering reactions, etc. Furthermore, the volume change rate of each compartment is reflected in the temperature-dependent term that defines the volume change rate determined by the thermal expansion coefficient, and an updated thermal stress analysis model is obtained. In this example, the value of the first physical property is calculated as a constant corresponding to the analysis temperature for each compartment. Then, a correction is made by adding the property value consisting of this constant to the temperature-dependent term. The value of the first physical property is set to a negative value when the change in the linear change rate is small.

[0045] The linear change used here was determined by actually heating the material and determining the volume change rate at that time. Then, using the thermal expansion coefficient, thermal stress is calculated within the range below the maximum experienced temperature. If the stress calculation range exceeds the maximum experienced temperature, the physical property values ​​related to irreversible expansion and contraction are re-assigned and the thermal stress is calculated again. In addition, since the tensile strength of refractory materials is temperature dependent, when evaluating strength, the tensile strength was calculated from the temperature distribution within the analytical model at the time of evaluation, and compared with the principal stress within the refractory material for evaluation.

[0046] When the standard model formula without correction was used as it was, it was not possible to take into account the irreversible volume change, and a lower thermal stress than the tensile strength was generated. On the other hand, when the corrected model formula was used, irreversible volume changes could be taken into account, and a stress greater than the tensile strength could be obtained, resulting in a thermal stress that was close to that of the actual object. Using the results of this analysis, the composition and material type of the refractories used in the heating furnace were selected.

[0047] (others) The present disclosure may also have the following configuration. (1) A thermal stress analysis method for performing stress analysis on a material using an analytical model having a temperature-dependent term, which is a term related to expansion and contraction having the product of the thermal expansion coefficient of the material and temperature as a variable, The first physical property is a property related to irreversible temperature-dependent expansion and contraction. A change in the first physical property with respect to temperature is calculated as a physical property value of the first physical property; using the analytical model in which the temperature-dependent term has been corrected using the calculated physical property value of the first physical property; A thermal stress analysis method characterized by: (2) A heat transfer analysis is performed on the target material to determine the analysis temperature generated in the material, and the temperature-dependent term is corrected using the physical property value of the first physical property corresponding to the analysis temperature. (3) A thermal stress analysis method under conditions in which a thermal change to be evaluated is applied to the material, The thermal change to be evaluated is divided into a plurality of sections, an analysis temperature is determined for each section by the heat transfer analysis, and the physical property value of the first physical property to be reflected in the analysis model is determined as a constant for each section based on the analysis temperature for each section. (4) A thermal stress analysis method for performing stress analysis on a material using an analytical model having a thermal expansion coefficient of the material, comprising: The first physical property is a property related to irreversible temperature-dependent expansion and contraction. A change in the first physical property with respect to temperature is calculated as a physical property value of the first physical property; using the analytical model in which the thermal expansion coefficient is corrected by the obtained physical property value of the first physical property; A thermal stress analysis method characterized by: (5) A heat transfer analysis is performed on the target material to determine the analysis temperature generated in the material, and the thermal expansion coefficient is corrected by the physical property value of the first physical property corresponding to the analysis temperature. (6) A thermal stress analysis method under conditions in which a thermal change to be evaluated is applied to the material, The thermal change to be evaluated is divided into a plurality of sections, an analysis temperature is determined for each section by the heat transfer analysis, and the physical property value of the first physical property reflected in the thermal expansion coefficient is determined as a constant for each section based on the analysis temperature for each section. (7) The target material is a refractory material. (8) The first physical property is the linear rate of change. (9) A heat transfer analysis is performed on the target material to determine the analysis temperature generated in the material, and the linear change rate or volume change amount of the material at the analysis temperature is set as the physical property value of the first physical property. (10) A thermal stress analysis method under conditions in which a thermal change to be evaluated is applied to the material, The thermal change to be evaluated is divided into a plurality of sections, an analysis temperature is determined for each section by the heat transfer analysis, and the physical property value of the first physical property to be reflected in the analysis model is determined as a constant for each section based on the analysis temperature for each section. (11) The analysis temperature above is the maximum temperature in each section. (12) A thermal dependency evaluation method for evaluating at least one of the stress value generated in a material and the tensile strength using the thermal stress analysis method disclosed herein. (13) A thermal stress analysis method for performing stress analysis using an analytical model on a material having a first property that is an irreversible property that is temperature-dependent with respect to a thermal change and a second property that is a reversible property that is temperature-dependent, the method comprising: performing a heat transfer analysis on the target material to determine an analysis temperature generated in the material, and determining the physical property value of the first physical property at the analysis temperature as a constant; an analytical model in which a temperature-dependent term of the material for calculating the second physical property and temperature as a variable is corrected by the calculated physical property value of the first physical property is used; A thermal stress analysis method characterized by: [Explanation of symbols]

[0048] 10 Creating an analysis model 20 Performing a Heat Transfer Analysis 30 Linear change rate calculation 40 Calculation of the first physical property 50 Analysis model update 60 Thermal Stress Analysis (Evaluation)

Claims

1. A thermal stress analysis method for performing stress analysis on a material using an analytical model having a temperature-dependent term, which is a term related to expansion and contraction having a product of the thermal expansion coefficient of the material and temperature as a variable, comprising: The target is a material having a first physical property, which is a physical property related to irreversible expansion and contraction that is temperature dependent, A change amount of the first physical property with temperature as a variable is calculated as a physical property value of the first physical property; using the analytical model in which the temperature-dependent term has been corrected using the obtained physical property value of the first physical property; As the correction, the physical property value of the first physical property is added to a temperature-dependent term based on the thermal expansion coefficient, which is a temperature-dependent reversible physical property. A thermal stress analysis method characterized by:

2. The physical property value of the first physical property is a value obtained as a constant by dividing a non-steady temperature change into a plurality of sections and analyzing them, and based on the analysis temperature of each section.

2. The thermal stress analysis method according to claim 1, wherein:

3. performing a heat transfer analysis on the target material to determine an analysis temperature generated in the material, and correcting the temperature-dependent term with the physical property value of the first physical property corresponding to the analysis temperature; 3. The thermal stress analysis method according to claim 1 or 2.

4. A thermal stress analysis method under conditions in which a thermal change to be evaluated is applied to the material, comprising: dividing the thermal change to be evaluated into a plurality of sections, determining an analysis temperature for each section by the heat transfer analysis, and determining, for each section, a physical property value of the first physical property to be reflected in the analysis model as a constant based on the analysis temperature for each section; 4. The thermal stress analysis method according to claim 3, wherein:

5. A thermal stress analysis method for performing stress analysis of a material using an analytical model having a thermal expansion coefficient of the material, comprising: The object is a material having a first physical property, which is a physical property related to irreversible expansion and contraction that is temperature dependent, A change amount of the first physical property with temperature as a variable is calculated as a physical property value of the first physical property; using the analytical model in which the thermal expansion coefficient is corrected by the obtained physical property value of the first physical property; As the correction, the physical property value of the first physical property is added to a temperature-dependent term based on the thermal expansion coefficient, which is a temperature-dependent reversible physical property. A thermal stress analysis method characterized by:

6. The physical property value of the first physical property is a value obtained as a constant by dividing a non-steady temperature change into a plurality of sections and analyzing them, and based on the analysis temperature of each section.

6. The thermal stress analysis method according to claim 5, wherein:

7. performing a heat transfer analysis on the target material to determine an analysis temperature generated in the material, and correcting the thermal expansion coefficient with the physical property value of the first physical property corresponding to the analysis temperature; 7. The thermal stress analysis method according to claim 5 or 6.

8. A thermal stress analysis method under conditions in which a thermal change to be evaluated is applied to the material, comprising: dividing the thermal change to be evaluated into a plurality of sections, determining an analysis temperature for each section by the heat transfer analysis, and determining, for each section, a physical property value of the first physical property reflected in the thermal expansion coefficient as a constant based on the analysis temperature for each section; 8. The thermal stress analysis method according to claim 7, wherein:

9. The target material is a refractory material.

7. A thermal stress analysis method according to claim 1, 2, 5 or 6.

10. The first physical property is a linear change rate.

10. The thermal stress analysis method according to claim 9, wherein:

11. A heat transfer analysis is performed on the target material to determine an analysis temperature generated in the material, and the linear change rate or volume change amount of the material at the analysis temperature is set as the physical property value of the first physical property.

11. The thermal stress analysis method according to claim 10.

12. A thermal stress analysis method under conditions in which a thermal change to be evaluated is applied to the material, comprising: the heat change to be evaluated is divided into a plurality of sections, an analysis temperature is determined for each section by the heat transfer analysis, and a physical property value of the first physical property to be reflected in the analysis model is determined as a constant for each section based on the analysis temperature for each section; 12. The thermal stress analysis method according to claim 11.

13. The analysis temperature above is the maximum temperature in each section.

13. The thermal stress analysis method according to claim 12.

14. 7. A thermal dependency evaluation method, comprising: evaluating at least one of a stress value generated in a material and a tensile strength, using the thermal stress analysis method according to claim 1.

15. A thermal stress analysis method for performing stress analysis using an analytical model on a material having a first physical property that is an irreversible physical property that is temperature-dependent with respect to a thermal change and a second physical property that is a reversible physical property that is temperature-dependent, the method comprising: performing a heat transfer analysis on the target material to determine an analysis temperature generated in the material, and determining a physical property value of the first physical property at the analysis temperature as a constant; using an analytical model in which a temperature-dependent term of a material for calculating the second physical property and temperature as a variable is corrected by the calculated physical property value of the first physical property; As the correction, the physical property value of the first physical property is added to a temperature-dependent term based on the thermal expansion coefficient, which is a temperature-dependent reversible physical property. A thermal stress analysis method characterized by:

16. The physical property value of the first physical property is a value obtained as a constant by dividing a non-steady temperature change into a plurality of sections and analyzing them, and based on the analysis temperature of each section.

16. The thermal stress analysis method according to claim 15.

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