1. Field of the Invention
The present invention relates to a method for analyzing thermal deformation, and in particular to a thermal deformation analyzing method for analyzing thermal deformation of a substance in response to temperature increase or decrease, and as time elapses during a temperature increase or decrease.
2. Description of the Related Art
Conventionally, a method for analyzing the structure of a substance (for example, a plastic molded part) has been proposed in which stress of the substance is analyzed based on the material data such as the linear expansion coefficient, Young""s modulus, and Poisson""s ratio of the substance, the shape and constraint condition of the substance, and, at the same time, the creep strain generated in response to the stress occurring on the substance is analyzed using Nutting""s formula shown as Equation (1) An example of analysis software is that marketed under the trade name ABAQUS.                                           ∂            ϵ                                ∂            t                          =                  A          ⁢                      xe2x80x83                    ⁢                      σ            n                    ⁢                      t            m                                              (        1        )            
However, in such an analyzing method, because the tensile creep characteristic is used as the creep characteristic when the substance is bent (referred to as the bending creep characteristic hereinafter), there is a problem that the precision of the analysis of the bending creep characteristic is low. Also, because thermal shrinkage which occurs as time elapses is not considered, there is an additional problem that for a substance having a thermal shrinkage characteristic, the conventional method may result in large error.
In order to solve the problem related to the bending creep characteristic KANTO JIDOSHA KOGYO KABUSHIKI KAISHA, a co-applicant of the present application, proposed a method for precisely analyzing the bending creep characteristic by multiplying the tensile creep or compressive creep after heating, obtained as a result of an analysis using Nutting""s formula, by an experimentally determined correction coefficient (Japanese Patent Application No. Hei 9-352189).
One object of the method for analyzing thermal deformation according to the present invention is to precisely analyze the thermal deformation of a substance which thermally shrinks over time.
In order to achieve at least the object mentioned above, the thermal deformation analysis according to the present invention employs the following method.
According to one aspect of the present invention, there is provided a thermal deformation analysis method for analyzing thermal deformation of a substance in which deformation occurs in response to an increase and the following decrease in temperature, and while the temperature increases and then decreases over time, wherein thermal deformation of the substance is analyzed based on a creep characteristic which relates to the creep deformation of the substance occurring during the temperature increase and the following temperature decrease as time elapses, and a thermal shrinkage characteristic which relates to the thermal shrinkage deformation of the substance occurring during the temperature increase and the following temperature decrease as time elapses.
In this aspect of the thermal deformation analysis method, thermal deformation of the substance is analyzed based on the creep characteristic which relates to the creep deformation of the substance occurring during the temperature increase and the following temperature decrease as time elapses, and the thermal shrinkage characteristic which relates to the thermal shrinkage deformation of the substance occurring during the temperature increase and the following temperature decrease as time elapses. As a result, analysis can be more precisely performed compared to an analysis of the conventional method which does not take thermal shrinkage characteristic into account.
It is also preferable to configure the thermal deformation analysis method to comprise a calculation step for deformation during temperature increase, for calculating the elasto-plastic deformation of the substance during the process of raising the temperature of the substance to a predetermined temperature, based on the elasto-plastic characteristic of the substance; a calculation step for creep deformation, for calculating the creep deformation of the substance when the substance is exposed to the predetermined temperature environment for a predetermined period of time, based on the creep characteristic; and a calculation step for deformation during the following temperature decrease, for calculating the elasto-plastic deformation of the substance during the process of cooling the substance from the elevated temperature to a predetermined low temperature, based on the elasto-plastic characteristic of the substance, wherein the thermal shrinkage characteristic is included in at least one of the three steps in calculating the deformation of the substance. In this manner, the deformation of the substance can be analyzed from the elasto-plastic deformation, creep deformation, and thermal shrinkage deformation, during a temperature increase and the following temperature decrease.
In the aspect of the thermal deformation analysis method of the present invention comprising the above three steps, it is also preferable that the creep deformation calculation step is a step for calculating the deformation by taking the sum of the deformation produced by the creep strain obtained from the creep characteristic with respect to time and the deformation produced by the thermal shrinkage obtained based on the thermal shrinkage characteristic with respect to time as the total deformation with respect to time of said substance. In such a case, in the calculation, the thermal shrinkage deformation occurring as time elapses is assumed to be simultaneous with the creep deformation.
Further, in the aspect of the thermal deformation analysis method of the present invention comprising the above three steps, it is also preferable that the calculation step for deformation during temperature increase is a step for calculating the elasto-plastic deformation of the substance based on the linear expansion coefficient of the substance obtained according to the elasto-plastic deformation characteristic and on the thermal shrinkage rate of the substance obtained according to the thermal shrinkage characteristic. In such a case, in the calculation, the thermal shrinkage deformation occurring as time elapses is assumed to be simultaneous with the elasto-plastic deformation during the temperature increase. Because the saturated amount of thermal shrinkage is calculated during temperature increase process, this is especially effective when the thermal shrinkage is saturated or nearly saturated at an early stage of the temperature increase.
Still further, in the aspect of the thermal deformation analysis method of the present invention comprising the above three steps, it is also preferable that the calculation step for deformation during the following temperature decrease is a step for calculating the elasto-plastic deformation of the substance based on the linear expansion coefficient of the substance obtained according to the elasto-plastic deformation characteristic and on the thermal shrinkage rate of the substance obtained according to the thermal shrinkage characteristic. In such a case, in the calculation, the thermal shrinkage deformation occurring as time elapses is assumed to be simultaneous with the elasto-plastic deformation during the temperature decrease.