CASTING SIMULATION METHOD
Provided is a casting simulation method capable of expressing influence of different inelastic strains produced at different temperatures on strain hardenability at room temperature. The following amount of effective equivalent inelastic strain εeffective inelastic is substituted into a constitutive equation in which an amount of equivalent inelastic strain is used as a degree of work hardening: an amount of effective equivalent inelastic strain εeffective inelastic=∫ot{h(T)/h(RT)}{(Δεinelastic/Δt)}dt , where T denotes a temperature with inelastic strain, h(T) denotes an increment of yield strength at room temperature with respect to an amount of inelastic strain at the temperature with inelastic strain, h(RT) denotes an increment of yield strength at room temperature with respect to an amount of inelastic strain applied at room temperature, h(T)/h(RT) denotes an effective inelastic strain coefficient α(T), Δεinelastic/Δt denotes an equivalent inelastic strain rate, and t denotes a time from 0 second in analysis.
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This disclosure relates to a casting simulation method using thermal stress and deformation analysis.
BACKGROUNDConventionally, elastoplastic constitutive equation is used in analysis programs in order to predict the residual stress and deformation that occurs as metals processed at high temperature, such as cast products, hot forged products, and hot rolled products, cool back to room temperature. JP2007330977A (PTL 1) and Dong Shuxin, Yasushi Iwata, Toshio Sugiyama, and Hiroaki Iwahori, “Cold Crack Criterion for ADC12 Aluminum Alloy Die Casting”, Casting Engineering, 81(5), 2009, pp. 226231, ADC12 (NPL 1) are reference examples of Toyota Central R&D Labs. Inc.
However, in elastoplastic constitutive equation and elastoviscoplastic constitutive equation that do not take into account recovery, the amount of equivalent inelastic strain (including the amount of plastic strain and the amount of viscoplastic strain) is used as a measure of hardening, and inelastic strain that occurs at such a high temperature at which recovery occurs simultaneously with deformation is also treated as contributing to work hardening as much as inelastic strain produced at room temperature. This causes an unrealistic increase in yield stress at room temperature, causing problems in the accuracy of thermal stress analysis.
To address this issue, there have been proposed a number of constitutive equations that can take into account some recovery. Any of these constitutive equations, however, fail to give physical or experimental grounds for how recovery should be considered, and thus suffer from problems with prediction accuracy.
The problems of conventional findings related to the abovedescribed inventions will be described below.
CITATION LIST Patent Literature

 PTL 1: JP2007330977A
 PTL 2: Japanese Patent Application No. 2014004578

 NPL 1: Dong Shuxin, Yasushi Iwata, Toshio Sugiyama, and Hiroaki Iwahori, “Cold Crack Criterion for ADC12 Aluminum Alloy Die Casting”, Casting Engineering, 81(5), 2009, pp. 226231, ADC12
 NPL 2: Hallvard G. Ejar and Asbjorn Mo, “ALSPENA mathematical model for thermal stresses in direct chill casting of aluminum billets”, Metallurgical Transactions B, December 1990, Volume 21, Issue 6, Pages 10491061
 NPL 3: W. M. van Haaften, B. Magnin, W. H. Kool, and L. Katgerman, “Constitutive behavior of ascast AA1050, AA3104, and AA5182”, Metallurgical and Materials Transactions A, July 2002, Volume 33, Issue 7, Pages 19711980
 NPL 4: Alankar Alankar and Mary A. Wells, “Constitutive behavior of ascast aluminum alloys AA3104, AA5182 and AA6111 at below solidus temperatures”, Materials Science and Engineering A, Volume 527, Issues 2930, 15 Nov. 2010, Pages 78127820
Hallvard et al. (NPL 2) proposes a constitutive equation that is expressed as Constitutive Eq. (I) below representing the relationship between stress and inelastic strain as described below, and that considers inelastic strain produced at or above a certain temperature as not contributing to hardening, while the other produced below that temperature as contributing to work hardening. From a metallurgical viewpoint, however, it is clear that recovery does not happen suddenly at a certain temperature. Therefore, this constitutive equation has a problem.
Constitutive Eq. (I) representing the relationship between stress and inelastic strain:
Van Haaften et al. (NPL 3) proposes a constitutive equation that is expressed as Constitutive Eq. (II) below between stress and inelastic strain, a function a which is 0 at high temperature and 1 at low temperature is used to smoothly consider the contributions of inelastic strain produced at different temperatures to work hardening.
However, the amount of cumulative inelastic strain is directly multiplied by a, which is not in incremental form, and inelastic strain produced at high temperature eventually contribute to work hardening at low temperature. Thus, as in Constitutive Eq. (I), the constitutive equation proposed by NPL 3 inevitably involves an unrealistic increase in yield stress.
Constitutive Eq. (II) representing the relationship between stress and inelastic strain:
Moreover, Alankar et al. (NPL 4) proposes a constitutive equation that is expressed as Constitutive Eq. (III) below representing the relationship between stress and inelastic strain. With this constitutive equation, recovery occurs more frequently as the ratio of a work hardening index at high temperature n_{(T) }to a work hardening index at room temperature n_{RT }decreases. However, there are no metallurgical grounds for considering that the ratio n_{(T)}/n_{RT }determines the ratio between plastic strain contributing to work hardening and creep strain not contributing to work hardening (strain making no contribution to work hardening). Additionally, it is not specified how to identify material constants in the constitutive equation when inelastic strain is divided into creep strain and plastic strain. Thus, K_{(T)}, n_{(T)}, and m_{(T) }in the following equation cannot be determined accurately.
Constitutive Eq. (III) representing the relationship between stress and inelastic strain:
Recently, one of the applicants of the present application proposed a constitutive equation to solve at least part of the above problems in Japanese Patent Application No. 2014004578 (PTL 2, an unpublished earlier application). This is expressed as a constitutive equation expressing the relationship between stress and elastic strain/inelastic strain as explained below. In this constitutive equation, inelastic strain is divided into plastic strain contributing to work hardening and creep strain not contributing to work hardening, and inelastic strain produced at high temperature is expressed mainly by creep strain. In this case, measures are taken to prevent the yield stress from excessively rising at room temperature by causing plastic strain to develop gradually as the temperature decreases.
Constitutive Eq. expressing the relationship between stress and elastic strain/inelastic strain:
where f denotes a yield function.
With the constitutive equation proposed by PTL 2, however, the proportion of plastic strain and creep strain is determined based on the shape of a stressequivalent inelastic strain curve obtained at different temperatures, rather than on the metallurgical grounds. In addition, as a steadystate creep law is used, it is inevitable to estimate plastic strain excessively beyond the actual value, while estimating creep strain low in low strain regions. Therefore, problems remain in the prediction accuracy of residual stress and deformation.
Recent metallurgical findings revealed that the extent to which inelastic strain at high temperature contributes to work hardening at room temperature depends on the composition of the alloy, thermal history such as in heat treatment, and solidified structure.
To date, however, there has been no such constitutive equation that takes into account all the factors listed above in order to predict the residual stress and deformation that occurs as metals processed at high temperature, such as cast products, hot forged products, and hot rolled products, cool back to room temperature.
It is thus desirable at present in construction of a constitutive equation to experimentally clarify how inelastic strain at high temperature contributes to work hardening at room temperature, and reflect it in the constitutive equation.
However, none of the conventional constitutive equations can reflect “the influence of inelastic strain produced at different temperatures on work hardening at room temperature” that is determined on an experimental or theoretical basis. There has also been no finding that shows how to determine material constants in a constitutive equation that can reflect this effect.
Solution to ProblemThe present disclosure has been developed in view of the above circumstances, and provides a casting simulation method using thermal stress and deformation analysis, in which an amount of equivalent inelastic strain effective for work hardening is determined by multiplying an equivalent inelastic strain rate calculated in the analysis by an effective inelastic strain coefficient α representing a proportion of inelastic strain contributing to work hardening to obtain an effective inelastic strain rate, and integrating it over a time from 0 second in analysis, and the amount of equivalent inelastic strain thus obtained is used as a measure of work hardening in a constitutive equation.
To solve the abovedescribed problems, the present disclosure also provides a method of experimentally determining an effective inelastic strain coefficient α(T) which represents the contributions of inelastic strain produced at different temperatures to work hardening.
Specifically, the primary features of this disclosure are as described below.
1. A casting simulation method capable of expressing influence of different inelastic strains produced at different temperatures on work hardening, namely on increase in yield stress, at room temperature, the influence varying with differences in recovery at the different temperatures, by introducing an amount of effective equivalent inelastic strain to an elastoplastic constitutive equation and/or an elastoviscoplastic constitutive equation in which an amount of equivalent inelastic strain is used as a degree of work hardening, namely an amount of increase in yield stress, such as an elastoplastic constitutive equation in which a yield function is expressed as f=f(σ_{eff},ε_{eff}^{p},T) or an elastoviscoplastic constitutive equation in which a relation between equivalent stress, equivalent viscoplastic strain, viscoplastic strain rate, and temperature is expressed as σ_{eff.}=F(ε_{eff.}^{vp},{dot over (ε)}_{eff.}^{vp},T), wherein an amount of effective equivalent inelastic strain ε_{effective inelastic }obtained by Eq. (1) below is used:
the amount of effective equivalent inelastic strain ε_{effective inelastic}=∫_{o}^{t}{t_{(T)}/h_{(RT)}}{(Δε_{inelastic}/Δt)}dt (1)
, where T denotes a temperature with inelastic strain, h_{(T) }denotes an increment of yield strength at room temperature with respect to an amount of inelastic strain at the temperature with inelastic strain, h_{(RT) }denotes an increment of yield strength at room temperature with respect to an amount of inelastic strain applied at room temperature, h_{(T)}/h_{(RT) }denotes an effective inelastic strain coefficient α(T), Δε_{inelastic}/Δt denotes an equivalent inelastic strain rate, and t denotes a time from 0 second in analysis.
2. The casting simulation method according to 1., the effective inelastic strain coefficient α(T) is obtained by: applying different inelastic prestrains to a test piece at different temperatures; cooling the test piece to room temperature; performing a tensile test or a compression test on the test piece at room temperature; and measuring influence of amounts of the inelastic prestrains applied at the different temperatures on the increase in yield stress.
3. The casting simulation method according to 1. or 2., wherein a stressequivalent inelastic strain curve is transformed into a stresseffective equivalent inelastic strain curve using α(T), and based on the stresseffective equivalent inelastic strain curve, a determination is made of a material constant in a constitutive equation to which the amount of effective equivalent inelastic strain ε_{effective inelastic }is introduced.
4. The casting simulation method according to any one of 1. to 3., wherein when α(T) is substituted into Eq. (1) in a temperature range in which α(T) is 0 or a negative value and a stressequivalent inelastic strain curve at the temperature T indicates work hardening, α(T) is corrected from 0 or the negative value to a small positive value.
Advantageous EffectAccording to the present disclosure, it is possible to eliminate the physical and metallurgical irrationality of the conventional methods, and to express, based on the experimental fact, the influence of different inelastic strains produced at different temperatures on work hardening at room temperature, which influence varies with differences in recovery at the different temperatures. As a result, it is possible to more accurately simulate the residual stress and deformation occurring as metals processed at high temperature cool back to room temperature.
In the accompanying drawings:
The following describes the present disclosure in detail.
As used herein, an equivalent inelastic strain rate calculated by thermal stress analysis is multiplied by an “effective inelastic strain coefficient α(T) indicative of temperature dependency”, which is preferably experimentally determined, and the result is used as an effective inelastic strain rate. The effective inelastic strain rate is then integrated over a time from 0 second in analysis to determine the amount of effective equivalent inelastic strain, which in turn is, in place of the amount of equivalent inelastic strain, used as a measure of hardening in a constitutive equation.
The amount of effective equivalent inelastic strain is applicable to any constitutive equation, whether an elastoplastic constitutive equation or an elastoviscoplastic constitutive equation, as long as it is a constitutive equation using the amount of equivalent inelastic strain conventionally as a measure of work hardening as described in paragraph 0008.
Specific examples are an elastoplastic constitutive equation and/or an elastoviscoplastic constitutive equation in which the amount of equivalent inelastic strain is used as a degree of work hardening (namely an amount of increase in yield stress) such as an elastoplastic constitutive equation in which a yield function is expressed as f=f(σ_{eff},ε_{eff}^{p},T) or an elastoviscoplastic constitutive equation in which a relation between equivalent stress, equivalent viscoplastic strain, viscoplastic strain rate, and temperature is expressed as σ_{eff.}=F(ε_{eff.}^{vp},{dot over (ε)}_{eff.}^{vp},T).
The determination of the effective inelastic strain coefficient α(T) is carried out by applying inelastic prestrains of different magnitudes at the corresponding temperatures at which α(T) is to be obtained, then cooling to room temperature, conducting a tensile test or a compression test, and measuring the increase in yield stress.
The following describes how to determine α(T) in detail.
A tensile test piece is heated in a way as presented in the temperature history in
Desirably, the same temperature history is set for all test conditions. The reason for this is to eliminate the influence of the temperature history of the test piece on the measured values.
In the context of the present disclosure, the abovedescribed test is not limited to a particular test, and may be a tensile test or a compression test as long as it can provide a stressstrain curve and enables measurement of yield stress. For the tensile test in this disclosure, for example, a publiclyknown and widelyused tensile test may be used, such as JIS Z 2241:2011. For the compression test, for example, a publiclyknown and widelyused compression test may be used, such as JIS K 7181:2011.
The results obtained in the above test are conceptually illustrated in
In a temperature range in which an effective inelastic strain coefficient α(T) is experimentally determined to be 0 or a negative value, i.e., in which inelastic strain applied at the temperature T should not contribute to work hardening at room temperature, if the stressequivalent inelastic strain curve at the temperature T indicates work hardening and if the effective inelastic strain coefficient α(T) is 0, then a constitutive equation to which the amount of effective equivalent inelastic strain is introduced involves no effective inelastic strain, and thus is not able to express work hardening in principle. In other words, the stressstrain curve displays elastoperfectly plastic behavior or elastoperfectly viscoplastic behavior. In that case, the reproducibility of the stressstrain curve deteriorates, resulting in lower accuracy of predictions on thermal stress and deformation.
An effective inelastic strain is produced as long as the effective inelastic strain coefficient α(T) is not 0, making it possible to express work hardening in the stressinelastic strain curve at the temperature T. Accordingly, even in a temperature range with the inelastic strain coefficient α(T) being 0 or a negative value, if a positive small value, rather than 0 or a negative value, is corrected appropriately for use as an effective inelastic strain coefficient α(T), it is possible to express work hardening in a stressequivalent inelastic strain curve with a slight ineffective inelastic strain. The value of α(T) at the time of correction is in a range of 0<α<0.5, and desirably 0<α<0.1, although it depends on the alloy type. As an example, α(T) is corrected by the following linear interpolation using an effective inelastic strain coefficient at maximum temperature α_{min }in a temperature range in which α(T) is experimentally determined to be nonzero and a maximum temperature T_{max }(which may alternatively be a solidus temperature) in a temperature range in which α is experimentally determined to be 0:
where
α_{extrapolation}(T) denotes a value of a as corrected in a temperature range in which α is experimentally determined to be 0;
T_{max }denotes the maximum temperature (which may alternatively be a solidus temperature) in a temperature range where a is experimentally determined to be 0,
T_{min }denotes a maximum temperature in a temperature range in which α is experimentally determined to be nonzero;
α_{min }denotes a value of α in T_{min}; and
T denotes a temperature above T_{min }
As an example, material constants in a constitutive equation to which the amount of effective inelastic strain is introduced are determined as explained below in the case of introducing the amount of effective inelastic strain to the constants (K(T), n(T), and m(T)) of the extended Ludwik's law.
The extended Ludwik's law is as follows. ε_{0 }is a constant necessary for calculation and usually a small value of 1×10^{−6}.
σ=K(T)(ε_{inelastic}+ε_{0})^{n(T)}({dot over (ε)}_{inelastic})^{m(T) }
When introducing the amount of effective inelastic strain, it is expressed as:
σ=K(T)(ε_{effective inelastic}+ε_{0})^{n(T)}({dot over (ε)}_{inelastic})^{m(T) }
The term with an index n_{(T) }representing the degree of work hardening includes the amount of effective equivalent inelastic strain as a variable. In addition, the term with an index m_{(T) }representing the strain rate dependence of the stressstrain curve includes an equivalent inelastic strain rate as a variable. Since the equation as a whole includes the amount of effective equivalent inelastic strain, for each temperature, by substituting the inelastic strain rate into the term with m_{(T)}, K_{(T)}, n_{(T)}, and m_{(T) }are determined by numerical optimization to fit the stresseffective equivalent inelastic strain curve.
Following the above procedure, the amount of effective equivalent inelastic strain ε_{effective inelastic }is determined. In the disclosure, the amount of effective equivalent inelastic strain is used to simulate the influence of inelastic strain applied at the temperature in question on work hardening at room temperature. Although details of the procedures for casting simulation will be described in the Examples, the points are summarized as follows.
In the simulation according to the disclosure, it is possible to adopt a constitutional expression that uses the amount of equivalent inelastic strain as a measure of work hardening conventionally used for casting simulation. An exemplary elastoplastic constitutive equation is:
ε_{ij}=ε^{e}_{ij}+ε^{p}_{ij }
σ_{ij}=D_{ijkl}(T)ε^{e}_{kl }
f=f(σ_{eff},ε_{eff}^{p},T)
, where T is the temperature, σ_{ij }is the stress, σ_{eff. }is the equivalent stress, ε_{ij }is the total strain, ε^{e}_{ij }is the elastic strain, ε^{p}_{ij }is the plastic strain, f is the yield function, and D_{ijkl }is the fourthorder constitutive tensor.
Alternatively, an exemplary elastoviscoplastic constitutive equation is:
ε_{ij}=ε^{e}_{ij}+ε^{vp}_{ij }
σ_{ij}=D_{ijkl}(T)ε^{e}_{kl }
σ_{eff.}=F(ε_{eff.}^{vp},{dot over (ε)}_{eff.}^{vp},T)
, where σ_{eff. }is the equivalent stress, ε_{eff.}^{vp }is the equivalent viscoplastic strain, {dot over (ε)}_{eff.}^{vp }is the equivalent viscoplastic strain rate.
To these constitutive equations, the amount of effective equivalent inelastic strain ε_{effective inelastic }defined by Eq. (1) according to the present disclosure, instead of the amount of equivalent inelastic strain conventionally used, may be introduced or substituted.
The wellknown and widelyused procedures for casting simulation are:
(I) element creation step;
(II) element definition step;
(III) heat transfer analysis step;
(IV) thermal stress analysis step; and
(V) analysis result evaluation step.
In the present disclosure, material constants in a constitutive equation are determined in step (II) using an equivalent stresseffective equivalent inelastic strain curve, and are input to a constitutive equation to which the amount of effective inelastic strain is introduced. Then, in the thermal stress analysis step (IV), the amount of effective equivalent inelastic strain is calculated, and the result, instead of the amount of equivalent inelastic strain conventionally used, is used as a parameter representing the amount of work hardening to calculate thermal stress.
EXAMPLESThe following describes how the present disclosure enables prediction with high accuracy of the influence of amounts of inelastic prestrains produced at different temperatures on the work hardening behavior at room temperature in a typical aluminum diecasting alloy, JIS ADC12, using an extended Ludwik equation, which is a typical elastoviscoplastic constitutive equation.
A specific form of the equation before and after the introduction of the amount of effective inelastic strain is as presented in paragraph 0032.
Firstly, a typical aluminum diecasting alloy, JIS ADC12, is analyzed for an effective inelastic strain coefficient α(T) and material constants (K(T), n(T), and m(T)) at each temperature according to the procedures described in paragraphs 0026 to 0033.
Firstly, tensile tests were performed to obtain stressequivalent inelastic strain curves required to determine material constants K(T), n(T), and m(T). Stressinelastic strain curves were obtained under a set of conditions including: experimental strain rates of 10^{−3}/s and 10^{−4}/s and test temperatures of RT, 200° C., 250° C., 300° C., 350° C., 400° C., and 450° C. Each test pieces was obtained by casting JIS ADC12 in a copper mold and processing it into the shape of a tensile test piece.
In these tests, all the test pieces were heated from room temperature to 450° C., then subjected to heat treatment at 450° C. for 1 hour to cause precipitates to be redissolved, and cooled to the test temperature as soon as possible so that the mechanical properties at the time of cooling can be examined accurately. As soon as the test temperature was reached, the tensile test was carried out.
In addition, tests for determining an effective inelastic strain coefficient α(T) were carried out at RT, 200° C., 250° C., 300° C., 350° C., 400° C., and 450° C. After solution treatment at 450° C. for 1 hour, the temperature was lowered to a temperature at which the target inelastic prestrain was to be applied to the test piece following the temperature history presented in
After application of prestrains, each test piece was cooled to room temperature and quenched with dry ice to eliminate the effect of the increase in yield stress caused by natural aging. Then, the 0.2% offset yield stress was determined by conducting a tensile test on each test piece at room temperature. The results are presented in
By using the effective inelastic strain coefficient α_{(T) }thus obtained, the stressequivalent inelastic strain curve obtained in paragraph 0040 was transformed into a stresseffective equivalent inelastic strain curve, and the values of K_{(T)}, m_{(T)}, and n_{(T) }were obtained as described in paragraphs 0032 and 0033. The values of K_{(T)}, m_{(T)}, and n_{(T) }are presented in
It is conceivable, however, that if α is corrected as described in paragraph 0031 with the temperature of α=0, T_{max }in paragraph 0031, being temporarily set as a liquidus temperature, the reproducibility of the stressinelastic strain curve also improves.
For extended Ludwik equations incorporating or not incorporating (in the case of a conventional example) the amount of effective equivalent inelastic strain according to the present disclosure, calculation was made to determine the effect of inelastic prestrains applied at different temperatures on the yield stress at room temperature, and the calculation results were compared as presented in
In the conventional extended Ludwik equation not incorporating the amount of effective equivalent inelastic strain, in principle, inelastic strains produced in different temperature ranges are all considered as equivalent to one another and included as a measure of hardening. Accordingly, as is clear from
On the other hand, as can be seen from
To examine the influence of inelastic prestrain at different temperatures on the yield stress at room temperature, a comparison was made between experimental values and calculated values according to the extended Ludwik equation to which the amount of effective equivalent inelastic strain is introduced, and the results are presented in
It can be seen from the figure that the analysis program incorporating the amount of effective equivalent inelastic strain could reproduce the behavior at 300° C. or higher at which an increase in yield stress is independent of the amount of inelastic prestrain. In addition, this program could accurately reproduce the behavior even at 300° C. or lower at which an increase in yield stress depends on the amount of inelastic prestrain.
It can be seen from the figure that prestrain applied at 700° C. does not contribute to work hardening at room temperature. In contrast, inelastic strain applied at 350° C. contributes to work hardening at room temperature and the amount of work hardening is proportional to the amount of inelastic strain applied. This behavior is identical to that observed in ADC12, and from this follows that the present disclosure is also applicable to FCD400.
Claims
1. A casting simulation method capable of expressing influence of different inelastic strains produced at different temperatures on work hardening, namely on increase in yield stress, at room temperature, the influence varying with differences in recovery at the different temperatures, by introducing an amount of effective equivalent inelastic strain to an elastoplastic constitutive equation and/or an elastoviscoplastic constitutive equation in which an amount of equivalent inelastic strain is used as a degree of work hardening, namely an amount of increase in yield stress, such as an elastoplastic constitutive equation in which a yield function is expressed as f=f(σeff,εeffp,T) or an elastoviscoplastic constitutive equation in which a relation between equivalent stress, equivalent viscoplastic strain, viscoplastic strain rate, and temperature is expressed as σeff.=F(εeff.vp,{dot over (ε)}eff.vp,T), wherein, where
 an amount of effective equivalent inelastic strain εeffective inelastic obtained by Eq. (1) below is used: the amount of effective equivalent inelastic strain εeffective inelastic=∫ot{h(T)/h(RT)}{(Δεinelastic/Δt)}dt (1)
 T denotes a temperature with inelastic strain,
 h(T) denotes an increment of yield strength at room temperature with respect to an amount of inelastic strain at the temperature with inelastic strain,
 h(RT) denotes an increment of yield strength at room temperature with respect to an amount of inelastic strain applied at room temperature,
 h(T)/h(RT) denotes an effective inelastic strain coefficient α(T),
 Δεinelastic/Δt denotes an equivalent inelastic strain rate, and
 t denotes a time from 0 second in analysis.
2. The casting simulation method according to claim 1, the effective inelastic strain coefficient α(T) is obtained by: applying different inelastic prestrains to a test piece at different temperatures; cooling the test piece to room temperature; performing a tensile test or a compression test on the test piece at room temperature; and measuring influence of amounts of the inelastic prestrains applied at the different temperatures on the increase in yield stress.
3. The casting simulation method according to claim 1, wherein a stressequivalent inelastic strain curve is transformed into a stresseffective equivalent inelastic strain curve using α(T), and based on the stresseffective equivalent inelastic strain curve, a determination is made of a material constant in a constitutive equation to which the amount of effective equivalent inelastic strain εeffective inelastic is introduced.
4. The casting simulation method according to claim 1, wherein when α(T) is substituted into Eq. (1) in a temperature range in which α(T) is 0 or a negative value and a stressequivalent inelastic strain curve at the temperature T indicates work hardening, α(T) is corrected from 0 or the negative value to a small positive value.
5. The casting simulation method according to claim 2, wherein a stressequivalent inelastic strain curve is transformed into a stresseffective equivalent inelastic strain curve using α(T), and based on the stresseffective equivalent inelastic strain curve, a determination is made of a material constant in a constitutive equation to which the amount of effective equivalent inelastic strain εeffective inelastic is introduced.
6. The casting simulation method according to claim 2, wherein when α(T) is substituted into Eq. (1) in a temperature range in which α(T) is 0 or a negative value and a stressequivalent inelastic strain curve at the temperature T indicates work hardening, α(T) is corrected from 0 or the negative value to a small positive value.
7. The casting simulation method according to claim 3, wherein when α(T) is substituted into Eq. (1) in a temperature range in which α(T) is 0 or a negative value and a stressequivalent inelastic strain curve at the temperature T indicates work hardening, α(T) is corrected from 0 or the negative value to a small positive value.
8. The casting simulation method according to claim 5, wherein when α(T) is substituted into Eq. (1) in a temperature range in which α(T) is 0 or a negative value and a stressequivalent inelastic strain curve at the temperature T indicates work hardening, α(T) is corrected from 0 or the negative value to a small positive value.
Type: Application
Filed: Jan 21, 2016
Publication Date: Jan 4, 2018
Applicant: National Institute of Advanced Industrial Science and Technology (Chiyodaku, Tokyo)
Inventors: Makoto YOSHIDA (Shinjukuku, Tokyo), Yuichi MOTOYAMA (Tsukubashi, Ibaraki), Toshimitsu OKANE (Tsukubashi, Ibaraki), Yoya FUKUDA (Suntogun, Shizuoka)
Application Number: 15/544,595