/MAT/LAW71

ブロックフォーマットキーワード この材料則は超弾性材料の挙動を記述します。この材料則を使用して、ニチノールなどの形状記憶合金の挙動をモデル化できます。

これらの材料の特徴は、大きな変形が発生しても除荷するとすべてのひずみが回復する点にあります。また、これらの材料は、載荷と除荷の完全なサイクルにおいてヒステリシス応答を示します。この完全回復は、微細構造の相変化に起因しています。このモデルは、1997年のAuricchioらの研究に基づいています。この材料則は、ビーム要素(/PROP/TYPE18 (INT_BEAM) のみ)、ソリッド要素およびシェル要素と適合性があります。

フォーマット

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW71/mat_ID/unit_ID
mat_title
ρ i                
E υ E_mart        
σ S AS MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZnaaDaaaleaacaWGtbaabaGaamyqaiaadofaaaaaaa@3AE5@ σ F AS MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaamOraaqaaiaadgeacaWGtbaaaaaa @3AE7@ σ S SA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaam4uaaqaaiaadofacaWGbbaaaaaa @3AF4@ σ F SA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaamOraaqaaiaadofacaWGbbaaaaaa @3AE7@ α
EpsL CAS CSA TS_AS TF_AS
TS_SA TF_SA Cp Tini  

定義

フィールド 内容 SI単位の例
mat_ID 材料識別子

(整数、最大10桁)

 
unit_ID 単位識別子

(整数、最大10桁)

 
mat_title 材料のタイトル

(文字、最大100文字)

 
ρ i 初期密度

(実数)

[ kg m 3 ]
E ヤング率

(実数)

[ Pa ]
υ ポアソン比

(実数)

 
E_mart マルテンサイトヤング率

デフォルト = 0.0(実数)

[ Pa ]
σ S AS MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZnaaDaaaleaacaWGtbaabaGaamyqaiaadofaaaaaaa@3AE5@ オーステナイトからマルテンサイトへの相変態(AS)の開始を定義する材料パラメータ。 1

(実数)

[ Pa ]
σ F A S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaamOraaqaaiaadgeacaWGtbaaaaaa @3AE7@ オーステナイトからマルテンサイトへの相変態(AS)の終了を定義する材料パラメータ。 1

(実数)

[ Pa ]
σ S S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaam4uaaqaaiaadofacaWGbbaaaaaa @3AF4@ マルテンサイトからオーステナイトへの相変態(SA)の開始を定義する材料パラメータ。 1

(実数)

[ Pa ]
σ F S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaamOraaqaaiaadofacaWGbbaaaaaa @3AE7@ マルテンサイトからオーステナイトへの相変態(SA)の終了を定義する材料パラメータ。 1

(実数)

[ Pa ]
α 引張と圧縮での応答の違いを評価する材料パラメータ。

デフォルト = 0(実数)

 
EpsL 最大残留ひずみ 2

(実数)

 
CAS 載荷中の温度に対する応力の比率。

デフォルト = 0(実数)

[ Pa K ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiGaccfacaGGHbaabaGaci4saaaaaiaawUfacaGLDbaaaaa@3A85@
CSA 除荷中の温度に対する応力の比率。

デフォルト = 0(実数)

[ Pa K ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiGaccfacaGGHbaabaGaci4saaaaaiaawUfacaGLDbaaaaa@3A85@
TS_AS 変態(AS)の開始の基準温度。

デフォルト = 298K(実数)

[ K ]
TF_AS 変態(AS)の終了の基準温度。

デフォルト = 298K(実数)

[ K ]
TS_SA 変態(SA)の開始の基準温度。

デフォルト = 298K(実数)

[ K ]
TF_SA 変態(SA)の終了の基準温度。

デフォルト = 298K(実数)

[ K ]
Cp 比熱容量。

デフォルト = 1030(実数)

[ J kgK ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaabQeaaeaacaqGRbGaae4zaiabgwSixlaabUeaaaaacaGL BbGaayzxaaaaaa@3DB3@
Tini 初期温度。

デフォルト = 360K(実数)

[ K ]

例(金属)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW71/1/1
metal
#              RHO_I
             6.50E-9
#                  E                  Nu              E_mart
               62500                  .3               51000
#           sig_AS_s            sig_AS_f            sig_SA_s            sig_SA_f              alpha
                 450                 600                 300                 200                0.20
#               EpsL                 CAS                 CSA               TS_AS               TF_AS
               0.045                   1                   1                 383                 343
#              TS_SA               TF_SA                  CP                TINI
                 363                 403                 837                 360
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

コメント

  1. E_mart=0の場合、ヤング率は、一定であり、Eに等しく、材料の相分率に依存しないと見なされます。
  2. 相変態の開始と終了を定義するさまざまな応力 σ S A S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaam4uaaqaaiaadofacaWGbbaaaaaa @3AF4@ σ F A S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaamOraaqaaiaadgeacaWGtbaaaaaa @3AE7@ σ S S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaam4uaaqaaiaadofacaWGbbaaaaaa @3AF4@ および σ F S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeo8aZ9aadaqhaaWcbaGaamOraaqaaiaadofacaWGbbaaaaaa @3AE7@ は、残留ひずみと並んで、単軸の引張テストに対応しています。

    law71_transformation
    図 1.
  3. パラメータ α は、以下の関係の引張 ( σ S A S ) T MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbmaabmaapaqaa8qacqaHdpWCpaWaa0baaSqaaiaadofaaeaacaWG bbGaam4uaaaaaOWdbiaawIcacaGLPaaapaWaaSbaaSqaa8qacaWGub aapaqabaaaaa@3DE9@ および圧縮 ( σ S A S ) C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbmaabmaapaqaa8qacqaHdpWCpaWaa0baaSqaaiaadofaaeaacaWG bbGaam4uaaaaaOWdbiaawIcacaGLPaaapaWaaSbaaSqaa8qacaWGub aapaqabaaaaa@3DE9@ におけるオーステナイトからマルテンサイトへの相変態の初期値から計算されます。(1)
    α = 2 3 ( σ S A S ) C ( σ S A S ) T ( σ S A S ) C + ( σ S A S ) T MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbiabeg7aHjabg2da9maakaaapaqaa8qadaWcaaWdaeaapeGaaGOm aaWdaeaapeGaaG4maaaaaSqabaGcdaWcaaWdaeaapeWaaeWaa8aaba Wdbiabeo8aZnaaDaaaleaacaWGtbaabaGaamyqaiaadofaaaaakiaa wIcacaGLPaaapaWaaSbaaSqaaiaadoeaaeqaaOWdbiabgkHiTmaabm aapaqaa8qacqaHdpWCdaqhaaWcbaGaam4uaaqaaiaadgeacaWGtbaa aaGccaGLOaGaayzkaaWdamaaBaaaleaapeGaamivaaWdaeqaaaGcba Wdbmaabmaapaqaa8qacqaHdpWCdaqhaaWcbaGaam4uaaqaaiaadgea caWGtbaaaaGccaGLOaGaayzkaaWdamaaBaaaleaacaWGdbaabeaak8 qacqGHRaWkdaqadaWdaeaapeGaeq4Wdm3aa0baaSqaaiaadofaaeaa caWGbbGaam4uaaaaaOGaayjkaiaawMcaa8aadaWgaaWcbaWdbiaads faa8aabeaaaaaaaa@5A47@

    MAT/LAW71をビーム要素で使用する場合は、パラメータを α = 1 2 3 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey ypa0JaaGymaiabgkHiTmaakaaabaWaaSaaaeaacaaIYaaabaGaaG4m aaaaaSqabaaaaa@3BE4@ に設定する必要があります。

  4. Drucker-Pragerタイプの載荷関数 F MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbaaaa@3833@ は、応力偏差 s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbaaaa@3833@ 、圧力 p MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbaaaa@3833@ および温度を使用して導入されます。(2)
    F = s + 3 α p MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbGaey ypa0ZaauWaaeaacaWGZbaacaGLjWUaayPcSdGaey4kaSIaaG4maiab eg7aHjaadchaaaa@418B@
    オーステナイトからマルテンサイトへの変態(A→S)またはマルテンサイトからオーステナイトへの変態(S→A)の開始点と最終点には、2つの関数が定義されています。
      (A→S) (S→A)
    変態の開始点 F S A S = F R S A S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadofaaeaacaWGbbGaam4uaaaakiabg2da9iaadAeacqGH sislcaWGsbWaa0baaSqaaiaadofaaeaacaWGbbGaam4uaaaaaaa@4118@

    R S A S = σ S A S ( 2 3 + α ) C A S ( T T S A S ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbWaa0 baaSqaaiaadofaaeaacaWGbbGaam4uaaaakiabg2da9iabeo8aZnaa DaaaleaacaWGtbaabaGaamyqaiaadofaaaGcdaqadaqaamaakaaaba WaaSaaaeaacaaIYaaabaGaaG4maaaaaSqabaGccqGHRaWkcqaHXoqy aiaawIcacaGLPaaacqGHsislcaWGdbWaaWbaaSqabeaacaWGbbGaam 4uaaaakmaabmaabaGaamivaiabgkHiTiaadsfadaqhaaWcbaGaam4u aaqaaiaadgeacaWGtbaaaaGccaGLOaGaayzkaaaaaa@5079@

    F S S A = F R S S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadofaaeaacaWGtbGaamyqaaaakiabg2da9iaadAeacqGH sislcaWGsbWaa0baaSqaaiaadofaaeaacaWGtbGaamyqaaaaaaa@4118@

    R S S A = σ S S A ( 2 3 + α ) C S A ( T T S S A ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbWaa0 baaSqaaiaadofaaeaacaWGtbGaamyqaaaakiabg2da9iabeo8aZnaa DaaaleaacaWGtbaabaGaam4uaiaadgeaaaGcdaqadaqaamaakaaaba WaaSaaaeaacaaIYaaabaGaaG4maaaaaSqabaGccqGHRaWkcqaHXoqy aiaawIcacaGLPaaacqGHsislcaWGdbWaaWbaaSqabeaacaWGtbGaam yqaaaakmaabmaabaGaamivaiabgkHiTiaadsfadaqhaaWcbaGaam4u aaqaaiaadofacaWGbbaaaaGccaGLOaGaayzkaaaaaa@5079@

    変態の最終点 F F A S = F R F A S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadAeaaeaacaWGbbGaam4uaaaakiabg2da9iaadAeacqGH sislcaWGsbWaa0baaSqaaiaadAeaaeaacaWGbbGaam4uaaaaaaa@40FE@

    R F A S = σ F A S ( 2 3 + α ) C A S ( T T F A S ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbWaa0 baaSqaaiaadAeaaeaacaWGbbGaam4uaaaakiabg2da9iabeo8aZnaa DaaaleaacaWGgbaabaGaamyqaiaadofaaaGcdaqadaqaamaakaaaba WaaSaaaeaacaaIYaaabaGaaG4maaaaaSqabaGccqGHRaWkcqaHXoqy aiaawIcacaGLPaaacqGHsislcaWGdbWaaWbaaSqabeaacaWGbbGaam 4uaaaakmaabmaabaGaamivaiabgkHiTiaadsfadaqhaaWcbaGaamOr aaqaaiaadgeacaWGtbaaaaGccaGLOaGaayzkaaaaaa@5052@

    F F S A = F R F S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadAeaaeaacaWGtbGaamyqaaaakiabg2da9iaadAeacqGH sislcaWGsbWaa0baaSqaaiaadAeaaeaacaWGtbGaamyqaaaaaaa@40FE@

    R F S A = σ F S A ( 2 3 + α ) C S A ( T T F S A ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGsbWaa0 baaSqaaiaadAeaaeaacaWGtbGaamyqaaaakiabg2da9iabeo8aZnaa DaaaleaacaWGgbaabaGaam4uaiaadgeaaaGcdaqadaqaamaakaaaba WaaSaaaeaacaaIYaaabaGaaG4maaaaaSqabaGccqGHRaWkcqaHXoqy aiaawIcacaGLPaaacqGHsislcaWGdbWaaWbaaSqabeaacaWGtbGaam yqaaaakmaabmaabaGaamivaiabgkHiTiaadsfadaqhaaWcbaGaamOr aaqaaiaadofacaWGbbaaaaGccaGLOaGaayzkaaaaaa@5052@

    条件 F S A S > 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadofaaeaacaWGbbGaam4uaaaakiabg6da+iaaicdaaaa@3CA2@

    F F A S < 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadAeaaeaacaWGbbGaam4uaaaakiabgYda8iaaicdaaaa@3C91@

    F ˙ > 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWGgbGbai aacqGH+aGpcaaIWaaaaa@39FE@

    F S S A < 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadofaaeaacaWGtbGaamyqaaaakiabgYda8iaaicdaaaa@3C9E@

    F F S A > 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaa0 baaSqaaiaadAeaaeaacaWGtbGaamyqaaaakiabg6da+iaaicdaaaa@3C95@

    F ˙ < 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWGgbGbai aacqGH8aapcaaIWaaaaa@39FA@

    マルテンサイトの進展方程式 載荷時:

    X ˙ m = ( 1 X m ) F ˙ F R F A S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWGybGbai aadaWgaaWcbaGaamyBaaqabaGccqGH9aqpcaGGOaGaaGymaiabgkHi TiaadIfadaWgaaWcbaGaamyBaaqabaGccaGGPaWaaSaaaeaaceWGgb GbaiaaaeaacaWGgbGaeyOeI0IaamOuamaaDaaaleaacaWGgbaabaGa amyqaiaadofaaaaaaaaa@458B@

    除荷時:

    X ˙ m = X m F ˙ F R F S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWGybGbai aadaWgaaWcbaGaamyBaaqabaGccqGH9aqpcaWGybWaaSbaaSqaaiaa d2gaaeqaaOWaaSaaaeaaceWGgbGbaiaaaeaacaWGgbGaeyOeI0Iaam OuamaaDaaaleaacaWGgbaabaGaam4uaiaadgeaaaaaaaaa@428A@

    σ S A S , σ F A S , T S A S , T F A S , α , C A S , σ S S A , σ F S A , T S S A , T F S A , C S A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda qhaaWcbaGaam4uaaqaaiaadgeacaWGtbaaaOGaaiilaiabeo8aZnaa DaaaleaacaWGgbaabaGaamyqaiaadofaaaGccaGGSaGaamivamaaDa aaleaacaWGtbaabaGaamyqaiaadofaaaGccaGGSaGaamivamaaDaaa leaacaWGgbaabaGaamyqaiaadofaaaGccaGGSaGaeqySdeMaaiilai aadoeadaahaaWcbeqaaiaadgeacaWGtbaaaOGaaiilaiabeo8aZnaa DaaaleaacaWGtbaabaGaam4uaiaadgeaaaGccaGGSaGaeq4Wdm3aa0 baaSqaaiaadAeaaeaacaWGtbGaamyqaaaakiaacYcacaWGubWaa0ba aSqaaiaadofaaeaacaWGtbGaamyqaaaakiaacYcacaWGubWaa0baaS qaaiaadAeaaeaacaWGtbGaamyqaaaakiaacYcacaWGdbWaaWbaaSqa beaacaWGtbGaamyqaaaaaaa@64BB@ は材料パラメータです。オーステナイトからマルテンサイトへの変換は、上記の条件(表内)が確認されたときに行われます。

  5. アニメーション出力(/ANIM/BRICK/USRI)のリスト:
    • USR 1=マルテンサイト相の分率
    • USR 2=載荷関数
    • USR 3=除荷関数