/MAT/LAW84

ブロックフォーマットキーワード Johnson-Cookのひずみ速度硬化と温度軟化を伴うSwift-Voce弾塑性則。この材料則を使用すれば、非関連2次流れ則のモデル化が可能になります。

フォーマット

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW84/mat_ID/unit_ID
mat_title
ρ i                
E ν            
P12 P22 P33 Q B
G12 G22 G33 K0 α
A ε 0 n C ε ˙ 0
η Cp Tini Tref Tmelt
m ε ˙ α      

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 ]
ν ポアソン比

(実数)

 
P12 降伏パラメータ

デフォルト = -0.5(実数)

 
P22 降伏パラメータ

デフォルト = 1.0(実数)

 
P33 降伏パラメータ

デフォルト = 3.0(実数)

 
G12 流れ則パラメータ

デフォルト = P12(実数)

 
G22 流れ則パラメータ

デフォルト = P22(実数)

 
G33 流れ則パラメータ

デフォルト = P33(実数)

 
Q Voce硬化係数

(実数)

[ Pa ]
B Voce塑性ひずみ係数

デフォルト = 0.0(実数)

 
K0 Voceパラメータ

(実数)

 
α 降伏重み係数
=1
Swift硬化則
=0
Voce硬化則

デフォルト = 0.0(実数)

 
A Swift硬化係数

(実数)

[ Pa ]
n Swift硬化指数

デフォルト = 1.0(実数)

 
ε 0 Swift硬化パラメータ

デフォルト = 0.00(実数)

 
C ひずみ速度係数。
= 0
ひずみ速度効果はなし

デフォルト = 0.00(実数)

 
ε ˙ 0 参照ひずみ速度

デフォルト = 1030、ひずみ速度効果はなし

(実数)

[ 1 s ]
η Taylor-Quinney係数は、熱に変換される塑性仕事の比率を定量化します。

(実数)

 
Cp 比熱

(実数)

[ J kgK ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaabQeaaeaacaqGRbGaae4zaiabgwSixlaabUeaaaaacaGL BbGaayzxaaaaaa@3DB3@
Tini time=0のときに初期化で使用される初期温度

(実数)

[ K ]
Tref 参照温度。

(実数)

[ K ]
Tmelt 溶融温度。

(実数)

[ K ]
m 温度指数。

(実数)

 
ε ˙ α 温度依存性に関するひずみ速度最適化パラメータ

(実数)

[ 1 s ]

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/LAW84/1/1
Swift-voce (metal)
#              Rho_i
                8E-9
#                  E                  Nu
              206000                  .3
#                P12                 P22                 P33                   Q                   B
                 -.5                   1                   3                 524                  25
#                G12                 G22                 G33                  K0               ALPHA
                 -.5                   1                   3                 100                  .5
#                  A                EPS0                   n                   C              EPSDOT
                1000              .00128                  .2                .014               .0011
#                ETA                  CP                Tini                Tref               Tmelt
                  .9         42000000000                 293                 293                1700
#                  m             EPSDOTA
                .921               1.379
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

コメント

  1. 降伏応力は、SwiftモデルとVoceモデル両方と、Johnson-Cook則に従ったひずみ速度依存性と温度依存性の組み合わせを使用した解析的表現を使用して計算されます。(1)
    σ y ={ α[ A ( ε ¯ p + ε 0 ) n ]+( 1α )[ K 0 +Q( 1exp( B ε ¯ p ) ) ] }( 1+Cln ε ¯ ˙ p ε ˙ 0 )[ 1 ( T T ref T melt T ref ) m ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadMhaaeqaaOGaeyypa0ZaaiWaaeaacqaHXoqydaWadaqa aiaadgeadaqadaqaaiqbew7aLzaaraWaaSbaaSqaaiaadchaaeqaaO Gaey4kaSIaeqyTdu2aaSbaaSqaaiaaicdaaeqaaaGccaGLOaGaayzk aaWaaWbaaSqabeaacaWGUbaaaaGccaGLBbGaayzxaaGaey4kaSYaae WaaeaacaaIXaGaeyOeI0IaeqySdegacaGLOaGaayzkaaWaamWaaeaa caWGlbWaaSbaaSqaaiaaicdaaeqaaOGaey4kaSIaamyuamaabmaaba GaaGymaiabgkHiTiGacwgacaGG4bGaaiiCamaabmaabaGaeyOeI0Ia amOqaiqbew7aLzaaraWaaSbaaSqaaiaadchaaeqaaaGccaGLOaGaay zkaaaacaGLOaGaayzkaaaacaGLBbGaayzxaaaacaGL7bGaayzFaaWa aeWaaeaacaaIXaGaey4kaSIaam4qaiGacYgacaGGUbWaaSaaaeaacu aH1oqzgaqegaGaamaaBaaaleaacaWGWbaabeaaaOqaaiqbew7aLzaa caWaaSbaaSqaaiaaicdaaeqaaaaaaOGaayjkaiaawMcaamaadmaaba GaaGymaiabgkHiTmaabmaabaWaaSaaaeaacaWGubGaeyOeI0Iaamiv amaaBaaaleaacaWGYbGaamyzaiaadAgaaeqaaaGcbaGaamivamaaBa aaleaacaWGTbGaamyzaiaadYgacaWG0baabeaakiabgkHiTiaadsfa daWgaaWcbaGaamOCaiaadwgacaWGMbaabeaaaaaakiaawIcacaGLPa aadaahaaWcbeqaaiaad2gaaaaakiaawUfacaGLDbaaaaa@81EE@
  2. Cauchy応力は次のように計算されます:(2)
    σ ¯ =f( σ ) = σ T Pσ = σ 11 2 + P 22 σ 22 2 +( 1+ P 12 + P 22 ) σ 33 2 +2 P 12 σ 11 σ 22 2( 1+ P 12 ) σ 11 σ 33 2( P 22 + P 12 ) σ 22 σ 33 +( P 33 +3 ) σ 12 2 +3 σ 23 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacuaHdp WCgaqeaiabg2da9iGacAgadaqadaqaaiabeo8aZbGaayjkaiaawMca aaqaauaabeqabeaaaeaaaaGaeyypa0ZaaOaaaeaacqaHdpWCdaahaa WcbeqaaiaadsfaaaGccaWGqbGaeq4WdmhaleqaaaGcbaqbaeqabeqa aaqaaaaacqGH9aqpcqaHdpWCdaqhaaWcbaGaaGymaiaaigdaaeaaca aIYaaaaOGaey4kaSIaamiuamaaBaaaleaacaaIYaGaaGOmaaqabaGc cqaHdpWCdaqhaaWcbaGaaGOmaiaaikdaaeaacaaIYaaaaOGaey4kaS YaaeWaaeaacaaIXaGaey4kaSIaamiuamaaBaaaleaacaaIXaGaaGOm aaqabaGccqGHRaWkcaWGqbWaaSbaaSqaaiaaikdacaaIYaaabeaaaO GaayjkaiaawMcaaiabeo8aZnaaDaaaleaacaaIZaGaaG4maaqaaiaa ikdaaaaakeaafaqabeqabaaabaaaauaabeqabeaaaeaaaaGaey4kaS IaaGOmaiaadcfadaWgaaWcbaGaaGymaiaaikdaaeqaaOGaeq4Wdm3a aSbaaSqaaiaaigdacaaIXaaabeaakiabeo8aZnaaBaaaleaacaaIYa GaaGOmaaqabaGccqGHsislcaaIYaWaaeWaaeaacaaIXaGaey4kaSIa amiuamaaBaaaleaacaaIXaGaaGOmaaqabaaakiaawIcacaGLPaaacq aHdpWCdaWgaaWcbaGaaGymaiaaigdaaeqaaOGaeq4Wdm3aaSbaaSqa aiaaiodacaaIZaaabeaakiabgkHiTiaaikdadaqadaqaaiaadcfada WgaaWcbaGaaGOmaiaaikdaaeqaaOGaey4kaSIaamiuamaaBaaaleaa caaIXaGaaGOmaaqabaaakiaawIcacaGLPaaacqaHdpWCdaWgaaWcba GaaGOmaiaaikdaaeqaaOGaeq4Wdm3aaSbaaSqaaiaaiodacaaIZaaa beaaaOqaauaabeqabeaaaeaaaaqbaeqabeqaaaqaaaaacqGHRaWkda qadaqaaiaadcfadaWgaaWcbaGaaG4maiaaiodaaeqaaOGaey4kaSIa aG4maaGaayjkaiaawMcaaiabeo8aZnaaDaaaleaacaaIXaGaaGOmaa qaaiaaikdaaaGccqGHRaWkcaaIZaGaeq4Wdm3aa0baaSqaaiaaikda caaIZaaabaGaaGOmaaaaaaaa@9885@
  3. 非関連塑性流れ則は次のように計算されます:(3)
    Δ ε p = Δ ε ¯ p g ( σ ) σ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq yTdu2aaSbaaSqaaiaadchaaeqaaOGaeyypa0JaeuiLdqKafqyTduMb aebadaWgaaWcbaGaamiCaaqabaGcdaWcaaqaaiabgkGi2kGacEgada qadaqaaiabeo8aZbGaayjkaiaawMcaaaqaaiabgkGi2kabeo8aZbaa aaa@485C@
    ここで、(4)
    g ( σ ) = σ T G σ = σ 11 2 + G 22 σ 22 2 + ( 1 + G 12 + G 22 ) σ 33 2 + 2 G 12 σ 11 σ 22 2 ( 1 + G 12 ) σ 11 σ 33 2 ( G 22 + G 12 ) σ 22 σ 33 + ( G 33 + 3 ) σ 12 2 + 3 σ 23 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaaciGGNb WaaeWaaeaacqaHdpWCaiaawIcacaGLPaaacqGH9aqpdaGcaaqaaiab eo8aZnaaCaaaleqabaGaamivaaaakiaadEeacqaHdpWCaSqabaaake aafaqabeqabaaabaaaauaabeqabeaaaeaaaaqbaeqabeqaaaqaaaaa faqabeqabaaabaaaaiabg2da9iabeo8aZnaaDaaaleaacaaIXaGaaG ymaaqaaiaaikdaaaGccqGHRaWkcaWGhbWaaSbaaSqaaiaaikdacaaI Yaaabeaakiabeo8aZnaaDaaaleaacaaIYaGaaGOmaaqaaiaaikdaaa GccqGHRaWkdaqadaqaaiaaigdacqGHRaWkcaWGhbWaaSbaaSqaaiaa igdacaaIYaaabeaakiabgUcaRiaadEeadaWgaaWcbaGaaGOmaiaaik daaeqaaaGccaGLOaGaayzkaaGaeq4Wdm3aa0baaSqaaiaaiodacaaI ZaaabaGaaGOmaaaaaOqaauaabeqabeaaaeaaaaqbaeqabeqaaaqaaa aafaqabeqabaaabaaaauaabeqabeaaaeaaaaGaey4kaSIaaGOmaiaa dEeadaWgaaWcbaGaaGymaiaaikdaaeqaaOGaeq4Wdm3aaSbaaSqaai aaigdacaaIXaaabeaakiabeo8aZnaaBaaaleaacaaIYaGaaGOmaaqa baGccqGHsislcaaIYaWaaeWaaeaacaaIXaGaey4kaSIaam4ramaaBa aaleaacaaIXaGaaGOmaaqabaaakiaawIcacaGLPaaacqaHdpWCdaWg aaWcbaGaaGymaiaaigdaaeqaaOGaeq4Wdm3aaSbaaSqaaiaaiodaca aIZaaabeaakiabgkHiTiaaikdadaqadaqaaiaadEeadaWgaaWcbaGa aGOmaiaaikdaaeqaaOGaey4kaSIaam4ramaaBaaaleaacaaIXaGaaG OmaaqabaaakiaawIcacaGLPaaacqaHdpWCdaWgaaWcbaGaaGOmaiaa ikdaaeqaaOGaeq4Wdm3aaSbaaSqaaiaaiodacaaIZaaabeaaaOqaau aabeqabeaaaeaaaaqbaeqabeqaaaqaaaaafaqabeqabaaabaaaauaa beqabeaaaeaaaaGaey4kaSYaaeWaaeaacaWGhbWaaSbaaSqaaiaaio dacaaIZaaabeaakiabgUcaRiaaiodaaiaawIcacaGLPaaacqaHdpWC daqhaaWcbaGaaGymaiaaikdaaeaacaaIYaaaaOGaey4kaSIaaG4mai abeo8aZnaaDaaaleaacaaIYaGaaG4maaqaaiaaikdaaaaaaaa@9595@
  4. 温度は次を使用して更新されます:(5)
    Δ T = ω ( ε ¯ ˙ p ) η ρ C p σ ¯ d ε ¯ p

    ここで、 ω ( ε ¯ ˙ p ) = { 0 if ε ¯ ˙ p < ε ˙ 0 1 if ε ¯ ˙ p > ε ˙ α ( ε ¯ ˙ p ε ˙ 0 ) 2 ( 3 ε ˙ α 2 ε ¯ ˙ p ε ˙ 0 ) ( ε ˙ α ε ˙ 0 ) 3 if ε ˙ 0 ε ¯ ˙ p ε ˙ α