/FAIL/COCKCROFT

Block Format Keyword A nonlinear stress-strain based failure criterion with linear damage accumulation.

Is compatible with shells and solids. Fracture occurs when the accumulated equivalent strain modified by maximum principal tensile stress reaches a critical value. Is compatible with visco-elastic and elasto-plastic materials.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/FAIL/COCKCROFT/mat_ID/unit_ID
C0 Alpha      
Optional Line
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fail_ID                  

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

  
unit_ID (Optional) Unit Identifier.

(Integer, maximum 10 digits)

  
C0 Cockcroft–Latham failure criterion. 1
< 0
Total equivalent strain is used in the failure criterion calculation. Normally used with visco-elastic materials without plasticity.
> 0
Plastic strain is used in the failure criterion calculation. Normally used for elasto-plastic material.

(Real)

 [ Pa ]
Alpha Exponential moving average filter on 1st principal stress σ 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaaeymaaqabaaaaa@3A0B@ . 4
= 0
Set to 1.
= 1.0 (Default)
No filtering.

(Real)

  
fail_ID (Optional) Failure criteria identifier.

(Integer, maximum 10 digits)

  

Example (Steel)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
#              MUNIT               LUNIT               TUNIT
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/PLAS_TAB/1/1
Steel
#              RHO_I
              7.8E-9                   0
#                  E                  Nu           Eps_p_max               Eps_t               Eps_m
              210000                  .3                   0                   0                   0
#  N_funct  F_smooth              C_hard               F_cut               Eps_f                  VP
         1         0                   0                   0                   0                   0
#  fct_IDp              Fscale   Fct_IDE                EInf                  CE
         0                   0         0                   0                   0
# func_ID1  func_ID2  func_ID3  func_ID4  func_ID5
         1
#           Fscale_1            Fscale_2            Fscale_3            Fscale_4            Fscale_5
                   1
#          Eps_dot_1           Eps_dot_2           Eps_dot_3           Eps_dot_4           Eps_dot_5
                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FAIL/COCKCROFT/1/1
#                 C0               Alpha
                 0.4
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1
function_36
#                  X                   Y
                0.00              270.00
                0.01              298.39
                0.02              313.04
                0.03              324.89
                0.04              335.23
                0.05              344.58
                0.06              353.20
                0.07              361.26
                0.08              368.87
                0.09              376.11
                0.10              383.03
                0.20              441.33
                0.30              488.52
                0.40              529.69
                0.50              566.89
                0.60              601.21
                0.70              633.30
                0.80              663.61
                0.90              692.43
                1.00              720.00
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. This failure criterion is defined based on the well-known Cockcroft–Latham criterion.(1)
    ∫ 0 ε ¯ f max ( σ 1 , 0 ) ⋅ d ε ¯ = C 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWdXbqaai Gac2gacaGGHbGaaiiEaiaacIcacqaHdpWCdaWgaaWcbaGaaGymaaqa baGccaGGSaGaaGimaiaacMcacqGHflY1caWGKbGafqyTduMbaebacq GH9aqpcaWGdbaaleaacaaIWaaabaGafqyTduMbaebadaWgaaadbaGa amOzaaqabaaaniabgUIiYdGccaaIWaaaaa@4D31@
    Where,
    σ 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaaeymaaqabaaaaa@3A0B@
    First principal tension stress.
    ε ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacuaH1oqzga qeaaaa@3927@
    The equivalent strain.
  2. No failure occurs in compression.
  3. When this failure is used with /MAT/LAW1, only N=1 (membrane) is supported. It does not work when N=0 global integration is used.
  4. An exponential moving average filter is used for filtering the 1st principal stress.(2)
    σ f ( t ) = α σ ( t ) + ( 1 − α ) σ ( t − Δ t ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadAgaaeqaaOWaaeWaaeaacaWG0baacaGLOaGaayzkaaGa eyypa0JaeqySdeMaeq4Wdm3aaeWaaeaacaWG0baacaGLOaGaayzkaa Gaey4kaSYaaeWaaeaacaaIXaGaeyOeI0IaeqySdegacaGLOaGaayzk aaGaeq4Wdm3aaeWaaeaacaWG0bGaeyOeI0IaeyiLdqKaamiDaaGaay jkaiaawMcaaaaa@4F8A@
    Where,
    σ f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadAgaaeqaaaaa@38D0@
    Filtered stress.
    α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3795@
    Degree of weighting decrease, a constant smoothing factor between 0 and 1. A higher α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3795@ value discounts previous values faster, which means the stress is less filtered.
1 Cockcroft, M. G., and D. J. Latham. "Ductility and the workability of metals." J Inst Metals 96, no. 1 (1968): 33-39