/FAIL/HC_DSSE

Block Format Keyword Strain-based Ductile Failure Model: Hosford-Coulomb with Domain of Shell-to-Solid Equivalence. A nonlinear strain based failure criteria for shells with linear damage accumulation.

The failure strain is described by the Hosford-Coulomb function (refer to /FAIL/EMC for solids). Works only with elasto-plastic material number > 28. This failure criteria was developed by Keunhwan Pack (Massachusetts Institute of Technology MIT) and Dirk Mohr (Swiss Federal Institute of Technology ETH Zurich). 1

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/FAIL/HC_DSSE/mat_ID/unit_ID
Ifail_sh P_thickfail I-Flag            
If I-Flag = 0; Card 2 - Damage accumulation parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
a b c d n f
If I-Flag = 1; Card 2 - Failure test value input
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
c2 c3 c4 Inst_str n f
Optional line
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fail_ID                  

Definitions

Field Contents SI Unit Example
mat_ID Material identifier

(Integer, maximum 10 digits)

 
unit_ID Unit Identifier

(Integer, maximum 10 digits)

 
Ifail_sh Shell failure flag.
= 1 (Default)
Shell is deleted, if the damage criterion is satisfied in one integration point or layer.
= 2
Shell is deleted, if the damage criterion is satisfied in all, or defined in P_thickfail, shell layers. For a single layer shell, the stress tensor is set to zero.

(Integer)

 
P_thickfail Percentage of through thickness integration points that must fail before the element is deleted. (shells only).

Default = 1.0 (Real)

 
I-Flag Input type flag.
= 0 (Default)
Parameter input using a, b, c, d, n f .
= 1
Failure test input using c1, c2, c3, c4 1.

(Integer)

 
a Failure model parameter a.

(Real)

 
b Failure model parameter b.

(Real)

 
c Failure model parameter c.

(Real)

 
d Failure model parameter d.

(Real)

 
c2 Failure strain in pure shear (triaxiality η = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiabeE7aOjabg2da98aacaaIWaaaaa@3B03@ ).

(Real)

 
c3 Failure strain in uniaxial tension (triaxiality η = 1 3 ).

(Real)

 
c4 Failure strain in plane strain tension (triaxiality = η = 1 3 ).

(Real)

 
Inst_str Instability strain in plane strain tension for localized necking.

(Real)

 
n f Parameter n f .

Default = 0.1 (Real)

 
fail_ID Failure criteria identifier.

(Integer, maximum 10 digits)

 

Example

This example uses the HC-DSSE parameter input (a, b, c, d parameters with I-Flag = 0).

I F l a g = 0 a = 1.742 b = 0.7 c = 0.029 d = 1.6 I F l a g = 1 c 2 = 0.8 ( P u r e S h e a r ) c 3 = 0.7 ( U n i a x i a l T e n s i o n ) c 4 = 0.58 ( P l a n e S t r a i n T e n s i o n )

and one use physical input (failure strain input with I-Flag=1). HC-DSSE parameters a, b, c, d will be calculated using a curve fit by the Radioss Starter.

Failure definition in these two examples are equivalent.


Figure 1.

Example (HC-DSSE Parameter Input)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
#              MUNIT               LUNIT               TUNIT
                  kg                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  1. MATERIALS:
/MAT/PLAS_TAB/2/1
DP600 from SSAB Homepage
#              RHO_I
              7.8E-6                   0
#                  E                  Nu           Eps_p_max               Eps_t               Eps_m
                 210                  .3                   0                   0                   0
#  N_funct  F_smooth              C_hard               F_cut               Eps_f
         1         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
        14
#           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/HC_DSSE/2/1
#   Ishell        P_thickfail     I_Flag
         1                 .5          0
#                  a                   b                   c                   d                 n_f
               1.742                 0.7               0.029                 1.6                 0.1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/14
Mat_Curev Quasi-static DOCOL DP 600 (Material from SSAB Homepage 2010)
#                  X                   Y
                   0                .306                                                            
              .00112                .415                                                            
              .00218                .445                                                            
                .003                .461                                                            
              .00404                .474                                                            
              .00517                .489                                                            
              .00613                .498                                                            
               .0071                .505                                                            
              .00806                .512                                                            
              .00901                .522                                                            
               .0102                 .53                                                            
               .0121                .543                                                            
                .013                 .55                                                            
                .014                .555                                                            
                .015                .561                                                            
               .0159                .567                                                            
               .0171                .572                                                            
               .0181                .577                                                            
               .0204                .592                                                            
               .0303                .632                                                            
               .0405                .663                                                            
               .0502                .687                                                            
                 .06                .706                                                            
               .0702                .722                                                            
               .0807                .737                                                            
                 .09                .749                                                            
               .0997                .758                                                            
                .101                .759                                                            
                 .11                .768                                                            
           .15000001                .805                                                            
                  .2                 .84                                                            
           .30000001                  .9                                                            
                  .5                   1                                                            
                   1                1.21                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Example (Physical Input)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
#              MUNIT               LUNIT               TUNIT
                  kg                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  1. MATERIALS:
/MAT/PLAS_TAB/2/1
DP600 from SSAB Homepage
#              RHO_I
              7.8E-6                   0
#                  E                  Nu           Eps_p_max               Eps_t               Eps_m
                 210                  .3                   0                   0                   0
#  N_funct  F_smooth              C_hard               F_cut               Eps_f
         1         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
        14
#           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/HC_DSSE/2/1
#   Ishell        P_thickfail     I_Flag
         1                 .5          1
#                 c2                  c3                  c4            Inst_str                 n_f
                 0.8                 0.7                0.58                 0.1                 0.1    
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/14
Mat_Curev Quasi-static DOCOL DP 600 (Material from SSAB Homepage 2010)
#                  X                   Y
                   0                .306                                                            
              .00112                .415                                                            
              .00218                .445                                                            
                .003                .461                                                            
              .00404                .474                                                            
              .00517                .489                                                            
              .00613                .498                                                            
               .0071                .505                                                            
              .00806                .512                                                            
              .00901                .522                                                            
               .0102                 .53                                                            
               .0121                .543                                                            
                .013                 .55                                                            
                .014                .555                                                            
                .015                .561                                                            
               .0159                .567                                                            
               .0171                .572                                                            
               .0181                .577                                                            
               .0204                .592                                                            
               .0303                .632                                                            
               .0405                .663                                                            
               .0502                .687                                                            
                 .06                .706                                                            
               .0702                .722                                                            
               .0807                .737                                                            
                 .09                .749                                                            
               .0997                .758                                                            
                .101                .759                                                            
                 .11                .768                                                            
           .15000001                .805                                                            
                  .2                 .84                                                            
           .30000001                  .9                                                            
                  .5                   1                                                            
                   1                1.21                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. This failure criterion is defined in the space of equivalent plastic strain at failure versus stress triaxiality (state of stress) for plane stress condition. This allows for definition of failure strain that varies with different loading conditions. It consists of two curves. One is the fracture locus (that is, below the red curve) and the other is the localized necking locus (blue curve).


    Figure 2.
    The former takes the following form:(1)
    ε ¯ H C p r ( η , θ ) = b ( 1 + c ) 1 n f { [ 1 2 ( ( f 1 f 2 ) a + ( f 2 f 3 ) a + ( f 1 f 3 ) a ) ] 1 a + c ( 2 η + f 1 + f 3 ) } 1 n f

    f 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiGacAgadaWgaa WcbaGaaGymaaqabaaaaa@37BE@ , f 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiGacAgadaWgaa WcbaGaaGymaaqabaaaaa@37BE@ and f 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiGacAgadaWgaa WcbaGaaGymaaqabaaaaa@37BE@ are functions of the Lode angle θ :

    w i t h { f 1 ( θ ) = 2 3 cos ( π 6 ( 1 θ ) ) f 2 ( θ ) = 2 3 cos ( π 6 ( 3 + θ ) ) f 3 ( θ ) = 2 3 cos ( π 6 ( 1 + θ ) )

    θ = 1 2 π a r c cos ( 27 2 η ( η 2 1 3 ) )

    d D H C = d ε ¯ p ε ¯ H C p r ( η )

    The latter is defined only between uniaxial and eqi-biaxial tension conditions for ( 1 3 < η < 2 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaalaaabaGaaG ymaaqaaiaaiodaaaGaeyipaWJaeq4TdGMaeyipaWZaaSaaaeaacaaI YaaabaGaaG4maaaaaaa@3CB1@ ) in which localized necking can occur.(2)
    ε ¯ D S S E p r ( η ) = b { [ 1 2 ( ( g 1 g 2 ) d + g 1 d + g 2 d ) ] 1 d } 1 p
    w i t h { g 1 ( η ) = 2 3 η + 1 3 3 4 η 2 g 2 ( η ) = 2 3 η 1 3 3 4 η 2 (3)
    d D D S S E = d ε ¯ p ε ¯ D S S E p r ( η )
    • The universal exponent of p MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCaaaa@36EB@ =0.01 is used.
    • Localized necking is predicted in a non-local manner when all integration points or layers have d D D S S E > 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadsgacaWGeb WaaSbaaSqaaiaadseacaWGtbGaam4uaiaadweaaeqaaOGaeyOpa4Ja aGymaaaa@3CDA@ > 1.
    • The failure curve parameters a, b, c, and d, must be calibrated based on test results.

      η is the triaxiality.

    • Alternatively, switching the I-Flag to 1, allows Radioss to do the parameter fit internally.
    • No shell fracture in compression area ( η < 1 3 ).
    • Damage is calculated as:(4)
      D = Δ ε ¯ p ε ¯ H C p r ( η ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadseacqGH9a qpdaaeabqaamaalaaabaGaaeiLdiqbew7aLzaaraWaaSbaaSqaaiaa dchaaeqaaaGcbaGafqyTduMbaebadaqhaaWcbaGaamisaiaadoeaae aacaWGWbGaamOCaaaakmaabmaabaGaeq4TdGgacaGLOaGaayzkaaaa aaWcbeqab0GaeyyeIuoaaaa@468F@
1 Pack, Keunhwan, and Dirk Mohr. "Combined necking & fracture model to predict ductile failure with shell finite elements." Engineering Fracture Mechanics 182 (2017): 32-51.