/FAIL/SYAZWAN

Block Format Keyword This simplified failure criterion is based on a fracture surface with linear damage accumulation. It also provides the initialization of damage value using strain histories with linear strain path assumptions.

Format

Card 1 – Fracture surface parameters 1
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/FAIL/SYAZWAN/mat_ID/unit_ID
IcardIcard εfpMINεfpMIN      
If IcardIcard = 1: classical input / Card 2 – Fracture surface parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
C1 C2 C3 C4 C5
C6        
If IcardIcard = 2: plastic strain input / Card 2 – Failure plastic strains
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
εcompfεcompf εshearfεshearf εtensfεtensf εplanefεplanef εbiaxfεbiaxf
Card 3 – Damage initialization parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Dinit Dsf Dmax
Card 4 – Instability and softening parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Inst Iform Nvalue Softexp
Card 5 – Element size scaling
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDEl El_ref Fscale_El
Card 6 - 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)

IcardIcard Card input format flag. 3
= 1 (Default)
Fracture surface parameters input.
= 2
Plastic strain at failure input.

(Integer)

εfpMINεfpMIN Minimum plastic strain at failure.

Default = 0.0 (Real)

C1 First constant for failure surface.

(Real)

C2 Second constant for failure surface.

(Real)

C3 Third constant for failure surface.

(Real)

C4 Fourth constant for failure surface.

(Real)

C5 Fifth constant for failure surface.

(Real)

C6 Sixth constant for failure surface.

(Real)

εcompfεcompf Plastic strain at failure for uniaxial compression.

(Real)

εshearfεshearf Plastic strain at failure for shearing.

(Real)

εtensfεtensf Plastic strain at failure for uniaxial tension.

(Real)

εplanefεplanef Plastic strain at failure for plane strain.

(Real)

εbiaxfεbiaxf Plastic strain at failure for biaxial tension.

(Real)

Dinit Damage value initialization from strain tensors flag.
= 0 (Default)
Damage is not initialized.
= 1
Damage is initialized.

(Integer)

Dsf Damage initialization scale factor.

Default = 1.0 (Real)

Dmax Damage initialization maximum value.

Default = 1.0 (Real)

Inst Necking instability flag.
= 0 (Default)
Instability is not activated.
= 1
Instability is activated.

(Integer)

Iform Necking instability formulation flag.
= 1 (Default)
Incremental formulation (loading path history).
= 2
Direct formulation (no loading path history).

(Integer)

Nvalue The N-value derived from Hollomon’s Law.

Default = 0.25 (Real)

Softexp Stress softening exponent.

Default = 1.0 (Real)

fct_IDEl Element size factor function identifier.

(Integer)

El_ref Reference element size.

Default = 1.0 (Real)

[m][m]
Fscale_El Element size factor function scale factor.

Default = 1.0

fail_ID (Optional) Failure criteria identifier.

(Integer, maximum 10 digits)

Example

Comments

  1. It is highly recommended to set the value of IplasIplas in /PROP/SHELL to 1. This will allow accurate calculation of the principal strain ratio ββ .
  2. The value of C1, C2, C3, C4, C5, and C6 is based on:(1)
    εfp=C1+C2η+C3ˉθ+C4η2+C5ˉθ2+C6ηˉθεfp=C1+C2η+C3¯θ+C4η2+C5¯θ2+C6η¯θ
    Where,
    εfpεfp
    Plastic strain at failure.
    ηη
    Stress triaxiality with η=13(σxx+σyy)σVMη=13(σxx+σyy)σVM
    with 23η2323η23
    ˉθ¯θ
    Normalized Lode angle ˉθ=12πarcosζ¯θ=12πarcosζ
    with Lode angle ( θθ ) parameter ζ=cos(3θ)=272η(η213)ζ=cos(3θ)=272η(η213)

    Where, σVMσVM is the von Mises stress.

    Figure 1 shows the example of curve fit of plane stress failure curve into failure surface criteria.


    Figure 1. Example of Syazwan failure criterion fit
  3. Two different parameter input card formats are available for /FAIL/SYAZWAN depending on the value of IcardIcard .
    • If IcardIcard = 1: you must directly input the Ci parameters
    • If IcardIcard = 2: you can specify some plastic strain at failure for several commonly tested loading conditions: uniaxial compression εcompfεcompf , shearing εshearfεshearf , uniaxial tension εtensfεtensf , plane strain εplanefεplanef and biaxial tension εbiaxfεbiaxf . In that case, the Ci parameter will be automatically computed by solving the set of equations below:(2)
      {C113C2C3+19C4+C5+13C6=εcompfC1=εshearfC1+13C2+C3+19C4+C5+13C6=εtensfC1+13C2+13C4=εplanefC1+23C2C3+49C4+C523C6=εbiaxfC218πC3+23C418π3C6=0⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪C113C2C3+19C4+C5+13C6=εcompfC1=εshearfC1+13C2+C3+19C4+C5+13C6=εtensfC1+13C2+13C4=εplanefC1+23C2C3+49C4+C523C6=εbiaxfC218πC3+23C418π3C6=0
    Note: The last equation imposes that the plane strain condition corresponds to a local minimum of the failure criterion.
  4. In some cases, the criterion may have negative or very low values for some loading conditions. In that case, it will be bounded by the minimum plastic strain at failure parameter εfpMINεfpMIN that must be positive or null (by default = 0.0). All values under εfpMINεfpMIN are then ignored.
    Figure 2 shows an example with a minimum value (orange curve) of 0.2.


    Figure 2. Failure criterion (blue curve) bounded by plastic strain at failure minimum value. εfpMINεfpMIN (orange curve) of 0.2
  5. The damage variable evolution is computed incrementally as:(3)
    D=t=0ΔεpεfpD=t=0Δεpεfp
  6. You may want to realize a simulation starting from existing total and plastic strains fields (after a previous forming simulation for instance). In the case where the failure criterion is not computed during the first simulation, it is possible to estimate a damage field from the total strain tensor and the plastic strain values obtained at the end of the first simulation (using .sta files). If the Dinit flag is set to 1, the damage field will be computed if the plastic strain ≠ 0. /INISHE/STRA_F, /INISHE/STRA_F, /INISHE/EPSP_F and /INISH3/EPSP_F must be present in the keywords of the status file. The initial stress tensors are not incorporated into the simulation model; thus, the stress triaxiality is derived using:(4)
    η=131+β1+β+β2η=131+β1+β+β2
    The ββ value can be recovered from the stress triaxiality value using the first root of Equation 4:(5)
    β=(23η2)3η2(49η2)2(3η21)β=(23η2)3η2(49η2)2(3η21)
    Then, an initial damage value can be estimated as:(6)
    Dt=0=εt=0pεfpDt=0=εt=0pεfp
    Figure 3 shows an example of initialized damage field in one-step after a forming simulation performed without failure criterion computation. Damage field is then deduced using the plastic strain and the strain tensor as presented above.


    Figure 3. Example of damage field “one-step” initialization after a forming simulation
  7. A controlled necking instability can be used if the flag Inst is set to 1. To trigger this instability, a criterion variable denoted ff is computed based on the Nvalue specified by you, using:(7)
    ε1=2(2α)(1α+α2)43α3α2+4αNvalueε2=2(2α1)(1α+α2)43α3α2+4αNvalueε1=2(2α)(1α+α2)43α3α2+4αNvalueε2=2(2α1)(1α+α2)43α3α2+4αNvalue
    Where, αα ratio between the minor principal and major principal stress computed from ββ using:(8)
    α=2β+12+βα=2β+12+β
    You can then compute an effective plastic strain at necking instability:(9)
    εinstp=ε143(1+β+β2)εinstp=ε143(1+β+β2)

    The parameter Nvalue is the value of the instability plastic strain taken in uniaxial tension (for which η=1/3η=1/3 and ˉθ=1¯θ=1 ). You can then use the relation linking ββ and the stress triaxiality described above to plot the instability strain evolution.

    Using the instability plastic strain, an instability criterion variable denoted ff is either computed:
    • Incrementally (if Iform = 1) to take into account the loading history(10)
      f=t=0Δεpεinstpf=t=0Δεpεinstp
    • Directly (if Iform = 2) to ignore the loading path history(11)
      f=εpεinstpf=εpεinstp
    If the criterion is reached ( f=1f=1 ), the instant value of the damage variable DD is saved in the value DcritDcrit that becomes an element history variable. The necking instability can then be triggered by a stress softening whose equation is:(12)
    D=ΔDf=ΔfDcrit={1whilef<1Dwhenf1σ=σeff(1(DDcrit1Dcrit)Softexp)D=ΔDf=ΔfDcrit={1whilef<1Dwhenf1σ=σeff(1(DDcrit1Dcrit)Softexp)
    Where,
    σσ
    Damaged stress tensor.
    σeffσeff
    Undamaged effective stress tensor.
    DcritDcrit
    Critical damage value that triggers stress softening.
    SoftexpSoftexp
    Exponent parameter.
    For visualization purposes, the instability curve ( εinstpεinstp versus ηη ) can be obtained from all the equations above. For instance, if the Nvalue is set to 0.175, the following curve (Figure 4) is obtained.


    Figure 4. Example of instability curve (orange) and its position with respect to failure criterion (blue)

    The effect of instability curve is restricted to positive stress triaxiality (as necking only occurs in tension) and only has an effect when it is under the failure criterion curve.

    Figure 5 shows several instability curves obtained with different Nvalue parameter values.


    Figure 5. Instability curves obtained with different Nvalue parameters
  8. Element size scaling can be used to regularize the failure and ensure to obtain an almost constant fracture energy dissipated with different mesh sizes. This element size dependency is introduced by computing a size scale factor denoted fsizefsize defined by the function fct_IDEl. The size scaling factor evolution is given with respect to the ratio of initial element characteristic length divided by a reference size El_ref (by default = 1.0): fsize(L0eLref)fsize(L0eLref) . An additional scale factor Fscale_El can also be applied to the entire regularization function. The element size scale factor fsizefsize thus computed is introduced in the damage variable evolution equation (and if defined, the instability variable evolution equation) as:(13)
    D=t=0Δεpεfpfsize(L0eLref)felscaleD=t=0Δεpεfpfsize(L0eLref)felscale
  9. Alternatively, the /NONLOCAL/MAT option which is compatible with Syazwan failure criterion (Figure 6) can be used to regularize the solution according to mesh size and orientation. If the non-local regularization is used, the non-local plastic strain is used to compute the damage evolution (and the instability variable, if used). In that case, the maximum non-local length parameter LE_MAX is used instead of the initial element size if an element size scaling is defined through fct_IDEl. Also, the non-local regularization is also available with the “one-step” damage field initialization.


    Figure 6. Example of /NONLOCAL/MAT option cumulated with /FAIL/SYAZWAN on automotive DP450 steel