generalized_debonding#

Description#

This behavior 1this behavior is Z-set specific, and therefore does not apply for Z-mat for other codes is used for the special problem of interface debonding. See the command **create_interface_elements (and similar) in the Z-set user manual on how to insert cohesive elements in the mesh. The Generalized model 2Vandellos T., Huchette C. and Carrere N., “Proposition of a framework for the development of a cohesive zone model adapted to Carbon-Fiber Reinforced Plastic laminated composites.”, Comp. Struct. 105 (2013), 199-206. is based on the consideration of the characterization of interfacial properties and permits to use three different shapes for the cohesive law (bi-linear, tri-linear and trapezoidal). This model is described through a scalar variable λ, which characterizes the relative crack opening:

λ=(1δδ(δδ))δδ0(δασδ0δ(δδ0))+(δδ(δδ))(1+ασδ0δfδδ(δδf)),

where x=x if x>0 and x=0 if x0. The parameter δ is the relative displacement defined as

δ=uN2+uT2.

With respect to the interface normal n, uN=uNn and uTuuN denote, respectively, the normal and shear opening displacements. The parameters δ0 and δf are respectively the relative displacement associated with the interfacial strength τ0 and the one attained when the energy release rate is equal to the fracture toughness GC. It should be noted that the evolution of τ0 (resp. GC), as a function of the mixed-mode ratio, is defined by the stress criterion (resp. the propagation law). Finally, the parameter δ is associated with the stress τ attained at the end of the first part of the damage process (Fig. 15). These both parameters depend on the shape of the cohesive law which is defined using two shape parameters : ασ and αδ determined by

ασ=ττ0,αδ=(δδ0)(δfδ0).
../../_images/Generalized_shapes.svg

Fig. 15 Shape of the tri-linear model for a constant mixed-mode ratio in the (δ,T) plane.#

The damage variable λmax, which is the maximum value of λ reached up until the current instant, increases from 0 (no damage) to 1 (for a broken element). The normal and shear components of the cohesive traction T, i.e. TN=(Tn)nTNn and TT=TTN, are defined by:

TN=KuN(1λ),TT=KuT(1λ),

where K is the interfacial stiffness. For the compressive case, where uN<0, the normal component of the traction is modified to

TN=αcKuN,

with αc a penalization factor. Fig. 16 illustrates the typical response of the cohesive zone model under specific loads, for the parameters as given in the example.

Remarks:

  • the parameter αδ is not required with the bi-linear shape;

  • the parameter ασ has to be defined only with the tri-linear law;

  • two stress criteria (puissance and reinforcement) and three propagation laws (puissance, benzeggagh and vandellos) are available;

  • 3Turon A., Camanho P.P., Costa J. and Renart J., “Accurate simulation of delamination growth under mixed-mode loading using cohesive elements: Definition of interlaminar strengths and elastic stiffness.”, Comp. Struct. 92 (2010), 1857-1864.
  • the option *turon is required for applying the modification proposed by Turon 3Turon A., Camanho P.P., Costa J. and Renart J., “Accurate simulation of delamination growth under mixed-mode loading using cohesive elements: Definition of interlaminar strengths and elastic stiffness.”, Comp. Struct. 92 (2010), 1857-1864..

Syntax#

***behavior generalized_cohesive_zone    *strength      Zt Zt      Sc Sc    *toughness      G1c GIC      G2c GIIC    *stiffness      K K      alphac αc    *propagation propagation law (puissance or benzeggagh or vandellos)      n n    *initiation stress criterion (puissance or reinforcement)    *softening shape of the cohesive law (bi_linear or tri_linear or trapezoidal)      alpha_delta αδ      alpha_sigma ασ   [ *turon ]

Example#

***behavior generalized_cohesive_zone
  *strength
   Zt      100.
   Sc      100.
  *toughness
   G1c       0.0005
   G2c       0.0005
  *stiffness
   K         1.e8
   alphac    1.e3
  *propagation benzeggagh
   n 1.142
  *initiation puissance
  *softening tri_linear
   alpha_delta 0.4
   alpha_sigma 0.8
***return
../../_images/Generalized_tu.svg

Fig. 16 Example in two dimensions of the evolution of the cohesive traction as a function of the opening displacement, for two different loading cases: uN(t) with uT(t)=0 (thick red curves), and uT(t) with uN(t)=0 (thin green curves). Top left: applied load u(t). Note: for 2t4 s, the applied loading becomes negative (but the response uN remains 0 because of an implicit non-penetration condition). Top right: response T(t), Bottom left: λmax(t). Bottom right: u(t) vs T(t).#