13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- are not considered, such as surrounding continuum element influence, element friction influence and constraint condition influence. Base on Roe and Siegmund’s method, some authors did further research work [14-16]. 2. Cohesive zone model 2.1. Fundamentals The CZM intends to describe the real physical fracture process by phenomenological equations. It treats the material separation in the fracture process zone as material damage. Separation is the displacement jump occurring in the cohesive element. In the CZM, the material separation behaviour is described within a constitutive equation relating the cohesive traction T to the material separation δ, called traction separation law (TSL). The TSL represents the material deterioration occurring in the damage zone under the monotonic loading condition. For the shape of the TSL many proposals have been given, but no one can easily decide which is right or wrong. For all TSLs, two parameters are contained: maximum traction T0 and critical separation δ0. The area under the TSL represents the cohesive energy Γ0. If the shape of the TSL is selected, the cohesive parameters should be determined from the correlative experiment. In this paper, the TSL from Scheider et al. is taken as a basis (Equation (1) and Figure 1). More details on application of this CZM can be taken from references [8-9]. ( ) ( ) 2 1 1 1 0 0 1 2 3 2 2 2 2 0 0 2 0 2 2 1 2 3 1 δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ δ ⎧ ⎛ ⎞ ⎛ ⎞ ⎪ − < ⎜ ⎟ ⎜ ⎟ ⎪ ⎝ ⎠ ⎝ ⎠ ⎪ = = ≤ ≤ ⎨ ⎪ ⎛ ⎞ ⎛ ⎞ − − ⎪ − + < ≤ ⎜ ⎟ ⎜ ⎟ ⎪ − − ⎝ ⎠ ⎝ ⎠ ⎩ T T f T (1) T0 δ1 δ2 δ0 δ(mm) T (MPa) Γ0 initial stiffness unloading/reloading path Figure 1. Traction separation law according to Scheider et al. [8], given by Equation (1) 2.2. Triaxiality dependent behaviour When the phenomenological TSL is applied for ductile fracture analysis, it is possible to find a fundamental relationship between this TSL and micromechanics. A micromechanical model - GTN model [17] is used to simulate a biaxial tension test for one volume element, a cohesion-decohesion curve can be obtained. Such cohesion-decohesion curve is considered as the micromechanical TSL and can be used to fit the phenomenological TSL. For this micromechanical traction separation curve, some investigators found that it was strongly dependent on the triaxiality condition of the
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