PSI - Issue 13

Reza H. Talemi et al. / Procedia Structural Integrity 13 (2018) 775–780 Author name / Structural Integrity Procedia 00 (2018) 000–000

778

4

One of the approaches within the framework of XFEM, which is also available in ABAQUS, is based on traction separation cohesive behavior. This approach is used to simulate crack initiation and propagation. This is a very general interaction modelling capability, which can be used for modelling brittle or ductile fracture. Unlike cohesive zone modelling approaches, which require that the cohesive surfaces align with element boundaries and the cracks propagate along a set of predefined paths, the XFEM-based cohesive segments method can be used to simulate the crack initiation and propagation along an arbitrary, solution-dependent path in the bulk material, since the crack propagation is not tied to the element boundaries in a mesh. In this case the near-tip asymptotic singularity F α (x) is not needed, and only the displacement jump across a cracked element is considered. Therefore, the crack has to propagate across an entire element at a time to avoid the need to model the stress singularity. Phantom nodes, which are superposed on the original real nodes, are introduced in ABAQUS to represent the discontinuity of the cracked elements. When the element is intact, each phantom node is completely constrained to its corresponding real node. When the element is cut through by a crack the cracked element splits into two parts. Each part is formed by a combination of some real and phantom nodes depending on the orientation of the crack. Each phantom node and its corresponding real node are no longer tied together and can move apart. Damage modelling allows simulation of crack initiation and eventual failure of the enriched area in the solution domain. The initial response is linear, while the failure mechanism consists of a damage initiation criterion and a damage propagation law. The damage initiation and evolution were defined based on the cohesive stress, σ max and fracture energy (Γ), respectively. The cohesive stress was determined by simulating the DWTT using von-Mises isotropic hardening elastic-plastic model without any damage accumulation. ABAQUS Dynamic/Explicit solver was used for this simulation. Next, the numerically obtained force versus displacement curve was compared against the experimental observations for both configurations. The onset of crack propagation was considered at the deviation point between the numerical and the experimental curves and the maximum value of the maximum principal stress at the notch tip was used for evaluating the cohesive stress. Using this approach, the maximum load carrying capacity can be captured during the damage initiation process under the given stress value, and the value of the maximum load carrying capacity is equal to the cohesive stress. The fracture energy (cohesive energy, Γ) was used for the damage evolution criteria. The cohesive energy was estimated using the relationship

(1 K

2

(2)

   G IC

IC

)

E

2  

where G IC is the fracture energy, K IC is the fracture toughness, E is the Young’s modulus and υ is Poisson's ratio. G IC becomes the critical value of the rate of release in strain energy for the material which leads to damage evolution and possibly fracture of the specimen. The relationship between stress intensity and energy release rate is significant because it means that the G IC condition is a necessary and sufficient criterion for crack propagation since it embodies both the stress and energy balance criteria. The value for the fracture toughness was estimated from DWTT energy. The relationship between the fracture toughness, K IC , the DWTT energy, J DWTT and the materials’ thickness, t , can be written as follows

1.38

J

 



(3)

6.76  

K

DWTT

IC

1.5    t

3.29

After calculating both material’s parameters for the XFEM crack propagation simulation, i.e. cohesive stress, σ max and fracture energy (Γ), new FE simulation was set-up using the same model shown in Fig. 1(c). In general, explicit codes are used to capture the complicated system response as a function of time, such as simulating dynamic crack propagation of DWTT. However, currently, the ABAQUS Dynamic/Explicit solver does not support the use of XFEM. Therefore, in this study, for the crack propagation model, this issue was overcome by using the Dynamic /Implicit solver. For more information, readers are referred to previous published works Hojjati-Talemi et al. (2016), Talemi (2016) and Talemi et al. (2016).