Cohesive Zone Model CZM

Kulkarni et al. [83] studied the failure processes occurring at the micro-scale in heterogeneous adhesives using a multi-scale cohesive scheme. They also considered failure effect on the macroscopic cohesive response. Investigating the representative volume element (RVE) size has demonstrated that for the macroscopic response to represent the loading histories, the microscopic domain width needs to be 2 or 3 times the layer thickness. Additionally, they analyzed the effect of particle size, volume fraction and particle-matrix interfacial parameters on the failure response as well as effective 

The hybrid discontinuous Galerkin/cohesive zone model (DG/CZM) has been proposed by Mergheim et al. [172] and developed by Radovitzky et al. [173] and Prechtel et al. [174]. The DG method is applied to the non-linear solid mechanics In which the unknown field between bulk elements is considered. It can be combined with the CZM, therefore on the beginning of simulation, the interface elements are inserted between bulk elements. Wu et al. [145] studied composite failures at the microscale using hybrid DG/extrinsic cohesive law framework. 

The cohesive zone stress can be extracted from experimental data. To determine the cohesive stresses, the J-integral as a function of crack opening displacement (COD) can be determined experimentally for a DCB specimen using the following relationship [175], 

Where P is the reaction force at the loading pin location, 0 is rotation at the loading pin obtained through DIG calculation, and b is the width of the specimen. Then, a smoothing spline fit is obtained to take the first derivative of J-integral with respect to COD (6) at each data point with following equation  

The COD can be obtained by measuring the crack opening displacement between two points (one above and one below) at the location of the crack tip in the unloaded state [176]. Fuchs and Major [177] described that cohesive stresses can be evaluated by taking the first derivative of J-integral with respect to COD (5) for Mode-I type failure. 

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Figure 17.10 Implementation of the Cohesive Zone Model (CZM) (a) the Traction Separation Law (TSL), (b) Intrinsic TSL and (c) Extrinsic TSL. The cohesive laws are characterized by the strength, the critical opening and the critical energy release rate [145].

The results for the values of Gc discussed above were all derived using the analytical approach [30] described in previous sections. However, the peel test data shown in Table 1 have also been analysed [51,53] employing a finite element analysis embodying a cohesive zone model (CZM). In the CZM model, a maximum stress, a, is defined and the area under the stress versus displacement... 

Another approach for dealing with the singularity points is to use a cohesive zone model (CZM). This approach is associated to interface elements and enable to predict crack initiation and crack growth. It is a combination of a stress limit and fracture mechanics approach and relatively mesh insensitive. Many researchers are using this tool with accurate results (de Moura et al. 2006). However, the parameters associated to the CZM require previous experimental tuning and the user needs to know beforehand where the failure is likely to occur. This subject is discussed in detail in O Chap. 25. 

The Cohesive Zone Modeling (CZM) approach is well-suited for simulating interface fracture (e.g. a less restrictive/complicated mesh is required) and was used to model potential coating spallation at the TBC-substrate interface. The cohesive zone approach models the... 

The cohesive zone model has the advantage that initial crack and fine meshes are not necessary In addition, CZM fits well explicit schemes. Thus, the method is suitable... 

Jumbo (2007) used both CZM and CDM, together with the procedure illustrated by O Fig. 31.18, to predict the effect of environmental aging on the mechanical performance of a number of different types of bonded joint, including the double lap joint (DLJ) shown in O Fig. 31.20a. A typical finite element mesh used in his analysis is shown in O Fig. 31.20b. In the cohesive zone modeling, a bilinear cohesive material model was used, as illustrated in O Fig. 31.21. The bilinear traction separation law is given by ... 

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