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The SEER*Stat software has an auto-update feature. After you have installed SEER*Stat for the first time, the software can be configured to automatically upgrade with the SEER*Stat release or to delay the update for a couple weeks after the release. See Auto-updating in SEER*Stat for more information.
In the field of polymers, many applications of multi-layered structures, such as printed circuit boards, classical carbon fiber reinforced composites, pipes, and containers for media transport, are already in use. To date, however, multi-layer build-ups are mainly used for the functional properties of the added materials and not to optimize mechanical properties, such as fracture toughness. A classical example of the former group is the enhancement of barrier properties, as seen in food-related packaging and fuel storage [17]. Some applications, such as multi-layer pipes in sewer applications, already utilize different materials for their mechanical properties or necessary chemical resistance. However, the exact architecture of the layers is mainly based on the experience of engineers, and extensive and expensive trial and error approaches. In order to optimize the possibilities of multi-layered structures with regard to their mechanical properties, easier and more precise methods are required. Adequate methods have to account for local damage mechanisms such as crack propagation, crack arrest at layers, and subsequent re-initiation.
One possibility to optimize layered materials for structural applications is the use of fracture mechanical approaches. For example, mathematical equations describe the behavior of cracks that are in the vicinity of an interface between materials of different mechanical properties. An example of this approach is the description by He and Hutchinson of crack deflection at an interface between dissimilar elastic materials [18,19], which is a favored model for the description of layered ceramics [20,21].
For inhomogeneous materials there is also the issue of crack deflection and/or crack arrest due to inhomogeneous stress fields or toughness, phase interface debonding, and initiation of cracks from microstructural features. For layered polymers with good adhesion and a straight crack perpendicular to the layer orientation, it can be assumed that only straight crack growth is relevant. Nevertheless, this crack growth can be severely influenced by the stress fields and plastic deformations of the layers.
Currently, different groups are working on approaches to solve the issue of changing crack-driving forces in layered materials. One possibility is the use of configurational-force-based concepts [22], which have shown promising results for several material classes, including polymers [9]. However, they are limited to applications where plastic strains in the vicinity of the crack tip can be separated from plastic strain fields at the scale of the specimen [23]. For very ductile polymers and high levels of plastic deformation, this condition may not be fulfilled. For example, in [9], separate cohesive zone elements had to be introduced to model the initiation of cracks in the brittle layer and further propagation of the crack.
Thus, the current work aims to provide an alternative approach for the description of the fracture behavior of multilayered polymeric materials. The chosen method uses the finite fracture mechanics concept [24] for predicting crack initiation, and the energy approach to assess crack growth (the energy release rate of the crack is compared to the critical energy release rate of the material). The finite fracture mechanics concept uses a combined energy-stress criterium to predict the crack initiation, as proposed by Leguillon et al. [25]. The energy approach for crack growth is used to account for high plastic strains and large regions of plastic deformations. In contrast, the configurational force-based concept with incremental plasticity is based on the separation of the crack tip-associated plastic region and the far-field plastic region [9,26].
The model of the SENB tests is shown in Figure 3b and its parameters are defined in Table 1. One-half of the specimen is modeled in a 2d plane stress model. In the x = 0 plane, the x-displacements are constrained. The outer rollers and the central rollers are modeled rigidly. While the outer roller is fixed, the top roller is constrained in the x-direction, and a displacement uy is applied to it. The crack lies in the x-symmetry plane, so that cracks can be propagated by releasing the x-constraints in the region of crack propagation. The model uses 8-node plane stress elements with reduced integration. The mesh size is 0.2 mm and is refined by a factor of 5 towards the region of the crack. The total number of elements in the SENB test model is 5700. The implicit solver of Abaqus is used. Between the specimen and the rollers, hard contact with a penalty formulation is defined. The coefficient of friction μ between rollers and specimen was studied using the test results of the homogeneous SENB specimens.
If the CDF obtained in this way is above the fracture toughness Gc of the material, the crack that was extended by Δa is regarded as the new, updated crack. If not, the computation with the extended crack is discarded.
In parallel, the model is checked for the initiation of additional cracks at different positions. In the layered SENB specimen, a crack can initiate in the x-plane from the bottom point of the EVOH layer upwards. This is due to the brittle behavior of the EVOH material compared to the HDPE material. For initiation, the combined stress-energy criterion as postulated in [25] is used, which states that a crack initiates when both a stress- and an energy criterion are fulfilled in a certain region. The stress can be directly evaluated in the FEA simulation and compared to a critical stress of the material. For the energy criterion, cracks with varied initiation length have to be introduced and computed. In the presented model, the stress criterion is checked first. If no crack can initiate based on the stress, the computationally costly energy criterion is not checked. The model starts with the longest possible crack where the stress criterion is fulfilled. Once a crack is initiated, it is regarded as an additional crack that can grow in an incremental manner. In this case, the SENB specimen has two crack tips that will subsequently be checked for crack growth.
(a) Forces plotted over the displacement for the layered SENB specimens for both the numerical models and the experiments. For the simulation results, the critical energy release rate Gc,HDPE is varied between 3000 and 12,000 J/m2. Frictionless contact is used between roller and specimen. Additionally, (b) shows the corresponding cracked regions in the specimen as dark gray, blue, green, and red areas. For Gc,HDPE = 3000 J/m2, the initial crack grows into the HDPE material. For higher Gc,HDPE values, there is very small growth in the initial crack, and at a displacement uy of 2.75 mm, a crack initiates in the EVOH layer and grows through the whole EVOH layer.
Important Note for Multi-User Installations: Before updating to Minitab Workspace, you should first verify you have the latest version of the License Manager. If you plan to mass deploy utilizing a software asset management tool, please download the Minitab Workspace Mass Deployment Package.
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