X-force CFD 2005 Crack

X-force CFD 2005 Crack >>>>> https://shoxet.com/2sXmYv

With the rapid growth of available data and computing resources, using data-driven models is a potential approach in many scientific disciplines and engineering. However, for complex physical phenomena that have limited data, the data-driven models are lacking robustness and fail to provide good predictions. Theory-guided data science is the recent technology that can take advantage of both physics-driven and data-driven models. This study presents a novel peridynamics-based machine learning model for one- and two-dimensional structures. The linear relationships between the displacement of a material point and displacements of its family members and applied forces are obtained for the machine learning model by using linear regression. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The accuracy of the coupled model is verified by considering various examples of a one-dimensional bar and two-dimensional plate. To further demonstrate the capabilities of the coupled model, damage prediction for a plate with a preexisting crack, a two-dimensional representation of a three-point bending test and a plate subjected to dynamic load are simulated.

Predicting progressive failures in structures is a challenging task in engineering. The classical continuum mechanics faces conceptual and mathematical difficulties in terms of predicting crack nucleation and growth, especially for multiple crack paths because it uses differential equations. In contrast, peridynamics (PD) is a nonlocal theory representing material behavior by using integro-differential equations that are valid in both continuous and discontinuous models [1,2,3,4,5]. Therefore, PD is suitable for predicting progressive damages.

The study in [55] proposed convolutional neural networks for predicting the damage patterns on a disk hit by an indenter. First, the PD simulations to predict crack patterns on a disk hit by an indenter are conducted to generate the data set. Later, the obtained data set is used to train the neural networks. Therefore, the trained neural networks can be used to predict damage patterns on a disk subjected to different impact loadings. Moreover, as the inverse problem, the trained neural networks can also identify the collision location, angle, velocity and size of the indenter from a given damage pattern on the disk.

As can be observed from [53, 55], the neural networks are trained by using the crack propagation data predicted by trial numerical predictions, which can be very computationally expensive and limited. On the other hand, when available data are limited, the vast majority of recent machine learning techniques are lacking robustness and accuracy [56]. Therefore, a hybrid approach of combining machine learning and physics-based modeling becomes highly beneficial. Therefore, in this study, a hybrid approach of coupling machine learning and peridynamic models for fracture prediction of structures is presented. Specifically, the PD model is applied for special regions in structures such as near crack surfaces or near boundary areas. Meanwhile, the ML model is used for the remaining regions to reduce the computational cost.

The machine learning models to find displacements of a material point based on displacements of its family members and its external body forces in one-dimensional (1D) and two-dimensional (2D) structures are presented. The numerical procedure for the coupling of the ML model and PD model is also provided. The capability of the hybrid approach is verified by considering various examples for 1D and 2D structures. The results predicted by the coupled models are compared with FEA and conventional PD results. For further verifying the capability of the coupling model, progressive damages in a plate with a preexisting crack subjected to tension, on a 2D representation of a three-point bending test, on a plate subjected to dynamic loads are presented.

As given in Sect. 4, the PD-based ML models for 1D and 2D structures are obtained for material points with full interactions with their family members. Specifically, the 1D ML model is applicable for material points with 6 interactions and the 2D ML model is applicable for material points with 28 interactions. However, for material points that have some missing family members or broken interactions such as material points near boundary surfaces or near crack surfaces, the developed ML models can produce significant errors. Moreover, generating training data for all of these special cases can be very time-consuming. Therefore, a hybrid approach that couples the ML model with the PD model is used. The behaviors of the material points with full interactions are predicted by using the ML model. Meanwhile, all other material points are predicted using the PD model.

Similar to 1D static case, Fig. 8 presents the algorithm for 2D static problems. In this case, PD region is defined by material points with less than 28 intact interactions (near boundaries and crack surfaces). Meanwhile, the ML region is defined by material points with 28 intact interactions (regions that are far from boundaries and crack surfaces). The displacements of material points in PD regions are obtained by solving the PD equations of motion given in Eq. (11) as shown in Loop 2.1, and the displacements of material points in ML regions are obtained by using the linear relations given in Eq. (22) as shown in Loop 2.2.

In this section, first, the PD-based machine learning models are verified by considering various examples of 1D and 2D structures. As presented in Sect. 5, a hybrid approach for coupling the machine learning models and bond-based PD models is used. The results obtained by the coupled approach are compared to PD and finite element analysis (FEA) solutions. The FEA solutions are conducted by using ANSYS commercial software with the LINK180 element for the 1D bar and PLANE182 element for the 2D plate. To further verify the capabilities of the coupled approach, damage predictions on a plate with preexisting crack subjected to tension, on a 2D representation of a three-point bending test and on plate subjected to dynamic loading are performed.

After verifying the accuracy of the hybrid approach by coupling of ML and PD models, in this section, damage predictions for 2D plates are presented. In order to properly capture the behavior of the structures with progressive damages, the PD regions and ML regions are updated adaptively. At each time step, material points with 28 intact interactions are updated and the behaviors of these material points are obtained by using the 2D ML model. On the other hand, the behaviors of material points with less than 28 intact interactions, which are either near boundary surfaces or near crack surfaces, are obtained by using PD solution. Similar to the previous examples, the surface correction [5] is adopted for the PD regions near boundary surfaces.

Figure 25 shows the damage evolution on the plate. As shown in Fig. 25a, the crack starts propagating when the applied displacements equal to \(3.5\times 10^{-4}\hbox { m}\). As the applied displacements increase, the crack propagates horizontally as expected and it nearly reaches two sides of the plate when applied displacements are \(5.3\times 10^{-4}\hbox { m}\). This observation has good agreement with the experimental results captured by .Simonsen, Törnqvist [64].

Figure 28 shows the damage evolution on the plate. As expected, the crack propagates towards the middle position of the specimen. As shown in Fig. 28b, the angle between the crack path and vertical axis is approximate \(35^{0}\) which shows good agreement with the experimental result [66]. Figure 29 shows the adaptive PD and ML regions at different load steps. Similar to the previous example, the PD and ML regions are automatically updated based on the progressive damages on the structure. As shown in Fig. 29c, when the applied displacement equals to \(14\times 10^{-5}\hbox { m}\), the number of material points in the PD region is 2523, which is 14.5% of the total number of material points in the discretized model, 17458.

Figure 31 presents the damage evolution on the plate. As can be seen from the figure, under dynamic loading conditions, the crack propagates up \(67.3^{0}\) orientation with respect to the horizontal axis. After \(80\upmu \)s, the crack propagates nearly to the top edge of the plate as shown in Fig. 31d. As can be seen from the figure, the crack paths captured by coupled ML and PD models match very well with the experimental results in [65, 67, 68]. Figure 32 shows the PD and ML regions at different time steps. As shown in Fig. 32d for the coupling model at \(80\upmu \)s, 12.68% of the total number of material points (2909 per 22950 material points) belong to the PD region.

Flaws arise in most materials joining processes. For example, when arc welding aluminium alloys, weld metal porosity[138] and, depending on the particular alloy, weld metal solidification cracking and HAZ liquation cracking[139] are among the most common flaw types. The occurrence of such problems has contributed to the widely held view that some aluminium alloys, in particular some of the high strength 2xxx and 7xxx series alloys, are difficult, or indeed impossible, to fusion weld successfully. Being a solid state joining process, FSW obviates the problems of porosity and hot cracking. In this respect it is worthwhile to make a distinction between flaws and defects, although the two terms are often used interchangeably within the literature. The usual distinction is that a flaw or imperfection is a feature that one would prefer not to be in the weld, but it may or may not compromise the integrity of the weld. If, after evaluation, the flaw is deemed unacceptable, then it becomes a defect. If it does not compromise the integrity, then it is a tolerable flaw. Flaws or discontinuities should be characterised as defects only when specific acceptance criteria, related to the engineering application, are exceeded, and the presence of the flaw compromises the integrity of the structure. Table 2 summarises the characteristic flaw types in butt and lap welds in friction stir welds and their principal causes. In fact the most common flaw types are caused by use of under optimised parameters or a lack of process control. Since understanding of the causes of these flaws/defects is good, it is usually possible to rectify these problems by changes to parameters, tool designs or operating practice. 2b1af7f3a8