Search for: All records

For the first time, the mixed-mode dynamic fracture in anisotropic functionally varying microcellular structures is investigated herein. To this end, a recently developed homogenization MATLAB implementation capable of considering material and geometry-induced anisotropy is used, and a continuous medium with equivalent functionality distributed mechanical properties to the original microcellular domain is obtained. Then, the resulting material domain is subjected to dynamic loads, and the crack propagation is predicted by using a novel Timoshenko-based peridynamic model. This innovative method unprecedentedly accounts for a bond-length dependent shear influence factor and a shear strain-based failure criterion. Finally, numerous cases consisting of compact-tension (CT) and Kalthoff-Winkler specimens with several void sizes, shapes, and distribution patterns are numerically solved. The results demonstrate that the crack path is significantly influenced by the void distribution pattern near the crack tip, providing a foundation for engineering crack propagation to prevent it from reaching critical areas of a structure. 

The original two-dimensional bond-based peridynamic (BBPD) framework, which only considers the pairwise forces (compression and tension) between two material points, is extended by incorporating the effect of shear deformation in the calculations and its influence on the failure of the bonds. To this end, each bond is considered as a short Timoshenko beam, and by doing so, the traditional BBPD is enhanced into a more comprehensive model known as multi-polar peridynamic (MPPD). The proposed novel approach explicitly considers the shear influence factor used in Timoshenko beams and introduces a strain-based shear deformation failure criterion. The model is then validated against two benchmark experimental tests (i.e., a standard pure mode I edge crack, and a Kalthoff-Winkler configuration) reported in the literature under in-plane dynamic loading and plane stress conditions. In most cases, the developed model is shown to be more accurate in predicting the crack paths obtained from the experimental results when compared to other theoretical methods delineated in the literature. Furthermore, a noticeable change in crack branching and crack path is observed in a study on the effects of Poisson’s ratio and the loading rate. This investigation also demonstrated that the proposed MPPD model can accommodate materials with Poisson’s ratios up to 1/3, expanding the range beyond the traditional BBPD limitations. 

This study advances the state of the art by computing the macroscopic elastic properties of 2D periodic functionally graded microcellular materials, incorporating both isotropic and orthotropic solid phases, as seen in additively manufactured components. This is achieved through numerical homogenization and several novel MATLAB implementations (known in this study as Cellular_Solid, Homogenize_test, homogenize_ortho, and Homogenize_test_ortho_principal). The developed codes in the current work treat each cell as a material point, compute the corresponding cell elasticity tensor using numerical homogenization, and assign it to that specific point. This is conducted based on the principle of scale separation, which is a fundamental concept in homogenization theory. Then, by deriving a fit function that maps the entire material domain, the homogenized material properties are predicted at any desired point. It is shown that this method is very capable of capturing the effects of orthotropy during the solid phase of the material and that it effectively accounts for the influence of void geometry on the macroscopic anisotropies, since the obtained elasticity tensor has different 𝐸1 and 𝐸2 values. Also, it is revealed that the complexity of the void patterns and the intensity of the void size changes from one cell to another can significantly affect the overall error in terms of the predicted material properties. As the stochasticity in the void sizes increases, the error also tends to increase, since it becomes more challenging to interpolate the data accurately. Therefore, utilizing advanced computational techniques, such as more sophisticated fitting methods like the Fourier series, and implementing machine learning algorithms can significantly improve the overall accuracy of the results. Furthermore, the developed codes can easily be extended to accommodate the homogenization of composite materials incorporating multiple orthotropic phases. This implementation is limited to periodic void distributions and currently supports circular, rectangular, square, and hexagonal void shapes. 

Many well-known fracture criteria rely on a mode-independent parameter measured under pure mode I loading conditions, called the critical distance, which is traditionally considered a material property representing the size of the fracture processing zone. Recent studies have unveiled the potential for significantly increased accuracy in fracture criteria by utilizing a mode-dependent critical distance in calculations. In response to this revelation, the concept of effective critical distance (ECD) was recently introduced and successfully examined in cracked components under in-plane and out-of-plane loading conditions, both theoretically and experimentally. In this work, for the first time, the concept of ECD is introduced for V- and U-shaped notches to form a new three-dimensional notch fracture criterion based on the maximum principal strain (MPSN). The fracture angle and the onset of fracture predicted by the proposed criterion are theoretically compared to other existing criteria, and experimentally, to the test data presented in the literature. It is shown that the developed criterion can more accurately predict the mixed-mode I/II/III fracture behavior of V- and U-notched components which accentuates the profound significance of embracing the ECD concept in constructing three-dimensional fracture criteria. 

ABSTRACT A recently developed Timoshenko‐based peridynamic model with a variable micropolar shear influence factor is extended to study the behavior of dynamic crack propagation in functionally graded materials (FGMs). To this end, first, the proposed model is validated against two experimental three‐point bending benchmark problems with different material functions as well as varying loading rates and durations. Then, numerous additional cases with different boundary conditions and material distribution are studied to predict crack initiation and propagation in such mediums. The examples consist of three‐point bending and Kalthoff–Winkler specimens with various material functions under dynamic loads. Finally, the effects of material anisotropy induced by functionally varying material properties on crack propagation path are addressed. It is shown that this new model is advantageous because of its capability to account for shear deformation effects in the bonds previously ignored by the original bond‐based peridynamic models. Moreover, comparing the proposed modified bond‐based model to more complex methods, such as state‐based peridynamics, reveals that the simplicity of the current approach results in lower computational costs while still achieving comparable results.