Two procedures to evaluate fracture resistance of notched components are proposed in this contribution: the Strain Energy Density (SED) over a control volume and the Cohesive Zone Model (CZM). With the aim to simplify the application of the two fracture criteria, the concept of the ‘equivalent local mode I’ is presented. The control volume of the SED criterion and the cohesive crack of the CZM, have been rotated along the notch edge and centered with respect to the point where the elastic principal stress is maximum. Numerical predictions are compared with experimental results from U and V shaped notches under three point bending with notch root radius ranging from 0.2 to 4.0 mm. In parallel the loading conditions vary, from pure mode I to a prevailing mode II. All specimens were made of PMMA and tested at -60°C. The good agreement between theory and experimental results adds further confidence to the proposed fracture criteria.
Application of cooling slope in casting is a relatively simple process with low equipment and processing costs, which is able to produce semi-solid slurries with different parameters such as pouring temperature, length and angle of slope plate, and plate type. In this study, the effect of angle and length of copper made slope plate on the microstructure of A360-Aluminum alloy is investigated. Microstructure study of metallographic samples in different conditions revealed that for 400mm slope length and 60° slope angle the optimum sphierized and homogenized microstructure is achieved. Also, under these conditions, the most hardness (77HB) was obtained, which might be because of suitable solidification conditions namely time and rate of shear stress. After finding the suitable conditions of slope length and angle, the effect of the circulation cooling system was examined; and the method with cooling system was found to result in more homogenized microstructure compared to ordinary method.
The present problem deals with the thermo-elastic interaction of a gold nano-beam resonator induced by ramp-type heating under the two temperature theory of generalized thermoelasticity. The governing equations are constructed in the context of two-temperature three-phase-lag model (2T3P) and two-temperature Lord-Shulman (2TLS) model of generalized thermoelasticity. Using the Laplace transform, the fundamental equations have been expressed in the form of a vector-matrix differential equation which is then solved by Eigen value approach and Mathematica software package has been used as a tool. The inversion of Laplace transforms are computed numerically using the method of Fourier series expansion technique. Numerical results for lateral vibration, temperature, displacement, stress, and the strain energy are presented graphically for Lord-Shulman model and also for three-phase lag model. A numerical instance of gold nano-beam in femtoseconds scale has been calculated to present the effect of the ramping time parameter on the entire studied field. The effect of two-temperature parameter is also discussed on the physical fields.
Different criteria are available in the literature to assess the fracture behaviour of sharp V-notches. A typical and well-known criterion is based on the application of the notch stress intensity factors (NSIFs), which are able to quantify the intensity of the stress fields ahead of the notch tip. This work considers two recent energy-based criteria applied here to sharp V-notches. The first criterion is based on the averaged value of the strain energy density (SED), while the second one called Finite Fracture Mechanics (FFM) criterion is available under two different formulations: that by Leguillon et al. and that by Carpinteri et al. Considering the averaged SED criterion, a new expression for estimating the control radius Rc under pure Mode II loading is proposed and compared with the sound expression valid under pure Mode I loading. With reference to pure Mode II loading the critical NSIF at failure can be expressed as a function of the V-notch opening angle. By adopting the three criteria considered here the expressions for the NSIFs are derived and compared. After all, the approaches are employed considering sharp V-notched brittle components under in-plane shear loading, in order to investigate the capability of each approach for the fracture assessment. With this aim a bulk of experimental data taken from the literature is used for the comparison.
Ductile failure is investigated experimentally and theoretically in U-notched Al 7075- T6 thin sheets under mixed mode I/II loading. First, several U-notched rectangular sheets are subjected to mixed mode I/II failure tests and the load-carrying capacity of the sheets are experimentally recorded. Then, the Equivalent Material Concept (EMC) is employed in conjunction with the U-notch maximum tangential stress (UMTS) and U-notch mean stress (UMS) criteria to theoretically estimate the load-carrying capacity of the U-notched Al 7075-T6 sheets. It is shown that the experimental failure loads are well predicted by means of both the UMTS-EMC and UMS-EMC criteria. Moreover, the experimental observations and the elastic-plastic finite element analyses indicate that the U-notched aluminum sheets fail by the large-scale yielding (LSY) regime.
Mixed mode I/II stress intensity factors of an edge slant-cracked plate under tensile loading were assessed. A two-dimensional finite element analysis was employed using ABAQUS. Various crack lengths and angles were analyzed. The effect of the crack location at the plate edge was also examined. Crack initiation angles were calculated. In general, modes I and II stress intensity factor increase with increasing crack length. However, the rate of increase in mode I SIF decreases with increasing the main crack angle. The results showed that stress intensity factors decreased ad the crack mouth approaches the edge mid line. The crack location becomes more significant as the crack length increases. The angle of first cracking depends on crack length, location, and angle.
This paper presents a numerical solution for vibration analysis of cantilevered non-uniform trapezoidal thick plates. Based on the first shear deformation theory, kinetic and strain energies of the plate are derived and using Hamilton's principle, governing equations and boundary conditions are derived. A transformation of coordinates is used to convert the equations and boundary conditions from the original coordinates into a new computational coordinates. Using Differential quadrature method (DQM), natural frequencies and corresponding modes are derived numerically. Convergence and accuracy of the proposed solution are confirmed using results presented by other authors and also results obtained based on the finite element method using ANSYS software. Finally, as the case studies, two cases for variation of thickness are considered and the effects of angles, aspect ratio and thickness of the plate on the natural frequencies are studied. It is concluded that two angles of the trapezoid have opposite effect on the natural frequencies. Also, it is shown that all frequencies rise as value of thickness increases or value of the aspect ratio of the plate decreases. The most advantage of the proposed solution is its applicability for plates with variable thickness.
In this paper, a method for severity fault diagnosis of ball bearings is presented. The method is based on wavelet packet transform (WPT), statistical parameters, principal component analysis (PCA) and support vector machine (SVM). The key to bearing faults diagnosis is features extraction. Hence, the proposed technique consists of preprocessing the bearing fault vibration signal using statistical parameters and energy obtained through the application of Db8- WPT at the third level of decomposition. After feature extraction from vibration signal, PCA is employed for dimensionality reduction. Finally, particle swarm optimization with passive congregation-based support vector machine is used to classify seven kinds of bearing faults. The classification results indicate the effectiveness of the proposed method for severity faults diagnosis in ball bearings.
When a structure is influenced by the earthquake external force, some energy imposed to the structure is dissipated and remained energy causes structure displacements. Dissipated energy in the structure depends on the type of structure and its optimal engineering design. In any typical structure, the type of connections, stiffness of structure, dampers, place of windfall and damper and other factors play significant role in the amount of dissipated energy. This article introduces a new resilience factor which is a function of energy dissipation factors of input seismic energy. Mathematical equations are presented for this factor and its limits are determined for different periods. The applicability of the proposed factor is also investigated for two typical structural examples.
This article deals with the thermoelastic interaction in a three-dimensional homogeneous and isotropic viscoelastic medium under the Dual-phase-lag model of generalized thermoelasticity. The resulting non-dimensional coupled equations are applied to a specific problem of a half-space whose surface is traction-free and is subjected to a time-dependent thermal shock. The analytical expressions for the displacement components, stress, temperature and strain are obtained in the physical domain by employing normal mode analysis. These expressions are also calculated for a copper-like material and have been depicted graphically. Discussions have been made to highlight the effect of viscosity on the studied field. The phenomenon of a finite speed of propagation is observed for each field. Also, if the effect of viscosity is neglected, the results agree with the existing literature.