Notched plates in mixed mode loading (I+II): a review based on the local strain energy density and the cohesive zone model
, Pages: 1-8
F. Berto and J. Gomez PDF (550K)
Abstract: 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.
Keywords: Notched plates, Mixed mode loading, Local strain energy density, Cohesive zone model
Effect of angle, length and circulation cooling system on microstructure A360 Aluminum alloy in semi-solid metal forming by cooling slope method
, Pages: 9-14
Mohammad Mahdi Kaykha PDF (550K)
Abstract: 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.
Keywords: Semi-Solid forming, Cooling slope method, A360, Microstructure, Circulation cooling system
Modeling and analysis of vibration of a gold nano-beam under two-temperature theory
, Pages: 15-30
Sudip Mondal, Abhik Sur and M. Kanoria PDF (550K)
Abstract: 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.
Keywords: Two-temperature theory, Three-phase-lag model, Euler-Bernoulli equation, Femtoseconds scale, Ramp-type heating
Some recent criteria for brittle fracture assessment under mode II loading
, Pages: 31-38
Alberto Campagnolo and Filippo Berto PDF (550K)
Abstract: 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.
Keywords: Sharp V-notch, Brittle failure, In-plane shear loading, Notch stress intensity factor, Strain energy density
Large plasticity induced crack initiation from U-notches in thin aluminum sheets under mixed mode loading
, Pages: 39-60
A. R. Torabi and B. Mohammad Hosseini PDF (4500K)
Abstract: 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.
Keywords: Load-carrying capacity, Equivalent Material Concept, Ductile failure, U-notch, Abrupt fracture, Mixed mode I/II loading
Numerical analysis of mixed mode I/II stress intensity factors of edge slant cracked plates
, Pages: 61-70
A. S. Fayed PDF (650K)
Abstract: 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.
Keywords: Stress intensity factor, Mixed mode I/II, Slant edge crack, Crack initiation angle, Two dimensional finite element
Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness
, Pages: 71-92
Keivan Torabi and Hassan Afshari PDF (650K)
Abstract: 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.
Keywords: Trapezoidal plate, Moderately thick plate, Variable thickness, Differential quadrature method
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