The time-discontinuous Galerkin method based upon using a finite element formulation in time is derived. This method is to use the weighted residuals to treat space and time in a uniform manner and thus integrating both the spatial and temporal variations of the unknown quantities simultaneously. The approximations are continuous with respect to the space variables for each fixed time, but they admit discontinuities with respect to the time variable at each time step. Interpolation functions and weighting functions are taken to be discontinuous across inter-element boundary. This method generates a complete space-time finite element discretization which eliminates the need for any additional ordinary differential equation solver to resolve the temporal behavior of the problem. No significant instability problems and much more rapid convergence to the analytical solution were experienced in this approach than the semidiscretization method.
A new dynamic stress-strain rate type constitutive model for mixed hardening material has been developed using evolutional Gurson type yield function for solving problems of rigid plastic porous materials. During the plastic process of ductile materials in many engineering problems, the failure of materials is mainly induced by the damage behaviors such as the nucleation of micro void, their evolutions and the coalescence. With the aid of some concept of parameters and formulations, such as generalized triaxiality function in stress space, void fraction, effective stress with micro void interaction and void induced effective strain rate, generalized triaxiality ratio and so on, the dynamic void evolutional process of mixed hardening material has been analyzed in detail. Based on the above constitutive law the rigid-plastic finite element modeling and the FEM computer system including the damage evolutional process have been developed. The micro damage phenomena caused by collision of a flying projectile on to a target is simulated in order to reveal the applicability of the method. The inherent relations between the penetration and perforation process, and damage evolution process during the impact of target plate by projectile are revealed.
The displacement rate-controlled tensile tests were performed for smooth and circumferentially notched specimens of the sintered silicon nitride ceramics in argon-gas atmosphere at 1300°C, and then the axial load-displacement response was measured. It was shown from the tests that inelastic deformation was greatly dependent on displacement rate and easier to generate at the lower displacement rate. The constitutive equation was constructed on the basis of tensile stress-strain curves in the smooth specimen. Then inelastic FEM analysis was performed for the smooth and notched specimens, using this equation. The calculated load-displacement responses quantitatively agreed quite well with the measured ones in the smooth and notched specimens, showing the validity of the proposed analysis. The development of the inelastic deformation in loading process was shown from the calculation around the notch root.
The extended form of Lord-Shulman (L-S) theory is formulated by the Jeffreys type heat conduction equation at first. The combined constitutive equations of the generalized thermoelastic theories, including the L-S theory, the Green-Lindsay (G-L) theory and the extended L-S theory, are given. The equations in the extended L-S and G-L cases are solved by the numerical inversion of Laplace transform for the Danilovskaya's problem. The temperature and strain fields in the semiinfinite elastic medium are calculated for various relaxation parameters and thermo-mechanical coupling factor. Various propagating characteristics of the thermal and elastic waves are discussed.
In the present study, an alternative strategy for elasto-dynamic crack problems using boundary element method is discussed. The Laplace transformation is applied to time variation in the formulation. Since the numerical solutions are obtained in the Laplace-transformed domain, the numerical-inverse Laplace transformation is adopted to obtain time histories of the solutions. In the present method, the distributions of the displacement and traction in the vicinity of the crack tip are expressed as the superposition of singular terms and regular ones. The singular terms are the analytical solutions including stress intensity factors of Modes I and II, while the regular terms are approximated by the discrete polynomial functions in general BEM formulations. Additionally, the ligament side is discretized by singular-type crack elements in order to increase the accuracy of the traction near the crack tip. It is shown that the dynamic stress intensity factors (DSIFs) of Modes I and II are determined directly without supplementary procedures such as extrapolation or J-integral scheme. The validity of the present method is confirmed through the analysis of mixed mode dynamic problems of crack.
An analytical model for lateral cracks occurring in abrasive wear of brittle materials was developed. The stress field around the lateral crack and the stress intensity factor at the crack tip were analytically modeled. The abrasive wear by abrasive particles was experimentally studied by sliding indentation. In soda-lime glass, it was observed that chipping by the lateral crack occurred and produced the greatest material removal when the normal load applied by the sliding indenter was about 1.5-2.0N. Prediction of length of the lateral crack from the model was compared with the experimentally measured length in the soda-lime glass.
The structure (crystalline or amorphous) and shape (globular or irregular) of silica fillers were varied and their effects on the impact fatigue and usual fatigue properties in the particle-filled epoxy resins were investigated. The fatigue crack extension process was discussed in terms of initiation and propagation processes. Furthermore, the mechanical characteristics of the material were evaluated by considering the tensile properties, fatigue resistance and the fracture behavior. It has been found that the epoxy resin filled with irregular crystalline silica-particles possessed the best combination of mechanical properties.
Fatigue tests of aluminum-silicon alloy A4032FD and spheroidal graphite cast iron FCD600 were carried out under cyclic compressive loading using circumferential notched round bar specimens. Non-propagating cracks were observed at the notch bottom of the specimens after 1×107 load cycles. It is considered that residual tensile stress caused by plastic deformation at the notch bottom is the driving force of crack propagation. Therefore we calculated the range of stress intensity factor ΔK of residual stress at the notch bottom. The ΔK was also compared with effective threshold stress intensity U·ΔKthto predict the crack depth. It is considered that the crack propagation rate disappears when ΔK<U·ΔKth. The predicted value of crack propagation depth was in line with the experimental value.
Using Raman spectroscopic analysis and the fractographical analysis, we investigated the relationship between the glass transition temperature, Tg, the fragility parameter, m, and the fracture toughness, KIc, of epoxy resin and composite. Tg and m derived from the thermo-viscoelasticity were used to characterize the epoxy resin and composite post-cured under various conditions. The Raman spectroscopic analysis showed that the Tg is directly related to the degree of cross-linking reaction of the epoxy resin and the matrix of composite. The fractography showed that m of the epoxy resin depends on the heterogeneous microstructure. The m of the composite was dominated by the volume fraction. KIc of the epoxy resin increased as m decreased when the Tg was saturated at approximately 400K. A composite with a high Tg and a low m had a high KIc value.
A laminated orthotropic plate theory is developed on the assumption that inplane displacements vary exponentially across plate thickness. Analytical solutions are obtained for simply supported, symmetric and anti-symmetric cross-ply rectangular laminates under transverse loading. The numerical results are compared with solutions of the three-dimensional elasticity theory, the third-order shear deformation theory, and the first-order shear deformation theory. It is found that the present exact exponential theory provides very accurate displacements and stresses in comparison to the three-dimensional elasticity theory. In particular, both transverse shear from constitutive equations and transverse normal stresses from equilibrium equations are more accurate than previously developed theories, even for small length-to-thickness ratios.
The use of colored random patterns for the calculation of the correlation coefficient is proposed to improve the accuracy of the digital image correlation technique for displacement measurements. The colored random pattern is created by spraying color paints on the surface of a sample. Then, not only the displacement distributions but the displacement gradients are determined using a set of color images before and after deformation. The effectiveness is demonstrated by applying the proposed method to the displacement measurement of rigid body rotation, and the results are compared with those obtained from the monochromatic images. The results show that the use of the color image in digital image correlation improves the measurement accuracy both of the displacements and the displacement gradients. In addition, the smaller size subset can be used for the calculation of the correlation. The proposed technique is effective in the fields of experimental mechanics and experimental stress analysis.