Volume 23, Issue 3-4

The mode III fracture analysis of a cracked graded plane in the framework of classical, first strain gradient, and second strain gradient elasticity is presented in this paper. Solutions to the problem of screw dislocation in graded materials are available in the literature. These solutions include various frameworks such as classical elasticity, and the first strain and second strain gradient elasticity theories. One of the applications of dislocations is the analysis of a cracked medium through distributed dislocation technique. In this article, this technique is used for the mode III fracture analysis of a graded medium in classical elasticity, which results in a system of Cauchy singular integral equations for multiple interacting cracks. Furthermore, the technique is modified for gradient elasticity. Owing to the regularization of the classical singularity, a system of non-singular integral equations is obtained in gradient elasticity. A plane with one crack is studied, and the stress distribution in classical elasticity is compared with those in gradient elasticity theories. The effects of the internal lengths, introduced in gradient elasticity theories, are investigated. Additionally, a plane with two cracks is studied to elaborate the interactions of multiple cracks in both the classical and gradient theories.

A recently presented closed-form analytic solution for the displacement field and stress field in a cracked Brazilian disc, under uniform radial pressure along two symmetric arcs of its periphery, revealed that for a wide range of crack-axis inclinations, the lips of the crack tend to overlap each other, leading to a kind of an “unnatural” geometrical configuration. It is here proven that this behavior is a consequence of the inability of the mathematical model to simulate the change of the boundary conditions that appears (for some special configurations) in the physical problem and render the mathematical problem an “ill-posed” one. Indeed, what happens in praxis is that for a given interval of crack inclination angles, the initially stress-free lips are coming in contact and contact stresses appear violating the boundary conditions initially adopted in the mathematical model. This problem is here solved by superposing to the above-mentioned solution the respective one of an auxiliary mixed fundamental problem solved according to Muskhelishvili’s complex potentials method. In this way, physically acceptable displacement fields and stress fields are obtained all over the cracked disc independently from the crack inclination angle. In addition, the contact stresses developed along the crack lips are determined. Moreover, naturally sound formulae for the corresponding stress intensity factors (in case of cracks with lips in contact to each other) are obtained, which are of crucial engineering importance. The solution obtained enlightens some critical aspects related to the practical application of the cracked Brazilian disc as a tool for the standardized determination of the fracture toughness of brittle rock-like materials and concrete.

Spring-block models were introduced several years ago to model avalanche-like dynamics for catastrophic landslides. This article aims to address precursor phenomena in rain-induced landslides through the enrichment of a two-dimensional spring-block model with displacement gradients and stochasticity. This approach is along the lines of Aifantis and coworkers, who introduced deterministic gradients to stabilize material behavior in the softening regime and later expanded on it by introducing stochastic terms to model the competition between deterministic gradients and random effects. To this end, an appropriate stochastic constitutive relation, introducing an effective dissipation parameter (which is related to structural heterogeneity and deformation processes at the failure plane) is used. It is shown that there is definite precursor activity before rain-induced landslides that can be modeled by a process of material yielding at the failure plane (a “weak” plane at a certain depth, parallel to the surface of the soil or rock mass, over which landslide takes place). This activity is related to the exponent b of the power-law distribution of the slip events within the failure plane. Cellular automaton simulations were used to verify the analytical predictions, which can be useful to geoscientists and engineers, as an early prediction of the initiation of a landslide can minimize its catastrophic results through proper safety and precautionary measures.

In this study, the coupled effects of gravity and nonhomogeneity on Rayleigh waves in an anisotropic layer placed over an isotropic viscoelastic half-space of higher order are discussed. The dispersion properties of waves are derived. The numerical solutions are also discussed for the Rayleigh waves. It is observed that the phase velocity of Rayleigh waves is influenced quite remarkably by the presence of inhomogeneity, gravity, and strain rates of the strain parameters in the half-space.

The present investigation emphasized the understanding of the mechanical behavior and progressive failure modes of Kevlar/epoxy-reinforced laminated composites subjected to a three-point bend test at liquid nitrogen (LN 2 ) temperature (77 K). The tests were conducted on the woven fabric laminates with different loading speeds and characterized by scanning electron microscopy (SEM). The effect of LN 2 temperature on the interlaminar shear strength (ILSS) of Kevlar/epoxy composites with various loading speeds was observed. The results indicate that the values of ILSS were increased at higher crosshead speeds compared to ambient temperature. The fibrillation progression and matrix failure (riverline marking) was observed by SEM. A change in crosshead speed may result in the variation of failure modes.

The strain hardening exponent and strength coefficient of the Ramberg-Osgood flow rule are required for the accurate design analysis of the materials of aeroengine components. A direct method of deriving these parameters involves the processing of the complete raw data of tensile testing as per ASTM E-646. More often, a first design effort of aeroengine components is made using catalogue data, as the evaluation of material tensile properties is a time-consuming process that takes place concurrently. Catalogue-supplied data on the monotonic loading typically contains elastic modulus, 0.2% proof stress, and ultimate tensile stress along with other data for various temperatures. A methodology was evolved in this work to construct the Ramberg-Osgood flow rule with these three parameters and was validated with laboratory test results and published data through a comparison with ASTM E-646. The strain hardening exponents and strength coefficients were established for a family of aeroengine metallic materials for various temperatures, which can serve as a first design effort input.

The Timoshenko beam theory, which deals with the deflection and rotation in two partial differential equations of motion, is transformed into a single partial differential equation with pure bending deflection as a potential function for the determination of the total deflection, rotation angle, and sectional forces. Inclusion of a nonlocal stress parameter results in the extension of the governing differential equation from the 4th to the 6th order. A simply supported nanotube is considered, and the governing differential equation is decomposed into a system of ordinary differential equations by employing the modal superposition method, separation of variables, and the Galerkin method. Both moving nanoparticle gravity and inertia force are consistently taken into account, resulting in ordinary and parametric excitation, respectively. As a novelty, the parameters are split into a constant and a time-dependent part. The former is added to the ordinary system of equations, which is solved analytically in the frequency domain by the harmonic balance method, while the system with variable coefficients is solved in the time domain by the perturbation method. The effects of slenderness ratio, nonlocal parameter, stiffness of elastic medium, nanoparticle gravity and inertia force, and velocity on the free and forced nanotube response are also investigated. Special attention is paid to the influence of damping on resonance. Performed parametric analysis is physically transparent due to the obtained semi-analytical solution. Some analytical results of illustrative examples are compared with numerical ones from the relevant literature, and notable differences are discussed.