Cracked plates subjected to out-of-plane tearing loads

Cracked plates subjected to out-of-plane tearing loads were investigated using both classical plate theory and Reissner/Mindlin plate theory. It was shown that the total strain energy release rate according to Reissner/Mindlin plate theory converges to that of classical plate theory as the thickness to crack length ratio approaches zero. It was demonstrated that it is not meaningful to separate mode II and mode III strain energy release rates using classical plate theory.     

Diffraction of shear waves by an edge crack in an elastic wedge

Low frequency diffraction of plane harmonic shear (SH) wave by an edge crack in an elastic wedge of arbitrary vertex angle is studied. Kontorowich-Lebedev transform is used to solve the mixed boundary value problem under consideration. For low frequency case, i.e. wavelength large compared to the length of the crack, the displacement field is obtained by successive approximation of the resulting Wiener-Hopf equation. For the limiting case of an elastic half space the results agree with those obtained by the method of matched asymptotic expansions.     

Deformation and tearing of clamped work-hardening beams subjected to impulsive loading

An approximate theoretical analysis, based on a power law stress-strain relationship throughout, is presented herein to examine the behaviour of clamped beams subjected to uniformly distributed impulsive loads, which represents an extension of the previous study. In particular, the rupture (tensile tearing) of the beams under impulsive loading is predicted by an effective strain failure criterion which takes into consideration the influence of the transverse shear on the axial tensile strain. It is found that the present theoretical predictions are in good agreement with the experimental observations in terms of the maximum permanent transverse displacement and the critical input impulse causing beam tensile tearing failure when material strain rate sensitivity is taken into account.     

Free convection about a wedge and a cone subjected to mixed thermal boundary conditions

Summary The paper deals with a similarity analysis of free convection about a wedge and a cone which are subjected to mixed thermal boundary conditions. The governing equations and the boundary conditions are reduced to a boundary value problem involving a non-negative parameterm which assumes the values 0,1 and for the cases of prescribed temperature, prescribed heat flux and radiation boundary condition. A numerical solution has been computed for the case of radiation boundary condition. The results for constant temperature and constant heat flux available in literature are deduced with the aid of a simple transformation. Critical cases have been found for which the solution is same for all values ofm.Notation a ₀,a ₁,a ₂ coefficients defined in Eq. (5) - A transition parameter used in Eq. (16) - c coefficient ofC in Eq. (7) - C function ofx defined in Eq. (7) - f dimensionless stream function - g acceleration due to gravity - g ₁ =g cos - G function ofx defined in Eq. (7) - m constant defined in Eq. (12) - n = 0 for wedge = 1 for cone - PHF prescribed heat flux - Pr Prandtl number - PT prescribed temperature - r =x sin - RBC radiation boundary condition - T temperature - T _e ambient temperature - u velocity component inx-direction - v velocity component iny-direction - x distance from the vertex measured along the surface - y distance normal to the surface - coefficient of thermal expansion - dimensionless similarity variable - dimensionless temperature - exponent inC in Eq. (7) - kinematic viscosity - semivertical angle - stream function     

Transient elastic waves in a wedge-shaped layer

Summary The theory of generalized ray is applied to analyzing transient elastic waves in a layered half-space with non-parallel interface. The propagation, reflection and refraction of longitudinal (P-) and transverse (SV-) waves which are generated by a line source in the surface layer of a two layer model are considered, each of the two homogeneous and isotropic layers having different density and inverse of wave speeds. Generalized ray integrals for multi-reflected rays in the top layer are formulated by using two rotated coordinate systems, one for each interface, and are expressed in terms of local wave slowness along each interface. Through a series of transformations of the local slowness, all ray integrals are expressible in a common slowness variable. Special attention is given to wave mode changes during reflection. The arrival time of each ray is then determined from the stationary value of the phase function with common slowness of the ray integral. Arrivals of head waves corresponding to rays refracted at a fast bottom are calculated from proper branch points of the Cagniard-mapping.With 3 FiguresPresented by F. Ziegler at the 16 th IUTAM Congress ICDAM Lyngby, Denmark, August 19–25, 1984.     

Transient response of a finite crack subjected to dynamic anti-plane loading

In this study, the transient response of a finite crack in an elastic solid subjected to dynamic antiplane loading is investigated. Two specific loading situations, a body force near the finite crack and a concentrated point loading applied on the crack face, are analyzed in detail. In analyzing this problem, an infinite number of diffracted waves generated by two crack tips must be taken into account which will make the analysis extremely difficult. The solutions are determined by superposition of proposed fundamental solutions in the Laplace transform domain.The fundamental solutions to be used are the problems for applying exponentially distributed traction and screw dislocation to the crack faces and along the crack-tip line respectively. Exact transient closed-form solutions for the dynamic stress intensity factor are obtained and expressed in very simple and compact formulations. The solutions are valid for an infinite length of time and have accounted for the contributions of an infinite number of diffracted waves. Numerical calculations for the two problems are evaluated and results indicate that the dynamic stress intensity factors will oscillate near the corresponding static values after the first three waves have passed through the specified crack tip.     

Propagation of waves in magneto-thermo-viscoelastic solids subjected to a uniform magnetic field

The propagation of magneto-thermo-mechanical (MTM) plane waves in electrically and thermally conductive magneto-thermo-viscoelastic (MTVE) unbounded solids is investigated with account for the mutual effects of the magnetic, thermal and strain fields. Concerning the mutual and thermo-electric effects in isotropic solids the governing equations are first linearized. In the linearization, the material is assumed to be subjected to a uniform and primary magnetic field in any direction while the material undergoes infinitesimal deformations. It is shown that the governing equations at the intermediate state are fulfilled by the presumed MTM-fields. Furthermore, the dispersion relation which allows us to consider the entire frequency range, the effect of the magnetic field and some nondimensional material parameters is obtained. Therefore, several modes of MTM-waves arise depending upon the direction of the magnetic field such as the uncoupled magnetic and mechanical S-mwaves, the coupled S-wave, the modified mechanical $\text{P}$-and thermal waves, and the modified and coupled MTM-waves. It is seen that all modes of the wave are dispersive and dissipative due to the conductivity and the viscosity of the material. Then the phase velocities and the attenuation constants for the coupling modes are obtained, and some limiting values are discussed. From the expressions follow, in particular, the results for the elastic case, the propagation of mechanical waves in nonconductive materials.     

Compliance of a microfibril subjected to shear and normal loads.

Many synthetic bio-inspired adhesives consist of an array of microfibrils attached to an elastic backing layer, resulting in a tough and compliant structure. The surface region is usually subjected to large and nonlinear deformations during contact with an indenter, leading to a strongly nonlinear response. In order to understand the compliance of the fibrillar regions, we examine the nonlinear deformation of a single fibril subjected to a combination of shear and normal loads. An exact closed-form solution is obtained using elliptic functions. The prediction of our model compares well with the results of an indentation experiment.     

Transient waves due to randomly moving dislocation

Stochastic motion of a dislocation and the radiated field are considered in this paper. The derived equations yield the relationships between the parameters of radiation and those of a dislocation movement. The exact solution is given for the transient elastic waves of shot noise type due to a screw dislocation motion of finite duration.     

Transient response of a surface crack subjected to dynamic anti-plane concentrated loadings

In this study, the transient response of a surface crack in an elastic solid subjected to dynamic anti-plane concentrated loadings is investigated. The angles of the surface crack and the half-plane are 60° and 90°. In analyzing this problem, an infinite number of diffracted and reflected waves generated by the crack tip and edge boundaries must be taken into account and it will make the analysis extremely difficult. The solutions are determined by superposition of the proposed fundamental solution in the Laplace transform domain and by using the method of image. The fundamental solution to be used is the problem for applying exponentially distributed traction on the crack faces. The exact transient solutions of dynamic stress intensity factor are obtained and expressed in formulations of series form. The solutions are valid for an infinite length of time and have accounted for the contribution of an infinite number of diffracted waves. The explicit value of the dynamic overshot for the perpendicular surface crack is obtained from the analysis. Numerical results are evaluated which indicate that the dynamic stress intensity factors will oscillate near the correspondent static values after the first three or six waves have passed the crack tip.     

Statistical properties of a 2D granular material subjected to cyclic shear

This work focuses on the evolution of structure and stress for an experimental system of 2D photoelastic particles that is subjected to multiple cycles of pure shear. Throughout this process, we determine the contact network and the contact forces using particle tracking and photoelastic techniques. These data yield the fabric and stress tensors and the distributions of contact forces in the normal and tangential directions. We then find that there is, to a reasonable approximation, a functional relation between the system pressure, P, and the mean contact number, Z. This relationship applies to the shear stress τ, except for the strains in the immediate vicinity of the contact network reversal. By contrast, quantities such as P, τ and Z are strongly hysteretic functions of the strain, ε. We find that the distributions of normal and tangential forces, when expressed in terms of the appropriate means, are essentially independent of strain. We close by analyzing a subset of shear data in terms of strong and weak force networks.     

A two-layer model for a non-Newtonian gravity current subjected to wind shear

Summary.  A theoretical model is developed for the gravity current resulting from the sudden release of a fixed volume of fluid of non-Newtonian power law rheology on top of a slightly denser Newtonian fluid layer in the presence of wind stress. The model incorporates the flow of both layers and accounts for the effects of inertial and viscous forces, and is suited for moderate Reynolds number flows. The governing equations are obtained by depth-averaging the unsteady equations of motion in accordance with the von Kármán's momentum integral method, and constitute a hyperbolic system of four equations for the flow rates and thicknesses of the fluid layers. Results are obtained by a well established numerical scheme for systems of nonlinear hyperbolic equations. For a particular case analytical results are obtained by employing an asymptotic matching approach. Good agreement is obtained between the numerical and analytical results. The effects of the thickness of the ambient layer, wind stress, Reynolds numbers, and rheology on the gravity current are discussed. Received July 22, 2002; revised November 27, 2002 Published online: May 8, 2003     

Dynamic responses of a crack in a layered graded magnetoelectroelastic sensor subjected to harmonic waves

The mechanical model is established for the dynamic fracture problem of a layered graded magnetoelectroelastic sensor subjected to harmonic waves. Fourier integral transform is employed to derive the system of Cauchy singular integral equations, numerical solutions of which are obtained by the Lobatto–Chebyshev collocation method put forth by Erdogan and Gupta. The energy release rate (ERR) is chosen as the fracture parameter. Parametric studies on ERRs yield some guidelines for engineering applications: (1) to avoid the peak value of ERR, the wave number of applied loading should be as large as possible; (2) smaller values for non-homogeneity parameters and larger thickness for the sensitive coating can be chosen to enhance the anti-fracture ability of the sensor; (3) cracks in the lower-half region of the guiding layer are more dangerous than those in the upper half, and the monitoring for the former should be specially strengthened.     

Propagation of a crack due to shear waves in a medium of monoclinic type

Summary In this paper the propagation of a crack due to shear waves in a medium having monoclinic symmetry is investigated. The stress intensity factor at the crack tip for concentrated force of a constant intensity and for constant loading is separately calculated. The Wiener-Hopf technique has been used to solve the problem. It has been shown that the stress intensity factor decreases as the length of the crack increases. The effect of anisotropy being distinctly marked.With 5 Figures     

Finite element micromechanical modelling of a unidirectional composite subjected to axial shear loading

A micromechanical model is presented which predicts the behaviour of a unidirectional composite subjected to axial shear load using standard finite elements. Only a three-dimensional model can handle the necessary shear loading boundary conditions when using such elements. These boundary conditions give shear stress components but no direct stress components within the composite. A parametric study is carried out on unidirectional carbon fibre/epoxy within the linear elastic regime of both constituents. The study reveals that the most critical parameters controlling the axial shear modulus of the composite are matrix modulus and fibre volume fraction whilst the stress state in the composite is mainly controlled by geometrical features of the composite, i.e., fibre volume fraction and fibre spacing. Comparison between the predicted axial shear modulus based on the concentric cylinder model and the current finite element model shows good agreement for low and intermediate fibre volume fractions. Both predictions lie within the Hashin bounds and the finite element prediction tends to be closer to the upper Hashin bound for fibre volume fractions greater than 60%. The initial tangent shear modulus predicted with the finite element model and that measured differ by less than 2.5%. The non-linear shear stress/strain response of the composite material is also predicted and agreement with the experimental results is good.     

The time-dependent interaction between inclusions and a cracked matrix subjected to antiplane shear

Summary. The time-dependent interaction between multiple circular inclusions and a cracked matrix in the antiplane viscoelastic problem is discussed in this paper. The fundamental elastic solution is obtained as a rapidly convergent series in terms of complex potentials via successive iterations of Möbius transformation in order to satisfy continuity conditions on multiple interfaces. Based on the correspondence principle, the Laplace transformed viscoelastic solution is then directly determined from the corresponding elastic one. In association with the singular integral technique, the time-dependent mode-III stress intensity factor of the crack tip can be solved numerically in a straightforward manner. Finally, some typical examples of an arbitrary crack lying in a matrix with various material properties under various loading types are also discussed. The results show that, depending on the relative locations and material properties of inclusions, the evolution of the stress intensity factor (SIF) may increase or decrease with time.     

Transient response of a finite crack in a rectangular plate with stress-free edges for the tearing mode

The purpose of this paper is to use the basic theorem of the Fourier series, Fourier transform and Laplace transform to find the dynamic stress intensity factor of a rectangular sheet with a central crack under sudden antiplane shear stress forming a self-equilibrating system. It is easily proved that the results for a strip containing a central crack are the special cases of the solution in this paper.