Search

A masonry dome cracks when the tension stresses in the hoop rings near the springing reach the masonry's weak tensile strength. These meridional cracks arrive and spread along the dome. In this condition, the pressure surface with zero hoop stresses represents the extension to the three-dimensional case of the problem of the catenary. This analytical approach is adopted in the paper first to develop an accurate description of the minimum thrust state for the hemispherical masonry dome and the corresponding configuration of the pressure surface. Furthermore, the minimum thickness state is studied. Contributions of the paper are either an analytical formulation of the minimum thrust, depending on the geometrical thickness-radius ratio, or a modification of the minimum thickness-radius ratio with respect to the commonly accepted value. In this last geometrical configuration, the pressure surface has to touch the intrados of the dome at the crown, instead of passing through the extrados at the springing. [ABSTRACT FROM AUTHOR]

The Erdogan fundamental solutions are derived from an infinite plane containing a crack. When they are used in the formulation of the boundary element method (BEM), the stress boundary conditions on the crack surface are automatically satisfied and the singular behavior at the crack tip can be naturally reflected. Using the multi-domain technique, the multi-crack problem can be transformed into a series of single-crack problems involving displacement continuity conditions along common boundaries. In this paper, the displacements which are expressed in terms of the integral of a complex function in the Erdogan fundamental solutions are derived in closed-form expressions. Then, the multi-domain spline fictitious boundary element method (SFBEM) based on the above fundamental solutions is proposed and formulated for analyzing multi-crack problems. The computational accuracy and stability of the proposed method are verified by comparing the stress intensity factor (SIF) results of a double-inner crack problem with different inclined angles and crack lengths against those calculated by the finite element method. Also, the SIF results of a double-edge crack problem with different crack lengths are compared with those obtained from studies. Finally, the proposed method is applied to the analysis of the triple-crack problem, in which the shielding effects of multi-crack and stress contours are studied with different crack lengths and locations. [ABSTRACT FROM AUTHOR]

In this paper a new criterion for fracture investigation of orthotropic materials with cracks under mixed mode I/II loading is presented. In this fracture criterion, orthotropic material will be considered as a reinforced isotropic material. It is supposed that the crack will grow in the matrix of the orthotropic material. A new definition named here as “isotropic-orthotropic stress reduction factor” (IO-SRF) is utilized to consider the effects of the fracture process zone by a macro-mechanics approach. Also, the stress reduction factors will present a valuable relationship between the orthotropic and isotropic fracture toughness. Experimental and finite element methods will be introduced for computing the stress reduction factors. The SRFs are calculated for samples of glass-epoxy as an orthotropic material and samples of epoxy as a related isotropic one. Experimental tests under mixed mode I/II are performed on glass-epoxy composite samples to evaluate the validity of the presented mixed mode fracture criterion. The results of experimental tests on composite samples show a good agreement with the results of the presented criterion. Thus, the proposed criterion could be utilized as an efficient criterion for investigating the fracture of orthotropic materials under mixed mode I/II loading. [ABSTRACT FROM AUTHOR]

The plastic zones of crack tips play a significant role in the fracture behavior of material. This paper proposes a semi-analytic solution for the plastic zones and stress distribution of an infinite space with multiple cracks and inhomogeneous inclusions under remote stress. In this solution, cracks can be treated as a distribution of edge dislocations with unknown densities according to the distributed dislocation technique, while inhomogeneous inclusions can be modeled as homogeneous inclusions with initial eigenstrain plus the unknown equivalent eigenstrain by using the equivalent inclusionmethod. These unknowns can be obtained by using the conjugate gradient method. The plastic zones ahead of crack tips are one-dimensional slender strips, and their sizes can be determined by canceling the stress intensity factor (SIF) due to the closure stress and that due to the applied load based on the Dugdale model of small-scale yielding. It is found that the plastic zones of crack tips are significantly affected by Young's modulus and the positions of inhomogeneous inclusions. [ABSTRACT FROM AUTHOR]

This paper considers several finite moving cracks in an orthotropic half-plane with non-homogenous coating subjected to anti-plane deformation. The distributed dislocation technique is used to carry out stress analysis in the medium containing moving cracks under anti-plane loading. By utilizing the complex Fourier transformation technique, the stress fields are obtained for an orthotropic half-plane containing a screw dislocation. The Galilean transformation is employed to express the wave equations in terms of coordinates that are attached to the moving crack. Stress fields are derived in the medium under anti-plane point forces. These solutions are Cauchy singular at the location of dislocations and the point of application of forces. The solution is employed to derive integral equations for a half-plane weakened by moving cracks. Numerical results are provided to show the effects of material properties, the crack length and the speed of the crack propagating upon the stress intensity factor. [ABSTRACT FROM AUTHOR]

In the present paper, the mixed-mode Dugdale model is applied to investigate the plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar layers. In the analysis, both normal and shear stresses are assumed to exist in the plastic zones and satisfy the Von Mises yield criterion. The plastic zone sizes can be determined on condition that the stress intensity factors caused by the stresses in the plastic zones and applied loading are zero. Then, the crack tip opening displacement can be obtained by dislocation theories. In numerical examples, the plane stress condition is considered. The plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar layers under a uniform load are examined. The effects of Dundurs' parameters and the thickness of materials on the plastic zone size and the crack tip opening displacement are investigated in detail. Numerical results show that in the case of small thickness, the values of the normalized plastic zone size and the normalized crack tip opening displacement decrease with increasing Dundurs' parameters, α and β, while, in the case of infinite thickness, the value of the normalized plastic zone size is independent of α, and the value is symmetric about the axis on which β = 0. [ABSTRACT FROM AUTHOR]

The stresses developed in a body due to a moving load causing fracture are an interesting problem of mechanics having its application toward the stability of a medium. This paper is concerned with the stresses developed in an irregular isotropic half-space due to a normal moving load at a rough free surface. The irregularity has been taken in the form of a parabola and a rectangular irregularity has also been discussed as a special case of parabolic irregularity. Closed-form expressions for the normal and shear stresses have been obtained. The effect of friction, irregularity factor, and maximum amplitude of irregularity has been discussed for both stresses. [ABSTRACT FROM AUTHOR]

The stress field around the crack tip near an elastically matched but strength-mismatched interface body in a bimetallic system is influenced when the crack tip yield or cohesive zone spreads to the interface body. The concept of crack tip stress intensity parameter, K, is therefore employed in fracture analysis of the bimetallic body. A computational model to determine K is reviewed in this paper. The model, based upon i) Westergaard's complex potentials coupled with Kolosov-Muskhelishvili's relations between a crack tip stress field and complex potentials and ii) Dugdale's representation of the cohesive zone clearly indicates shielding or amplifying effects of strength mismatch across the interface, depending upon the direction of the strength gradient, over the crack tip. The model is successfully validated by conducting series of high cycle fatigue tests over Mode I cracks advancing towards various strength-mismatched interfaces in bimetallic compact tension specimens prepared by electron beam welding of elastically identical weak ASTM 4340 alloy and strong MDN 250 maraging steels. [ABSTRACT FROM AUTHOR]

In this paper, the mixed-mode fracture problem of a functionally graded piezoelectric material strip with two penny-shaped or annular cracks is considered. It is assumed that the electroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under electric loading. The problem is formulated in terms of a system of singular integral equations, which are solved numerically. Numerical calculations are carried out, and the stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity. [ABSTRACT FROM AUTHOR]

In this paper, we restore the already constructed approximate asymptotic solutions extracted in [10] concerning the HRR [1] strongly nonlinear fourth-order ordinary differential equation (ODE) for plane strain conditions in nonlinear elastic (plastic) fracture. It is proved that the above equation, for low strain hardening exponents (0 < N « 1), is reduced to a strongly nonlinear ODE of the second order. The method of the total differentials is used so that the last equation is reduced to Abels' equations of the second kind of the normal form, that can be analytically solved in parametric form. In addition, the case of rigid perfect-plasticity ( N=0) is extensively investigated and several important results are extracted. [ABSTRACT FROM AUTHOR]

As strain localization is usually prognostics of localized failure in solids and structures, prediction of its occurrence and quantification of its adverse effects are of both theoretical and practical significance. Regarding plastic solids, onset of strain localization was presumed to be coincident with strain bifurcation, and the discontinuous bifurcation analysis was usually adopted to determine the discontinuity orientation though it does not apply to rigid-plastic solids. However, recent studies indicate that strain bifurcation and localization correspond to distinct stages of localized failure and should be dealt with separately. In this work, the mechanics of strain localization is addressed for perfect and softening plasticity in the most general context. Both isotropic and orthotropic, elasto- and rigid-plastic solids with associated and non-associated flow rules are analytically considered and numerically validated, extending our previous work on softening plasticity with associated evolution laws. In addition to Maxwell's kinematics and continuity of the traction rate for strain bifurcation, a novel necessary condition, i.e., the stress rate objectivity (independent from the discontinuity bandwidth), and the resulting kinematic and static constraints, are derived for the occurrence of strain localization. In particular, the localization angles of the discontinuity band (surface) depend only on the specific stress state and the plastic flow tensor, irrespective from the material elastic constants and from the plastic yield function. Moreover, it is found that a transition stage generally exists in the case of plane strain during which the orientation of plastic flow rotates progressively such that strain localization may occur. Back-to-back numerical predictions of some benchmark problems, involving both perfect and softening plasticity, also justify the analytical results. [ABSTRACT FROM AUTHOR]

The plane strain problem for an interface crack between two bonded piezoelectric semi-infinite planes under remote electromechanical loading is considered. Mechanically frictionless and electrically permeable contact zones are assumed at the crack tips and the remaining part of the crack is considered as electrically limited permeable with a certain permeability of the crack medium. Patron’s way of modelling limited permeable conditions is used. By means of integral transforms the problem is reduced to a nonlinear system of singular integral equations. An iterative scheme together with discretization and utilization of Gauss-Chebishev quadrature rule is applied for the solution of this system. Distributions of the electric displacement along the crack region as well as the stress and electric intensity factors and the energy release rate are found for different electromechanical loads and crack permeabilities. Calculations are performed for an artificial contact zone length, however the way of an easier determination of the associated values for the real contact zone length is shown. As a particular case of the obtained solution the crack in a homogeneous piezoelectric media is considered. The results of the calculations are compared to the corresponding results obtained earlier by means of Hao and Shen’s way of modelling the crack permeability. Even though the electric displacements obtained in the respective framework of these models differ essentially, it appears that the fracture mechanical parameters are in good agreement with each other. [ABSTRACT FROM AUTHOR]

Summary. In this paper, the multiple Zener-Stroh crack problem is studied. We choose the distributed dislocations as unknown functions in the integral equation. The crack faces are assumed to be traction free. The applied “generalized loading” for cracks is the initial displacement jump (abbreviated as IDJ), which in turn is the increment of displacement when a moving point goes around the crack in a closed loop. A system of singular integral equations is obtained. After solving the integral equations, the stress intensity factors at crack tips can be evaluated immediately. Numerical examples are given. It is found that interactions between Zener-Stroh cracks are quite different from those for the Griffith cracks, in the qualitative and quantitative aspects. [ABSTRACT FROM AUTHOR]

In this investigation, general approximate solutions for the stress intensity factor (SIF) and configuration force (CF) are derived, respectively, based on the Eshelby theory for the interaction between an inhomogeneous inclusion of arbitrary shape undergoing a stress-free transformation strain and plane stress mode II crack. For common inclusion shapes, some simplified approximate formulae are also developed. Then, the relationship between the normalized CF and SIF is discussed, as well as the effects of inclusion shape, location, and size on the CF and SIF of a plane stress mode II crack. To give deep insight into the complex three-dimensional interaction between an inclusion undergoing a stress-free transformation strain and a crack, two typical cases of the triaxial stress state are analyzed, and no significant difference occurs among most engineering materials. [ABSTRACT FROM AUTHOR]

In polymer composites, inclusions (fillers) are introduced into the glassy polymeric matrices in order to improve the toughness properties as the brittleness is one of the fatal drawbacks for glassy polymers. For the first time, in our current study, the stress analysis has been performed on the interaction between a circular inclusion and a craze with an internal small crack in polymeric composites. A craze can be treated as a crack with fibrils bridging the two crack surfaces. The forces applied by the fibrils to the crack surfaces (pulling the two surfaces closer) depend on the crack opening displacement. However, the crack opening displacement is directly related to the forces applied by the craze fibrils. To solve this dilemma, an iterative procedure is proposed for the first time to solve the formulated singular integral equations. The craze thickness profiles, the cohesive stress distribution, and the fracture toughness of the polymeric composites are investigated thoroughly. Moreover, due to the influence of the inclusion, the uneven craze thickness profiles are observed from the left to the right part of the entire craze zone. [ABSTRACT FROM AUTHOR]

Mode-III crack problems in a cubic piezoelectric medium are investigated. Electromechanical fields near the crack tip are derived, and explicit expressions are obtained. It is shown that the asymptotic stress and electric fields are characterized by the inverse square root of the distance from the tip with at most two independent coefficients. The energy release rate associated with the crack is determined, and comparison is made with the counterpart in materials of hexagonal symmetry. The fundamental problem concerning a screw dislocation which is accompanied by other line singularities of different physical nature is addressed. A class of crack problems is solved by reducing it to the standard Riemann-Hilbert problem in complex function theory. It is concluded that under certain conditions, for the same crack configuration and loading, the stress intensity factors found for isotropic elastic materials are applicable to cubic piezoelectric media. Finally, three crack problems are explicitly solved. [ABSTRACT FROM AUTHOR]

In the present work, we study the effective fracture toughness of ferroelectrics by taking the microscopic as well as the macroscopic level into account. On the macroscopic length scale, we apply an extended theory of stresses at interfaces in dielectric solids. Further, on the microscopic length scale, nonlinear effects are introduced by applying the small-scale switching approximation, that is, the effects are limited to a small region around the crack tip. Finally, we discuss the effective fracture toughness and crack resistance curves for different loading and poling conditions. In contrast to previous approaches, the analysis is done considering the full anisotropy and electromechanical coupling of the material by using piezoelectric weight functions. Thus, the presented model also takes the inverse switching (180°) into account yielding a contribution to both the stress and the electric displacement intensity factors. [ABSTRACT FROM AUTHOR]

In this study, a stress analysis of a substrate coated by nanomaterials with a vacancy under uniform extension load is investigated. The behavior of the coated substrate is modeled with the behavior of a two-layered beam, in which one of the layers is elastic and described by the continuous medium and the second layer consists of a nanomaterial with damage of a vacancy. The extension of the coating is carried out by stretching of the first layer, which lies on the substrate and by the cohesive forces between the layers. It is assumed that vacancies do not vary along the width of the substrate. The constitutive equations of the first layer (i.e., an elastic substrate) are given in the framework of Hooke's law and the constitutive equations of the second layer; that is, the coating is carried out by taking into account discreteness of the nanomaterial with a vacancy. The expressions for the determination of the contact pressure and stresses of the substrate with a nanocoating that have vacancies are obtained. In addition, damage conditions for the substrate and nanocoating are determined. Finally, carrying out some computations, effects of the characteristics of a nanocoating with and without vacancies on the values of contact pressure and stresses of the coated substrate have been studied. [ABSTRACT FROM AUTHOR]

Mixed-mode dynamic crack growth behavior along an arbitrarily smoothly varying path in functionally graded materials (FGMs) under transient thermo-mechanical loading is studied. An asymptotic analysis in conjunction with displacement potentials is used to develop transient thermo-mechanical stress fields around the propagating crack-tip. Asymptotic temperature field equations are derived for exponentially varying thermal properties, and later, these equations are used to derive transient thermo-mechanical stress fields for a curving crack in FGMs. The effect of the transient parameters (loading rate, crack-tip acceleration, and temperature change) and temperature gradient on the maximum principal stress and circumferential stress associated with the propagating crack-tip is discussed. Finally, using the minimum strain energy density criterion, the effect of temperature gradient, crack-tip speeds, and T-stress on crack growth directions is determined and discussed. [ABSTRACT FROM AUTHOR]

The problem of an eccentric penny-shaped crack embedded in a piezoelectric layer is addressed by using the energetically consistent boundary conditions. The Hankel transform technique is applied to solve the boundary-value problem. Then two coupling Fredholm integral equations are derived and solved by using the composite Simpson's rule. The intensity factors of stress, electric displacement, crack opening displacement and electric potential together with the energy release rate are further given. The effects of the thickness of a piezoelectric layer and the discharge field inside the penny-shaped crack on the fracture parameters of concern are discussed through numerical computations. The observations reveal that an increase of the discharge field decreases the stress intensity factor and the energy release rate. An eccentric penny-shaped crack is easier to propagate than a mid-plane one in a piezoelectric layer, and the geometry of the crack along with the layer thickness have significant influences on the electrostatic traction acting on the crack faces. The solutions for a penny-shaped dielectric crack in an infinite or a semi-infinite piezoelectric material can be obtained easily. [ABSTRACT FROM AUTHOR]

The fracture parameters, stress intensity factor and T-stress are obtained for edge cracks aligned along the gradient in finite size elastically graded plates using the technique of boundary collocation. A scheme for extending the recently derived crack tip stress field for elastically graded materials is proposed. Using this extended stress field, the fracture parameters are evaluated for edge cracks subjected to far field tension and three point bending. The results for far field tension agreed well with published theoretical results over a good range of elastic gradients. The maximum shear stress calculated over the entire domain of the cracked plate using boundary collocation agrees very well with that obtained from finite element analysis. The efficacy of the extended stress field in capturing the effects of the elastic gradient on the stresses and fracture parameters is thus established in this study. [ABSTRACT FROM AUTHOR]