Stress singularities at the vertex of a cylindrically anisotropic wedge

The plane elasticity problem for a cylindrically anisotropic solid is formulated. The form of the solution for an infinite wedge-shaped domain with various homogeneous boundary conditions is derived and the nature of the stress singularity at the vertex of the wedge is studied. The characteristic equations giving the stress singularity and the angular distribution of the stresses around the vertex of the wedge are obtained for three standard homogeneous boundary conditions. The numerical examples show that the singular behavior of the stresses around the vertex of an anisotropic wedge may be significantly different from that of the isotropic material. Some of the results which may be of practical importance are that for a half plane the stress state at r=0 may be singular and for a crack the power of stress singularity may be greater or less than 1/2.This work was supported by NASA Langley Research Center under the Grant NGR 39-007-011 and by NSF under the Grant ENG 78-09737.     

Analysis of inplane composite wedges under traction-displacement or displacement-displacement boundary conditions

Summary The inplane problem of dissimilar isotropic wedges of arbitrary angles that are bonded together along a common edge is considered. The surfaces of the wedges are subjected to traction-displacement or displacement-displacement boundary conditions. The characteristic equation is derived to determine the dependence of the order of the stress singularity on the wedge angles and material constants for plane strain and plane stress problems. Numerical results for several special wedge geometries are presented for different material combinations. The asymptotic behavior of the stresses in the vicinity of the apex is also investigated. Explicit solutions for the order of stress singularity are presented for some special cases.     

Numerical analysis of stress singularity at singular points of three-dimensional elastic bodies

A numerical method of constructing eigensolutions for arbitrary elastic conical bodies with smooth and non-smooth lateral surfaces is considered. Different variants of its numerical implementation based on the finite element method are discussed. The results of numerical experiments demonstrating the efficiency and reliability of the proposed method are presented. The character of stress responses (the character of stress singularities) in the vicinity of vertices of circular and non-circular cones, composite and hollow cones, cones with non-smooth lateral surfaces, trihedral wedge, one and two intersecting wedge-shaped cracks is estimated based on the obtained solutions.     

Influence of heat-resistant coatings on the state of thermal stress of model of gas turbine engine blades in nonsteady heat exchange

The finite-element method was applied to calculate the thermal state and the state of stress and strain of a wedge-shaped model with a heat-resistant coating (heat shield) subjected to heat cycling by a gas stream. We analyzed the influence of the method of discretization of the section of the model and of the method of specifying the characteristics of the materials of the base and of the coating on the accuracy of the solution of the problem of thermoelasticity. We obtained data on the influence of the technological factors and of the thickness of the heat shield on the kinetics of the state of thermal stress of the material of the models. It was established that a ceramic layer changes the asymmetry of the cycle to the side of tensile stresses and shifts the maximum of the stresses into the range of lower temperatures.Translated from Problemy Prochnosti, No. 6, pp. 24–30, June, 1994.     

Finite deformations at the vertex of a bi-material wedge

The paper gives an asymptotic analysis of finite plane-strain deformations near the vertex of a bi-material wedge of arbitrary angle and subjected to the traction-free surface conditions. Each of two edge-bonded dissimilar wedges is assumed to be hyperelastic with the harmonic-type strain energy density introduced by John (1960). In contrast to the results of linearized elastostatics, the deformations and stresses around the vertex of an arbitrary bi-material wedge are found to be free of oscillatory singularities within the context of finite elastostatics. A simple relation is found between the material moduli and two wedge angles that classifies the higher-order singular field into two different types. The explicit conditions for the strict positivity of the Jacobian determinant in the vicinity of the vertex are given in terms of the known material and geometric parameters independently of the loading conditions. In particular, these conditions can be easily verified for several typical kinds of bi-material wedge. Finally, the expressions for the singular field near the wedge vertex are given and the main features of deformations and stresses are summarized. This revised version was published online in August 2006 with corrections to the Cover Date.     

Multiaxial thermo‐mechanical fatigue on material systems for gas turbines

Material systems made from nickel based superalloys with protective coatings have been tested in thermo‐mechanical fatigue with superposed thermal gradients, which generated multiaxial stress states. The testing conditions were selected for simulating the fatigue loading in the wall of an internally cooled gas turbine blade of an aircraft engine. After thermo‐mechanical testing the damage behaviour of the materials has been investigated by means of microscopic methods. The laboratory experiments have been accompanied by numerical simulations. Based on the results of the simulations and observed damage features the test parameters in subsequent laboratory tests have been controlled to facilitate the validation of models describing the initiation and propagation of damages. This contribution gives an overview over results on the influence of multiaxial stress states on (i) oriented deformation and coagulation of γ’‐precipitates (‘rafting’) in the substrate, (ii) on morphological instabilities of the surface of metallic oxidation protection coatings (‘rumpling’), and (iii) on crack initiation and growth in material systems with additional ceramic thermal barrier coating.     

An assessment of the role of near-threshold crack growth in high-cycle-fatigue life prediction of aerospace titanium alloys under turbine engine spectra

Increasingly accurate life prediction models are required to utilize the full capability of current and future advanced materials in gas turbine engines. Of particular recent interest are predictions of the lifetimes of engine airfoil materials that experience significant intervals of high-frequency, high-cycle fatigue (HCF). Conventional life management practices for HCF in the turbine engine industry have been based principally on a total-life approach. There is a growing need to develop damage tolerance methods capable of predicting the evolution and growth of HCF damage in the presence of foreign object damage (FOD), low cycle fatigue (LCF), and surface fretting fatigue. To help identify key aspects of the HCF life prediction problem for turbine engine components, a review is pressented of the extensive results of an Air Force research contract with Pratt & Whitney on the high strength titanium alloy Ti-8Al-1Mo-1V. Data from this representative turbine-airfoil material are used to examine the applicability of linear elastic fracture mechanics methods for prediction of service lifetimes under load spectra that include high cycle fatigue. The roles of fatigue crack initiation and growth are examined for materials that are nominally-defect-free, as well for materials that have experienced significant prior structural damage. An assessment is presented of the potential utility of the conventional threshold stress intensity factor range, ΔK _th, defined by testing specimens containing large cracks. Although the general utility of a large-crack-ΔK _th approach is questionable due to the potentially rapid growth of small fatigue cracks, the low allowable stresses involved in turbine engine high cycle fatigue appear to limit and simplify the small-crack problem. An examination is also presented of the potential effects of high-cycle fatigue and low-cycle fatigue (HCF/LCF) interactions.     

Intensity of Local Effects at the Core Junctions in Sandwich Panels

Local effects that occur in the vicinity of junctions between different cores in sandwich panels subjected to the in-plane axial force and bending moment are considered. These local effects manifest themselves in a rise of locally induced bending normal stresses in the sandwich faces and shear and normal stresses in the cores in the near vicinity of the core junctions. Intensity of the local effects is measured experimentally for a representative sandwich beam subjected to both types of loadings. The numerical simulations are performed using Finite Element Analysis, and they reveal significant rates of stress concentrations in the faces and cores adjacent to the core junctions. The intensity of the local effects is dependable on the geometry and elastic properties of the sandwich faces and a degree of dissimilarity of elastic properties of the adjoined cores.     

Similarity of Stress-Singularity Problems for Materials with Linear and Bilinear Behaviors

An analogy is established between the solutions of the problems of singularities of stresses in linear and bilinear elastic isotropic media. It is shown that the distributions of stresses and displacements in the vicinity of singular points on the boundary of the body (characterized by the singularities of stresses) are described, in both cases, by the same functional dependences on the space coordinates but with different characteristics of the material. We deduce expressions for the effective moduli of elasticity and Poisson's ratio of the bielastic medium including the parameter of hardening of the material. The solution of the problem of singularities of stresses in bilinear materials is obtained from the solution of the corresponding problem for the linear elastic medium by replacing the elastic constants with the corresponding effective values depending on the parameter of hardening of the material. The cases of wedge-shaped notches (for various boundary conditions imposed on their edges), two-component wedges, plane wedge-shaped cracks, and circular conic notches or rigid inclusions in the bielastic space are studied in detail.     

Influence of the Microstructure on Magnetic Stray Fields of Low-Carbon Steel Welds

This study examines the relationship between the magnetic mesostructure with the microstructure of low carbon steel tungsten inert gas welds. Optical microscopy revealed variation in the microstructure of the parent material, in the heat affected and fusion zones, correlating with distinctive changes in the local magnetic stray fields measured with high spatial resolution giant magneto resistance sensors. In the vicinity of the heat affected zone high residual stresses were found using neutron diffraction. Notably, the gradients of von Mises stress and triaxial magnetic stray field modulus follow the same tendency transverse to the weld. In contrast, micro-X-ray fluorescence characterization indicated that local changes in element composition had no independent effect on magnetic stray fields.     

Plain concrete modeled as an elastic strain-softening material at fracture

Concrete is modeled as a linear-elastic softening material and introduced into fracture mechanics. A discrete crack is considered with softening zones at the crack tips. Following the approach of Dugdale and Barenblatt, closing stresses are applied to the crack faces in the softening zone. The stresses are described by a power function. Relations are worked out between the remote stress on a cracked plate, the tensile strength of the material and the size of the softening zone. The finite width of a plate is considered and so are various stress distributions of the softening zone. Experiments were performed to establish the stress-strain behavior of concrete in deformation-controlled uniaxial tensile loading. The results show that nonlinear fracture mechanics can be applied to concrete in order to predict the load-bearing capacity of a cracked structure.     

Bending of curved sandwich beams

Curved sandwich beams in bending are analyzed with analytical elasticity methods and compared to simple analytical formulae and FEM calculations. Solutions to Airy's stress function in polar co-ordinates are used to obtain the stress distributions in the radial and circumferential directions. Plane stress and plane strain solutions are given with isotropic and orthotropic material models. It is shown that the properties of the core can have a significant influence on the circumferential stresses of the faces, but that the radial stress of the core is nearly constant with varying core properties. The radius of curvature can have a large influence on the circumferential stresses of the faces when the radius of curvature to sandwich thickness ratio is small to moderate. It is shown that simple analytical methods can be utilised to calculate the radial stresses in the core and the circumferential stresses of the faces for beams with large to moderate radii of curvature and thin to moderately thick faces.     

Plastic stress singularity near the tip of a V-notch

In this study, a new practical method is proposed to analyze the plastic stress singularity at a V-shaped notch tip. By dividing the domain around the notch tip into a number of wedge-shaped elements, the problem is reduced to determining the stress singularity in a wedge composed of multiple materials with different stiffness matrix. The results so obtained appear to be quite satisfactory. Based on the numerical results, the effects of the notch geometry and the hardening exponent on the singularity are discussed. In particular, an approximate expression is presented for the evaluation of the plastic stress singularity.     

Stress-strain state of a cracked elastic wedge under anti-plane deformation with mixed boundary conditions on its faces

A problem about the stress-strain state of an elastic wedge with an arbitrary angel of opening, when on its bisector there is a system of a finite number collinear cracks, is studied by the means of the theory of elasticity. The anti-symmetric mixed boundary conditions given on both wedge-faces, together with the forces applied to the cracks' surfaces are provoking the anti-plane deformation of the wedge. The displacement components are given for the same group of nonintersecting intervals on each wedge-face and the stress components are given on the rest of the faces. The problem is formulated as a known mixed boundary problem of the theory of harmonic functions for a half-wedge because of the wedge symmetry relative to its bisector. The solution of this mixed boundary problem is derived in the closed form by using the Mellin integral transformation in combination with the methods of singular integral equations. Based on this the density of displacements' dislocations on the cracks' surfaces, the stress intensity factors, the stresses on those intervals on the wedge-faces, where the displacements are given, and other characteristics of the investigating problem are determined by explicit analytical formulas. Particular cases are discussed as well.     

Distinctive features of physical fields near the edge of a composite piezoceramic wedge (antiplane deformation)

We consider a composition in the form of a wedge made of two different conjugate piezoceramic or anisotropic piezopassive wedges and study the distinctive features of the behavior of physical fields in the vicinity of the edge of this composite wedge under homogenous boundary conditions imposed on its external faces. The problem is solved by the method of complex representations of the components of electroelastic fields for two principal types of mechanical and electrical boundary conditions. The results of numerical computations are also presented. Sumy State University, Sumy. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 2, pp. 27–32, March–April, 1999.     

Longitudinal Shear of an Elastic Wedge with Cracks and Notches

We study the problem of longitudinal shear of an infinite wedge with cracks and notches. The integral representations of the complex stress potential are constructed in terms of the jumps of displacements and stresses on curvilinear contours identically satisfying the boundary conditions imposed on the faces of the wedge (stresses or displacements are equal to zero). By using these representations, we deduce singular integral equations of the analyzed problem for a wedge weakened by a system of cracks and holes of any shape. In some cases (a crack along the bisectrix of the wedge, a crack along a circular arc whose center is located at the edge of the wedge, and a circular notch near the edge of the wedge), we obtain exact closed solutions.     

Three-dimensional asymptotic stress field at the front of a bimaterial wedge of symmetric geometry under antiplane shear loading

Three-dimensional asymptotic stress field in the vicinity of the front of a bimaterial wedge is obtained by a new eigenfunction expansion method, subjected to three combinations of wedge-side boundary conditions – free–free, clamped–clamped and free–clamped. The bimaterial wedge has symmetric geometrical configuration with respect to the bimaterial interface. Each material is isotropic and elastic, but with different elastic properties. Additionally, numerical results pertaining to the variation of the lowest eigenvalues (or stress singularities) with respect to the half-aperture angle of the bimaterial wedge, subjected to the afore-mentioned wedge-side boundary conditions, are also presented. Dependence of the same on the material properties of the component material phases (if any) is also presented.     

Two-dimensional simulation of crystalline growth fronts in a polypropylene/glass-fibre composite depending on processing conditions

The application of a mechanical stress at the glass-fibre/polypropylene interface during cooling of the matrix may give rise to different crystalline superstructures, depending on the stress intensity and temperature. For a given stress-intensity/temperature combination, the transcrystalline phase growing in the vicinity of the fibre may have an monoclinic or a β hexagonal crystallographic nature. On that account, variable boundary lines may be observed between a transcrystalline superstructure and the bulk spherulites. The intersections between the crystalline entities are calculated, and their computer simulations may be generalized to represent a multifilament wick in a unidirectional composite material. Knowledge of the application temperature of the mechanical stresses, and of the statistical distribution of the crystallization nuclei in the bulk, allows us to predict and to simulate the total crystalline morphology of a polypropylene/glass-fibre composite material. Finally, the model proposed is compared with experimental results.     

A study of fatigue failure initiation in high cycle high-pressure automotive applications and conventional rotating bending fatigue testing

The search for greater power and efficiency from automotive engines places components under ever increasing stress. This study compares results obtained from testing of engine components under extreme operating conditions with those obtained from laboratory-based tests. Conventional rotating bending fatigue testing has been applied to high strength alloy steel samples processed and heat treated under the same conditions as engine test components. The results are compared with those obtained from engine components tested under high-pressure cyclic loading using specially designed engine test rigs. Failure initiation sites in the high strength alloy steel samples have been identified and categorised using scanning electron microscopy with X-ray mapping. The influence of inclusion content, heat treatment process and surface finish have been determined and used to inform design considerations, heat treatment processing conditions and material selection.