Showing papers on "Stress field published in 1977"

An advanced boundary integral equation method for three‐dimensional thermoelasticity

Abstract: The features of an advanced numerical solution capability for boundary value problems of linear, homogeneous, isotropic, steady-state thermoelasticity theory are outlined. The influence on the stress field of thermal gradient, or comparable mechanical body force, is shown to depend on surface integrals only. Hence discretization for numerical purposes is confined to body surfaces. Several problems are solved, and verification of numerical procedures is obtained by comparison with accepted results from the literature.

The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids

Abstract: The present paper is concerned with an infinite slab containing a crack and deformed at infinity to a state of finite simple shear. The material of the slab is taken to be homogeneous, isotropic, elastic, and incompressible, and is further assumed to belong to a class of materials which admit nontrivial states of anti-plane shear. The analysis is carried out for the fully nonlinear equilibrium theory of finite elasticity. The stress field near the crack-tips is studied in detail; one of the special materials considered is such that the shear stresses near a crack tip remain bounded, despite the presence of unbounded displacement gradients. An analogy between the crack problem in finite anti-plane shear and the problem of transonic flow of a gas past a flat plate is pointed out and discussed.

Edge Effects on Thermally Induced Stresses in Composite Laminates

Abstract: Thermally induced stresses in fiber composite laminates play an important role in the strength and failure of such laminates as load carrying members. When laminates have free edges, cutouts or holes, interlaminar stress concentration will usually develop near the free-edge region under service loads. An accurate evaluation of thermally induced edge stresses will further the understanding of the laminates' behavior. The present paper examines the stress field of a finite-width, symmetrical laminate when subjected to a uniform temperature change. A finite-element proce dure employing advanced sparse matrix solution technique is employed to study the singular nature of stresses near the free-edge region. Edge effects on the overall response of the laminate under thermal loading are discussed.

Fatigue crack propagation in biaxial stress fields

Abstract: The propagation of fatigue cracks in notched and un-notched biaxially stressed plates is investigated. The rate of propagation is found to be affected by both the stress field associated with the notch and the biaxial stress state of the bulk material. It is found that the propagation rate of a crack from a notch may be predicted by the use of a theoretical notch contribution factor in conjunction with propagation data for a crack in un-notched material.

Central Europe: Active or Residual Tectonic Stresses

Abstract: The regional stress field in the Western Alps and their northern foreland has been investigated by in situ stress determinations. More than 600 strain relief measurements were made with resistance strain gages in boreholes carried out in mines, tunnels and quarries. The stresses calculated and data obtained from other papers were used to get a detailed idea of the stress conditions in Central Europe.

Influence of elastic and thermal mismatch on the local crack-driving force in brittle composites

Abstract: An expression is derived for the change of localK 1 value of a crackfront near circular and spherical inclusions with elastic moduli and thermal expansion coefficient different from those of the matrix. The derivation is based on the concept of an “image stress” which is imposed on the crack, to illustrate the interaction between elastic and thermal stress concentrations developed around inclusions in a composite material and the crack-tip stress field.

On the wrinkling of a free surface

Abstract: We consider an elastic half‐space whose free surface is capable of supporting its own stress field. This stress is a linear function of surface strain and is related to the stress in the interior of the body by a nonclassical boundary condition. We study the wrinkling (buckling) of the surface and show that this type of behavior is possible whenever the surface has a compressive residual stress or a negative stress‐strain modulus.

Stress fields round indentations in poly(methyl methacrylate)

Abstract: The authors discuss the stress field in the neighbourhood of an indentation made by a steel ball in poly(methyl methacrylate), the special characteristics of which have been described by Puttick (1973). These results suggest that the deformation in the interior of the solid approximates to that round a spherical cavity expanded by internal pressure in a plastic-elastic medium, as proposed for other materials both by Marsh (1964) and by Johnson (1970). The approximations required to apply ideal plastic-elastic theory to polymers are discussed, and Hill's solution (1950) of the equilibrium equation for the expanded cavity is modified to take into account the sensitivity of the yield stress of PMMA to strain rate and hydrostatic pressure; the result gives the indentation pressure in terms of the radius of the plastic zone. The latter dimension is experimentally determined by measuring the indentation pressure, so that the scale of the stress field in the interior is known. The state of plane stress in the surface is interpreted in terms of the plastic-elastic expansion of a hole in a plate. The tensile component of the stress field thus derived appears to explain well the orientation, shape and size of the stable cracks initiated at such indentations.

A method for finding critical stresses of dislocation movement

Abstract: A method is presented which makes possible the determination of the critical resolved shear stress, τc, for dislocation movement in a crystal. The method is based on the analysis of dislocation rosettes which are generated either by microindentation, or by precipitates of a second phase. The method does not require a knowledge of the indentation (or precipitate) stress field; it requires only information on the positions of a set of leading dislocation loops. At once one can also obtain the effective indentation stress field and, for the first time, the precipitate stress field. For illustration, the method is applied to the determination of τc in silicon, using both indentation and precipitate dislocation rosettes. The value of τc thus obtained varies from a low of 3×107 dyn/cm2 in oxygen‐free samples to a high of 5.5×108 dyn/cm2 in a sample containing ∼2×1018 atoms/cm3 of oxygen with clustering. The SiO2 precipitate stress field in the present case was found to vary as x−1, suggesting that the precipita...

A circular disc containing a radial edge crack opened by a constant internal pressure

Abstract: A circular disc of radius a, made of homogeneous, isotropic, linearly elastic material, contains a radial edge crack of length b(0 < b < 2a). The disc is in equilibrium in a state of generalized plane stress caused by loading the faces of the crack by a constant internal pressure. The problem of determining the resulting stress field throughout the disc is solved analytically in closed form. The principal results are that the stress concentration factor at the crack tip, the total strain energy W, and the opening U at the mouth of the crack, are given exactly bywhere A is a constant whose value correct to 6 significant figures isand , W0, U0 are normalising factors defined in section 6.

Stress and Shear Fracture (Fault) Patterns Resulting from a Suite of Complicated Boundary Conditions with Applications to the Wind River Mountains

Abstract: The Airy stress function is used, via the Principle of Superposition and the series summation concept, to obtain stress states in a static, self-gravitating elastic beam subjected to boundary stresses. The boundary conditions investigated are more complicated than those previously published and include cases with sawtooth-, step-, and sinusoidally-shaped lower-boundary loads, with and without additional tectonic end leads. Potential shear fracture (fault) patterns derived from the calculated stress fields indicate co-existing (simultaneous) regions of lateral shortening and extension. Application of one of the cases to the study of the structural geometry of the Wind River Mountains of Wyoming yields a good ‘fit’ and forms a possible explanation for the observed rotations and zones of shortening and extension.

The influence of the choice of connectors in the finite element method

Abstract: The patch test is interpreted from a variational point of view. This leads to conclude that non conforming (or non stress diffusive) displacement (stress) models can be considered as special hybrid models. A simple choice of mixed connectors is proposed that satisfy a priori the patch test for any assumed displacement or stress field. Finally some numerical examples are given of finite elements that do not pass the patch test but still converge.

The stress dependence of the crack growth rate during creep

Abstract: An equation is derived for the crack growth rate under creep conditions. In the model, the propagation of a grain boundary crack is controlled by the plastic growth of cavities located in the grain boundaries ahead of the crack. It is assumed that the cavities grow by power law creep in the elastic crack tip stress field. Hence, the stress dependence of the crack velocity is provided through the elastic stress intensity factor, i.e., dC/dt=BK . The cavity spacing, λ, appears as an important factor in the coefficient,B ∝ λ−(p−2)/2. At large values of λ, corresponding to less severe creep damage in the grain boundaries, the above equation would predict very low values for the crack velocity. Under such conditions, we suggest that another mechanism, whose stress dependence is provided through the net section stress, becomes active, i.e., dC/dt=B′σ net ′ . Since λ increases with decreasing applied stress, one should observe the σnet correlation at low stresses. The results of recent creep crack growth experiments which tend to support this hypothesis are presented.

Antiplane Strain Problems of an Elliptic Inclusion in an Anisotropic Medium

Abstract: The antiplane strain problem of an elliptic inclusion in an anisotropic medium with one plane of symmetry is solved. Explicit expressions of compact form are obtained for the elastic field inside the inclusion, the stress at the boundary, and the strain energy of the system. The perturbation of an otherwise uniform stress field due to an elliptic inhomogeneity is studied, and explicit solutions are given for the extreme cases of an elliptic cavity and a rigid elliptic inhomogeneity. It is found that both the stress magnification at the edge of the inhomogeneity and the increase of strain energy depend only on the component P23A of the applied stress for an elongated cavity; and depend only on the component E13A of the applied strain for a rigid line inhomogeneity.

Stress singularities in cracked composite full-planes

Abstract: The nature of the singular stress field developed at the point where a crack intersects the bonded interface of a bimaterial full-plane was investigated by the complex variable method. The crack lips were assumed to be under homogeneous stress, displacement or mixed boundary conditions. The order of the singularity was shown to be dependent on both the geometry and the four elastic constants of the two materials of the composite. Graphs showing the variation of the stress singularity with the aforementioned parameters were given. Valuable results indicating how the stress singularity depends on the geometry, the elastic constants and the boundary conditions of the cracked composite full-plane were derived.

Theoretical and Experimental Analysis of Surface Cracks Emanating from Fastener Holes

Abstract: : The finite element-alternating method is used to determine stress intesity factors along the periphery of a part-elliptical crack emanating from a fastener hole in a finite-thickness plate. The method performs a sequence of iterations between an analytic solution for an elliptical crack embedded in an infinite solid and a finite element solution for a finite-thickness uncracked plate with a fastener hole to obtain the stress field near the crack, the stress intensity factor and the crack opening displacements. Mode-one stress intensity factors around the crack front are presented for three classes of crack location relative to the hole and numerous crack shapes and sizes. Calculations are performed for cracks emanating from both loaded and unloaded fastener holes. Crack opening displacements for all cases are presented. The results of this study are compared to static fracture tests in polymethylmethacrylate and with experiments and estimates of other authors.

Experimental solution of the problem of a curvilinear crack in bonded dissimilar materials

Abstract: An experimental technique based on the optical method of caustics for the solution of the two-dimensional problem of an arc-shaped crack lying along the interface of a circular inclusion embedded in a matrix and subjected to a uniaxial tension at infinity was developed The study was directed towards the determination of the complex stress intensity factorK *characterizing the near to the crack tip stress field A detailed analysis of the caustics obtained by illuminating the near to the crack tip region by a coherent light beam was undertaken and nomograms for the direct experimental determination ofK *in the Dundurs parallelogram, incorporating all the physically relevant material combinations of the two bodies, were given Extensive experimental evidence for the new technique was given

On the dynamical process of fault motion in the presence of friction and inhomogeneous initial stress

Abstract: The Partial differential equation, which represents approximately the propagation of a crack, obtained by YAMASHITA (1976) is solved numerically, and the dependence on the tectonic field of the source parameters is studied in detail. Main results are as follows:The importance of effective stress and the fracture strength distribution for the dynamical process of fault motion is ascertained from the numerical computation and in the interpretation of observed data. The proportional relation between effective stress and dislocation velocity exists, but the ratio is widely different from BRUNE'S (1970) result. Effective stress is linearly proportional to stress drop. When initial stress fields are represented by a pair of linear functions and a quadratic function of the distance in the direction of dislocation surface, the approximate relations σeff≅10Δσ andσeff≅6Δσ hold respectively. Initial stress field of a Japanese inland earthquake is approximated by a pair of linear functions with small slopes. That of an earthquake along the trench is approximated by a quadratic function with a firly large coefficient. The dislocation velocity is in direct proportion to the stress drop.

Visco‐plastic behaviour during the excavation phase of a salt cavity

Abstract: The stress field and flow characteristics are studied for a cavity with the shape of a prolate spheroid in dome salt with emphasis given to the excavation phase. A semi-empirical creep law is derived from thermodynamic principles and experimental results. In this paper, an elementary non-linear form is used in the kinetic relation. A finite element solution procedure is discussed which incorporates the creep law, excavation sequence, and arbitrary non-homogeneous initial stress field.

Stress in an elastic bedrock hump due to glacier flow

Abstract: The stress field in an isotropic elastic hump representing a typical bedrock feature is obtained for plane strain conditions. Gravity effects are included and the applied load is a normal pressure distribution deduced from an idealized model of glacier flow. A Coulomb failure criterion is applied, including the effective stress change due to pore-water pressure, and stresses on the predicted failure planes determined for different pressure amplitudes and relative gravity contributions. The latter make little difference to the maximum “failure stress" but influence the regions where such stress levels occur. Levels of cohesive stress required to inhibit Coulomb failure are obtained, and are low in general, implying that coherent rock in the adopted hump profile, subject to the model pressure, would not fail. That is, this profile is stable unless jointing introduces an easier failure mechanism.

Numerical simulations of tectonic processes in Southern California

Abstract: Summary. A relaxation model for crustal tectonics, using the Finite Element method, was developed and applied to the region of Southern California. Both the existence of the Transverse Ranges and the geometry of the San Andreas fault in the region of Southern California, imply a stress pattern deviating from the simple horizontal shear which parallels the spreading between the Pacific and the North American plates. A number of possible mechanisms responsible for this anomalous stress field were examined quantitatively in the light of seismicity and other tectonic observations, and in particular to the Palmdale uplift which was reported to have occurred between the years 1960-65.

Plates and shells with cracks : a collection of stress intensity factor solutions for cracks in plates and shells

Abstract: 1 Interaction of arbitrary array of cracks in wide plates under classical bending.- 1.1 Introduction.- 1.2 Basic relations.- 1.3 Complex potentials for traction free cracks.- 1.4 Arbitrary array of cracks in wide plate.- 1.5 Numerical results.- 1.6 Discussions.- References.- 2 Improved approximate theories of the bending and extension of flat plates.- 2.1 Introduction.- 2.2 Approximate theories by variational methods.- 2.3 Applications to crack problems.- 2.4 Guidelines for practical applications.- References.- 3 Through cracks in multilayered plates.- 3.1 Introduction.- 3.2 Minimum complementary energy applied to a layered plate.- 3.3 An approximate three-dimensional theory of multi-layered plates.- 3.4 Through crack in a layered plate.- 3.5 Stress distribution across the plate thickness.- 3.6 Discussion of numerical results.- 3.7 Appendix: Definition of constants.- References.- 4 Asymptotic approximations to crack problems in shells.- 4.1 Introduction.- 4.2 General theory - classical.- 4.3 The stress field in a cracked spherical shell.- 4.4 The stress field in a cracked plate.- 4.5 The stress field in a cracked cylindrical shell.- 4.6 Approximate stress intensity factors for other shell geometries.- 4.7 Plates on elastic foundations.- 4.8 Particular solutions.- 4.9 Discussion.- References.- 5 Crack problems in cylindrical and spherical shells.- 5.1 Introduction.- 5.2 Formulation of the specially orthotropic cylindrical shell problem.- 5.3 The skew-symmetric problem.- 5.4 The symmetric problem.- 5.5 Results for a specially orthotropic cylindrical shell.- 5.6 The effect of Poisson's ratio.- 5.7 Interaction of two cracks.- 5.8 Further results for isotropic shells.- References.- 6 On cracks in shells with shear deformation.- 6.1 Introduction.- 6.2 Shell theory with shear deformation.- 6.3 Symmetric loading.- Appendix: Integrand and Kernel functions.- References.- 7 Dynamic analysis of cracked plates in bending and extension.- 7.1 Introduction.- 7.2 Classical plate bending theory.- 7.3 Mindlin's theory of plate bending.- 7.4 Kane-Mindlin's equation in plate extension.- 7.5 Plates subjected to sudden loading.- References.- 8 A specialized finite element approach for three-dimensional crack problems.- 8.1 Introduction.- 8.2 Three-dimensional elastic calculations.- 8.3 Finite element method - background.- 8.4 Specialized elements for the crack edge.- 8.5 Applications to crack problems.- 8.6 Details of the analysis.- 8.7 Results of the finite element analysis.- 8.8 Summary.- References.- Author's Index.

Crystallography of cleavage in BCC metals

Abstract: 1. Due to the high degree of symmetry of cubic crystals and the large range of possible slip systems, the calculated minimum values of F(α) function maxima for various cleavage systems do not differ significantly, but allowing for crystal anisotropy substantially affects which crystallographic plane should be given preference from the point of view of ease of cleavage. It is therefore essential to take elastic anisotropy into account when making calculations on the Ayres and Stein model. 2. The method of setting the stress field at the crack tip, is also important. Calculations using various types of stress tensor component may lead to various conclusions about the plane of easy cleavage. Calculations for a crack in an anisotropic crystal are most correct, and formulas for a dislocation in an isotropic medium are the least accurate. 3. The results of calculations on the given model accord satisfactorily with experimental data for crystals of W. Mo, and α-Fe (see Table 3), whereas the results of Ayres and Stein and those obtained according to the minimum surface energy criterion cannot explain all the experimental data. 4. Of the two types of slip system characteristic of bcc metals at moderate and low temperatures, i.e., {011} 〈111〉 and {112} 〈111〉, the minimum values of F(α) function maxima are higher in the system {112} 〈111〉 for all four cleavage systems studied. Taking into account the differing mobility of dislocations in these systems, one may expect that the first or the second system may control the processes of stress relaxation at the crack tip, depending upon the temperature.

Elastic relaxation coefficients for a spherical cavity in a prestressed medium of arbitrary orientation

Abstract: Archambeau gave elastic relaxation coefficients for a spherical cavity introduced into a pure shear prestress field. The technique is generalized to a stress field for which only the trace of σ_(ij)^(0) is zero. The coefficients are given for a general deviatoric prestress field of arbitrary orientation. They are then specialized to the case of a pure shear stress expressed in terms of the orientation angles commonly used in fault plane descriptions, i.e. dip and slip angle. The extension of this technique to an arbitrary homogeneous prestress field and its limitations are discussed.