Impact of surface stress on stress concentration

Effect of surface stress on stress concentration near a spherical void in an elastic medium is examined in the framework of continuum surface elasticity. It is assumed that the void is of spherical shape, and the elastic medium is elastically isotropic and infinitely extended. By using the Papkovitch–Neuber displacement potentials, the elastic field caused by a unidirectional remote load is obtained explicitly. Numerical results show that the influence of surface stress becomes remarkable when the size of the void is reduced to nanometer scale, leading to that stress concentration near the void depends not only on the void size but also on the remote load.     

Relations between stress growth and stress relaxation functions

The stress relaxation function after steady shear flow and the stress growth function at inception of steady flow are derived for several constitutive equations of the integral and differential types. Relationships between these functions are deduced and discussed.     

Assembly stress for the reduction of stress concentration

A systematic study utilizing the experimental method of reflected photoelasticity was undertaken to determine the effects of assembly stress on the stresses around circular holes under uniaxial tension. The assembly stresses are the result of the contact and bearing stresses between the bolts and the member. It has been concluded that assembly stress contributes to reducing the stresses around the hole.     

Assumed stress quasi-conforming triangular element for couple stress theory

In this paper, a 3-node triangular element for couple stress theory is proposed based on the assumed stress quasi-conforming method. The formulation starts from polynomial approximation of stresses. Then the stress-function matrix is treated as the weighted function to weaken the strain-displacement equations. Finally, the string-net functions are introduced to calculate strain integration and the stress smooth technique is adopted to improve the stress accuracy. Numerical results show that the proposed new model can pass the C~(0-1) patch test with excellent precision, does not exhibit extra zero energy modes and can capture the scale effects of microstructure.     

Determination of all stress components from measurements of the stress invariant by the thermoelastic stress method

A method for the resolution of all stress components from the first invariant J₁ measured by thermoelastic stress analyzer is described. This method may be used to determine, not only surface stress, but also internal stress and stress on the underside.The method is based on the following procedure:

1. (1) Pick an arbitrary domain Ω, within the structure, for which the stresses are required.

2. (2) Measure J₁ on the surface of Ω.

3. (3) Determine the optimum traction along the boundary Γ, which is a part of Ω, by the least squares method such that the difference between the measured J₁ and the calculated J₁ is at a minimum. Either FEM or BEM may be used for this calculation.

Examples of stress resolution for a two-dimensional stress concentration problem and a three-dimensional stress concentration problem are shown. The accuracy of the stress resolution is discussed.     

Acoustoelastic stress analysis of residual stress in a patch-welded disk

The acoustoelastic stress analysis is based on the fact that an initially isotropic material becomes anisotropic under stress. The birefringent effect for polarized ultrasonic shear waves in the stressed material will then be similar to the photoelastic effect in which a light wave and a transparent model specimen are used. In this paper, the velocity differences of acoustical, perpendicularly polarized waves are measured directly by a ‘sing-around’ method using a 5-MHz shear-type transducer. The residual-stress distribution in a mild-steel circular plate with a concentrically patch-welded joint is measured by this method. The acoustoelastic coefficient is obtained separately by uniaxial testing of the base material. The results show that the acoustical stress measurement, carried out nondestructively, agrees well with those obtained by conventional destructive methods as well as with theoretical predictions.     

On divergence-free stress fields and zero-energy stress functions in elasticity

Applying two identities for divergence-free non-symmetric and symmetric second-order tensors, novel type of first- and second-order stress functions are proposed for three-dimensional elasticity problems. It is shown that self-equilibrated but non-symmetric 3D stress fields can be generated by one first-order stress function vector, whereas a self-equilibrated and symmetric 3D stress field can be generated by one Airy-type second-order stress function. Assuming linearly elastic materials, the zero-energy modes of the stress functions introduced are derived and investigated. It is pointed out that the structure of the zero-energy modes of the proposed first-order stress function vector is the same as that of the rigid-body displacements in the linear theory of elasticity.     

Derivation of some special stress function from Beltrami-Schaefer stress function

Using Beltrami-Schaefer stress function in the theory of elasticity in this paper, we derive the stress functions of torsion, plane problem, axisymmetric deformation in solid of revolution and torsion on solid of revolution.     

极坐标中应力与应力函数之间的关系

在极坐标下,通过极坐标的应力平衡方程推导出极坐标应力（）与应力函数之间的关系．     

Normal stress measurements

An apparatus designed to measure the dynamic viscoelastic response of polymer melts is described. Dynamic elasticity (G) and viscosity () can be measured over a frequency range 10^–2-10^–3 Hz and at temperatures up to 350 °C. The sample under test is held in a cone and plate assembly. A small strain is introduced by driving the plate with a variable speed synchronous motor and off-centre cam at low frequencies and by an electromagnetic vibrator at high frequencies. The amplitudes of the cone and plate are detected using the optical lever principle and photocell strips. The phase difference between the cone and plate is measured from a recorder trace at low frequencies and by direct reading on a meter at high frequencies.Results are described of measurements on silicone fluids, and on commercial grades of polyethylene with different molecular weight distributions and degrees of branching.A discussion is given of the correlation between the dynamic viscosity measurements and those taken under steady-flow conditions.Paper presented at the Conference on Experimental Rheology, University of Bradford, April 17–19, 1968. — Original paper published in J. Sci. Instruments Series 2,1, 1102–1112 (1968).     

Natural stress tensors

The notion of natural stress tensors is introduced, which are tensors obtained from Cauchy and Kirchhoff stress tensors by operations of mapping, halfmapping, and mixed mapping of the actual configuration onto the reference configuration, and also onto two intermediate configurations. A complete class of natural stress tensors is obtained and analyzed.     

Normal stress measurements

A review of the methods for obtaining the normal stress differences in simple shear flow from force measurements on the walls of apparatus in which curvilinear shear flows are generated is given. Indirect methods, for example the flow birefringence method, are considered. Some new work on normal stress measurement using cone and plate, parallel plate pressure distribution and total thrust measurements in conjunction with flow birefringence methods are reviewed. The difficulties found in obtaining consistant results are discussed.Paper presented at the Conference on Experimental Rheology, University of Bradford, April 17–19, 1968. — Original paper published in Rheo. Acta,7, 368 (1968).     

Maximum normal stress fatigue criterion applied to random triaxial stress state

Fatigue criterion based on the maximum normal stress acting on a fracture plane with random triaxial stress state is related to an equivalent stress state. Probability density function of the equivalent stress state and its associated parameters are obtained. Planes on which the maximum values of the equivalent stress variance occur are assumed to coincide with the sites of fatigue fracture.     

Effect of surface stress and surface-induced stress on behavior of piezoelectric nanobeam

A new continuum model is developed to study the influence of surface stress on the behaviors of piezoelectric nanobeams. Different from existing piezoelectric surface models which only consider the surface properties, the proposed model takes surfaceinduced initial fields into consideration. Due to the fact that the surface-induced initial fields are totally different under various boundary conditions, two kinds of beams, the doubly-clamped beam and the cantilever beam, are analyzed. Furthermore, boundary conditions can affect not only the initial state of the piezoelectric nanobeam but also the forms of the governing equations. Based on the Euler-Bernoulli beam theory, the nonlinear Green-Lagrangian strain-displacement relationship is applied. In addition, the surface area change is also considered in the proposed model. The governing equations of the doubly-clamped and cantilever beams are derived by the energy variation principle. Compared with existing Young-Laplace models, the proposed model for the doubly-clamped beam is similar to the Young-Laplace models. However, the governing equation of the cantilever beam derived by the proposed model is very different from that derived by the Young-Laplace models. The behaviors of piezoelectric nanobeams predicted by these two models also have significant discrepancies, which is owing to the surface-induced initial fields in the bulk beam.     

Hybrid experimental-numerical stress analysis

The hybrid experimental-numerical stress-analysis technique, which saw limited applications during the 1950's, has been resurrected with the vastly improved numerical techniques of the 1970's. By inputing the experimental results as initial and boundary conditions, modern computer codes are executed in its generation and application modes to yield results which are unobtainable when only one of the two techniques is used. The hybrid technique thus exemplifies the complementary role of the experimental and numerical techniques.