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From the decomposition theorem of elastic beams, two classes of exact stress states are investigated for the equations of three dimensional elasticity governing elastic beams in bending deformations with free faces. One of these is the analogue of the Levy solution for elastic plates and is designated as the interior state. The other complementary class corresponds to a decaying state and is designated as the Papkovich-Fadle state. The appropriate boundary conditions have been established recently for the prescribed data at the end edge of beams to induce only an exponentially decaying elastostatic state. The present paper describes how these conditions may be used to determine the boundary conditions of these two states. The decomposition theorem of beams effectively allows us to split the prescribed edge-data correctly into two parts, one for the interior solution components and the other for the decaying solution components. An analytical solution of the decaying state is formulated to verify the validity of our boundary conditions. The results in turn show that the necessary conditions for the Papkovich-Fadle state are also sufficient conditions. The boundary conditions obtained for the interior state show that the interior solution determined by these conditions is the correct solution in the beam interior up to exponentially small terms. Moreover, with the separate consideration of the interior and decaying solution components, a relatively simple analytical solution is often practical and desirable, and the numerical computation process is essentially simplified. As an illustrative example, the present results are applied to the end-loaded cantilever beam. [ABSTRACT FROM AUTHOR]

This article discusses various issues related to the arithmetic mean theorem for the N-fold rotational symmetrical inclusion in anti-plane elasticity. In the anti-plane problem, a cylindrical body undergoes a displacement that remains parallel to the generatrix of the cylinder and independent of the axial coordinate. The anti-plane inclusion problems have their significance in applications that have attracted attention of the researchers.

Although Peng Yafei and his co-workers discovered some faults with the pseudo-stress function method suggested by Y. S. Lee in 1987, the authors did not provide convincing arguments. We investigate the crucial assumption in Lee's method by rewriting it as the form of real part and imaginary part. Through a specific counterexample, we point out that the crucial assumption in Lee's theory is untenable. Namely, for given Airy's stress function, it cannot be guaranteed that the pseudo-stress function Λ(x,y) exists. The root cause of the fault with Lee's method is found in this paper. [ABSTRACT FROM AUTHOR]

Indentation stress relaxation tests were carried out on high-purity polycrystalline copper specimens at room temperature with a flat cylindrical indenter. The experimental results showed that the resulting load-time relaxation curves can be described by a power law, which coupled an internal stress and an integral constant between the effective stress and relaxation time. Then the internal stress, integral constant, and dislocation velocity stress exponent can be extracted from load relaxation curves. The derived values from this way were consistent with the results of conventional uniaxial compression stress relaxation tests. These agreements are not only useful to understand deformation (dislocation) mechanisms under the indenter, but also exhibit an attractive potential of measuring nano/micromechanical properties of materials by indentation test. [ABSTRACT FROM AUTHOR]

The finite element method (FEM) was used to study the flat cylindrical indentation fatigue behavior using a kinematic hardening model (A-F model). This study was motivated by the experimental work of the preceding paper [B.X. Xu and Z.F. Yue, J. Mater. Res.21, 1793 (2006)], in which there were obvious similarities in the behavior of conventional fatigue specimens and indentation fatigue specimens. It is proposed that the A-F model can predict the indentation fatigue behavior. Generally, the experimental behavior of the indentation fatigue testing can be explained by the FEM analysis. In addition, the effect of residual stress on the indentation depth per cycle was studied. The effect of friction between the indenter and the specimen and evolution of von Mises stress beneath the indenter was also investigated. Numerical results showed that the effect of friction on the indentation depth propagation can be neglected. Further analysis showed that the steady-state indentation depth per cycle increases with increasing compressive residual stress and decreasing tensile residual stress. [ABSTRACT FROM AUTHOR]

Experiments and numerical simulations have been carried out to study residual stress of copper specimens by the indentation method with a flat cylindrical indenter. Copper specimens were annealed at different temperatures for 35 min to obtain different residual stress levels. The experiments carried out on these specimens demonstrated the influence of residual stress on indentation behavior. The influence of annealing temperature on the elastic-plastic transition region is quite obvious. A method has been presented to determine material properties, such as elastic modulus and Poisson ratio. This method can also be applied to determine residual stress with the assumption of knowing the yield stress in advance. The advantage of this method is that it can avoid calculating the contact area. In the finite element modeling (FEM), residual stresses on copper specimens are simulated by preapplying stresses. The influence of residual stress on the indentation load-depth curves has been studied by FEM. There is good agreement between experimental and FEM numerical results. A numerical method has also been presented to determine residual stress. In addition, Mises stress and plastic distribution ahead of the indenter have also been studied to help us further understand the influence of residual stress. [ABSTRACT FROM AUTHOR]