Sanboh Lee

Elastic interaction between general parallel screw dislocations and a surface crack

The dislocation‐modeling technique and complex variable method are used to analyze the interaction between the general parallel screw dislocations and a surface crack. For the case of one dislocation, the dislocation distribution in the crack, the stress field, the strain energy, the image force, the stress intensity factor, and the crack extension force are obtained. The results are compared with various special cases of other papers. Under the applied stress without the frictional force, there are two metastable points and no stable point in the strain energy diagram. Therefore, the dislocation will move to the free surface, crack surface, or infinity depending on its location. The two‐dislocation system or the even dislocation dipole is analyzed. Although this approach gets the same results as the conformal mapping method, the former is superior in analyzing two or more dislocations.

Modeling of elastic thermal stresses in two materials joined by a graded layer

The distribution of elastic thermal stresses in two dissimilar materials joined by a graded layer is a critical issue and has been analyzed previously. However, numerical methods have often been used. The difficulty in obtaining an analytical solution in existing analyses is discussed, and an exact closed-form solution is derived in the present study. To illustrate applications of the present solution, results are calculated for elastic thermal stresses in thermal barrier coatings, which consist of substrate, graded bond coat, and top coat. Different profiles of the thermomechanical properties in the bond coat are considered to examine how the graded interlayer modifies the elastic thermal stress distribution in the system.

THEORY FOR THE RATE OF CRACK CLOSURE

The theory for the constant rate of crack closure was investigated. The aim of this theory is to explain why the rate of crack closure is constant during the wetting stage of healing. Assuming that a surface crack in a material is treated by compression or with solvent, its crack closes up at a constant rate and its shape is independent of time. This approach was based on the Gibbs energy of an atom near the boundary between healed and unhealed zones. The results are in satisfactory agreement with experimental data in the literature.

Load-displacement relations for nanoindentation of viscoelastic materials

A model based on the Burgers viscoelastic concept has been developed to describe the nanoindentation behaviors of polymeric materials. An analytical solution of displacement at the indenter tip has been derived based on the analog of the governing equation of elasticity in the time coordinate system to the governing equation of the viscoelastic model in Laplace transform coordinate system. The solution consists of the elastic, viscous, and plastic displacements during loading and unloading. Nanoindentation experiments have been conducted for poly(methyl methacrylate), polycarbonate, hydroxyethyl methacrylate copolymer, amorphous syndiotactic polystyrene, and fast-cure acrylic polymers to provide data for validating the model. The results show excellent agreement between experimental load-displacement data and model prediction for both the loading and unloading before the contact area decreases for all five polymers. The viscosity decreases but the hardness increases with increasing loading rate. Young’s m...

Anisotropic methanol transport in PMMA after mechanical deformation

Abstract Transport of methanol in compressed PMMA (23–34% strain) was found to be anisotropic. It was faster by a factor of two to three in penetration velocity and by a factor of 10 in diffusivity in the direction of compression than in the perpendicular direction. However, the penetration velocity in the slow direction is still a factor of two to five larger than that of the undeformed PMMA (two at 40°C and five at 25°C). The two-dimensional mixed diffusion and case II transport problem was solved analytically so that the diffusivity and the penetration velocity could be obtained from experimental weight gain data. The penetration front was found to correspond approximately to a front of constant concentration of methanol. When methanol was mixed with glycerol to lower the methanol concentration (glycerol does not penetrate PMMA), the penetration velocity was smaller due to reduced swelling but the diffusivity was unchanged as expected.

Effect of chemical stress on diffusion in a hollow cylinder

The effect of chemical stress on diffusion in a hollow cylinder for plane strain and zero axial force has been investigated. Two diffusion processes of constant surface stress and constant surface potential are studied. No matter what the plane strain or zero axial force is the influence of chemical stress on the diffusion process of constant surface potential is similar to that of constant surface stress. Chemical stress enhances both the diffusion coefficient and the concentration. For a given time, the level of concentration becomes lower with a greater ratio of outer radius to inner radius for constant surface potential with given FXf and for constant surface stress with given FXi. F=2EV/[9(1−v)RT] where E, V, R, and T are the Young’s modulus, partial molal volume, gas constant, and absolute temperature, respectively; Xi and Xf are the initial and final mole fractions at boundary surfaces. The results are also compared with those in thin plates and solid cylinders reported in the literature.The effect of chemical stress on diffusion in a hollow cylinder for plane strain and zero axial force has been investigated. Two diffusion processes of constant surface stress and constant surface potential are studied. No matter what the plane strain or zero axial force is the influence of chemical stress on the diffusion process of constant surface potential is similar to that of constant surface stress. Chemical stress enhances both the diffusion coefficient and the concentration. For a given time, the level of concentration becomes lower with a greater ratio of outer radius to inner radius for constant surface potential with given FXf and for constant surface stress with given FXi. F=2EV/[9(1−v)RT] where E, V, R, and T are the Young’s modulus, partial molal volume, gas constant, and absolute temperature, respectively; Xi and Xf are the initial and final mole fractions at boundary surfaces. The results are also compared with those in thin plates and solid cylinders reported in the literature.

Thermal stresses in double‐coated optical fibers at low temperature

The thermal stresses in double‐coated optical fibers at low temperature have been analyzed. The lateral pressure and normal stresses in the glass fiber, primary coating, and secondary coating have been derived. The thermal stresses in the optical fiber are affected by the temperature drop, material properties of the primary and secondary coatings, and their thickness. It is possible to select a suitably polymeric coating to produce minimum lateral pressure in the glass fiber. In order to minimize the thermally induced bending loss, it was found that if the thickness of the polymeric coatings increases, the Young’s modulus of primary coating should increase, but the Young’s modulus of the secondary coating should decrease.

Diffusion-induced stresses in a hollow cylinder:: Constant surface stresses

Abstract Diffusion-induced stresses in a hollow cylinder with constant stress at boundary surfaces are investigated. The solute diffusion follows Fick’s law. In order to maintain stress constant at the boundaries, the surface concentration is determined using Laplace transformation. Then using the Duhamel method, we obtain the concentration distribution. The radial stress, tangential stress and axial stress for zero axial force are calculated. From the numerical results, we study the possibility to avoid the mechanical failure including plastic deformation and fracture. In summary, the present solution is the fastest mass transfer process in the hollow cylinder without plastic deformation.

The elastic interaction between screw dislocations and cracks emanating from an elliptic hole

Based on the solution of an internal crack, we have investigated the elastic interaction of a screw dislocation and cracks emanating from an elliptic hole by using a conformal mapping technique. We have derived the stress field, the image force on the dislocation, the stress intensity factor at the crack tip, and the crack extension force. From the image force, we find the unstable equilibrium positions of dislocation. It is possible to form a plastic zone from the region containing the unstable equilibrium position by collecting dislocations. By extending the concept of the unstable equilibrium position, we also develop the dislocation emission criterion. It is found that the critical applied stress for dislocation emission is dependent on the geometry of the crack. In addition, we also find that the elliptic hole prefers to emanate double cracks. Finally, it is worthwhile to mention that the mapping function cannot be arbitrarily chosen.

An analysis of the elastic interaction between an edge dislocation and an internal crack

Abstract The elastic interaction between an edge dislocation and a finite crack has been investigated using the dislocation-modelling approach. We considered not only the applied stresses of modes I and II but also dislocations inside the crack. We obtained the stress field, the force and strain energy of the dislocation and the stress intensity factors at both crack tips. The unstable equilibrium positions of dislocation have been studied. Also, the criterion of dislocation emission from the crack tip has been analysed in order to understand the crack tip as a major source of dislocation.