Static and dynamic stability modeling of a capacitive FGM micro-beam in presence of temperature changes

Stability of a functionally graded (FG) micro-beam, based on modified couple stress theory (MCST), subjected to nonlinear electrostatic pressure and thermal changes regarding convection and radiation, is the main purpose of this paper. It is assumed that the functionally graded beam, made of metal and ceramic, follows the volume fraction definition and law of mixtures, and its properties change as an exponential function through its thickness. By changing the ceramic constituent percent of the bottom surface, five different types of the micro-beams are investigated. The static pull-in voltages in presence of temperature changes are obtained by using step-by-step linearization method (SSLM) and, by adapting Runge–Kutta approach, the dynamic pull-in voltages are obtained numerically. Though the temperature distribution through the thickness of FG micro-beam (due to its too small measurement) is considered uniform, owing to the different thermal expansions of layers, temperature changes cause deflection in the micro-beam, and consequently affect pull-in values. Hence the profound effects of different material constituent over the pull-in voltages are illustrated and it is graphically displayed that how in some cases neglecting components of the couple stress leads to inaccurate results.     

Basic solution of two parallel mode-I permeable cracks in functionally graded piezoelectric materials

The basic solution of two parallel mode-I permeable cracks in functionally graded piezoelectric materials was studied in this paper using the generalized Almansi’s theorem. To make the analysis tractable, it was assumed that the shear modulus varies exponentially along the horizontal axis parallel to the crack. The problem was formulated through a Fourier transform into two pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surface. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. The solution of the present paper shows that the singular stresses and the singular electric displacements at the crack tips in functionally graded piezoelectric materials carry the same forms as those in homogeneous piezoelectric materials; however, the magnitudes of intensity factors depend on the gradient of functionally graded piezoelectric material properties. It was also revealed that the crack shielding effect is also present in functionally graded piezoelectric materials.     

Dynamic stress intensity factor of a crack perpendicular to the weak-discontinuous interface in a nonhomogeneous coating–substrate structure

A mechanical model was established for the antiplane dynamic fracture problem of a functionally graded coating–substrate structure with a coating crack perpendicular to the weak-discontinuous interface. The problem was reduced to a Cauchy singular integral equation by the methods of Laplace and Fourier integral transforms. Erdogan’s collocation method and the Laplace numerical inversion proposed by Miller and Guy were used to calculate the dynamic stress intensity factors. Three conclusions were drawn through parametric studies: (a) unlike the conclusion drawn for an interfacial crack, reducing the weak discontinuity of the interface will not necessarily decrease the dynamic stress intensity factor (DSIF) of the coating crack perpendicular to the interface; (b) increasing the stiffness of the substrate when that of the coating is fixed, or decreasing the stiffness of coating when that of the substrate is fixed, will be beneficial for the reduction of the DSIF of a coating crack perpendicular to the interface; and (c) the free surface has a greater influence on the DSIF than the interface does, and the effect of the interface on the DSIF is greater than that of the material stiffness in the crack-tip region.     

Anti-plane shear of an arbitrary oriented crack in a functionally graded strip bonded with two dissimilar half-planes

An internal crack located within a functionally graded material (FGM) strip bonded with two dissimilar half-planes and under an anti-plane load is considered. The crack is oriented in an arbitrary direction. The material properties of strip are assumed to vary exponentially in the thickness direction and two half-planes are assumed to be isotropic. Governing differential equations are derived and to reduce the difficulty of the problem dealing with solution of a system of singular integral equations Fourier integral transform is employed. Semi closed form solution for the stress distribution in the medium is obtained and mode III stress intensity factor (SIF), at the crack tip is calculated and its validity was verified. Finally, the effects of nonhomogeneous material parameter and crack orientation on the stress intensity factor are studied.     

A novel technique for the fabrication of laboratory scale model functionally graded materials

In this work, the authors describe the design, fabrication and testing of model functionally graded materials (FGMs). The inhomogeneous property variations were generated by altering material properties through selective ultraviolet (UV) irradiation. Poly(ethylene co-carbon monoxide) (ECO) was chosen to make the FGMs because of its rapid degradation under UV light. Irradiated ECO becomes stiffer, stronger and more brittle with increasing irradiation time. Through a series of tension tests, the authors characterized the mechanical behavior of the specific ECO used as a function of UV exposure time. Furthermore, by controlling exposure time, specimens with continuously and discretely varying mechanical properties were produced. The resulting graded materials exhibited a Young's modulus that varied from about 160 MPa to 250 MPa and a strain to failure that varied from about 900 percent to 10 percent over the width in a 150 mm wide specimen. Microhardness measurements were used to determine the differences between discretely and continuously varying mechanical properties.     

On the screw dislocation in a functionally graded material

This paper presents the stress field of a screw dislocation in a medium graded in y-direction. The medium is exponentially graded. For such a graded material theories of elasticity as well as gradient elasticity are applied. By means of the stress function technique we found exact analytical solutions of the corresponding master equations. Using the stress field, the Peach–Koehler force is given. The axial symmetry of a screw dislocation is lost due to the gradation in the y-direction.     

A preparation method of functionally graded materials with phase transition under shock loading

The propagation of phase boundary in a material undergoing shock induced irreversible phase transition is studied theoretically using a model based on simple-mixture rule. It is found that along with the decay of the phase boundary, a functionally graded material (FGM) forms in the mixed-phase region. Such FGMs are composed of parent phase and product phase, and the composition and physical properties are changing continuously without apparent macro-interfaces. The effect of stress boundary conditions on formation of the FGM is investigated in detail with a numerical method. The possibility of producing FGMs with impact method is proposed and the limit of this method is discussed.     

Effects of moisture on the glass transition temperature of polyurethane shape memory polymer filled with nano-carbon powder

One simple approach to produce electrically conductive polymers is to fill them with conductive powders. This paper investigates the effects of moisture on the glass transition temperature of a polyurethane shape memory polymer (SMP) filled with nano-carbon powders. It is found that the SMP composites before immersion in water have a slightly lower glass transition temperature, and in the mean time, the moisture fraction at the saturation point upon immersion is also lower. On the other hand, the moisture can remarkably reduce the glass transition temperature of the composites. Heating to over 180 °C is an effective way to remove the moisture, which also results in the glass transition temperature back to the original. As the glass transition temperature can be greatly reduced by moisture, a novel feature, namely, the water actutable recovery of SMP composites is also proposed based on this study.     

Dynamic stress intensity factors of multiple cracks in a functionally graded orthotropic half-plane

In the present paper dynamic stress intensity factor and strain energy density factor of multiple cracks in the functionally graded orthotropic half-plane under time-harmonic loading are investigated. By utilizing the Fourier transformation technique the stress fields are obtained for a functionally graded orthotropic half-plane containing a Volterra screw dislocation. The variations of the material properties are assumed to be exponential forms which the equilibrium has an analytical solution. The dislocation solution is utilized to formulate integral equation for the half-plane weakened by multiple smooth cracks under anti-plane deformation. The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to determined stress intensity factor and strain energy density factors (SEDFs) for multiple smooth cracks under anti-plane deformation. Numerical examples are provided to show the effects of material properties and the crack configuration on the dynamic stress intensity factors and SEDFs of the functionally graded orthotropic half-plane with multiple curved cracks.     

An analytical method for magnetothermoelastic analysis of functionally graded hollow cylinders

This paper considers magnetothermoelastic behavior of a functionally graded material (FGM) hollow cylinder, placed in a uniform magnetic field, subjected to thermal and mechanical loads. Exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow cylinders is determined by using the infinitesimal theory of magnetothermoelasticity. Numerical results indicate that the inhomogeneous constants presented in the present study are useful parameters from a design point of view in that it can be tailored for specific applications to control the stress and perturbation of magnetic field vector distributions. This research is helpful for the optimum design annular cylindrical FGM sensors/actuators.