Stress concentration factor due to a circular hole in functionally graded panels under uniaxial tension

The effect of the material property inhomogeneity on the stress concentration factor (SCF) due to a circular hole in functionally graded panels is numerically investigated. The multiple isoparametric finite element formulation is used to simulate the elastostatic boundary value problem. A parametric study is performed by varying the functional form and the direction of the material property gradation. The material property inhomogeneity is characterized by the intrinsic inhomogeneity length scale, modulus ratio and the power-law index. The results from our parametric study showed that the SCF is reduced when Young’s modulus progressively increased away from the hole. The angular position of the maximum tensile stress on the surface of the hole remains unaffected by the material property inhomogeneity. The SCF is seen to be most influenced by the power-law index, followed by the variation of the inhomogeneity length scale. The SCF is least affected by the modulus ratio

Finite element simulations of microvoid growth due to selective oxidation in binary alloys

Selective oxidation induced void growth is observed in thermal barrier coating systems used in gas turbines. These voids occur at the interface between the bond coat (BC) and the thermally grown oxide (TGO) layer. In this paper we develop the modelling framework to simulate microvoid growth due to coupled diffusion and creeping in binary alloys. We have implemented the modelling framework into an existing finite element programme. The developed modelling framework and programme is used to simulate microvoid growth driven by selective oxidation in a binary \beta -NiAl alloy. Axisymmetric void growth due to the combined action of interdiffusion and creeping is simulated. The sharpness of the void and direction of creeping are considered as parameters in our study. Our simulations show that the voids dilate without any change in shape when creeping is equally likely in all the directions (isotropic). Void growth patterns similar to those observed in experiments are predicted when the creeping is restricted to occur only along the radial and tangential directions. A hemispherical void grows faster compared to a sharp void. The sharpness increases in the case of a sharp void and could lead to interactions with the neighbouring voids leading to spallation of the TGO layer as observed in experiments

Mode-3 spontaneous crack propagation along functionally graded bimaterial interfaces

The effects of combining functionally graded materials (FGMs) of different inhomogeneous property gradients on the mode-3 propagation characteristics of an interfacial crack are numerically investigated. Spontaneous interfacial crack propagation simulations were performed using the newly developed spectral scheme. The numerical scheme derived and implemented in the present work can efficiently simulate planar crack propagation along functionally graded bimaterial interfaces. The material property inhomogeneity was assumed to be in the direction normal to the interface. Various bimaterial combinations were simulated by varying the material property inhomogeneity length scale. Our parametric study showed that the inclusion of a softening type FGM in the bimaterial system leads to a reduction in the fracture resistance indicated by the increase in crack propagation velocity and power absorbed. An opposite trend of increased fracture resistance was predicted when a hardening material was included in the bimaterial system. The cohesive tractions and crack opening displacements were altered due to the material property inhomogeneity, but the stresses ahead of the cohesive zone remained unaffected

Mode-3 spontaneous crack propagation in unsymmetric functionally graded materials

The effects of the inhomogeneous material property variation on the mode-3 crack propagation characteristics have been analyzed. The spectral form of the elastodynamic boundary integral equations are derived for a functionally graded material, which is used as the numerical tool in our analysis. The material property gradient is assumed to vary unsym-metrically in the direction normal to the fracture plane. A parametric study has been performed by systematically varying the inhomogeneity length scale. In comparison with a homogeneous material, an unsymmetric functionally graded material offers lesser fracture resistance. The fracture resistance progressively decreases with increase in inhomogeneity, quantified by the increase in crack sliding displacement jumps, crack tip velocities and accelerations. The material property inhomo-geneity affects only the transient crack propagation velocities, while the quasi-steady-state velocity remains unaltere

Mode-3 spontaneous crack propagation in symmetric functionally graded materials

The effects of spatially varying the material properties on the mode-3 planar crack propagation characteristics are numerically investigated. The spectral scheme that is available for homogeneous materials is modified to account for the symmetrically varying material properties. Crack propagation in hardening, softening and unsymmetric type of functionally graded have been simulated. A parametric study was performed by systematically varying the material inhomogeneity length scale. Our study indicated that softening and unsymmetric graded materials reduce the resistance to fracture, while a hardening material offers higher fracture resistance with increase in inhomogeneity. Only the transient phase of crack propagation speed was affected by the material property variation, irrespective of whether the material was hardening, softening or an unsymmetric type. The crack always reached a quasi-steady-state velocity, which remained unaffected by the material property inhomogeneity

Indentation strength of a piezoelectric ceramic: Experiments and simulations

The spherical indentation strength of a lead zirconate titanate (PZT) piezoelectric ceramic was investigated under poled and unpoled conditions and with different electrical boundary conditions (arising through the use of insulating or conducting indenters). Experimental results show that the indentation strength of the poled PZT is higher than that of the unpoled PZT. The strength of a poled PZT under a conducting indenter is higher than that under an insulating indenter. Poling direction (with respect to the direction of indentation loading) did not significantly affect the strength of material. Complementary finite element analysis (FEA) of spherical indentation of an elastic, linearly coupled piezoelectric half-space is conducted for rationalizing the experimental observations. Simulations show marked dependency of the contact stress on the boundary conditions. In particular, contact stress redistribution in the Coupled problem leads to a change in the fracture initiation, from Hertzian cracking in the unpoled material to Subsurface damage initiation in poled PZT. These observations help explain the experimental ranking of strength the PZT in different material conditions or under different boundary conditions

Strain field measurement using digital image correlation

Digital Image Correlation and Tracking (DIC/DDIT) is an optical method that employs tracking & image registration techniques for accurate 2D and 3D measurements of changes in images. This is often used to measure deformation (engineering), displacement, and strain, but it is widely applied in many areas of science and engineering. One very common application is for measuring the motion of an optical mouse