Optimization of the sintering temperature, cooling time and grain size parameters to reduce residual stresses of copper-aluminum functionally graded material using response surface methodology

One of the urgent needs for the medical, aerospace and military industries is to combine materials with heat-resistant as well as flexible structures. To create such a property, a ceramic must be placed next to metal. FGM materials have such a property in terms of thickness. Functionally graded materials (FGM) are examples of materials with different properties in the thickness direction. In the functionally graded materials, different properties can be created, by changing the percent weight of materials in each layer. It is very important to study the number of residual stresses in these materials due to the fact that several materials with different properties are combined with each other. The purpose of this study is to investigate the effect of production parameters on the number of residual stresses in the aluminum-copper FGM part and also to optimize the production process of these materials. The results indicate that the number of residual stresses decreases with increasing the sintering temperature, cooling time of the sample as well as uniformity along the thickness. In the experiments, the maximum residual stress was 171 MPa, which was obtained for a grain size of 100 microns, sintering temperature of 600°C and cooling time of 24 h and the minimum value of pressure residual stress was 120 MPa, which was obtained for grain size of 20 microns, sintering temperature of 900°C and cooling time of 48 h. Also, finite element modeling of the process was performed and shown a good agreement with experimental results.

An efficient semi-analytical static and free vibration analysis of laminated and sandwich beams based on linear elasticity theory

Based on the two-dimensional (2D) elastic theory without enforcing any beam assumption, an efficient semi-analytical scaled boundary finite element method (SBFEM) is proposed to solve the bending and free vibration responses of composite laminated and sandwich beams under the mechanical load. The scaled center is placed at infinity, which produces the accurate result by discretizing only the longitudinal direction of the beam structure treated as a one-dimensional (1D) discretization problem. A new kind of 1D high-order spectral element shape functions with the advantages of high accuracy and superior convergence is introduced in SBFEM coordinate system to approximate the geometric model and corresponding variables. The principle of weighted residual in conjunction with the Green’s theorem are applied to obtain the SBFEM governing equation of each layer with respect to radial displacement fields. The solution of equation is indicated analytically by a matrix exponential function, which can be accurately solved by using the precise integration technique (PIT). Finally, an effective and simple stiffness matrix is obtained. By comparing two examples with the solutions based on the finite element method (FEM), the results show that the proposed method has good accuracy and rapid convergence with only a few meshes. The numerical examples are given to investigate the parametric effects of the stacking sequence, thickness ratio, boundary condition, and load form on the variation of the displacement, stress and natural frequency. The results validate that the present technique is also applicable to the complex beam structure with softcore layer inside.

Subsurface stresses in an elliptical Hertzian contact

The traditional solution for the stresses below an elliptical Hertzian contact expresses the results in terms of incomplete Legendre elliptic integrals, so are necessarily based on the length of the semi-major axis a and the axis ratio k. The result is to produce completely different equations for the stresses in the x and y directions; and although these equations are now well-known, their derivation from the fundamental, symmetric, integrals is far from simple. When instead Carlson elliptic integrals are used, they immediately match the fundamental integrals, allowing the equations for the stresses to treat the two semi-axes equally, and so providing a single equation where two were needed before. The numerical evaluation of the Carlson integrals is simple and rapid, so the result is that more convenient answers are obtained more conveniently. A bonus is that the temptation to record the depth of the critical stresses as a fraction of the length of the semi-major axis is removed. Thomas and Hoersch’s method of finding all the stresses along the axis of symmetry has been extended to determine the full set of stresses in a principal plane. The stress patterns are displayed, and a comparison between the answers for the planes of the major and minor semiaxes is made. The results are unchanged from those found from equations given by Sackfield and Hills, but not previously evaluated. The present equations are simpler, not only in the simpler elliptic integrals, but also for the “tail” of elementary functions.

Effect of porosity and skew edges on transient response of functionally graded sandwich plates

This work for the first time presents the effect of porosity and skew edges on the transient response of functionally graded material (FGM) sandwich plates using a layerwise finite element formulation. Two configurations of FGM sandwich plates are considered. In the first configuration, the top and the bottom layers are made of the FGM and the core is made of pure metal, whereas in the second configuration, the bottom, core and the top layers are made of pure metal, FGM and pure ceramic, respectively. Four micromechanics models based on the rule of mixture are used to model porosity for these two configurations of FGM sandwich plates. A layerwise theory based on a first-order shear deformation theory for each layer that maintains the displacement continuity at the layer interface is used for the present investigation. An eight-noded isoparametric element with nine degrees of freedom per node is used to develop the finite element model (FEM). The governing equations for the present investigation are derived using Hamilton’s principle. A wide range of comparison studies are presented to establish the accuracy of the present FEM formulation. It has been shown here that the parameters like skew angle, porosity coefficient, volume fraction index, core to facesheet thickness ratio and boundary conditions have a significant effect on the transient response of FGM sandwich plates. Also, the present finite element formulation is simple and accurate.

Assessment of the degradation in mild structural steel using electron backscatter diffraction (EBSD) technique

This paper reports the degradation assessment of mild steel during the plastic tensile process. The electron backscatter diffraction (EBSD) technique was adopted in this study. The orientation maps showed that with the increase of tensile strain, the grain surface become wrinkled, and the deviation level of intragranular orientation also increased. Meanwhile, the parameters based on the image quality of the Kikuchi bands (i.e. BC and MAD) as well as the crystallographic orientation (i.e. LAGBs content, GND density, GOS, and GROD) can be used to evaluate the degradation degree of the mild steel. The results showed that the change of BC and MAD was significant at the end of plastic stage, but was not sufficiently distinctive at the early stage; Meanwhile, the LAGBs content and GND density increased evidently during the plastic tensile. Compared with the former, the GND density exhibited stronger regularity and better evaluation effect; Besides, a general upward trend of GOS and GROD was observed at this tensile process. However, the GROD changed less at the certain plastic stage. Compared with GROD, the GOS exhibited a relatively better evaluation effect; To sum up, the GND density and GOS are the better indicators for evaluating the degradation degree of mild steel.

Strain gauge placement optimization methodology to measure multiaxial loads of complex structure

The use of a strain gauge to measure loads is, in some respects, similar to its use in determining stress, but a different approach is required. In load measurement, it is necessary to compile a suitably selected configuration of strain gauges, which can be used to measure often very complex loads of the structure. For designing the engine mount instrumentation for the Flying Test Bed, an optimization tool has been developed. The algorithm and the theory behind the instrumentation design are described in detail. The basic principle is to find the strain gauge configuration that eliminates the measurement error due to the noise in the measured signal as much as possible. The input for optimization is the strain response of the structure to the applied loads analyzed using the FE model. In contrast to the common strategy using purely stochastic methods, this developed tool uses a hybrid approach based on a combination of a heuristic approach with repeated deterministic local optimization. The optimization is focused on the connection of a simple uni-axial strain gauge to a quarter-bridge and a T-rosette to a half-bridge that provides temperature compensation. Furthermore, an approach is proposed that takes into account the possibility of failure of some strain gauges. The instrumentation is thus robust and allows to obtain quality data even in the event of failure of some of the strain gauges.

Use of a digital image correlation method for full-field shrinkage measurement in injection molding

An original methodology using Digital Image Correlation (DIC) has been designed to precisely measure full-field shrinkages of injection molded polymer plates and then to give the opportunity to compare quantitatively extensive numerical simulations to experiments. The principle of the methodology is based on the full-field strain determination between a reference image of the mold and that of injection-molded parts, which are 275 × 100 × 2.2 mm3 plates. To allow for DIC calculation, 50 µm-depth engravings were machined by electro-discharge process at the surface of the mold. The result of the analysis is a 2D full-field shrinkage map over the whole plate surface (i.e. flow and transverse), with a standard deviation of 0.03%. The marking density has been shown to have a roughly linear influence on the precision of shrinkage measurement. This methodology allows the quantification of the effect of several injection parameters on in-plane shrinkage fields: holding pressure, injection flow rate and direction, geometry of injection gates, or geometrical constraints. Once the best set of parameters of material constitutive laws is identified for the simulation of polymer plates, the simulation procedure is ready to be applied on more complex 3D geometries.

Thermo-mechanical stress analysis of rotating fiber reinforced variable thickness disk

Circumferentially fiber reinforced composite disk, which has a variable thickness, is modeled via analytical approaches. The disk is subjected to rotation in traction free conditions and decreasing, constant, and increasing steady state radial temperature gradients along the disk radius. Limit angular velocities are calculated by operating Tsai-Wu and Norris failure indexes to the problem. Subsequently, these limit velocities are gradually decreased to examine the stress and displacement fields. Acquired results show that as the angular velocity drops, the effects of temperature gradients become more visible. At lower angular velocities, these gradients may even alter the stress field directions. Also, different failure criteria implementation may change the calculated limit velocities to a considerable degree. Therefore, the failure index should be chosen attentively to procure conservative results. In the investigation, the influence of disk geometry on the directional stresses is studied as well. Without further ado, it can be expressed that the geometry causes slight alterations in stresses and displacements.

A novel approach to envisage effects of boron in P91 steels through Gleeble weld-HAZ simulation and impression-creep

This paper induced a novel methodology for the characterization of creep behavior of weld heat-affected zone (HAZ) for boron-free P91 (PM) and boron modified P91B (B-PM) steels. Gleeble-3800 thermo-mechanical simulator replicated specimens, representing coarse-grain HAZ (CGHAZ), fine-grained HAZ (FGHAZ), and inter-critical HAZ (ICHAZ). Short-term impression creep tests were conducted at 625°C/270-410MPa on PM/B-PM and their simulated HAZs after being subjected to post-weld heat treatment (PWHT) of 760°C/3 h. Microstructural characterization and local strain analyses were accomplished by electron back-scattered diffraction. Simulated microstructures of P91B-FG/ICHAZ after PWHT exhibited lath martensitic structure and large prior-austenite grain size as regards P91-FG/ICHAZ, correspondingly. Average values of local microstructural strain from local average misorientation were relatively high in B-PM and P91B-ICHAZ than PM and P91-ICHAZ, respectively. Similar observations were found for P91-CG/FGHAZ with their counterparts. Stress dependent steady-state creep-rate (SSCR) followed power-law for all specimens except PM. The minimum and maximum ranges of SSCR for P91B specimens were observed to be in a narrower range than P91 specimens. The value of stress exponent for all specimens was evaluated, and corresponding mechanisms were discussed. The analyses of microstructures and corresponding impression creep behavior of P91/P91B samples suggested that modification of 100 ppm boron to P91 steel improved creep-rupture ductility that delayed type IV failure at outer HAZ of P91 steel weldments.

Validation of a structural model of an aircraft cockpit panel: An industrial case study

Computational models of structures are widely used to inform decisions about design, maintenance and operational life of engineering infrastructure, including airplanes. Confidence in the predictions from models is provided via validation processes that assess the extent to which predictions represent the real world, where the real world is often characterised by measurements made in experiments of varying sophistication dependent on the importance of the decision that the predictions will inform. There has been steady progress in developing validation processes that compare fields of predictions and measurements in a quantitative manner using the uncertainty in measurements as a basis for assessing the importance of differences between the fields of data. In this case study, three recent advances in a validation process, which was evaluated in an inter-laboratory study 5 years ago, are implemented using a ground-test on a fuselage at the aircraft manufacturer’s site for the first time. The results show that the advances successfully address the issues raised by the inter-laboratory study, that the enhanced validation process can be implemented in an industrial environment on a complex structure, and that the model was an excellent representation of the measurements made using digital image correlation.