The Journal of Strain Analysis for Engineering Design

Thin-walled structural elements are often subjected to cyclic loadings. This paper presents a material model describing creep behaviour under high-cycle loading conditions (N ≥ 5 × 104-105). Assuming that the load can be split into two joint acting parts (a static and a superposed, rapidly varying small cyclic component), the asymptotic expansion of two time-scales has been applied to the governing equations of the initial-boundary value creep problem. The system of equations determine two problems. The first is similar to the creep problem by quasi-static loading. The second is the problem of forced vibrations. Both the problems are coupled by constitutive equations. The model is applied to the simulation of the cyclic creep damage behaviour of thin-walled structural elements. The results are discussed for two special numerical examples (a conical shell and a circular plate). The simulations show that the creep and the damage rates as well as the failure time are strongly sensitive to the redistribution of the stress state cycle asymmetry parameter A_s. The values of A_s increase during the creep process. For particular cases of the loading frequency, A_s can exceed the critical value. In this case the material model must be extended in order to consider the creep-fatigue damage interaction.

The stress distribution in a rotating, spherically isotropic, functionally graded material (FGM) spherical shell that has its elastic constants and mass density as functions of the radial coordinate is exactly investigated in the paper. Three displacement functions are employed to simplify the basic equations of equilibrium for a spherically isotropic, radially inhomogeneous elastic medium. By expanding the displacement functions in terms of spherical harmonics, the basic equations are finally turned into an uncoupled second-order ordinary differential equation and a coupled system of two such equations. Exact analysis of a steadily rotating spherical shell with the material constants being power functions of the radial coordinate is carried out and a numerical example is presented.

There are many instances where it is necessary to measure strains inside polymethyl methacrylate. For instance, most cemented prosthetic devices fail owing to cement failure. Thus, it is important to measure the cement stresses in vitro, in order to optimize the design. Measuring internal strains with an embedded gauge is extremely difficult. The techniques proposed in the literature either are inaccurate or require large-scale models. In the present work a technique is proposed where a single strain gauge rosette is used. The strain gauge is calibrated to correct the errors deriving from the pressure acting on the grid. Thus accurate measurements can be obtained with a small sensor. The errors associated with this technique are estimated. A pilot study is presented (a) to verify whether the procedure can be applied to the actual geometry of the prosthesis, (b) to verify whether the gauges could safely be inserted into the femur, (c) to estimate the variability of this preparation and (d) to test the robustness of the preparation to repeated loading. Promising results were found in terms of accuracy, precision and robustness of the technique.

Finite element analyses of cracked short-radius piping elbows are reported. Both axial and circumferential cracks, centred about the bend crown or intrados respectively, are considered. The defects are internal, with depth-thickness ratios a/t in the range 0.25 ≤ a/t ≤ 1.0. Since the aim is to assess limit loads, the analysis assumes elastic-perfectly plastic material behaviour with no geometric non-linearities. The loadings considered are (a) opening bending moment, (b) internal pressure and (c) combined loading of steady pressure, set at the design value of the pipe elbow, with a superimposed monotonically increasing opening bending moment.

For each type of loading, the general component behaviour, by consideration of the global deformation with increasing load, is reported. Limit load values for each case are presented and the relative reductions in load-carrying capacity, compared with that predicted for a defect free elbow of the same material and dimensions, are given.

Experimental and finite element (FE) plastic load results of cracked piping elbows under opening in-plane bending are presented and compared with data from similar defect-free components. The elbows used were short-radius components with an outside diameter of 88.9 mm and thickness 5.49 mm. Axial (at the crown) and circumferential (at the intrados) blunt crack-like defects were produced using electric discharge machining (EDM) procedures. Both short (0 = 21° axial or 2β = 46° circumferential) and long (0 = 75° axial or 2β = 120° circumferential) defects were investigated with three depth-thickness ratios a/t = 0.5, 0.75 and 1.0. The FE simulations employed the measured true stress-strain properties for the elbow material and included geometric non-linear behaviour.

The results obtained show that piping elbows under opening bending can tolerate substantial defects, with reductions in plastic loads compared with the defect-free component of the order of 15 per cent or less in most cases, except when the defect is through-wall and circumferential and covers an angle 2β = 120° or more, in which case the reduction in plastic load can be as high as 40 per cent.

The initial buckling load of flat trapezoidal plates of special orthotropy when loaded in axial compression is determined. Two types of boundary condition are considered: (a) the plate is clamped at one end and free on the other sides; (b) the plate is clamped along opposite ends and free along the sloping sides. The problem is twofold; determining the buckling load and providing a comprehensive parametric understanding of the buckling behaviour. An affine transformation scheme is infused into the solution process such that a minimum number of parameters remain. Using the potential energy functional, the problem of finding the buckling load is then solved by the finite element method. The results are presented for various rigidity ratios of the composite plates. It is observed that increasing the generalized rigidity ratio caused an increase in the stability of the plate.

In this paper the stress field in the proximity of a circular (cylindrical) inclusion is considered. The conditions for in-plane plastic flow in the matrix are examined from a classical elasticity solution obtained by Goodier. Elementary cases are considered such as remote loading ranging from pure tensile and pure shear to equibiaxial tension. For proportional loading, it is argued that the upper bound to the shakedown limit is always twice the elastic limit; therefore, within the limits of our assumptions, if the elastic stress concentration for the equivalent stress is greater than two, there is a possibility of cyclic plasticity before bulk yielding, which means that possibly an arbitrarily large plastic strain can cumulate with increasingly high risk of exhaustion of ductility and void nucleation or detachment of the interface.

Consequently, conditions under which it is possible to reach twice the elastic limit before full-scale yielding are shown in the Dundurs plane representing all possible combinations of elastic parameters. Following these lines, it is shown that there is no possibility of cyclic plasticity under remote shear; there is a limited area of the Dundurs plane for tension, including the hole case; finally, in the equibiaxial limiting case, cyclic plasticity is always possible for any combination of elastic properties.