Showing papers in "Journal of Strain Analysis for Engineering Design in 2000"

Numerical and experimental uniaxial loading on in-plane auxetic honeycombs

Abstract: Auxetic honeycombs show in-plane negative Poisson's ratio properties; they expand in all directions when pulled in only one, and contract when compressed. This characteristic is due to the reentrant shape of the honeycomb unit cell. The cell convoluteness gives a geometric stiffening effect that affects the linear elastic properties of the whole cellular solid. In this paper finite element simulations are carried out to calculate the in-plane Poisson's ratio and Young's moduli of re-entrant cell honeycombs for different geometric layout combinations (side cell aspect ratio, relative thickness and internal cell angle) subjected to uniaxial loading. The results show a high sensitivity of the mechanical properties for particular ranges of the geometric cell parameters. An image data detection technique is used to extract displacements and strains from an aramid paper re-entrant honeycomb sample in a tensile test. The comparison between numerical and experimental results shows good agreement.

Measurement and prediction of residual stresses in thick section steel welds

Abstract: Significant levels of residual stress are developed in the production of thick-section steel welds. Residual stress can be measured by a variety of methods, although few offer the ability to determine the spatial distribution completely through the thickness. This paper summarizes recent developments in the deep-hole method for measuring residual stresses in thick-section welds. Experimental results obtained from a variety of welded steel components are described. The measurement method has also been used to provide validation for finite element simulations of residual stresses in a welded cylinder-to-nozzle stainless steel component. The paper describes the finite element weld analysis and compares the results with measurements obtained from several locations in the complex geometry. Overall, there is good agreement between the predicted and measured distributions of residual stress, but the magnitudes of predicted stress tend to be greater.

The elastic compensation method for limit and shakedown analysis: A review:

Abstract: A comprehensive review of the elastic compensation method for calculating limit and shakedown load bounds for complex structures is presented. The origins of the method in pressure vessel design by analysis is described and related methods for load and shakedown analysis considered, in particular Marriott's reduced modulus method, Seshadri's GLOSS r-node method and Ponter's modified elastic modulus method. The paper concludes with a recommendation for future work: development of an element level formulation of the method.

Effects of residual stresses on fracture behaviour—experimental results and assessment methods

Abstract: The influence of residual stresses on fracture behaviour depends on the level of plasticity in a component. Under predominantly elastic conditions, residual stresses can significantly reduce the load-carrying capacity of a defective structure. Conversely, the effects of residual stresses can be minimal when plasticity is widespread. In this paper, a set of experiments with well-characterized residual stresses is used to demonstrate these effects. A new method for assessing defects in practical structures with residual stresses is then described and related to existing methods. The method is applied to the experimental data and shown to be generally accurate and yet conservative.

Piping elbows with cracks Part 2: Global finite element and experimental plastic loads under opening bending

Abstract: 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. T...

Twisted impregnated yarns : elastic properties

Abstract: Twisted yarns are normally used for increasing the lateral cohesion of filaments and also for ease of handling. By twisting yarns, the microdamage can be localized, leading to possible increase in the failure strength of the yarns. In this paper, an analytical method is presented for predicting the elastic properties of twisted impregnated yarns made of long unbroken filaments. In the analysis, various degrees of twist in filaments at different radii of the yarn and possible migration and microbuckling are considered. The effects of the twist angle and the extent of migration and microbuckling on the elastic properties and the pre-straining of the yarn are presented.

Development of a representative test specimen for frictional contact in spline joint couplings

Abstract: The frictional contact conditions in a helical spline joint coupling under torsional and axial loads are studied using finite element analyses. Comparisons of spline root torsional stresses are made with photoelastic measurements. Surface contact tractions, relative slip distributions and subsurface localized stress component and equivalent stress distributions are presented for both the external and the internal spline contact surfaces. The work is important as a basis for understanding and predicting the fatigue, contact fatigue, fretting fatigue, wear and fretting wear characteristics of the coupling. A representative test specimen concept is presented which seeks to capture the local contact variable distributions in the spline coupling, with a view to predicting the wear and the contact and fretting fatigue performance of the coupling.

Analytical expressions of the influence functions for accuracy and versatility improvement in the hole-drilling method

Abstract: Analytical expressions of the influence functions suitable for obtaining variable through-thickness residual stresses by the hole-drilling method are proposed. They were determined by interpolating the results of accurate finite element simulations of the experimental arrangement as prescribed by the ASTM standard. The effects of the geometrical parameters and material properties were included. The influence functions allow the relaxed strain measured by the strain gauge rosette to be directly calculated for a general residual stress distribution. With no interpolation of tabular values, they can be employed to evaluate the coefficients required for the application of the integral method. It is also shown how the influence functions can be used to obtain residual stress distribution on the basis of a fully general series expansion.

Piping elbows with cracks Part 1: A parametric study of the influence of crack size on limit loads due to pressure and opening bending

Abstract: 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.

Non-linear bending of shear deformable laminated plates under lateral pressure and thermal loading and resting on elastic foundations:

Abstract: A non-linear bending analysis is presented for a simply supported shear deformable composite laminated plate subjected to a combined uniform lateral pressure and thermal loading and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on Reddy's higher-order shear deformation plate theory, including the plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine the load-deflection curves and load-bending moment curves. Numerical examples are presented that relate to the performances of antisymmetric angleply and symmetric cross-ply laminated plates subjected to thermomechanical loading and resting on two-parameter elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influences due to a number of effects e.g. foundation stiffness, plate aspect ratio, total number of plies, fibre orientation and initial thermal bending stress, are studied. Typical...

The determination of the residual strains and stresses in a tungsten inert gas welded sheet of IN718 superalloy using neutron diffraction

Abstract: The residual stress state in a tungsten inert gas (TIG) welded sheet of IN718, a high-strength nickel-based superalloy, has been characterized using neutron diffraction. The measurements were performed using a time-of-flight diffractometer, which allowed lattice strains from the γ-γ′ {111} and γ-γ′ {311} composite peaks to be compared with the Reitveld-refined spectra. Residual stresses were estimated using plane-specific values of Young's modulus and Poisson's ratio for the {311} and {111} peaks, and the macroscopic material response for the Reitveld-refined data. These values were obtained from a theoretical analysis of existing data after Kroner.The weld considered was an autogenous TIG weld 180mm long placed centrally on to a 2mm × 100mm × 200mm solution heat-treated sheet of IN718. The strain was mapped over the central 140mm of the plate; within this region, the measured strains were almost constant along the length, with the peak bulk longitudinal strain of 1700 × 10-6 detected 4mm from the weld ce...

Comparative measurements on autofrettaged cylinders with large Bauschinger reverse yielding zones

Abstract: A comparative study to map the residual strain/stress states through the walls of autofrettaged thick-walled steel cylinders has been conducted with neutron diffraction, Sachs boring and the compliance methods. Test samples with different wall thickness ratios were prepared to have significant amounts of reverse yielding due to the Bauschinger effect. All three methods indicate that the autofrettage action primarily influenced the hoop stresses, which varied rapidly close to the bores from compressive to tensile within the first half of the wall thickness. Quantitatively, results from the neutron diffraction and Sachs boring techniques compare favourably across large regions of the cylinder walls, while the compliance results showed different features. The existence of reverse yielding close to the cylinder bores has been sensed to different magnitudes and distances from the bores. Plastically yielded material regions identified from the neutron diffraction results correlated well with theoretical modelling.

Development and validation of a technique for strain measurement inside polymethyl methacrylate

Abstract: 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 ...

Modelling of the hardening characteristics for superplastic materials

Abstract: Combined analotical and numerical techniques and procedures have been developed to characterize the hardening due to grain growth for materials under superplastic deformation. The conventional grain growth rate equation is modified to enable accurate modelling of isothermal and plastic-strain-induced grain growths for different microstructures of a titanium alloo. A set of unified viscoplastic constitutive equations for Ti-6Al-4V at 927 °C, which incorporates isotropic hardening and grain growth, has been fullo determined from experimental data for different initial grain sizes and strain rates. Close agreement between the predicted and experimental stress-strain relationships is achieved. In addition, the contributions of hardening constituents, such as strain rate hardening, isotropic hardening and the hardening due to grain growth are modelled.

Investigation of shape optimization for the design of life extension options for an F/A-18 airframe FS 470 bulkhead

Abstract: Shape reworking and bonded reinforcement are two procedures available to extend the fatigue life of cracked metallic aircraft components already in service. Typically for realistic applications, the design of reworks has been undertaken through trial-and-error finite element analyses, guided by simplified analytical formulations, the aim being to achieve reduced stresses while generally restricting the shape boundaries to circular and straight segments. In the present work, an automated sensitivity-based shape optimization procedure has been developed for the optimal design of free-form reworks and bonded reinforcements and demonstrated through application to a realistic practical problem, the F/A-18 FS 470 bulkhead. Here, a least-squares objective function written in terms of selected stress quantities is used, together with multiple basis shape vectors to specify allowable shape changes. For the rework option, a unique optimal solution has been determined, which achieves a region of constant boundary ho...

Measurement of cyclic bending strains in steel wire rope

Abstract: This paper reports strain gauge measurements of cyclic bending strain in the wires of a six-strand right-handed Lang's lay steel wire rope running on and off a pulley. The paper describes the measu...

Beneficial residual stress from the cold expansion of large holes in thick light alloy plate

Abstract: Beneficial residual compressive stress is induced around fastener holes by the process of cold expansion in civil aircraft. Fatigue performance is enhanced by increasing the allowable fatigue stres...

Stress distribution in a rotating elastic functionally graded material hollow sphere with spherical isotropy

Abstract: 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.

Inverse modelling of constitutive parameters for elastoplastic problems

Abstract: To obtain an improved identification of constitutive parameters to be used in finite element method simulations of elastoplastic deep-drawing processes an inverse method was applied using an explicit finite element code to simulate material tests. This problem was addressed by formulating the constitutive parameter identification as an optimization problem. The method was to minimize the objective function defined as the error between the result from the material test and the result from the finite element simulation. The optimization technique is based on the Levenberg-Marquardt method. The objective function was established in a least-squares sense where the design variables were the constitutive parameters of the material. The inverse method was started and, when a global optimum was reached, a set of constitutive parameters were identified. This was performed for both a linear hardening model and a power-law hardening model. It is shown that the inverse method predicts two models which qualitatively s...

Measurement of residual stresses in beams and plates using the crack compliance technique

Abstract: The crack compliance method provides a useful extension to the range of techniques available for the measurement of residual stress fields. The method is most suitable for simple geometries where the stresses vary in one direction only (e.g. usually depth). This paper describes the application of the dislocation density method to the calculation of the compliance functions required for the analysis of experimental data (the surface strain changes as a slot is cut). In particular, the kernel functions appropriate to a specimen of finite thickness (i.e. a beam or a plate) are given. The use of the technique for this geometry, including the use of multiple strain gauges, is discussed. Some sample results are given for the case of a plastically bent beam and these are compared with predictions from beam theory and with neutron diffraction measurements.

Cyclic creep damage in thin-walled structures

Abstract: 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 × 10 4 -10 5 ). 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 iii order to consider the creep- fatigue damage interaction.

Frictional contact analysis of coated axisymmetric bodies using the boundary element method

Abstract: This paper presents a boundary element analysis of the contact mechanics between elastic indenters and other compliant structures with hard coatings of different properties and thicknesses. Two types of indenter are considered: spherical and conical. The first produces a non-linear contact problem while the latter, used in the soft impresser hardness-testing technique, has a flat tip which results in a conformal type of contact. Frictional conditions are introduced and partial slip phenomena observed. The relevance of friction is verified in all cases. An efficient iterative axisymmetric boundary element formulation has been developed for this purpose, which incorporates features such as subregion modelling and a fast solution procedure. Results with the two types of indenter are compared with available analytical expressions and a commercial finite element package.

Neutron diffraction analysis of the residual stress distribution in a bent bar

Abstract: A well-characterized residual stress distribution resulting from four-point bending has been analysed using the neutron diffraction technique. Residual stresses were obtained from the strains measured at discrete positions through the bent bar on the (111) and (311) crystal planes of a nickel-based alloy using the appropriate diffraction elastic constants. In addition a profile refinement method was used to determine the residual stresses from average strains from all the diffraction peaks in the spectrum. The measured residual stress profiles have also been compared with strain gauge data and with analytical and finite element predictions. It has been established that the profile refinement approach gives stresses which most closely match those obtained by the non-diffraction techniques.

Stress analysis of cylindrical shells with nozzles due to external run pipe moments

Abstract: In this paper the analytical results of two normally intersecting cylindrical shells subjected to external moments on the ends of main shells are presented. The thin shell theoretical solutions are obtained on the basis of the modified Morley equation for the main shell with a cut out with large diameter ratio and of the Goldenveizer equation for the branch tube with a nonplaner end. The results are in good agreement with the previous test results and with Moffat's three-dimensional finite element method results. The design curves based on the present solution can be applied to d/D ≤ 0.8 successfully.

Variable material property method in the analysis of cold-worked fastener holes

Abstract: Based on a general axisymmetric method of elastic-plastic analysis presented by Jahed and Dubey, elastic-plastic boundaries and residual stress fields induced by cold expansion of fastener holes is predicted. The method uses a linear elastic solution to construct an elastic-plastic solution. The material parameters are treated as field variables and their spatial distributions are obtained as part of the solution. This method uses the actual loading-unloading behaviour of the material and therefore is capable of predicting an accurate residual stress field. Results obtained here are compared with available experimental and finite element results. The agreement of the results with experimental measurements is very good. It is shown that employment of the actual unloading material curve can make a significant change in residual field prediction.

An inductive procedure for determining the stresses in multi-material components under steady state creep

Abstract: A general formulation obtained based on an inductive procedure is presented for the stress distribution in multi-material power-law creeping structures. The ratios of the nominal creep rates for the various materials are explicitly included in the formulation. It is only necessary to define the effects of the stress exponent n. The results are generalized to the case where n varies between materials. The formulation allows the effects of the material properties to be easily assessed and the results of parametric analyses to be presented in compact and easily manageable forms.

Solution of axisymmetric crack problems using distributed dislocation ring dipoles

Abstract: A solution procedure for the calculation of crack tip stress intensity factors arising at the edges of an arbitrarily shaped crack lying on a surface of revolution is described. The cracks are subject to an arbitrary axisymmetric stress field, devoid of torsion, and may be present in either an infinite space or two elastically dissimilar bonded half-spaces, of which one may, as a special case, have vanishing elastic constants. The technique employed is a one-dimensional integral equation approach, in which the kernel is formed from rings of dislocated pairs, arranged to form ring 'dipoles'. The equation is hypersingular but may readily be inverted using powerful numerical quadratures, providing a computationally efficient solution. Examples of the use of the techniques are then described.

On the prediction of elastic-plastic generalized load-displacement responses for tubular joints:

Abstract: An energy-based method is presented for the prediction of the elastic-plastic force-displacement and/or moment-rotation responses of tubular joints for arbitrary radial loading paths under the action of up to four combined forces and moments. The method is based on the results of a sample of load paths obtained from computational models or measured from experimental tests. The work is important in the context of the elastic-plastic behaviour of structures in general and in particular as a basis for the development of single elastic-plastic tubular joint elements. The method employs normality of the generalized displacement vector to level hypersurfaces of total (elastic-plastic) complementary work.

Life assessment of weld repairs in 1/2Cr1/2Mo1/4V main steam pipes using the finite element method

Abstract: Weld repair at heavy section weldments is often a natural consequence following inspection of plant under high-temperature conditions. Four typical weld geometries and conditions have been studied: an ‘as new’ weld, a weld taken from plant after long-term service, a ‘full weld repair’ and partial repairs of two forms where repair was associated with either one or both weld interfaces. The parent material was 1/2CrMoV welded with 2CrMo weld metal and was removed from plant after 174 800 h operation. Material properties were obtained at 640 ° C and covered service-aged and new parent materials and weld metals. The heat-affected zone (HAZ) properties, as relevant to the weld models, were measured using indentation creep procedures. Realistic weld models were analysed using the finite element method and Norton's creep law. The expected lifetimes were found using peak representative rupture stresses in each zone, thereby taking account of the multi-axiality effects.For the particular material data used in this...

Predicting rupture and low strain times for a 225Cr-1Mo steel using a six-ϑ projection technique

Abstract: The ϑ projection method of creep analysis is known to produce the poorest predictions of creep properties at low strains. This paper applies a recently suggested modification of the ϑ concept to 2.25Cr-1Mo steel where long term data exist to enable an assessment of this modification to be made. The modification takes the form of two additional ϑ terms that allow the initial stages of any creep curve to be modelled more accurately. The paper shows that the resulting six-ϑ approach produces predictions of long-term failure times that are marginally better than those obtained using the traditional four-ϑ approach. However, the six-ϑ approach is shown to be much more capable of accurately predicting times to low strains (1 per cent strain) at stress levels as low as 40 MPa at 838 K and 80 MPa at 813 K (well below the lowest stresses used in the ϑ analysis). Finally, weighting each ϑij in the six-ϑ approach is not recommended as it is shown to have a detrimental impact on the longer-term predictions obtained. ...