Experimental investigations into the influence of cyclic phenomena of metals on structural ratchetting behaviour

The results of experiments on 2-bar structures of 99.9% copper are compared with the prediction of classical plasticity models for loading histories which simulate the effects of thermal cycling in the presence of constant primary loading. Two material phenomena, cyclic hardening and material ratchetting, are shown to have important effects upon cyclic strain growth. Neither of these effects are contained in classical plasticity models. The steady state growth of strain due to material ratchetting is modelled in a simple way. An approximate solution method, based on the “rapid cycle” method for creep analysis, is shown to give a good prediction of the experimental data.     

An experimental study of the ratchetting and creep of thick flanged tubes subjected to steady axial mechanical loading and transient thermal loading

The aims of the investigation were to obtain experimental data against which finite element predictions can be assessed and to see whether the lead alloy used was suitable as a “ratchetting” model material. Thermal ratchetting tests were performed on lead alloy flanged tube components. In some of the tests, dwell periods were allowed between successive thermal shocks. Electrical resistance strain gauges were used to measure the ratchet and creep strains in plain tube and stress concentration regions.It was found that both the plain tube and peak fillet ratchet strains increased with increasing mechanical and thermal load for short dwell periods. However, the ratio of the peak fillet to plain tube ratchet strains reduced with increasing mechanical and thermal load. Also, the ratio of the peak fillet to plain tube ratchet strains increased with increasing dwell period.The data obtained from the lead alloy model component tests were found to correlate with data from a number of different components made from various materials, indicating that the material may be useful as a “ratchetting” model material.     

Damage evolution in creep bulging of thin sheet metal

The creeping motion of thin sheet metal, damaged by artificial cavities is observed in bulging tests and simulated ‘semi’-analytically. The sheet metal satisfies Norton’s Law for secondary creep and is subjected to a bi-directional stretch. The stretch is produced by creep bulging through elliptical dies with the virtue of sustaining nearly uniform background stress ratio for each aspect ratio of the die axes. In order to reach large deformations with significant shape evolution of the cavities, the tests were conducted at superplastic conditions. The sheet is double layered (only one layer is cavitated) made of Tin–Lead (50–50 Pb–Sn). The measured damage growth is compared to an approximate simulation. The simulation of the damage evolution, throughout its time history, makes repeated use of a so-called “Green-function solution” for the motion of a single isolated cavity in an infinite viscoplastic continuum. The solution is modified from Muskhelishvili’s elastic solution by replacing the elastic shear modulus by a “viscous-like” variable (“plastic shear modulus”) which depends (non-linearly) on the evolved average strain-rate. Similarly, the stresses in the ligaments between cavities were averaged to approximate the local stress concentrations. Due emphasis is given to the rotation of each elliptical cavity, beside its expansion (contraction) and elongation.     

Reference stresses and temperatures for cylinders and spheres under internal pressure with a steady heat flow in the radial direction

The paper examines the creep behavior of thick cylinders and spheres subjected to internal pressure and a negative temperature gradient in the radial direction. It is found that at stationary state the rate of radial displacement of the vessel wall is simply proportional to the material creep behavior associated with a single stress and temperature. Such “reference stresses” and “reference temperatures” are defined for spheres and cylinders of varying wall thicknesses. These reference stresses and reference temperatures are valid for any creep problem where the material behavior may be characterized by a function of the form exp (γT)σ^m. The extension of these results to variable pressure and temperature loading cases is discussed.     

Representation of uniaxial creep curves using continuum damage mechanics

A methodology has been developed for the numerical determination of the material constants in the uniaxial creep constitutive equations based on continuum damage mechanics. The method developed overcomes former problems with convergence, and is based on a normalization technique. Temperature variation is included in the model.An algorithm for the digitization of continuous creep curves has been developed that enables a true representation of uniaxial creep behaviour using only 20 data points. Consequently large amounts of data covering many tests may therefore be stored in data bases, and, the method leads to short CPU times for fitting the material model.The algorithm for digitization and the constant determination methods have been applied to data for alloy 800H at 850°C; and, to at 550°C. For both materials good comparisons have been obtained between experimental and predicted uniaxial creep behaviour. The material model has been shown to be suitable for large strain behaviour.Uniaxial creep tests have been carried out on grade 1 cast copper nominal composition 99.99% Cu, 0.005% O₂, B.S. 1035–1037 at 150, 250 and 500°C, and an anisothermal continuum damage mechanics creep model developed for the temperature range 150–500°C. Model predictions are in good agreement with test results.     

Hydro-rim deep-drawing processes of hardening and rate-sensitive materials

The conventional deep drawing process is limited to a certain limit drawing ratio (LDR) beyond which rupture will ensue. An asymptotic solution of the complete governing equations of this process indicates that this relatively low LDR results from the steep build-up of radial tensile stress with maximum value at the die lip. This tensile stress is significantly enhanced by interfacial friction along the die/flange and by high speed of the operating load and thus holds responsible for premature ruptures. The intention of this work is to examine the possibilities of relaxing the above limitation, aiming towards a process with an ‘unlimited drawing ratio’. The ideas which may lead to this goal are:(a) exerting an external fluid pressure on the outside rim of the blank (“Hydro-rim process”) to reduce radial stress and to decrease, in parallel, the interfacial friction,(b) increasing the blank temperature to a level at which the material is more rate sensitive, and thus less prone to early failure. The benefits of these ideas are examined via parametric analysis of the solution and with experiments in deep drawing processes.A clear outcome from the solution is that if changes in the material properties (strain hardening, strain-rate sensitivity, yield stress, etc.) can be controlled, say, by controlling the temperature and/or the operating speed, the process can reach higher drawing ratios with substantially less assisted fluid pressure.     

Prediction of creep failure in aeroengine materials under multi-axial stress states

The creep and creep rupture behaviour of two, significantly different, aeroengine materials, namely a nickel-base superalloy at 700°C and a high temperature titanium alloy at 650°C, were studied. Experimental creep tests were conducted on uniaxial specimens and axisymmetric notched bars under constant tensile loads conditions. From the uniaxial creep test results, a creep continuum damage model was established for each of the materials. The skeletal point stress approach was used to obtain the approximate creep rupture stress criterion in the multi-axial generalization of the creep continuum damage models. This approximation was cross-checked using axisymmetric Finite Element (FE) analyses in a trial and error procedure. Multi-axial creep continuum damage models were then used in further FE creep analyses to predict the creep rupture times in specimens subjected to different tensile loads. The FE predictions of the rupture times in these notched specimens were found to be in good agreement with the experimental results for the nickel-base superalloy (Waspaloy) at 700°C and the titanium alloy (IMI834) at 650°C.     

Bending of nonhomogeneous bars

The bending of a nonhomogeneous prismatical bar loaded by a terminal force and a moment is considered in which the elastic “constants” E and G may vary in an arbitrary manner over the cross-section, subject to the restriction that Poisson's ratio is constant. Using an extension of a previous plane-stress solution,¹ a partial differential equation for the stress function is derived. It is then proved that bending and stretching of a nonhomogeneous bar are, in general, coupled.

When the deviation from homogeneity is uniformly small, the solution may be obtained as a perturbation expansion near the homogeneous solution. Using this technique, an analytic solution is worked out in detail for an elliptical bar with a particular type of inhomogeneity, the contour lines of which are ellipses.     

Multi-axial creep rupture of a model structure using a two parameter material model

A simplified, two parameter creep curve model is developed, which represents primary-secondary-tertiary creep behaviour. The two parameters are related via the secondary strain respectively to: the sum of secondary and primary strains; and, the sum of secondary and tertiary strains. Techniques are described for fitting the model to laboratory data; and, for the determination of the parameters which characterize primary-secondary and secondary-tertiary creep. The single state variable theory used to describe tertiary creep is compared with mechanisms based models and shown to closely predict the effect of stress-state on rupture strain. A two bar plane strain model component subjected to steady load is studied and used to determine the effect on the component lifetime of primary creep; and, of the multi-axial creep rupture criterion. The representative rupture stress is found to be weakly dependent on primary creep and strongly dependent on the multi-axial rupture criterion of the material.     

Analytical solution for interface stresses due to concentrated surface force

The two-dimensional analytical solution for interface stresses due to concentrated surface force has been deduced, by introducing infinite mirror points which are the images of the load point reflected by the interface and the free surface, and adopting the interchange law of differentiation. The analytical solution can be represented in terms of the summation of the “partial” Goursat's complex stress functions defined in the local coordinate systems with their origins placed at each of the mirror points. It is found that the “partial” stress functions corresponding to a higher order mirror point can be determined from those to the lower one. It is also found that the contribution of the “partial” stress functions to the stress field decreases with the increase of the corresponding mirror point order, therefore, only considering the stress functions corresponding to the first several order mirror points can give the accurate enough solution. Numerical examination by the use of boundary element method has also been carried out to verify the theoretical development.     

Strain-rate and inertia effects in the collapse of two types of energy-absorbing structure

The dynamic plastic collapse of energy-absorbing structures is more difficult to understand than the corresponding quasi-static collapse, on account of two effects which may be described as the “strain-rate factor” and the “inertia factor” respectively. The first of these is a material property whereby the yield stress is raised, while the second can affect the collapse mode, etc. It has recently been discovered [6,7]that structures whose load-deflection curve falls sharply after an initial “peak” are much more “velocity sensitive” than structures whose load-deflection curve is “flat-topped” (Fig. 1a); that is, when a given amount of energy is delivered by a moving mass, the final deflection depends more strongly on the impact velocity. In this paper we investigate strain-rate and inertia effects in these two types of structure by means of some simple experiments performed in a “drop hammer” testing machine, together with some simple analysis which enables us to give a satisfactory account of the experimental observations. The work is motivated partly by difficulties which occur in small-scale model testing of energy-absorbing structures, on account of the fact that the “strain-rate” and “inertia” factors not only scale differently in general, but also affect the two distinct types of structure differently.     

Determination of creep constitutive model for 28-48WCo alloy based on experimental creep tests at 817–982 °C

The high-chromium high-nickel alloy is widely used as a heat-resistant material for components in plants under elevated temperatures, and thus, prediction of its creep deformation and rupture life is required for safe design. In this study, a creep constitutive model for the 28-48WCo alloy was determined by employing the Sherby-Dorn equation. Creep deformation tests were conducted at temperatures of 817, 871, 927 and 982 °C, under an applied stress ranging from 27.58 to 82.74 MPa. High temperature tension tests were also conducted to measure the change in elastic modulus with temperature variation. The model provided good predictability of the minimum creep strain rate in the range of experimental test conditions, with a coefficient of determination of 0.92. The creep rupture life was characterized using the Larson-Miller parameter. Creep design curves were proposed to estimate the creep rupture life of the 28-48WCo alloy at a temperature range of 817–982 °C.     

Some observations on the CLNA model in fretting fatigue

Using the Atzori–Lazzarin criterion, the author has recently proposed a unified model for Fretting Fatigue denominated Crack-Like Notch Analogue—CLNA model, considering only two possible behaviours: either “crack-like” or “large blunt notch”. In a general FF condition, the former condition is treated with a single contact problem corresponding to the MIT Crack Analogue (CA) improved in some details also by the author. The latter, with a simple peak stress condition, i.e. a simple Notch Analogue model, simply stating that below the fatigue limit, infinite life is predicted for any size of contact. In the typical condition of constant normal load and in phase oscillating tangential and bulk loads, both limiting conditions are immediately written, and the CLNA model permits to collapse the effect of the contact loads on a single closed form equation (differently from many other models which do not permit this flexibility). For not too large contact areas (“crack-like” contact) no dependence at all on geometry is predicted, but only on 3 load factors (bulk stress, tangential load and average pressure) and size of the contact. Only in the “large blunt notch” region occurring typically only at very large sizes of contact does size-effect disappear, but the dependence on all other factors including geometry remains. The model compares favourably with some experimental results in the literature. In this paper, some aspects of the CLNA model are further elucidated.     

Yield loci of anisotropic aluminium sheets

AA8014 aluminium sheets were tested in uniaxial, equibiaxial (bulge test) and plane-strain tension at an almost constant strain rate of 2 × 10⁻³s⁻¹. The results were compared with predictions at different levels of strain, based on macroscopic and crystallographic theories of yielding. While most of the previous investigations compare the results at a strain level of 0.10, the present comparison was made in early stages of the deformation, which might be considered as the real yielding strain of the material. It was concluded that, at the high strain levels Hosford's method, which is a modification of Hill's “old” criterion, gives a proper fit to the experimental data. However, at the lower strain levels the experimental results were very close to the crystallographic loci.     

An internal state variable plasticity-based approach to determine dynamic loading history effects on material property in manufacturing processes

Worked materials in large deformation processes such as forming and machining experience a broad range of strain, strain rate, and temperatures, which in turn affect the flow stress. However, the flow stress also highly depends on many other factors such as strain path, strain rate and temperature history. Only a model that includes all of these pertinent factors is capable of predicting complex stress state in material deformation. In this paper, the commonly used phenomenological plasticity models (Johnson–Cook, Usui, etc.) to characterize material behavior in forming and machining were critically reviewed. Although these models are easy to apply and can describe the general response of material deformation, these models lack the mechanisms to reflect static and dynamic recovery and the effects of load path and strain rate history in large deformation processes. These effects are essential to understand process mechanisms, especially surface integrity (residual stress, microhardness, and microstructure) of the manufactured products.As such a dislocation-based internal state variable (ISV) plasticity model was used, in which the evolution equations enable the prediction of strain rate history and temperature history effects. These effects can be quite large and cannot be modeled by the equation-of-state models that assume that stress is a unique function of the total strain, strain rate, and temperature, independent of the loading path. The temperature dependence of the hardening and recovery functions results in the prediction of thermal softening during adiabatic temperatures rises, which are common in metal forming and machining.The dynamic mechanical behaviors of three different benchmark work materials, titanium Ti-6Al-4V, AISI 52100 steel (62 HRc), and aluminum 6061-T6, were modeled using the ISV approach. The material constants were obtained by using a nonlinear regression-fitting algorithm in which the stress–strain curves from the model were correlated to the experiments at different (extreme) temperatures. Then the capabilities of the determined material constants were examined by comparing the predicted material flow stress with the test data at different temperatures, strains, and strain rate history. The comparison demonstrates that the internal state variable plasticity model can successfully recover dynamic material behavior at various deformation states including the loading path effect. In addition, thermal softening due to adiabatic deformation was also captured by this approach.     

考虑高温蠕变损伤的2．25CrlMo钢的弹塑性本构模型

考虑造成蠕变损伤的物理机制,结合损伤力学理论,利用Ramberg—Osgood弹塑性本构方程,推导了含有蠕变损伤的材料弹塑性本构模型。对225CrlMo钢进行了相同条件不同时长的蠕变试验以得到不同蠕变损伤的材料,并对这些材料进行高温短时拉伸,得到不同损伤对应的应力应变曲线。并用试验数据及文献数据对模型进行了验证。     

Ductile fracture and lifetime prediction of structural materials and components under high-temperature creep conditions

The problem of long-term strength prediction of structural materials under uniaxial and biaxial creep conditions, which give rise to ductile fracture, is considered. A new approach to long-term fracture modelling based on constitutive equations of the “isochronous creep theory” and criteria of ductile fracture is suggested. The change in the momentary tangential modulus specifies the materials rheological behaviour and a value tending to zero is assumed as the ductile fracture criterion. Using the model the times to fracture of rods, beams and thin-walled tubes made of high-temperature and heat-resistant materials are estimated and they show good agreement with experimental data.     

Creep and recovery behaviors of magnetorheological elastomers

This paper presents experimental and modeling study of creep and recovery behaviors of magnetorheological elastomers (MREs) under constant stresses. Experimental study was accomplished using a rheometer with parallel-plate geometry. Under constant stresses ranging from a small value to a large one, the resultant strains were recorded. The experimental results demonstrated that MREs behave as linear visocleastic properties. The effects of the magnetic field and stress on MRE creep behaviors were discussed. Moreover, a four-parameter viscoelastic model was developed to describe MRE creep behaviors. The comparison between the experimental results and the modeling predictions indicates that the model can predict MRE creep behaviors very well.