Specific Features of the Behavior of the Coercive Force in Low-Carbon Plastically Deformed Steels

The relationship between the coercive force in low-carbon steels under plastic extension and compression and the values of deformation and actual and residual stresses are studied. This relationship is investigated for both “ slow” loading (when an equilibrium deformation is attained for each load value) and “fast” loading (when such equilibrium is not attained). It is shown that (i) a comparatively small increase in the coercive force in a loaded condition is due only to an increase in the density of dislocations in the process of plastic extension; (ii) a significant steep increase in the coercive force accompanying removal of the load from a plastically stretched specimen is fully due to residual compression stresses; (iii) the values of the coercive force under “slow” and “fast” loading are significantly different in the region of small deformations less than 2.5%; (iv) these values are close to each other in the loaded state for all deformations up to 10%; (v) a relief of the compression stress that creates plastic deformations causes a steep decrease in the coercive force that is as large as its increase following relief of plastic extension; this is explained by the emergence of a significant residual tension stress. The obtained results are of importance for the use of the method based on measuring the coercive force to test steel structures under the conditions when plastic deformations develop.__________Translated from Defektoskopiya, Vol. 41, No. 5, 2005, pp. 24–38.Original Russian Text Copyright © 2005 by Kuleev, Tsar’kova, Nichipuruk.     

Modelling the evolution of residual stresses during tensile testing of elastoplastic wires subjected to a previous bending operation

During coiling operations high residual stresses are frequently developed in steel wire. In this paper the stress distribution in wires during coiling, unwinding and subsequent tensile testing is modelled for numerous bending degrees, assuming perfect Voce plastic deformation and linear elastic behaviour. The influence of such residual stresses on the observed tensile test data can be deduced. It is shown that coiling with spool radii as used today industrially can lead to measurement of wire properties deviating significantly from the “true” properties of a properly coiled wire. Also, a method is proposed to deduce the original flow behaviour of coiled samples from tensile test curves, hence filtering the effect of the residual stresses.     

Buckling phenomena related to rolling and levelling of sheet metal

The paper deals with analytical and numerical considerations of buckling phenomena in thin plates or strips under in-plane loads which typically appear during rolling and levelling, i.e. straightening by stretching, of sheet metal. Buckling due to self-equilibrating residual stresses, caused by the rolling process, in eventual conjunction with global tensile stresses (denoted as “rolling buckling”) as well as buckling during the levelling process (denoted as “stretching buckling” or “towel buckling”) are considered. Analytical estimates are derived and compared against results of numerical simulations and field observations. Mode jumping by varying the global strip tension is explained on the basis of the derived analytical solutions. It is shown how from the waves, i.e. height and length, observed on the strip sliding over or lying on a rigid plane one can provide information about the distribution of the differences in the plastic strains over the width of the strip which lead to the buckled configuration. And, vice versa, knowledge of the plastic strain distribution can be used for estimating the expected wave heights representing a measure for the geometrical quality of the rolled product. The influence of the dead weight of the strip on the post-buckling pattern is also discussed on the basis of non-linear analyses.     

Stress and failure probability analysis for a transversely isotropic, brittle, elastic cylinder subjected to internal pressure and axisymmetric thermal loading

Procedures are developed for the determination of the stresses in and thence the probability of failure of a transversely isotropic cylinder made of a brittle material and loaded by an internal pressure and an axisymmetric radial temperature gradient. As examples of the application of the procedures a cylinder is analysed first with isotropic material properties, then with various degrees of anisotropy including both the “fibrous” and “laminar” types. The treatment is non-dimensional; results are presented graphically in the form of failure probability “contours”. For the dimensions and materials considered it is shown that the probability of failure is affected only slightly by the fibrous form of anisotropy but markedly by the laminar form when the thermal loading predominates.     

Modelling of fretting fatigue in a fracture-mechanics framework

The use of fracture mechanics as an alternative to (Cauchy) stress-based fatigue criteria is illustrated in this paper, using the “crack analogue” concept to deal with crack initiation in a fracture mechanics framework. A very simple model, based entirely on independently derived parameters, is shown to be able to capture the qualitative effects of the normal and tangential loads of fretting-fatigue performance. The accuracy of the total life predictions is also satisfactory. Examples of how to account for residual stresses and size effect with such a model are discussed.     

Palliatives in fretting: A dynamical approach

Fretting damages are connected to numerous aspects like friction, wear, contact mechanics, fatigue and material sciences. Its quantification also requests to consider the loading history as well as the sliding condition. Based on a “fretting sliding” approach, and considering fretting wear test conditions, various palliative solutions have been investigated. Shot peening treatment, introducing compressive residual stresses, appears pertinent against crack propagation but ineffective against crack nucleation due to the activation of surface relaxation phenomena. Hard thin coatings present stable residual stresses independently of the sliding conditions. However, they only delay the crack nucleation process, when the coating is worn through, cracking phenomena are activated. To quantify the coating endurance against wear, an energy density approach has been developed. The stability of this approach has been confirmed regarding the contact size effect and illustrated through the analysis of synergic interaction between soft thick coating and solid lubricant.     

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.     

Non-linear one-dimensional continuum damage theory

The background of Non-Linear Continuum Damage Mechanics is presented for the case of one-dimensional tensile stresses. A brief critical analysis of the existing methods of non-linear damage models construction is given. A new approach to the damage theory development based on the “separability” principle is suggested. The condition of non-linearity and the criterion of long-term failure are formulated. The non-linear damage constitutive equations for static and cyclic loading, allowing one to take into account the loading history, are proposed on this basis. Within the framework of the approach suggested the problems of total and residual lifetime calculation under additional loads and partial unloads are solved. The predictions are compared with experimental data obtained using some particular heat-resistant materials.     

Effect of temperature on stresses and delamination failure of z-pinned joints

Although z-pins have been shown effective in preventing delaminations in adhesively bonded and co-cured joints, their applicability depends on a reliable assessment of the strength of a z-pin-composite assembly. In particular, high residual thermal stresses that have been found in experiments dictate the necessity in a local stress analysis. Elevated temperature applied to the joint during its lifetime may also affect its effectiveness in preventing delaminations. The present paper illustrates an approach to determining local residual stresses confirming the observations regarding a possible delamination and cracking in the composite structure due to high post-processing transverse stresses. The analysis of the effect of elevated temperature applied at one of the surfaces on the response of a z-pinned joint is conducted using the concept of a double cantilever beam with an “insulated” crack. In addition, it is illustrated that an elevated temperature may actually benefit the integrity of the joint if it causes an increase in the z-pin-composite interfacial strength.     

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.     

Prediction of cutting forces and machining error in ball end milling of curved surfaces -II experimental verification

This paper presents the results of a series of experiments performed to examine the validity of a theoretical model for evaluation of cutting forces and machining error in ball end milling of curved surfaces. The experiments are carried out at various cutting conditions, for both contouring and ramping of convex and concave surfaces. A high precision machining center is used in the cutting tests. In contouring, the machining error is measured with an electric micrometer, while in ramping it is measured on a 3-coordinate measuring machine. The results show that in contouring, the cutting force component that influences the machining error decreases with an increase in milling position angle, while in ramping, the two force components that influence the machining error are hardly affected by the milling position angle. Moreover, in contouring, high machining accuracy is achieved in “Up cross-feed, Up cut” and “Down cross-feed, Down cut” modes, while in ramping, high machining accuracy is achieved in “Left cross-feed, Downward cut” and “Right cross-feed, Upward cut” modes. The theoretical and experimental results show reasonably good agreement.     

High precision lapping for polygonal holes

Lapping has been used as a finishing method to improve the roundness of shafts and holes. This paper introduces two methods for the finishing of polygonal holes whose shapes are ellipsoidal, three-lobed, four-lobed, and so on. One method is the “regular polygonal lap” in which the amplitude of the desired Fourier component of the out-of-roundness is kept constant and the other components are decreased. The other is the “tripod lap,” which can increase the amplitude of any Fourier component using special types of lapping tools produced by applying the “tripod roundness measuring method.” Based on a theoretical analysis, this study shows that any component of the out-of-roundness can be increased by using the new tripod lap method.     

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.     

Geometry of “developable cones”

When a thin disc is supported on the rim of a bowl, and its centre is pushed down by a finger, it adopts a characteristic conformation, known as a “developable cone”, and sketched in Fig. 1(a): the main, broadly conical, shape can only form if about one-quarter of the disc buckles upwards. There is a curved intersection between the two parts, which takes the form of a crescent-shaped “crease” near its apex, but with the flanking regions less tightly deformed. The “developable cone” is a recurring motif in a wide range of physical situations—crumpling, buckling, draping—and its mechanics provides a key to understand the phenomena, whether the disc deforms in the elastic or the plastic range. The task of this paper is to study only geometrical features of the “developable cone”. The first step is to replace the actual crease (Fig. 1(a)) by an idealised “sharp” crease (Fig. 1(b)). The second step is to study the apparently “large-rotation” problem of kinematics by means of an adaptation of the classical “yield-line” pattern of folding, but with a crucial added constraint that springs from Gauss's analysis of inextensional deformation. We illustrate the method via a graded sequence of examples, and we close with a discussion.     

Strength and residual stress of Mg-PSZ after grinding

The influence of grinding with two grinding wheels, differing mainly in diamond-grain size, on the properties of Mg-PSZ was examined. The residual stress, the amount of monoclinic zirconia and the strength of the material were determined. From these measurements depth profiles were obtained for the phase content and the residual stress. The fracture surfaces were examined optically to estimate the critical flaw size. Material ground with “coarse” diamond grains was significantly weaker than that ground with “fine” diamond grains. “Coarse” diamond grains in the grinding wheel resulted in more residual stress and a thicker layer of transformed zirconia than when “fine” grains were in the wheel. This apparent discrepancy is explained with a model based on the occurrence of localized spots of tensile stress beneath the residual stress layer near grain boundaries. These spots are assumed to be larger in number and to contain higher tensile stresses after grinding with “coarse” grains.     

An international length comparison at an industrial level using a photoelectric incremental encoder as transfer standard

A Japanese–German interlaboratory comparison of length measurements was conducted. A photoelectric incremental encoder with a measurement length of 270 mm was used as transfer standard. An agreement of better than 27 nm over the entire length was ascertained, and the “short-range” deviations within a length interval of approximately 10 mm could be characterized with a standard deviation of σ=0.8 nm. The results attained are considered as consistent with the estimated uncertainties of measurement. Since the measurements performed are directly traceable to the SI unit of the “metre”, the comparison supports ideas currently being discussed by some National Metrology Institutes and dealing with the question of how foundations can be laid for a generally accepted application of this method of traceability.     

Analysis of asymmetrical sheet rolling by a genetic algorithm

Slab analysis of asymmetrical sheet rolling is presented by considering non-uniform normal and shear stress profiles across the section of product. An important phenomenon considered in this paper is the deflection of plate at entry to the deformation zone and the amount of which is predicted by using a genetic algorithm (GA). In the utilized GA, the elimination/replacement operator and a new operator called “the adaptive mutation” are developed in order to increase the efficiency of the search. Shear stresses are taken into account in applying the Von-Mises yield criterion, and it is shown that this improves the accuracy of the model. Rolling force and pressure distribution predicted by the present model are shown to be in good agreements with the experimental and theoretical results of other investigators.     

New results for the fretting-induced stress concentration on Hertzian and flat rounded contacts

Recent work on fretting fatigue has emphasized the role of stress concentration on fretting damage, while previous work had concentrated on empirical parameters to assess influence of fretting on fatigue life. In particular, analogies with fatigue in the presence of a crack or a notch have been noticed, suggesting that the stress field induced by frictional contact per se may explain the reduction of fatigue life due to fretting.In the paper, new analytical and numerical solutions are produced for the stress concentration induced in typical fretting contacts involving the Hertzian geometry or the flat punch with rounded corners in view of application to the dovetail joints. Normal and tangential load (in the Cattaneo–Mindlin sense) is considered with “moderate” or “large” bulk stresses.     

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.