The influence of composition, temperature and strain rate on the deformation of F.C.C. metals and alloys

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Mechanical properties of sheet metal under forming conditions

In the bulge test, a sheet metal specimen is clamped over a circular hole in a die and formed into a bulge by the hydraulic pressure on one side of the specirnen. As the unsupported part of the specimen is deformed in this way, its area is increased, in other words, the material is generally stretched and its thickness generally decreased. The stresses causing this stretching action are the membrane stresses in the shell generated by the hydraulic pressure, in the same way as the rubber in a toy balloon is stretched by the membrane stresses caused by the air inside it. The bulge test is a widely used sheet metal test, to determine the "formability" of sheet materials. Research on this forming process (2)-(15)* has hitherto been almost exclusively confined to predicting the behaviour of the bulged specimen through the constitutive equations (stresses and strains in relation to displacements and shapes) and empirical work hardening characteristics of the material as determined in the tension test. In the present study the approach is reversed; the stresses and strains in the specimen are measured and determined from the geometry of the deformed shell. Thus, the bulge test can be used for determining the stress-strain relationship in the material under actual conditions in sheet metal forming processes. When sheet materials are formed by fluid pressure, the work-piece assumes an approximately spherical shape, The exact nature and magnitude of the deviation from the perfect sphere can be defined and measured by an index called prolateness. The distribution of prolateness throughout the workpiece at any particular stage of the forming process is of fundamental significance, because it determines the variation of the stress ratio on which the mode of deformation depends. It is found. that, before the process becomes unstable in sheet metal, the workpiece is exactly spherical only at the pole and at an annular ring. Between the pole and this annular ring the workpiece is more pointed than a sphere, and outside this ring, it is flatter than a sphere. In the forming of sheet materials, the stresses and hence the incremental strains, are closely related to the curvatures of the workpiece. This relationship between geometry and state of stress can be formulated quantitatively through prolateness. The determination of the magnitudes of prolateness, however, requires special techniques. The success of the experimental work is due to the technique of measuring the profile inclination of the meridional section very accurately. A travelling microscope, workshop protractor and surface plate are used for measurements of circumferential and meridional tangential strains. The curvatures can be calculated from geometry. If, however, the shape of the workpiece is expressed in terms of the current radial (r) and axial ( L) coordinates, it is very difficult to calculate the curvatures within an adequate degree of accuracy, owing to the double differentiation involved. In this project, a first differentiation is, in effect, by-passed by measuring the profile inclination directly and the second differentiation is performed in a round-about way, as explained in later chapters. The variations of the stresses in the workpiece thus observed have not, to the knowledge of the author, been reported experimentally. The static strength of shells to withstand fluid pressure and their buckling strength under concentrated loads, both depend on the distribution of the thickness. Thickness distribution can be controlled to a limited extent by changing the work hardening characteristics of the work material and by imposing constraints. A technique is provided in this thesis for determining accurately the stress distribution, on which the strains associated with thinning depend. Whether a problem of controlled thickness distribution is tackled by theory, or by experiments, or by both combined, the analysis in this thesis supplies the theoretical framework and some useful experimental techniques for the research applied to particular problems. The improvement of formability by allowing draw-in can also be analysed with the same theoretical and experimental techniques. Results on stress-strain relationships are usually represented by single stress-strain curves plotted either between one stress and one strain (as in the tension or compression tests) or between the effective stress and effective strain, as in tests on tubular specimens under combined tension, torsion and internal pressure. In this study, the triaxial stresses and strains are plotted simultaneously in triangular coordinates. Thus, both stress and strain are represented by vectors and the relationship between them by the relationship between two vector functions. From the results so obtained, conclusions are drawn on both the behaviour and the properties of the material in the bulge test. The stress ratios are generally equal to the strain-rate ratios (stress vectors collinear with incremental strain vectors) and the work-hardening characteristics, which apply only to the particular strain paths are deduced. Plastic instability of the material is generally considered to have been reached when the oil pressure has attained its maximum value so that further deformation occurs under a constant or lower pressure. It is found that the instability regime of deformation has already occurred long before the maximum pressure is attained. Thus, a new concept of instability is proposed, and for this criterion, instability can occur for any type of pressure growth curves.

The mechanical properties and formability of dual-phase steel

In recent years dual phase steels comprising of 5-20% martensite in a ferrite matrix have come into the limelight of high strength cold formable steels because of their potential for vehicle weight saving. They show the following features: no yield point; relatively low initial flow stress; high initial workhardening rate; well sustained work hardening. As a consequence of these characteristics, dual phase steels exhibit a better combination of strength and elongation than other HSLA steels. In this thesis, a broad view of the factors which influence their properties is presented. Mechanical properties and forming ability of a commercially available dual phase steel and an AL-Si killed steel processed to dual phase form are investigated to ascertain the effect of their microstructure on their properties. It is found that the yield phenomena are masked by the transformation induced stresses present during processing and so yield point could be recovered under suitable ageing treatment; that apart from giving the above properties dual phasing gives rise to very low strain-rate sensitivity and a low R value ~ 1; that the mechanical response under rolling conditions is not different from those under tension; that there is a danger of damage to tooling during forming operations of these steels if fracture should precede instability as a result of grain size dependent strength found for these steels. It is also found that very little deformation of the martensite islands took place during deformation except at high strains. The work-hardening and the strength levels can be controlled by either decreasing the grain size or increasing the martensite volume fraction, but it is found that increasing martensite has a detrimental effect on ductility and the ductility and fracture strength can be controlled better by refining the grain size. A remarkable effect found in the dual phase steel tested is that the compressive strength is higher than the tensile strength. The reason for this observation is not yet clear but it is suggested that it might be due to the introduction of emissary type dislocations into the ferrite lattice as a result of twins formed in the martensite during transformation from austenite. The twins are envisaged to be {111} <112> in character.

Effects of dynamic strain ageing on fatigue crack propagation and threshold behaviour in a Ni-base superalloy

In the temperature range 200-400 degree C the Ni-base superalloy, N901, develops marked dynamic strain ageing effects in its tensile behavior. These include inverse strain rate sensitivity, especially in UTS values, strongly serrated stress-strain curves and a heavily sheared failure mode at the higher test-temperatures. As for steels these effects seem to be due to interactions between the dislocations and the interstitial carbon atoms present. The results of tensile and fatigue threshold tests carried out between 20 degree C and 420 degree C are reported and the fatigue behavior is discussed in terms of the effects of surface roughness induced closure, temperature and strain aging interactions.

Pricing-to-market for UK export sector

This thesis investigates the pricing-to-market (PTM) behaviour of the UK export sector. Unlike previous studies, this study econometrically tests for seasonal unit roots in the export prices prior to estimating PTM behaviour. Prior studies have seasonally adjusted the data automatically. This study’s results show that monthly export prices contain very little seasonal unit roots implying that there is a loss of information in the data generating process of the series when estimating PTM using seasonally-adjusted data. Prior studies have also ignored the econometric properties of the data despite the existence of ARCH effects in such data. The standard approach has been to estimate PTM models using Ordinary Least Square (OLS). For this reason, both EGARCH and GJR-EGARCH (hereafter GJR) estimation methods are used to estimate both a standard and an Error Correction model (ECM) of PTM. The results indicate that PTM behaviour varies across UK sectors. The variables used in the PTM models are co-integrated and an ECM is a valid representation of pricing behaviour. The study also finds that the price adjustment is slower when the analysis is performed on real prices, i.e., data that are adjusted for inflation. There is strong evidence of auto-regressive condition heteroscedasticity (ARCH) effects – meaning that the PTM parameter estimates of prior studies have been ineffectively estimated. Surprisingly, there is very little evidence of asymmetry. This suggests that exporters appear to PTM at a relatively constant rate. This finding might also explain the failure of prior studies to find evidence of asymmetric exposure in foreign exchange (FX) rates. This study also provides a cross sectional analysis to explain the implications of the observed PTM of producers’ marginal cost, market share and product differentiation. The cross-sectional regressions are estimated using OLS, Generalised Method of Moment (GMM) and Logit estimations. Overall, the results suggest that market share affects PTM positively.Exporters with smaller market share are more likely to operate PTM. Alternatively, product differentiation is negatively associated with PTM. So industries with highly differentiated products are less likely to adjust their prices. However, marginal costs seem not to be significantly associated with PTM. Exporters perform PTM to limit the FX rate effect pass-through to their foreign customers, but they also avoided exploiting PTM to the full, since to do so can substantially reduce their profits.

The Mechanics of the drawing of polygonal sections from round at elevated temperature

Economic factors such as the rise in cost of raw materials, labour and power, are compelling manufacturers of cold-drawn polygonal sections, to seek new production routes which will enable the expansion in the varieties of metals used and the inclusion of difficult-to-draw materials. One such method generating considerable industrial interest is the drawing of polygonal sections from round at elevated temperature. The technique of drawing mild steel, medium carbon steel and boron steel wire into octagonal, hexagonal and square sections from round at up to 850 deg C and 50% reduction of area in one pass has been established. The main objective was to provide a basic understanding of the process, with particular emphasis being placed on modelling using both experimental and theoretical considerations. Elevated temperature stress-strain data was obtained using a modified torsion testing machine. Data were used in the upper bound solution derived and solved numerically to predict drawing stress strain, strain-rate, temperature and flow stress distribution in the deforming zone for a range of variables. The success of this warm working process will, of course, depend on the use of a satisfactory elevated temperature lubricant, an efficient cooling system, a suitable tool material having good wear and thermal shock resistance and an efficient die profile design which incorporates the principle of least work. The merits and demerits of die materials such as tungsten carbide, chromium carbide, Syalon and Stellite are discussed, principally from the standpoint of minimising drawing force and die wear. Generally, the experimental and theoretical results were in good agreement, the drawing stress could be predicted within close limits and the process proved to be technically feasible. Finite element analysis has been carried out on the various die geometries and die materials, to gain a greater understanding of the behaviour of these dies under the process of elevated temperature drawing, and to establish the temperature distribution and thermal distortion in the deforming zone, thus establishing the optimum die design and die material for the process. It is now possible to predict, for the materials already tested, (i) the optimum drawing temperature range, (ii) the maximum possible reduction of area per pass, (iii) the optimum drawing die profiles and die materials, (iv) the most efficient lubricant in terms of reducing the drawing force and die wear.

The behaviour of granular material in pure shear, direct shear and simple shear

In biaxial compression tests, the stress calculations based on boundary information underestimate the principal stresses leading to a significant overestimation of the shear strength. In direct shear tests, the shear strain becomes highly concentrated in the mid-plane of the sample during the test. Although the stress distribution within the specimen is heterogeneous, the evolution of the stress ratio inside the shear band is similar to that inferred from the boundary force calculations. It is also demonstrated that the dilatancy in the shear band significantly exceeds that implied from the boundary displacements. In simple shear tests, the stresses acting on the wall boundaries do not reflect the internal state of stress but merely provide information about the average mobilised wall friction. It is demonstrated that the results are sensitive to the initial stress state defined by K0 = sh/sv. For all cases, non-coaxiality of the principal stress and strain-rate directions is examined and the corresponding flow rule is identified. Periodic cell simulations have been used to examine biaxial compression for a wide range of initial packing densities. Both constant volume and constant mean stress tests have been simulated. The characteristic behaviour at both the macroscopic and microscopic scales is determined by whether or not the system percolates (enduring connectivity is established in all directions). The transition from non-percolating to percolating systems is characterised by transitional behaviour of internal variables and corresponds to an elastic percolation threshold, which correlates well with the establishment of a mechanical coordination number of ca. 3.0. Strong correlations are found between macroscopic and internal variables at the critical state.

A study of the micro-mechanics of granular media

The development of more realistic constitutive models for granular media, such as sand, requires ingredients which take into account the internal micro-mechanical response to deformation. Unfortunately, at present, very little is known about these mechanisms and therefore it is instructive to find out more about the internal nature of granular samples by conducting suitable tests. In contrast to physical testing the method of investigation used in this study employs the Distinct Element Method. This is a computer based, iterative, time-dependent technique that allows the deformation of granular assemblies to be numerically simulated. By making assumptions regarding contact stiffnesses each individual contact force can be measured and by resolution particle centroid forces can be calculated. Then by dividing particle forces by their respective mass, particle centroid velocities and displacements are obtained by numerical integration. The Distinct Element Method is incorporated into a computer program 'Ball'. This program is effectively a numerical apparatus which forms a logical housing for this method and allows data input and output, and also provides testing control. By using this numerical apparatus tests have been carried out on disc assemblies and many new interesting observations regarding the micromechanical behaviour are revealed. In order to relate the observed microscopic mechanisms of deformation to the flow of the granular system two separate approaches have been used. Firstly a constitutive model has been developed which describes the yield function, flow rule and translation rule for regular assemblies of spheres and discs when subjected to coaxial deformation. Secondly statistical analyses have been carried out using data which was extracted from the simulation tests. These analyses define and quantify granular structure and then show how the force and velocity distributions use the structure to produce the corresponding stress and strain-rate tensors.

Cleavage initiation in the intercritically reheated coarse-grained heat affected zone:Part II. Failure criteria and statistical effects

In part 1 of this article, cleavage initiation in the intercritically reheated coarse-grained heat affected zone (IC CG HAZ) of high-strength low-alloy (HSLA) steels was determined to occur between two closely spaced blocky MA particles. Blunt notch, crack tip opening displacement (CTOD), and precracked Charpy testing were used in this investigation to determine the failure criteria required for cleavage initiation to occur by this mechanism in the IC CG HAZ. It was found that the attainment of a critical level of strain was required in addition to a critical level of stress. This does not occur in the case of high strain rate testing, for example, during precracked Charpy testing. A different cleavage initiation mechanism is then found to operate. The precise fracture criteria and microstructural requirements (described in part I of this article) result in competition between potential cleavage initiation mechanisms in the IC CG HAZ.

Fracture behaviour of an aluminide coating on a single crystal nickel base superalloy

Measurement of the coating fracture strain of an aluminide coating on a single crystal nickel base superalloy has been performed both in three-point bending and using variable wall thickness testpieces. As-aged specimens, 28 to 33 μm in thickness, were tested at room temperature, 600, 700 and 750 °C; specimens pre-exposed for 140 h at 850 and 1100 °C in air and vacuum were tested at room temperature. Fracture strains varied from 0.52 to 0.70% for as-aged specimens tested at temperatures up to 700 °C and specimens exposed at 850 °C and tested at room temperature. The crack path for these conditions was intergranular or transgranular in the main coating, along carbide-matrix interfaces in the coating transition zone, and at an angle of 30-45° to the original crack path in the substrate. The as-aged coating tested at 750 °C was ductile; a ductile-brittle transition occurs between 700 and 750 °C for the strain rate used (1 × 10-5 s-1). Following 1100 °C pre-exposure, specimens were ductile at room temperature with fractures strains of several percent. In this condition the crack morphology changed to one of subsurface nucleation in β grains and at β-γ′ interfaces. © 1993.

Characterization of viscoplastic yielding of asphalt concrete

A temperature and strain rate dependent yield surface model was proposed to characterize the viscoplastic yielding of asphalt concrete. Laboratory tests were conducted on specimens that have two binders, two air void contents, and three aging periods. Strain decomposition was performed to obtain viscoplastic strain and stress-pseudostrain curves were constructed to determine the model parameters accurately and efficiently. Results indicate that a stiffer asphalt concrete has greater cohesion and strain hardening amplitude, both of which decline as temperature increases or strain rate decreases. The temperature and strain rate factors of the yield surface can be accurately determined solely by the peak stress of the strength tests. © 2013 Elsevier Ltd. All rights reserved.

Monocyte subpopulation counts and associations with left ventricular ejection fraction post ST elevation myocardial infarction

Background: Monocytes are implicated in the initiation and progression of the atherosclerotic plaque contributing to plaque instability and rupture. Little is known about the role of the three phenotypically and functionally different monocyte subpopulations in determining ventricular remodelling following ST elevation myocardial infarction (STEMI). Mon1 are the ‘classical’ monocytes with inflammatory action, whilst Mon3 are considered reparative with fibroblast deposition ability. The function of the newly described Mon2 subset is yet to be fully described. Method: STEMI patients (n=196, mean age 62±13 years; 72% male) treated with percutaneous revascularization were recruited within the first 24 h post-infarction. Peripheral blood monocyte subpopulations were enumerated and characterised using flow cytometry after staining for CD14, CD16 and CCR2. Phenotypically, monocyte subpopulations are defined as: CD14++CD16-CCR2+ (Mon1), CD14++CD16+CCR2+ (Mon2) and CD14+CD16++CCR2- (Mon3) cells. Transthoracic 2D echocardiography was performed within 7 days and at 6 months post infarct to assess ventricular volumes, mass, systolic, and diastolic functions as well as strain and strain rate. Results: Using linear regression analysis higher counts for Mon1, and lower counts for Mon2 and Mon3 were significantly associated with the baseline left ventricular ejection fraction (LVEF) within 7 days post infarct (table 1). At 6 months post STEMI lower counts of Mon2 remained positively associated with a decrease in LVEF at completion of remodelling (p=0.002). Conclusion: Peripheral monocytes of all three subsets correlate with LVEF after a myocardial infarction. High counts of the inflammatory Mon1 are associated with the reduced baseline ejection fraction post infarction. After remodelling, the convalescent ejection fraction was independently predicted by monocyte subpopulation 2. As lower counts depicted negative ventricular remodelling, this suggests a possible myofibroblast deposition and angiogenesis role for the newly described intermediate monocyte subpopulation Mon2 as opposed to the previously anticipated inflammatory role.