Taylor Equation Research Articles

The fundamental mechanisms of wear of cemented carbide in continuous cutting of medical grade cobalt chromium alloy (ASTM F75)

Medical grade cobalt chromium alloys are one of a select number of material types approved for use in the components of orthopaedic implants. However, there has been minimal published research into the fundamental mechanisms in the cutting processes used in their manufacture. These processes affect the form accuracy, surface finish and integrity of these safety critical devices.The present work reports on a scientific investigation into the fundamental mechanisms of tool wear in continuous cutting of the biomedical grade Co-Cr-Mo ASTM F75 alloy using uncoated tungsten carbide tools. Confocal and scanning electron microscopy (SEM) is used to examine and characterise the progression of tool wear at intervals up to a defined “end of life limit” for each combination of speed (vc) and feed rate (f) in experiments where the range of these parameters vary from 20 to 60 m/min and 20–60 μm/rev respectively to reflect the ranges used in industry.An empirical model is then established for progressive tool wear which demonstrates that the wear rates vary by over an order of magnitude. The parameters for the Taylor equation are also determined for this material for the first time. Microscopic examination shows the presence of characteristic tool wear “zones” with consistent size, shape and composition. These zones evolve depending on combination of speeds and feeds as determined in the full factorial experiment. Detailed characterisation of the wear surfaces and cross sections provide a number of insights into the possible mechanisms of wear. It is hypothesised that micron thick layers of Co-Cr-Mo, found on the rake and flank wear surfaces, indicate primary wear mechanism involving adhesion of the work material and subsequent removal of WC hard particles by entrainment in the work material flow.

Study of two hardening mechanism caused by geometrically necessary dislocations in thin films with passivation layer

At microscale, thin films with passivation layer exhibit strong size effect during loading and prominent Bauschinger effect during reverse loading. It is commonly recognized that the hardening, which is caused by geometrically necessary dislocations (GNDs) near the passivation layer, is responsible for these phenomena. However, GNDs may contribute to hardening either by slip resistance via a generalized Taylor equation or by back stress originating from elastic interaction between dislocations. Which one dominates the thin film plasticity has not been well understood yet. In this paper, a dislocation-based crystal plasticity model is proposed, which includes both slip resistance and back stress hardenings. The model is applied to simulate passivated thin films with different thickness and the results are compared with experimental data. In the case where slip resistance hardening is considered, the predicted size effect of flow stress is much smaller than that in experiments and there is no obvious Bauschinger effect. While in the case where back stress hardening is considered, the predicted size effect matches well with experiments and the Bauschinger effect is clearly revealed. Also, it is found that the reverse plastic flow during unloading comes from the heterogeneous distribution of stress caused by the pile up of dislocations near the passivation layer.

Application of the Taylor Equation to Five-Power-Law Creep Considering the Influence of Solutes

This study determines the feasibility of describing the flow stress within the five-power-law creep regime, using a linear superposition of a dislocation hardening term and a significant solute strengthening term. It is assumed that the solutes are randomly distributed. It was found that by using an energy balance approach, the flow stress at high temperatures can be well-described by the classic Taylor equation with a solute strengthening term, τo, that is added to the αMGbρ1/2 dislocation hardening term.

A Continuum Deformation Model for Steel Coated with Nanolaminate Metallic Systems

This paper develops a continuum model of deformation of X70 steel coated with Cu/Nb–nanolaminate metallic systems (NMSs). The developed model is based on an elastic/viscoplastic framework that includes the effects of dislocation density, size effect, and strain hardening on the plastic deformation. The X70 steel is modeled according to a modified Taylor equation that considers the effects of statistically stored and geometrically necessary stored dislocation densities. NMSs obey two different mechanisms, the confined layer slip (CLS) and dislocation nucleation (Nu), during plastic deformation. NMSs are modeled according to the CLS mechanism when the individual lamina thickness is between 100 nm and 5 nm and the Nu mechanism when the individual lamina thickness is 5 nm or below. The model is implemented in a subroutine of a commercial finite element analysis code. Simulating a tensile test is the benchmark to generate flow curves of the model that agree with experimental data found in the literature.

Exogeneity of world oil prices to the Russian Federation’s economy and monetary policy

This research investigates the interrelationship between the Russian Federation’s main macroeconomic indicators, monetary policy and world oil prices using a vector autoregressive approach and monthly time-series data from January 1993 to December 2016. We selected the Russian Federation for this analysis because it is one of the largest oil exporting countries that is not a member of the Organization of the Petroleum Exporting Countries, and its oil revenues account for a significant proportion of the country’s total export and budget revenues. We assume that oil prices are exogenously given to this country, despite being a large oil-exporter, and explain the oil price transition mechanisms to the Russian Federation’s economy from the export side and through the fiscal channel taking into account the monetary policy factor. The results suggest that the impact of the oil price fluctuations on the country’s gross domestic product, consumer price index inflation rate, interest rate, and exchange rate was more significant between 2000 and 2016 than between 1993 and 1999. To estimate the monetary policy rule for the Russian Federation, we test the modified Taylor equation and associated Taylor rule, including the oil price gap, since the latter may have a significant impact on the key policy rate. The evidence suggests that the Taylor rule describes the post-financial crisis monetary policy of the Russian Federation relatively well.

Effect of water content on the glass transition and textural properties of hazelnut

This study is based on the assumption that the change in the texture of hazelnut, induced by water sorption or desorption, can be derived from the glass transition. No previous study has investigated the glass transition properties of hazelnuts. This study aimed to investigate the effect of water content on the glass transition and textural properties of a roasted hazelnut product. Water content of the sample was adjusted in various relative humidity conditions, and the mechanical glass transition temperature Tg was investigated using thermal rheological analysis (TRA), a type of thermomechanical analysis. The TRA curve exhibited a clear force drop induced by the glass transition, and mechanical Tg of the samples was determined. Water plasticizing effect caused mechanical Tg to decrease as the water content increased. The reduction in Tg was analyzed using the Gordon–Taylor equation and linear equation, and the critical water contents (water content at mechanical Tg = 25 °C) were obtained. The fracturing properties of the hazelnut changed from brittle to ductile at the critical water contents. This suggested that the change in the texture of hazelnut can be characterized by the glass transition.

A new method for calculating the viscosity of W/O and O/W emulsion

The viscosity of water-in-oil and oil-in-water emulsions is a key parameter to understand during oil exploitation and transportation. Water content increases with the extraction of crude oil, especially in the middle and late periods of exploitation. Apparent viscosity increases as formation water content increases. However, apparent viscosity decreases when the water cut is beyond the phase transition point, after which, the water-in-oil emulsion becomes an oil-in-water emulsion. Many models for calculating the viscosity of W/O emulsions has been proposed, but methods for predicting the viscosity of O/W emulsions are rare. In this article, a method to calculate viscosity of W/O and O/W emulsions based on the Richardson and Taylor equations is introduced. Contrary to the existing correlations, the method presented here takes into account more factors, including water cut, temperature, shear rate, viscosity of oil and formation water. Additionally, whereas conventional correlations have been able to only calculate the viscosity of water-in-oil emulsions, the proposed method can also calculate the viscosity of oil-in-water emulsions. The accuracy and reliability of 5 conventional correlations and of this new method are assessed using the experimental data. The proposed model better fits the data when predicting the viscosity of W/O and O/W emulsions, with average absolute error of 12.71–16.43%.

Structural and Thermal Analysis of Carbon Nano-Particles/Polypyrrole/Poly (Ethylene – Co – Vinyl Acetate) Composites

Polymeric materials and their composites have attracted great attention because of their great significance. This study includes preparation of composites of carbon nano-particles/Polypyrrole (CB/PPY) embedded in Ethylene-vinyl acetate copolymer (EVA) with different contents as 0, 5, 10, 15, 20 and 30 parts per hundred parts by weight of polymer (pph). X-ray diffraction (XRD) was investigated to characterize the structure of the prepared composites. Thermal analysis including differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) were measured to detect the miscibility degree of the composites and their thermal stability, respectively. The Gordon – Taylor equation was modified to fit the experimental values of the glass transition temperatures (Tg) at low and high contents of CB/PPY. The obtained values of Tg showed complete miscibility of most of the composites. From XRD measurements, the crystallinity of the composites was found to be decreased by embedding (CB/PPY) into EVA. The curves of TGA show more thermal stabilities for the composites compared to the pristine EVA.

Micro-indentation hardness model of AISI1045 steel during micro-plasticity indentation experiment considering size effect

The analytical method is used to study micro-plasticity indentation and the increment equation is worked out by analyzing the contacted nodes between rigid indenter with material. Then the experiment under various maximum loads (50mN, 100mN, 200mN, 300mN, 400mN, 500mN and 650mN) at the constant loading speed 9.6841mN/s is carried out on MCT-W501 micro-indentation tester and the constitutive equation of AISI1045 steel is obtained by Taylor equation. The experimental result shows great indentation size effects, so the intrinsic material length is introduced to accurately simulate the micro-indentation plasticity changes. Based on ABAQUS analyzing software, the equation obtained by experiment is input to simulate the loading curve between indentation load and indentation depth considering the effect of strain gradient. The result shows that the square of hardness relative value has a linear decrease with the increase of indentation diagonal. Based on the result of simulation and calculation, the final constitutive equation is proposed and the data of modified equation is quite coordinate with experimental and calculated data with relative error less than 4.92% thus the constitutive equation is verified.

Geometrically Necessary Dislocation Density Evolution in Interstitial Free Steel at Small Plastic Strains

Measurement of geometrically necessary dislocation (GND) density using electron backscatter diffraction (EBSD) has become rather common place in modern metallurgical research. The utility of this measure as an indicator of the expected flow behavior of the material is not obvious. Incorporation of total dislocation density into the Taylor equation relating flow stress to dislocation density is generally accepted, but this does not automatically extend to a similar relationship for the GND density. This is discussed in the present work using classical equations for isotropic metal plasticity in a rather straight-forward theoretical framework. This investigation examines the development of GND structure in a commercially produced interstitial free steel subject to tensile deformation. Quantification of GND density was carried out using conventional EBSD at various strain levels on the surface of a standard dog-bone-shaped tensile specimen. There is linear increase of the average GND density with imposed macroscopic strain. This is in agreement with the established framework.

Intercomparison of three methods to estimate evapotranspiration over temperate meadow in Inner Mongolia: Penman–Monteith, Makkink and Priestley–Taylor equation

AbstractThree methods of calculating evapotranspiration (ET), Penman–Monteith (PM), Makkink (MK) and Priestley–Taylor (PT) equation, were applied to a temperate meadow in Inner Mongolia, China. We compared these methods with eddy covariance (EC) method. The results indicated that a reduction in mean absolute error (MAE) and root mean squared error (RMSE) was achieved for MK and PT methods (45.6–83.0%) when using site‐specific parameters compared with referenced ones, but an increase of 75.9–93.9% for PM method. Intercomparison of three methods through comparison with EC measurements indicated that PT method with site‐specific parameters performed the best to estimate ET, followed by PM method with referenced parameters, and then MK equation with site‐specific parameters (overestimate ET by 8.2, 12.1, 16.5% and 3.4, 12.8, 21.0% respectively for half‐hourly and daily values).

Evaluation of microstructure and mechanical properties of aluminum AA7022 produced by friction stir extrusion

Friction stir extrusion (FSE) is a process in which a sample is produced through the heat generated by the friction between die and materials, and the extrusion pressure. The extruded sample could be wire, tube, rod or another form. The wired samples were produced of aluminum alloy AA7022 at different rotational speeds and extrusion forces, and impacts of these two parameters were studied. The samples produced at higher rotational speeds and lower forces had a far better surface quality and less surface cracks were seen on them. The optical microscopy and scanning electron microscopy (SEM) were used to examine the microstructural properties of samples and the mechanical properties of specimens were studied by micro hardness and compression tests. Using X-ray diffraction technique and Rietveld method, the average crystallite size and micro-strain and dislocation density of samples were calculated and the yield strength of each sample was estimated by Taylor Equation. The average crystallite size and grain size were increased and the mechanical properties and dislocation density were decreased with the rise of rotational speed. Increasing the extrusion force to a certain level caused increase in yield strength of material. The experimental yield strength of compression test and Taylor’s yield strength were compared with each other and had a good conformity.

Effect of twining on dynamic behaviors of beryllium materials under impact loading and unloading

As a rare metal material with low density, high strength and high melting point, beryllium (Be) is widely utilized in many fields including aerospace and vehicles. Dynamic loadings such as impact and high-rate compression often happen in the applications of Be materials in these fields. However, the dynamic behaviors of Be materials under high pressure and high-rate loading have not been fully investigated, although they are valuable for better applications of Be materials. articularly, the effect of twinning on dynamic behaviors of Be material is very important for better understanding the plasticity deformation mechanism of Be material. In this paper, a thermoelastic-viscoplastic crystal plasticity model is developed for dynamic behaviors of Be material under high pressure and high strain-rate loading based on the physical mechanism of plasticity deformation. Besides, the dislocation motion and work hardening are considered within the constitutive framework by the Orowan relation and the Taylor equation respectively, and the contribution of twinning to the plasticity deformation is also considered via twinning fraction evolution and fragmentation of crystal due to twinning deformation. With the model, dynamic behaviors of Be material are investigated, including effect of pressure on the dynamic yield strength, the quasi-elastic unloading behavior, and evolution of twinning in shock loading and unloading. Compared with the classical SG model, the model developed in this paper accords better with the experimental results in predicting yield strength of Be material under impact loading, especially with high pressure. Moreover, it is revealed that the condition of yield strength of the Be material is divided into three cases, namely the non-twinning under low pressure, the twinning deformation under moderate pressure, and the twinning fragmentation under high pressure. The unloading behavior of Be material under impact loading is also studied with the model, and the quasi-elastic unloading behavior observed in experiments many times, is faithfully predicted. It is found that the quasi-elastic unloading phenomenon of the material is closely related to the variation of the shear velocity of shock wave with the shear strain, which suggests that the non-linear elastic property of the material is an important reason for this phenomenon. Finally, the evolution of twinning of Be material in the shock loading is studied, showing that the increasing of twinning friction happens not only in the loading process but also in the unloading process of the shock waves. Some crystals break up into sub-crystals due to the fact that the volume fraction of twinning exceeds the critical fraction in the evolution of twinning.

Water state diagram and thermal properties of fructans powders

The thermal analyses and the water state diagrams of agavin and inulin were investigated. The thermogravimetric analysis and differential scanning calorimetry (DSC) were used to know the difference between fructans. Linear inulin (220.0 °C) showed a higher thermal stability than the branched agavins (206.7 °C). The samples displayed different physical states and lightness depending on the water activity of storage (a w). The agavin showed different physical states: powder (a w < 0.33), soft lump (a w ≈ 0.43), sticky (0.55 < a w < 0.77), and liquid (a w > 0.85), while inulin showed two physical states: an amorphous powder at a w < 0.55 and a semicrystalline solid at a w > 0.69. These physical states decreased the lightness of fructans. The GAB equation and the Gordon–Taylor equation showed a good fit to the experimental data (R 2 > 0.95). The K constant of GAB equation predicted a lower water affinity of inulin powder, while the agavin powder presented a higher water affinity. The DSC showed a glass transition temperature of 118.1 and 135.3 °C for agavin and inulin anhydrous powders, respectively. An increase in water content in agavin showed a higher depression in the glass transition temperature than in inulin. Also, the inulin exhibited a melting point while agavin not. The water state diagrams showed the critical water activity at which the agavin (0.50) and inulin (0.59) powders were stable to physical changes. This knowledge is used to understand the physical and structural behaviors of agavin and inulin at the different water activities.

Water use intensity of Canadian beef production in 1981 as compared to 2011

The amount of beef produced per animal in Canada increased significantly from 1981 to 2011, due to enhanced production efficiency and increased carcass weight. This study examined the impact of improvements in production efficiency on water use intensity over this period. Temporal and regional differences in cattle categories, water use for drinking, feed production and meat processing, feeding systems, average daily gains, and carcass weight were considered in the analysis. Potential evapotranspiration (PET) was estimated by the National Drought Model (NDM) from 679 weather stations across Canada using the Priestley and Taylor equation. To adjust PET estimates for each crop included in cattle diets, FAO crop coefficients were used to calculate total feed water demand. Estimates of drinking water consumed by a given class of cattle accounted for physiological status, body weight and dry matter intake as well as ambient temperature. In both years, drinking water accounted for less than 1% of total water use with precipitation (i.e., green water) included for feed and pasture production. With exclusion of green water, drinking water accounted for 24% and 21% of total water use for Canadian beef production in 1981 and 2011, respectively. The estimated intensity of blue water (surface and groundwater) use per kilogram of boneless beef was 577L in 1981 and 459 in 2011, a 20% decline. The observed reduction in water use intensity over the past three decades is attributed to an increase in average daily gain and slaughter weight, improved reproductive efficiency, reduced time to slaughter as well as improvements in crop yields and irrigation efficiency. Given that feed production accounts for the majority of water use in beef production, further advances may be achieved by improving feeding efficiencies and reducing water use per unit of feed crop and pasture production.

Correlation Between Structural Parameters and Mechanical Properties of Al5083 Sheets Processed by ECAR

In the paper, structural parameters and mechanical properties of Al5083 alloy sheet during equal channel angular rolling (ECAR) process and their relationship are studied. In order to evaluate the effect of ECAR process, Al5083 strips were subjected to the ECAR process for 1, 2, and 3 passes through the die channel angles 110°, 120°, and 130° at two routes. The effect of the process on the microstructural evolution of samples was investigated by means of x-ray diffraction and EBSD techniques. X-ray pattern has been analyzed using Rietveld method to compute structural parameters, including microstrain, average crystallite size, and dislocation density. The results showed that the dislocation density and microstrain were increased, and crystallite size was decreased during ECAR process. It was found that the behavior of variations in mechanical properties was in accordance with the dislocation density changes. This paper revealed that the increase in the strength of ECARed samples could be attributed to reduction in high-angle grain boundaries and the increase in dislocation density. Moreover, the yield strength estimated from Taylor equation was found in accordance very well with the experimentally measured yield strength of the samples.

Unravelling dislocation networks in metals

Understanding the intricate structure of dislocations in metals is a major issue in materials science. In this paper we present a comprehensive approach for the characterisation of dislocation networks, resulting in accurate quantification and significantly increasing the insight into the dislocation structure. Dislocation networks in metals consists of dislocation segments, pinned by microstructural obstacles. In the present paper a model is introduced that describes the behaviour of these dislocation segments in the pre-yield range of a tensile test on the basis of fundamental concepts of dislocation theory. The model enables experimental quantification of the dislocation density and segment length from the tensile curve. Quantitative results are shown and discussed on the development of the dislocation network as a function of increasing degree of plastic deformation, including validation and physical interpretation of the classical Taylor equation.

Grain size effects in aluminum processed by severe plastic deformation

We investigated the effects of the grain size on the yield strength of aluminum using a group of samples with grains successively refined by equal-channel angular pressing (ECAP) and another group of samples produced by 8 ECAP passes and subsequently annealed step by step to produce coarser grains. Tensile tests were performed on all the samples. Adopting a linear addition model for different strengthening contributions, the observed yield strength was resolved into dislocation-related and grain size-related strengthening contributions. The former was directly evaluated using the Taylor equation with dislocation densities determined by the Williamson–Hall method, and the latter was quantified by subtracting the former and the friction stress from the observed yield strength. It was found that for the as-ECAP-processed samples, the amount of the grain size-related strengthening was consistent with an extrapolation of the conventional Hall–Petch relation, and marked extra strengthening, which was clearly related to the grain refinement, appeared after annealing.

Strengthening mechanisms in Fe-Al based ferritic low-density steels

Low-density steels with different aluminium contents have been investigated with an aim to examine the occurrence of different strengthening mechanisms leading to its higher strength. A composition corresponding to 6.8wt% aluminium has been studied to understand the underlying strengthening mechanisms. Different factors contributing to the strengthening mechanisms have been separately analyzed. Microstructural features have been analyzed using Mössbauer spectroscopy, small angle X-ray scattering (SAXS), X-ray line profile analysis and transmission electron microscopy (TEM). The enhanced yield strength of the low-density steel containing 6.8wt% Al was attributed to the strengthening effects arising from the ferrite grain size, dislocations incorporated during processing, ordered phase formation and the presence of Al atoms in the solid solution. Each of these operating mechanisms was modelled by using its constitutive equation for example, grain size strengthening by classical Hall-Petch equation and the strengthening from dislocations by Taylor's equation. In addition, the formation of nano-sized ordered phase was evaluated by TEM, Mössbauer spectroscopy, SAXS and hence order strengthening was modelled by using the size and volume fraction (as determined by TEM and SAXS). Strengthening due to lattice frictional stress required for dislocation motion was also incorporated into the model.

In Situ Neutron Diffraction Study of the Influence of Microstructure on the Mechanical Response of Additively Manufactured 304L Stainless Steel

In situ neutron diffraction measurements were completed during tensile and compressive deformation of stainless steel 304L additively manufactured (AM) using a high power directed energy deposition process. Traditionally produced wrought 304L material was also studied for comparison. The AM material exhibited roughly 200 MPa higher flow stress relative to the wrought material. Crystallite size, crystallographic texture, dislocation density, and lattice strains were all characterized to understand the differences in the macroscopic mechanical behavior. The AM material’s initial dislocation density was about 10 times that of the wrought material, and the flow strength of both materials obeyed the Taylor equation, indicating that the AM material’s increased yield strength was primarily due to greater dislocation density. Also, a ~50 MPa flow strength tension/compression asymmetry was observed in the AM material, and several potential causes were examined.