The present work has been conducted in order to develop a novel approach to predict the inhomogeneous flow of a 20MnCr5 steel during an axisymmetric hot compression test, by using the element-free ...Galerkin (EFG) method under a differential constitutive description. The governing equations have been solved on the basis of the EFG global weak formulation. A detailed explanation concerning the characteristics inherent to the application of the EFG method to this problem, has also been provided. Furthermore, a return mapping algorithm for the solution of associative von Mises inelastic problems, has been formulated for the differential constitutive description employed in this communication, namely, a differential return mapping algorithm (DRMA). The feasibility and suitability of the EFG method for solving the axial compression problem has been shown by comparing its results with a FEM based solution employing a simple constitutive description. The reliability of the proposed DRMA has been demonstrated by a comparison of a homogeneous deformation numerical test with the experimental and direct integration results reported in a previous communication. Finally, the EFG model has been used to predict the stress, strain and volume fraction recrystallized distributions under steady and transient nominal strain rate and temperature deformation conditions. These parametric studies have been carried out by considering the differential constitutive description, but also a conventional integrated constitutive model of a 20MnCr5 steel. The results have revealed the suitability of the EFG formulation under the proposed DRMA, for predicting the performance of an axisymmetric hot compression test. The differences between the use of differential and integrated constitutive descriptions on the performance of hot-working processes under inhomogeneous deformation conditions, have also been evidenced in this research work.
•A differential constitutive description-based hot-compression model has been proposed.•The numerical solutions have been derived by means of the element-free Galerkin method.•A novel differential return mapping algorithm (DRMA) has been developed.•The DRMA was developed by computing the flow stress into an implicit difference scheme.•Notable differences were found with solutions based on integrated constitutive descriptions.
In nanoindentation, especially at very low indenter displacements, the indenter/material contact area must be defined in the best possible way in order to accurately determine the mechanical ...properties of the material. One of the best methodologies for the computation of the contact area has been proposed by Oliver and Pharr W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992) 1564, which involves a complex phenomenological area function. Unfortunately, this formulation is only valid when the continuous stiffness measurement mode is employed. For other conditions of indentation, different contact area functions, which take into account the effective truncation length or the radius of the rounded indenter tip, as well as some fitting parameters, have been proposed. However, most of these functions require a calibration procedure due to the presence of such parameters. To avoid such a calibration, in the present communication a contact area function only related to the truncation length representative of the indenter tip defect, which can be previously estimated with high resolution microscopy, has been proposed. This model allows the determination of consistent indentation data from indenter displacements of only few nanometers in depth. When this proposed contact area function is applied to the mechanical characterization of a TiHfCN film of 2.6μm in thickness deposited onto a tool steel substrate, the direct determination of the hardness and elastic modulus of the film leads to values of 35.5±2GPa and 490±50GPa, respectively.
•Hardness and elastic modulus of TiHfCN thin film have been determined by indentation.•A simple area function describing the contact area in indentation is proposed.•The function only considers the truncation length of the tip defect.•The hardness of the film is found to be close of 35.5GPa.•The elastic modulus of the film is found to be close of 490GPa.
•The work-softening transient due to dynamic recrystallization of a C–Mn steel have been investigated.•Plane strain compression tests were conducted between 850°C and 1100°C, at strain rates of ...0.3–24s−1.•The temperature and strain rate dependence of several important stress parameters has been described.•The time for 50% recrystallization as a function of deformation conditions have been determined.•A novel constitutive description in differential form for this material has been proposed.
The flow softening brought about by dynamic recrystallization (DRX) during the plastic deformation of metals and alloys under hot-working conditions is of a great practical significance for the computation of the loads, torques and power consumption required in industrial hot forming operations. The present communication reports the main results of an investigation that was carried out in order to analyze in detail the work-softening transient present on the flow curves of a C–Mn steel deformed in a wide range of temperatures and strain rates. The analysis of the experimental stress–strain curves allowed the description of the temperature and strain rate dependence of four important stress parameters: yield, critical, saturation and steady-state, by means of the Sellars-Tegart-Garofalo model (STG). Also, it has been possible to derive an expression for the time required to achieve 50% recrystallization as a function of the deformation conditions, as well as the computation of the Avrami exponent of the material. All this information has been subsequently employed in the description of the flow stress of the material as a function of deformation conditions. For this purpose, an original constitutive description in differential form, which combines a work-hardening and dynamic recovery term, described by the phenomenological equation earlier advanced by Sah et al. and an additional softening term, which involves the Avrami relationship, is proposed. The evolution equation that has been advanced is independent of strain. Therefore, it is shown that, in principle, it is possible to describe satisfactorily the evolution of the flow stress during transient loading conditions as a consequence of changes in strain rate or deformation temperature, regardless if the material undergoes DRX during such a transient. Contrary to many different models reported in the literature, the approach here proposed is independent of the peak parameters exhibited on the flow curves.
Modeling and optimization of industrial hot-working operations by means of commercial finite element computer codes require robust constitutive descriptions, which could be easily implemented. Also, ...it is expected that such formulations are able to describe as accurate as possible the flow stress, work-hardening and work-softening rate of the material, as a function of microstructure and deformation conditions. The present communication describes the development of a novel constitutive description of metals which exhibit dynamic recrystallization during deformation under hot-working conditions. The formulation is founded on the extension of the model earlier developed by Anand and co-workers for the constitutive description of metals which exhibit dynamic recovery as the only dynamic restoration mechanism during hot deformation. The advanced constitutive formulation has been validated by conducting axisymmetric compression tests with samples of a R260 steel employed for the manufacture of rail tracks. The specimens were deformed in a wide range of temperatures and strain rates, both under constant and variable strain rate conditions. The latter involve either an increase or a decrease in the Zener-Hollomon parameter as plastic deformation is applied. The results obtained indicate that the proposed constitutive description is able to reproduce quite accurately the experimental flow stress data. It has also been shown that the correct computation of the recrystallization time and volume fraction recrystallized dynamically, by means of an appropriate differential or incremental formulation of the Avrami equation, constitutes an essential aspect of the model. Such an approach is particularly important for predicting correctly the changes in flow stress under variable strain rate conditions.
•A new constitutive model for metals which exhibit dynamic recrystallization is proposed.•The formulation is based on the earlier model advanced by Anand and co-workers.•A new evolution equation for the flow stress, once DRX has started, is proposed.•Constant deformation conditions tests are employed for determining the parameters involved.•Ramped variable strain rate tests are employed for validating the new advanced model.
Cu-Ni-Si alloys and their variants constitute very important engineering materials, which have found a number of applications in different fields, as potential substitutes of the toxic Cu-Be alloys ...traditionally employed for the manufacture of different parts and components. However, the hot-working behavior of these materials has not been deeply investigated and only few studies have reported some limited information regarding the relationship between flow stress and deformation conditions. The present communication reports the main findings of an original investigation aimed at analyzing in detail the flow stress, work-hardening and work-softening behavior of a Cu-Ni-Si alloy deformed in the temperature range of 600°C to 950°C, at nominal strain rates in the range of 0.1–10s−1. Particularly, for the first time, a general constitutive formulation able to describe the changes in flow stress, work-hardening and work-softening rates of this material as a function microstructure and deformation conditions, in the temperature range between 800°C and 950°C, is proposed. The nature of the constitutive description here advanced allows the computation of the flow stress either under constant and transient loading conditions, on the basis of physically-based and well established models. Such a constitutive formulation is able to reproduce the experimental values of the experimental flow stress with an accuracy of ±7MPa and therefore, it represents a valuable tool for modeling hot-working operations conducted on this material. It has been concluded that, in order to take full advantage of the grain refining effects associated with dynamic recrystallization, hot-working of the alloy should be carried out at temperatures above 850°C. Deformation at temperatures below 800°C leads to a significant increase in the mechanical properties of the alloy and even fracture, as a consequence of the possible precipitation of fine secondary phases.
Considerable improvement in the tribological response was achieved during sliding wear tests against alumina ball, when AA 2024-T3-aluminium alloy substrate was coated with DLC/NiP duplex coating. ...Quantitative EPMA analysis carried out on the coated sample cross-section coupled with nanoindentation techniques allowed the identification of the coated system architecture as composed of 4 main layers, with distinct mechanical properties, on top of the aluminium substrate: DLC (a:C-H chromium dopped layer and graded layer of CrC), a newly formed graded layer of CNiPCr, product of the interdifusion during PVD processing, and the NiP coating. The change in the elastic modulus with penetration depth was described by means of an original approach that was developed for its specific application to multilayer coatings.
•Sliding wear of 2024-T3 aluminum alloy coated with a DLC duplex coating was analyzed.•Presence of a new CNiPCr graded layer was found by means of EPMA analysis.•The DLC/CrC/CNiPCr/NiP coated system has been characterized by nanoindentation tests.•A modified form of the model earlier advanced by Perriot and Barthel is employed.•The integrity of the coated system was evaluated by means of a Hertzian formulation.
The experimental flow stress curves of structural steels obtained from axisymmetric compression tests conducted under hot-working conditions very often include the frictional effects present at the ...tool/specimen interface. Such effects have a significant influence on the flow stress and therefore, should be corrected prior to any quantitative analysis aimed at determining the constitutive description of these materials. Commonly, such a correction is carried out by assuming a constant friction coefficient (μ) or friction factor (m) independent of deformation conditions, which is an unrealistic approach. The present investigation analyzes experimentally the frictional effects that occur when steel is deformed under axisymmetric compression conditions in the temperature range of 850 to 1200 °C at a strain rate of 0.1 s
−1
and applied effective strains of 1, employing cylindrical samples with an initial diameter to initial height ratio (d
0
/h
0
) in the range of 0.5 to 2. Finite element modeling (FEM), as well as element-free Galerkin modeling (EFGM), have been employed for the analysis and prediction of the von Mises stress distribution, barreling and amount of metal folding undergone by the compression specimens. It has been shown that the increase in flow stress due to frictional effects can be corrected on the basis of either μ or m, by assuming that these parameters vary in the course of plastic deformation and are strongly dependent on deformation temperature. A novel procedure for the systematic correction of the flow stress curves, taking into consideration the changes in friction conditions during plastic deformation, has been proposed.
The change in the composite hardness with penetration depth derived from nanoindentation tests conducted on coated systems, which involve the deposition of multilayer coatings, in general exhibits a ...complex shape, as a consequence of the sequential contribution of each coating layer to the composite hardness during indentation loading. In spite that there are a number of models, which have been proposed for describing the change of the composite hardness with penetration depth for monolayer coatings, as well as for determining the coating and substrate hardness, very few research works have addressed the problem of describing this kind of data for multilayer coatings. In the present communication, a rational approach is proposed for extending two models widely used for the analysis of monolayer coatings, in order to describe the composite hardness data of multilayer coatings, as well as for determining the hardness of each individual layer and that of the substrate. Thus, a modified form of the models earlier advanced by Korsunsky et al. and Puchi-Cabrera, as well as their computational instrumentation, are proposed. The extension of both models to deal with multilayer coatings is conducted on the basis of the model developed by Iost et al., in order to adapt the Jönsson–Hogmark model to the analysis of indentation data of multilayer coatings. Such a methodology provides a means of computing the volume fraction of each individual layer in the coating, which contributes to the composite hardness. According to the results obtained, this scheme seems to be general enough to be applicable to different hardness models other than the Jönsson–Hogmark model. The proposed modified models are validated employing nanoindentation results obtained from a 2024-T6 aluminum alloy coated with a diamond-like carbon film, employing electroless NiP as intermediate layer. The advantages and disadvantages of the different models employed in the analysis are thoroughly discussed.
•Two models have been modified for describing the hardness of multilayer coatings.•The computational instrumentation of the advanced modified models is also proposed.•The proposed modified models have been tested employing nanoindentation data.•The proposed models allow the determination of the intrinsic hardness of each layer.
The experimental and numerical modeling of cold forging operations conducted on commercial Al alloys requires a precise knowledge of the functional dependence of both flow stress and work-hardening ...rate on microstructure and deformation conditions. In order to contribute to the improvement of the finite element computer modeling of forming operations conducted on Al alloys, under cold-warm working conditions, an original and rational constitutive description, able to predict accurately both the flow stress and work-hardening rate of an AA6082-T6 Al alloy is proposed. The constitutive formulation has been developed on the basis of the Mechanical Threshold Stress (MTS) model and its applicability is limited to the deformation of the material under cold-warm working conditions, that is to say, in the temperature range of 298–423 K. A novel differential equation for the description of the continuous change in the work-hardening rate of the alloy has been developed, which allows the prediction of the changes in flow stress and work-hardening rate during deformation either under constant and variable temperature and strain rate conditions. The validation of the developed constitutive description has been accomplished by its implementation into a finite element (FE) model for the accurate prediction of the change in some local contact parameters, such as contact pressure, sliding velocity and interface temperature, during the friction test employed in the evaluation of friction conditions in metalworking, known as the Upsetting Sliding Test (UST).
•An original and rational constitutive description for the 6082-T6 Al alloy is proposed.•A novel differential equation for describing the change in the work-hardening rate of the alloy has been developed.•The model developed is able to describe the changes in flow stress under transient deformation conditions.•The model has been validated by means of experiments and FEM analysis of the upsetting sliding test.
The present investigation has been conducted in order to determine the residual stresses of an as-ground WC–12Co coating of two different thicknesses, by means of two different methods. Firstly, ...X-ray diffraction techniques, which allowed the determination of the surface residual stresses of the coating by means of the method called “sin
2
ψ” method. Secondly, an incremental hole drilling technique together with the integral method, which allowed the analysis of the non-uniform through-thickness residual stresses present in the coatings. It has been determined that the surface residual stresses are of a compressive nature, which could be due to the grinding that was applied to the coatings in order to achieve the desired thicknesses. On the contrary, the results of the incremental hole drilling tests indicated that the through-thickness residual stress distributions are not uniform and are characterized by the presence of tensile peak stresses, at depths in the range of ~
50–125 μm. Such stresses were observed to decrease towards the coating–substrate interface where the compressive component of the stress state becomes greater than the tensile component. It has been found that the mean residual von Mises stress is higher in the thinner coating than in the thicker one, of approximately 180 and 107 MPa, respectively.
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