Flow Stress Strain Research Articles

Constitutive equations for prediction of the flow behaviour of duplex stainless steels

The high temperature workability of a 2205 duplex stainless steel has been investigated by torsion testing between 950 and 1200 °C. The constitutive equations relating peak flow stress, temperature and strain rates were obtained, and the composite model, where austenite and ferrite are the hard and soft phases, respectively, was found to give an excellent description of the experimental data. The peculiar shape of the equivalent stress vs. equivalent strain flow curves has been discussed; a model based on the hypothesis that during torsion of wrought duplex stainless steels the load transfer from ferrite and austenite is delayed to a later stage of the straining process has been developed, and successfully used to describe the experimental data. Thus it was concluded that during the early stage of the tests the deformation is inhomogeneous, since strain accumulates in ferritic regions, while austenite is almost undeformed.

Optimization technics to identify the characteristics of a hydroformed structure

This paper presents an experimental/numerical methodology which aims to improve 3D welded tube considering their anisotropic effect, geometrical singularities found in the welded joint, and heat affected zone behaviour by hydroforming process. This process contributes to reduce the number of welding and assembly operations needed to generate complex structures, while improving the weight saving and quality of finished parts. In spite of the advances in the performance of this manufacturing technology, some problems are linked to particularities of certain raw materials and additional studies must be developed, like in the case of welded tubes. The experimental study is dedicated to the identification of stress-strain flow of the base metal and the heat-affected zone from the global measure of tube displacement, thickness evolution and internal pressure expansion. Nanoindentation test is adapted to investigate the heat affected zone mechanical behaviour. Workpiece behaviour's models used to simulate the expansion tests, made it possible to highlight the combined effects of the inhomogeneous behaviour of basic material and heat affected zone, as well as the geometrical singularities found in the welded tubes. From the simulations carried out, it is clear the influence of the plastic flow behaviour of the welded tube in the final results (thickness distribution, stress instability, tube circularity, critical thinning and rupture).

Strain hardening behavior during manufacturing of tube shapes by hydroforming

Safe and robust process design relies on knowledge of the evolution of the mechanical properties in a tube during hydroforming. The manufacturing of tubular shapes generally consists of three main stages: bending, preforming, and expansion. The latter is usually called hydroforming. As a result of these three steps, the final product’s strain hardening history is nonlinear. In the present study, the strain hardening behavior during hydroforming was experimentally investigated. The variation of local flow stress and/or local hardness was used as an index of the strain hardening during the various steps and the local flow stress and/or local hardness were used with respective correlations to determine the effective strain. The strain hardening behavior during hydroforming after preforming has been successfully analyzed by using the relationships between hardness, flow stress, and effective strain for variable pre-strains prior to hydroforming. The comparison of predicted hardness with measured hardness confirms that the methodology used in this study is feasible, and that the strain hardening behavior can be quantitatively estimated with good accuracy.

Studies on the Work-Hardening Behavior of AA2219 under Different Aging Treatments

Uniaxial tensile tests were performed to examine the influence of the precipitation state on the yield strength and work-hardening behavior of AA2219 for different aging treatments. The microstructural observations in four aging treatments (viz. natural aging, underaging, peak aging, and overaging) were made through transmission electron microscopy (TEM) to understand the type of phase or intermediate stages of the phase present (Guinier–Preston (GP) zones, θ″, θ′, and θ). To characterize the work-hardening behavior, the analysis of the experimental results has focused on two parameters, viz. the initial work-hardening rate Θmax (≡dσ/de) and the slope (dΘ/dσ) of the Θ-σ plot, which is related to the rate of dynamic recovery. The initial work-hardening rate (Θmax) first drops as aging proceeds and then increases significantly upon overaging. The large increase in Θmax is also associated with a concomitant increase in the slope (dΘ/dσ) of the Θ-σ curve. The material constants in the differential equation for the dislocation density are evaluated and flow stress vs plastic strain curves are generated using the flow stress contributions from the solid-solution, dislocation, and precipitation hardening. The model predictions are found to be in excellent agreement with the experimental data for a range of precipitation states from underaged (UA) to overaged (OA) conditions. Curves of flow stress due to dislocation hardening with the plastic strain were also generated in the presence of shearable and nonshearable precipitates.

Modeling and simulation on dynamic recrystallization of 30Cr2Ni4MoV rotor steel using the cellular automaton method

The cellular automaton (CA) method coupling fundamental metallurgical principles was used to simulate the initial microstructure and dynamic recrystallization (DRX) of 30Cr2Ni4MoV rotor steel. For the initial microstructure generation, reasonable transformation rules were established based on the thermodynamic mechanism, the activation energy and the curvature-driven mechanism. For the purposes of obtaining the material constants which were used in the CA model for DRX, including initial grain size, nucleation rate, softening parameter and activation energy, the hot deformation characteristics of 30Cr2Ni4MoV rotor steel were investigated by uniaxial hot compression tests on Gleeble-3500 machine. The effect of a wide range of thermomechanical processing parameters (temperature and strain rate) on the nucleation rate, the percentage of DRX and the final grain size were investigated. By comparison of the flow stress–strain curves and the metallographs, it was shown that the CA model coupling fundamental metallurgical principles can accurately simulate the microstructural evolution and the plastic flow behavior for 30Cr2Ni4MoV rotor steel at various deformation parameters.

Serrated flow behavior in AL6XN austenitic stainless steel

Serrated flow behavior of the AL6XN austenitic stainless steel has been investigated at different temperatures and strain rates. The results show the serrated flow, peak/plateau in flow stress and negative strain rate sensitivity appearing in tensile deformation of the AL6XN steel at 773–973 K and 3.3 × 10 −5–3.3 × 10 −3 s −1 (excluding 873 K, 3.3 × 10 −5 s −1), suggesting the occurrence of dynamic strain aging (DSA). The activation energy for type-A and -(A + B) serrations was calculated to be 304 kJ/mol and diffusion of substitutional solutes, such as chromium and molybdenum is considered as the mechanism of serrated flow. TEM observations further revealed a typical planar slip mode in the regime of DSA of the deformed AL6XN steel.

Influence of advanced yield criteria on predictions of plastic anisotropy for aluminium alloy sheets

Extruded aluminium alloy sheets of AA7003-T6 are characterised by performing an experimental programme and numerical simulations. The anisotropic behaviour of the aluminium alloy is investigated using two linear transformation based anisotropic yield criteria Yld2000-2d (Barlat et al. [1]) and Yld2004-18p (Barlat et al. [2]). The yield criteria are calibrated using previously reported measured values of flow stress ratios and strain ratios obtained from uniaxial tensile tests and disc compression tests. The results from the model calibrations show that Yld2004-18p gives improved prediction. The evaluation of the selected yield functions is extended by performing numerical simulations of in-plane shear tests and plane-strain tension tests using the general-purpose non-linear FE code LS-DYNA. The results from the simulations show that the constitutive model based on Yld2000-2d predicts too low strength for the determined model parameters and indicates that the shape of the yield surface is inadequate. Predictions with the constitutive model based on Yld2004-18p gave better agreement with the experiments.

튜브 액압성형품의 가공 경화 특성 연구

Strain hardening behavior during hydroforming has been experimentally investigated. The variation of flow stress was used as an index of strain hardening during respective processes and the flow stress was estimated from the correlationship between flow stress and effective strain. The local hardness after hydroformig was also predicted by effective strain. By using the inter-relationships between hardness-flow stress-effective strain at variable pre-strains, the strain hardening behavior during hydroforming has been successfully analyzed. The comparison of predicted hardness with measured hardness confirmed that the methodology used in this study was feasible and the strain hardening behavior can be quantitatively estimated.

Work hardening characteristics of copper from constant strain rate and stress relaxation testing

Tensile tests interrupted by stress relaxation periods were carried out on copper specimens at different temperatures and strain rates. Strain rates before and after stopping the cross-head were determined. Rather than interpreting the difference to be due to mechanically activated deformation, as has been considered elsewhere, deformation was considered to be thermally activated with a component responsible for hardening and a component unaccompanied by hardening. From a rate equation that can describe thermally activated glide controlled deformation, flow stresses were calculated from the strain rate differences together with the strains estimated to be due to the hardening component of deformation. Flow stress–strain curves so obtained were found to be independent of testing temperature and tensile strain rate. These curves were compared to hardening curves determined previously from constant force creep tests and were found to be similar.

Application of Complete Gurson Model for Prediction of Ductile Fracture in Welded Steel Joints

Ductile fracture process includes three stages: void nucleation, their growth and coalescence. The voids nucleate due to the fracture or separation of non-metallic inclusions and secondary-phase particles from the material matrix. Micromechanical models based on the Gurson plastic flow criterion are often used for analysis of ductile fracture. They consider the material as a porous medium in which the effect of voids on the stress-strain state and plastic flow cannot be neglected. Another important property of the Gurson criterion is that the hydrostatic stress component influences the plastic flow of the material.

The Influence of Cell Shape Anisotropy on the Tensile Behavior of Open Cell Aluminum Foam

Tensile tests have been performed on annealed (AN) and heat treated (HT) Duocel open cell aluminum foam (20 PPI) samples for relative densities ranging between 3 and 13%. The long axis of the cell was oriented longitudinal (LD) or transverse (TD) to the loading direction to observe the effect of the cell shape anisotropy on the tensile behavior. During the tensile tests the evolution of damage was monitored by measuring the electrical resistance. All changes in the tensile behavior between orientations, such as the flow stress, peak stress and peak strain, can be explained by both the cell shape anisotropy and the change in damage evolution.

A numerical approach to determine flow stress–strain curve of strip and friction coefficient in actual cold rolling mill

Abstract An inverse scheme-based approach for the prediction of flow stress–strain curve and friction coefficient using actual mill data is presented. The equations for roll force and forward slip are selected as the basic ones. Then they are inverted such that the deformation resistance and friction coefficient can be expressed as a function of process parameters measurable during rolling such as strip width, entrance and delivery thickness, forward and backward tensile stress, forward slip, roll force and roll diameter. A procedure for solving the inverse equations is described in detail. It includes steps which solve non-linear equation and generate the flow stress–strain curve from the data set of deformation resistances using the least square method. The capability of the present approach is verified by applying it to a reversible cold rolling mill. A good agreement is noted between the predicted flow stress–strain curve and the measured one.

A mixtures-based model for the grain size dependent mechanical behavior of nanocrystalline materials

Abstract A mixtures-based constitutive model was developed on the basis of the analysis of the real mixtures status of nanocrystalline materials. The grain boundary phase was assumed to have two equivalent parts: parts I and II. The strain of part I is the same as that of the interior of the grain, the stress of part II is equal to the sum of the total stress on the interior of the grain and that of part I of the boundary. The model developed in this paper was used to calculate Young's moduli for nanocrystalline materials. The predictions are in good agreement with the results in the literature. The model was then applied to evaluate the stress–strain relation in nanocrystalline materials. Overall, the model seems to have captured the effect of the size of the grains on the transitions of the yield strength, the strain-hardening features and the flow stress–strain relations for nanocrystalline materials.

Load relaxation behavior of a Zr 41.2Ti 13.8Cu 12.5Ni 10 Be 22.5 bulk metallic glass

The load relaxation behavior within the supercooled liquid region of Zr 41.2Ti 13.8Cu 12.5Ni 10Be 22.5 bulk metallic glass has been investigated. To explain the relationship between normalized stress and relaxation time, two different stress relaxation modes such as a Kohlrausch–Williams–Watts (KWW) behavior and a simple power law were applied to the short and long relaxation time regimes, respectively. The apparent activation energy for stress relaxation is 126 ± 10 kJ/mol. Flow curves were obtained by converting load–displacement data into a flow stress–strain rate relation, resulting in three different deformation characteristics through a wide strain rate region interpreted in terms of strain rate sensitivity. A prediction of hot workability has also been attempted by constructing a power dissipation map based on a dynamic materials model.

Hot Compression Behavior of As-Cast Precipitation-Hardening Stainless Steel

High temperature deformation characteristics of a semiaustenitic grade of precipitation-hardening stainless steels were investigated by conducting hot compression tests at temperatures of 900—1 100 °C and strain rates of 0. 001—1 s−1. Flow behavior of this alloy was investigated and it was realized that dynamic recrystallization (DRX) was responsible for flow softening. The correlation between critical strain for initiation of DRX and deformation parameters including temperature and strain rate, and therefore, Zener-Hollomon parameter (Z) was studied. Metallographic observation was performed to determine the as-deformed microstructure. Microstructural observation shows that recrystallized grain size increases with increasing the temperature and decreasing the strain rate. The activation energy required for DRX of the investigated steel was determined using correlations of flow stress versus temperature and strain rate. The calculated value of activation energy, 460 kJ/mol, is in accordance with other studies on stainless steels. The relationship between peak strain and Z parameter is proposed.

3D nano-scale cutting model for nickel material

Abstract This paper proposes a method that combines molecular dynamics with finite element deformation model (MDFM) to calculate the stress and strain of a single crystal nickel material that occur during the nano-scale cutting by concial tool. The flow stress–strain curve used in the MDFM model was obtained by nano-scale tension simulation using molecular dynamics method in this paper. Since the Young's modulus of the nano-scale single crystal nickel material is different from macroscopic scale. Therefore, the Young's modulus of the single crystal nickel material used in the MDFM model was obtained through a nano-indentation test under very low indentation loading. The MDFM only requires the elastic–plastic constitutive equation. The position and displacement components of atom in any temporary situation during nano-scale cutting could be found by using the 3D MD simulation. The atom is regarded as a node and the lattice is regarded as an element. The shape function concept of FEM is applied to calculate the strain of element from atom displacement. After simulation, it can be found that the accumulation behavior of cutting chip done by nano-cutting is quite similar to macroscopic cutting. This paper also finds that residual stress and residual strain will remain on the machined surface of single crystal nickel after cutting.

Development of processing maps for Al/SiC p composite using fuzzy logic

In the present study the aluminium reinforced with 10% SiC p particulate composites were produced through powder metallurgy route and processing map was developed. The composite specimens were subjected to compression test at different strains, strain rates and temperatures. Using the load-stroke data, flow stress–strain were evaluated. Fuzzy logic has been implemented for the prediction of flow stress. Power dissipation efficiency and instability parameter were evaluated and plotted with temperature and stain rate using the predicted values of flow stress from fuzzy logic. The contour plots were superimposed to obtain the processing maps. The dynamic recrystallisation zones and instable zones were identified and validated through micrographs. The processing maps can be used to select optimum strain rates and temperatures for effective hot working of Al/10% SiC composites.

Microstructure Changes in Alloy AZ31B in Semisolid State and Its Mechanical Properties

The structural changes of the wrought magnesium alloy AZ31B in semisolid state were clarified using optical microscopy and hot-stage microscopy. The influence of heat treatment variables was assessed. Compression tests covering a range from room temperature to 673 K were carried out for mechanical property assessment; flow stress and breaking strain were determined. The following are the results: (1) The grain growth of the hot-extruded AZ31B without preprocessing sensitively reacted at temperature and retention time. (2) The hot-extruded AZ31B with 30 % preprocessing showed an almost perfectly spheroidized structure in a semisolid state under certain conditions. (3) Heating velocity markedly affected the spheroidizing rate of grains. (4) From the direct observation of the hot-extruded alloy AZ31B by hot-stage microscopy, spheroidization was observed in some crystal populations. (5) Spheroided materials in the semisolid temperature range had a lower flow stress and a larger breaking strain than nonspheroidized materials. These results indicate the possibility of manufacturing wrought magnesium alloy by cold working.

Characterization on ferrite microstructure evolution during large strain warm torsion testing of plain low carbon steel

Ferrite grain/subgrain structures evolution during the extended dynamic softening of a plain low carbon steel was investigated throughout the large strain warm deformation by hot torsion. Microstructural analysis with electron back-scattering diffraction (EBSD) scanning electron microscope (FEG/SEM) was carried out on the ferrite microstructural parameters. The results showed that the warm flow stress–strain curves are similar to those affected only by dynamic softening and an extended warm flow softening is seen during large strain deformation up to 30. Furthermore, with an increase in strain up to ∼1 the grain size of ferrite, misorientation angle and fraction of high-angle boundaries gradually decrease and fraction of low-angle boundaries increases. With a further increase in the strain beyond ∼2, these parameters remain approximately unchanged. No evidence of discontinuous dynamic recrystallisation involving nucleation and growth of new grains was found within ferrite. Therefore, the dynamic softening mechanism observed during large strain ferritic deformation is explained by continuous dynamic recrystallization (CDRX).

Impact and fracture response of sintered 316L stainless steel subjected to high strain rate loading

This paper describes the use of a material testing system (MTS) and a compressive split-Hopkinson bar to investigate the impact behaviour of sintered 316L stainless steel at strain rates ranging from 10 − 3 s − 1 to 7.5 × 10 3 s − 1 . It is found that the flow stress–strain response of the sintered 316L stainless steel depends strongly on the applied strain rate. The rate of work hardening and the strain rate sensitivity change significantly as the strain rate increases. The flow behaviour of the sintered 316L stainless steel can be accurately predicted using a constitutive law based on Gurson's yield criterion and the flow rule of Khan, Huang and Liang (KHL). Microstructural observations reveal that the degree of localized grain deformation increases at higher strain rates. However, the pore density and the grain size vary as a reversible function of the strain rate. Impacts at strain rates higher than 5.6 × 10 3 s − 1 are found to induce adiabatic shear bands in the specimens. These specimens subsequently fail as a result of crack propagation along the dominant band. The fracture surfaces of the failed specimens are characterized by dimple-like structures, which are indicative of ductile failure. The depth and the density of these dimples are found to decrease with increasing strain rate. This observation indicates a reduction in the fracture resistance and is consistent with the observed macroscopic flow stress–strain response.