Plastic Strain Regime Research Articles

Evolution of dislocation and stacking-fault densities for a Cu-0.7Cr-0.07Zr alloy during cryogenic tensile test: An in-situ synchrotron X-ray diffraction analysis

Processing at cryogenic temperatures is one of the ways of improving mechanical properties of copper alloys. However, such processing routes may result in unstable microstructures, which make it difficult to understand the deformation mechanisms controlling microstructure evolution during cryogenic deformation. In this study, the microstructure evolution of a Cu-0.7Cr-0.07Zr alloy was analyzed as a function of the flow behavior during tensile tests performed at 123 K and 298 K, through in-situ X-ray diffraction (XRD) experiments in a synchrotron source. The tensile behavior was analyzed in terms of the dynamic recovery rate using the Kocks-Mecking model, while the evolution of stacking-fault density, dislocation density and crystallite size during the tests was estimated by the modified Williamson-Hall method. Solution-treated and peak-aged conditions were tested to assess the influence of particles distribution. At 298 K, the strain-hardening rate was controlled by dislocation glide and the flow stress was affected mainly by particle strengthening. At 123 K, a simultaneous increase in strength and ductility was attributed to the twinning induced plasticity (TWIP) effect, promoted by precipitate interfaces acting as nuclei for stacking-faults, thus delaying necking and increasing the plasticity. Based on the evolution of dislocation and stacking-fault densities with increasing plastic strain, it was concluded that, at 123 K, mechanical twinning predominated at strain levels below 0.15, mainly for aged conditions, while dislocation glide between twin boundaries, and its accumulation, started after TWIP mechanism reached its saturation. • In-situ synchrotron X-ray diffraction of Cu-0.7–0.07Zr has been performed. • Solutionized and peak-aged conditions were evaluated at 298 K and 123 K. • Both temperature and precipitates affected the plastic strain regime. • At 123 K, mechanical twinning predominated at strains below 0.15. • Twinning induced plasticity (TWIP) effect occurred during plastic flow at 123 K.

Mechanistic Modeling of Strain Hardening in Ni-Based Superalloys

This article presents a mechanistic approach for modeling the strain hardening response of polycrystalline Ni-based superalloys such as ME3, RR 1000, Alloy 720 Li, and IN 100. The mechanistic approach considers strain hardening in Ni-based superalloys in two stages: (a) self-hardening of individual {111} slip systems in the low plastic strain regime and (2) latent hardening of multiple {111} slip systems in the high plastic strain regime. Both strain hardening regimes have been modeled on the basis of interactions of superkinks with Kear–Wilsdorf locks and related to pertinent microstructural parameters such as the volume fractions of γ′ precipitates, grain orientation, and dislocation substructure. The mechanistic strain hardening model predicts that the strain hardening exponents in both the low plastic strain (n1) and the high plastic strain (n2) regimes increase with increasing values of the sum of the squares of the volume fractions of the primary and secondary γ′ precipitates, the number of {111} and {010} slip systems activated, and the critical height of the superkinks. A comparison of model predictions against experimental strain hardening exponents indicates good agreement between model predictions and experimental data. Implications of the operative strain hardening mechanisms during low-cycle fatigue and high-cycle fatigue are elucidated.

Determining the effective hydrogen diffusion coefficient in 100Cr6

AbstractIn the present study, the diffusion constant for hydrogen in hardened 100Cr6 was measured in permeation tests. The tests were conducted on samples of different thicknesses. The diffusivity of hydrogen was also measured in prestrained samples to study the influence of plastic strain on the diffusion rate. A finite element‐based diffusion model was applied to confirm the experimental results by computing the concentrations of diffusible hydrogen and trapped hydrogen due to deformation‐induced defects. The results showed that the concentration of trapped hydrogen remained very low throughout the plastic strain regime under consideration. The average effective diffusion coefficient of hydrogen in 100Cr6 at 30°C was found to be Deff = 4.9 × 10−12 m2/s.

Effect of initial dislocation density on hydrogen accumulation behavior in martensitic steel

We investigated hydrogen accumulation behavior of martensite structures with different initial dislocation densities. The hydrogen micro-print technique and microstructure observation revealed that the higher initial dislocation density facilitated hydrogen accumulation around prior austenite grain boundaries during deformation within the apparent elastic strain regime. In contrast, once deformation was applied to the plastic strain regime, hydrogen accumulation behavior did not change with initial dislocation density. Based on the obtained results, we concluded that transportation of hydrogen by dislocation motion played an important role on hydrogen accumulation around prior austenite grain boundaries.

MicroROM: A Physics-Based Constitutive Model for Ni-Based Superalloys

In this article, a physics-based constitutive model is developed for representing the stress–plastic strain response of Ni-based superalloys by considering the hardening mechanisms that contribute to the macroscopic yield stress and the subsequent strain-hardening response in order to derive the entire tensile stress–strain curve. It is demonstrated that the log stress vs log plastic strain curves of Ni-based superalloys such as 702 Li and ME3 exhibit a bilinear behavior with a lower strain-hardening exponent in the low plastic strain regime and a much higher strain-hardening exponent in the high plastic strain regime. These two hardening regimes can be modeled on the basis of self-hardening of individual slip planes and latent hardening of five operative independent slip systems due to cross-slip from {111} planes to {001} planes, leading to the formation of incomplete and complete Kear-Wilsdorf locks. The proposed physics-based constitutive model, dubbed as MicroROM, exhibits a form that is similar to the Ramberg–Osgood (RO) constitutive model, which is widely used in structural analyses of engineering designs and components. MicroROM is applied to predict the tensile stress–strain curves of 720 Li and ME3 with either a subsolvus or supersolvus microstructure for temperatures ranging from 24 °C to 815 °C. The agreement is good between model predictions and experiment data from the literature. The sensitivity of the predicted stress–strain response to individual microstructural parameters is highlighted and the relation to individual hardening mechanisms is elucidated.

A Study of Tensile Flow and Work-Hardening Behavior of Alloy 617

The simple power relationship σ = Κe satisfactorily expresses the tensile flow behavior of many metals and alloys in their uniform plastic strain regime. However, many FCC materials with low stacking fault energy have opposed such power law relationship. Alloy 617, an age-hardenable Ni-based superalloy is also observed not to obey the simple power law relationship neither in its solution-treated nor in its aged conditions. Various flow relationships were used to obtain the best fit for the tensile data, and different relationships were identified for the different aged conditions. The work-hardening rate (θ) demonstrates three distinct regions for all aged conditions, and there is an obvious change in the trend of θ versus σ. In the initial portion, θ decreases rapidly followed by a gradual increase in the second stage and again a decrease in its third stage is perceived in the Alloy 617. These three-stage characteristics are attributed to a commonly known precipitate, γ′: Ni3(Ti, Al) which evolves during aging treatment and well recognized under transmission electron microscopy (TEM) observation. TEM results also reveal a slight degree of coarsening in γ′ over aging. The tensile flow and the work-hardening behavior are well correlated with other microstructural evolution during the aging treatments.

A fractional transient model for the viscoplastic response of polymers based on a micro-mechanism of free volume distribution

In the present work, the nonlinear viscoelastic/viscoplastic response of polymeric materials is described by introducing essential modifications on a model developed in previous works. A constitutive equation of viscoelasticity, based on the transient network theory, is introduced in a more generalized form, which takes into account volume changes during deformation. This time-dependent equation accounts for the nonlinearity and viscoplasticity at small elastic and finite plastic strain regime. The present description was proved to be more flexible, given that it contains a relaxation function that has been derived by considering instead of first order kinetics a fractional derivative that controls the rate of molecular chain detachment from their junctions. Therefore, the new equation has a more global character, appropriate for cases where heavy tails are expected. On the basis of the distributed nature of free volume, a new functional form of the rate of plastic deformation is developed, which is combined with a proper kinematic formulation and leads to the separation of the total strain into the elastic and plastic part. A three-dimensional constitutive equation is then derived for an isotropic, compressible medium. This analysis was proved to be capable of capturing the main aspects of inelastic response as well as the instability stage taking place at the tertiary creep, related to the creep failure.

Dynamic tensile behavior of electron beam additive manufactured Ti6Al4V

High rate and quasi-static tensile experiments examined strain rate dependence on flow stress and strain hardening of additive manufactured Ti6Al4V. Variations on strain-hardening coefficient indicate that the rate of thermal softening is greater than strain hardening during plastic deformation. Strain rate sensitivity calculations within the plastic strain regime suggest changes in deformation mechanisms. Fractography revealed cup-and-cone fracture for quasi-static samples and shear mechanisms for high rate samples. As-deposited microstructure consisted of bimodal α+β with the presence of secondary martensitic phase.

Deformation and fracture behavior of commercially pure titanium with gradient nano-to-micron-grained surface layer

Titanium with gradient nano-to-micron scale grains from surface to matrix was fabricated by surface mechanical grinding treatment (SMGT) at room temperature. The SMGT-treated titanium shows higher strength than that of as-received one, but moderate ductility between those of ultra-fine grained (UFG) and coarse-grained titanium. Tensile stress–strain curves of SMGT-treated titanium show double strain hardening regimes. The strain hardening rate (dσ/dɛ) decreases with increasing strain in tensile deformation. The high strain hardening rate at initial yielding is attributed to nano-to-micron-grained surface layer. The low strain hardening rate at large plastic strain regime primarily results from coarse-grained matrix. The SMGT-treated titanium shows a ductile fracture mode with a large number of dimples. The small size of dimples in the treated surface layer is due to the combination of the high strength and strain hardening exponent. The difference between dimple size in nano-to-micron-grained surface layer and coarse-grained matrix is discussed in terms of plastic zone size at the tip of crack in the SMGT-treated titanium.

Microstructural evolution and the variation of tensile behavior after aging heat treatment of precipitation hardened martensitic steel

The effects of aging temperature on the microstructural evolution and the tensile behavior of precipitation hardened martensitic steel were investigated. Microscopic analysis using transmission electron microscope (TEM) was combined with the microstructural analysis using the synchrotron X-ray diffraction (XRD) to characterize the microstructural evolution with aging temperature. Peak hardness was obtained by precipitation of the Ni3Al ordered phase. After aging at temperature range from 420 to 590°C, spherical Ni3Al precipitates and ellipsoidal M23C6 carbides were observed within laths and at lath boundaries, respectively. Strain hardening behavior was analyzed with Ludwik equation. It is observed that the plastic strain regimes can be divided into two different stages by a rapid increase in strain hardening followed by a comparatively lower increase. At the first strain hardening stage, the aged specimen exhibited higher strain hardening exponent than the as-quenched specimen, and the exponent in the aged specimen was not changed considerably with increasing aging temperature. It is revealed that the strain hardening exponents at the first and the second stages were associated with the Ni3Al precipitates and the domain size representing the coherent scattering area, respectively.

Serration behavior and shear band characteristics during tensile deformation of an ultrafine-grained 5024 Al alloy

The main objective of this work is to understand the major deformation mechanisms operative in the entire plastic strain regime of an ultrafine-grained (UFG) 5024 Al alloy. The initial microstructure in both coarse-grained (CG) and UFG conditions was characterized by transmission electron microscopy and orientation imaging microscopy to better correlate the observed deformation behavior with the microstructural elements. The engineering stress–strain curves in both CG and UFG conditions were serrated from onset of yielding to the point of sample failure although the net intensity of the serrations varied in both the conditions. Interrupted tensile testing with corresponding surface analysis using scanning electron microscopy (SEM) was carried out to clearly demarcate the micro-mechanisms operative in various plastic strain regimes. The serration amplitude as a function of time in UFG material was studied and displayed a different behavior when compared with CG material. The reason for higher non-uniform elongation has been explained in terms of micron-sized shear bands and void coalescence mechanism. Dislocation slip was observed to be the major strain accommodation mechanism, along with shear bands and grain rotation. Analysis of failed specimen surfaces using SEM further assisted in understanding and quantifying the damage accumulation and failure mechanism.

Strain-dependent transition of time-dependent deformation mechanism in single-crystal ZnO evaluated by spherical nanoindentation

We have systematically explored the time-dependent plasticity of (0 0 0 1)-oriented ZnO single crystal through spherical indentation tests. Constant load indentation creep tests were performed in elastic strain and elastic–plastic strain regimes. In both regimes, creep indeed occurred at ambient temperature. With the observed quasi-steady-static strain rate, the stress exponent was found as ~1.361 for elastic contact regime and ~3.077 for elastic–plastic regime, suggesting predominant creep mechanism of diffusion and dislocation, respectively. This strain-dependent transition of creep mechanism is discussed in terms of possible factors affecting the creep in each regime.

Viscoplastic response and creep failure time prediction of polymers based on the transient network model

The nonlinear viscoelastic/viscoplastic response of polymeric materials is described by a new model based on previous works in terms of monotonic loading, stress–relaxation, and creep. In the proposed analysis, following a constitutive equation of viscoelasticity, based on the transient network theory, essential modifications are introduced, which account for the nonlinearity and viscoplasticity at small elastic and finite plastic strain regime. In addition, viscoplastic response is successfully analyzed by a proper kinematic formulation, which is combined with a functional form of the rate of plastic deformation. A three-dimensional constitutive equation is then derived for an isotropic incompressible medium. This analysis is capable of capturing the main aspects of inelastic response and the instability stage taking place at the tertiary creep, related to the creep failure. Model simulations described successfully the experimental data of polypropylene, which were performed elsewhere.

Temperature dependent dynamics transition of intermittent plastic flow in a metallic glass. II. Dynamics analysis

By reducing the testing temperatures down to the temperature well below the glassy transition temperature, the serrated flow behaviour during plastic deformation of a Zr-based metallic glass was experimentally investigated and the results were presented in Part I of the present paper. It shows that the yield strength, the plastic deformation ability, the density of shear bands of the metallic glass increase with decreasing temperature. In order to understand the mechanisms for the changes of the mechanical behaviour at low temperatures, in Part II of this study, the stress-time sequence in the plastic strain regime is characterized by a comprehensive dynamical and statistical analysis. The stress-time sequence is found to exhibit a chaotic state at high temperatures (>203 K), whereas a self-organized critical state is obtained at low temperatures (≤203 K) due to the freezing effect. The reasons for the transition between these two distinct spatio-temporal dynamical states are elucidated by investigating the effect of temperature on the deformation units (shear transformation zones) and the elastic interactions between neighbouring shear bands. The results demonstrate that the low temperatures results in an enhancement of the interactions between the elastic strain fields initiated by neighbouring shear bands, which is primarily responsible for the enhanced plasticity of the metallic glass and a dynamics transition.

Strain-induced martensite formation in austenitic stainless steel

In situ measurements of the strain-induced martensitic transformation (SMTs) of SUS304 stainless steel that takes place during tensile loading at room temperature were performed around the notch of a dumbbell-shaped specimen where high stress concentration occurs. Even in the low plastic strain regime, with loading to 0.2 % proof stress (σ 0.2), some SMTs occurred. However, the area fraction of the Fe-α′-martensite phase did not increase significantly even when the sample was loaded to the ultimate tensile strength (σ UTS). After the σ UTS point, the total fraction of the Fe-α′ phase increased dramatically to the fracture point (σ f). The phase textures of Fe-α′ and Fe-γ were almost equal at (σ UTS − σ f)/2, and the Fe-α′ phase was observed over almost the entire measurement area around the notch at the σ f point. However, the area fraction of the Fe-α′ phase at the σ f point decreased far away from the fracture surface, to an extent that the total fraction of the Fe-α′ phase was almost the same as that of the Fe-γ phase in an area about 1.7 mm from the fracture face. Different martensite characteristics were detected in the stainless steel, depending on the applied load level. This was attributed to the severity of deformation. In particular, deformation twinning, created around σ UTS, and severe plastic deformation before fracture make a strong Fe-α′ phase. Details of this phenomenon are interpreted using various approaches, including electron backscatter diffraction analysis and finite element analysis.

Plastic dynamics transition between chaotic and self-organized critical states in a glassy metal via a multifractal intermediate

Changes in intermittent serrated flow behavior during plastic deformation of Zr${}_{64.13}$Cu${}_{15.75}$Ni${}_{10.12}$Al${}_{10}$, a representative glassy metal with characteristic ductility, in response to variant strain rates and temperatures were examined. The influence of strain rates and environmental temperatures on the stress-time sequence of the plastic strain regime was investigated using comprehensive dynamical, statistical, and multifractal analyses. Three distinct spatiotemporal dynamical regimes were explored. Under small strain rates or high temperatures, the time-stress sequence exhibited a chaotic behavior. Conversely, under large strain rates or low temperatures, a transition to the self-organized critical state was observed. In addition to chaotic time series and statistical analysis, multifractal analysis was also applied to study the crossover between these two unique plastic dynamic transitions. This plastic dynamical behavior was elucidated based on the interactions between shear avalanches in the glassy metal.

A Comparison of Fatigue Properties of Austempered Versus Quenched and Tempered 4340 Steel

This study was conducted to determine if austempered 4340 steel had different fatigue resistance compared to quench and tempered (Q&T) 4340 steel with an identical hardness of nominally 45 HRC and an identical yield strength of nominally 1340 MPa (194 ksi). Strain-life and stress-life fatigue testing was conducted at room temperature under identical test conditions. The standard array of strain-life and stress-life regression constants was obtained. The two heat treatments produced virtually identical total strain-life curves and fatigue limits at 5 million cycles. However, the two materials exhibited different trends in the elastic and plastic strain regimes. The austempered steel exhibited greater high cycle fatigue (finite) lives than the Q&T samples at comparable elastic strain amplitudes in strain-life fatigue testing and at comparable stress amplitudes in stress-life fatigue testing. However, the Q&T samples exhibited greater low cycle fatigue lives than the austempered samples at comparable plastic strain amplitudes in strain-life testing. Although both materials generally exhibited similar fatigue fracture characteristics, the overload regions of the Q&T samples were composed entirely of dimple rupture, whereas the austempered samples exhibited both dimple rupture and quasicleavage.

Influence of short time annealing on strain hardening rate and flow stress of ultrafine grained material processed by severe plastic deformation

In this paper, the ultrafine grained (UFG) copper achieved by the equal channel angular pressing method was annealed at 473 K for 2 min and compressed at room temperature under quasi‐static loading condition. The experimental results show that virtually no strain hardening is observed after an initial rapid strain hardening over a small plastic strain regime. While for the as recieved material, slight strain softening is even observed at room temperature. At the same time, the annealed UFG copper also displays higher flow stress than its as received counterpart. Although there are several mechanisms including dynamic recovery and dynamic recrystallisation proposed to explain the strain softening in nanocrystalline or UFG metals, the fact that enhancements in strain hardening and flow stress after annealing cannot be explained. Based on the experimental results, it is proposed that residual internal stress formed during the fabrication of the UFG material may be a main reason for the enhancements of strain hardening and flow stress of annealed UFG copper.

Extension of generalized plasticity to finite deformations and non-linear hardening

The generalized plasticity model, as presented by Lubliner, 1991 , Lubliner et al. (1993) and Auricchio et al. (1992) , is a generalization of classical rate-independent plasticity with a yield surface. This material model is able to describe a reloading transient during the reloading process of a specimen, which is shown in the asymptotic approach of the reloading curve to the initial load curve in the stress–strain diagram, as observed in Lubhahn and Felger, 1961 for copper or in Greenstreet et al. (1971) for graphite. In the present paper an advantageous extension of the generalized plasticity model to finite plastic strain regimes is given. Classical plasticity and the model in Auricchio and Taylor (1995) for linear kinematic and isotropic hardening rules are included as special cases in the proposed concept. It will be shown that the suggested modification yields a mathematically simple structure of the constitutive relations and an efficient stress algorithm, adaptable to finite element programs similar to that in Auricchio and Taylor (1995) . Special attention is focused on a correct treatment of the loading criteria.