Strain Rate Dependence Of Flow Stress Research Articles

Temperature and strain-rate dependence of flow stress of nanocrystalline nickel fabricated by electrolytic deposition

ABSTRACT Nanocrystalline nickel, having a grain size of about 40 nm, was fabricated by electrolytic deposition and strain-rate jump tests were performed at temperaures between 77 and 473 K to obtain the strain-rate sensitivity and the activation volume . The values of changed from about 0.05 to about 0.005 with increasing stress, indicating that the deformation is governed by the motion of glide dislocations. increased as the temperature increased from 77 to 200 K, but decreased with further increase in temperature. It is concluded that the rate-controlling deformation mechanism in nanocrystalline nickel is temperature sensitive and changes from forest dislocation cutting to dislocation bowing-out and depinning from grain boundaries as the temperature increases.

Numerical simulation of hybrid joining processes: self-piercing riveting combined with adhesive bonding

Reliable simulation of hybrid joining processes using conventional finite element (FE) tools is challenging, because the liquid adhesive must be somehow included in the model. Thus, in this work the viscoelastic properties of the adhesive are substituted with “equivalent” mechanical properties. The complex viscosity of an epoxy-based single-component adhesive was determined at five temperatures between 20‒55 °C and at seven shear rates between 1‒150 s-1 using a rheometer. Flow stresses and strain rates were calculated from the complex viscosities and from the shear rates. For each temperature investigated the relationship between flow stress and strain rate was fitted with a power-law, which enables modeling the actually liquid adhesive as solid with strain rate-dependent flow stress. In order to validate the material model, a defined volume of adhesive was uniaxially compressed. This testing setup was also modelled using the FE software Simufact Forming 15. In the model the Young’s modulus of the adhesive was iteratively adapted until good agreement between the numerical and the experimental force-displacement curves was achieved. The obtained mechanical properties were finally used for modeling the adhesive layer between two 2.0 mm-thick 6xxx aluminum alloy blanks in the hybrid riveting-bonding process. An axisymmetric model including deformable (rivet, upper blank, lower blank, adhesive layer) and rigid (punch, die, blankholder) components was built in Simufact Forming. The cross-section of the hybrid joint obtained from simulation showed very good geometrical agreement with cross-sections obtained from the joining experiments, and just small differences between the calculated and the measured force-displacement curves was observed.

Dynamic Steady State by Unlimited Unidirectional Plastic Deformation of Crystalline Materials Deforming by Dislocation Glide at Low to Moderate Temperatures

This paper presents an outline of the quest for the mechanical steady state that an unlimited unidirectional plastic strain applied at low to moderate temperature is presumed to develop in single-phase crystalline materials deforming by dislocation glide, with particular emphasis on its athermal strength limit. Fifty years ago, the study of crystalline plasticity was focused on the strain range covered by tensile tests, i.e., on true strains less than unity; the canonic stress–strain behavior was the succession of stages I, II, and III, the latter supposedly leading to a steady state defining a temperature and strain rate-dependent flow stress limit. The experimentally available strain range was increased up to Von Mises equivalent strains as high as 10 by the extensive use of torsion tests or by combinations of intermittent deformations by wire drawing or rolling with tensile tests during the 1970s. The assumed exhaustion of the strain-hardening rate was not verified; new deformation stages, IV and V, were proposed, and the predicted strength limit for deformed materials was nearly doubled. Since the advent of severe plastic deformation techniques in the 1980s, such a range was still significantly augmented. Strains of the order of several hundreds were routinely reached, but former conclusions relative to the limit of the flow stress were not substantially changed. However, very recently, the plastic strain range has allegedly been expanded to 105 true strain units by using torsion under high pressure (HPT), surprisingly for some common metals, without experimental confirmation of having reached any steady state. This overview has been motivated by the scientific and technological interest of such an open-ended story. A tentative explanation for the newly proposed ultra-severe hardening deformation stage is given.

Dynamic Strain Aging and Serration Behavior of Three High-Manganese Austenitic Steels

The strain-rate dependence of the flow stress of three high-manganese austenitic steels with different compositions was studied in terms of dynamic strain aging and serration behavior at room temperature under quasi-static strain-rate ranges from 10−4 to 10−1 s−1. Tensile stress–strain curves showed that serrated flow occasionally appeared and the strain-rate dependence of flow stress was measured to be negative at all strains for Fe-22Mn-0.3C and Fe-30Mn-0.2C steels and at higher strain for Fe-30Mn-0.2C-1.5Al steel. Based on the tendency for a critical strain corresponding to the onset strain of serrated flow and electron back-scattered diffraction analysis, it was found that serrated flow was not induced by deformation twinning and $$ \gamma \to \varepsilon $$ martensitic transformation, but by dynamic strain aging associated with the interaction between partial dislocation and solute carbon. Also, the addition of Al content increased the critical strain, meaning that it effectively prohibits dynamic strain aging. In addition, dynamic strain aging promoted deformation twinning and/or $$ \gamma \to \varepsilon $$ martensitic transformation and resulted in negative strain-rate dependence of flow stress in the high-manganese austenitic steels.

Analysis of rate dependency on roll force calculation during hot strip rolling based on Karman equation

Due to the development of thin slab hot rolling technology, hot rolling thin strip at a higher speed is inevitable. As a result of high-speed rolling, thin slab is deformed at a wide range of strain rate inside the rolling zone. Because the flow stress of steel is strongly dependent on strain rate at elevated temperature, it is imperative to consider its variation when calculating roll force and roll pressure. By substituting time with speed and length, strain rate variation is obtained. A strain rate–dependent flow stress curve for non-oriented silicon steel is implemented into Karman equation to calculate rolling pressure distribution. It is revealed that the rolling force can be effectively reduced by decreasing the radius of work roll. It is further revealed that the appearance of strip/roll surface sticking is more likely at the exit of rolling zone than the neutral point, because strain rate reaches zero and the flow stress drops at the exit. Combined with Influence Function Method for elastic deformation of roll surface, the proposed model can predict roll force with a good accuracy compared with industrial data.

Effect of strain rate on tensile and serration behaviors of an austenitic Fe-22Mn-0.7C twinning-induced plasticity steel

In this study tensile and serration behaviors of an austenitic Fe-22Mn-0.7C twinning-induced plasticity steel was investigated in terms of dynamic strain aging and deformation twinning. Under quasi-static strain rate range, serrated flow and negative strain-rate dependence of flow stress were found during room-temperature tensile testing. The serrated flow is closely related to dynamic strain aging induced by the interaction of dislocation and interstitial carbon. In order to understand the flow stress contribution of strain hardening rate and strain rate sensitivity, strain rate jumping test was performed. The results showed that the negative strain-rate dependence of flow stress was more dependent on strain hardening rate factor than strain rate sensitivity factor by dynamic strain aging. EBSD and TEM analysis revealed that the higher strain hardening rate at lower strain rate was attributed to the higher fraction and finer thickness of deformation twin. The localized stress accompanied by dynamic strain aging plays an important role in twinning process since it decreases effective stacking fault energy and promotes deformation twinning in localized region at lower strain rate.

Strain Rate Dependent Flow Stress Characterization Using Piezo-actuated Micropress

The effect of strain rate on the mechanical response during microforming deformation is investigated for commercially pure titanium and aluminum. Piezoelectric actuated micropress is used to generate controlled constant strain rate between 0.1 and 10 sec-1 in a compression experiment using three different sizes of specimens. Investigations suggest that the increase of free and constrained surface grains results in hardening-softening competition with miniaturization. In addition, loading rate in micro compression significantly influence the work hardening behavior for both materials.

A meshfree study of the Kalthoff–Winkler experiment in 3D at room and low temperatures under dynamic loading using viscoplastic modelling

A new model for studying the fracturing of metals under impact using Smoothed Particle Hydrodynamics is presented. The model combines a temperature and strain rate dependent flow stress with a criterion for brittle fracture and is suitable for metallic materials undergoing high strain rate loadings. First, the well documented Kalthoff–Winkler experiment was used to validate our approach. A series of simulations was then conducted to model the behaviour of a 4340 steel at 223K (−50°C) under different impact speeds to investigate the simultaneous effect of temperature and impact velocity towards the failure of the material. In some cases a lower temperature brought about failure for the same impact velocity, highlighting the role of combining factors in failure analysis. This paper demonstrates the relevance of SPH in the prediction of the initiation and propagation of brittle cracks in structures, thus opening new areas for future research.

Suzuki segregation in Co–Ni-based superalloy at 973 K: An experimental and computational study by phase-field simulation

Suzuki segregation in Co–Ni-based superalloys is of longstanding interest. In this study, the development of widely extended stacking fault (SF) ribbons was confirmed in a Co–Ni-based superalloy aged at 973K after deformation at room temperature, which supports the decrease in stacking fault energy (SFE) due to Suzuki segregation. In addition, the plastic deformation behaviors of Co–Ni-based superalloys with various Nb contents up to 3wt.% were investigated focusing on the effect of Nb addition on dynamic strain-aging by Suzuki segregation. The negative strain-rate dependence of flow stress due to dynamic strain-aging became more significant with increasing Nb content; however, attempts to detect segregating elements by scanning transmission electron microscopy and energy-dispersive spectroscopy analysis were not successful. A phase-field simulation of Suzuki segregation suggested strong Ni depletion with segregation of Cr and Mo atoms at the SF, and the SFE can become negative as a consequence of the segregation. This agrees with the experimentally observed formation of wide SFs by the aging at 973K after cold deformation. It is also suggested that Nb atoms are strongly depleted at SFs, and a small amount of Nb addition dramatically enhances Cr segregation, resulting in further decreases in the SFE, which is probably responsible for the observed enhancement of dynamic strain-aging by Nb addition. In addition, the local structural changes, such as short-range ordering and/or an in-plane ordering, accompanying the segregation were discussed as possible additional mechanisms for strain-aging enhancement.

Load bearing capacity of tool pin during friction stir welding

Although friction stir welding (FSW) is now widely used for the welding of aluminum and other soft alloys, premature tool failure limits its application to hard alloys such as steels and titanium alloys. The tool pin, the weakest component of the tool, experiences severe stresses at high temperatures due to both bending moment and torsion. It is shown that the optimum tool pin geometry can be determined from its load bearing capacity for a given set of welding variables and tool and work-piece materials. The traverse force and torque during friction stir welding are computed using a three-dimensional heat transfer and viscoplastic material flow model considering temperature and strain rate-dependent flow stress of the work-piece material. These computed values are used to determine the maximum shear stress experienced by the tool pin due to bending moment and torsion for various welding variables and tool pin dimensions. It is shown that a tool pin with smaller length and larger diameter will be able to sustain more stress than a longer pin with smaller diameter. The proposed methodology is used to explain the failure and deformation of the tool pin in independent experiments for the welding of both L80 steel and AA7075 alloy. The results demonstrate that the short tool life in a typical FSW of steels is contributed by low values of factor of safety in an environment of high temperature and severe stress.

Constitutive modeling of temperature and strain rate dependent elastoplastic hardening materials using a corotational rate associated with the plastic deformation

In this paper, a constitutive model with a temperature and strain rate dependent flow stress (Bergstrom hardening rule) and modified Armstrong–Frederick kinematic evolution equation for elastoplastic hardening materials is introduced. Based on the multiplicative decomposition of the deformation gradient,new kinematic relations for the elastic and plastic left stretch tensors as well as the plastic deformation-dependent spin tensor are proposed. Also, a closed-form solution has been obtained for the elastic and plastic left stretch tensors for the simple shear problem.To evaluate model validity, results are compared with known experimental data for SUS 304 stainless steel, which shows a good agreement with the results of the proposed theoretical model.Finally, the stress-deformation curve, as predicted by the model, is plotted for the simple shear problem at room and elevated temperatures using the same material properties for AA5754-O aluminium alloy.

On the strain-rate dependence of flow stress in crystals with high intrinsic lattice friction

An analytical expression for the strain-rate dependence of the critical resolved shear stress (CRSS) (τ) of crystals with high intrinsic lattice friction has been derived within the framework of a kink-pair nucleation model of flow stress. It predicts a linear relationship between τ1/2 and at a given deformation temperature, as embodied in , where C and D are positive constants. Comparison of theory and experiment, using the wealth of data available in the literature, shows an excellent agreement between the predicted and the observed response of the CRSS to the strain rate. Evaluation of the low-temperature slip parameters of the model leads to identification of the slip system responsible for yielding of crystals.

Effects of Temperature and Strain Rate on Compressive Mechanical Properties of Ultrafine-Grained CP Titanium

Ultrafine-grained (UFG) CP Ti were successfully prepared by Equal Channel Angular Extrusion (ECAE) at 390°C~400°C, small than 0.5 um in size. The compressive tests for coarse grain (CG) and UFG Ti were carried out at room temperature (RT) and 77K. UFG Ti showed excellent ductility and higher strength than CG Ti at RT and 77 K. The strain hardening of UFG Ti was improved at 77 K. The compressive ultimate strengths of CG Ti and UFG Ti were both enhanced as the strain rate increased, but CG Ti showed more obvious temperature and strain rate dependence of flow stress, comparing with UFG Ti. When the strain rate increased to 1×10-1/s, the compressive ultimate strength of UFG Ti was kept almost constant, while the ultimate strength of CG Ti increased to the strength level of UFG Ti.

Three-dimensional heat and material flow during friction stir welding of mild steel

Three-dimensional viscoplastic flow and heat transfer during friction stir welding of mild steel were investigated both experimentally and theoretically. The equations of conservation of mass, momentum and energy were solved in three dimensions using spatially variable thermo-physical properties and a methodology adapted from well-established previous work in fusion welding. Non-Newtonian viscosity for the metal flow was calculated considering temperature and strain rate dependent flow stress. The computed results showed significant viscoplastic flow near the tool surface, and convection was found to be the primary mechanism of heat transfer in this region. Also, the results demonstrated the strong three-dimensional nature of the transport of heat and mass, reaffirming the need for three-dimensional calculations. The streamlines of plastic flow indicated that material was transported mainly along the retreating side. The computed temperatures were in good agreement with the corresponding experimentally determined values.

Modeling dynamic plasticity and spall fracture in high density polycrystalline alloys

The dynamic thermomechanical response of a tungsten heavy alloy is investigated via modeling and numerical simulation. The material of study consists of relatively stiff pure tungsten grains embedded within a more ductile matrix alloy comprised of tungsten, nickel, and iron. Constitutive models implemented for each phase account for finite deformation, heat conduction, plastic anisotropy, strain-rate dependence of flow stress, thermal softening, and thermoelastic coupling. The potentially nonlinear volumetric response in tungsten at large pressures is addressed by a pressure-dependent effective bulk modulus. Our framework also provides a quantitative prediction of the total dislocation density, associated with cumulative strain hardening in each phase, and enables calculation of the fraction of plastic dissipation converted into heat energy. Cohesive failure models are employed to represent intergranular fracture at grain and phase boundaries. Dynamic finite element simulations illustrate the response of realistic volume elements of the polycrystalline microstructure subjected to compressive impact loadings, ultimately resulting in spallation of the material. The relative effects of mixed-mode interfacial failure criteria, thermally-dependent fracture strengths, and grain shapes and orientations upon spall behavior are weighed, with interfacial properties exerting a somewhat larger influence on the average pressure supported by the volume element than grain shapes and initial lattice orientations within the bulk material. Spatially resolved profiles of particle velocities at the free surfaces of the volume elements indicate the degree to which the incident and reflected stress waves are altered by the heterogeneous microstructure.

Elevated temperature deformation behavior of discontinuous-reinforced titanium aluminide matrix composites

Abstract A series of Al 3 Ti- and near-γ TiAl-matrix discontinuously-reinforced composites have been produced and their elevated temperature flow behavior evaluated. Specifically, steady state compressive flow stress (i.e. maximum flow stress) was determined as a function of temperature (1000, 1100, 1200 °C), strain-rate (10 −3 , 10 −4 s −1 ), and composite reinforcement loading percentage (30, 40, 50 v%). The experimental results have been used to develop unified constitutive equations for each matrix type that can be used to survey the sensitivity of the respective flow behavior to the independent variables of high temperature wrought processing. The results indicate that while the temperature and strain-rate dependence of flow stress can be described in terms of a traditional Zener–Holloman (temperature-compensated strain-rate) analysis, reinforcement volume percentage may additionally represent a non-traditional but influential independent variable of processing. It is shown that particulate volume loading can be used to positively influence the deformability characteristics of the composite.

Compressive behavior of an electrodeposited nanostructured copper at quasistatic and high strain rates

Uniaxial compression experiments for an electrodeposited nanostructured copper were performed at quasistatic strain rates of 4×10 −4 s −1 and high strain rates of 3×10 3– 2×10 4 s −1 . The mechanical behavior of the nc-Cu, including strength, strain hardening and strain-rate dependence of flow stress, is presented.

Stoichiometric effect on the strain-rate dependence of flow stress in binary Ni3Al

The strain-rate dependence of the flow stress has been studied by strain-rate change test in binary, stoichiometric and Ni-rich Ni3Al single crystals at 400 K. In the stoichiometric alloys, the flow stress has been found to be independent of strain rate for all the orientations, though it changes temporarily after the strain-rate change. This stain-rate independence of the flow stress was also confirmed in Ni–24.5 at.% Al and Ni–24 at.% Al. The CRSSs of these Ni-rich alloys were the same as the stoichiometric one. These results indicate that the anti-site defects in the off-stoichiometric alloy have very little effect on the dislocation motion. It is also suggested that the small strain-rate dependence reported in ternary alloys may be due to the ternary elements. In binary Ni3Al without these elements, the flow stress is considered to be controlled by an athermal process such as dislocation multiplication.

Strain-rate dependence of microstructure and superplasticity of an Al–16 wt.% Si–5 wt.% Fe–0.9 wt.% Cu–0.4 wt.% Mg–0.9 wt.% Zr alloy fabricated by powder metallurgy

Strain-rate dependence of flow stress and elongation of an Al–16 wt.% Si–5 wt.% Fe–0.9 wt.% Cu–0.4 wt.% Mg–0.9 wt.% Zr alloy fabricated by powder metallurgy processing was examined in a range of strain rate from 1.4×10 −4 to 7×10 −1 s −1 under a constant temperature of 783 K. A superplastic elongation of 350% is obtained at a strain rate of 1.4×10 −1 s −1, and it rapidly decreases with an increasing strain rate. Transmission electron microscopic observations of the alloy showing the superplastic elongation reveal the same fine-grained morphology as that of an as-extruded alloy, whereas in the alloy tensile-tested at 1.4×10 −4 s −1, which show a small elongation of 100%, grain growth occurs.

The strain-rate dependence of flow stress and work-hardening rate in three Al-Mg alloys

Uniaxial compression tests have been carried out on Al-0.5% Mg, Al-1.0% Mg and Al-3.0% Mg alloys at 265°C and at constant true strain-rates in the range 10 -3 to 10 s -1 . Uniaxial compression tests with true strain-rate sudden change from 1 to 10 s -1 , which are applied at true strains of 0.1, 0.3 and 0.5, have been performed at 160, 365 and 520°C. The work-hardening rate, θ = ∂σ/∂e, has been evaluated at 265°C and found to exponentially decrease with increasing strain. The total strain-rate exponent, m t , at 265°C and the instantaneous strain-rate exponent, m i , at 160, 365 and 520°C are determined. It is found that m i is strain independent irrespective of temperature, while m t is less sensitive to strain when strain-rates are high (10 -1 to 10 s -1 ); however, it increases with strain when strain-rates become low (10 -3 to 10 -1 s -1 ). The difference between m i and m t could be attributed to the strain-rate dependence of the work-hardening rate. The possible correlation between the strain-rate exponents of flow stress (m i and m t ) and the strain-rate exponent of work-hardening rate (m h ) could be outlined as m t = αm i +m h , where a is a correlation coefficient.