Rate Sensitivity Coefficient Research Articles

The loading-rate dependent tensile behavior of CNT film and its bismaleimide composite film

Carbon nanotube (CNT) macroscopic assembly, as a promising candidate for the protective and anti-collision materials, has attracted lots of researchers to explore its mechanical behavior under different loading rates. In this paper, the loading-rate dependent mechanical behavior of CNT film and its composite with bismaleimide (BMI) matrix is investigated. The pristine CNT film shows decreased tensile strength by 33.8% when the loading rate increases from 0.05mm/min to 40mm/min. An obvious necking extending phenomenon is observed in the CNT film during the tensile test under lower tensile rates, e.g. 0.05mm/min and 0.5mm/min. However, the random composite film and the oriented composite film both display increased tensile strength, by 58.2% and 35.7% respectively, with the increasing loading rate from 0.05mm/min to 40mm/min. The different loading-rate dependence of tensile behavior is ascribed to the different tensile-induced motions of CNTs and CNT bundles in composite film. Moreover, strain rate sensitivity coefficients of different film are calculated according to a simplified Johnson-Cook model. The results suggest that the pristine CNT film with the strain rate sensitivity coefficient of −0.0941 has a high loading-rate sensitivity, meanwhile polymer infiltration and oriented alignment can weaken the loading-rate sensitivity of CNT film.

Superplastic Behavior of an Al-Cu-Mg-Mn-Ag Alloy

The superplastic properties and microstructural evolution of a commercial Al-4.4%Cu-0.5%Mg-0.4%Mn-0.5%Ag-0.1%Ti alloy were examined under tension at temperatures ranging from 450 to 520°C and strain rates ranging from 6.9x10-5 to 6.9x10-2s-1. The refined microstructure with an average grain size of about 11m was produced in thin sheets by a commercially viable thermomechanical process. The highest elongation to failure of 540% was attained at a temperature of 500°C and an initial strain rate of 6.9x10-4 s-1 with the corresponding strain rate sensitivity coefficient of 0.55. The microstructural evolution during superplastic deformation of the aluminum alloy has been studied quantitatively. Processing at temperatures above 475°C and strain rate below 1.4x10-3s-1 resulted in fracturing almost without necking with cavitation playing a major role in the failure. In contrast, at low temperatures and/or high strain rates, fracture occurred in a ductile manner by localized necking. The relationship between superplastic ductility and microstructural evolution is analyzed.

Modified Fields–Backofen model for constitutive behavior of as-cast AZ31B magnesium alloy during hot deformation

Uniaxial hot compression tests were carried out over a wide range of strain rates (0.005–5s−1) and temperatures (200–450°C) to study the constitutive behavior of as-cast AZ31B magnesium alloy. Considering the macro results of compressions, deformation characteristics were analyzed to explain the abnormal extension of compressive curves at 200°C and then the mathematical model was established approximately to predict the moment at which an occurrence of demarcation point took place. Constitutive behavior at (250–450°C) was modeled using the Fields-Backofen (F-B) equation, which was modified in view of the dependency of flow stress on temperatures and its specific form. However, strain-rate sensitivity and temperature softening coefficient, characterizing the hardening and softening effect respectively, are constants in the F-B equation, resulting in the F-B equation cannot accurately characterize the complex deformation mechanism under different conditions. Later, another modified F-B equation with a higher prediction accuracy was proposed, including the effect of strain by considering the strain rate sensitivity and temperature softening coefficient as different functions of strain.

A new strain rate dependent continuum framework for Mg alloys

Magnesium (Mg) alloys have recently been put under the spotlight for their specific strength, the highest among structural metals. Although the mechanical behaviour of Mg alloys at quasi-static strain rates has been extensively modelled in the recent years, high strain rate studies have been much scarcer. This is mainly due to the rate dependent (RD) mechanical response of their hexagonal close-packed (hcp) crystalline structure. As a result, existing RD models do not account for the differentiated rate sensitivities of each slip and twin systems. Instead, the rate dependency is often conceived as a numerical artefact utilised to smooth the elasto-plastic transition and facilitate the scheme convergence. We thus propose a novel efficient RD crystal plasticity model for hcp metals, applied here to a rolled Mg AZ31 alloy sheet at room temperature. The constitutive RD equations are solved at each time step by either a Newton–Raphson based implicit scheme or an explicit scheme modified so as to ensure convergence independently of the stochastic bursts of slip systems inherent to such approach. Most of the model parameters are taken from the previously calibrated rate independent (RI) model of Fernández et al. (2011), except for the new RD variables (strain rate sensitivity coefficients and reference shear strain rates), taken from the literature when available, or chosen so as to fulfill full compatibility with the RI model under quasi-static conditions. The model is validated against uniaxial compression tests at high strain rate (103s-1), in the rolling and normal directions. The results reveal the ability of the model to simulate the mechanical behaviour of Mg AZ31 alloy under a very large range of loading rates. To the best of the knowledge of the authors, the proposed model is the first RD continuum model for hcp metals involving physically accurate slip and twin system rate sensitivities, while ensuring convergence.

Rate-dependent phenomenological model for self-reinforced polymers

The visco-elastoplastic nature of self-reinforced polymers (SRPs) implies that their mechanical behaviour depends on strain rate. Such dependence, when significant, must be taken into account in order to predict the impact response of these materials. In this paper, the strain rate dependence of the mechanical behaviour of a self-reinforced polypropylene (SRPP) and a self-reinforced poly(ethylene terephthalate) (SRPET) is determined and constitutively modelled. To do this, stress–strain curves corresponding to constant strain rates are deduced for each material by using a characterization method presented and validated in previous works. The strain rate dependence of the stress–strain response is quantified based on the ‘strain rate sensitivity coefficient’, defined by G’Sell and Jonas for their material model for semi-crystalline polymers. Such dependence is found to be higher in the SRPET than in the SRPP and, moreover, in both materials it depends on strain. Finally, a modified phenomenological constitutive model based on the G’Sell–Jonas one is proposed. The results show that the modified model improves the prediction of the original model reproducing accurately the rate-dependent behaviour of both SRPs.

Superplasticity of an AA2519 Aluminum Alloy

A commercial AA2519 alloy with a chemical composition of Al-5.64Cu-0.33Mn-0.23Mg-0.15Zr (in wt. %) was subjected to two-step thermomechanical processing (TMP) providing the formation of fully recrystallized structure with an average grain size of ~7 mm in 3 mm thin sheets. Superplastic tensile tests were performed in the temperature interval 450-535°C and initial strain rates ranging from ~2.8 x 10-4 to ~6.0 x 10-1 s-1. The highest elongation-to-failure of ~750% appears at a temperature of ~525°C and an initial strain rate of ~1.4 × 10-4 s-1 with the corresponding strain rate sensitivity coefficient of ~0.46.

Mechanism of Low-Temperature Superplastic Deformation in Aluminum Alloys Containing a Dispersion of Nanoscale Al<sub>3</sub>(Sc,Zr) Particles

The ultrafine grained (UFG) structure with an average size of ∼0.8 μm was produced in an Al-Li-Mg-Sc alloy by equal-channel angular extrusion (ECAE) at 325oC with a total strain of ~16. Superplastic behavior was examined in the temperature range 150-250oC at strain rates ranging from 10-5 to 10-2 s-1. A maximum elongation-to-failure of 440% was recorded at 175oC (~0.5 Tm, where Tm is the melting point) and a strain rate of 2.8×10-5 s-1 with the corresponded strain rate sensitivity coefficient of 0.32. Mechanisms of low-temperature superplasticity (LTSP) and high-strain-rate superplasticity (HTSP) are essentially the same. The difference between superplastic behaviors at low and high temperatures is attributed to applied stress.

Low-Temperature Superplasticity in an Al-Mg-Sc Alloy Processed by ECAP

The ultrafine grained structure of an AA5024 with an average size of ∼0.7 μm was produced by equal-channel angular pressing (ECAP) at 300°C with a total strain of ~12. Superplastic behavior of this alloy was examined in the temperature interval 175 - 300°C at strain rates ranging from 10-4 to 10-1 s-1. The maximum elongation-to-failure of ~1200% with the corresponding strain rate sensitivity coefficient, m, of ∼0.49 was attained at a temperature of 275°C and a strain rate of 5.6×10–3s–1. At 175°C (~0.53Tm, where Tm is the melting point), the elongation-to-failure of ~370% with the m value of ~0.3 was found at ε̇=1.4×10–4 s–1.

Superplastic Behavior of Friction-Stir Welded Joints of an Al-Mg-Sc Alloy with Ultrafine-Grained Microstructure

The commercial Al-5.4Mg-0.2Sc-0.1Zr alloy was subjected to equal-channel angular pressing at 300°C to a true strain ~12 followed by cold rolling to a total thickness reduction of 80%. The ultrafine-grained sheets were joined by friction stir welding (FSW). To evaluate superplastic properties of the weldments, the tensile samples including all of the characteristic FSW microstructural zones were machined perpendicular to the welding direction and pulled up to failure in the temperature range of 400 to 500°C and at strain rates of 2.8×10-4 s-1 to 5.6×10-1 s-1. The friction-stir welded material exhibited excellent superplastic properties. The highest elongation-to-failure of ~1370% was recorded at a temperature of ~450°C and an initial strain rate of 5.6×10-2 s-1, where the strain rate sensitivity coefficient was about 0.64. The relationship between superplastic ductility and microstructure is discussed.

Extraordinary superplastic properties of hot worked Ti–45Al–8Nb–0.2C alloy

Superplastic behavior of the Ti–45Al–8Nb–0.2C alloy in ultrafine-grained condition has been investigated. The ultrafine-grained condition was produced via hot extrusion at T ≈ 1250 °C followed by unidirectional isothermal forging at T = 950 °C. The produced material showed extraordinary superplastic elongations (δ = 770–1342%) at T = 850–1050 °C and enhanced values of the strain rate sensitivity coefficient, m > 0.3 at ε′∼10−4–10−3 s−1. The obtained superplastic properties and the results of microstructural examination of the tensile strained specimens suggest that the grain boundary sliding was the predominant deformation mechanism during superplastic flow. In spite of a low content of the α2−Ti3Al phase and absence of the β(B2) phase, the produced ultrafine-grained microstructure showed surprisingly slow dynamic grain growth during superplastic flow at T = 850–1050 °C. The activation energy was defined to be Q = 303 kJ/mol suggesting that the predominant deformation mechanism during superplastic flow was grain boundary sliding controlled by volume diffusion of equally aluminum and titanium in γ-TiAl.

The identification of dynamic recrystallization type during hot deformation process

The type of dynamic recrystallization process during the high-temperature deformation under different conditions has been identified through the analysis on the dislocation evolution involving with recrystallized grains growing. And the dependence of the type of dynamic recrystallization on the deformation parameters has been discussed. The conditions with lower temperatures and higher strain rates, higher temperatures and lower rates correspond to continuous and periodic DRX, respectively. A constitutive model, describing the response of steady flow stress to deformation parameters, has been proposed based on the balance state of working-hardening and dynamic softening. The constitutive model has a similar type with Arrhenius equation with the coefficients possessing their physical meanings. The true stress-true strain curves during the deformation, with temperatures ranging from 800 to 900℃ and strain rates ranging from 0.0005 to 10 s-1, of TC18 alloy have been obtained through the isothermal compression experiment. The proposed model, identifying the type of dynamic recrystallization, has been verified through the analysis of the flow characteristics of the stress-strain curves under certain deformation conditions. And the power dissipation efficiency map, utilized in DMM model, has been employed to verify the applicability of the model. The correspondence of different types of DRX on the coarsening or refining effect of DRX-ed grains during hot deformation of TC18 alloy has been analyzed through microstructure observation. The proposed constitutive model, suitable to the steady state, has also been verified through substitution of steady stress at strain of 0.8 and the value range of strain rate sensitivity coefficient has been analyzed according to the constitutive model.

Effect of Deformation Temperatures on High Temperature Tensile Instability of Austenitic Stainless Steel

AbstractThe characteristics of instability have been investigated on two low nickel austenite stainless steel at the temperatures of 950–1200 °C through the uniaxial tensile test and tensile unload test. The results show geometrical instability is not concurrent with load instability in high temperature tensile. The deformation of specimens are uniform before the load instability, then appear non-uniform in some local area of specimen but they do not directly lead to the geometric instability. With the increase of deformation temperature, load instability strain and strain hardening exponent n are both no obvious variation, and load instability true strain is close to n and depends on n. The geometric instability strain and strain rate sensitivity coefficient m both increase with the increase of temperature, and the strain between load instability and geometric instability depends on m and is the main part of the geometric instability strain.

Hot tensile deformation behaviors and constitutive model of an Al–Zn–Mg–Cu alloy

The hot tensile deformation behaviors of an Al–Zn–Mg–Cu alloy are studied by uniaxial tensile tests under the deformation temperature of 340–460°C and strain rate of 0.01–0.001s−1. The effects of deformation temperature and strain rate on the hot tensile deformation behaviors and fracture characteristics are discussed in detail. The Arrhenius-type constitutive model is developed to predict the peak stress under the tested deformation condition. The results show that: (1) The true stress–true strain curves under all the tested deformation conditions are composed of four distinct stages, i.e., elastic stage, uniform deformation stage, diffusion necking stage and localized necking stage. The flow stress decreases with the increase of deformation temperature or the decrease of strain rate. (2) The elongation to fracture increases with the increase of deformation temperature. Under the tested conditions, the strain rate sensitivity coefficient varies between 0.1248 and 0.2059, which indicates that the main deformation mechanism is the lattice diffusion-controlled dislocation climb. (3) The localized necking causes the final fracture of specimens under all the deformation conditions. Microvoids coalescence is the main fracture mechanism under relatively low deformation temperatures. With the increase of deformation temperature, the intergranular fracture occurs. (4) The peak stresses predicted by the developed model well agree with the experimental results, which indicate the validity of the developed model.

New Dynamic Constitutive Model for OFHC Copper Film

The material properties of OFHC copper film was investigated with the High-Speed Material Micro Testing Machine (HSMMTM) at the high strain rates. The rate-dependent stress-strain curves from the experiment and the Johnson−Cook curve fitting showed large discrepancies as the plastic strain increases since the constitutive model implies no rate-dependent strain hardening effect. A new constitutive model was proposed in consideration of rate-dependent strain hardening effect. The strain rate hardening term in the new constitutive model consists of the strain rate sensitivity coefficients of the yield strength and strain hardening. Keywords—Rate dependent material properties, Dynamic constitutive model, OFHC copper film, Strain rate.

Effects of initial δ phase on hot tensile deformation behaviors and fracture characteristics of a typical Ni-based superalloy

Uniaxial tensile tests of a typical Ni-based superalloy are conducted under the deformation temperature range of 920–1010°C and strain rate range of 0.01–0.001s−1. The effects of initial δ phase (Ni3Nb) on the hot tensile deformation behaviors and fracture characteristics are discussed in detail. The results show that: (1) For the studied Ni-based superalloy with a large amount of δ phase, the flow stress curves are composed of three distinct stages, i.e., work hardening stage, flow softening stage and the final fracture stage. (2) The initial δ phase has significant effects on the deformation behaviors of the studied superalloy. δ phase can cause the obvious work hardening at the beginning of hot deformation, and then accelerates the flow softening by promoting the dynamic recrystallization with further straining. With the increase of initial δ phase, the strain rate sensitivity coefficient decreases firstly and then increases. (3) The combined effects of localized necking and microvoid coalescence cause the final fracture of specimens. The increase of initial δ phase increases the density of nucleus for the formation of microvoids, and promotes the nucleation and coalescence of microvoids.

Low-Temperature Superplasticity in an Al–Mg–Mn Alloy Subjected to ECAP and Subsequent Isothermal Rolling

An ultra-fine grained structure with an average size of ~ 1 μm was produced in a commercial Al–5.4%Mg–0.5%Mn–0.1%Zr–0.12%Si–0.014%Fe alloy by hot equal-channel angular pressing (ECAP) followed by isothermal rolling (IR). It was found that in the strain rate interval from 5.6×10-4 to 2.8×10-2 s-1 the alloy exhibits a low-temperature superplasticity with elongation-to-failure exceeding 400% and the strain rate sensitivity coefficient of ~0.3. The highest elongation-to-failure of ~ 620% appeared at a temperature of ~ 275°C and an initial strain rate of ~ 5.6×10-3 s-1. The relationship between superplastic properties and microstructural evolution of the examined alloy is discussed.

Material characterization of duplex stainless steel by superplastic free bulging test

AbstractMacroscopic superplastic behaviour of metallic or non metallic materials is usually represented by the strain rate sensitivity, and it can be determined by tensile tests at elevated temperature. However, a uniaixal stress state occurs in the test whilst a multiaixal stress state is induced in actual superplastic forming processes. The difference of the stress state might affect the reliability of the strain rate sensitivity obtained from the tension test. In the current study, the material characterization of duplex stainless steel, UNS S31803, has been carried out to determine the strain rate sensitivity throughout superplastic free bulging test under constant pressure. The measured height of bulged plate during the test was transformed into strain rate and stress corresponding to height at each time by theoretical considerations. The strain rate sensitivities were calculated for each pressure level. After calculating the strain rate sensitivity and strength coefficient for each test case, the flow stress equations have been employed in the finite element simulation to verify the experiments. The bulged height obtained from the simulation showed a reasonable agreement with the experimental findings. In the future, if a study on the effect of fillet radius of test tool and microstructure evolution is carried out, it is thought that the reliability of the material characterization by superplastic free bulging test can be enhanced.

A Polycrystal Plasticity Model and its Application in Deep Drawing of a FCC Metal

This study developed a new polycrystal plasticity model by deducing a set of linear controlling equations with respect to the controlling equation of rate dependent crystal plasticity (RDCP). It was proved numerically efficient and stable by means of the comparison with experiment and an implicit model. The model was then applied to describe earing in deep drawing process. Remarkable effects of rate sensitivity coefficient of the material, drawing speed and dies clearance on earing were found.

Influences of material properties of components on formability of two-layer metallic sheets

Formability of two-layer metallic sheet is constrained by plastic instability and localized necking. Forming limit diagram (FLD) is an accepted measure of sheet metal formability. The formability of two-layer sheets depends on the material properties of their components such as strain hardening exponent, strain rate sensitivity coefficient, stiffness coefficient, and grain size. In this paper, the effects of the mentioned parameters on the FLD of two-layer sheets are investigated with a theoretical model which has been verified with an experimental approach. The results show that the forming limit of two-layer sheet lies between the forming limits of its components depends on their material properties.

Microstructure and Properties of Nanostructured Alloy 718

Nickel-iron Alloy 718 is widely used for fabricating parts by superplastic deformation. Refinement of grains down to a nanostructure (NS) size improves the alloy’s processing properties. Thermomechanical treatment has been carried out to form a NS state in bulk alloy by multiple isothermal forging (MIF) at gradually decreasing temperatures. Investigation of superplastic properties and processing behavior of Alloy 718 has been performed. The alloy with a grain size of 80 nm displays superplasticity (SP) at a temperature which is lower than for a conventional fine grained alloy by about 350°C. The values of the relative elongation  and the strain rate sensitivity coefficient m are 350% and 0.37, respectively. The experimental data on the influence of grain size on solid-state weldability in the range of SP have been obtained. The application of the effect of low temperature SP yields lower temperatures of superplastic forming (SPF) and pressure welding (PW) as compared with conventional SP of fine-grained material. The experiment of the combined process of SPF and PW by counter-forming of two polished sheets, demonstrates its low temperature processing feasibility using NS specimens. The SPF processing of NS sheets in a cylindrical die has been investigated. It has revealed that macro-deformation is uniform in cross and longitudinal sections. Mechanical properties of Alloy 718 in NS condition and after strengthening heat treatment have been discussed.