Step Strain Rate Research Articles

Extensional Step Strain Rate Experiments on an Entangled Polymer Solution

The dynamics of chain entanglement/disentanglement in concentrated polymer solutions are matters of current debate. We report the results of step strain rate experiments in uniaxial extensional flow on a well-characterized polymer solution containing about 22 entanglements per chain which allows these dynamics to be probed. In these experiments the polymer solution is subjected to homogeneous stretching at a given strain rate up until a predetermined value of strain. After this strain is reached, the strain rate is changed to a new value, and stretching is continued until steady state is acquired in the extensional stress. The strain rates are increased in step-up experiments and decreased in step-down experiments. The strain rates are adjusted so that both the orientation and the stretching dynamics can be probed. Additionally, the predictions of two recent single-mode molecular models are evaluated against the experimental data. These models include the effects of entanglement dynamics in their predicti...

Unified modeling of flow behavior and microstructure evolution in hot forming of a Ni-based superalloy

In this paper, the flow behavior and microstructure evolution of a Ni-based superalloy were investigated by hot compression tests with true strain between 0.223 and 0.916, strain rate between 0.001 and 1s−1 and deformation temperature between 1223 and 1373K. Based on the experimental results, a set of internal-state-variable based unified constitutive equations were proposed to model the flow stress and microstructure evolution of the studied superalloy. The evolution models of dislocation density, average grain size, and dynamic recrystallization fraction were developed and embedded into the constitutive law, which was derived from thermal activation theory and composed of athermal and thermal stresses. The proposed model was calibrated using experimental flow stress and dynamic recrystallization fraction. The predicted flow stress and dynamic recrystallization fraction under different deformation conditions agreed well with the experimental results. Additionally, flow stress under step-strain rate condition was also precisely predicted by the model. The contributions of long and short range barriers to the overall flow stress, variation of corresponding stress components, and microstructure evolution with strain were further analyzed using the unified model. The thermal stress only varied with deformation temperature and strain rate, while the grain boundary strengthening component and stress contribution of dislocation interactions varied with the evolution of grain size and dislocation density, respectively.

Choosing a proper loading rate for bonded-particle model of intact rock

Bonded-particle model (BPM) is widely used to model geomaterials, in which calibration against the results from uniaxial/triaxial compressive tests, Brazilian tensile tests and shear tests have been commonly conducted. However, since different loading rates were used, it is difficult to assess the numerical results of these studies if the effects of the loading rate are ignored. This paper discusses the loading mechanisms associated with different loading rates in the BPM and examines the numerical outputs under these different rates. The results indicate that the time step is an important factor controlling the loading rate of the BPM and should be considered in addition to the velocity of the loading platen. The strain rate, which is usually employed to describe the loading rate in a physical test, cannot be used for the direct comparison of different numerical tests in $$\hbox {PFC}^{\mathrm{2D}}$$ due to the time step. A proposed “step strain rate”, which considers the time step, is found to be more appropriate for comparing the loading velocity on specimens of varying sizes. Six different loading rates (0.005, 0.01, 0.02, 0.08, 0.2 and 0.6 m/s) are employed in uniaxial compressive tests and Brazilian tests during this study. After comprehensive examinations, a maximum step strain rate of $$1.1 \times 10^{-8}\, \hbox {step}^{-1}$$ is considered to be appropriate for quasi-static uniaxial compressive tests and Brazilian tests using the BPM.

Simulation of hot forming processes: Using cost effective micro-structural constitutive models

Abstract Constitutive models for dominant mechanisms in hot forming are proposed. These models consider inter-granular deformation, grain boundary sliding, grain boundary diffusion and grain growth. New stress–strain rate relationships are proposed to predict deformation due to grain boundary sliding and grain boundary diffusion. Besides a Taylor type polycrystalline constitutive model, a visco-plastic relation in conjunction with two different yield functions is used to predict inter-granular deformation. Step strain rate tests and bulge forming test are simulated with the proposed models. Results are compared with experimental data to verify the constitutive models. It is concluded that the visco-plastic models can predict material behavior in hot deformations as accurately as the polycrystalline model but with much less computational costs. To examine the hardening effects, the model is calibrated with tensile test data of AA5083 at 550 °C, where hardening is remarkable. Then, as an example, it is used to simulate a tray forming experiment. Dome heights and tray thicknesses at various positions during forming process are very close to experimental observations.

Quantitative analysis on the anisotropic behaviour of superplastic deformation in laser melted (LM) Ti–6Al–4V alloy

In this study, the effects of anisotropy on the superplastic deformation mechanisms in direct metal laser melted (LM) Ti–6Al–4V alloys were investigated. An analysis is presented based on inelastic deformation theory, which consists of grain matrix deformation (GMD) and phase/grain boundary sliding (P/GBS). Flow stress–strain rate curves of the alloy were obtained by the load relaxation test and the step strain rate test at 775, 825, 875 and 925 °C. The results showed that GMD and P/GBS in tensile tests, with either transverse, parallel or 45° inclined microstructures with respect to the tensile axis and the additive layer build (ALM) direction, were well described at 875 °C by the plastic deformation and viscous flow equation of the theory. With change in the microstructural directionality, the flow stress curves for GMD significantly deviate in comparison to those for P/GBS. The mode of GMD, with respect to anisotropic microstructural build direction, agrees well with the extreme iso-stress model. Excellent elongations, over 1000%, were achieved in spite of relatively modest measured strain rate sensitivity values, m, in the range 0.35–0.45, due to excellent deformation accommodation in β phase.

Effect of two step strain rate on superplastic behaviour of Al–Zn–Mg–Cu–Zr alloy 7010 containing Sc

A suitable thermomechanical process, different from the Rockwell route, before the superplastic deformation together with the utilisation of a ‘two step strain rate’ during the superplastic deformation has been employed to evaluate the total percentage elongation in a high strength Al–Zn–Mg–Cu–Zr alloy containing Sc. It is shown that the utilisation of a two step strain rate under appropriate combinations of temperature and strain rate results in superior values of elongations.

Simulation of Hot Sheet Metal Forming Processes Based on a Micro-Structural Constitutive Model

A constitutive model is proposed for simulations of hot forming processes. Dominant mechanisms in hot forming including inter-granular deformation, grain boundary sliding and grain boundary diffusion are considered in the constitutive model. A Taylor type polycrystalline model is used to predict inter-granular deformation. Previous works on grain boundary sliding and grain boundary diffusion are extended to drive three dimensional macro stress-strain rate relationships for each mechanism. In these relationships, the effect of grain size is also taken into account. It is shown that for grain boundary diffusion, stress-strain rate relationship obeys the Prandtl-Reuss flow rule. The proposed model is used to simulate step strain rate tests and the results are compared with experimental data. It is concluded that the model can be used to predict flow stress for various grain sizes and strain rates. The proposed model can be directly used in simulation of hot forming processes and as an example the bulge forming process is simulated and the results are compared with experimental data.

Deformation-induced accelerated dynamics in polymer glasses

Molecular dynamics simulations are used to investigate the effects of deformation on the segmental dynamics in an aging polymer glass. Individual particle trajectories are decomposed into a series of discontinuous hops, from which we obtain the full distribution of relaxation times and displacements under three deformation protocols: step stress (creep), step strain, and constant strain rate deformation. As in experiments, the dynamics can be accelerated by several orders of magnitude during deformation, and the history dependence is entirely erased during yield (mechanical rejuvenation). Aging can be explained as a result of the long tails in the relaxation time distribution of the glass, and similarly, mechanical rejuvenation is understood through the observed narrowing of this distribution during yield. Although the relaxation time distributions under deformation are highly protocol specific, in each case they may be described by a universal acceleration factor that depends only on the strain.

2 상 Ti3Al-xNb 계 금속간 화합물들의 초소성 특성에 미치는 상분율의 영향

A study has been made to investigate the boundary sliding and its accommodation mode with respect to the variation of <TEX>$\alpha$</TEX><TEX>$_2$</TEX>/<TEX>$ eta$</TEX> volume fraction during superplastic deformation of two-phase Ti<TEX>$_3$</TEX>Al-xNb intermetallics. Step strain rate and load relaxation tests have been performed at 950, 970 and 99<TEX>$0^{\circ}C$</TEX> to obtain the flow stress curves and to analyze the deformation characteristics by the theory of inelastic deformation. The results show that the grain matrix deformation and boundary sliding of the three intermetallics containing 21, 50 and 77% in <TEX>$ eta$</TEX> volume fractions are well described by the plastic deformation and viscous flow equations. Due to the equal accommodation of both <TEX>$a^2$</TEX> and <TEX>$\beta$</TEX> phases, the accommodation modes for fine-grained materials are in good agreement with the iso-strain rate models. The sliding resistance analyzed for the different boundaries is the lowest in the <TEX>$\alpha$</TEX><TEX>$_2$</TEX>/<TEX>$\alpha$</TEX><TEX>$_2$</TEX> boundary, and increases in the order of <TEX>$\alpha$</TEX><TEX>$_2$</TEX>/<TEX>$\alpha$</TEX><TEX>$_2$</TEX><< <TEX>$\alpha$</TEX><TEX>$_2$</TEX>/<TEX>$\beta$</TEX> = <TEX>$\beta$</TEX>/<TEX>$\beta$</TEX>, which plays an important role in controlling the superplasticity of the alloys with the various <TEX>$\alpha$</TEX><TEX>$_2$</TEX>/<TEX>$\beta$</TEX> phase ratio.

Superplastic Characteristics of Ti-Alloy and Al-Alloy Sheets by Multi-Dome Forming Test

The present study evaluates the superplastic material characteristics of Ti-alloy “Ti–4.5Al–3V–2Fe–2Mo”, SP-700, and Al-alloy “A5083”, which have been obtained by utilizing a multi-dome forming test. First, the flow stress vs. strain rate relationship was established for certain strain rate range, from a single circular sheet containing four different domes, sized 35, 30, 25, and 20 mm diameter, respectively. The multi-dome forming experiments were conducted under constant pressure at a superplastic temperature of 800°C for Ti-alloy and of 530°C for Al-alloy. The bulge forming of domes was also simulated by finite element method (FEM) to verify the experimentally-obtained material characteristics. Then the material characteristics obtained through multi-dome forming test were compared to those obtained by tensile step strain rate tests. In contrast to the predictions of the tensile test, the multi-dome forming test’s predicted time of deformation was generally in reasonable agreement with the results of the FEM simulation. There was no great difference, however, between the multi-dome forming test and the tensile testing with regard to the predicted final thickness distribution.

Anisotropic behavior and constitutive equations of superplastic deformation of a Ti-6Al-4V alloy

In this study, the effects of anisotropy on the superplastic deformation mechanisms in direct metal laser melted (LM) Ti–6Al–4V alloys were investigated. An analysis is presented based on inelastic deformation theory, which consists of grain matrix deformation (GMD) and phase/grain boundary sliding (P/GBS). Flow stress–strain rate curves of the alloy were obtained by the load relaxation test and the step strain rate test at 775, 825, 875 and 925 °C. The results showed that GMD and P/GBS in tensile tests, with either transverse, parallel or 45° inclined microstructures with respect to the tensile axis and the additive layer build (ALM) direction, were well described at 875 °C by the plastic deformation and viscous flow equation of the theory. With change in the microstructural directionality, the flow stress curves for GMD significantly deviate in comparison to those for P/GBS. The mode of GMD, with respect to anisotropic microstructural build direction, agrees well with the extreme iso-stress model. Excellent elongations, over 1000%, were achieved in spite of relatively modest measured strain rate sensitivity values, m, in the range 0.35–0.45, due to excellent deformation accommodation in β phase.

Probing the dynamics of polymer solutions in extensional flow using step strain rate experiments

This paper sets out to examine the response of polymer solutions to time-dependent strain rates. Following a step-change in strain rate, the polymer solution was observed to respond almost instantaneously to the imposed flow rate. Under all extension histories having a positive extension rate that were investigated, the instantaneous stress is proportional to instantaneous strain rate multiplied by a function of the strain. Simulations using the FENE-P model were unable to capture these trends. A pause was introduced in a constant strain rate experiment and revealed that the stress growth upon re-inception of flow was significantly faster predicted by simple constitutive equations. The stress growth depends not only on the current stress and imposed deformation but also on the history of deformation as stored in the configuration distribution of the chain.

Alloying effects on superplastic behaviour of Ti-Fe-AI-Ni alloys

The aim of the present investigation was to develop a new titanium alloy with improved superplastic performance (higher elongation and lower forming temperature) through alloying with iron, nickel, and aluminium. A total of nine alloy compositions were used in which the iron content was fixed while nickel and aluminium contents were varied. Superplastic tension tests were conducted at various temperatures in the range 625-750° C with a strain rate of l0−3 S-1. Step strain rate tests were performedin a strain rate range 10-4-2.5 x 10-2 s-1 at 700, 725, and 750°C to study some important superplastic deformation properties.The alloy Ti-5Fe-4AI-2Ni proved to be promising in that it gave a large elongation of more than 1500% at a low deformation temperature of 650°C, which was possible mainly because of the existence of iron and nickel. Alloying with nickel within a suitable amount was found to increase the strain rate sensitivity and to decrease the flow stress, while the effect of aluminiumaddition was found to be insignificant regarding superplastic behaviour, but its content should be limited. Possible mechanisms for superplasticity in the present alloy system are also discussed.

Processing, microstructure, and elevated temperature mechanical properties of MoSi 2 containing Er 2Mo 3Si 4 and Er 2O 3 particles

Powders of MoSi 2 containing Er 2Mo 3Si 4 and Er 2O 3 particles were produced by abll milling rice-melted buttons of MoSi 2 containing 20 vol.% Er 2Mo 3Si 4. Two composites with grain diameters of 9 and 16 μm were produced by hot pressing the powders to 98% of theoretical density at 1565 °C and 1650 °C respectively. Some evidence of mechanical alloying was observed, but the majority of the Er 2Mo 3Si 4 and Er 2O 3 particles were situated on grain boundaries. Compressive decremental step-strain rate tests were performed in the homologous temperature range of 0.54 T m to 0.7 T m (1100–1400 °C) for strain rates ranging from 5 × 10 −4 s −1 to 1 × 10 −6 s −1. Nominal values for the stress exponent, n, and the activation energy for creep, Q, were determined using a constitutive equation for power-law creep. Below 1200 °C, creep was controlled by dislocation climb and glide mechanisms with n ≈ 4.5 and Q 425 ± 15 kJ mol −1. At 1300 °C and above, the creep resistance was shown to be grain size dependent with creep resistance increasing with larger grain size.

Microstructural analysis and high-temperature strength of a directionally solidified Er 2Mo 3Si 4-MoSi 2 eutectic

Recent investigations have shown that Er[sub 2]Mo[sub 3]Si[sub 4] is an effective reinforcement for strengthening MoSi[sub 2]. When present in hot-pressed MoSi[sub 2] compacts, the Er[sub 2]Mo[sub 3]Si[sub 4] improved both hot hardness and creep resistance of the MoSi[sub 2]. The crystal structure of Er[sub 2]Mo[sub 3]Si[sub 4], as reported by Bodak et al., is monoclinic with lattice parameters of 0.667 nm, 0.689 nm, and 0.681 nm. The point group and space group of this phase have been identified as 2/m and P2[sub 1]/c, respectively. A theoretical density for Er[sub 2]Mo[sub 3]Si[sub 4] was calculated to be 8.25 g/cm[sup 3] and this compares favorably with other refractory silicide compounds (e.g., Mo[sub 5]Si[sub 3] = 8.25 g/cm[sup 3]). Because of the low crystal symmetry, this intermetallic compound is expected to exhibit limited plasticity, but may possess good high temperature mechanical properties. Mechanical property data on Er[sub 2]Mo[sub 3]Si[sub 4] is still quite limited; however, preliminary creep results from a decremental step-strain rate test show that the directionally solidified (DS) Er[sub 2]Mo[sub 3]Si[sub 4]-MoSi[sub 2] eutectic has excellent creep resistance at 1,300 C. At this temperature a flow stress of 625 MPa was observed for a strain rate of 5 [times] 10[supmore » [minus]5]s[sup [minus]1], but failure occurred as the strain rate was reduced to 10[sup [minus]5]s[sup [minus]1]. In this paper the authors present further results obtained from constant engineering strain rate compression tests on the same DS eutectic bar.« less

Rubber Viscoelasticity Using the Physically Constrained System's Stretches as Internal Variables

Abstract The simulation of rubber viscoelasticity with the tube reptation model for topological interactions is investigated for large dynamic strains. The chemically crosslinked (CC) system of molecules acts as a constraint box per unit volume for the physically constrained (PC) system and carries the PC system during the deformation process. A stick—slip model is used to simulate the interaction between the CC and PC systems Stretch ratios describe the history of the PC system's energy. Rubber energy density functions for both the CC and time dependent PC systems are shown to model large strain viscoelastic deformations. In this approach the energy is split into two terms. The long term energy function for the CC molecules represents one part and a time dependent energy function for the PC molecules comprises the second part. The PC systems' stretches then appear as internal variables in the expression of the total energy. The relaxation of the PC molecules during a general deformation is determined by the history of the CC system's strain state and the box (tube) stick—slip relaxation equation(s). Examples are presented in which step-strain relaxation test data and strain rate data are simulated for large deformations of a rubber compound with differing short and long term energy functions.

Characterization of the Plasticity Enhancement of MoSi 2Obtained at Elevated Temperatures by the Addition of TiC

Decremental step strain rate tests in compression were performed on MoSi 2 and MoSi 2 -10 vol % TiC at 1150°C and 1200°C. The composite exhibits a lower stress exponent than MoSi 2 between 10 -4 s- 1 and 10 -5 s -1 TEM observations reveal the deformation of the carbide phase, as well as the efficient generation of dislocations into the matrix from the carbide-matrix interfaces. The substructures of both the matrix of the composite and monolithic MoSi 2 appear to consist of mixed dislocations of predominantly edge character which occur on the same slip systems.

Creep Deformation Studies in Directionally Solidified MoSi2-Mo5Si3 Eutectics

The high temperature deformation behavior of directionally solidified (DS) MoSi2-Mo5Si3 eutectics was studied and compared to powder processed MoSi2-Mo5Si3 composites having the same volume fraction of Mo5Si3. Decremental step strain rate tests were performed in the temperature range of 1100-1300°C and at strain rates between 10−4 to 10−6/s. A considerable increase in the flow stress was observed for the directionally solidified material. At 1200°C and a strain rate of 10−6/s the flow stress of the DS eutectic was 255 MPa as compared to 20 MPa for the powder processed composite. The high temperature strength of the DS eutectic was unaffected by changes in the scale of the lamellar micro-structure and these results were modeled using a constitutive relation for power law creep. A stress exponent of 4.5 and an activation energy of 300 kJ/mol was determined for the DS eutectic. Evidence of dislocation glide and climb was observed in the MoSi2 lamellae whereas the dislocation density was small in the Mo5Si3 phase. The improved creep strength of the eutectic is believed to be a result of both the fibrous morphology and a stronger interface structure as compared to the powder processed composite.

Some Comments on the Role of Macroscopic and Molecular Inertia in the Theory and the Practicability of Transient Flow Experiments on Dilute Polymer Solutions

Two basic issues are addressed: the experimental question of whether it is practicable to generate an instantaneous jump in strain rate to a liquid, and the theoretical question of how a dissolved polymer chain will respond if the solvent around it is suddenly set into motion. It is argued that it is experimentally impossible to perform tests in which the strain rate exhibits a step change. In actual experiments the strain acceleration is bounded and the strain rate as well as the strain vary continuously. It is shown, on the basis of the equation of internal motion for a dumbbell with internal viscosity, that in idealized step strain rate flows the velocities of the beads at the very moment of inception are lower than the flow rates locally imposed on the fluid. In that case, also the mass of the beads affects the strain rate of the dumbbell. Theoretically, the stress jump at the inception of constant strain rate flows depends on φ, φ/f, and φm/f2, where φ is the internal viscosity coefficient, f the bea...

Superplastic forming and diffusion bonding of Inconel 718

This paper presents the results of a program designed to delineate the capabilities of Inconel 718 for superplastic forming (SPF) and diffusion bonding (DB) as low cost, weight saving processes for fabricating rocket engine parts. Elevated tem- perature total elongation and step-strain rate tests indicated that specially processed, fine-grained Inconel 718 behaved sufficiently superplastically to indicate the potential for the SPF of parts of con- siderable complexity. This was further confirmed with the SPF of a model part and a section of an actual rocket engine part. 718 can be diffusion bonded using a nickel interface layer to form high shear strength bonds. It was shown that Inconel