Constant Strain Rate Deformation Research Articles

Split Hopkinson pressure bar experiments on polymeric foams

Proper modifications are required when a split Hopkinson pressure bar (SHPB) is used to determine the dynamic compressive properties of polymeric foams. Pulse shaping is necessary to ensure valid testing conditions: constant strain-rate deformation under dynamically equilibrated stresses, which need to be experimentally verified. A more sensitive method must be employed to examine the weak signal transmitted through the foam specimen. These necessary dynamic experimental techniques for polymeric foam testing are briefly reviewed. As an example, the dynamic compressive stress-strain behaviour of a rigid polyurethane foam with a density of 0.24 × 103 kg/m³ has been determined at various strain rates using such a modified SHPB. Due to the low density and non-linear behaviour of the specimen, valid experimental results were obtained separately for small and large strains, respectively, since valid testing conditions could not be maintained over the entire duration of a dynamic experiment to large strains at high rate.

A model for steady state plasticity of ice single crystals

Stress and temperature dependences of the strain rate for ice single crystals are derived from evolution equations of mobile dislocation densities. This model is based on the mechanisms generally agreed for multiplication and annihilation of mobile dislocations in monocrystalline ice. It gives the correct stress exponent value n = 2 for steady state creep or constant strain rate deformation. The activation energy predicted by the model is that for dislocation climb, in agreement with experimental activation energies that are closer to the self-diffusion energy than to the activation energy associated with dislocation glide velocities.

The onset of secondary slip in the plastic deformation of tetrahedrally bound semiconductors

The shape of the stress–strain curves of tetrahedrally coordinated semiconductors strongly depends on temperature. Prominent features such as the yield point and the recovery-controlled stage III exhibit Arrhenius-law behavior with characteristic activation energies, which may be connected with microscopic dislocation processes. The transition from stage I to stage II of the stress–strain curve, however, has not found much interest, although reliable data sets with well-defined temperature and strain-rate dependences are available. In the present work data from nine undoped and doped semiconductors are analysed. The behavior of the transition stress τII clearly resembles that of the lower yield stress, although the resulting parameters are somewhat different. The transition is eventually traced back to the onset of secondary glide in the course of constant strain-rate deformation. The results are discussed in terms of microscopic processes occurring in the dislocation core, and are in agreement with recent findings of positron annihilation spectroscopy.

The onset of secondary slip in the plastic deformation of tetrahedrally bound semiconductors

The shape of the stress–strain curves of tetrahedrally coordinated semiconductors strongly depends on temperature. Prominent features such as the yield point and the recovery-controlled stage III exhibit Arrhenius-law behavior with characteristic activation energies, which may be connected with microscopic dislocation processes. The transition from stage I to stage II of the stress–strain curve, however, has not found much interest, although reliable data sets with well-defined temperature and strain-rate dependences are available. In the present work data from nine undoped and doped semiconductors are analysed. The behavior of the transition stress τ II clearly resembles that of the lower yield stress, although the resulting parameters are somewhat different. The transition is eventually traced back to the onset of secondary glide in the course of constant strain-rate deformation. The results are discussed in terms of microscopic processes occurring in the dislocation core, and are in agreement with recent findings of positron annihilation spectroscopy.

Electrical Response of β-PVDF in a Constant Uniaxial Strain Rate Deformation

The microstructure of β-PVDF has great influence on its piezo- and pyroelectric responses. The microstructure of β-PVDF drastically changes upon a mechanical deformation perpendicular to the preferred chain orientation, mainly above the yielding point. The voltage (open-circuit response) developed in β-PVDF films was monitored while the material is subjected to a constant strain rate program.

MOLECULAR DYNAMIC STUDY OF A SINGLE DISLOCATION IN A TWO-DIMENSIONAL LENNARD–JONES SYSTEM

In this work the motion of a single dislocation in a two-dimensional triangular lattice is studied by using classical Molecular Dynamics method with the Lennard–Jones inter-atomic potential. The dislocation motion is investigated with an interactive simulation program developed to track automatically the movement of lattice defects. Constant strain and constant strain-rate deformations were applied to the system. From constant strain simulations a curve of shear stress versus dislocation velocity is obtained, showing a nonlinear power law relation. An equation of motion for the dislocation is proposed and found to be applicable when the movement of dislocation follows a quasi-static process. Numerical simulations at different strain rates show an elastic-to-plastic transition that modifies the dynamics of the dislocation motion.

On the yield point of icosahedral AlCuFe quasicrystals

Transient creep 1 In this paper, the term ‘transient creep’ designates creep experiments that are performed after interrupting conventional constant strain rate deformation tests at various stress or strain levels. The combination of both types of experiments will be referred to as ‘composite test’. 1 tests have been performed at the yield point of icosahedral AlCuFe poly-quasicrystalline specimens in order to investigate the actual causes of this phenomenon. The experimental results strongly suggest that the yield point occurrence is essentially related to the lack of dislocation mobility and that a competition does exist between dislocation velocity and short range recovery.

Flow state in molecular-dynamics-simulated deformed amorphousNi0.5Zr0.5

Results are reported from molecular dynamics simulations about the deformation behavior of amorphous metallic ${\mathrm{Ni}}_{0.5}{\mathrm{Zr}}_{0.5}$ alloys near their glass transition temperature. Constant shear strain rate and constant shear stress deformations are analyzed. Stress-strain curves from constant shear strain rate deformations reveal different stages of deformation, first a regime with approximately linear stress-strain relation, then a transient regime with pronounced strain softening, and finally, for large strains, a nearly strain-independent flow stress region. The strong stress overshoot in the transient regime is ascribed to a delayed transition under steady-state deformations from the initial glassy state into a structurally and dynamically different one. This flow state shows a decreased viscosity, an increased potential energy per atom, and a loss of short-range order, the latter being deduced from the radial distribution functions. In the flow state, the self-part of the intermediate scattering function reveals an unchanged vibration spectrum of the system but a faster decay of density correlations compared to the starting structure. Creep curves from constant shear stress deformations show a nearly linearly increasing strain for moderate shear stresses and moderate deformations. The strain rate depends in a non-Newtonian manner on stress with an activation volume of $7--8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}29}{\mathrm{m}}^{3}.$ Deformation simulation with large constant shear stress leads to an instability, identified as the transition into the flow state.

Microstructure and mechanical behaviour of Nb–Al–V alloys with 10–25 at.% Al and 20–40 at.% V—II: mechanical behaviour and deformation mechanisms

The mechanical behaviour of three Nb–Al–V alloys with nominal compositions Nb–10Al–20V, Nb–15Al–20V and Nb–25Al–40V (in at.%) have been investigated. Both conventional constant strain rate deformation and compressive creep tests have been performed and the deformation microstructures have been examined by transmission electron microscopy (TEM). At room temperature all three alloys deform by planar slip, with dislocation/particle interactions giving significant strengthening for the two phase alloys. Deformation at higher temperatures occurs by a combination of dislocation glide and climb processes, giving more homogeneous microstructures. All of the dislocations in the B2 phase of these alloys are uncoupled superpartial dislocations with b=1/2<111>. The influence of dislocation/domain boundary interactions on the formation of slip bands and uncoupled superpartials is discussed.

Deformation mechanisms and microtensile behavior of single colony Ti–6242Si

The constant strain rate deformation behavior of individual α–β colonies of the titanium aeroengine alloy Ti–6Al–2Sn–4Zr–2Mo–0.1Si (compositions in wt.%) has been investigated through microsample tensile testing techniques. The mechanical behavior and deformation mechanisms observed were found to depend strongly on colony orientation. A near-Burger's orientation relationship (OR) has been observed for the α (hcp) and β (bcc) phases in these colonies, grown utilizing a vertical float zone technique. The Burger's OR is believed to be responsible for the observed anisotropy in the critical resolved shear stress for the three a/3〈11-20〉{10-10} prism slip systems. A more pronounced anisotropy was observed in the critical resolved shear stress (CRSS) for the three a/3〈11-20〉{0001} hcp basal slip systems. Scanning Electron Microscopy (SEM) investigations of the slip line morphology of the deformed samples indicates an inhibition of β-lath shearing for colonies oriented for basal slip, while frequent shear offsets of the β phase by slip lines were observed in the samples oriented for prism slip. The effects of the Burger's OR, slip line spacing and elastic interactions stresses arising from the α–β interface are considered in explaining the observed anisotropy in CRSS.

Crossover in the dynamics of Portevin–Le Chatelier effect from chaos to SOC

We demonstrate the existence of a crossover in the dynamics of the PLC effect from chaotic to self-organized critical nature by analysing the stress–strain curves obtained from single crystals of Al–10%Cu subjected to three levels of constant strain rate deformation. At the lowest and intermediate strain rates, we provide an unambiguous support for the existence of a chaotic regime. For these two strain rates, the distributions of stress drops are peaked. At the highest strain rate, we find that the distributions of stress drops and their durations exhibit a power law behaviour reminiscent of a self-organized critical state. We also show that scaling relations are obeyed by the various exponents.

Modeling of stress–strain curves for Pd 40Ni 10Cu 30P 20 glass alloy under constant strain-rate deformation

A model which is based on the hypothesis of stress-induced structural relaxation and the concepts of fictive stress for viscoelastic deformation of glass materials around the glass transition temperature is proposed. It expresses both linear and non-linear viscoelastic behaviors. For constant strain-rate deformation, it performs the stress-overshoot phenomenon observed in the condition of non-Newtonian flow. The model calculation reproduces fairly well the experimental results of Pd 40Ni 10Cu 30P 20 glass alloy, in particular, the development of stress-overshoot with increasing strain-rate and lowering temperature. Moreover, this model performs oscillatory behavior (stress-overshoot and -undershoot) which has been observed in many polymer solutions and glass alloy recently observed in stress–strain curves.

A Fictive Stress Model and Nonlinear Viscoelastic Behaviors in Metallic Glasses

Transition behaviors from linear to nonlinear viscoelasticity under constant strain-rate deformation near the glass transition have been investigated for Pd- and Zr-based alloy glasses. The transition occurs at critical strain-rate, and the steady-state viscosity may decrease by many orders of magnitude above the critical strain-rate. Concurrently with the transition, the growth of the stress shows a stress-overshoot; the stress increases initially attaining a maximum, then decreases and attains a steady-state flow. The transition between steady-state Newtonian and non-Newtonian flows can be analyzed by a stretched exponent relaxation function, and both the normalized viscosity and the flow stress can be represented by a master curve in terms of the product of the strain-rate and the Newtonian viscosity. These results imply that the occurrence of the transition from the Newtonian to non-Newtonian is explicitly determined by the flow stress. A model, based on the hypothesis of stress-induced structural relaxation and the concept of fictive stress for the nonlinear viscoelastic behaviors has been proposed. The model calculation has reproduced fairly well the experimental results of the Pd- and Zr-based glasses, in particular, the development of the stress-overshoot behavior. In addition, the model reveals a stress-overshoot and under-shoot oscillation at very high strain-rate. This oscillatory nonlinear behavior has been observed in many polymer solutions, and also the latest study in metallic glasses. The model calculations of other nonlinear viscoelastic behaviors, such as stress relaxation during stress growth after abrupt cessation of steady-state flow, and a stress regrowth after a brief interval of relaxation, are also presented.

Transient creep behaviour of Ni3Al polycrystals

ABSTRACTRepeated creep tests were used for measuring various constant strain-rate deformation parameters. The results are consistent with those of repeated stress relaxations, although the precision is lower for creep in the present case. The small yield point observed in reloading after the transient is directly related to the amount of exhausted mobile dislocations, i.e. it originates from multiplication processes. During the transient test (180s total), the total exhaustion rate of mobile dislocations can be as high as 99%. It exhibits a maximum at the same T (about 500 K) as the work hardening. This supports the validity of a model which considers the work-hardening peak temperature to correspond to the stress under which incomplete Kear-Wilsdorf locks yield.

Transition from Linear to Nonlinear Viscoelasticity during Deformation in a Zr-based Glassy Alloy

The transition behaviors from linear to nonlinear viscoelasticity during constant strain-rate deformations of a Zr-based glassy alloy near the glass transition temperature are investigated and a model calculation based on concept of a fictive stress is performed. The experimental results show that the viscoelastic behavior of the glassy alloy is characterized by a very narrow relaxation-time distribution due to its simple atomic structure. Hence, the transition between steady-state Newtonian and non-Newtonian flows can be analyzed by a stretched exponent relaxation-function of strain rate. And the condition at which the transition occurs in the Zr-based glassy alloy is investigated with a new model proposed on the basis of the hypothesis of stress-induced structural relaxation and a concept of fictive stress that expresses the structure of the material indirectly. Stress-strain curves calculated from the model agree quantitatively well with experimental results. The calculated curves of sufficiently higher strain-rates in the nonlinear viscoelastic regime show a stress- oscillation. This has been observed in many polymers, but has not been reported previously in glassy alloys. In the Zr-based glassy alloy, the oscillation is observed as predicted by the model.

High Temperature Plastic Behaviour of Icosahedral AlCuFe Quasicrystals.

AbstractIcosahedral AlCuFe poly-quasicrystalline specimens were deformed in constant strain rate compression tests at temperatures ranging between 300K - 1020K. Below nearly 0.7 Tm (Tm is the melting temperature) the specimens were brittle. Above the brittle-to-ductile transition temperature, after the elastic stage the stress-strain curves exhibit a marked yield-point followed by a stage of strain softening only. Transient creep tests were performed at different given stress/strain levels after interrupting the constant strain-rate deformation tests. After the transient tests, the flow strength of the specimens was investigated anew at constant strain rate. The results are interpreted in the framework of a dislocation model, where two effects opposing dislocation movement are considered: firstly, the usual elastic dislocation interaction, yielding a work-hardening contribution, and, secondly, a friction stress specific to the quasiperiodic lattice, leading to a softening effect.

The breaking strength of imperfect (real) polymer fibers

The thermodynamic fusion theory of strength of perfect polymer fibers of finite molecular weight is extended to include imperfect (i.e. real) fibers of incomplete crystallinity and orientation. Approximate equations for failure strength, strain, and work of failure are derived by extracting from the real visco-elastic fiber an equivalent reversible component suitable for thermodynamic analysis. This is facilitated by an explicit relationship between fiber breaking stress, σ*, and breaking strain, ε*, which is shown to be σ*=0.632Kε* (K=modulus) for constant strain-rate deformations. It is shown that fiber breaking time is equivalent to the fiber visco-elastic mechanical relaxation time. Experimental data shows that the activation energy of rupture of polyethylene fibers is not the activation energy of covalent bond rupture. Instead it agrees with the activation energy expected of crystal melting in accordance with the fusion theory of rupture. The activation volume of the polyethylene fibers also agrees with the value expected from this theory.

Deformation of adaptive materials. Part I. Constrained deformation of polydomain crystals

Deformation of an adaptive heterophase crystal with variable microstructure is considered. Under mechanical constraint the phase transformation in single component systems result in an equilibrium two-phase mixture. A typical equilibrium microstructure of a constrained crystal is a polydomain, i.e. an alternation of the plane-parallel layers, or domains, of the parent and product phases with a special crystallographic orientation of interfaces between domains. The relative fractions of the domains are determined by the external conditions. The free energy of a polydomain is a non-convex function of constrained strain. Therefore, the stress–strain relation at displacement controlled deformation of the polydomain is characterized by a negative Young’s modulus. If deformation proceeds under stress control, a hysteretic stress–strain curve on loading and unloading should be observed instead of a negative stress–strain slope. Besides this thermodynamic hysteresis, anelastic hysteresis appears at a constant strain-rate deformation, if the microstructure relaxes more slowly than the strain changes.

An Analytical Model of the Superplastic Bulge Forming of Sheet Metal

This paper presents analytical and experimental study on the superplastic bulge forming of hemispherical shell. Most of the simple engineering models proposed to date do not consider the stress and strain variation from apex to the periphery of the bulged shape, although its effect in the calculations of the thickness distribution is well understood. An analytical model is formulated on the basis of the incremental strain theory of plasticity and non-equal biaxial stress states in deformed shell. Simulation programs were developed to predict some deformation parameters such as stresses, strains and thickness distribution, bulging time, pressure-time cycling for constant apex strain rate deformation. In addition to the analytical calculation, Finite Element Analysis (FEA) was conducted to examine the validity of the present analytical model. Bulge forming experiments were conducted by using Ti-alloy SP-700 sheets of thickness 0.75 mm under Ar gas pressure at the temperature 800 °C. The suggested model showed good agreement with the experiments and FEA.

Modeling of the mechanical behavior of semisolid metallic alloys at high volume fractions of solid

A two-phase strain rate and pressure-dependent model that describes the mechanical behavior of semisolid materials at high volume fractions of solid as an interpolation between the limits of fully cohesive and fully cohesionless materials is presented. An internal variable that describes the degree of cohesion in the material is introduced. The proposed model predicts a reduction of the stress required to sustain undrained constant strain rate deformation. From numerical simulations it is shown that high strain rates result in near-undrained conditions and minimal phase segregation. This effect has important consequences in semisolid processing operations.