Constant Engineering Strain Rate Research Articles

A Conical Striker Bar to Obtain Constant True Strain Rate for Kolsky Bar Experiments

Many split Hopkinson pressure bar (SHPB) or Kolsky bar techniques use pulse shaping methods to obtain constant engineering strain rate for the specimen response. However, constitutive models for numerical simulations use the axial rate of deformation which is the true axial strain rate. In this study, we present an equation for the incident bar strain produced by a truncated conical striker bar. These incident bar strains are shaped so that we can obtain constant true strain rate for the specimen.

Closed-form and numerical stress solution-based parameter identification for incompressible hyper-viscoelastic solids subjected to various loading modes

This paper presents closed-form and numerical stress solutions for incompressible hyper-viscoelastic solids considering the following loading modes: uniaxial and equibiaxial tension/compression, pure shear and simple shear. The analytical stress solutions are based on three widely-used hyperelastic material models (Neo-Hookean, Mooney–Rivlin, Ogden model) and assume constant engineering strain rate. On the contrary, the numerical stress solutions are independent of both the hyperelastic law and the loading history. It has been confirmed that these stress solutions can be utilised to identify the hyper-viscoelastic material model parameters. In addition, the closed-form stress solutions may allow verifying different numerical time integration schemes. The accuracy of the constitutive constants extracted for an isoprene rubber has been investigated by comparing the predicted and the measured behaviour. The very good agreement between them shows clearly the benefit of the stress solutions presented.

A Viscoplastic Constitutive Equation from Kolsky Bar Data for Two Steels

Kolsky bar data for viscoplastic materials are usually presented as true stress versus true strain curves at nearly constant values of engineering strain rates. However, constitutive models for numerical simulations require the true axial rate of deformation which is true strain rate. We present a procedure that uses existing data with constant engineering strain rate to obtain a constitutive equation in terms of true strain rate for 304 stainless steel and 4340 Rc 45 steel.

Effects of Constant Engineering and True Strain Rates on the Mechanical Behavior of 304 Stainless Steel

Kolsky bar (split Hopkinson pressure bar) with a pulse shaping technique was utilized to study the dynamic behavior of 304 stainless steel at high constant engineering and true strain rates. To show the differences between the strain rates, equations were presented for the engineering strain rate and strain as a function of true strain rate. To deform the specimen at constant true strain rates at 600–2500 s−1, a bi-linear incident pulse was necessary. Furthermore, a trapezoidal incident wave was required to deform the specimen at a constant true strain rate of 7000 s−1. The results show that the dynamic flow stresses of the specimens increased with increasing strain rates. At the highest strain rate of 7000 s−1, the flow stress of specimen deforming at constant engineering strain rate was clearly higher than the flow stress obtained at a similar constant true strain rate.

Analysis of rate-dependent tensile properties of polypropylene fibres used in thermally bonded nonwovens

The stress–strain behaviour of polypropylene fibres is evaluated for various tensile strain rates. Fibre samples are extracted from a thermally bonded nonwoven and fixed in a low-load tensile test machine. A methodology is introduced to implement a constant true strain rate at high strain tests for conventional tensile test machines. The obtained results indicate that polypropylene fibres show a highly viscous behaviour, especially during the initial stage of load application. No significant difference in a tensile behaviour of fibres was observed for loading regimes with a constant true strain rate and a constant engineering strain rate.

Moderate temperature compression incorporating plastic deformation and rearrangement in Al2O3–ZrO2 ceramics

In this article, we described an unusual plastic deformation of Al2O3–ZrO2 ceramics under uniaxial compression at 500°C with constant engineering strain rate of 3.5×10−3s−1. The Al2O3–ZrO2 ceramics displayed different deformations from either the traditional ceramics or the amorphous material. The Al2O3–ZrO2 ceramics started to yield at about 1.5GPa. A large elastic strain of about 27% had been achieved when the material began to yield. The elastic deformation transited to yield smoothly without any evident peak stress. The compressive stress continuously increased to about 2.2GPa before unloading. This unusual deformation might be related to the porous structure of the sample and coexistence of the amorphous phases and crystalline phases.

Grain Refinement by High Temperature Plane-Strain Compression of Fe-2%Si Steel

An Fe-2%Si alloy, which was designed for electromagnetic applications was submitted to a series of plane strain compression (PSC) tests with reductions of 25, 35 and 75% at temperatures varying from 800 to 1,100°C and at a constant engineering strain rate corresponding to a constant cross velocity of 20 mm/s. The initial structure of the material displayed nearly equi-axed grains with an average size of 80 μm. The as-received texture was characterised by a nearly random cube fibre (<100>//ND) with a relatively weak maximum on the rotated cube component ({001}<110>). After deformation the samples were water quenched in order to avoid post-process static recrystallization events. The microstructures were analysed by orientation imaging microscopy (OIM) revealing that the zone of PSC was restricted to the central layers of the sample but minimally covering 50% of the sample thickness. After deformation at 800°C the conventional lamellar deformation structures were observed on the sections perpendicular to the transverse direction of PSC. At higher deformation temperatures the structure was of a bimodal nature consisting of lamellar deformation bands and equi-axed small grains. The volume fraction of these small equi-axed grains increased from 19.9% after 75%reduction at 800°C to 67.8% after 75% reduction at 1.100°C. After 75% reduction the equi-axed grains exhibited an average size of 10 μm which represents a strong grain refinement with respect to the initial size of 80 μm prior to PSC. Ferrite Silicon steels undergo extensive dynamic recovery during hot working. Dynamic recrystallization (DRX), though, has not yet been reported for these alloys although the present data suggest that a DRX mechanism might be responsible for the remarkable grain refinement after relatively low amounts of strain applied at high temperatures.

Elevated temperature deformation of Cr 3Si alloyed with Mo

Four-point bend, constant load compressive creep and constant engineering strain rate tests were conducted on arc-melted and powder-metallurgy (PM) processed Cr 40Mo 30Si 30 specimens in the temperature range 1400–1700 K. This is a two-phase alloy consisting of (Cr,Mo) 3Si and (Cr,Mo) 5Si 3 phases. The PM specimens, which were substantially weaker than the arc-melted materials, exhibited a stress exponent, n, of about 2 and an apparent activation energy for creep, Q a, of 485 kJ/mol. The mechanism in these specimens appeared to be controlled by creep of a glassy phase. In the case of arc-melted specimens for which n ~ 3 and Q a ~ 430 kJ/mol, the rate-controlling creep mechanism appeared to be that dominant in the (Cr,Mo) 5Si 3 phase. In this case, it is suggested that the Nabarro creep mechanism, where dislocation climb is controlled by Bardeen–Herring vacancy sources, is the dominant creep mechanism. Finally, an analysis of the present and literature data on Cr 3Si alloyed with Mo appeared to suggest that the creep rate decreases sharply with an increase in the Mo/Si ratio.

Mechanical properties of Al-Li-Cu icosahedral quasicrystals

Poly-quasicrystalline samples of an icosahedral Al-Li-Cu alloy have been deformed in compression at a constant engineering strain rate, at temperatures ranging from 300 to 773 K ( T m ≅ 896 K). The samples are very brittle below about 500 K but rather ductile above this temperature, with an upper yield stress decreasing linearly with increasing temperature, from 225 MPa at about 473 K to 22 MPa at 773 K. Load relaxation behavior and activation parameter values suggest that, in this material, plastic deformation at high-temperature is controlled by a thermally activated process that involves atomic diffusion.

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