Showing papers on "Strain rate published in 2011"

A Computational Constitutive Model for Glass Subjected to Large Strains, High Strain Rates and High Pressures

Abstract: This article presents a computational constitutive model for glass subjected to large strains, high strain rates and high pressures. The model has similarities to a previously developed model for brittle materials by Johnson, Holmquist and Beissel (JHB model), but there are significant differences. This new glass model, presented in Fig. 1, provides a material strength that is dependent on the location and/or condition of the material. Provisions are made for the strength to be dependent on whether it is in the interior, on the surface (different surface finishes can be accommodated), adjacent to failed material, or if it is failed. The intact and failed strengths are also dependent on the pressure and the strain rate. Thermal softening, damage softening, timedependent softening, and the effect of the third invariant are also included. The shear modulus can be constant or variable. The pressure-volume relationship includes permanent densification and bulking. Damage is accumulated based on plastic strain, pressure and strain rate. Significant features of the model are the ability to compute size effects (small scales are stronger than large scales), surface effects (smooth surfaces are stronger than rough surfaces), and high internal tensile strength (as demonstrated by spall plate-impact experiments). Simple (single-element) examples are presented to illustrate the capabilities of the model. Several example computations are presented in Figs. 2-4 to demonstrate the ability to compute more complex, high-velocity-impact conditions. Figure 2 presents computed results for a gold projectile impacting a borosilicate target with a copper buffer attached to the impact surface. The computed results produce interface defeat (no glass penetration) at Vs = 800 m/s and prompt penetration at Vs = 900 m/s. This is consistent with the test results provided by Anderson et al. [1]. Behner et al. [2] performed experiments using no buffer (gold rod impacting bare glass) which produced penetration at much lower impact velocities. For these experiments the penetration velocities were determined using a series of flash x-rays and are presented as a function of impact velocity in the lower protion of Fig. 3. Also shown are the computed penetration velocities for Vs = 900 m/s and Vs = 2400 m/s. The computed results are in good agreement with the experiments. Anderson et al. [3] also performed experiments using a pointed steel projectile impacting thin plates of borosilicate glass at three different scales. The smaller scale targets were stronger than the larger scale targets. Figure 4 demonstrates the capability to compute size effects. Computed results are presented for the 0.50-cal (scale = 1.0) and the 0.22cal (scale = 0.44) projectile for Vs = 300 m/s and Vs = 400 m/s. At 300 m/s the 0.50-cal projectile exits the target at Vr = 22 m/s but the smaller scale 0.22-cal projectile is stopped. As the impact veloicty is increased the computed size effect diminshes as shown at Vs = 400 m/s. The ability for the computations to produce size effects is due to the time-dependent features in the model.

Lagrangian Dynamics and Models of the Velocity Gradient Tensor in Turbulent Flows

Abstract: Many fundamental and intrinsic properties of small-scale motions in turbulence can be described using the velocity gradient tensor. This tensor encodes interesting geometric and statistical information such as the alignment of vorticity with respect to the strain-rate eigenvectors, rate of deformation and shapes of fluid material volumes, non-Gaussian statistics, and intermittency. In the inertial range of turbulence, similar properties can be described using the coarse-grained or filtered velocity gradient tensor. In this article we review various models that aim at understanding these phenomena using a small number of ordinary differential equations, written either as a low-dimensional dynamical system or as a set of stochastic differential equations. Typically these describe the Lagrangian evolution of the velocity gradient tensor elements following fluid particles and require models for the pressure Hessian and viscous effects. Sample results from various models are shown, and open challenges are high...

Nanoindentation strain-rate jump tests for determining the local strain-rate sensitivity in nanocrystalline Ni and ultrafine-grained Al

Abstract: A nanoindentation strain-rate jump technique has been developed for determining the local strain-rate sensitivity (SRS) of nanocrystalline and ultrafine-grained (UFG) materials. The results of the new method are compared to conventional constant strain-rate nanoindentation experiments, macroscopic compression tests, and finite element modeling (FEM) simulations. The FEM simulations showed that nanoindentation tests should yield a similar SRS as uniaxial testing and generally a good agreement is found between nanoindentation strain-rate jump experiments and compression tests. However, a higher SRS is found in constant indentation strain-rate tests, which could be caused by the long indentation times required for tests at low indentation strain rates. The nanoindentation strain-rate jump technique thus offers the possibility to use single indentations for determining the SRS at low strain rates with strongly reduced testing times. For UFG-Al, extremely fine-grained regions around a bond layer exhibit a substantial higher SRS than bulk material.

The effect of punch velocity on the compaction of a variety of materials.

Abstract: The effect of punch velocity over the range 0.033-400 mms-1 on the compaction of a variety of materials has been studied using constants derived from the Heckel equation as criteria to describe their behaviour. For materials known to deform plastically, e.g. maize starch and polymeric materials, there was an increase in the yield pressure with punch velocity attributable to a change either from ductile to brittle behaviour or a reduction in the amount of plastic deformation due to the time dependent nature of plastic flow. For materials known to consolidate by fragmentation, e.g. magnesium and calcium carbonates, there was no change in yield pressure with increasing punch velocity. The data has been analysed in terms of the strain rate sensitivity of the materials calculated from their yield pressure at low and high punch velocities.

Strain-induced crystallization of natural rubber: a review of x-ray diffraction investigations

Abstract: Strain-induced crystallization of natural rubber was discovered in 1925 by the means of x-ray diffraction and has been widely investigated by this technique until today. The studies devoted to the structure of the crystalline phase of natural rubber are first reviewed. This structure is strongly anisotropic and can be related to the exceptionally good strength and fatigue properties of this material. The relationships between strain-induced crystallization of natural rubber and its mechanical response, during static or tension-retraction tests, are also reviewed and discussed; in particular, the hysteresis of the stress-strain curve is mainly explained by strain-induced crystallization. The kinetics of crystallization under both static and cyclic deformation is also discussed, as well as the influence of different factors, depending either on material composition (crosslink density, carbon black fillers) or on external parameters (temperature, strain rate…).

Recrystallization of 30Cr2Ni4MoV ultra-super-critical rotor steel during hot deformation. Part I: Dynamic recrystallization

Abstract: The metadynamic recrystallization (MDRX) behavior of 30Cr2Ni4MoV ultra-super-critical (USC) rotor steel during hot deformation was investigated based on the first part of this study, in which the evolution of the dynamically recrystallized structure was studied in detail. Compression tests were performed using double hit schedules at temperatures of 970–1250 °C, strain rates of 0.001–0.1 s−1 and inter-pass time of 1–100 s. Based on the experimental results, the kinetic equations and grain size model were established. Results show that the effects of deformation parameters, including forming temperature and strain rate, on MDRX softening fractions and austenite grain size in the two-pass hot deformed 30Cr2Ni4MoV steel are significant. Results also reveal that the pre-strain (beyond the peak strain) has little influence on the MDRX behaviors in 30Cr2Ni4MoV steel. Comparisons between the experimental and the predicted results were carried out. A good agreement between the experimental and the predicted results was obtained, which verified the developed models.

Study of the hot deformation behaviour in Ti-5Al-5Mo-5V-3Cr-1Zr

Abstract: Structural applications of near beta titanium alloys are gradually increasing in the aerospace industry because of their high specific mechanical properties and good corrosion resistance. Furthermore, a wide range of microstructures can be obtained by thermomechanical processes. This work determines by the use of EBSD technique the mechanism of restoration active in the near beta titanium alloy Ti–5Al–5Mo–5V–3Cr–1Zr for deformations in both α + β and β field near to the β transus temperature ( T β = 803 °C). Hot compression tests are carried out up to 0.7 true strain by means of a Gleeble ® 1500 machine at strain rates of 0.01, 0.1 and 1 s −1 . Dynamic recovery of β phase and rotation of the α grains take place predominantly in the α + β field. Further deformation produces continuous dynamic recrystallization of the β phase influenced by the strain rate. Dynamic recovery is observed during deformation above the T β , where the misorientation is increasing towards the grain boundaries forming new small grains with a substructure at high strain rates and larger deformation. The stress exponent and the apparent activation energy for the sinh constitutive equations are determined and the microstructural features are correlated with the Zener–Hollomon parameter.

A Lagrangian framework for analyzing microstructural level response of polymer-bonded explosives

Abstract: A cohesive finite element method (CFEM) framework for quantifying the thermomechanical response of polymer-bonded explosives (PBXs) at the microstructural level is developed. The analysis carried out concerns the impact loading of HMX/Estane at strain rates on the order of 104?105?s?1. Issues studied include large deformation, thermomechanical coupling, failure in the forms of microcracks in both bulk constituents and along grain/matrix interfaces, and frictional heating. The polymer matrix is described by a thermo-elasto-viscoelastic constitutive formulation, accounting for temperature dependence, strain rate sensitivity and strain hardening. The HMX crystals are assumed to be elastic. The CFEM framework allows the contributions of individual constituents, fracture and frictional contact along failed crack surfaces to heating to be tracked and analyzed. Digitized micrographs of actual PBX materials and idealized microstructures with Gaussian distributions of grain sizes are used in the analysis. The formation of local hot spots as potential ignition sites is primarily due to the viscoelastic dissipation in the matrix in early stages of deformation and frictional heating along crack surfaces in later stages of deformation. The framework is a useful tool for the design of energetic composites and the results can be used to establish microstructure?response relations that can be used to assess the performance of energetic composites.

Hot deformation behavior and microstructural evolution of homogenized 7050 aluminum alloy during compression at elevated temperature

Abstract: Hot compression tests of homogenized 7050 aluminum alloy were carried out on the Gleeble-1500 thermal simulation machine, and the associated microstructure was studied using electron back scattered diffraction technique and transmission electron microscopy. The results showed that the peak stress levels decreased with the increase of deformation temperatures or the decrease of strain rates, which can be represented by the Zener–Hollomon parameter in the exponent-type equation with the hot deformation activation energy of 160.3 kJ/mol. With the decrease of Z values, results showed a continuous decrease in very low angle boundaries, exhibiting a misorientation between 2° and 5°, associated to substructure, and a steady increase in the other higher angle boundaries, especially with the misorientation angles between 30° and 60°. And such an evolution is due to the increase of subgrain size with the decrease of Z values. At lower Z , the dislocations collected into more widely spaced and less dense tangles. As strain rose, the tangles reorganized into subgrains with walls that were more widely spaced and straighter; they had fewer, more regularly arranged dislocations. The main softening mechanism of homogenized 7050 aluminum alloy is dynamic recovery.

Hot working behavior of 2205 austenite–ferrite duplex stainless steel characterized by constitutive equations and processing maps

Abstract: The hot deformation characteristics of the 2205 duplex stainless steel were analyzed using constitutive equations and processing maps. The hot compression tests were performed at temperature range of 950–1200 °C and strain rate of 0.001–1 s−1. Flow stress was modeled by the constitutive equation of hyperbolic sine function. However, the stress exponent and strain rate sensitivity were different at low and high deformation temperatures where austenite and ferrite are dominant, respectively. It was recognized that strain at the peak point of flow curve increases with the Zener–Hollomon parameter, Z, at low temperature deformation while at high temperature deformation it actually decreases with Z. The power dissipation map, instability map and processing map were developed for the typical strain of 0.3. It was realized that dynamic restoration mechanisms could efficiently hinder the occurrence of flow instability at low and medium strain rates. Otherwise, the increase in strain rate at low and high temperatures could increase the risk of flow instability.