Constant Strain Rate Conditions Research Articles

A unique time-dependent deformation behavior of coral reef limestone

Catastrophic failure in engineering structures of island reefs would occur when the tertiary creep initiates in coral reef limestone with a transition from short- to long-term load. Due to the complexity of biological structures, the underlying micro-behaviors involving time-dependent deformation are poorly understood. For this, an abnormal phenomenon was observed where the axial and lateral creep deformations were mutually independent by a series of triaxial tests under constant stress and strain rate conditions. The significantly large lateral creep deformation implies that the creep process cannot be described in continuum mechanics regime. Herein, it is hypothesized that sliding mechanism of crystal cleavages dominates the lateral creep deformation in coral reef limestone. Then, approaches of polarizing microscope (PM) and scanning electronic microscope (SEM) are utilized to validate the hypothesis. It shows that the sliding behavior of crystal cleavages combats with conventional creep micro-mechanisms at certain condition. The former is sensitive to time and strain rate, and is merely activated in the creep regime.

Controllable Stress of Magnetorheological Fluid Elastomeric Encapsulations

This study experimentally investigated the different designs of magnetorheological fluid elastomeric encapsulations (MREEs) in order to improve their controllable mechanical properties range. To this end, four different MREE design samples were fabricated, and their stress–strain tests were conducted at constant strain rate conditions by using materials testing machines (i.e., Instron and MTS systems). A compact round electromagnet was used to produce four different magnetic field inputs to activate the MRF inside the MREEs. From the measured stress–strain hysteresis loops, the secant modulus and dissipated energy density of the MREEs were obtained, and their controllable ranges by applied current input were also determined. In addition, in order to evaluate the viscoelastic behavior of MREEs, a dynamic mechanical analysis (DMA) was conducted and the complex modulus was obtained under vibratory loading conditions. By comparing the mechanical properties obtained under constant strain rate conditions, as well as vibratory loading conditions, more effective MREE designs were developed to widen the range of controllable mechanical properties when current input was applied to the electromagnet.

Toward accurate evaluation of bulk hardness from nanoindentation testing at low indent depths

Estimations of bulk hardness from nanoindentation are frequently subject to considerable uncertainties due to indentation size effects (ISE), pileup effects, and potential influence of surface quality or test methods. This study examined materials science principles of nanoindentation test methods to enable accurate prediction of bulk hardness for a series of high purity Fe and Fe-(3–25 wt%) Cr alloys. These materials were tested in as-annealed and thermally aged (100–900 h at 475 ℃ to produce Cr-rich α’ precipitates) conditions. Nanoindentation with a Berkovich indenter at constant strain rate (0.05–0.5 /s) and constant loading rate conditions provided comparable bulk equivalent hardness (H0) extracted by Nix-Gao model, indicating a weak strain rate sensitivity at room temperature. Results from electropolished and fine mechanically polished samples gave comparable measured hardness. Pileup corrections produced a 5–14% correction to H0 which agreed with the experimental bulk Vickers hardness within ∼10% for most tested materials. The microstructural model-predicted and measured strength values agreed for aged samples. A derived analytic expression demonstrates that an ISE error, associated with inappropriate methods such as hardness ratios or changes at a reference depth, would be as large as 60% in estimated bulk hardness for the investigated Fe-Cr alloys.

Temperature Dependent Dynamic Strain Localization and Failure of Ductile Polymeric Rods under Large Deformation

Ductile polymers have been increasingly applied in engineering applications to enhance the structural reliability under impact loading. Due to the limitation of experimental setup to achieve large tensile deformation and the difficulty to achieve dynamic force equilibrium, the localization and post-necking stages up to fracture of ductile polymers at high strain rates have less been investigated. In the present work, the dynamic strain localization of ductile polymeric rods under large tensile deformation up to fracture is studied on the bespoke Hopkinson tension bar synchronized with a high-speed camera. Transparent polycarbonate (PC) is used as a model material in the present study. Likewise, the constitutive response and fracture behaviour of polycarbonate are also characterized with the assistance of Digital Image Correction (DIC) from low to high strain rates under various temperature conditions. The results quantitatively show that the dynamic local strain rate initially increases dramatically to 200 % of the nominal strain rate due to strain localization. This is followed by a rapid drop with necking propagation, and finally tends to stay at strain rate of approximately 20 % of the nominal strain rate until fracture. The elevated temperatures would result in higher local strain rates. Two constitutive models with and without the consideration of constant strain rate condition are constructed for PC and incorporated in finite element simulations. The trend of dynamic local strain rate history with respect to nominal strain rate is successfully reproduced in simulations. The constitutive models particularly the simple dynamic amplification model, are able to reflect the phenomenological key features of the experimentally observed macroscopic and local responses of polycarbonate, and would find their potential applications in impact resistant transparency design.

Rheology of Felsic Granulite at High Temperature and High Pressure

AbstractRheological properties of continental lower crust (CLC) are essential for understanding many geodynamical processes in the Earth. Here we performed a series of deformation experiments on synthetic felsic granulite (65% plagioclase + 15% quartz + 9% clinopyroxene + 6% orthopyroxene + 5% amphibole) using a 5 GPa modified Griggs‐type deformation apparatus at 827–927°C and 1 GPa. All experiments have reached a steady‐state creep under conditions of constant pressure, temperature, and strain rate. Our data yield the following flow law:, whereis in s−1,σin MPa, andTin Kelvin. Microstructural observations show that plagioclase and pyroxene in deformed samples develop noticeable intracrystalline plasticity and shape preferred orientation (SPO). Electron backscatter diffraction (EBSD) measurements demonstrate more significant crystallographic preferred orientations (CPOs) of pyroxene and plagioclase in deformed granulites compared to those in hot‐pressed ones. By contrast, quartz develops nearly random fabrics probably due to the simultaneous activation of multiple slip systems during deformation. These features indicate that dislocation creep dominates the deformation of these minerals and felsic granulite, consistent with the obtained stress exponent. Our data imply that a CLC consisting of felsic granulite is weaker rheologically compared to the quartz‐dominated upper crust and the olivine‐dominated uppermost mantle, which supports the ‘jelly sandwich’ model for the strength of continental lithosphere. Additionally, extrapolations of flow laws of our felsic granulite and formerly‐reported mafic granulite strongly favor the hypothesis of delamination‐induced decratonization of the North China Craton.

Strain localization of a frozen sand under different test conditions

In this paper, a series of plane strain tests were conducted on a coarse frozen sand under different temperatures and loading conditions of constant strain rate and stress. With the overall strain fields obtained with particle image velocimetry (PIV) technique, the influence of loading conditions, temperature and strain rate on the strain localization characteristics of the frozen sand was analyzed. It is indicated that, under the same loading conditions, the temperature and strain rate have little influence on the shear band formation process. Both of the single and X shape shear band are observed under different test conditions. The X shape shear bands are more likely to be generated under strain rate lower than the magnitude of 10−3 min−1. When the sand samples are at failure, most part of the strain field is at dilatancy state. The shear band inclination angle and width are inversely proportional to the temperature and independent of strain rate and loading conditions. Further analysis indicated that, within the testing temperature range in this study, the widely accepted Coulomb's solution of unfrozen soils is applicable as the upper bound of the measured shear band inclination angle of the tested frozen sand, and the measured shear band width falls in the range of 10 to 20 times of mean particle size.

Accelerated hot deformation and heat treatment of the TiAl alloy TNM-B1 for enhanced hot workability and controlled damage

Abstract The titanium aluminide alloy TNM-B1 displays a strong softening behavior (i.e. flow stress reduction) during hot deformation. By taking advantage of this, the deformation speed can be increased according to the rate of softening. Thus, the deformation process can be accelerated, leading to reduced costs for formed TNM-B1 parts. However, accelerated deformation can lead to increased workpiece damage. Therefore, a heat treatment prior to deformation was utilized in order to both produce a desirable microstructure for accelerated deformation conditions and to prevent increased damage. In this work, a cast and hot isostatically pressed (HIPed) TNM-B1 alloy was investigated and compared to a HIPed and heat treated version under constant strain rate conditions at the temperatures 1150, 1175 and 1200 °C. The developed method of applying accelerated deformation was based on a damage model and a material model that were fitted to titanium aluminides. For constant strain rate conditions, the heat treatment improved both the hot workability and the damage tolerance of the HIPed material state. Therefore, only the heat treated state was investigated under accelerated strain rate conditions at the same constant temperatures. The results show that, depending on deformation temperature, the processing times can be reduced by around 51.4–59.6% by applying accelerated deformation with an initial strain rate of 0.0013 s−1 and by around 56.1–69.3% for an initial strain rate of 0.005 s−1, compared to deformation at the corresponding constant strain rates. Furthermore, the amount of damage observed for accelerated deformation was comparable to constant strain rate deformation. The microstructure characteristics were similar for accelerated and constant strain rate deformation at 1200 °C. However, increased lamellar fractions occurred at 1150 and 1175 °C for accelerated deformation compared to constant strain rate deformation.

Residual strength prediction for unidirectional CFRP using a nonlinear viscoelastic constitutive equation considering entropy damage

We propose a viscoelastic/plastic constitutive equation for viscoelastic media based on irreversible thermodynamics and the viscoelastic theory. Uniaxial tensile tests on a TriA-X polyimide resin are performed at different temperatures and strain rates to determine the material parameters for the constitutive equation. In the numerical analysis, the FORTRAN programming language is used to apply the proposed equation to the matrix resin. Transverse tensile failure analysis is performed on the unidirectional carbon fiber reinforced plastic (CFRP) in constant strain rate condition after holding constant strain. In this condition, the failure strength is lower than the static tensile strength. The same tendency is observed in the three-point bending fracture test of the unidirectional CFRP. The proposed model expresses the accumulation of resin damage while holding a constant strain and predicts the residual strength and lifetime of the unidirectional CFRP.

Re-entrant Formation on Superplastic Forming Process by Mechatronics Approach in 5083 Al Alloy

Superplastic materials are attributed viscous in behavior which exhibit very narrow and steady grain formation at half of the melting point temperature of given components. Superplastic deformation characteristics are carried out in different pressure control with constant strain rate conditions. In different alloy, the maximum (optimum) strain rate changes from 0.001 to 0.00001s-1. The objective of this research work is to predict the pressure requirements (optimize) to obtain smooth (uniform) profile in a re-entrant shape formation of 5083 Aluminium alloy by using mechatronics approach of Programming Logic Control method. The effect of various forming parameter such as, forming pressure, bulge forming time and thickness distribution of the sheet in a re- entrant shape product. Finite Element analysis is a powerful tool to evaluate the superplastic forming processes (SPF) with accurate prediction of the deformation characteristics.

Thermo-poromechanics-based viscoplastic damage constitutive model for saturated frozen soil

This study is primarily intended to present a viscoplastic damage theory for saturated frozen soil based on thermo-poromechanics. On the basis of the irreversible process of thermodynamics, an elasto-viscoplastic damage constitutive theoretical framework for saturated frozen soils is formulated by use of the Lagrangian saturation and solid-fluid interface interactions, for which the upscaling microscopic properties of saturated frozen soil in plasticity are provided to elucidate the macro stress-strain relation. Furthermore, a corresponding constitutive model for simulating the cryogenic triaxial stress state of saturated frozen soils is presented to take the influence of creep and loading strain rate into account. Compared with the cryogenic triaxial tests on saturated frozen soils, it is demonstrated that the time-dependent model proposed here can simulate the salient properties of frozen soils under constant shear stress and loading strain rate conditions. The constitutive theory proposed here provides a potential basis for analyzing the stress deformation considering the effects of creep and loading strain rate for saturated frozen soils in cold regions.

Critical Strain for Dynamic Recrystallisation. The Particular Case of Steels

The knowledge of the flow behavior of metallic alloys subjected to hot forming operations has particular interest for metallurgists in the practice of industrial forming processes involving high temperatures (e.g., rolling, forging, and/or extrusion operations). Dynamic recrystallisation (DRX) occurs during high temperature forming over a wide range of metals and alloys, and it is known to be a powerful tool that can be used to control the microstructure and mechanical properties. Therefore, it is important to know, particularly in low stacking fault energy materials, the precise time at which DRX is available to act. Under a constant strain rate condition, and for a given temperature, such a time is defined as a critical strain (εc). Unfortunately, this critical value is not always directly measurable on the flow curve; as a result, different methods have been developed to derive it. Focused on carbon and microalloyed steels subjected to laboratory-scale testing, in the present work, the state of art on the critical strain for the initiation of DRX is reviewed and summarized. A review of the different methods and expressions for assessing the critical strain is also included. The collected data are well suited to feeding constitutive models and computational codes.

Atomistic simulation of crack propagation along γ-TiAl lamellar interface

Due to start-up and shut-down operations of engine, TiAl structural components usually undergo not only static but also cyclic mechanical loading. The crack propagation mechanisms of γ-TiAl under two types of loading are studied in this work to reveal the differences of the mechanisms under constant strain rate and cyclic loading. Since the crack prefers to nucleate at the interface, two types of loadings are applied to a γ-TiAl interface system with a pre-existing micro-crack at the interface by the means of classical molecular dynamics simulation, the loading direction is along [111] perpendicular to the interface. The evolution of crack tip and dislocation is observed in atomistic scale. The results show that, under both loading types, the crack propagates asymmetrically, Shockley dislocations emit on the (-1-11) slip plane from the right crack tip and slip along [-1-1-2] direction. The dislocations blunt the extension of crack while the left crack tip propagates in a brittle way. During the cyclic loading, different with constant strain rate condition, the crack advances and dislocations slip with increasing loads and retreat during unloading. In addition, the stress decreases and the crack length increases with the increase of the cyclic loading number.

Physically-based constitutive description of a commercial Al-Mg-Si alloy deformed under cold-warm working conditions

The experimental and numerical modeling of cold forging operations conducted on commercial Al alloys requires a precise knowledge of the functional dependence of both flow stress and work-hardening rate on microstructure and deformation conditions. In order to contribute to the improvement of the finite element computer modeling of forming operations conducted on Al alloys, under cold-warm working conditions, an original and rational constitutive description, able to predict accurately both the flow stress and work-hardening rate of an AA6082-T6 Al alloy is proposed. The constitutive formulation has been developed on the basis of the Mechanical Threshold Stress (MTS) model and its applicability is limited to the deformation of the material under cold-warm working conditions, that is to say, in the temperature range of 298–423 K. A novel differential equation for the description of the continuous change in the work-hardening rate of the alloy has been developed, which allows the prediction of the changes in flow stress and work-hardening rate during deformation either under constant and variable temperature and strain rate conditions. The validation of the developed constitutive description has been accomplished by its implementation into a finite element (FE) model for the accurate prediction of the change in some local contact parameters, such as contact pressure, sliding velocity and interface temperature, during the friction test employed in the evaluation of friction conditions in metalworking, known as the Upsetting Sliding Test (UST).

An Effective Pulse-Shaping Technique for Testing Stainless Steel Alloys in a Split-Hopkinson Pressure Bar

Pulse shaping techniques are an integral component of designing and executing valid Split-hopkinson pressure bar (SHPB) experiments. Proper pulse shaping is vital for achieving stress equilibrium and a constant strain rate within the dynamically tested sample. A systematic method based on two-dimensional finite element (FE) analysis was developed to design an optimized single material pulse shaper for SHPB testing of two stainless steel alloys. The tested alloys exhibit high strain-hardening, but have significantly different mechanical properties: Lean Duplex Stainless Steel 2101 (LDSS 2101) and austenitic stainless steel 316L. Results show that pulse shapers made of LDSS 2101 are capable of satisfying stress equilibrium and constant strain rate conditions for the studied materials at different strain rates regimes. The outlined FE analysis workflow is an effective approach to define the optimal dimensions of pulse shapers without the need for costly pulse-shaper-development experimental trials.

Numerical Investigation on the Necessity of a Constant Strain Rate Condition According to Material’s Dynamic Response Behavior in the SHPB Test

The split Hopkinson pressure bar (SHPB) apparatus is frequently used to investigate the dynamic compression properties of various materials at strain rates from 102 to 104 s−1. Keeping the strain rate constant during loading is an important condition for obtaining accurate experimental results. However, we do not always need to take additional measures to control the constant strain rate loading conditions for materials with different dynamic response behaviors. To investigate the necessity of a constant strain rate condition in the SHPB test according to the different dynamic mechanical response behaviors of materials, a comprehensive numerical analysis scheme combined with the Cowper-Symonds plastic kinematic model was designed to perform the simulation tests. There are two factors primarily resulting in the errors in the calculated stress-strain response for the representative material model. One of them is the dynamic scale factor, which represents the strain rate sensitivity and controls the variation amplitude of flow stress with the change in strain rate. The other factor is the work-hardening rate, which affects the results by expanding the decrease in strain rate. This paper quantitatively describes the effects of strain rate sensitivity and the strain-hardening modulus on the accuracy of the reconstructed stress-strain behavior of a sample under a constant incident pulse. The conclusion presents several reference guides for the necessity of a constant strain rate condition for different dynamic response behaviors of materials based on the representative constitutive model.

Dislocation Based Flow Stress Model of 300M Steel in Isothermal Compression Process.

The relationship between microstructure and flow behaviour has attracted attention from many researchers for the past decades, whilst the influences of dislocation and recrystallization on flow stress have not been well understood, which led to failure in flow stress prediction at high temperature compressions. In this work, we tried to provide a novel explanation of the relationship between microstructure evolutions and flow behaviour, and the influence of dislocation and recrystallization on flow stress was investigated. A dislocation based flow stress model was proposed and applied for 300M steel at the strain rate of 0.01–10 s−1 and the temperature of 950–1150 °C. Results showed the established model could predict the flow stress both at constant strain rate conditions and at variable strain rate conditions. The present investigation is helpful to a better understanding of hardening and softening mechanisms in hot compression of 300M steel.

Plausible extension of Anand's model to metals exhibiting dynamic recrystallization and its experimental validation

Modeling and optimization of industrial hot-working operations by means of commercial finite element computer codes require robust constitutive descriptions, which could be easily implemented. Also, it is expected that such formulations are able to describe as accurate as possible the flow stress, work-hardening and work-softening rate of the material, as a function of microstructure and deformation conditions. The present communication describes the development of a novel constitutive description of metals which exhibit dynamic recrystallization during deformation under hot-working conditions. The formulation is founded on the extension of the model earlier developed by Anand and co-workers for the constitutive description of metals which exhibit dynamic recovery as the only dynamic restoration mechanism during hot deformation. The advanced constitutive formulation has been validated by conducting axisymmetric compression tests with samples of a R260 steel employed for the manufacture of rail tracks. The specimens were deformed in a wide range of temperatures and strain rates, both under constant and variable strain rate conditions. The latter involve either an increase or a decrease in the Zener-Hollomon parameter as plastic deformation is applied. The results obtained indicate that the proposed constitutive description is able to reproduce quite accurately the experimental flow stress data. It has also been shown that the correct computation of the recrystallization time and volume fraction recrystallized dynamically, by means of an appropriate differential or incremental formulation of the Avrami equation, constitutes an essential aspect of the model. Such an approach is particularly important for predicting correctly the changes in flow stress under variable strain rate conditions.

Microstructure and flow stress evolution during hot deformation of 304L austenitic stainless steel in variable thermomechanical conditions

Most of industrial hot deformation processes are performed in variable conditions where the strain rate and/or deformation temperature are not constant. In this work, hot compression tests in both constant and varying strain rate conditions were performed on 304L austenitic stainless steel using a Gleeble 3800 machine. The variations in microstructure and flow stress during and after the transient deformation stage are carefully analysed. It is clearly shown that, following the abrupt increase of strain rate, both the flow stress and substructural changes are subjected to a transient period over strains of ~0.2, before reaching states similar to those developed through constant strain rate conditions at the new strain rate. When the strain rate was rapidly decreased, the flow stress transient stage extended over a lower strain interval than the substructure transient period. It is shown that local misorientation distributions are good indicators of the deformation microstructure of low SFE materials as they capture small variations in deformation structures which cannot be analysed from stress-strain curves alone.

Probing the limits of metal plasticity with molecular dynamics simulations.

Ordinarily, the strength and plasticity properties of a metal are defined by dislocations-line defects in the crystal lattice whose motion results in material slippage along lattice planes. Dislocation dynamics models are usually used as mesoscale proxies for true atomistic dynamics, which are computationally expensive to perform routinely. However, atomistic simulations accurately capture every possible mechanism of material response, resolving every "jiggle and wiggle" of atomic motion, whereas dislocation dynamics models do not. Here we present fully dynamic atomistic simulations of bulk single-crystal plasticity in the body-centred-cubic metal tantalum. Our goal is to quantify the conditions under which the limits of dislocation-mediated plasticity are reached and to understand what happens to the metal beyond any such limit. In our simulations, the metal is compressed at ultrahigh strain rates along its [001] crystal axis under conditions of constant pressure, temperature and strain rate. To address the complexity of crystal plasticity processes on the length scales (85-340 nm) and timescales (1 ns-1μs) that we examine, we use recently developed methods of in situ computational microscopy to recast the enormous amount of transient trajectory data generated in our simulations into a form that can be analysed by a human. Our simulations predict that, on reaching certain limiting conditions of strain, dislocations alone can no longer relieve mechanical loads; instead, another mechanism, known as deformation twinning (the sudden re-orientation of the crystal lattice), takes over as the dominant mode of dynamic response. Below this limit, the metal assumes a strain-path-independent steady state of plastic flow in which the flow stress and the dislocation density remain constant as long as the conditions of straining thereafter remain unchanged. In this distinct state, tantalum flows like a viscous fluid while retaining its crystal lattice and remaining a strong and stiff metal.

Multiaxial elastoplastic cyclic loading of austenitic 316L steel

Cyclic stress-strain response and fatigue damage character has been investigated in austenitic stainless steel 316L. Hollow cylindrical specimens have been cyclically deformed in combined tension-compression and torsion under constant strain rate condition and different constant strain and shear strain amplitudes. In-phase and 90° out-of-phase cyclic straining was applied and the stress response has been monitored. Cyclic hardening/softening curves were assessed in both channels. Cyclic softening followed for higher strain amplitudes by long-term cyclic hardening was observed. Cyclic stress-strain curves were determined. Study of the surface damage in fractured specimens revealed the types and directions of principal cracks and the sources of fatigue crack initiation in slip bands.