Strain Rate Conditions Research Articles

Constitutive model of GH4720Li high temperature nickel base alloy at high strain rate and large temperature range

The dynamic mechanical properties of GH4720Li nickel base superalloy under high and low strain rates in a wide temperature range have been studied, and a constitutive model with higher fitting progress have been established. The experimental results show that the abnormal phenomenon of dynamic mechanical properties of GH4720Li alloy appears under the condition of high strain rate. This is because the change of Cr (MO) content in precipitates and the change of precipitate morphology lead to the difference of dynamic mechanical properties of GH4720Li alloy at high and low strain rates. Besides, A new piecewise function model based on a phenomenological representation of the stress-strain curves is proposed to describe the constitutive equation of Nickel-based superalloy GH4720Li of stress-strain curves. Meanwhile, new methods to obtain the material constant k and C are proposed to predicted accurately the flow stress. The comparison between calculated values and experimental values based on the new constitutive modeling shows that these methods for obtaining material constants k and C are valid and the new function model is significant for establishing constitutive equations of Nickel-based superalloy GH4720Li in hot deformation processes.

Tensile behaviour of Inconel 718 alloys under extreme conditions of temperature and strain-rate

Nickel-based superalloys are widely used in critical applications where structural components are subjected to harsh operating conditions such as elevated temperatures and high strain-rate. These alloys are also among the most hard-to-cut materials. For this reason, some critical components with complex geometrical features along with critical dimensions cannot easily manufactured by conventional technologies. A rising disruptive Additive Manufacturing (AM) technique, namely powder-based Laser Metal Deposition (LMD), is able to overcome these limitations in terms of manufacturing costs, tool wear, as well as lead time. As a consequence, the mechanical response under harsh condition of additively manufactured Nickel-based superalloys has to be accurately understood in order to guarantee the reliability of the structural parts made with them. Presently very few researches were addressed to study the dynamic tensile behaviour of Inconel 718 produced by additive manufacturing under high strain-rate combined with elevated temperature. To overcome this lack, the coupled effect of strain rate (0.001 s−1, 250 s−1 and 800 s−1) and temperature (20°C, 350°C and 550°C) on the tensile properties of Inconel 718 alloys produced through cast and additive manufacturing technologies has been experimentally studied. The experiments were also addressed to investigate and compare the flow stress behaviour in function of strain rate and temperature considering the differences in terms of microstructure. A modest strain-rate sensitivity has been observed for both as-cast and as-built material, as well as a moderate decrease of the mechanical strengths has been highlighted for increasing temperatures. Finally, comparable mechanical behaviour has been observed between additively manufactured samples produced with a power laser of 400W and as-cast samples.

Thermomechanical tensile properties of deposited Inconel 718 superalloy over a wide range of strain rate and temperature

Nickel-based superalloys show high strength retained also at high temperature and they are widespread used for structural components exposed during services to high temperature combined with high strain rate or impact loading conditions. The objective of this study was the investigation of the plastic flow behaviour of Laser Metal Deposited Nickel-based superalloy Inconel718. The material was manufactured at Northwestern Polytechnical University in China. Specimens with three different heat treatment conditions were investigated: as-deposited, directly aged and aged after homogenization and solution. High strain rate tensile tests were performed on the direct Hopkinson bar setup developed at DYNLab laboratory at Politecnico di Torino. At a nominal strain rate of 1500 s-1the temperature sensitivity was investigated between 20 and 1000°C. An induction heating system was adopted, and the temperature was monitored by thermocouples and infrared pyrometer and high-speed camera. The results showed the materials strength decreases as a function of temperature with a significant drop starting from 800 °C. An asymmetric tension-compression behaviour was found by comparing the results with data in compression. The strain rate influence was investigated at room temperature and very limited or negligible sensitivity was found covering six orders of magnitude in strain rate.

Dynamic Properties Test and Constitutive Relation Study of Lightweight Aggregate Concrete under Uniaxial Compression

For the purpose of studying the dynamic properties of lightweight aggregate concrete, dynamic performance tests under uniaxial compression were conducted by considering 10 different strain rates ranging from 10−5/s to 10−1/s, from which the stress‐strain curves under various compressive loads were obtained. From the stress‐strain curves, parameters including peak stress, peak strain, and elastic modulus of lightweight aggregate concrete, as well as the concrete failure mode, were determined and examined. By reviewing the relevant literature on ordinary concrete, the dynamic properties of lightweight aggregate concrete were analyzed accordingly. Meanwhile, by applying the dynamic elastoplastic damage constitutive model, the effect of dynamic rate on lightweight aggregate concrete was calculated. The experimental results showed that the damage mode of lightweight aggregate concrete under the static and dynamic strain rates belonged to shear failure, which is different from that of ordinary concrete (binding material failure). On the other hand, it was also found that the peak stress and elastic modulus of lightweight aggregate concrete could be increased by 54.48% and 28.75%, respectively, with the increase of strain rate, suggesting that the loading strain rate has a stronger influence on lightweight aggregate concrete than on ordinary concrete. Based on the experimental data, both the peak stress and nondimensionalized elastic modulus are in linear relationship with the logarithm of the nondimensionalized strain rate. Moreover, the established constitutive model had been verified as an effective and reliable tool for simulating the dynamic rate effect of lightweight aggregate concrete.

Effect of uniaxial loading direction on mechanical responses and texture evolution in cold pilgered Zircaloy-4 tube: Experiments and modeling

Mechanical responses of cold pilgered Zircaloy-4 (Zr-4) tubes are measured under different uniaxial (tension/compression) loading directions. Tensile tests were carried out along three directions: rolling direction (RD), transverse direction (TD) and 45° to the rolling direction (45RD) at quasi static strain rate. Compression test was also performed in the RD. Texture was characterized at intermediate strains with electron backscattered diffraction method. For different uniaxial loading conditions, anisotropic yield stress and strain hardening behavior can be observed. Such complex mechanical behavior is well explained with the variations in activation of deformation mechanisms predicted by the Schmid factor distribution and visco-plastic self-consistent (VPSC) model. In order to calibrate the VPSC model’s parameters more accurately, both mechanical responses and texture changes for four different directional tests are compared with VPSC simulations. The calculated Lankford coefficients are also calibrated with anisotropic tensile results. Furthermore, a deepening understanding of the texture evolution under different loading directions were disclosed based on VPSC method. The results indicate that the activity of deformation mechanisms changes significantly with different uniaxial loading directions. Non-prismatic slips with higher critical resolved shear stress, e.g. basal and pyramidal slip, make larger contributions to the yield and strengthening stress resulting in the highest stress in TD compared with RD and 45RD. Compression test along RD prefers the activation for tensile twinning (TTW). Meanwhile, TTW can be detected in 45RD and TD tension owing to the spread distribution of initial texture towards TD.

The mechanism of dynamic strain aging for type A serrations in tensile curves of a medium-Mn steel

The objective of the present study is to clarify the mechanism of dynamic strain aging (DSA) causing serrations in tensile flow curves of Fe-5.15Mn-0.15C-0.37Si-0.0039N (wt%) medium-Mn steel specimens with triple phases of retained austenite (γR), ferrite (α) and tempered martensite (α'T). For the purpose, tensile tests were performed at various conditions of deformation temperature (Td = 273 - 333 K) and initial strain rate (έini = 5 × 10−4 - 1 × 10−2 s−1). The medium-Mn steel specimens revealed type A serrations after the propagation of the Lüders band in their tensile curves. The serrations were not related to both α and α'T; they were not caused by strain-induced martensitic transformation, but by DSA in γR. The DSA was not explained by the short-range diffusion model based on the interaction between partial dislocations and C-Mn complexes due to the absence of intersection between staying time and reorientation time. In a viewpoint of the dislocation arrest model involving long-range diffusion, critical strains of γR for serrations (ecγ) were measured. They showed the normal Portevine-Le Châtelier behavior that the ecγ value decreases with increasing Td and with decreasing έini. The activation energy measured using the ecγ values was similar to the activation energy for the dislocation pipe diffusion of C atoms. This result indicates that the DSA occurring in the present medium-Mn steel is explained by the dislocation arrest model involving the long-range pipe diffusion of C atoms, not by the short-range diffusion model involving the reorientation of C-Mn complexes.

CAPTURING OF UNEVEN DEFORMATIONS OF LIGHTENED 3D PRINTED PARTS

This paper deals with the problematics of tensile testing of maraging steel lightweight cylindrical samples with internal structures, intended for automotive application. The samples were made with DMLS technology and tensile tested under the static strain rate of 0.002 s-1. During the loading, uneven deformations and multiple necking occurred on the samples. The mentioned effect significantly affects the state of stress and deformation at the final fracture zone, as well as the total deformation into the fracture, which means that it actually distorts the standard tensile test record. Therefore, a methodology for capturing the deformation response using the ARAMIS optical system was proposed. The methodology is presented and verified by a set of experiments for BCC internal structure.

Granule attrition by coupled particle impact and shearing

A novel device has been developed for continuous shearing and repeated impact of granules in order to simulate granule attrition and dust formation under realistic plant conditions of mechanical stresses, shear strains and strain rates. The device subjects the granules to multiple impacts at a range of velocities prevailing in typical process plants, and to shear deformations using two rollers with an adjustable gap to simulate the level of shear stresses and strains experienced during bulk motion, e.g. discharge from silos onto conveyor belts, etc. In this paper, the device operation and tests carried out to determine the settings required for attaining a desired impact velocity and shear strain rate are described. Subsequently, the extent of breakage of the granules is determined for the specified settings and the results are compared with data obtained by more established methods, e.g. annular shear cell and single particle impact tests.

Macroscopic and microscopic characterizations of Portevin-LeChatelier effect in austenitic stainless steel using high-temperature digital image correlation analysis

Using digital image correlation (DIC) analysis in an Fe-19Cr-13Ni-0.2C austenitic stainless steel (mass%), the tensile deformation behavior accompanied with the Portevin-LeChatelier (PLC) effect was investigated at high temperatures of 723-823 K under various applied strain rates of 10−4 s−1–5 × 10−3 s−1. With the help of the DIC analysis, the global strain in the gauge part of a tensile specimen and the local strain in a PLC band were precisely measured regardless of the lowering machine stiffness at a high temperature. The high-temperature DIC analysis could identify the critical strain and strain rate conditions where stress-strain curve indicated serrated flow. The analytical results revealed that dynamic strain aging in the austenitic stainless steel was controlled by the pipe diffusion of Cr atoms. Further, it was also confirmed that the local strain gently increased in a gauge part through a PLC band propagation, which promoted a repeatable A-type PLC band propagation in the same direction. Furthermore, the local strain was discontinuously developed by the repeatable formation of PLC bands; consequently, the local strain rate became remarkably high within a PLC band. In addition, the local strain rate in the PLC band monotonically increased with the increase in the number of PLC bands. From this viewpoint, it was discovered that necking deformation occurs suddenly at the PLC band, when the local strain rate exceeds the critical value, where dynamic strain aging is ineffective.

Effect of the Strain Rate on Damage in Filled EPDM during Single and Cyclic Loadings.

The effect of the strain rate on damage in carbon black filled Ethylene Propylene Diene Monomer rubber (EPDM)stretched during single and multiple uniaxial loading is investigated. This has been performed by analyzing the stress–strain response, the evolution of damage by Digital Image Correlation (DIC), the associated dissipative heat source by InfraRed thermography (IR), and the chains network damage by swelling. The strain rates were selected to cover the transition from quasi-static to medium strain rate conditions. In single loading conditions, the increase of the strain rate yields in a preferential damage of the filler network while the rubber network is preserved. Such damage is accompanied by a stress softening and an adiabatic heat source rise. Conversely, increasing the strain rate in cyclic loading conditions yields in a filler network accommodation and a high self-heating whose combined effect is proposed as a possible cause of the ability of filled EPDM to limit damage by reducing cavities opening during loading, and favoring cavities closing upon unloading.

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.

On the Strain Rate Sensitivity of Fused Filament Fabrication (FFF) Processed PLA, ABS, PETG, PA6, and PP Thermoplastic Polymers

In this study, the strain rate sensitivity of five different thermoplastic polymers processed via Fused Filament Fabrication (FFF) Additive Manufacturing (AM) is reported. Namely, Polylactic Acid (PLA), Acrylonitrile-Butadiene-Styrene (ABS), Polyethylene Terephthalate Glycol (PETG), Polyamide 6 (PA6), and Polypropylene (PP) were thoroughly investigated under static tensile loading conditions at different strain rates. Strain rates have been selected representing the most common applications of polymeric materials manufactured by Three-Dimensional (3D) Printing. Each polymer was exposed to five different strain rates in order to elucidate the dependency and sensitivity of the tensile properties, i.e., stiffness, strength, and toughness on the applied strain rate. Scanning Electron Microscopy (SEM) was employed to investigate the 3D printed samples’ fractured surfaces, as a means to derive important information regarding the fracture process, the type of fracture (brittle or ductile), as well as correlate the fractured surface characteristics with the mechanical response under certain strain rate conditions. An Expectation–Maximization (EM) analysis was carried out. Finally, a comparison is presented calculating the strain rate sensitivity index “m” and toughness of all materials at the different applied strain rates.

Numerical simulation of polymers at low and moderate strain rates

Abstract The mechanical behavior of amorphous polymers and semicrystalline polymers is modeled using finite element analysis (FEA) through user material subroutine VUMAT in ABAQUS/Explicit. The DSGZ constitutive model is implemented using radial return method through user material subroutine VUMAT written in Fortran language. The finite element simulations are done for amorphous polymers called polymethyl-methaacrylate (PMMA) and polycarbonate (PC) and for semicrystalline polymer called Polyamide 12. The FEA prediction using DSGZ model is able to capture elasticity, yield, strain softening and strain hardening in case of amorphous polymers and elasticity, yield and strain hardening behavior in case of semicrystalline polymers. The numerical FEA simulations are done for PMMA for low strain rates of 0.0001 s−1, 0.0005 s−1 and 0.001 s−1 with temperatures of 296 K and 323 K and for PC with the same strain rates as PMMA and temperatures of 296 K and 348 K. Similarly, FEA simulations are done for Polyamide 12 for low to moderate strain rates of 0.001 s−1, 0.1 s−1 and 100 s−1 for temperatures of 300 K, 273 K and 260 K respectively. This study can be used to design various products/structures with these materials used in various service conditions of different strain rates and temperatures using finite element simulations. The FEA simulations are able to capture the behavior of material with higher stresses for higher strain rates and lower stresses for lower strain rates and it showed higher stresses for lower temperatures and lower stresses for higher temperatures. The FEA prediction results and statistical data shows a close match with experimental data and G’Sell Jonas model curves.

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.

Stress-strain behavior and microstructural evolution of ultra-high carbon Fe-C-Cr-V-Mo steel subjected to hot deformation

Numerous processes have been applied to refine the microstructure and the precipitation of carbides in ultra-high carbon steel (UHCS). However, the evolution of microstructure and carbide precipitation in UHCSs during the hot deformation compression process remains poorly understood. The present study addresses this issue by applying hot deformation compression to Fe-C-Cr-V-Mo UHCS specimens at temperatures of 950–1150 °C under strain rates of 0.01–5 s−1, and evaluating the resulting flow curves and microstructures of the specimens after cooling in air. High deformation temperature and high strain rate conditions are observed to generate flow curve stress peaks, which result in dynamic recrystallization. In addition, dislocation cell formation and substructure are observed at deformation temperatures of 950 °C and 1050 °C, respectively, under a strain rate of 1 s−1. The recrystallized grain structure fraction is found to be positively correlated with the deformation temperature at strain rates less than 5 s−1, and a fully recrystallized grain structure is not obtained at a strain rate of 5 s−1 even at a temperature of 1150 °C. Moreover, the concentration of primary M7C3 carbides is observed to decrease with increasing deformation temperature, and fine precipitated M23C6 particles are observed in the matrix during hot deformation. An increased concentration of precipitated M23C6 particles is also observed in the specimen microstructure at a deformation temperature of 1150 °C and a strain rate of 5 s−1. The recrystallization process is also observed to vary according to M23C6 particle size, where large M23C6 particles are observed to stimulate the formation of recrystallization nuclei and fine M23C6 particles delay or hinder the recrystallization process.

Study of Khan-Huang-Liang (KHL) Anisotropic Deformation Model for Deep Drawing Behaviour of Inconel 718 Alloy

Study of anisotropic deformation behavior of a material plays a crucial role in optimizing hot working process parameters and trustworthy Finite Element (FE) analysis in sheet metal forming processes. In this work, Khan–Huang–Liang (KHL) phenomenological based constitutive model and anisotropic yield criteria has been formulated for Inconel 718 alloy. Firstly, uniaxial tensile tests have been conducted at different temperatures (room temperature -700°C) and slow strain rates (0.0001-0.1s-1) conditions. KHL constitutive model has been formulated and validated with experimental flow stress data. The prediction capability of the model is evaluated based on correlation coefficient (R), average absolute error, AAE (Δ) and its standard deviation (s). Subsequently, anisotropic yielding behavior of Inconel 718 alloy is predicted based on KHL yield criterion. Anisotropic coefficient (Lankford parameters) and tension compression asymmetry parameters have been calculated experimentally. The prediction capability of KHL yield criterion is analyzed based on yield locus, yield stress variation and anisotropic coefficient variation. The quality index of performance, namely global accuracy index (β) is evaluated. Further, Finite Element (FE) analysis has been carried out for deep drawing of Inconel 718 alloy using commercially available ABAQUS software. The developed KHL constitutive model and anisotropic yield criterion has been incorporated in FE simulation using UMAT/VUMAT code. The FE results are validated with experimental deep drawn cups at different process conditions.

Blast loaded plates: Simplified analytical nonlinear dynamic approach

In this study, a novel simplified nonlinear dynamic method was presented to investigate the blast loaded plates. The material nonlinearity, strain rate, and various boundary conditions were included in the method together with plate geometry, scaled distance, and charge weight. The novelty of this work is that this method is easy-to-use while it covers all the important parameters affecting the blast-related dynamic responses of the isotropic plates. Equations of motion were achieved by applying the Navier solution to the dynamic governing equation of the plate. To include the material nonlinearity, the Ramberg-Osgood model, and hardening behavior were adopted. For the strain rate, the Cowper-Symonds relation was considered. Two types of boundary conditions were considered; simply supported and clamped plates. The scaled distance and charge weigh were included in the description of the blast load while the plate geometry was shown up in the stiffness and frequency of the plate. The method was validated by comparing the time history and maximum deflection of the plates obtained from the proposed method and those of the literature and finite element model through ABAQUS. Thereafter, a parametric study was carried out to examine the effects of plate aspect ratio, thickness, charge weight, and boundary conditions on the dynamic responses of the steel plates. The results showed that the plate deflection had a nonlinear relation with plate thickness, aspect ratio, and explosive charge while the clamped boundary condition resulted in a significant decrease in the maximum plate deflection.

The Off-Axis IBII Test for Composites

Composite components regularly experience dynamic loads in service. Despite this, it is still difficult to obtain accurate mechanical properties of composite materials under high strain rate conditions. In this study, a new application of the Image-Based Inertial Impact (IBII) test methodology was developed, to generate an accurate in-plane transverse and shear moduli dataset from unidirectional (UD) off-axis composite specimens. The obtained dataset was consistent across different sample configurations, where results from the UD45^{circ } off-axis specimens agreed well with the UD90^{circ } values. Validation of the shear modulus identification was also undertaken by comparing the results from the UD90^{circ } and UD45^{circ } specimens with a multi-directional (MD) configuration. Here, it was found that MD±45^{circ } specimen shear modulus values where marginally lower than that from the UD specimens, in accordance with the lower fibre volume fraction of the MD laminate. Low strain rate sensitivities in the 0.5-2times10^{3} hbox {s}^{-1} regime evidenced in this work suggest previously published data (often from split-Hopkinson bar tests) may include both a material and system i.e. testing apparatus response.

An Alternate Approach to SHPB Tests to Compute Johnson-Cook Material Model Constants for 97 WHA at High Strain Rates and Elevated Temperatures Using Machining Tests

AbstractWith advances in computational techniques, numerical methods such as finite element method (FEM) are gaining much of the popularity for analysis as these substitute the expensive trial and error experimental techniques to a great extent. Consequently, selection of suitable material models and determination of precise material model constants are one of the prime concerns in FEM. This paper presents a methodology to determine the Johnson-Cook constitutive equation constants (JC constants) of 97 W Tungsten heavy alloys (WHAs) under high strain rate conditions using machining tests in conjunction with Oxley’s predictive model and particle swarm optimization (PSO) algorithm. Currently, availability of the high strain rate data for 97 WHA are limited and consequently, JC constants for the same are not readily available. The overall methodology includes determination of three sets of JC constants, namely, M1 and M2 from the Split-Hopkinson pressure bar (SHPB) test data available in literature by using conventional optimization technique and artificial bee colony (ABC) algorithm, respectively. However, M3 is determined from machining tests using inverse identification method. To validate the identified JC constants, machining outputs (cutting forces, temperature, and shear strain) are predicted using finite element (FE) model by considering M1, M2, and M3 as input under different cutting conditions and then validated with corresponding experimental values. The predicted outputs obtained using JC constants M3 closely matched with that of the experimental ones with error percentage well within 10%.