Strain Rate History Effects Research Articles

The strain rate history effect in a selective-laser-melt 316L stainless steel

The strain rate history effect in a selective laser melt 316L (SLM-316L) alloy was investigated through quasi-static (10−3 s−1) and high strain rate (1600-3200 s−1) interrupted and reloading compression tests. The specimens pre-tested until about prescribed strains at quasi-static and high strain rates were reloaded dynamically and quasi-statically, respectively. The results revealed that the flow stress depended on strain and strain rate as well as strain-rate history. Quasi-static reloading the dynamically pre-tested specimens until about prescribed strains induced a higher flow stress than the specimens tested quasi-statically. The strengthening was ∼70 MPa at 0.11 pre-strain and decreased as the dynamic test pre-strain was increased due to adiabatic heating. On the other side, reloading the quasi-statically pre-tested specimens dynamically at 0.11 pre-strain resulted in ∼60 MPa lower flow stress than the specimens tested dynamically. The grains of the quasi-statically tested specimens until 0.11 strain were shown to have a lower Taylor factor for twinning and geometrically necessary dislocation density, indicating more potential for twinning than dynamically tested specimen. Although, quasi-statically and dynamically tested specimens were deformed predominantly by the twinning induced plasticity, a higher fraction of twin boundaries was shown microscopically in the dynamically pre-tested specimens until 0.11 pre-strain. This phenomenon of boundary strengthening could be used as a tool of strengthening of SLM-316L alloy at low strains.

Influence on strain-rate history effects on the development of necking instabilities under dynamic loading conditions

The present paper is devoted to the analysis of strain-rate history effects on neck formation under dynamic loading. For materials presenting strain-rate history effects, two different strain-rate sensitivities should be distinguished: the instantaneous strain-rate sensitivity and the work-hardening strain-rate sensitivity. We have analysed the relative contributions of these two kinds of strain-rate sensitivities to neck retardation for two different configurations: a bar under impact tension and a dynamically expanding ring. For this purpose, we have developed finite element models and, for the second configuration, an analytical model based on the linear stability analysis. The obtained results show that strain-rate history effects have a significant influence on the onset and development of necking. The reason of this phenomenon is that, contrary to the instantaneous strain-rate sensitivity, the work-hardening strain-rate sensitivity does not contribute to delay the neck formation.

Development of LSTM networks for predicting viscoplasticity with effects of deformation, strain rate and temperature history

Abstract In this paper, long short-term memory (LSTM) networks are used in an original way to model the behavior of a viscoplastic material solicited under changing loading conditions. The material behavior is dependent on history effects of plasticity which can be visible during strain rate jumps or temperature changes. Due to their architecture and internal state (memory), the LSTM networks have the ability to remember past data to update their current state, unlike the traditional artificial neural networks (ANNs) which fail to capture history effects. Specific LSTM networks are designed and trained to reproduce the complex behavior of a viscoplastic solder alloy subjected to strain rate jumps, temperature changes or loading-unloading cycles. The training datasets are numerically generated using the constitutive viscoplastic law of Anand which is very popular for describing solder alloys. The Anand model serves also as a reference to evaluate the performances of the LSTM networks on new data. It is demonstrated that this class of networks is remarkably well suited for replicating the history plastic effects under all the tested loading conditions.

Effect of strain rate history on the piezomagnetic field of ferromagnetic steels

The goal of this research is to investigate the effect of strain rate history on the piezomagnetic behavior of ferromagnetic steels. Cyclic tensile tests were carried out to record the magnetic fields on the surfaces of Q345 and X80 steel specimens. The impacts of different strain rate histories on the magnetic signals were investigated and the evolutions of piezomagnetic fields of Q345 and X80 steels are closely related to the strain rate history. The magnetic fields demonstrate a systematic evolution when the strain rate history increases from 0.03 min−1 to 0.3 min−1. When the strain rate history decreases from 0.3 min−1 to 0.03 min−1, the magnetic fields remain relatively stable. The results were explained by the movement of magnetic domains and the strength of pinning sites induced by the external stress. This study shows that strain rate history should be considered as one of the variables that influence the piezomagnetic field of ferromagnetic steels.

Effect of Strain Rate on the Formation of Strain-Induced Martensite in AISI 304L Stainless Steel

The effect of strain rate on the stress–strain response and the austenite to strain-induced α′-martensite transformation of austenitic steel 304L was studied. Compression tests were carried out at room temperature in the strain rate range of 10−3 to 103 s−1 and the evolution of martensite was quantified using a ferritoscope. Higher strain rates resulted in lower strain-induced α′-martensite. Strain incremental tests were carried out at 1 s−1 to simulate isothermal tests and to delineate effect of adiabatic heating on the α′-martensite transformation. Strain rate change tests were also carried out to determine the effect of prior strain rate history on the strain-induced α′-martensite content. These experiments showed that apart from the effect of adiabatic heating at high strain rates on the α′-martensite content, there is an additional effect of strain rate. While the adiabatic heating effect could be based on the increase in stacking fault energy (reduction of stacking fault width) with temperature, the additional effect due to strain rate was explained based on the expected reduction in stacking fault width with increasing strain rate.

Strain Rate Sensitivity of Tensile Properties in Ti-6.6Al-3.3Mo-1.8Zr-0.29Si Alloy: Experiments and Constitutive Modeling.

The complex deformation usually involves wide strain-rate change. However, few efforts have been devoted to investigate the effect of strain rate history on the tensile behavior of α + β titanium alloy. In present paper, tensile tests of Ti-6.6Al-3.3Mo-1.8Zr-0.29Si alloy were carried out under both constant and variable strain-rate conditions within the region from 10−3~500 s−1. A single stress pulse experimental technique was utilized to conduct the recovery tests. The strain-rate history effect was examined. It is found that the flow stress is independent on the strain rate history, though the alloy exhibits obvious positive strain rate sensitivity. The Taylor-Quinney coefficient of the plastic work converted to heat is proved as 0.9 at high strain rates. The cavitation fracture mechanism is revealed by microstructural observation over the full range explored. In basis of the experimental results and other pulished literatures, empirical Khan-Huang-Liang constitutive model was suitably modified to account for the strain-rate dependent behavior. Good agreement is achieved between the modeling prediction results and experimental data.

An energy transport based evolving rheology in high-shear rotor–stator mixers

Rotor–stator mixers such as the inline Silverson are widely used by the process industry. Existing literature on experimental and computational investigations of these devices focus on characterising the power draw and turbulent mixing of Newtonian fluids and non-Newtonian fluids such as emulsions. The current knowledge on the performance of these mixers in blending and mixing fluids with an underlying complex structure is limited. Modelling and simulation of such structured liquids has traditionally been challenging due to the complexity of the constitutive governing equations which are to be solved for the prediction of rheology. In this paper a novel approach to model evolving rheology is proposed. This approach incorporates important physical phenomenon such as the strain rate history effects in the generalised Newtonian fluid model. The new approach is used to model mixing in a pilot scale inline Silverson mixer via Computational Fluid Dynamics (CFD) simulations. A sliding mesh algorithm coupled to eddy viscosity turbulence closure is used. Experiments have been performed with the inline Silverson mixer placed in a recirculation loop for two different rotor speeds, and rheological measurements have been performed on the samples taken at the outlet of the mixer. Computational results are compared with the viscosity measurements and it is found that the model predictions for the evolution of viscosity are in reasonable agreement with the experimental data.

Microstructure based modeling of the strain rate history effect in wear resistant Hadfield steels

The strain rate history dependency of Hadfield steel is investigated by numerical modeling. A crystal plasticity model is employed to study the effect of strain rate jump/drop on the material's strain hardening and twinning propensity. Single crystal orientations are first examined to assess the importance of the strain rate and its history effects. Then a representative 3D microstructure aggregate is used to investigate the effects of strain rate history in a polycrystalline structure. It was found that strain rate affects the evolution of deformation twins in the microstructure, generating a strain rate history dependent deformation and hardening response. A Hadfield steel used in mineral crushing conditions is also characterized to provide details of the deformation and hardening behavior of the material under realistic low/high strain rate loading conditions. The importance of strain rate changes to strengthening and increasing the hardness of the polycrystal microstructure is discussed and considered from the wear resistance point of view.

Damage evolution and recrystallization enhancement of frozen loess

A series of multistage triaxial compression, creep, and stress relaxation tests were conducted on frozen loess at the temperature of −6℃ in order to study the damage evolution and recrystallization enhancement of mechanical properties during deformation process. The effect of strain rate, confining pressure, and hydrostatic stress history in the degradation laws of mechanical properties is investigated further. The strain rate has a significant influence on the stress–strain curve which dominates the evolution trend of mechanical properties. The mechanical behaviors (strength, stiffness, and viscosity) of frozen loess all exhibit evident response for the consolidation and pressure melting phenomenon caused by the confining pressure. The multistage loading tests under different hydrostatic stresses are capable of differentiating the development characteristics of mechanical properties during axial loading and hydrostatic compression process, respectively. The testing results indicated that the recrystallization of the ice particle in the frozen soils is an important microscopic factor for enhancement behaviors of mechanical parameters during the deformation process. This strengthening degree of mechanical properties is determined by temperature, duration time, deformation degree, and stress state during the recrystallization process. The phase transformation led by pressure melting and ice recrystallization is a nonnegligible changing pattern of frozen soils microstructure, which has apparent role in the damage evolution of mechanical properties.

A PHENOMENOLOGICAL INTERNAL VARIABLE MODELING OF HIGH-STRAIN-RATE COLD DEFORMATION OF FCC METALS

Abstract. In this work a macroscopic viscoplastic model, accounting for strain, strain rate hardening and instantaneous rate sensitivity of FCC metals, is formulated. Within the present approach, a single phenomenological internal variable representing an effective microstructural feature is introduced. In a phenomenological way, this internal variable is related to hardening mechanisms associated with large strain processes. Aiming at applying the constitutive proposal in solving engineering problems, associated numerical formulation is also described. Reasoning on the numerical context, an exponential implicit integration scheme is adopted together with an elastic predictor-plastic corrector algorithm. Constitutive capabilities are assessed by solving simple numerical problems involving high-strain-rate deformation. Simulation results and comparisons with experimental data available in the literature, considering an annealed high purity copper, demonstrate the model aptitude in predicting strain rate history effects on material response. In general, proposed model proves to be a useful modeling alternative to describe the macroscopic behavior of FCC metals subjected to high-strain-rate cold deformation. Keywords: High strain rate effects, Finite strains, Viscoplasticity, Numerical algorithms

An equivalent dissipation rate model for capturing history effects in non-premixed flames

The effects of strain rate history on turbulent flames have been studied in the past decades with 1D counter flow diffusion flame (CFDF) configurations subjected to oscillating strain rates. In this work, these unsteady effects are studied for complex hydrocarbon fuel surrogates at engine relevant conditions with unsteady strain rates experienced by flamelets in a typical spray flame. Tabulated combustion models are based on a steady scalar dissipation rate (SDR) assumption and hence cannot capture these unsteady strain effects; even though they can capture the unsteady chemistry. In this work, 1D CFDF with varying strain rates are simulated using two different modeling approaches: steady SDR assumption and unsteady flamelet model. Comparative studies show that the history effects due to unsteady SDR are directly proportional to the temporal gradient of the SDR. A new equivalent SDR model based on the history of a flamelet is proposed. An averaging procedure is constructed such that the most recent histories are given higher weights. This equivalent SDR is then used with the steady SDR assumption in 1D flamelets. Results show a good agreement between tabulated flamelet solution and the unsteady flamelet results. This equivalent SDR concept is further implemented and compared against 3D spray flames (Engine Combustion Network Spray A). Tabulated models based on steady SDR assumption under-predict autoignition and flame lift-off when compared with an unsteady Representative Interactive Flamelet (RIF) model. However, equivalent SDR model coupled with the tabulated model predicted autoignition and flame lift-off very close to those reported by the RIF model. This model is further validated for a range of injection pressures for Spray A flames. The new modeling framework now enables tabulated models with significantly lower computational cost to account for unsteady history effects.

A simplified approach to high strain rate effects in cold deformation of polycrystalline FCC metals: Constitutive formulation and model calibration

This work describes a macroscopic finite elastic–viscoplastic constitutive formulation that accounts for the individual contributions of strain hardening, strain rate induced hardening and viscous behavior in cold deformation of polycrystalline FCC metals. The constitutive modeling follows a Perzyna-type formulation within the thermodynamics with internal variables framework. The approach introduces a single phenomenological internal variable defining an effective microstructural feature, which comprises strain hardening contributions related to large strain processes. Internal variable evolution is based on physical considerations and gives rise to a modified Voce hardening law, which allows for predicting both the strain rate history effects and the linear hardening at large strains. Instantaneous rate-sensitivity is accounted for by a phenomenological overstress function. Material parameters are adjusted using experimental data available in literature for annealed high purity copper. Comparisons with experimental results and other viscoplastic models have demonstrated the model aptitude to properly predict high strain rate effects in cold deformation of polycrystalline FCC metals.

OS1910 アルミニウムのひずみ速度履歴

High-speed and quasi-static compression tests were conducted using short cylinder of pure aluminum A1050-0. The objective is to examine the effect of strain-rate history on the deformation behavior. The order of strain-rate was around 10^3 /s in high-speed or 10^<-2> /s in low-speed. The yield stress increased when the strain-rate changed from low-speed to high. The stress increased after the strain-rate change was more rapid comparing the slope where the bar was compressed under the low-speed condition only. On the other, the yield stress decreased in the case where the strain-rate changed from high-speed to low. The slope in stress-strain curve after the strain-rate change was steeper, in comparison with the result by low-speed compressive operation only. Further, the 3-step compressive operation was performed, where the specimen was compressed under high - low - high or low - high - low speed condition. Similarly, the positive effect in strain-rate history appeared.

A new approach for determination of material constants of internal state variable based plasticity models and their uncertainty quantification

Physically-based plasticity models such as the BCJ model include internal state variables that represent the current state of the material and allow capturing strain rate and temperature history effects as well as the coupling of rate- and temperature-dependence with material hardening. However, the inclusion of internal state variables increases significantly the number of unknown material constants that need to be found through fitting of the model to experimental stress–strain data at different strain rates and temperatures. This makes the fitting process extremely challenging and increases the uncertainty in the material constants. The paper presents a physics-guided numerical fitting approach that reduces the associated difficulties and uncertainties involved in determining the material constants of the BCJ plasticity model. The approach uses experimental data from monotonic and reverse loading stress–strain curves at different temperatures and strain rates to determine the 18 material constants of the model. An evidential uncertainty quantification approach is used to determine uncertainties rooted in experimental data, selection of stress–strain curves at different loading conditions, variability of material properties, numerical aspects of the fitting method and mathematical formulations of the BCJ model. The represented uncertainty of the BCJ material constants based on mathematical tools of evidence theory is propagated through Taylor impact simulations of a 7075-T651 aluminum alloy cylinder. Uncertainty quantification results verify the presented numerical fitting approach for the BCJ model and its potential applicability to other similar material models.

Bladder tissue passive response to monotonic and cyclic loading

The fundamental passive mechanical properties of the bladder need to be known in order to design the most appropriate long-term surgical repair procedures and develop materials for bladder reconstruction. This study has focused on the bladder tissue viscoelastic behavior, providing a comprehensive analysis of the effects of fibers orientation, strain rate and loading history. Whole bladders harvested from one year old fat pigs (160 kg approximate weight) were dissected along the apex-to-base direction and samples were isolated from the lateral region of the wall, as well as along apex-to-base and transverse directions. Uniaxial monotonic (stress relaxation) and cyclic tests at different frequencies have been performed with the Bose Electroforce(®) 3200. Normalized stress relaxation functions have been interpolated using a second-order exponential series and loading and unloading stress-strain curves have been interpolated with a non-linear elastic model. The passive mechanical behavior of bladder tissue was shown to be heavily influenced by frequency and loading history, both in monotonic and cyclic tests. The anisotropy of the tissue was evident in monotonic and in cyclic tests as well, especially in tests performed on an exercised tissue and at high frequencies. In contrast, transverse and apex-to-base samples demonstrated an analogous relaxation behavior.

Flow stress and ductility of AA7075-T6 aluminum alloy at low deformation temperatures

The present investigation has been conducted in order to develop a rational approach able to describe the changes in flow stress of AA7075-T6 aluminum alloy with deformation temperature and strain rate, when this material is deformed at temperatures in the range of 123–298K at strain rates in the range of 4×10−4 to 5×10−2s−1. The constitutive formulation that has been advanced to accomplish these objectives represents a simplified form of the mechanical threshold stress (flow stress at 0K) model developed at Los Alamos National Laboratory (Los Alamos, New Mexico, USA). Thus, it is assumed that the current flow stress of the material arises from both athermal and thermal barriers to dislocation motion. In the present case, the effect of three thermal barriers has been considered: solid solution, precipitation hardening and work-hardening. The first two effects do not evolve during plastic deformation, whereas the last one is considered as an evolutionary component of the flow stress. Such an evolution is described by means of the hardening law earlier advanced by Estrin and Mecking (1984) [20]. The law is implemented in differential form and is integrated numerically in order to update the changes in strain rate that occur during tensile tests carried out both at constant and variable crosshead speed. The extrapolation of the hardening components from 0K to finite temperatures is accomplished by means of the model earlier advanced by Kocks (1976) [19]. The results illustrate that the constitutive formulation developed in this way is able to describe quite accurately both the flow stress and work-hardening rate of the material, as well as temperature and strain rate history effects that are present when deformation conditions change in the course of plastic deformation. The evaluation of the ductility of the alloy indicates that the changes in this property are mainly determined by deformation temperature rather by strain rate. When deformation temperature decreases from 298 to 123K, ductility also decreases from ∼35 to 24%. However, despite these relatively small variations, significant changes in the fracture morphology could be observed on the fracture surfaces of the examined specimens, with the predominance of a mixed ductile-brittle mechanism at lower temperatures.

The Effect of Strain Rate History on the Dynamic Grain Growth Behaviour of AA 5083

Dynamic grain growth in superplastic AA5083 deformed at constant strain rates and varying strain rates has been studied. It has been found that the strain rate history has a significant influence on the grain growth behaviour. It is proposed that differences in mechanical behaviour of AA5083 for the strain rate conditions examined can be attributed to differences in the grain growth behaviour. The influence of dynamic grain growth on the superplastic behaviour of AA5083 is discussed.

Internal variable modeling of the high strain-rate behavior of metals with applications to multiphase steels

A phenomenological constitutive model with a single internal parameter is proposed to characterize the behavior of metals for a large range of strain-rate. The flow stress is defined as the sum of an internal stress, representing long range interactions, with an effective stress which is thermally activated. The internal stress is a function of a single internal parameter which allows us to describe strain-hardening effects. This model is used to reproduce the behavior of four multiphase cold rolled steels which are new high performance materials for the automotive industry. The model predictions show a very good agreement with experimental results for a wide range of strain-rate 8 × 10 −3 s −1 ≤ ε ˙ ≤ 10 3 s −1. In addition, strain-rate history effects are well accounted for.

A constitutive theory for metallic glasses at high homologous temperatures

The elastic–viscoplastic constitutive theory of Anand and Su [Anand L, Su C. J Mech Phys Solids 2005;53:1362] for metallic glasses has been extended to the high homologous temperature regime. The constitutive equations appearing in the theory have been specialized to model the response of metallic glasses in the temperature range 0.7 ϑ g ⪅ ϑ ⪅ ϑ g and strain rate range [10 −5, 10 −2] s −1. The material parameters appearing in the theory have been estimated for the metallic glass Pd 40Ni 40P 20 from the experimental data of De Hey et al. [De Hey P, Sietsma J, Van Den Beukel A. Acta Mater 1998;46:5873]. The model is shown to capture the major features of the stress–strain response, and the evolution of an order-parameter for this metallic glass. In particular, the phenomena of stress overshoot and strain softening in monotonic experiments at a given strain rate and temperature, as well as strain rate history effects in experiments involving strain rate increments and decrements, are shown to be nicely reproduced by the model.

Constitutive relations in 3-D for a wide range of strain rates and temperatures – Application to mild steels

An original phenomenological thermo-visco-plastic model is reported that encompasses strain hardening, strain rate and temperature sensitivity. The model is based to some extent on the concept of physical modeling proposed earlier by Klepaczko [Klepaczko, J.R. 1975. Thermally activated flow and strain rate history effects for some polycrystalline FCC metals. Mater. Sci. Engng. 18, 121–135] , and also by different authors, for example: [Becker, R. 1925. Uber die plastizitat amorpher und kristalliner fester korper. Z. Physik 26, 919–925; Seeger, A., 1957. Dislocations and Mechanical Properties of Crystals, Wiley, New York; Conrad, H., 1964. Thermally activated deformation of metals J. Metals 16, 582; Gilman, J.J. 1968. Dislocation dynamics and response of materials to impact Appl. Mech. Rev. 21, 767–783; Gibbs, G.B., 1969. Thermodynamic analysis of dislocation glide controlled by dispersed local obstacles. Mater. Sci. Engng. 4, 313–328; Kocks, U.F., Argon, A.S., Ashby, M.F., 1975. Thermodynamics and kinetics of slip. In: Progress in Materials Science, vol. 19. Pergamon Press, New York, p. 19; Kocks, U.F. 1976. Laws for work-hardening and low-temperature creep. J. Eng. Mater. Technol. 98, 76–85, and later by many others. The thermo-visco-plastic formulation, called RK and applied in this paper, has been verified experimentally for strain rates of 10 - 4 s - 1 ⩽ ε ¯ ˙ p ⩽ 5 × 10 3 s - 1 and temperatures 213 K ⩽ T ⩽ 393 K, it covers the range of dynamic loadings observed during crash tests and other impact problems. In order to implement the RK constitutive relation, a thermo-visco-plastic algorithm based on the J 2 theory of plasticity is constructed. The type of algorithm is a return mapping one that introduces the consistency condition ( f = σ ¯ - σ y , f = 0 ) , without the overstress state proposed by Perzyna [Perzyna, P. 1966. Fundamental problems in viscoplasticity. Advances in Applied Mechanics, vol. 9. Academic Press, New York, pp. 243–377]. The coupling of the RK constitutive relation with the integration scheme of the thermo-visco-plastic algorithm has demonstrated its efficiency for numerical analyses of different dynamic processes such as Taylor test [Zaera, R., Fernández-Sáez, J. 2006. An implicit consistent algorithm for the integration of thermoviscoplastic constitutive equations in adiabatic conditions and finite deformations. Int. J. Solids Struct., 43, 1594–1612.], ring expansion [Rusinek, A., Zaera, R., 2007. Finite element simulation of steel ring fragmentation under radial expansion. Int. J. Impact Eng. 34, 799–822], dynamic tension test [Rusinek, A., Zaera, R., Klepaczko, J.R., Cherigueme, R., 2005. Analysis of inertia and scale effects on dynamic neck formation during tension of sheet steel. Acta Mater. 53, 5387–5400], perforation of metallic sheets [Rusinek, A., 2000, Modélisation thermoviscoplastique d’une nuance de tôle d’acier aux grandes vitesses de déformation. Etude expérimentale et numérique du cisaillement, de la traction et de la perforation, Ph.D. thesis, University of Metz, France], and other cases. All the equations are implemented via the user subroutine VUMAT in the ABAQUS/Explicit code for adiabatic conditions of plastic deformation.