Intermediate Strain Rates Research Articles

Validated tensile characterization of the strain rate dependence in soft materials

A major obstacle in the accurate measurement of the dynamic tensile response of soft materials is the issue of obtaining material response under simultaneous stress equilibrium, stress uniaxiality and constant strain rate. To resolve this issue, a split-Hopkinson pressure bar (SHPB)-based dynamic tension experiment is developed in this study, which has sufficient fidelity to ensure temporal and spatial accuracy of the stress state, to investigate soft materials under large deformations and intermediate dynamic strain rates (100-102 s−1). Cross-linked polydimethylsiloxane (PDMS) elastomer is chosen as a model material. By examining the evolution of full-field strain and strain rate measured using digital image correlation (DIC) and employing analytical criteria for quantifying stress equilibrium and deformation uniaxiality, it is demonstrated that the proposed test method yields a true steady-state and inertia-free stress-strain material response when all three conditions of equilibrium, uniaxiality and strain rate constancy are satisfied. Quasi-static experiments at 10−3-10−1 s−1 strain rate are also conducted for comparison. By analyzing the quasi-static and dynamic stress-strain plots and the variation of uniaxial moduli in the investigated range of strain rates, it is shown that the tensile response of PDMS points to limiting chain extensibility and exhibits a weak nonlinear strain rate sensitivity. Finally, a visco-hyperelastic model based on the Gent strain energy density function and a recently proposed viscous dissipation potential is employed to capture the experimentally obtained response. It is shown that all the features of the rate-dependent stress-strain response are modeled with good fitting accuracy.

Mechanical Properties of Spark Plasma Sintering-Processed Pure Ti and Ti-6Al-4V Alloys: A Comparative Study between Harmonic and Non-Harmonic Microstructures

Microstructure characteristics and compressive property relationships of so-called harmonic (composed by fine and coarse grains) and conventional pure titanium (Ti) and Ti-6Al-4V alloy processed by powder metallurgy route are presented in the present work. Electron backscatter diffraction (EBSD) analysis was performed to characterize the as-processed microstructures. The harmonicity structure of selected samples is described, and relevant EBSD maps are presented. The bulk samples’ hardness is reported, along with compressive responses at quasi-static and intermediate strain rates, ranging from 0.005 s−1 to 16 s−1. The strain rate sensitivity of these metallic samples is discussed, and the benefits in terms of mechanical properties of the harmonic microstructures compared with the non-harmonic conventional ones are highlighted. Finally, a modified Johnson–Cook model was shown to predict fairly the experimental results.

Experimental investigation of the strain‐rate effects on the failure of composite materials with off‐axis tensile tests on unidirectional plies

AbstractThe present study experimentally investigates the mechanical response of T700/M21 Carbon Fibre Reinforced Polymers subjected to coupled shear and transverse tension at intermediate strain rates ranging from 10−3 to 15 s−1. Off‐axis tension specimens with transverse and oblique tabs are used for the various tests. Moreover, the specimen aspect ratio is quite low, since dynamic tests are performed in this study. The axial stress–strain curves are successfully simulated using finite element simulations with a viscoelastic model. Based on these numerical simulations, specific stress correction factors are computed to take the effect of end constraints into account for such low aspect ratio specimens. Finally, an increase in the material strength with the strain rate is observed.

Molecular dynamics study of coupled layer thickness and strain rate effect on tensile behaviors of Ti/Ni multilayered nanowires* *Project supported by the National Natural Science Foundation of China (Grant No. 11572259), the Natural Science Foundation of Shaanxi Province, China (Grant No. 2019JQ-827), and the Scientific Research Program Funded by Shaanxi Provincial Education Department, China (Grant No. 19JK0672).

Novel properties and applications of multilayered nanowires (MNWs) urge researchers to understand their mechanical behaviors comprehensively. Using the molecular dynamic simulation, tensile behaviors of Ti/Ni MNWs are investigated under a series of layer thickness values (1.31, 2.34, and 7.17 nm) and strain rates (). The results demonstrate that deformation mechanisms of isopachous Ti/Ni MNWs are determined by the layer thickness and strain rate. Four distinct strain rate regions in the tensile process can be discovered, which are small, intermediate, critical, and large strain rate regions. As the strain rate increases, the initial plastic behaviors transform from interface shear (the shortest sample) and grain reorientation (the longest sample) in small strain rate region to amorphization of crystalline structures (all samples) in large strain rate region. Microstructure evolutions reveal that the disparate tensile behaviors are ascribed to the atomic fractions of different structures in small strain rate region, and only related to collapse of crystalline atoms in high strain rate region. A layer thickness-strain rate-dependent mechanism diagram is given to illustrate the couple effect on the plastic deformation mechanisms of the isopachous nanowires. The results also indicate that the modulation ratio significantly affects the tensile properties of unequal Ti/Ni MNWs, but barely affect the plastic deformation mechanisms of the materials. The observations from this work will promote theoretical researches and practical applications of Ti/Ni MNWs.

A novel methodology for large strain under intermediate strain rate loading

Hopkinson bar has already worked to measure mechanical properties of materials under high strain rates, but it fails to conduct intermediate strain rates loading with considerable deformation. Thereby, a methodology is proposed for achieving enough large strains under intermediate strain rates. The experimental system based on it is then constructed: a striker bar with same length as incident bar is selected to generate continuous stress wave loading, and a long polymethylmethacrylate bar is preferred as the transmitted bar to guide and record transmitted signals. Thus, loading stress wave is achievable with a nearly constant amplitude and an infinite loading duration. The involved data interpretations are deduced, and verified both theoretically and experimentally. Its measurement capacity is confirmed by loading a thermoplastic polyurethane, and maximum strains up to 12% and 65% under strain rates of 40/s and 270/s, respectively. Finally, the involved influences and factor sensitivities are analyzed for enough experimental accuracy and extensive measurements.

On the mechanisms of nucleation and subsequent development of the PLC bands in an AlMg alloy

The nucleation and subsequent development of the Portevin-Le Chatelier bands during tensile deformation in a binary AlMg alloy was investigated by the digital image correlation technique. The following states of the material were employed for the current investigation: coarse-grained (CG), fine-grained (FG) after equal channel angular pressing (ECAP), severely strained (SS) after ECAP followed by cold rolling. Special attention was paid to the nucleation of an embryo band by maximizing the contrast of the deformation images. Particular spatiotemporal patterns of the alloy in three different conditions, testifying to the initiation of an embryo band having a wedge shape on the lateral surface of the specimen, were obtained at high and intermediate strain rates. The evaluation of the serration amplitude and the band velocity showed that the dependence of these values on strain consists of two stages (the linear growth-up/drop stage and the steady-state stage) for CG materials and only one stage (the linear growth-up/drop stage) for FG materials. The nucleation of deformation bands always occurs according to a mixed mechanism, in which the thickening of the embryo slows down with a decrease in the strain rate.

Compression impact behaviour of agglomerated cork at intermediate strain rates

This work analyses the influence of intermediate strain rates, between 25 and 75 s−1, on compressive behaviour of agglomerated cork. Quasi-static and dynamic compressive tests on an agglomerated cork with two different densities were carried out. This work complements previous research focused on higher strain rates. The influence of strain rate on less studied properties as densification strain or Poisson ratio is also studied. Digital image correlation (DIC) is applied to the estimation of the strain distribution in the longitudinal and transversal directions for both materials quantifying their heterogeneity through the specimen. Under the studied dynamic conditions, no significant influence of strain rate on the mechanical properties was found. Young's modulus, plateau stress, and Poisson ratio are higher in the densest agglomerate, whereas the densification strain is similar in both material densities. Differences in properties such as Young's modulus, Poisson ratio, plateau stress, and densification strain have been found between quasi-static and dynamic conditions for both agglomerates. In the agglomerate with the lowest density, all properties are higher in dynamic conditions than in quasi-static conditions. In the material with the highest density, Young`s modulus and plateau stress increase significantly, whereas the Poisson ratio decreases.

An alternative method for the measurement of mechanical properties at intermediate strain rates: a numerical study

A feasibility study of an innovative apparatus for dynamic characterization of materials at intermediate strain rates is presented. The working principle is based on the Split Hopkinson bar, but the wave propagation occurs through properly sized springs. The system is designed to generate and transmit tension or compression waves having a low propagation speed, in order to reduce the specimen strain rate at the impact. At first, a simplified theory is presented for the estimation of longitudinal wave speed in springs as a function of the main engineering parameters of the coil dimensioning. Then, a preliminary sizing of the apparatus is proposed based on basic considerations of wave propagation theory. Finally, a numerical model of a compression test is presented as a proof-of-concept.

A Laboratory-Scale Instrumented Forging Hammer as an Intermediate Strain Rate Testing Device

Mechanical characterisation of metallic materials at intermediate strain rates is essential to calibrate and validate computational models for industrial applications such as high-speed forming processes i.e. hammer forging, blanking, forming, etc. The most common devices that perform medium to high loading rate experiments are the servo-hydraulic universal testing machines and Split Hopkinson bar systems. Here we analyse the possibility of employing an in-house designed and constructed DirectImpact Drop Hammer (DIDH) for material mechanical characterisation at medium strain rates, ranging from 100 to 300 s-1. To show the suitability of the DIDH for mechanical characterisation, uniaxial compression experiments on S235JR structural steel are conducted and compared with finite element (FE) simulations performed with an elasticthermoviscoplastic material model previously calibrated with Split Hopkinson Pressure Bar (SHPB) tests.

A multispecies investigation of the strain rate sensitivity of the modulus of cortical bone

The stiffness of cortical bone shows both inter- and intra-species variation. Currently, it is unclear whether this variation is due to differing testing protocols or an inherent feature of the material. Additionally, there is a lack of literature dealing with species other than human and bovine, particularly in the intermediate strain rate regime. In this study, cortical bone specimens were machined from the femurs of four species: baboon, crocodile, sheep and ostrich. Specimens were tested in the quasi-static and intermediate strain rate regimes using consistent testing protocols implemented by a single researcher. The results show a similar strain rate dependence for all species, i.e. the modulus shows negligible rate effects in the quasi-static regime, but a significant increase when moving to intermediate strain rates. This suggests that while the stiffness of the bone is species dependent, the effect of strain rate may be species independent. The observed intra- and inter-species variation is less than that reported in literature, highlighting the importance of a consistent testing protocol in multi-species studies.

Experimental Investigations of 3D Woven Layer to-Layer Carbon/Epoxy Composites at Different Strain Rates

This paper reports experimental investigations of 3D woven carbon/epoxy composites on quasi-static and dynamic tensile properties in the longitudinal (warp) and transverse (weft) directions. Firstly, quasi-static tests were conducted to determine a baseline tensile strength and to find out the adequate specimen geometry required for dynamic testing. Secondly, dynamic tensile properties at intermediate strain rates (nominal strain rates from 0.1 to 200 s-1) were investigated alongside the corresponding failure mechanisms. Detailed information on failure patterns is obtained with strain field measurements from Digital Image Correlation (DIC) and CT scans. The results show that 3D woven composites are strain rate insensitive and the crack initiation is located near weft yarns and binding interlacement points due to the presence of resin rich areas.

Strain rate sensitivity of the aluminium-magnesium-scandium alloy - Scalmalloy®

This work investigates the strain rate sensitivity of the aluminiummagnesium-scandium alloy Scalmalloy, which is used extensively for additive manufacturing of lightweight structures. This high strength aluminium alloy combines very good weldability, machinability and mechanical strength: it can be heat-treated to reach nominal ultimate tensile strengths in excess of 500 MPa. We report tensile tests at strain rates ranging from 10−3 /s to 103 /s at room temperature. It is well known that Al-Mg alloys exhibit a negative strain rate dependency in combination with serrated flow caused by the Portevin-Le Chatelier effect, which describes the interaction of Mg solutes with dislocation propagations. In contrast, in Al-Sc alloys, the flow stress increases with increasing strain rate and displays positive strain rate dependency. Additionally, the presence of Sc in the form of Al3-Sc provides a fine-grained microstructure which allows higher tensile and fatigue strength. This research shows how these combined effects interact in the case of Scalmalloy, which contains both Mg and Sc. Tests are performed at quasi-static, intermediate and high strain rates with a servohydraulic testing machine and a Split-Hopkinson tension bar. Local specimen strain was performed using 2D Digital Image Correlation.

Plasticity and fracture of aluminium 7075 at high strain rates and elevated temperatures

Slow, intermediate and high strain rate experiments with UT geometries are performed on aluminum AA7075-T6 sheet metal at various temperatures. The comprehensive experimental program characterizes the plasticity response at temperatures ranging from 20°C to 360°C and at strain rates ranging from 0.001/s to 150/s. The elevated temperature - elevated strain rate experiments are performed on a hydraulic tensile testing machine and a Split Hopkinson Pressure Bar system with a Load Inversion Device along with a custom-made induction heating system. A machine learning based modified Johnson-Cook plasticity model is calibrated to capture the complex strain rate and temperature effect of the observed hardening response.

Experimental Analysis and Behaviour Modelling of the Deformation Mechanisms of a Ti-6242S Alloy under Hot and Superplastic Forming Conditions

In this work, the hot deformation characteristics of a near-α Ti-Al-2SnZr-2Mo alloy (Ti6242 alloy) with a Fine-Grained (FG) microstructure (dα = 2.86 μm) were investigated at two levels of temperature, T = 730 ∘C and T = 840 ∘C. The initial microstructure consists of equiaxed nodules of the α phase as well as some α lamellae sparsely distributed and separated by thin layers of the BCC β phase. For both temperatures, three strain rates (10−4,10−3,10−2s−1) were analysed during loading. Moreover, the microstructural evolution (α size and morphology) was also evaluated by conducting interrupted tensile tests. The different tensile testing conditions greatly influence the stress-strain response of the material as well as the microstructure evolution. Indeed, various phenomena can take place such as elongation of the grain structure, globularization, dynamic recrystallization and grain growth of the equiaxed areas depending on the temperature, the strain rate and the strain level. The FG Ti6242 alloy exhibits interesting superplastic ductility at T = 840 ∘C. At this temperature either a very gradual flow softening (at higher strain rate) or flow hardening (at lower strain rate) can be observed and are related respectively to one or more of the following mechanisms: lamellae globularization, DRX and grain growth. At the intermediate strain rate, both mechanisms, strain hardening and softening, coexist. At T = 730 ∘C, the onset of the α lamellae globularization was only promoted at low strain rate. A mechanical behavior model was developed in the temperature range of 730–840 ∘C, which was able to take into account all the observed phenomena: viscosity, softened behavior and strain hardening. Constitutive equations were calibrated from the stress-strain responses and microstructural observations, and the computed results were in good agreement with the experiments.

Experimental Investigation of Strain-Rate- and Temperature-Dependent Mechanical Properties of SA516Gr.70 Steel and Development of an Appropriate Material Model

The objective of this work is to develop an appropriate strain-rate- and temperature-dependent material constitutive model to simulate plastic deformation behavior of SA516Gr.70 steel in the sub-zero temperature regime (− 128 to 25 °C). For this purpose, tests have been conducted at three different strain rates covering an order of 6 in the rates, i.e., from 0.001 to 1400/s. Tests at high strain rates have been conducted using a modified split Hopkinson pressure bar test setup. The tensile tests have been designed in such a way that the strain rate remains almost constant during the test. A critical comparison of results of both tension and compression high strain-rate tests has been carried out, and the suitability of tensile experiments has been highlighted. A modified Ramberg–Osgood model, with temperature- and strain-rate-dependent parameters, has been presented. The parameters of the new model have been evaluated from a large set of experimental data. It was observed that the yield stress and ultimate tensile strength of the material increase monotonically with decreasing temperature and increasing strain rates. The ductility at fracture and extent of uniform elongation of the specimen decrease for the intermediate strain rate of 0.925 s−1, when compared to the corresponding values at quasistatic rate of loading. At very high rate of loading, ductility increases due to the increased resistance of the material to growth and coalescence of voids. From the comparison of results of model and experiment, it has been observed that the modified material model is able to predict the true stress–strain curve of the material satisfactorily in the sub-zero temperature regime over a wide range of strain rates. The nature of variation of mechanical properties with temperature and strain rate has been explained from the point of view of dislocation-based micromechanism of the plastic deformation process.

Mechanical characterization of 304L-VAR stainless steel in tension with a full coverage of low, intermediate, and high strain rates

A 304L-VAR stainless steel is mechanically characterized in tension over a full range of strain rates from low, intermediate, to high using a variety of apparatuses. While low- and high-strain-rate tests are conducted with a conventional Instron and a Kolsky tension bar, the tensile tests at intermediate strain rates are conducted with a fast MTS and a Drop-Hopkinson bar. The fast MTS used in this study is able to obtain reliable tensile response at the strain rates up to 150 s−1, whereas the lower limit for the Drop-Hopkinson bar is 100 s−1. Combining the fast MTS and the Drop-Hopkinson bar closes the gap within the intermediate strain rate regime. Using these four apparatuses, the tensile stress-strain curves of the 304L-VAR stainless steel are obtained at strain rates on each order of magnitude ranging from 0.0001 to 2580 s−1. All tensile stress-strain curves exhibit linear elasticity followed by significant work hardening prior to necking. After necking occurrs, the specimen load decreases, and the deformation becomes highly localized until fracture. The tensile stress-strain response of the 304L-VAR stainless steel exhibits strain rate dependence. The flow stress increases with increasing strain rate and is described with a power law. The strain-rate sensitivity is also strain-dependent, possibly due to thermosoftening caused by adiabatic heating at high strain rates. The 304L-VAR stainless steel shows significant ductility. The true strains at the onset of necking and at failure are determined. The results show that the true strains at both onset of necking and failure decrease with increasing strain rate. The true failure strains are approximately 200% at low strain rates but are significantly lower (~100%) at high strain rates. The transition of true failure strain occurs within the intermediate strain rate range between 10−2 and 102 s−1. A Boltzmann description is used to present the effect of nominal strain rate on true failure strain.

Large amplitude oscillatory rheology of silica and cellulose nanocrystals filled natural rubber compounds

Nanoparticles reinforce rubbers and enhance Payne effect for the compounds experiencing large amplitude oscillatory shear deformation. Herein the effects of silica and cellulose nanocrystals on the Payne effect of natural rubber compounds are investigated by stress decomposition methods for clarifying the elastic and viscous nonlinearities varying with filler content and composition. The Payne effect is in general characterized by intercycle strain softening and shear thinning behaviors and intracycle hardening and thinning behaviors at high strain (strain rate) amplitudes while the filler influences the behaviors markedly at intermediate strain (rate) amplitudes. Especially, the addition of cellulose nanocrystals in the silica filled compounds improves the elastic nonlinearity and greatly weakens the viscous nonlinearity, providing a perspective on understanding the Payne effect for manufacturing high-performance rubber materials.

Adiabatic heating and damage onset in a pultruded glass fiber reinforced composite under compressive loading at different strain rates.

Damage onset and adiabatic heating of a pultruded Glass Fiber-Reinforced Plastic (GFRP) composite was investigated using compression tests at low, intermediate and high strain rates (10−3 s−1, 1 s−1 and 103 s−1). Optical and infrared (IR) cameras monitored the specimens during testing, so that the mechanical response, damage onset, and damage evolution were obtained along with the adiabatic heating of the specimen due to plastic deformation and fracture. The results revealed clear strain rate effects on stiffness, strain softening and damage initiation. The simultaneous optical and IR imaging allowed quantitative description of thermomechanical response of the material and studying the formation and propagation of shear localizations and their temperature history. The maximum temperatures in the fracture zones exceed 80 °C at the strain rate of 103 s−1. Scanning Electron Microscopy (SEM) was used to identify the micro-scale crack paths at different strain rates. The findings allow more exact numerical predictions and design of tubular GFRP pipes for impact applications.

Dynamic Mechanical Behavior and Constitutive Models of S890 High-Strength Steel at Intermediate and High Strain Rates

High-strength steel is an effective choice to satisfy the demands of advanced manufacturing engineering and construction engineering. The complex and severe working environments for high-strength steel require the designer to take the dynamic mechanical properties into consideration. Thus, the main subjects of this paper are the dynamic strain–stress relationship and the strain rate-strengthening effect of S890 high-strength steel. Experimental studies with a wide range of strain rates were conducted using a dynamic tensile testing system (for intermediate strain rate) and a Split Hopkinson Pressure Bar testing system (for high strain rate). The strain rate effect of S890 steel was quantitatively investigated. The global dynamic increase factor (DIFavg) values were tested to be 1.132 at a strain rate of 200 s−1 and 1.214 at 5292.8 s−1, which indicates that S890 high-strength steel was less sensitive to strain rates than mild steel and other structural steels with lower strength. Based on the Johnson–Cook (J–C) model and the Cowper–Symonds (C–S) model, strain rate models for the S890 steel are presented for describing the dynamic stress–strain relationship. The C–S model has better accuracy owing to the nonlinear characteristic of the DIFavg of S890 steel.

Anomalous tensile response of bacterial cellulose nanopaper at intermediate strain rates

Nanocellulose network in the form of cellulose nanopaper is an important material structure and its time-dependent mechanical response is crucial in many of its potential applications. In this work, we report the influences of grammage and strain rate on the tensile response of bacterial cellulose (BC) nanopaper. BC nanopaper with grammages of 20, 40, 60 and 80 g m−2 were tested in tension at strain rates ranging from 0.1% s−1 to 50% s−1. At strain rates le 2.5% s−1, both the tensile modulus and strength of the BC nanopapers stayed constant at ~ 14 GPa and ~ 120 MPa, respectively. At higher strain rates of 25% s−1 and 50% s−1 however, the tensile properties of the BC nanopapers decreased significantly. This observed anomalous tensile response of BC nanopaper is attributed to inertial effect, in which some of the curled BC nanofibres within the nanopaper structure do not have enough time to uncurl before failure at such high strain rates. Our measurements further showed that BC nanopaper showed little deformation under creep, with a secondary creep rate of only ~ 10–6 s−1. This stems from the highly crystalline nature of BC, as well as the large number of contact or physical crosslinking points between adjacent BC nanofibres, further reducing the mobility of the BC nanofibres in the nanopaper structure.