Moderate Strain Rates Research Articles

Competition between shear band nucleation and propagation across rate-dependent flow transitions in a model metallic glass

Shear transformation zone (STZ) dynamics is used to examine the transition between different regimes of flow serration in the strain rate dependent deformation of metallic glass. To capture the strain rate independent yield strength of Vitreloy 1 at low to moderate strain rates, the model is adapted to include STZ volume and activation energy that decrease with increasing strain rate. The different stages of shear banding are examined in a statistical fashion over six different strain rates ranging from 10−5 to 100 s−1, with twelve replicates at each strain rate. Examination of flow serration, shear band nucleation rates, propagation rates, and sliding rates in each simulation find support for the hypothesis that the flow transition is caused by high shear band propagation and sliding rates at low strain rates, and high shear band nucleation rates at high strain rates. The underlying cause for the flow transition is hypothesized to be a strain rate dependent critical shear band nucleus size that increases with increasing strain rate. This critical shear band nucleus size results from the strain rate dependent STZ volume and activation energy, in which very small variations can cause a large change in shear banding behavior.

A new approach to obtaining a 3D shear wave velocity model of the crust and upper mantle: An application to eastern Turkey

We present a new approach to the joint inversion of surface wave dispersion data and receiver functions by utilizing Common Conversion Point (CCP) stacking to reconcile the different sampling domains of the two datasets. Utilizing CCP stacking allows us to suppress noise in the data by waveform stacking, and correct for backazimuthal variations and complex crustal structure by mapping receiver functions back to their theoretical location. When applied to eastern Turkey, this approach leads to a higher resolution image of the subsurface and clearly delineates different tectonic features in eastern Turkey that were not apparent using other approaches. We observe that the slow seismic velocities near the Karliova Triple Junction correlate to moderate strain rates and high heat flow, which leads to a rheologically weak crust that has allowed for the upward propagation of Miocene and younger volcanics near the triple junction. We find seismically fast, presumably rigid blocks located in the southeastern Anatolian Plate and Arabian Plate are separated by a band of low shear wave velocities that correspond to the East Anatolian Fault Zone, which is consistent with the presence of fluids in the fault zone. We observe that the Arabian Plate has underthrust the Eurasian Plate as far as the northern boundary of the Bitlis Massif, which can explain the high exhumation rates in the Bitlis Massif as a result of slab break-off of the Arabian oceanic lithosphere. We also find a shallow (~33km) anomaly beneath eastern Turkey that we interpret as a localized wedge of mantle that was underthrust by a crustal fragment during the collision of Arabia and Eurasia. These observations are possible because of the high-resolution images obtained by combining common conversion point receiver function stacks with ambient noise dispersion data to create a data-driven three-dimensional shear wave velocity model.

Microstructure and Dynamic Compression Properties of PM Al6061/B4C Composite

Aluminum 6061 matrix composite reinforced by 35 wt% B4C particle was fabricated by power metallurgy method. Then, the as-deformed composite was tested by quasi-static (0.001 s−1) and dynamic (760–1150 s−1) compression experiments. The Johnson–Cook plasticity model was employed to model the flow behavior. The damage mechanism of composite was analyzed through the microstructure observations. The results showed that the B4C particles exhibited uniform distribution and no deleterious reaction product Al4C3 was found in the composite. Al6061/B4C composite showed high yield strength, moderate strain rate sensitivity and strain hardening under the dynamic loading, and a constitutive model under dynamic compression was established based on Johnson–Cook model, and accorded well with experimental results. The microstructure damage was dominated by particle fracture and interface debonding, and the dislocation was observed in the composite at a higher strain rate.

In situ X-ray synchrotron tomographic imaging during the compression of hyper-elastic polymeric materials

Cellular structures are present in many modern and natural materials and their proper utilization is crucial within many industries. Characterizing their structural and mechanical properties is complicated, in that they often have a stochastic cellular structure, and in addition, they often have hyper-elastic (i.e., non-linear) mechanical properties. Understanding the 3D structure and the dynamic response of polymer foams to mechanical stress is a key to predicting lifetime performance, damage pathways, and stress recovery. Therefore, to gain a more complete picture, experiments which are designed to understand their mechanical properties must simultaneously acquire performance metrics during loading. In situ synchrotron X-ray computed tomography can image these cellular materials in 3D during uniaxial compression at a 10−2 s−1 strain rate. By utilizing the high X-ray photon flux and high-speed camera provided by beamline 2-BM at the advanced photon source, it is possible to collect a full 3D tomogram (900 radiographs as the sample is rotated 180°) within 1 s. Rotating the sample stage in a washing machine motion allows for a 1 s tomogram to be collected every fifth second. In this study, a series of 20 tomograms were collected as the sample was continuously stressed to a nominal 60 % compression. Several types of silicone foams with various structures were used to explore this technique. Stress–strain curves, collected simultaneously with the 3D tomograms, can be used to directly correlate the morphology with the mechanical performance and visualize in real-time, the buckling of ligaments. In addition, this method allows for the accurate measurement of the Poisson’s ratio as a function of compression. Coupling this moderate strain rate 3D data with finite element analysis provides a direct comparison between the true mechanical response and the modeled performance and adds a level of robustness that is not possible with other techniques.

Predicting the Uniaxial Compressive Response of Granular Media over a Wide Range of Strain Rates Using the Strain Energy Density Concept

An empirical non-linear method to predict stress–strain response of sand over a wide range of strain rates is presented. The method is inspired by the equivalence of the strain energy density (SED) of the material, at different strain rates. Silica based and calcium based sands were subjected to one-dimensional compression radially constrained tests to calibrate the methodology. Axial stress, axial strain and stiffness are also presented to assess the sensitivity of mechanical properties to strain rate. The observations show that sand under monotonic loading exhibits moderate strain rate dependency. This extent of rate varies with sand composition. There is good agreement between the strain rate behavior obtained from conventional tests and SED predictions derived from the proposed analysis.

Effects of Thermal Parameters on the Mechanical Characteristics of Ti6Al4V Sheets Deformed at Elevated Temperatures

Over these last decades, titanium and its alloys have been largely used for many applications in different sectors such as aerospace, military and biomedical ones. Many studies have investigated the behaviour of the most broadly used alloy, the Ti6Al4V, under hot forging and superplastic forming conditions, whereas almost no records can be found about the Ti6Al4V sheet behaviour at elevated temperature and moderate strain rate (i.e. above 0.1 s-1). The research starts analysing the influence of the thermal cycle parameters of on the Ti6Al4V mechanical properties and microstructural characteristics by means of micro-hardness measurements and Optical Microscopy (OM) analysis. Different soaking times, cooling rates and heating technologies, namely furnace and induction, were considered and their effects investigated. Based on these results, uniaxial tensile tests were carried out at different temperatures, ranging from room temperature up to 900°C, and strain rates of 0.1 and 1s-1, adopting the thermal parameters and heating means previously investigated. The Ti6Al4V sensitivity to the rolling direction was highlighted, calculating the average normal anisotropy as a function of the testing parameters. The samples fracture areas were then measured in order to calculate the strain at fracture as a function of the temperature and strain rate, while the fracture morphology was investigated through Scanning Electron Microscopy (SEM). OM and SEM analyses were also used to investigate the deformed samples microstructure. Finally, the samples micro-hardness, as a measure of the post-forming characteristics, was measured in order to evaluate its sensitivity to the temperature and strain rate.

Influence of copper inclusions on the strength of aluminum matrix at high-rate tension

In this work, we perform the molecular dynamics (MD) investigations of Al–Cu nanocomposite strength in the conditions of a high-rate uniaxial tension. The investigated material is an Al matrix with spherical nanoinclusions of Cu. The obtained results show that the formation of voids leading to fracture begins inside the aluminum matrix near the interface between Al and Cu. From a viewpoint of the nanocomposite strength, the main effect of Cu inclusions is connected with the stress concentration that leads to an action of increased stresses inside the matrix near the interface with inclusions; these increased stresses are 1.2–1.3 times higher than the volume-average value of stress (for the temperature of 300K). With the increase of temperature, the plastic relaxation becomes more active due to increased rate of dislocations generation that reduces the role of stress concentrators; the effect finally disappears at temperatures >700K. A few atomic layers of aluminum remain on the copper inclusions after the fracture, which indicates good adhesion properties of the Al–Cu interface. We propose a continuum model of the nanocomposite fracture that is based on the equations of nucleation and growth of voids inside the aluminum matrix; the model takes into account the stress concentration around inclusions. A comparison with the MD results shows that the continuum model allows us to describe the rate and temperature dependences of the nanocomposite strength at least for strain rates ≥108s−1. At moderate strain rates, the strength values that are calculated with the continuum model correspond to the experimental data for the aluminum alloy 2024 with the second phase precipitates.

Composite nature of fresh skin revealed during compression

Biological systems are subjected to moderate-to-high strain rates in blast-type traumatic injuries. An improved understanding of the responses of cells and tissues to extreme mechanical stresses could improve mitigation and post-injury treatment strategies. A key aim of this research is to create biologically meaningful injury models of soft tissues. Here the authors examine the material and cellular properties of freshly harvested porcine skin in compression. The data presented suggest that fresh skin differentially responds low to moderate strain rates as a composite rather than that of a homogeneous polymer. The implications of this work are discussed in terms of creating improved analytical models to describe the material properties of fresh skin.

New constraints on the Nubia–Sinai–Dead Sea fault crustal motion

The subduction between Nubia and Eurasia and activities along the Red Sea, Gulf of Suez and Gulf of Aqaba may control the surface deformation in the north-eastern corner of the African continent. Using very few GPS stations in the Egyptian region, previous studies indicate northward motion of northern Nubia with respect to Eurasia of about 5mm/yr (McClusky et al., 2000; Reilinger et al., 2006; Mahmoud et al., 2005). In order to constrain better the movement rate of northern Nubia and interaction between Nubia, Eurasia and Arabia plates, we are using for the first time 16 permanent GPS stations in combination with 47 non-permanent stations covering Egypt for the period 2006–2012. This paper extends the previous study (Saleh and Becker, 2013) by processing in addition to the Egyptian stations 86 permanent stations belonging to three different tectonic plates. This led to a considerably better coverage of the Sinai–Dead Sea region. This work intends to be the first comprehensive analysis of the permanent stations in combination with the various campaign data in selected regions of special interest in Egypt. The GPS sites show a relative motion between Nubia and Eurasia of about 6.5±1mm/yr, which increased toward the Hellenic trench, 8.2±0.8mm/yr in Sinai peninsula, 14.2±1.4mm/yr in the north of Arabian plate and 22.3±0.7mm/yr in eastern and central Turkey. The strain computation indicates high strain rates, where the deformation is strongly localized along the Dead Sea fault, and low to moderate strain rate in the Gulf of Suez and southern Sinai.

High-strain-rate tensile mechanical response of a polyurethane elastomeric material

The dynamic tensile mechanical response of a soft polymer material (Clear Flex 75) is investigated using a split Hopkinson tension bar (SHTB). Stress-strain relations are derived to reveal the mechanical properties at moderate and high strain rates. These relations appear to be rate dependent. Under static loading, the polymer exhibits an elastomeric behaviour, while under dynamic loading, the response is elasto-plastic with a hardening branch. The critical strain rate for transition from a rubbery-like behaviour at low strain rates to a glassy-like behaviour at high strain rates at room temperature is determined. The axial and lateral deformation of the specimen in the SHTB test is recorded by a high-speed camera. The final fracture surface is examined by SEM to explore the physical origins of deformation and fracture behaviour: void formation, craze nucleation, craze extension, crack initiation and propagation. Meanwhile, a shielding mechanism is revealed by the observation of crazing and micro cracking in the crack tip zone, which contributes to the dynamic tensile toughness of CF 75 polymer material.

Deformation of a crystalline olivine aggregate containing two immiscible liquids: Implications for early core–mantle differentiation

Deformation-assisted segregation of metallic and sulphidic liquid from a solid peridotitic matrix is a process that may contribute to the early differentiation of small planetesimals into a metallic core and a silicate mantle. Here we present results of an experimental study using a simplified system consisting of a polycrystalline Fo90-olivine matrix containing a small percentage of iron sulphide and a synthetic primitive MORB melt, in order to investigate whether the silicate melt enhances the interconnection and segregation of FeS liquid under deformation conditions at varying strain rates. The experiments have been performed at 2 GPa, 1450 °C and strain rates between 1×10−3 s−1 to 1×10−5 s−1. Our results show that the presence of silicate melt actually hinders the migration and segregation of sulphide liquid by reducing its interconnectivity. At low to moderate strain rates the sulphide liquid pockets preserved a roundish shape, showing the liquid behavior is governed mainly by surface tension rather than by differential stress. Even at the highest strain rates, insignificant FeS segregation and interconnection were observed. On the other hand the basaltic melt was very mobile during deformation, accommodating part of the strain, which led to its segregation from the matrix at high bulk strains leaving the sulphide liquid stranded in the olivine matrix. Hence, we conclude that deformation-induced percolation of sulphide liquid does not contribute to the formation of planetary cores after the silicate solidus is overstepped. A possible early deformation enhanced core–mantle differentiation after overstepping the Fe–S solidus is not possible between the initial formation of silicate melt and the formation of a widespread magma ocean.

Elasto-viscoplasticity Behaviour of a Structural Adhesive Under Compression Loadings at Low, Moderate and High Strain Rates

Crashworthiness performance of automotives by introducing new materials is of high interest based on the global mass’ reduction of cars. Bonded techniques are tested at present with respect to the reduction of the mass/energy’s ratio combined with recycling processes. In this study, a compression test program is performed on a bulk structural adhesive under a very large range of strain rates, thus [0.1; 5000]/s. Uniaxial compression tests at 0.1 and 50/s are achieved using a high-speed hydraulic testing machine. A split Hopkinson bar’ device made of PA66 is experimented so as to characterize soft materials in the upper domain of strain rates, thus [500; 5000]/s. A special mold is used for the preparation of the adhesive plates. Two sheets are prepared (thickness 4 mm with 1 MPa pressure and 6 mm with 4 MPa pressure) in order to consider the effect of the pressure during the curing process. Water jet technique is used to extract cylindrical samples from the plates with accurate dimensions. The identification of the compression behaviour of the structural adhesive is lead with objective to find material parameters of a modified G’sell model for finite element modeling of crashworthiness.

Processing of β-treated Zircaloy-4 by warm compressions along three orthogonal axes

The purpose of this work is to refine the grains of Zircaloy-4 before it is processed into cladding tubes containing the nuclear fuel. This raises the question of the mechanisms by which the Widmanstatten lamellae inherited from the β-quenching transform into smaller crystallites. With a view to accelerate this transformation, strain steps of compression along three orthogonal axes were performed in the upper α-range (i.e. 550–810 °C). The effects of the temperature, the size of the strain steps, the strain rate and the number of cycles of three compressions were investigated. All have a direct influence on the mechanical behavior, the global texture and the microstructural evolution. The latter was studied mostly by electron backscattering diffraction. The best conditions to break the initial lamellae were found at high strain rate (4 s−1): small recrystallized grains around 10 μm were obtained after one cycle at 750 °C. But at moderate strain rates (0.1 s−1), good results were also reached after two cycles at 650 °C. The mechanisms of globularization are different in both cases: in the first, germination of new grains prevails while in the second, a progressive evolution of the subgrains into grains was observed. Some consequences of heat treatments are also briefly described, pointing out the sensitivity of Zircaloy-4 to undesirable grain growth. The conclusion emphasizes the interest of multiaxial forging in the thermomechanical treatment of hexagonal alloys.

Separation of the elastic waves’ system in pre-stretched bar devices

The loading mode generated by Kolsky bars apparatus is limited due to physical reasons to a duration time of around 0.4 ms. This is not suited in the characterization of high ductility metallic alloys up to fracture at moderate strain rates, since the duration time is too short. The pre-stretched bar device is a good candidate to characterize these materials up to the moderate strain rates. Unfortunately, the elastic waves are generally not separated in time at measurements points in the input bar, and post treatment leads to assumptions. A configuration of the pre-stretching conditions that ensures no superposition of the elastic waves’ system developed along the input bar is thus proposed so as to fulfill standard data analysis requirements, i.e. without any assumptions. However, a drawback of the proposed device is that one of its hydraulic devices generates a loosen tail. This statement comes from a FE numerical model of the whole set-up including the generation of the loosen tail. Finally, an analytical correction to cancel the loosen tail is proposed and validated with respect to a numerical model featuring ideal pre-loading conditions.

Material modelling of a filled rubber material with different approaches in the representation of a statical hysteresis

AbstractIn this contribution, two different approaches for the description of an incompressible carbon black‐filled EPDM (ethylene propylene diene monomer) are presented. Regarding the material's behaviour, especially for cyclic loading conditions, a kind of statical hysteresis loop is present. Even for the slowest possible strain rate, a clearly visible hysteresis occurs in loading‐unloading experiments. The first shown model approach is basically a purely viscoelastic description. Because of the non‐linearities in the material behaviour, the material parameters have to be reformulated by complex functions including further parameters that are strongly coupled. This description is able to display very well the behaviour of the EPDM with respect to quasi‐statical experiments, as well as to dynamical tests for moderate strain rates. The major problem of this model liess in the parameter identification. The coupling of the material parameters leads to a difficult, long‐durating and non‐unique identification. Therefore, initial ideas for an alternative description, escpecially concerning the above‐mentioned statical part of the hysteresis, are outlined in this article. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Multi-Scale Modeling of the Impact Response of a Strain-Rate Sensitive High-Manganese Austenitic Steel

A multi-scale modeling approach was applied to predict the impact response of a strain rate sensitive high-manganese austenitic steel. The roles of texture, geometry and strain rate sensitivity were successfully taken into account all at once by coupling crystal plasticity and finite element (FE) analysis. Specifically, crystal plasticity was utilized to obtain the multi-axial flow rule at different strain rates based on the experimental deformation response under uniaxial tensile loading. The equivalent stress – equivalent strain response was then incorporated into the FE model for the sake of a more representative hardening rule under impact loading. The current results demonstrate that reliable predictions can be obtained by proper coupling of crystal plasticity and FE analysis even if the experimental flow rule of the material is acquired under uniaxial loading and at moderate strain rates that are significantly slower than those attained during impact loading. Furthermore, the current findings also demonstrate the need for an experiment-based multi-scale modeling approach for the sake of reliable predictions of the impact response.

Influence of Temperature and Strain Rate on the Mechanical Behaviour of Aluminium Alloy AA6060

In an attempt to improve the constitutive models for 6xxx aluminium alloys at high temperatures and high strain rates, a comprehensive test series has been carried out for AA6060. Uniaxial tension tests were performed at various strain rates from 0.01 s-1 to 1000 s-1 and temperatures from 20 °C to 350 °C. The tests were carried out using a standard tensile machine for low to moderate strain rates and a split-Hopkinson tension bar (SHTB) system for high strain rates. In both cases, an induction apparatus was used to heat the sample while local deformation measurements were obtained with a high-speed camera and used to estimate the true strain beyond necking. Strong coupling between the influence of strain rate and temperature on the stress-strain behaviour was found. At room temperature, the strain rate has a minor effect on the behaviour of AA6060. On the other hand, a significant increase of the yield stress and work-hardening with strain-rate is observed for temperatures above (K), being the melting temperature; i.e., above 673 K.

Unusual behaviour of usual materials in shock waves

Exotic results of investigations of inelastic deformation and fracture under shock wave loading are presented and briefly discussed. Temperature effects on the flow stress at high strain rate may differ even in sign from those we observe at low and moderate strain rates. Investigations of the temperature-rate dependence of the yield stress at shock compression demonstrate intense multiplication of dislocations. At the highest strain rates, so-called ideal (ultimate) shear and tensile strength is reached in experiments with picosecond durations of shock loading. Although grain boundaries, in general, reduce resistance to fracture as compared to single crystals, the spall strength of ultra-fine-grained metals usually slightly exceeds that of coarse-grain samples. Failure wave phenomena have been observed in shock-compressed glasses.

Deformation Behavior of ZK60 Magnesium Alloy at Elevated Temperature

The high temperature compressive tests of squeeze casting ZK60 magnesium alloy in the testing temperature range of 523-723K and strain rate range of 0.001-10s-1 were performed on Gleeble-1500D thermal simulator testing machine. Optical microscopy was performed to elaborate on the dynamic recrystallization (DRX) grain growth. TEM observation indicated that the mechanical twinning, dislocation slip, and dynamic recrystallization are the materials typical deformation features. Variations of flow behavior with deformation temperature as well as strain rate were analyzed. Analysis of the flowing deformation behavior and microstructure observations indicated that the flow localization was observed at lower testing temperature and higher strain rates. Dynamic recrystallization occurred at higher testing temperature and moderate strain rates, which improved the ductility of the material. The results indicated that at the testing temperatures lower than 573K and strain rates higher than 1s-1, the material exhibited flow instability manifesting as bands of flow localizations. These temperatures and strain rates should be avoided in processing the material. Dynamic recrystallization occurs in the temperature range 573-723K and the strain rate range 0.001-0.1s-1. The number of dynamic recrystallization grains is less at lower temperature and higher strain rate than higher temperature and lower strain rate. The dynamic recrystallization is inadequate at 573-623K while the dynamic recrystallization grain growth has been observed in the temperature range of 673-723K. Therefore it may be considered that the optimum processing parameters for hot working of squeeze casting ZK60 magnesium alloy are 648K and 0.001-0.01s-1, at which fine dynamic recrystallization microstructure can be obtained.

Novel temperature measurement method & thermodynamic investigations of amorphous polymers during high rate deformation

Polymers are frequently used in applications in which they may be exposed to high rate or impact loading, and there is growing industrial importance in understanding their mechanical behavior at different strain rates. An important aspect of this is the temperature rise due to adiabatic conditions in high rate loading. This paper describes research that has been performed to measure the temperature rise that occurs in specimens undergoing rapid deformation. A novel thermocouple design is presented and applied to PMMA and 20 wt% DINP-plasticized PVC, deformed at moderate and high strain rates. The measurements are accompanied by investigations of strain energy.