Quasi-static Range Research Articles

From quasi-static to dynamic: Experimental study of mechanical and fracture behaviour of epoxy resin

Epoxy polymers are extensively used in various engineering applications such as aerospace, defence, sports, automotive etc. This article focuses on the in-depth mechanical characterisation of EPOFINE®-1564, a Bisphenol-A-based liquid epoxy resin under various loading conditions. To predict the tensile and compressive behaviour of the representative epoxy resin, quasi-static experiments were performed in the range of 10−4 to 10−2s−1 on Universal testing machine (UTM) while the dynamic experiments were conducted using Split Hopkinson Pressure Bar (SHPB) for high strain rates (1136–2833 s−1). In this study, 3D Digital Image Correlation (DIC) was also used to evaluate the specimen's full-field displacement profile over a wide range of strain rates. Analysis of various mechanical properties such as elastic modulus, yield strength, and ultimate strength, revealed that the epoxy polymer is strain rate dependent within the considered strain rate range. For understanding the fracture behaviour, three-point bend (TPB) experiments were also carried out for both quasi-static (1–10 mm/min) as well as dynamic (10–15 m s-1) regimes. Dynamic fracture experiments were performed using the modified Hopkinson Pressure Bar (MHPB). The fracture toughness was determined through load vs crack mouth opening displacement (CMOD). Fracture toughness was found to increase with the displacement rate due to the significant plastic deformation under quasi-static range. Conversely, it was found to decrease under dynamic loading because of absence of plastic deformation resulting in brittle fracture. The fracture surface of the specimen was examined through a high magnification digital microscope.

Micromechanical response of an electrodeposited NiP metallic glass by pillar compression under extreme conditions

In this work, the mechanical properties of pulse electrodeposited amorphous nickel phosphorous (NiP), with ∼16 wt% P, was investigated for an improved understanding of the deformation behavior of metallic glasses at extreme conditions, particularly at the microscale. Upon decreasing the temperature to sub-ambient, both the yield strength and the shear band density increase. While the change of yield strength with temperature can be well explained by a cooperative shear model, the increase in the number of shear bands can be related to an increase in potential sites for activation of shear transformation zones due to the enhanced structural heterogeneity at lower temperatures. This, however, hinders the percolation of deformation units and leads to a decrease in the shear band propagation speed, from ∼50 nm/s at 295 K to ∼20 nm/s at 195 K. By testing micropillars across seven orders of magnitude in strain rate, a two-stage strain rate sensitivity is observed, from nearly negligible at the quasi-static range (m1 = 0.001 ± 0.002 for 10−3 s−1 to 10−1 s−1) to highly positive at dynamic high strain rate range (m2 = 0.02 ± 0.004 for 1 s−1 to 1000 s−1). This transition implies a change in the yield-controlling process, from the diffusion-assisted relaxation at quasi-static conditions to the rate of energy barrier crossing of shear transformation zones at high strain rates. These findings highlight several distinctive features of microscale metallic glasses, including the reduced shear band velocity at sub-ambient temperature and the two-stage strain rate sensitivity.

Study on strength damage model considering resistivity and failure characteristics of the frozen soil–rock mixture under different loading rates

The strength damage and deformation failure of frozen soil–rock mixture (FSRM) often restrict the safety of the major engineering construction in cold areas or the spatial development of urban underground water-rich rock and soil masses. To investigate the uniaxial strength damage evolution and failure characteristics of FSRM under different loading rates (0.3, 0.6, 3, 6, 30, and 60 mm·min−1) in the quasi-static range, resistivity monitoring and image recognition technology were used to study the time-stress-volumetric strain-resistivity changes. The results indicate that the peak stress, peak strain, initial yield modulus, and tangential modulus of FSRM increase rapidly before increasing slowly as the loading rate increases, and there are critical loading rates and post-peak failure phenomenon. Three distinct types of failure modes, bulge failure, oblique shear failure, and fragmentation failure were observed at low (0.3–0.6 mm·min−1), medium (3–6 mm·min−1), and high loading rates (30–60 mm·min−1), respectively. The macroscopic failure of the FSRM at different loading rates arises from a combination of strain rate hardening of the strength and damage softening of the structure. To predict the stress-strain characteristics at various loading rates, a damage prediction model with a damage variable correction factor considering residual strength was employed based on the improved Duncan–Chang model and damage theory of electrical resistivity, and the predicted results were in good agreement with the experimental data.

Shape Control of a Unimorph Deformable Mirror for Space Active Optics under Uncertainties.

This paper focuses on the change of morphing capabilities for a unimorph deformable mirror impacted by environmental factors, which works in space for active optics applications. Various aspects of disturbing sources are considered, including complex thermal and mechanical conditions on ferroelectric behaviours of strain actuation, and influences of preconfigured initial shapes and stress-induced geometric stiffness on the structural rigidity of the mirror; changes on both the perturbed shape and the Jacobian matrix are discussed. Those variations are regarded as uncertainties in the design of control methods with both open-loop and iterative control strategies tested in the quasi-static range.

On implementation of fibrous connective tissues’ damage in Abaqus software

Connective fibrous tissues, such as tendons and ligaments, in humans and animals exhibit hyperelastic behaviour. The constitution of the material of these tissues is anisotropic due to the presence of the collagen fibres, where one family of fibres is the typical case. Traumatic events and/or aging may sometimes lead to the damage of the tissue. The study of motion of affected joints or limbs is usually not permitted in vivo. This is where finite element method (FEM) becomes useful as a premise for general analysis, surgical planning or designing of implants and medical treatment. One of the most often used FEM commercial programs is the field of the biomechanics is Abaqus. The present study discusses the potential of user subroutine UANISOHYPER_INV in this code to analyse response of transversely isotropic tissue with damage in quasi-static range. This subroutine requires providing the material energy function and its derivatives only. The stress tensor and constitutive matrix are computed by the software automatically. To the best of the Authors’ knowledge this procedure provides the easiest way to simulate the anisotropic hyperelastic material behaviour in Abaqus. In this study its usage is extended onto the damage response simulation. The verification of the approach and its validation against experimental data indicates its efficiency.

Unravelling the Size‐Dependent Mechanical Properties of Nanocrystalline Face‐Centered‐Cubic Metals: From the Dislocation Point of View

The grain size dependence of strain rate sensitivity, apparent activation volume, and yield stress of nanocrystalline (NC) face‐centered‐cubic metals (FCC) are modeled based on the bow‐out model of single dislocation. It is found that the grain size limitation on the dislocation length gives rise to the grain size effects on the mechanical properties. The model gives predictions that when temperature is at or below room temperature and the strain rate is in the quasistatic range, dislocation‐mediated mechanisms play a dominant role in the plastic deformations of FCC NC metals even for the grain size of several nanometers, which is consistent with known experimental and simulation results. Based on the model, abnormal mechanical phenomena of nanostructured metals, such as the appearance of the inverse Hall–Petch relationship, the existence of the critical grain size, and its strain rate dependence, are well predicted and interpreted.

Establishing flow stress behaviour of Ti-6Al-4V alloy and development of constitutive models using Johnson-Cook method and Artificial Neural Network for quasi-static and dynamic loading

Ti-6Al-4V alloy is one of the most widely used material in both research as well as in commercial industries at present due to its high strength-to-weight ratio, low density and excellent high-temperature properties. Understanding the behaviour of this alloy at various deformation conditions (strain, strain rate and temperature) is crucial to fit the material in demanding applications. In our present work, the mechanical behaviour of α + β dual phase Ti-6Al-4V alloy is studied in the temperature ranging from 25 ℃ to 200 ℃ and rate of deformation ranging from 10-3 s−1 to 104 s−1. Tensile tests were done using uniaxial tensile tester for quasi-static range of deformation and Split-Hopkinson bar machine for dynamic range of deformation. Post deformation fracture surface analysis were carried out to understand the effects of strain rate and temperature variations on the deformation behaviour, and to establish a structure–property correlation. For the studied range of deformation parameters, constitutive models are developed. As Johnson-Cook model is one of the widely used model in various numerical analysis software, a modified Johnson-Cook model has been developed for the alloy. Moreover, artificial intelligence (AI) is found to be an efficient tool these days to solve complex problems in various fields of engineering. An attempt is also made in this study to develop an artificial neural network (ANN) framework for the prediction of flow stress at various deformation condition for Ti-6Al-4V alloy. Our study revealed that the AI based ANN technique is more efficient in calculating the flow stress as compared with the traditional Johnson-Cook model.

Influence of double rods and interbody cages on quasistatic range of motion of the spine after lumbopelvic instrumentation.

This in vitro biomechanical study compares residual lumbar range of motion (ROM) and rod strain after lumbopelvic instrumentation using 2 rods, 4 rods and interbody cages. Seven human cadaveric specimens were instrumented from L1 to sacrum, and pelvic screws were implanted. The pelvis was constrained and moments up to 7.5Nm were applied to T12. Segmental L1-S1 ROM was analyzed by tracking radiopaque balls implanted in each vertebra using biplanar radiographs. Deformation within principal rods was measured by strain gauges. Four configurations were compared: 2 rods (2R), 4 rods (4R), 4 rods + ALIF at L4-L5 and L5-S1 (4R + ALIF), 2 rods + ALIF (2R + ALIF). Intact average global L1-S1 ROM was 42.9° (27.9°-66.0°) in flexion-extension (FE), 35.2° (26.8°-51.8°) in lateral bending (LB), 18.6° (6.7°-47.8°) in axial rotation (AR). In FE, average ROM was 1.9° with both 4-rod configurations versus 2.5° with 2R and 2.8° with 2R + ALIF (p < 0.05). In LB, ROM ranged between 1.2° and 1.5° without significant differences. In AR, ROM was 2.5° with both 4-rod configurations versus 2.9° with 2R (p = 0.07) and 3.1° with 2R ALIF (p = 0.01). In FE, strain decreased by 64% and 65% in principal rods at L3-L4 with 4-rod. When comparing 2-rod configurations, strain decreased by 1% in flexion and increased by 22% in extension at L3-L4 when adding an ALIF at L4-L5 and L5-S1. Double rods and interbody cages decrease residual ROM in FE and AT. Double rods seem efficient in limiting strain in principal rods. The use of single rods with cages at the lumbosacral junction increases strain at the first adjacent level without cage.

Mechanical behaviour of NiTiNb shape memory alloy wires– strain localisation and effect of strain rate

Over the past few years, shape memory alloys (SMAs) have received increased attention in civil engineering research due to their unique features such as superelasticity, shape memory effect (SME), high ductility and good corrosion resistance. SMAs, however, have complex material behaviour which depends on many parameters such as chemical composition, thermo-mechanical treatment and ambient temperature. SMAs exhibit high strain-rate sensitivity and strong strain localisation during the stress-induced martensitic (SIM) phase transformation. Both have serious implication in civil engineering applications. Strain rate effects and the strain localisation in SMAs have been commonly investigated separately in the literature which has been mostly focused on NiTi SMA. This paper investigates the strain localisation phenomenon, the effect of strain rate and their interaction in NiTiNb SMA. The digital image correlation (DIC) technique was used to investigate the strain localisation phenomenon. The effect of strain rates is investigated within the quasi-static range and varies from 3.3 × 10−5/s to 3.3 × 10−2/s in strain-controlled tests and 2 × 10−5/s to 2 × 10−1/s in displacement-controlled tests. Significant non-uniform strain distribution is observed during the SIM phase transformation, which progresses through the nucleation and broadening of the transformation bands (TBs). The nucleation of the TBs and the unloading strain recovery within the TBs show high strain-rate sensitivity. At high strain rates, the nucleation of a TB is accompanied by a significant stress-drop.

Effect of Strain Rate on the Tensile Behavior of CoCrFeNi and CoCrFeMnNi High-Entropy Alloys

High-entropy alloys (HEAs), a novel class of metal alloys, have been receiving increasing attention from the scientific community. HEAs have the potential to be used in critical load-bearing applications in replacement of conventional alloys such as stainless steel and nickel-base superalloys. Tensile experiments at quasi-static to dynamic strain rates (10−4-103 s−1) were performed on two single-phase face-centered cubic HEAs, CoCrFeNi and CoCrFeMnNi. Electron backscatter diffraction was used to study the microstructure of the samples before the experiments, and transmission electron microscopy was performed postmortem. The dominant deformation mechanisms were dislocation slip at quasi-static strain rates with the addition of deformation nano-twins at dynamic strain rates. Ultimate dynamic tensile strength and ductility improved with the increase in strain rate, which can be attributed to the activation of deformation nano-twins in HEAs. CoCrFeNi and CoCrFeMnNi both have low stacking fault energies, which could promote twinning at high strain rates to accommodate plastic deformation. The strain rate sensitivity of the flow stress increased with increasing strain rate, beginning with negligible strain rate sensitivity in the quasi-static range to high strain rate sensitivity in the dynamic range. CoCrFeMnNi showed greater strain rate sensitivity of flow stress. CoCrFeNi, with less configurational entropy, had higher mechanical properties and strain-hardening rates compared to CoCrFeMnNi, which was attributed to the weakening effect of the addition of Mn on the solid solution hardening.

Evaluation of Length, Dependent Earth Return Transmission-Line Parameters for Overhead Conductors in the Quasistatic Range

In this paper, a novel application of the matrix pencil method (MPM) is used to evaluate the length-dependent earth return parameters of overhead transmission lines in the quasistatic frequency range. The MPM is used to approximate the reflection coefficient by a series of complex exponentials, which allows the length-dependent transmission-line parameters to be evaluated in closed form. This methodology improves the accuracy of the length-dependent formulation when compared with the single image approximation used in previous publications, and can be applied to both parallel and angled overhead conductor configurations. Where large differences in results exist between the two methods, numerical integration confirms the accuracy of the MPM method. The proposed method can accurately evaluate the earth return parameters for conductors of arbitrary length and separations. This enables the proposed method to be applied to transmission-line configurations of all lengths, even in instances where the application of the per-unit method is not valid. This makes the length-dependent methodology ideal for generating transmission-line models from routing coordinates.

Tympanic membrane pressure buffering function at quasi-static and low-frequency pressure variations

Deformation of the tympanic membrane is known to contribute to the pressure regulation processes in the middle ear cleft. In this paper we investigated pressure variations in the rabbit middle ear in response to sinusoidal varying pressures applied to the ear canal, with frequencies ranging from 0.5 Hz to 50 Hz and pressure amplitudes ranging between 0.25 kPa and 1 kPa. The transtympanic pressure difference was found to be smallest in the quasi-static range, and quickly increased as a function of frequency. The response curves showed asymmetry, with larger transtympanic pressures when positive pressures were applied in the ear canal. Normalized transtympanic pressure amplitudes remained fairly constant as a function of input pressure, with values in the range of 60%–70% relative to the applied pressure. The total harmonic distortion of the middle ear pressure signal was calculated and was found to be very small (≤2%) for low-pressure amplitudes and low frequencies. For pressure amplitudes in the order of 0.25 kPa–0.5 kPa, it increased to about 10% at 50 Hz. When a 1 kPa pressure amplitude was applied, variation between animals became large and distortion values up to 30% at 50 Hz were observed. The results showed that pressure buffering due to tympanic membrane displacement was most effective for compensating small transtympanic pressure loads at low frequencies.

Enhanced dielectric properties induced by loading cellulosic nanowhiskers in natural rubber: Modeling and analysis of electrode polarization

Natural rubber (NR) isolated from Hevea Brasiliens and reinforced with different amounts of cellulose nanowhiskers (extracted from the rachis of date palm tree) was investigated using differential scanning calorimetry and dielectric spectroscopy in the frequency range 0.1 Hz to 1 MHz, and the temperature range −80 to 200 °C. The experimental dielectric data were analysed within the formalisms of dielectric permittivity, complex conductivity and complex modulus. The results were discussed in terms of dc conductivity, interfacial polarization and electrode polarization. The paper aims to investigate especially the electrode polarization observed at low frequency and/or high temperature (LF/HT). It is exhibited that the understanding of the frequency space charge relaxation behaviour trapped close to the material/electrode interface will help one to elucidate the charge dynamics in the quasi static range. So charge carrier concentration and mobility in the sample at high temperature can be evaluated through the electrode polarization modeling of broadband dielectric spectroscopy data.

Static and Dynamic Large Strain Properties of Methyl Cellulose Hydrogels

Methyl cellulose (MC) hydrogels display thermoreversible gelation upon heating. These hydrogels are abundantly employed in a variety of applications, rendering study of their mechanical properties relevant and important. Here we report on their basic elastic properties, based on ultrasonic measurements, and focusing on the heated solid gel, their mechanical properties in the quasi-static and dynamic (impact) large strain regimes are characterized. Unlike most other solids which soften upon heating, we find that methyl cellulose gels toughen increasingly on heating beyond the gelation point. Flow stress curves reveal polymer concentration dependent hardening. Contrary to most other soft materials, MC hydrogels do not present strain-rate sensitivity in the quasi-static range. Nevertheless, a dramatic change is observed in the dynamic regime, where at strain rates of ∼1500 s–1 a 10–20-fold increase in flow strength is observed relative to the quasi-static regime. The results of this investigation complement ...

Experimental and FEM analysis of three carbon steel characterization under quasi-static strain rate for bumper beam application

This paper investigates the mechanical behavior of three selected steel materials which are considered to be the bulk material of front most bumper beam of a vehicle that is suddenly loaded in the quasi-static range. Thirty-six constant strain rate uniaxial tension tests were performed. The test was performed on a HUALONG electro-hydraulic universal testing machine at four strain rates ( 3.33 × 10 -3 ,3.33 × 10 -2 , 3.33 × 10 -1 , 3. 33s -1 ). The FEM which is ABAQUS/CAE is used to simulate the bumper subsystem using the three selected steel. The outcome shows that ultimate tensile strength (UTS) increase with an increase in strain rate and high alloy steel (HAS) material has the maximum mean UTS. The FEM in the post -processing stage gives the minimum displacement and maximum strain energy for HAS material when compared to the other two materials. Finally, from both experimental and ABAQUS explicit analysis the result shows HAS material is better suit for the bumper beam application.

Appraisal of Strain Rate Sensitivity of Polypropylene Nanocomposites

Neat polypropylene (PP) and PP reinforced with nano clay platelets were tested at a fixed quasi-static strain rate on UTM and at corresponding limiting strain rates on SHPB (Split Hopkinson Pressure Bar). Enactment with minimum possible thickness of specimens cum maximum impact pressure on SHPB experiments is found important to set limiting strain rate. Combination of stress-strain responses of the material systems from both high strain rate impact and quasi-static loading is used to estimate the representative strain rate sensitivity index ‘m’ values: A new approach more justified than the trend of using strain rates limited the quasi-static range. Particular constant strain value of 0.0125 m/m and room temperature of 21±3 oC at which ‘m’ values are calculated were considered. The increase in weight fraction of nano-reinforcement was found to increase strain rate sensitivity index of PP to the level comparable with the lower bound of the range for superplastic alloys.

Deformation and fracture behavior of physical gelatin gel systems

Food scientists usually used biopolymer physical gels as model systems because they are structurally and mechanically similar to many gel-like food products. In this paper, eight gelatin gel systems with different stiffness were prepared by varying gelatin concentration (10–30%w/w), collagen source (bovine/porcine) and solvent composition (0/40%w/w glycerol/buffer mixture). The swelling behavior was evaluated and the mechanical response was characterized through puncture tests, uniaxial compression experiments and wire cutting fracture tests. From these tests, apparent gel strength, first order Ogden constitutive parameters (shear modulus, μ, and strain hardening capability, α) and fracture toughness (Gc) were determined. Samples that display apparent gel strength and swelling behavior consistent with a more physically cross-linked structure exhibit larger μ and Gc and lower α values. It is shown that α and Gc are related with μ independently of gelatin concentration, collagen source and glycerol presence. α decreases exponentially with increasing μ whereas Gc increases linearly with μ. The found experimental trends suggest that in the quasi-static range the overall mechanical behavior of gelatin gel systems is mainly controlled by the initial shear modulus, which is a direct measure of gel stiffness.

Cyclic Deformation Behavior of Friction Drilled Internal Threads in AlSi10Mg and AZ31 Profiles

Metallic lightweight materials are used for enhancing dynamic range, resource optimization and emission reduction in many fields of traffic engineering, whereby aluminium and magnesium components are manufactured by means of welded, adhesive and screw joints. Friction drilling, as forming process with subsequent manufacturing of threads, offers the opportunity to produce an internal thread in lightweight profiles with a usable thread depth larger than the profile thickness, making use of local material expansion. Moreover, the direct manufacturing offers a huge potential for time and cost saving in comparison to conventional thread machining.Microscopic-based characterization of mechanical properties of aluminium AlSi10Mg and magnesium AZ31 internal threads in thin-walled profile specimens was carried out using tensile tests and fatigue tests in tensile loading range. The internal threads were chipless manufactured by means of thread forming. Variations in the geometric process parameter wall thickness were compared. Differences between the AlSi10Mg chill casting alloy and the AZ31 continuous casting alloy in maximum tolerable loads and fatigue limits were correlated with the production-related profile qualities of the profile specimens. The maximum tolerable loads increase linearly with increasing wall thickness of the specimens, whereby AlSi10Mg specimens were about 20-24% lower in the quasi-static range and about 37-47% lower in the cyclic range in comparison to AZ31 specimens due to oval forms of the core holes caused by the friction drilling process. Plastic strain behavior and deformation-induced changes in temperature in load increase tests were evaluated to reliably estimate the fatigue limit of magnesium AZ31 internal threads.

Compression and shear behavior of epoxy SA 80 bulk adhesive over wide ranges of strain rate

Abstract This paper deals with the experimental characterization of a bulk adhesive fracture in the quasi-static range using a conventional machine and at high strain rates using the Hopkinson bar technique. For very high strain rates, the direct impact Hopkinson bar technique is used. The studied adhesive is a toughened epoxy which can be used for impact resistance in bonded assemblies. It is worth studying the adhesive sensitivity to strain rate as a bulk material in order to distinguish between its response within a structure when used to bond substrates and its response as pure material. Experiments were carried out under compression and shear loadings. A special grip was conceived to mount the specimen for shear tests. In both loading types, this adhesive was found to be highly strain-rate-sensitive. The adhesive strength increases with strain rate until reaching a maximum value then it drops for very high strain rates. Although this behavior is uncommon, it has been reported already in three previous works.

Influence of the production process on the deformation and fatigue performance of friction drilled internal threads in the aluminum alloy 6060*

Aluminum alloys are used for enhancement of dynamic range, resource optimization and emission reduction in many fields of traffic engineering, whereby aluminum components are manufactured by means of welded, adhesive and screw joints. Friction drilling, as forming process with subsequent manufacturing of threads, offers the opportunity to produce an internal thread in lightweight profiles with a usable thread depth larger than the profile thickness, making use of local material expansion. Moreover, the direct manufacturing offers a huge potential for time and cost saving in comparison to conventional thread machining. Microstructural characterization of mechanical properties of EN AW-6060 internal threads, both in profile and bulk material specimens, was carried out using tensile tests and fatigue tests in the tensile loading range. A comparison was made between the manufacturing techniques tapping, thread forming and thread milling. The maximum tolerable loads of the profile specimens are about 50 % lower in the quasi-static range and about 25 % lower in the cyclic range in comparison to bulk material specimens. Formed threads show the best and cut threads the worst mechanical properties which were correlated with the production-related profile qualities and changes in microstructure. Multiple step tests prove that the fatigue limit of aluminum internal threads, validated in single step tests until 107 cycles, can be reliably estimated by means of plastic strain.