Dynamic hardening properties identification utilizing acceleration data by the Virtual Fields Method

Reinforcing cement-based materials by nanomaterials has attracted extensive attention over the past decades. It has been reported that the mechanical properties of cement-based materials can be greatly improved by incorporating a small amount of nanomaterials. However, experimental and theoretical works have all focused on the enhancement of cement-based materials subjected to static loading. To the author’s knowledge, no studies have reported on the mechanical properties of nanomaterial- reinforced cement-based composites under high strain rate loadings. This study investigates the reinforcing effect of graphene oxide (GO) on cement mortar under high strain loadings. GO is an emerging nano-scale candidate for enhancing cement-based materials, which is valued for its two-dimensional geometry, superior mechanical properties and large surface area. Tensile splitting and compression tests were conducted on GO-reinforced cement mortar under both static and high strain rate loadings. The high strain rate testing was performed using a Split Hopkinson Pressure Bar (SHPB) apparatus. Static experiments showed that incorporation of GO (of 0.02 wt% of cement) improved the tensile splitting and compression strength of plain cement mortar by 8.9% and 10.8%, respectively, and there was little difference between the 0.02 wt% and 0.04 wt% GO addition. The SHPB tests showed that the reinforcing effect of GO under high strain rate is directly related to the number of cracks. In tensile splitting tests, because the major crack is always localized in the centre of the specimen regardless of the strain rate, the reinforcing effects of GO on cement mortar were the same for different strain rates. In compression tests, however, because the cracks were diffused and there were more cracks under high strain rates, the reinforcing effect of GO was also more significant under higher strain rates. To understand the reinforcing mechanisms of the nanomaterials, the key is to determine the interaction properties between the nano-scale reinforcements and the cement matrix. However, understanding of the governing forces in the reinforcement’s pull-out behaviour at such a small scale is still very limited. The present study is the first to identify the governing force during the pull-out of atomically thin two dimensional (2D) nanosheets (e.g. graphene and its derivative GO) and to develop corresponding theoretical models. In molecular dynamic (MD) simulations, friction was found to make negligible contribution to the pull-out force because of the lack of asperities on atomically thin materials (ATM). The pull-out force was revealed to be governed by a “crack plane adhesion”. Unlike frictional pull-out, crack plane adhesion produces a pull-out force independent of the embedded length of ATM. The magnitude of pull-out force and its affecting factors were investigated by MD simulations. On the basis of crack plane adhesion, the relations between the pull-out force and the pull-out displacement for ATMs was formulated. Furthermore, a new theoretical model was developed to predict the crack bridging stress (σB) of 2D ATMs. The magnitude of maximum σB was estimated to be 3MPa for 0.2 wt% of GO in cement matrix, which was used in the finite element simulations as discussed herein. The fundamental theory and new model proposed here serve as theoretical support for understanding and development of ATM-reinforced composite materials. Finite element simulations for static and SHPB compression tests were conducted using a micromechanical model, the microplane model. First, the microplane model was examined by comparative study with the commonly used concrete damaged plasticity model. Then finite element simulation models of static and SHPB compression tests were built in ABAQUS. For simulation of the static test, by including the calculated crack bridging stress into microplane model, the experimental compressive strength of GO-reinforced cement mortar could be accurately simulated, which validated the calculation of the crack bridging stress by the proposed model in Chapter 4 and the effectiveness of the microplane model to simulate the static behaviour of GO-reinforced cement-based composites. For simulation of the SHPB test, the microplane model with a logarithmic relation between the dynamic increase factor (DIF) and the strain rate to account for the strain rate effect worked for the simulations of plain cement mortar samples. However, for simulation of the GO-reinforced mortar samples, the simulation results give a significant underestimation compared with the experimental results under higher strain rates.

In order to perform experimental identification of high strain rate material models, engineers only have a very limited toolbox based on test procedures developed decades ago. The best example is the so-called Split Hopkinson Pressure Bar (SHPB) which has proved extremely useful but has important intrinsic limitations due to the stringent assumptions required to process the test data. The recent advent of full-field deformation measurements using imaging techniques has allowed novel approaches to be developed and exciting new testing procedures to be imagined for the first time. One can then use this full-field information in conjunction with efficient numerical inverse identification tools such as the Virtual Fields Method (VFM) identify material parameters at high rates. The underpinning novelty is to exploit the inertial effects developed in high strain rate loading.

A comprehensive mechanical characterization of a commercially available hot curing epoxy system (Araldite® LY 564 with Aradur® 2954, HUNTSMAN Corp.) is performed including compression tests at quasi-static and high strain rates, as well as creep and relaxation tests. High strain rate tests (770/s and 875/s) are conducted by using a split-Hopkinson pressure bar (SHPB) apparatus and compared with the quasi-static compression tests at three strain rates (0.001/s; 0.01/s; 0.1/s). Elasticity modulus and yield stress increase with increasing strain rate, for both quasi-static and high strain rate conditions. The change in the mechanical behavior from quasi-static to high strain rate conditions is quite prominent. While strain rate changes from 0,001/s to 875/s, elasticity modulus increases from 1465 to 3193 MPa (118% increase) and yield stress from 119 to 204 MPa (72% increase). The evident exponential hardening at the viscoplastic region seen on quasi-static stress–strain curves is not observed at high strain rates. Creep tests are performed for three different stress levels (50, 100 and 200 MPa) and 120 min (7200 s). In addition, relaxation tests are done for three different strain levels (3.16, 7.15 and 35.5%) also for 120 min (7200 s). Creep compliance and relaxation modulus are calculated and plotted. It is observed that creep strain values at the stress levels lower than the yield point are lesser compared to creep strain values around yield strength since rate dependency is increasing with increasing stress. Creep at the hardening region is not prominent due to polymer chain entanglement. Stress drop during relaxation is increasing with the increasing strain level.

A key limitation of current moderate and high strain rate test methods is the need for external force measurement. For high loading rate hydraulic machines, ringing in the load cell corrupts the force measurement. Similarly, the analysis of split-Hopkinson bar tests requires the assumption that the specimen is in a state of quasi-static equilibrium. Recently, image-based inertial test methods have shown that external force measurement is not required if full-field measurements are available and inertial effects are significant enough. In this case the load information is provided by the acceleration fields which are derived from full-field displacement measurements. This article describes a new image-based inertial test method that can be used for simultaneous quasi-static and high strain rate stiffness identification on the same test sample. An experimental validation of the new test method is provided using PMMA samples. A major advantage of this new test method is that it utilises a standard tensile test machine and the only specialist equipment that is required is an ultra-high speed camera.

Nylon 66 is widely used in the vehicle interior, electronic parts and accessories. Nylon 66 as polymer material is added reinforce glass fiber to increase material properties. In parts forming process, injection mold method is widely used in polymer forming industry. In the study, the effects of injection molding process on the pseudo-static and high strain rate tensile properties of Nylon 66 composites are discussed. From the results, the tensile strength and Young’s modulus increase with increasing the amount of glass fibers, but the elongation decreases with opposite trend. In high strain rate, the ultimate tensile stress, elongation of Nylon 66 composites increases with increasing strain rate apparently, while elongation is almost invariant for unreinforced Nylon 66. About fracture surface observation, the fibers in melt flow direction are broke and pulled out at quasi-static tensile test. And the fiber is breakage and the fibers are pull out from base material in melt flow direction are at high strain rate test. In this study, the results could provide nylon 66 composite properties for design application. Keywords-tensile; Nylon 66; short glass fiber; injection molding; high strain rate

The effects of loading-direction and strain-rate on the mechanical behaviors of human frontal skull bone

Transformation and twinning induced plasticity in metastable Ti-Mo alloys under high strain rate deformation

In this research project the behaviour of strain-hardening cement-based composites (SHCC) subjected to low and high strain rates was studied. Uniaxial tension tests on dumbbell-shaped SHCC specimens were performed at rates ranging from 10-5s-1 to 50s-1. For the tests performed at strain rates of 10-2s-1 and below, SHCC yielded a moderate increase in tensile strength and simultaneous decrease in strain capacity with increasing strain rate. When tested for higher strain rates from 10 to 50s-1 a considerable increase in tensile strain and strain capacity was measured. Microscopic investigation of the fracture surfaces showed that almost no fibre failure and an average pullout length of 2.5mm were found in the high strain rate test. This observation is in contrast to that of rapid quasi-static testing, where the average fibre pullout length of 300μm was much shorter. Furthermore, the fibres on the fracture surfaces produced in the high rate tests exhibited pronounced plastic deformations. Finally, quasi-static and high-speed tension tests on individual fibres and single fibre pullout tests were performed. While the increase in the tensile strength of the fibre was only moderate in the range of strain rates investigated, a considerable increase in bond strength between fibre and matrix was determined.

The image-based inertial impact test has previously shown that inertial effects generated with high-strain-rate loading can be used to measure the dynamic constitutive properties of composites at strain rates on the order of 1600,{rm s}^{-1}. This work represents an important next step in exploring the potential of this concept with two tests presented where loading heterogeneity is exploited to measure the interlaminar shear modulus and stress–strain behaviour at high strain rates. The first test configuration used a short-beam with asymmetric loading to activate the shear behaviour. The virtual fields method was used to directly identify the interlaminar shear modulus from heterogeneous full-field maps of strain and acceleration. Simulated experiments were used to optimise the test configuration, select optimal smoothing parameters, and quantify uncertainty from grid rotation on the shear modulus identifications. The test was validated experimentally with three different virtual fields identifying an average shear modulus ranging from 5.7 to 5.9 GPa measured at 1600,{rm s}^{-1}, representing a 16–19% increase compared to quasi-static measurements. The shear modulus could also be identified from shear introduced into specimens tested in the standard, end-on interlaminar IBII configuration from slight in-plane misalignments of the impactor. The identified value of 5.6 GPa validates measurements from the first configuration and also demonstrates the capability to identify multiple interlaminar stiffness parameters from a single test.

This study uses a recently developed cavitation approach,laser-inducedmembrane expansion (LIME), to study the high strain rate mechanicalproperties of three elastomers: poly­(styrene-b-isoprene-b-styrene) (SIS), cross-linked linear polydimethylsiloxane(lPDMS), and cross-linked bottlebrush PDMS (bPDMS) with different network topologies. The cavitationevent was modeled as a damped harmonic oscillator to quantify theshear modulus and dissipation of the elastomer as a function of strainrate. Interestingly, the high strain rate shear moduli obtained fromLIME of the three elastomers were similar, whereas they had markedlydifferent shear moduli measured under quasi-static conditions. Thelength of the elastically active polymer during the cavitation eventwas also calculated, which is an important parameter for understandingthe amount of energy dissipated in this high strain rate test. Thedifference in fundamental polymer dynamics that results in differentmechanical properties as measured at high versus low strain rateshas important implications for designing polymer networks that store,release, and dissipate energy effectively during high-rate deformationevents.

Interlaminar shear behavior of plain-weave GRP at static and high rates of strain

Interface tensile and fracture behavior of the Ti/Al3Ti Metal-Intermetallic Laminate (MIL) composite under quasi-static and high strain rates

Strain rate is essential in study of the physics of fluids and solids undergoing deformation. State-of-art high strain rate tests have mainly been in macro-scale with an upper limit of [Formula: see text]. A graphene-based layered system is proposed to conduct nanometer-scale high strain rate testing. The process is investigated by molecular dynamics simulations. Accelerated single ion or group of ions are used to impact on the proposed system to generate ballistic or plate-like impact scenarios. The effects of impact energy, shape of impact absorber and the impaction location are investigated. The graphene layer is the key of the proposed system to spread the load and protect the sample. The results indicate that ion group and single ion impacts produce strain rates of [Formula: see text]–[Formula: see text] and [Formula: see text]–[Formula: see text], respectively. Ion group impact produces a more significant signal than single ion impact on the sensing nano-layer in the system. The ultimate strength of an Al-Cu alloy sample during ion impact is estimated to be 215[Formula: see text]MPa to 251[Formula: see text]MPa, significantly lower than predicted by the Johnson–Cook model because of the rapidly increased temperature and melting in the sample. The results demonstrate new possibilities for understanding high strain rate effects at nano-scale.

Solder joints in automotive electronic assemblies are exposed to thermomechanical and vibrational loads. Usually, passive thermal cycling results in thermomechanical loads in the low strain rate plastic and creep regime of the solder alloy. In the case of vibrational loads, high strain rate plastic deformations in solder interconnections are expected. In order to investigate the deformation and failure behavior of the solder material in the high strain rate regime, we performed several high cycle fatigue (HCF) experiments on standardized specimens of a SnAgCu alloy under varying mean stresses and ambient temperatures. As a first step, high cycle fatigue tests with a frequency of 40 Hz at room temperature have been performed. From a statistical evaluation of the number of cycles to failure at different stress amplitudes and zero mean stress, we obtained a high cycle fatigue Woehler curve. Subsequently, the mean stress and temperature levels were changed, and the load frequency has been kept constant. The aim of this high cycle fatigue Woehler experiments was to explore the temperature and mean stress effects on the fatigue performance of the solder alloy. In order to assess the reliability of a solder ball grid array (BGA) under vibrational loading by means of finite elements (FE) simulations, a viscoplastic material model is calibrated based on the experimentally observed stress-strain material behavior in the HCF measurement. FE simulations using a fatigue material model were used to address the lifetime of the BGA solder joints under vibration during electrodynamic shaker testing on board level. The FE-based lifetime prognosis is discussed and compared to experimental statistical failure data of real solder joints obtained from electrodynamic shaker testing.

The present work aims at studying the influence of strain rate on the frictional behaviour of AA7075 aluminium alloy in the O-annealed temper state. To this purpose, ring compression tests were performed both under quasi-static and dynamic loading conditions. The high strain rate tests were carried out by means of the Split Hopkinson Tension-Compression Bar in the direct version. In both cases, hollow cylindrical samples, characterised by an initial outer diameter to inner diameter to height ratio of 6:3:2, were tested under dry condition and by lubricating with molybdenum disulphide grease. The different frictional behaviour exhibited by AA7075-O under quasi-static and dynamic loading conditions can be attributed to the strain rate effect both on the plastic flow behaviour of the deformed material, and on the thickness of the lubricant film.