Strain Rate Levels Research Articles

Investigation of the strain rate and stretch level dependent behavior of elastomeric nanocomposites in complex uniaxial tests under finite strains

The mechanical behavior of elastomeric nanocomposites in experiments with nested stress-strain cycles and cyclic tests with increasing strain amplitude were considered. In our proposed testing procedures, long time stops at each stage of the change in loading direction were of great importance. This revealed two significant features of the behavior of elastomeric nanocomposites that have received little attention. It was shown that material softening (the Mullins effect) should be considered not only in the elastic part of the Cauchy stress tensor, but also in its dissipative part. The second peculiarity was the difference between the characteristic relaxation time at loading and the characteristic relaxation time at unloading observed in the experiments.This paper focuses on the behavior of highly-filled elastomeric materials based on different matrices (styrene-butadiene rubber (SBR) and nitrile-butadiene rubber (NBR)) and with different concentrations of carbon black (CB) or a combination of two fillers (CB and purified multi-walled carbon nanotubes (MWCNTs)).A mathematical model of the viscoelastic behavior of elastomeric nanocomposites under finite strains was proposed. It takes into account the peculiarities of the behavior of highly filled elastomers observed in the experiments. The specificity of the model consists in a new variant of the form of the free energy potential. It was shown that the new model satisfies the thermodynamic inequality, which is a consequence of the first law of thermodynamics and the second law in the form of the Clausius-Duhem inequality. A good agreement between theoretical calculations and experimental data was obtained.

Hydrogen embrittlement in Nickel oligocrystals: Experimentation and crystal plasticity-phase field fracture modeling

This work investigates the hydrogen embrittlement (HE) behavior of Nickel-201 alloy using experimental and numerical approaches. In experimentation, the effect of electrochemical hydrogen charging on the deformation behavior of tensile oligocrystals is investigated at different strain rates. Irrespective of the strain rate levels, all the hydrogen-charged tensile oligocrystals exhibited intergranular (IG) fracture exclusively along the random high-angle grain boundaries (RHAGBs). At the same time, no crack was observed along the coincident site lattice (CSL) Σ3 type grain boundaries. The absence of an interconnected grain boundary network, lower stress levels, and insensitivity of H-induced IG fracture to the strain rate levels of investigated FCC oligocrystals (with low lattice hydrogen diffusion coefficient) established the insignificance of dynamic H-redistribution toward HE. In numerical simulations, a crystal plasticity-phase field fracture finite element model simulates the macroscopic tensile response and corresponding microscopic fracture evolution behavior for hydrogen-free and hydrogen-charged tensile oligocrystals. The experimental results corroborated by numerical simulations, validate that the reduction in fracture energy of RHAGBs, induced by hydrogen segregation through thermodynamic equilibrium during hydrogen charging prior to deformation, is the dominating factor governing HE.

Analysis of the mechanical behavior of porous materials containing two populations of voids under dynamic spherical loading

A computational homogenization analysis is performed on three-dimensional representative volume elements (RVE) that contain two distinct populations of voids, to demonstrate the influence of the interaction between cavities. RVEs are constructed as cubic elastic perfectly-plastic matrices embedding two families of spherical voids, and subjected to dynamic loading under homogeneous kinematic boundary conditions. Multiple microstructure models are considered by varying the number, position, and size of voids to evaluate the micro-inertia contribution to the overall macroscopic stress. Velocity fields within numerical RVEs are investigated to reveal the interaction of voids and their key role in the dynamic macroscopic response of the porous material. Based on numerical simulation results, a homogenization analytical model considering void interaction is proposed to describe the mechanical behavior under dynamic loadings. This model relies on adjusting the strain rate level at the boundary of unit cells composing the porous material. Comparison between our numerical and analytical results with those obtained using the classical Taylor homogenization scheme highlights the limitations of the Taylor model in the case of porous materials under dynamic loading.

FCA-based efficient prediction of effective properties for 3D braided composites considering the effect of strain rate

The existing fast concurrency algorithms are difficult to predict the dynamic mechanical performance of three-dimensional (3D) braided composites from different scales. A modified Finite Element Method Cluster Analysis (FCA) method is employed to address this challenge. The modified FCA method is consisted of an offline and an online stage. In the offline stage, the high-fidelity Representative Unit Cell (RUC) is compressed to form a cluster-based RUC via the k-means method. Additionally, the cluster interaction matrix is calculated. In the online stage, the cluster interaction matrix is updated according to the strain rate levels for predicting the stress–strain curves for the RUC. Based upon the comparison with the data obtained from the Split Hopkinson Pressure Bar (SHPB) experiments, it is found that the modified FCA method can accurately predict the stress–strain curves under different strain rates for RUCs. Additionally, the modified FCA method provides a great improvement on computing efficiency when predicting the dynamic behavior of 3D braided composites.

Combining fracture mechanics and rheology to investigate the impact of micro-aeration on chocolate oral processing.

This study presents a rigorous mechanical characterisation investigation on milk chocolate with varying porosities, at different temperatures and strain rate levels. Uniaxial compression tests at temperatures varying from 20 °C to 30 °C were performed to measure the bulk properties of chocolate as a function of porosity and temperature. Fracture experiments were also conducted to compute the fracture energy at temperature levels between 20 °C and 30 °C for all tested samples. Additionally, rheological experiments are conducted to compute the viscosity of the different chocolates at 37 °C. This combined experimental analysis of solid mechanics, fracture mechanics, and rheology aims to define the impact of temperature and chocolate's phase change from solid to liquid on its mechanical properties. Moreover, the impact of micro-aeration on the relationship between material properties and temperature is discussed. The results demonstrate a significant impact of both temperature and micro-aeration on the chocolate's material properties; fracture stresses decrease with micro-aeration due to the presence of micro-pores creating weak links in the chocolate matrix, the critical strain energy release rate decreases with micro-aeration at temperatures up to 25 °C and increases at temperatures above 30 °C. Finally, the viscosity at 37 °C increases with increasing porosity due to the obstruction of the flow by micro-pores acting as "solid" particles. The results highlight how the impact of micro-aeration on the material properties of chocolate alters as the testing temperature rises and the material changes phase. The relationships between the micro-aeration and material properties and the dependence of temperature on the different mechanical properties are used to explain the difference in textural attributes as obtained from temporal dominance sensation tests. This study seeks to contribute valuable insights into the field of chocolate technology, emphasizing the need for a combined engineering approach to understand the structural breakdown of chocolate during oral processing as mechanisms such as chewing, melting, mixing and shearing occur.

Prediction of grain size and dislocation density in the cold spraying process using a dislocation-based model

The cold spray particle deposition process was simulated by modeling the high-velocity impacts of spherical particles onto a flat substrate at different velocities. In addition to simulating the single particle, this study also employed a unique simulation technique to predict the evolution of the material's microstructure under real process conditions. A dislocation-based model was implemented as a VUMAT subroutine to model the microstructure. Additionally, Python scripting was also utilized in the multi-particle impact simulation to create particles and assign velocity and interaction randomly. The relationships between stress-strain values and material microstructure are linked together. By using this model, calculations were done for the equivalent plastic strain, dislocation density, and grain size in the particle, substrate, and interface. At the interface, there were high levels of plastic strain and strain rates reaching up to, which formed a bond between the particles and the substrate. It was found that a minimum plastic strain of approximately 1 is needed to create this bond. At velocities exceeding a critical velocity, a jet was produced. The particle grain size in regions distant from the interface measured between 200 and 500 nm, which is in good agreement with the experimental results. The smallest grain size was observed at the interface, measuring 140 nm. The validation outcomes demonstrated that the suggested model effectively replicates the cold spraying process. As a result, the suggested model has the capability to predict and evaluate the changes in the material's microstructure during the cold spraying process using various factors.

Clinical study of left ventricular structure and function in patients with Anderson-Fabry disease before and after enzyme replacement therapy.

Cardiac left ventricular hypertrophy (LVH) is the most common manifestation of heart involvement in Anderson-Fabry disease (AFD). Conventional cardiac imaging is not sensitive enough to detect early signs of LVH in AFD. It remains uncertain whether enzyme replacement therapy (ERT) can prevent LVH progression and improve myocardial function. This study aimed to assess the effectiveness of two-dimensional speckle tracking echocardiography (2D-STE) in early detection of cardiac involvement in AFD and monitoring the efficacy of agalsidase alfa and agalsidase beta therapy. Thirteen consecutive AFD patients and 12 healthy controls underwent standard transthoracic 2D, color Doppler, tissue Doppler echocardiography, and 2D strain analysis. Global longitudinal strain (GLS) and global circumferential strain (GCS) were measured. Diastolic strain rate (SR) was extracted. Compared to healthy subjects, AFD patients without LVH showed lower levels of GLS (p < 0.001) and SR (p = 0.01), while there was no difference in GCS (p = 0.82). Following treatment, apical circumferential strain (ACS) showed improvement (p = 0.01). In AFD patients without LVH, there was a decrease in global and segmental LS. Higher plasma Lyso-GL-3 concentrations were associated with elevated ACS values after ERT, indicating that ACS in AFD patients without LVH, albeit normal, is involved in early LV dysfunction.

Effect of loading/unloading rate on instrumented indentation measurements in alloy Cu-2%Be

The influence of the loading/unloading rate on the indentation strain rate, hardness and elastic modulus in Cu-2wt%Be samples subjected to different aging treatments was analyzed. Homogenized samples were aged for 1 and 10 h at 400 °C to induce the formation of γ′ and γ precipitates, and instrumented indentation tests were performed at different loading rates between 0.15 and 1 mN s−1. The indentation curves of all the samples were influenced by the loading/unloading rate, but the behavior of the samples with precipitates was different from that of the homogenized samples. Strain rate levels during loading were also influenced by the loading rate. The strain rate increased almost linearly with the loading rate in the homogenized sample and the sample with γ′ nanoprecipitates, while it experienced a decelerated increase with the loading rate in the sample with γ phase. The hardness and reduced modulus were estimated from the indentation curves using the Oliver and Pharr method. Hardness remained almost constant at approximately 2.4 GPa as the rate was varied in the homogenized sample. On the other hand, the samples with γ′ and γ phase exhibited higher hardness values at 0.15 mN s−1, while it remained approximately constant for the other rates. The reduced modulus increased with the loading/unloading rate and this increase was more pronounced for the sample with γ precipitates, with a higher sensitivity of the reduced modulus increase.

Influence of material properties on the high-speed wheel-rail rolling contact behaviour

Here a comprehensive 3-D wheel-rail rolling contact finite element model was developed to investigate the influence of wheel-rail material properties on the dynamic wheel-rail interaction. The wheel-rail contact responses induced by two typical wheel tread defects (i.e. wheel flat and tread spalling) were discussed and compared to the responses of perfect wheel in this work. The dynamic wheel-rail responses of three typical material models involved (i.e. rigid, elastic, and elastic-plastic models) were investigated in terms of contact force, contact pressure/stress, and wheel/rail degradation. Furthermore, the strain rate levels during wheel-rail rolling contact at various train speeds were estimated with emphasis on the elastic-plastic model, which was helpful for determining strain rate range of wheel/rail material property tests. Finally, the influences of strain rate effect and initial fatigue damage of wheel/rail materials on dynamic wheel-rail responses were discussed. These results illustrated that the rigid model grossly overestimated wheel-rail impact force caused by wheel tread defects, while the elastic model overestimated wheel-rail contact pressure/stress, damage index, and frictional work. The strain rate effect could significantly increase Mises stress and inhibit plastic deformation of wheel-rail system, while the initial fatigue damage would reduce Mises stress and aggravate plastic deformation.

Power Law Creep Behavior Model of Third Generation Lead-Free Alloys Considering Isothermal Aging

Abstract In realistic applications, the solder joint is continually subjected to thermal-mechanical stress due to the difference in the coefficient of thermal expansion between the printed circuit board substrate and the electronic packaging components. Creep and fatigue processes were the most common causes of failure in electronic assemblies. Under isothermal aging, creep deformation becomes more prominent. The aged microstructure was recognized by intermetallic coarsening and the appearance of intergranular fracture generated by dynamic recrystallization in the bulk solder joint. In this study, the influence of Bi content on the creep behaviors of solder joints was investigated under various aging conditions. Three lead-free solder alloys, including SAC305, SAC-3Bi, and SAC-6Bi, are tested at room temperature. For each alloy, preliminary micro-indentation tests were conducted to define three stress levels for distinct aging conditions. After each test, displacement versus time data was gathered. A novel approach based on an empirical model was developed to systematically examine the development of the steady-state creep rate. A power dependency prediction model was developed to investigate the relationship between creep strain rate and stress levels. The steady-state creep rate of SAC305 is significantly higher than that of SAC-Bi alloys owing to the presence of bismuth (Bi) in the solid solution at room temperature. The creep properties showed less variation after 100 h of aging. SAC-Bi alloys showed less coarsening of the intermetallic compounds precipitates after aging than SAC305. In the SAC-Bi solder alloys, combinations of precipitate and solid solution hardening mechanisms were observed, while Ag3Sn particles were the dominant strengthening mechanism in the SAC305 alloy system.

Effects of Strain Rate and Size on Concrete under Shear Using Push-Off Tests

The direct shear behavior of concrete sections is evaluated using push-off specimens. The experimental program consists of three strain rates, ε˙=10−7 s−1, ε˙=10−5 s−1 and ε˙=10−3 s−1, that are used to understand how changes in strain rates affect concrete sections at brittle failures. The strain rates used in the tests represent the rates of the shear strain demands on structures due to mild-to-severe earthquakes. The rate effect on a broader range is extrapolated by finite element models. A robust and realistically prescribed material damage constitutive law, Microplane Model M7, is used to perform the computational analysis. A size effect analysis is also conducted to reveal the size dependence of the monolithic concrete joints under shear. It is shown that the rate effect on shear strength of concrete joints is not negligible at and above the strain rate levels examined in this study, and the size dependence of concrete sections under direct shear complies with the Size Effect Law, Type I.

Mechanical behaviors and failure mechanisms of CMDB propellant under wide strain rate tension loading

Composite modified double-base (CMDB) is a sort of mature propellant with a stable structure and high performance. Its tensile mechanical properties should be considered in the structural integrity design of solid propellant charges. The tensile tests were performed on the CMDB by a quasi-static measurement machine. The Hopkinson tension bar (SHTB) under strain rates from 0.0001s−1 to 2500s−1 was modified for structural integrity evaluation, and the stress-strain curves were accurately obtained. After comparing under different strain rates, the results show that the initial modulus of elasticity and stress level are significantly affected by the level of strain rate. Furthermore, the strain hardening becomes more distinct with increasing strain rates. Failure specimens were observed by scanning electron microscopy (SEM). It is indicated that the failure under a low strain rate is mainly debonding of filled particles from the matrix. However, it is mainly caused by their embrittlement under dynamic loading.

A New, Precise Constitutive Model and Thermal Processing Map Based on the Hot Deformation Behavior of 2219 Aluminum Alloy

To study the hot deformation behavior of and obtain the optimal hot processing parameters for 2219 aluminum alloy, a new, precise constitutive model based on the partial derivative of flow data was constructed and hot processing maps were constructed based on the new model. First, isothermal compression experiments were conducted at strain rates of 0.01–10 s−1 and temperatures of 573–773 K, and the high-order differences of the logarithmic stress with respect to the temperature and logarithmic strain rate were calculated. Second, a new, precise constitutive model based on the high-order differences was constructed, and the predictive accuracies of the new model and the Arrhenius model were compared. Finally, the hot processing maps of 2219 aluminum alloy were constructed using the new model, and its optimal hot processing parameters were validated with metallographic experiments. The results showed that a first-order approximation between logarithmic stress and temperature and a third-order approximation between logarithmic stress and the logarithmic strain rate need to be considered to construct a high-precision constitutive model without significantly increasing material parameters. The new model exhibited a significantly higher prediction accuracy than the Arrhenius model at a high strain rate and low temperature levels. With an increase in temperature, the energy dissipation increased at a constant strain rate, and with an increase in the strain rate, the energy dissipation first increased and then decreased at constant temperature. The best region for hot processing was located in the temperature range of 673–773 K and the strain rate range of 0.1–1 s−1. The results of microstructure analysis were in good agreement with the prediction results of hot processing maps. Hot processing maps can be used to guide the hot working process formulation of 2219 aluminum alloy.

Impacts of reference strain rate and strain level dependency on rate effects in fine-grained soils

Viscous rate effects in fine-grained soils may occur in many engineering applications (e.g. dynamically penetrated anchors, sampling, rapid load testing of piles or high-speed soil characterisation), where high strain rates are induced during shear. Often it is difficult to correct for this enhancement of soil strength as fundamental understanding and quantification of rate effects is an area where further research is required. This is at least in part due to limitations of soil characterisation equipment and instrumentation. With the aim of tackling some of these issues a high-speed triaxial testing system was developed incorporating lubricated end platens, which was used to test kaolin at strain rates from 0·1 to 180 000%/h. This allowed observation of behaviour from fully drained, partially drained and undrained conditions, through to viscous effects. Results were used to investigate how rate effects are influenced by strain and consolidation level and how rate normalisation parameters are affected. This was then used to improve a commonly adopted rate characterisation approach such that it performed better across a wider range of strain rates and can be used for more consistent evaluation of rate effects between studies.

Dynamic compressive impact tests of building sandstone with a large split hopkinson pressure bar

The uniaxial compression behavior of building sandstone at high strain rates is not well understood. In this study, standard and flattened cylinders were fabricated for dynamic and static compression tests. A split Hopkinson pressure bar was employed to perform the impact tests at strain rates up to 93.2 s−1. The static compression strength of the flattened cylinders was 112.7 MPa, which was 50% higher than that of the standard cylinder. The fracture damage of the cylinder was closely correlated to the strain rate. Incomplete fragmentation appeared at low strain rates, whereas complete fragmentation appeared at a higher strain rate. Representative diagrams were developed using the characteristic points of the Type I and Type II diagrams, which were characterized by the rebounding and dropdown portions due to the strain rate level. The correlations between the dynamic strength, strain rate, and dynamic modulus were analyzed based on the experimental results. The dynamic increase factor (DIF) was overestimated when the static compressive strength of the standard cylinder was used. A two-portion expression for DIF was developed in accordance with the experimental data. The energy absorption density was proportional to the strain rate and dynamic strength. Two mathematical expressions were obtained based on the experimental energy absorption density, characterized by the experimental peak stresses. The present study is valuable for evaluating the dynamic behavior of sandstone under extreme loads.

Application of material constitutive and friction models parameters identified with AI and ALE to a CEL orthogonal cutting model

The identification of input parameters for funite element modelling of the cutting process is still a complex task as the experimental testing equipment cannot reach its combined levels of strains, strain rates and temperatures. Inverse identification using Artificial Intelligence method provides a relevant alternative. In this paper, material constitutive and friction models parameters identified with an Efficient Global Optimization algorithm and an ALE orthogonal cutting model are introduced in a CEL model. Assessment of the differences in the results due to the formulation and dependence of parameters identification to the finite element model are then performed.

FRP-confined rubber concrete with effect of strain rate: Tests and analysis-oriented stress–strain model

Rubber concrete is attracting more and more investigations and applications in recent years, due to its environmental advantages and lightweight performance. As the replacement by rubber particles can reduce the concrete strength, an efficient and lightweight solution for strengthening and repairing rubber concrete is to apply fiber-reinforced polymer (FRP) confinement. This paper is the first to consider the influence of strain rate on the stress–strain relationship of rubber concrete with FRP confinement. To develop a stress–strain model of FRP-confined rubber concrete under different strain rates, an experimental program with 36 FRP-confined concrete specimens was conducted in this work. In the experiments, rubber particles were used to replace 0–30 % fine aggregates by volume. Strain rates of 3.3 × 10-5/s, 3.3 × 10-4/s, and 3.3 × 10-3/s were used to simulate three different strain rate levels of quasi-static loading, fast loading, and seismic loading, respectively. The experimental results showed that the compressive strength of FRP confined rubber concrete obviously increased with the strain rate increases, and decreased with an increasing rubber replacement ratio. Based on the experimental results, this paper proposed analytical models to predict the lateral strain-axial strain relationship, peak strength, and peak strain for FRP confined rubber concrete considering the strain rate influence. Finally, an analysis-oriented stress–strain model of FRP confined rubber concrete under different strain rates was established. The predicted results of the analysis-oriented stress–strain model showed good agreement with the experimental data.

Tensile performance of normal and high-strength structural steels at high strain rates

The split Hopkinson tensile bar (SHTB) tests are carried out for three structural steels, i.e., Q355 steel, Q460 steel and Q620 steel, for the increasing demand on the mechanical properties of steels at high strain rates. Four strain rate levels, i.e., 1000 s−1, 2000 s−1, 3000 s−1 and 4000 s−1, are used in the tests. The corresponding quasi-static tensile loading tests are also performed for comparison. The observation of fracture morphology and the metallographic organization is also conducted to reveal the mechanism of steel under high strain rate loading. Subsequently, a stress–strain relationship model is proposed based on the modified Johnson–Cook model, and the parameters are calibrated by data from both quasi-static tensile tests and SHTB tests. The results show that the effect of strain rate hardening on the strength of steel is significant, and the proposed model can well describe the mechanical behaviour of these three structural steels at high strain rates.

Strain-rate-dependent mechanics and impact performance of epoxy-based nanocomposites

Strain-rate-dependent mechanical properties and impact performance of manufactured epoxy-based nanocomposites are investigated. As reinforcements, fumed silica (FS) and halloysite nanotube (HNT) are used alongside Albipox 1000 and Nanopox F700. First, the internal structures of the composites are visualised using scanning electron microscopy (SEM). To identify the strain-rate-dependent mechanical properties, three-point bend tests are conducted at three different strain rate levels. For the impact resistance, Charpy impact tests are performed. For further investigations of the mechanical properties of the composites, mean-field homogenisation (MFH) and finite element (FE) analyses on the representative volume elements (RVE) are performed for each type of composite material. Overall, the modelling and experiments are in good agreement and account for the mechanical behaviour of these epoxy-based nanocomposites.

Experimental study on dynamic tensile performance of Q345 structural steel considering thickness differences

This paper experimentally investigates the dynamic tensile performance of Q345 structural steel, especially taking the tested coupon thickness as the key parameter. The tests of low alloy Q345 structural steel widely used in China are carried out under intermediate strain rate level loading of 101s−1 to 102s−1, as well as under static loadings for comparison. A purpose-built experimental arrangement is set up for dynamical coupon test, which can convert the compression triggered by the impact hammesr into rapid tension action. Firstly, the reliability of the proposed experimental technique and measurement method is verified by evaluating the influence of inertia and stress wave propagation. Then, a detailed description of the test results concerning the effect of strain rates on steel material is provided, including failure modes, the yield strength, ultimate strength, elongation, and dynamic increase factors (DIF) of the specimens. Additionally, the results of previous tests on the dynamic properties of steel materials and their relationships to evaluate the validity of the test results are summarized and compared, and the levels and sources of DIF inconsistency are also discussed. Based on the test results, the modified Cowper-Symonds formula was proposed to predict the DIFy-ε̇ relationship curve of yield strength of Q345 steel considering the size effect. Meanwhile, the applicability of Malvar formula for predicting ultimate strength by DIFu-ε̇ relationship curve of Q345 steel with different sizes was verified.