Wide Range Of Strain Rates Research Articles

Constitutive modeling of amorphous thermoplastics from low to high strain rates: Formulation and critical comparison employing an optimization-based parameter identification

A finite strain elasto-visco-plastic model is proposed to describe the low to high strain rate-dependent behavior of amorphous polymers. The predictive capability of the model is extensively assessed by comparing its numerical response against experimental data and some state-of-the-art models for both polycarbonate (PC) and poly(methyl methacrylate) (PMMA). A program is developed to expedite the implementation of different material models by accounting only for the model’s constitutive equations instead of the numerical derivation of their state update procedure and consistent tangent operator. A two-stage optimization-based calibration procedure is proposed to determine the models’ material parameters efficiently. The models are compared for the same set of experimental compression tests, and each model’s material parameters are identified with the adaptive LIPO optimizer, providing a significant speed-up compared to the classical trial-and-error calibration approach. The experimental–numerical comparison shows that the proposed constitutive model is in close agreement with the experimental data for a wide range of strain rates, and slightly outperforms the state-of-the-art constitutive models in predicting the behavior of PC. All models present limitations in predicting the intricate behavior of PMMA, where the proposed constitutive model predicted excessive hardening at medium to high strain rates.

A nonlinear and rate-dependent fracture phase field framework for multiple cracking of polymer

Designing durable polymer-based materials and structures requires understanding how the physical processes and failure mechanisms associated with moisture intrusion and loading rate combine to produce the complex damage modes observed in their applications. While numerous experiments have assisted us in gaining general insight into the above issues, in-situ characterization is still lacking, and rational prediction on the failure procedure of polymer in the moisture–mechanical​ coupling environment remains challenging. Here we present a thermodynamically consistent theoretical framework and its computational implementation to reveal how the dependence of epoxy’s mechanical behavior on rate- and moisture dictates the initiation and evolution of highly localized deformation zones and cracks. A multi-physical hydrothermal-viscoelastic–viscoplastic-damage model is first proposed to fully couple the effects of strain rate, moisture degradation, strain softening, and adiabatic heating of the bulk epoxy in a highly humid environment. The constitutive models are augmented by a phase field that enables spontaneous tracing of the nucleation and growth of cracks under a wide range of strain rates (from 4.60 × 10−5/s to 3.80 × 103/s). The theoretical model is implemented into an efficient computational procedure that is used to calculate illustrative examples to demonstrate the influence of the intimate coupling between the multi-physical phenomena. The results highlight significant mechanisms underlying the coupled damage process, including: heat accumulation along the crack propagation path; identification of the energies associated with moisture-induced toughening; prediction of crack deflection in the presence of moisture absorption; and illustration that a portion of the plastic work plays a dominant role in the nucleation of cracks at a wide scale of strain rates.

Flow behaviour of Ti-6Al-4V alloy in a wide range of strain rates and temperatures under tensile, compressive and flexural loads

The design and analysis of lightweight structures subjected to impact loads require detailed understanding of impact phenomena, and dynamic responses of the selected materials for their safety and reliability. Titanium alloys are in demand for such structures due to high strength to weight ratio, high toughness, and the ability to withstand extreme temperatures. Therefore, this paper investigates the flow behaviour of the titanium alloy Ti-6Al-4V under tensile, compressive and flexural loads at different strain rates and temperatures. Quasi-static tests are performed under tension and compression at strain rates 0.0001–0.1 s−1 while flexural (three-point bending) tests at crosshead speeds 1–100 mm/min are conducted for 90–150 mm span lengths with varying specimen orientations (flat and transverse) on electromechanical universal testing machine (UTM) at room temperature 25 °C. High temperature (300–700 °C) experiments are performed on this UTM under tensile strain rate 0.001s−1 where, the effects of soaking time (5–25 min) and heating rate (10–50 °C/min) are studied. Superplastic behaviour of the alloy is observed at temperature 700 °C with maximum engineering strain nearly 200%. High strain rate experiments on split Hopkinson tension bar (SHTB) and split Hopkinson pressure bar (SHPB) setups are conducted under tension with strain rates 850–1150 s−1, and compression with strain rates 1100–2300 s−1, respectively at room temperature. Ductility and toughness (energy dissipation) are determined at different loading rates. The dependency of the material properties is observed on specimen geometry. Fractography analysis is done for fractured tensile specimens by scanning electron microscope (SEM), and thereafter, existing Cowper-Symonds (CS) and Johnson-Cook (JC) material models are evaluated for the alloy based on the experimental data obtained at different loading conditions.

Mechanical response of four polycarbonates at a wide range of strain rates and temperatures

Mechanical response of four polycarbonates at a wide range of strain rates and temperatures

Recurrent and convolutional neural networks in structural dynamics: a modified attention steered encoder–decoder architecture versus LSTM versus GRU versus TCN topologies to predict the response of shock wave-loaded plates

The aim of the present study is to analyse and predict the structural deformations occurring during shock tube experiments with a series of recurrent and temporal convolutional neural networks. The goal is to determine the architecture that can best learn and predict physically and geometrically nonlinear deformations. For this approach, four different architectures are proposed. Firstly, the multi-layered long-short term memory is developed followed by the multi-layered gated recurrent unit (GRU). Both the RNNs allow accounting for history dependent behaviors through their corresponding internal variables. Further, a multilayered temporal convolutional network is initialized, where the dilated convolution operation is responsible for tracing the path dependent behavior. In the mentioned architectures a sequence of mechanical data is passed through the network and a transformation to corresponding displacements is established. These sequences and corresponding deflections belong to a wide range of strain rates in the dynamic response of structures consisting of steel, aluminum, and copper plates including geometrical and physical non-linearities. Finally, an encoder–decoder architecture consisting of GRU layers is introduced with a modified attention mechanism which showed the best result for predicting the dynamic response. Employing comparative calculations between the neural network (NN) enhanced predictions and the measurements, the nature of approximation of each mentioned NN architecture is discussed and the capabilities of these developed surrogate models are demonstrated by its prediction on validation experiments. These validation experiments have displacement and input data ranges beyond the range of data used for training the aforementioned models.

Modelling and optimisation of TPMS-based lattices subjected to high strain-rate impact loadings

Lattices structures show promising applications in aerospace, biomedical and defence sectors, in which high energy absorption and lightweight structures are required. This work studies Triply Periodical Minimal Surfaces (TPMS) with potential for impact engineer applications, focusing on material characterisation, modelling and performance optimisation. For this purpose, stainless steel 316 L lattice samples made by additive manufacturing were tested in a wide range of strain-rates and various building directions using a universal testing machine and Split Hopkinson Pressure Bar, equipped with a Digital Image Correlation system. Then, the obtained properties were implemented in an explicit finite element model and validated against experimental results related to different TMPS topologies and impact scenarios. A theoretical model is also proposed to predict the TPMS-based lattices quasi-static and impact responses up to the densification threshold. Finally, the validated numerical models were used to predict the behaviour of several functionally graded TPMS topologies, indicating the architectures with superior impact performance. The graded topologies were then manufactured and experimentally tested. The results indicate that graded topologies exhibit up to 18% higher energy absorption when compared to their non-graded counterparts. The theoretical and numerical models developed in this paper provide an effective approach for designing and predicting high energy absorption architectures subjected to quasi-static and impact loadings.

Atomistic-Continuum Constitutive Modeling Connection for Gold Foams under Compression at High Strain Rates: The Dislocation Density Effect

Constitutive description of the plastic flow in metallic foams has been rarely explored in the literature. Even though the material is of great interest to researchers, its plasticity remains a topic that has a much room for exploration. With the help of the rich literature that explored the material deformation mechanism, it is possible to introduce a connection between the results of the atomistic simulations and the well-established continuum constitutive models that were developed for various loading scenarios. In this work, we perform large-scale atomistic simulations of metallic gold foams of two different sizes at a wide range of strain rates (107−109 s−1) under uniaxial compression. By utilizing the results of those simulations, as well as the results we reported in our previous works, a physical atomistic-continuum dislocations-based constitutive modeling connection is proposed to capture the compressive plastic flow in gold foams for a wide range of sizes, strain rates, temperatures, and porosities. The results reported in this work present curated datasets that can be of extreme usefulness for the data-driven AI design of metallic foams with tunable nanoscale properties. Eventually, we aim to produce an optimal physical description to improve integrated physics-based and AI-enabled design, manufacture, and validation of hierarchical architected metallic foams that deliver tailored mechanical responses and precision failure patterns at different scales.

Interpolation and Extrapolation Performance Measurement of Analytical and ANN-Based Flow Laws for Hot Deformation Behavior of Medium Carbon Steel

In the present work, a critical analysis of the most-commonly used analytical models and recently introduced ANN-based models was performed to evaluate their predictive accuracy within and outside the experimental interval used to generate them. The high-temperature deformation behavior of a medium carbon steel was studied over a wide range of strains, strain rates, and temperatures using hot compression tests on a Gleeble-3800. The experimental flow curves were modeled using the Johnson–Cook, Modified-Zerilli–Armstrong, Hansel–Spittel, Arrhenius, and PTM models, as well as an ANN model. The mean absolute relative error and root-mean-squared error values were used to quantify the predictive accuracy of the models analyzed. The results indicated that the Johnson–Cook and Modified-Zerilli–Armstrong models had a significant error, while the Hansel–Spittel, PTM, and Arrhenius models were able to predict the behavior of this alloy. The ANN model showed excellent agreement between the predicted and experimental flow curves, with an error of less than 0.62%. To validate the performance, the ability to interpolate and extrapolate the experimental data was also tested. The Hansel–Spittel, PTM, and Arrhenius models showed good interpolation and extrapolation capabilities. However, the ANN model was the most-powerful of all the models.

Computational homogenization based crystal plasticity investigation of deformation behavior of AA2024-T3 alloy at different strain rates

PurposeModeling of material behavior by physically or microstructure-based models helps in understanding the relationships between its properties and microstructure. However, the majority of the numerical investigations on the prediction of the deformation behavior of AA2024 alloy are limited to the use of phenomenological or empirical constitutive models, which fail to take into account the actual microscopic-level mechanisms (i.e. crystallographic slip) causing plastic deformation. In order to achieve accurate predictions, the microstructure-based constitutive models involving the underlying physical deformation mechanisms are more reliable. Therefore, the aim of this work is to predict the mechanical response of AA2024-T3 alloy subjected to uniaxial tension at different strain rates, using a dislocation density-based crystal plasticity model in conjunction with computational homogenization.Design/methodology/approachA dislocation density-based crystal plasticity (CP) model along with computational homogenization is presented here for predicting the mechanical behavior of aluminium alloy AA2024-T3 under uniaxial tension at different strain rates. A representative volume element (RVE) containing 400 grains subjected to periodic boundary conditions has been used for simulations. The effect of mesh discretization on the mechanical response is investigated by considering different meshing resolutions for the RVE. Material parameters of the CP model have been calibrated by fitting the experimental data. Along with the CP model, Johnson–Cook (JC) model is also used for examining the stress-strain behavior of the alloy at various strain rates. Validation of the predictions of CP and JC models is done with the experimental results where the CP model has more accurately captured the deformation behavior of the aluminium alloy.FindingsThe CP model is able to predict the mechanical response of AA2024-T3 alloy over a wide range of strain rates with a single set of material parameters. Furthermore, it is observed that the inhomogeneity in stress-strain fields at the grain level is linked to both the orientation of the grains as well as their interactions with one another. The flow and hardening rule parameters influencing the stress-strain curve and capturing the strain rate dependency are also identified.Originality/valueComputational homogenization-based CP modeling and simulation of deformation behavior of polycrystalline alloy AA2024-T3 alloy at various strain rates is not available in the literature. Therefore, the present computational homogenization-based CP model can be used for predicting the deformation behavior of AA2024-T3 alloy more accurately at both micro and macro scales, under different strain rates.

Mechanics of ABS Polymer under Low & Intermediate Strain Rates

Thermoplastics polymers like Acrylonitrile Butadiene Styrene (ABS) are often reinforced with nano/micro reinforcements to enhance their mechanical, thermal and electrical properties. However, the viscoelastic nature of these polymers results in their strong dependence on the applied strain rate and temperature sensitivity, leading to their characterization complexity. Hence it is paramount to study the strain rate-dependent mechanics of neat ABS. In this study, the effect of strain rate and temperature on Young’s modulus of ABS polymer was characterized using a dynamic mechanical analyzer (DMA). Storage modulus curves at various temperatures and frequencies were transformed into a representative master curve at a specific temperature using the time-temperature superposition (TTS) principle. Based on this curve‘s storage modulus and frequency relation, an empirical fit function was developed and the strain rate values were extrapolated. Using integral relations of viscoelasticity, the results were further transformed to a time domain relaxation function to extract the strain rate-sensitive Young’s modulus at different loading rates. This method was validated by comparing the data with tensile tests conducted on ABS coupons as per ASTM D638-14. The results were acceptable over a wide range of strain rates and indicated a clear sensitivity of ABS to strain rate and temperature. The strategy used in this work can be employed to study the effect of reinforcement morphology in ABS thermoplastics using DMA.

Mechanical behavior of nanorubber reinforced epoxy over a wide strain rate loading

Nanorubber/epoxy composites containing 0, 2, 6 and 10 ​wt% nanorubber are subjected to uniaxial compression over a wide range of strain rate from 8 ​× ​10−4 s−1 to ∼2 ​× ​104 s−1. Unexpectedly, their strain rate sensitivity and strain hardening index increase with increasing nanorubber content. Potential mechanisms are proposed based on numerical simulations using a unit cell model. An increase in the strain rate sensitivity with increasing nanorubber content results from the fact that the nanorubber becomes less incompressible at high strain, generating a higher hydro-static pressure. Adiabatic shear localization starts to occur in the epoxy under a strain rate of 22,000 s−1 when the strain exceeds 0.35. The presence of nanorubber in the epoxy reduces adiabatic shear localization by preventing it from propagating.

Strain-rate dependent crystal plasticity model and aluminum softening/hardening transition

Hardening or softening associated with the increase of dislocation density is correlated with strain rate and dislocation density. Taking aluminum as a model material, we investigate the strain rate and dislocation density dependence of the strength and the accompanying hardening or softening effect upon a dislocation increase. This investigation is enabled by employing a newly developed crystal plasticity model, which is validated against the mechanical behaviors in an extremely wide strain rate range, and featured by a parameter-free mobile dislocation fraction law based on the exponential distribution of dislocation link lengths and an averaged dislocation velocity model that considers both thermally-activated waiting mechanism and drag-dominated running mechanism. Results show that at different strain rates, the material strength varies with a universal feature that it first softens as the dislocation density increases from a sufficiently low initial value, and then hardens after reaching the minimum strength, where the critical dislocation density separating the softening from hardening regimes increases with the strain rate. Microscopically, the strength dependence on dislocation density and strain rate originates from their influence on the two competing effects of a dislocation increase, where the hardening effect comes from the higher resistance to dislocation slip by increased forest dislocations while the softening effect comes from the larger quantity of mobile dislocations. These two competing effects are quantitatively evaluated by the crystal plasticity model and are further cast into the competition between the partial derivatives of normalized dislocation velocity and of normalized mobile dislocation density, and the governing equation for the critical dislocation density is thus furnished by balancing these two competing effects. Further, a complete map in the entire space of strain rate and dislocation density (ε̇,ρ) is constructed for the zones of dislocation hardening or softening, where the zone-boundary curve for critical dislocation density exhibits a two-stage character and it agrees well with the available experimental data. Such a map is expected to help predict the trend for strength evolution under different serving conditions and also guide the material design according to the requirements for strength variation in service.

A high-accuracy dynamic constitutive relation of die-cast Alâ¿¿Si aluminium alloy

Die-cast Al–Si aluminium alloys are increasingly used in the lightweight design of automobiles; their mechanical properties under dynamic loading are crucial and thus must be investigated. The original Johnson–Cook (J–C) constitutive model does not accurately predict the mechanical properties of this alloy, which further affects the reliability of subsequent analysis and calculations. To improve the predictive accuracy of the constitutive model and investigate the dynamic mechanical properties of this alloy, high-speed tensile tests of die-casting aluminium alloy Al–10Si–yCu–xMn–zFe are conducted. The tests are executed at room temperature using a universal electrical testing machine and a high-velocity testing system in a wide strain rate range of 1–800 s−1. The tensile deformation behaviour of this alloy at various strain rates is investigated. The experiments show that the flow stress of the alloy gradually increases with strain and varies significantly with the strain rate. The J–C model is unsuitable for predicting the flow stress of this alloy owing to its unsatisfactory goodness-of-fit. To accurately predict the flow stress of die-cast Al–Si aluminium alloys, we propose a new model based on experiments. Unlike other models, the proposed model incorporates the critical strain and flow stress limit value, which allows the flow stress to be predicted more precisely at various strain rates over a wide strain range of 0–0.17. The experimental data of other die-cast Al–Si alloys validate our model. The goodness-of-fit of the proposed model for this alloy is higher than that of the J–C model, which demonstrates that our model outperforms existing models in terms of estimation accuracy.

A Study of Aluminum Honeycomb Structures under Dynamic Loading, with Consideration Given to the Effects of Air Leakage

Aluminum honeycomb structures are used in the construction of protective materials due to the positive relationship between their mass and their energy-absorbing properties. Applying such materials in the construction of large machinery, such as military vehicles, requires the development of a new method of finite element modeling, one that considers conditions with high strain rates, because a material model is currently lacking in the available simulation software, including LS-DYNA. In the present study, we proposed and verified a method of numerically modeling honeycomb materials using a simplified Y element. Results with a good level of agreement between the full core model and the Y element were achieved. The obtained description of the material properties was used in the subsequent creation of a homogeneous model. In addition, we considered the influence of increases in pressure and the leakage of the air entrapped in the honeycomb cells. As a result, we were able to attain a high level of accuracy regarding the stress values across the entire range of progressive failure, from the loss of stability to full core densification, and across a wide range of strain rates.

The effect of initial texture on multiple necking formation in polycrystalline thin rings subjected to dynamic expansion

In this paper, we have investigated, using finite element calculations, the effect of initial texture on the formation of multiple necking patterns in ductile metallic rings subjected to rapid radial expansion. The mechanical behavior of the material has been modeled with the elasto-viscoplastic single crystal constitutive model developed by Marin (2006). The polycrystalline microstructure of the ring has been generated using random Voronoi seeds. Both 5000 grain and 15000 grain aggregates have been investigated, and for each polycrystalline aggregate three different spatial distributions of grains have been considered. The calculations have been performed within a wide range of strain rates varying from 1.66⋅104s−1 to 3.33⋅105s−1, and the rings have been modeled with four different initial textures: isotropic texture, 001∥Θ Goss texture, 001∥ R Goss texture and 111∥ Z fiber texture. The finite element results show that: (i) the spatial distribution of grains affects the location of the necks, (ii) the decrease of the grain size delays the formation of the necking pattern and increases the number of necks, (iii) the initial texture affects the number of necks, the location of the necks, and the necking time, (iv) the development of the necks is accompanied by a local increase of the slip activity. This work provides new insights into the effect of crystallographic microstructure on dynamic plastic localization and guidelines to tailor the initial texture in order to delay dynamic necking formation and, thus, to improve the energy absorption capacity of ductile metallic materials at high strain rates.

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.

Modelling of ductile fracture in pure iron considering the ductile–brittle transition at very high strain rate

At different deformation rates, a ductile material may fail by isothermal deformation fracture, thermoplastic shear instability, or even brittle fracture. The failure mode transition at sound speed deformation rate has not been well described. This paper aims to establish a new fracture model which considers the strain rate embrittlement effect (SREE) at the sound speed deformation rate, and can be used to predict the failure of the material in a large range of strain rate. Taking pure iron DT 8 as the experimental material, impact tests of pure iron specimens under different stress states, strain rates, and temperatures were carried out. Fracture strains under different stress states, strain rates, and temperatures were obtained. The strain rate was increased to 227450/s (5.36/s in log10) to obtain the ductile–brittle transition point. A new fracture model is proposed to describe the evolution of fracture strain over the wide range of strain rate. The new proposed model is experimentally validated and compared with the J-C failure model. It shows the new proposed fracture model can predict the ductile fracture behavior of a ductile material in the full strain rate range, and capture the failure mode transition at the sound speed deformation rate of a material.

In-Situ X-ray Diffraction Analysis of Metastable Austenite Containing Steels Under Mechanical Loading at a Wide Strain Rate Range

This paper presents and discusses the methodology and technical aspects of mechanical tests carried out at a wide strain rate range with simultaneous synchrotron X-ray diffraction measurements. The motivation for the study was to develop capabilities for in-situ characterization of the loading rate dependency of mechanically induced phase transformations in steels containing metastable austenite. The experiments were carried out at the DanMAX beamline of the MAX IV Laboratory, into which a custom-made tensile loading device was incorporated. The test setup was supplemented with in-situ optical imaging of the specimen, which allowed digital image correlation-based deformation analysis. All the measurement channels were synchronized to a common time basis with trigger signals between the devices as well as post-test fine tuning based on diffraction ring shape analysis. This facilitated precise correlation between the mechanical and diffraction data at strain rates up to 1 s−1 corresponding to test duration of less than one second. Diffraction data were collected at an acquisition rate of 250 Hz, which provided excellent temporal resolution. The feasibility of the methodology is demonstrated by providing novel data on the kinetics of the martensitic phase transformation in EN 1.4318-alloy following a rapid increase in strain rate (a so-called jump test).

On the Prediction of the Flow Behavior of Metals and Alloys at a Wide Range of Temperatures and Strain Rates Using Johnson–Cook and Modified Johnson–Cook-Based Models: A Review

This paper reviews the flow behavior and mathematical modeling of various metals and alloys at a wide range of temperatures and strain rates. Furthermore, it discusses the effects of strain rate and temperature on flow behavior. Johnson-Cook is a strong phenomenological model that has been used extensively for predictions of the flow behaviors of metals and alloys. It has been implemented in finite element software packages to optimize strain, strain rate, and temperature as well as to simulate real behaviors in severe conditions. Thus, this work will discuss and critically review the well-proven Johnson-Cook and modified Johnson-Cook-based models. The latest model modifications, along with their strengths and limitations, are introduced and compared. The coupling effect between flow parameters is also presented and discussed. The various methods and techniques used for the determination of model constants are highlighted and discussed. Finally, future research directions for the mathematical modeling of flow behavior are provided.

Phenomenological understanding of kappa-carbides on strengthening mechanism of low-density steel

We elucidate here the phenomenological understanding of deformation mechanisms over a wide range of strain rates (5.5 × 10–4s–1 to 5.5 × 10–1s–1) based on the evolution of microstructure. Atom probe tomography (APT), transmission electron microscopy (TEM) and electron back-scattered diffraction (EBSD) experiments were conducted to reveal the spatial distribution of precipitates and microstructure evolution. The ordered kappa-carbides were characterised by a layered-type structure, which made it difficult for dislocations to by-pass kappa-carbides in the same layer individually and the corresponding strengthening mechanism was cutting mechanism. Dislocations and microbands evolution analysis shows that compared to dislocations, slip band width was the key factor that governed the strength of the experimental steel at different strain rates.