Strain Rate Dependent Material Research Articles

Strain-rate-dependent performance of alkali-activated binder-based ultra-high strength concrete

Ultra-high performance concrete(UHPC) is a superior protective material in impact and blast resistance, but negatively influences the environment due to the large amount of cement consumption and CO2 emissions during the preparation process. Alkali-activated binders were invented as a promising alternative to Portland cement for preparing UHPC in a method that saves energy and emits less CO2. However, the strain-rate-dependent performance of alkali-activated binder-based ultra-high strength concrete (AAB-UHSC) is still unknown. Therefore, this work focused on the strain-rate-dependent performance, e.g., dynamic mechanical properties, energy absorption and failure patterns, of AAB-UHSC materials incorporated with different steel fiber contents, as well as the microdamage at different strain rates. The quasi-static compression test, split Hopkinson pressure bar test, the sieving test and the scanning electron microscope test were carried out. The results indicated that the AAB-UHSC material is a strain rate-dependent material, the different stress-strain curves corresponding to different failure patterns vary with the strain rate, and an obvious strain rate transition zone existed for different failure patterns, as did the energy for different failure patterns. Additionally, the addition of steel fibers could effectively enhance the dynamic macromechanical performance and reduce the microdamage. An impact toughness index suitable for AAB-UHSC was defined. Eventually, a modified ZWT dynamic constitutive model with a new damage evolution equation for the AAB-UHSC material was proposed, and results show that this model can well describe the stress-strain relationship of the AAB-UHSC under impact load.

Study of effect of loading rate on mechanical properties of SS316LN and evaluation of parameters of Johnson-Cook model using parametric FE analysis and experimental data

The objective of this work is to evaluate the parameters of strain rate dependent Johnson-Cook material model using a hybrid procedure which uses finite element analysis as well as experimental data. The large strain rate tests were conducted to using split Hopkinson pressure bar test setup, whereas the quasi-static test was carried out using conventional testing machines. Johnson-Cook material model has been used to simulate the plastic deformation behavior of material under the high strain loading. This model provides the flow stress of the material as a function of equivalent plastic strain, plastic strain rate and temperature. The parameters, i.e., A, B, n, C and m of the model have been determined using a hybrid procedure as mentioned earlier. One of the important issues in split Hopkinson pressure bar testing is the variation of strain rate during the duration of loading. Due to decrease in reflected strain magnitude, the strain rate continuously decreases (as strain rate is proportional to reflected strain signal) and it is a characteristic of the above test method. However, this creates problem in evaluation of parameters of Johnson-Cook material model using conventional procedure. In this work, a modified procedure has been developed in order to take into account of this variation in strain rate as function of applied strain. The results of the method has been validated with experimental data. The parameters have been evaluated only for room temperature data and the effect of temperature shall be studied in future.

Calibration of tensile tests in drop-weight impact machine and implementation in simulation of Charpy impact tests

Material modeling and simulation of deformation under very high loading rate in the dynamic/impact range are applied in crash resistance, ballistic impact analysis, and other time-sensitive phenomena. Servo-hydraulic UTM tensile test data from medium to higher strain rate > (500 s-1) is reliable but expensive and complexity in experiment. Tensile testing at very high strain rate (upto 1500 s-1) can be done in a drop-weight impact testing machine with a special fixture and the impactor velocity controls strain rate. In INSTRON CEAST 9350 drop weight impact testing machine tensile tests are conducted at four velocities for amour steel. A 5MHz data acquisition system (DAQ) measures strain in specimen gauge length mounted with high-elongation strain gauge. An extensometer is used to calibrate the strain gauge in a quasi-static 10-4 s-1 tensile test. Tensile test data from impact machine is compared with stress-strain data from the INSTRON servo-hydraulic testing machine with DIC for different strain rates. Close matching in elastic modulus, yield strength, tensile strength, and elongation are observed. Material parameters of a strain rate-dependent material model (modified J-C model) are extracted from drop weight impact testing machine data clubbed with other tensile test data, used in FE simulation of very high strain rate tensile tests, and validated with experimental results. Later, the same material model and material parameters are used to simulate Charpy impact tests at various velocities and compared with experimental results which also show close matching.

Mesoscale modelling of the dynamic tensile strength enhancement of concrete in spalling tests using interface elements

The dynamic tensile strength of concrete has been experimentally reported to increase significantly with the increase of imposed strain rates. However, the intrinsic mechanisms accounting for the strength increase are not well understood so far. This paper presented numerical simulations based on the spalling technique to further explore mechanisms of the dynamic responses of concrete under impact loadings. Numerical results have been verified and validated against experimental evidence with various strain rates. The validity of utilizing the Novikov acoustic processing approximation for obtaining the spalling strength of concrete is identified and discussed. Results demonstrate that this indirect processing approach could overestimate the spalling strength because real material behavior tends to deviate from its basic assumption. Mechanisms accounting for the spalling strength increase from key aspects including the meso-structure, the strain rate-dependent material behaviour, the micro-crack inertia, and the structural inertial are also identified accordingly. Results demonstrate that the increment of concrete dynamic tensile strength in spalling tests is mainly caused by the strain rate-dependent material behaviour which should be incorporated in the material constitutive description. Besides that, the material heterogeneity also makes a considerable contribution to the increase of dynamic tensile strength in spalling tests and this contribution becomes increasingly prominent with the increase of the imposed strain rates. On the other hand, the structure inertial and the micro-crack inertial have little effect on the increase of spalling strength of concrete and thus may be ignored within the imposed strain rate range in spalling tests.

Tunable and recoverable energy absorption of foam-embedded architected cellular composite material at multiple strain rates

Cellular multistable architected material has been widely studied for its promising energy absorption applications for personnel protection, protective packaging, and crash mitigation. Despite the tailorable properties enabled by their geometric features, a major issue in the actual application is their lower strengths in the elastic behavior of the multistable architected material. Herein, a novel design strategy of strain rate-dependent architected cellular composite material (FACCM) is proposed, aiming to achieve enhanced energy-absorbing properties with the proposed composite system than the single material constituent. Guided by numerical simulations and experimental tests, the compressive behaviour of FACCM at multiple strain rates and the effect of filled foam on it with specific geometric parameters are characterized. The quasi-static performances of the FACCM specimens were evaluated both at the cell level and planar array level. Our results indicate that the strength, stiffness, and snap-through behaviour of multistable architected material can be significantly improved by the filled foam at elevated loading rates regardless of quasi-static loading or impact tests. The current study offers a new strategy for developing novel packing, shock absorption, and impact protection systems.

Wear Evolution on PVD Coated Cutting Tool Flank and Rake Explained Considering Stress, Strain and Strain-Rate Dependent Material Properties

Impact loads developed on a tool cutting edge when milling into a workpiece material are prevailing metrics for explaining coating fatigue failure and the subsequent tool-wear evolution. For predicting related stress and strain fields in the compound coating-substrate, stress, strain, and strain-rate, dependent material properties are required. The attainment of such data is briefly described in the paper. Considering these data, the occurring strains in the cutting edge at various entry impact durations, i.e., strain rates, were calculated and compared with fatigue-critical strains. In this way, the wear phenomena causing the coating failure on the flank and rake during milling were clarified. The attained results were also correlated to corresponding ones in turning, where the dynamic loads of the cutting edge are comparably negligible. The conducted investigations showed that the fatigue-critical strains strongly diminish, when the relevant strain rates increase; thus, leading to a remarkable tool-life reduction. This happens, because the increase of the strain-rate restricts the time for the dislocations movements; thus, regions with stress concentrations occur, deteriorating the material ductility, increasing its brittleness, and diminishing the fatigue critical strains. In cutting operations, where the coating fatigue is the main wear factor, the tool-life can be predicted considering these phenomena. In the paper, relevant experimental analytical procedures are introduced.

Nonlinear dynamic responses of ballasted railway tracks using concrete sleepers incorporated with reinforced fibres and pre-treated crumb rubber

Abstract Damages on railway sleepers due to heavy impact loads induced by the movement of trains can be reduced by improving their impact resistance. Fibre-reinforced/pre-treated crumb rubber concrete sleepers (RCSs) have the potential to display significant impact resistance to withstand a high-magnitude impact load. The ideal proportions of pre-treated crumb rubber, steel fibres, and polypropylene fibres (PFs) can be identified based on the minimum cost-to-impact energy ratio after conducting a drop weight impact test on prisms. The numerical model developed to assess the behaviour of ballasted tracks has been validated using both simulation results and field measurements. Numerical studies have been conducted on ballasted rail tracks with steel and PF-reinforced/pre-treated RCSs using LS-DYNA software. Dynamic strain rate-dependent material parameters are introduced in the numerical simulations. The nonlinear effect of higher train speeds on dynamic track responses has been highlighted in this article. Although the static load-carrying capacity and modulus of elasticity of rubber concrete are low, their dynamic performance controls the track displacements from exceeding permissible limits. The outcome of this study will provide new insights into the effects of railway concrete sleepers incorporated with reinforced fibres and pre-treated crumb rubber on railway track performance in order to ensure safety and reliability before it is put into services.

Prediction of skull fractures in blunt force head traumas using finite element head models.

Traumatic head injuries remain a leading cause of death and disability worldwide. Although skull fractures are one of the most common head injuries, the fundamental mechanics of cranial bone and its impact tolerance are still uncertain. In the present study, a strain-rate-dependent material model for cranial bone has been proposed and implemented in subject-specific Finite Element (FE) head models in order to predict skull fractures in five real-world fall accidents. The subject-specific head models were developed following an established image-registration-based personalization pipeline. Head impact boundary conditions were derived from accident reconstructions using personalized human body models. The simulated fracture lines were compared to those visible in post-mortem CT scans of each subject. In result, the FE models did predict the actual occurrence and extent of skull fractures in all cases. In at least four out of five cases, predicted fracture patterns were comparable to ones from CT scans and autopsy reports. The tensile material model, which was tuned to represent rate-dependent tensile data of cortical skull bone from literature, was able to capture observed linear fractures in blunt indentation loading of a skullcap specimen. The FE model showed to be sensitive to modeling parameters, in particular to the constitutive parameters of the cortical tables. Nevertheless, this study provides a currently lacking strain-rate dependent material model of cranial bone that has the capacity to accurately predict linear fracture patterns. For the first time, a procedure to reconstruct occurrences of skull fractures using computational engineering techniques, capturing the all-in-all fracture initiation, propagation and final pattern, is presented.

Effect of a strain rate dependent material modeling of a steel on the prediction accuracy of a numerical deep drawing process

In the production of sheet metal components, batch and process fluctuations cause deviations in the resulting component properties, which often lead to production rejects. To counteract this inline, the computing time for predicting the process result and optimizing the process parameters must be very short, which is why analytical models are advantageous. A large database is usually required for modeling, and numerical simulations are well suited for generating it. The stamping velocity is a process parameter possibly varying, but strain rate dependency of the material often is neglected in numerical simulations. The objective of this study is to analyze the effects of strain rate dependent material modeling on the simulation accuracy of a sheet metal forming process. Therefore, uniaxial tensile tests and layer compression tests at different strain rates are conducted on the steel HC340LA. Based on this, the material behavior is captured in a strain rate dependent material card, which is used for the numerical simulation of a deep drawing process of a geometry with complex shape. For the validation of the model, experiments are carried out and being compared with the computational results in terms of force–displacement curves and part geometry. Furthermore, numerical investigations are used to analyze if drawbead height and blankholder force have an influence on the strain rate distribution and whether this affects the process force.

A coupled thermo-mechanical cohesive zone model for strain rate-dependent fracture of hat-shaped specimens under impact

A coupled thermo-mechanical cohesive zone model for strain rate-dependent materials is proposed to illustrate the shear failure in the hat-shaped specimens made of U75V rail steel at various impact loads and temperatures.The cohesive energy and the maximum cohesive stress in the proposed cohesive zone model depend on strain rates and temperatures. The coefficients in the functions of cohesive energy, maximum cohesive stress, and the cohesive law are obtained through a combination of experimental and simulation data. The experimental strain waveforms are obtained by a split Hopkinson pressure bar system and the cohesive zone model is implemented using ABAQUS finite element software with the assistance of user subroutines.The findings substantiate the efficacy of the proposed cohesive zone model in accurately predicting the shear failure of hat-shaped specimens under high-speed impacts, as evidenced by the notable concurrence between experimental and computational outcomes within an acceptable margin of error. Notably, the cohesive energy and maximum cohesive stress in the model demonstrate a dual dependency on strain rates and thermal conditions, emphasizing the significance of considering both thermal and mechanical effects when simulating shear failure in materials experiencing high temperatures and high strain rates.

A strain rate dependent and anisotropic failure material model for short fiber reinforced plastics based on energy density accounting for local fiber orientation

A failure model for SFRP for FEM simulations is developed to describe the strain rate dependency, the influence of the local fiber orientation and of the stress state on the failure behavior. The material is considered as a continuum while internally calculating the micro-mechanics analytically. The described micro-mechanics are based on experimental observations and on analyzation with numerical studies. In particular the strain rate dependent delamination of fibers and matrix is incorporated in the model. The distortion energy density is defined as the driving value for failure and estimated by the model. This is achieved with the analytic solution by Eshelby for the stress field in the matrix and by introducing an additional phase for the plasticly deformed volume. The validation on characterization specimens as well as component test demonstrates that the influence of strain rate, fiber orientation, and stress state on the failure behavior can be described with only one material parameter, the critical distortion energy density.

Dynamic numerical prediction of plasticity and damage in a turbofan blade containment test

For the light designs of new aircraft engines, constitutive plasticity and fracture models sensitive to strain rate and temperature are essential for the accurate prediction of deformations and internal stresses of the components during simulations of impact and explosion events. The work described in this article consists of the development and numerical analysis by finite elements of the blade containment test of a commercial aircraft turbofan engine, conducted to evaluate the structural integrity of the casing after being impacted by a detached fan blade. Two simulation models of the test are proposed, in which the resistance behavior of the strain rate-dependent material is described by isotropic laws of strain hardening and Johnson–Cook damage. The strength analysis is based on the numerical field results of equivalent stresses and deformations, along with the internal damage rates of the casing. The first simplified model considers half of the casing impacted by a blade at different speeds and angles of impact. The second model consists of a complete discretization of casing and rotating turbofan, with the initial detached condition of a blade simulated at different rotating speeds of the fan. The material used in this study is the Ti-6Al-4V alloy. The results analysis and advances obtained make it possible to approach an efficient computational tool with more accurate calculations to study a casing redesign with a safe reduction in mass and that fulfills the certification requirements using the blade containment test.

A Strain Rate Dependent Damage Model for Evaluating the Dynamic Response of CFRTP Laminates with Different Stacking Sequence

Carbon fiber reinforced thermoplastic polymer (CFRTP) laminates can be used in packaging electronics components to reduce weight and shield external disturbance. The CFRTP structures in operation are inevitably to suffer dynamic loading conditions such as falling rocks, tools and impacts. In this study, a strain rate dependent material model for accurately evaluating the dynamic response of CFRTP laminates with different stacking sequence was proposed. The model was composed of three components: a strain rate dependent constitute model, a strain rate related damage initiation model and an energy-based damage evolution model. The strain rate effect of modulus and strength was described by a stacking sequence related matrix, and the damage initiation model could describe the matrix, fiber and delamination damage of CFRTP laminates without introducing cohesive elements. The material model was implemented into finite element software ABAQUS by user defines subroutine VUMAT. The low velocity impact tests of CFRTP laminates with quasi-isotropic and angle-ply stacking sequence were used to provide validation data. The dynamic response of CFRTP laminates from numerical results were highly consistent with the experimental results. The mechanical response of CFRTP laminates were affected by stacking sequence and impact energy, and the numerical error of proposed material model significantly decreased with the increasing impact energy especially for the laminae with damage occur.

Temperature and Strain Rate Effects on the Uniaxial Tensile Behaviour of ETFE Foils.

With the first use of ETFE foils in building structures in the 1980s at the Burgers’ Zoo in Arnhem, Netherlands, the implementation of ETFE foils in roof and façade systems in large-span structures has become steadily more prominent. To safely design ETFE foil structures, their mechanical behaviour has to be fundamentally understood. Until now, several research studies have been published investigating this material’s behaviour. However, the parameters influencing these plastic’s mechanical behaviour, such as the strain rate or the test temperature, have only been investigated separately but not simultaneously. In this contribution, an analytical model is presented which describes the mechanical behaviour of ETFE foils under varying test temperatures and strain rates simultaneously. The material model has been checked against experimental results achieved for materials from three different international producers and two different commonly used foil thicknesses with significant differences in their mechanical responses (so that it can be assumed that the international market is represented). In the first step, uniaxial tensile tests on strip specimens were performed to describe the nonlinear and viscoelastic temperature- and strain rate-dependent material behaviour under uniaxial tension. The achieved stress-strain curves exhibited, as expected, the two commonly so-called yield points, which can be taken as separators for three different material stages: viscoelastic, viscoelastic-plastic, and viscoplastic. In the second step, by separating the uniaxial tensile response into these three stages, two interdependent functions could be derived based on the well-known Ramberg-Osgood material model to simulate the viscoelastic and viscoelastic-plastic material behaviour of ETFE foils. For this purpose, analytical functions were developed to calculate the model parameters considering the influence of the test temperature and the test speed. It can be shown that the newly developed analytical material model fits well with the experimental results. With the use of the derived nonlinear material model, design engineers can predict the material’s mechanical behaviour considering the environmental conditions on site while maintaining independence from the material’s supplier.

Deep drawing of DC06 at high strain rates

Velocity effects in production technology provide technological and economic advantages, but they require consideration of strain rate dependent material behaviour in numerical process modelling. This paper proposes a deep drawing process with DC06 at high strain rates of up to 100 s-1. Basis of the investigation are the results of the inverse parameter investigation at high strain rates in [1]. In addition to the velocity dependent flow curve in numerical modelling, the damage parameters are also taken into account. The drawing ratio and the punch velocity that affects the strain rate and the stress state in the deep drawing process are varied while the blank holder force is constant. Due to the high punch speed and the pronounced inhomogeneity of the strain rate over the work piece volume, the punch speed and punch force is very well suited to verify the numerical results. Additionally, the mesh dependency of the temperature evolution in the sheet metal is examined for further investigations of the adiabatic heating of the work piece during deformation in experiment and simulation. In this context, the deep drawing tools as well as the results of the numerical and experimental investigations are presented and discussed.

Strain rate-dependent crash simulation of woven glass fabric thermoplastic composites

Woven fabric thermoplastic composites possess high specific strength and stiffness along with thermoformability. To utilize the full potential of these materials to achieve better crash-safe designs in automotive structural parts, their crash behavior must be predicted accurately. For reliable crash simulations, strain rate-dependent material data and equally capable material modeling are required. In this study, quasi-static and high-speed tests are carried out to measure tensile and in-plane shear properties. A strain rate-dependent continuum damage mechanics model is formulated to describe the deformation and damage behavior of woven glass fabric composites. Tensile and in-plane shear tests on a lab scale are used to calibrate the material parameters of the model. The model was implemented as a user-defined material subroutine (VUMAT) for Abaqus. Experimental results from coupon tests were used to verify the results of a single-element simulation. Finally, a structural level dynamic crash test of a u-profile on a drop tower was used to validate the predictions of the user material model.

Ballistic penetration simulation of a 3D woven fabric using high strain-rate dependent yarn model

3D woven fabric has great application potential in military armor systems. Here we report numerical simulation of 3 D angle interlock woven fabric(3DAWF) subjected to the ballistic impact using LS-DYNA. We employed membrane elements to construct the mesoscale yarn-level 3DAWF model to improve computational efficiencies and accuracy. The simplified Johnson-Cook (SJC) material model was proposed for simulating yarns' dynamic behaviors under high-speed impact loadings. The SJC material model and commonly used strain-rate dependent material model Cowper-Symonds (CS) were taken into the FEA model to simulate the fabric's ballistic impact behaviors separately. The ballistic impact tests of 3DAWF subjected to the Full Metal Jacket (FMJ) projectile under the strike velocity 190 ∼ 320 m/s were carried out to validate the new material model. Comparing the results between the tests and theoretical model found that the FEA model using the SJC material model can accurately predict projectile's residual velocities and fabric's deformation and damages. The numerical model using SJC yarn constitutive models can precisely capture the impact mechanism of 3DAWF.

Identification of the LLDPE Constitutive Material Model for Energy Absorption in Impact Applications.

Current industrial trends bring new challenges in energy absorbing systems. Polymer materials as the traditional packaging materials seem to be promising due to their low weight, structure, and production price. Based on the review, the linear low-density polyethylene (LLDPE) material was identified as the most promising material for absorbing impact energy. The current paper addresses the identification of the material parameters and the development of a constitutive material model to be used in future designs by virtual prototyping. The paper deals with the experimental measurement of the stress-strain relations of linear low-density polyethylene under static and dynamic loading. The quasi-static measurement was realized in two perpendicular principal directions and was supplemented by a test measurement in the 45° direction, i.e., exactly between the principal directions. The quasi-static stress-strain curves were analyzed as an initial step for dynamic strain rate-dependent material behavior. The dynamic response was tested in a drop tower using a spherical impactor hitting a flat material multi-layered specimen at two different energy levels. The strain rate-dependent material model was identified by optimizing the static material response obtained in the dynamic experiments. The material model was validated by the virtual reconstruction of the experiments and by comparing the numerical results to the experimental ones.

A comparison of Gurson and Cocks–Ashby porosity kinetics and degradation functions

Effects of porosity play a key role in ductile fracture and many modern metals are less than fully dense with a finite porosity created either unintentionally (as in additively manufactured or powder processed materials) or intentionally (as in metallic meta-materials and foams). This study compares the Gurson and Cocks–Ashby models’ predictions of porosity evolution (kinetics) and material degradation against unit cell simulations of a strain-rate dependent material under varying triaxiality. Previous comparisons do not address varying triaxiality and direct comparisons between the Gurson and Cocks–Ashby models are limited. This study also uses triaxiality, flow stress, strain rate, and strain-rate sensitivity from unit cell simulations as inputs to each model to give an accurate depiction of the models’ performance under complex evolving loading and material states. A fitting procedure for porosity evolution is also shown. This study shows the overall predictive power of the Gurson model over the Cocks–Ashby model. It also highlights the accuracy of the Cocks–Ashby porosity evolution model and Cocks–Ashby degradation function when each model is calibrated independently.

Discrete-Direct Model Calibration and Uncertainty Propagation Method Confirmed on Multi-Parameter Plasticity Model Calibrated to Sparse Random Field Data

Abstract A discrete direct (DD) model calibration and uncertainty propagation approach is explained and demonstrated on a 4-parameter Johnson-Cook (J-C) strain-rate dependent material strength model for an aluminum alloy. The methodology's performance is characterized in many trials involving four random realizations of strain-rate dependent material-test data curves per trial, drawn from a large synthetic population. The J-C model is calibrated to particular combinations of the data curves to obtain calibration parameter sets which are then propagated to “Can Crush” structural model predictions to produce samples of predicted response variability. These are processed with appropriate sparse-sample uncertainty quantification (UQ) methods to estimate various statistics of response with an appropriate level of conservatism. This is tested on 16 output quantities (von Mises stresses and equivalent plastic strains) and it is shown that important statistics of the true variabilities of the 16 quantities are bounded with a high success rate that is reasonably predictable and controllable. The DD approach has several advantages over other calibration-UQ approaches like Bayesian inference for capturing and utilizing the information obtained from typically small numbers of replicate experiments in model calibration situations—especially when sparse replicate functional data are involved like force–displacement curves from material tests. The DD methodology is straightforward and efficient for calibration and propagation problems involving aleatory and epistemic uncertainties in calibration experiments, models, and procedures.