Strain Rate Dependent Material Behavior Research Articles

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.

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.

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.

Optimization and Validation of a Load-Controlled Numerical Model for Single Asperity Scratch

Abrasive wear due to particles sliding along a surface (two-body abrasion) or in between two surfaces (three-body abrasion) often leads to early failure of machine components exposed to, e.g., slurry, sand, wear debris, and so on. The primary cause for failure due to abrasive wear is the interaction between abrasive particles and the material surface. Simulation of an entire abrasive system is complicated and involves several challenges. Therefore, a single scratch test is the most fundamental and simplest abstraction of abrasive wear that can be simulated using finite-element modeling (FEM). A novel load-controlled quasi-static explicit three-dimensional (3D) scratch model has been developed using ABAQUS (6.14) for the current study. The FE model was validated using experimentally performed scratch tests on an abrasion-resistant martensitic steel. The influence of load and indenter geometry on scratch geometry was studied in detail. Future work will focus on introducing damage and strain rate dependent material behavior into the model in order to deepen the understanding of the interaction between an abrasive and the material.

A finite-strain thermomechanical model for severe superplastic deformation of Ti-6Al-4V at elevated temperature

This paper presents a new finite-strain and thermomechanically-coupled constitutive model for severe superplastic deformation of Ti-6Al-4V at elevated temperature. The kinematic hypothesis of this model is a multiplicative decomposition of the deformation gradient into elastic, superplastic and thermal components, allowing the model to simultaneously take into account the large superplastic flowing deformation, the evident thermal expansion and the local temperature evolution. The model begins with the establishment of a thermodynamically consistent framework, including the Helmholtz free energy function, the entropy inequality and the heat production, from which constitutive equations are derived. The strain rate and temperature dependent material behavior is formulated by using a bilinear interpolation scheme and an exponential function. The ABAQUS/Explicit user-defined material subroutine VUMAT is employed to realize the numerical implementation of the model. The model is validated against the experimental data obtained in tensile tests on Ti-6Al-4V specimens. Finite element simulation of the superplastic gas-blow forming of Ti-6Al-4V sheet well demonstrates the model capabilities of accurately describing large superplastic deformation of Ti-6Al-4V at elevated temperature.

Modelling the strain rate dependent hardening of constructional steel using semi-empirical models

The importance of modelling the strain rate dependent material behaviour increases since structural components more and more have to be designed against extreme events. With growing usage of numerical programmes, good models become necessary. The goal of the ongoing research project is to find reasonable models for simulations concerning steel constructions. This paper discusses various models to describe the strain rate dependent hardening of mild steel. In this context, high speed tensile tests were performed and evaluated. Four commonly used material models and a new model were introduced and calibrated to the test results: The Johnson-Cook model, a modified Johnson-Cook model by Huh and Kang, the Cowper-Symonds model and a combined Johnson-Cook/Cowper-Symonds model. These four models do not describe the observed behaviour of constructional steels satisfactorily. Unlike these models, a newly introduced model is able to describe both a yield plateau and the slope of the strain hardening, both as a function of the strain rate. The quality of the approximations is discussed and further investigated by performing notched bar tensile tests and simulations. Finally, recommendations are given on the basis that the modelling of a yield plateau and the negative strain rate sensitivity of the strain hardening is necessary for modelling structural components under extreme events.

Investigation on the thickness distribution of highly customized titanium biomedical implants manufactured by superplastic forming

Mechanical performances of titanium biomedical implants manufactured by superplastic forming are strongly related to the process parameters: the thickness distribution along the formed sheet has a key role in the evaluation of post-forming characteristics of the prosthesis. In this work, a finite element model able to reliably predict the thickness distribution after the superplastic forming operation was developed and validated in a case study. The material model was built for the investigated titanium alloy (Ti6Al4V-ELI) upon results achieved through free inflation tests in different pressure regimes. Thus, a strain and strain rate dependent material behaviour was implemented in the numerical model. It was found that, especially for relatively low strain rates, the strain rate sensitivity index of the investigated titanium alloy significantly decreases during the deformation process. Results on the case study highlighted that the strain rate has a strong influence on the thickness profile, both on its minimum value and on the position in which such a minimum is found.

A numerical and experimental study of temperature effects on deformation behavior of carbon steels at high strain rates

Both in research and in the light of industrial applications, there is a growing interest in methods to characterize the mechanical behavior of materials at high strain rates. This is particularly true for steels (the most important structural materials), where often the strain rate-dependent material behavior also needs to be characterized in a wide temperature range. In this study, we use the Finite Element Method (FEM), first, to model the compressive deformation behavior of carbon steels under quasi-static loading conditions. The results are then compared to experimental data (for a simple C75 steel) at room temperature, and up to testing temperatures of 1000 °C. Second, an explicit FEM model that captures wave propagation phenomena during dynamic loading is developed to closely reflect the complex loading conditions in a Split-Hopkinson Pressure Bar (SHPB) – an experimental setup that allows loading of compression samples with strain rates up to 104 s-1 The dynamic simulations provide a useful basis for an accurate analysis of dynamically measured experimental data, which considers reflected elastic waves. By combining numerical and experimental investigations, we derive material parameters that capture the strain rate- and temperature-dependent behavior of the C75 steel from room temperature to 1000 °C, and from quasi-static to dynamic loading.

Principle and setup for characterization of material parameters for high speed forming and cutting

Abstract Velocity effects in production technology provide technological and economic advantages, but at the same time they necessitate consideration of strain rate dependent material behavior in process modelling. This paper proposes an innovative approach for material characterization in terms of strain rate dependent flow curves and failure describing parameters. Two driving concepts for high velocity testing, which can be used for examining the material behavior under different load cases by considering different specimen geometries, are presented: a pneumatic one for plastic strain rates up to 1,000 s -1 and an electromagnetic one for strain rates of 5·10 2 s -1 up to 10 5 s -1 . Compared to the Split-Hopkinson-Bar-Test normally used, there are some advantages regarding achievable strain rates and achieved measurement data. In principle, knowledge about the strain paths, stress paths and local distributions of stress and strain in the specimen is essential for identifying material characteristics. Short process times, fast changes of the measurement values, small specimen size and frequently limited accessibility of the specimen during the test hinder directly measuring these parameters at high velocity testing. Therefore, here auxiliary test parameters, which are easier to measure, are recorded and used as input data for an inverse numerical simulation that provides the desired material characteristics as a result. For a first evaluation of the test arrangement, the concept was investigated in a numerical sensitivity study and the measuring principle was verified experimentally in a drop tower test.

Investigation of the Anisotropic Strain Rate Dependency of AA5182-O and DC04 for Different Stress States

A more precise numerical simulation of sheet metal forming processes leads to a demand for more detailed material characterisation. Hence, it is advisable to consider the strain rate reliant and anisotropic material characteristics. There are various common sheet metals that have beside of an anisotropic a more or less distinct strain rate dependent material behaviour. With regard to these material characteristics, for a more detailed numerical prediction of a sheet metal forming process, it is necessary to include the aspect of deformation velocity. A characterisation of the strain rate dependent hardening behaviour for the two common sheet metals DC04 and AA5182-O is performed under tensile as well as shear load and their behaviour is compared after v. Mises equivalent stress and strain. The two strain rate models from Norton-Hoff and Tanimura are calibrated on basis of the experimental data and their applicability for the investigated materials is evaluated. The calibration of the strain rate sensitive models showed for both materials a very good comparability, respectively.

Determination of strain rate dependent material data for FEA crash simulation of polymers using digital image correlation

The measurement of the temporal and local true strain behavior of polymer materials is important for the advancement in the sector of crash simulation of plastics parts. To simulate the strain rate dependent plastic material behavior of polymers under impact conditions using FEA (Finite Element Analysis), true stress/strain-curves at different constant strain rates are required as input data. A new approach for the measurement of true stress/strain-curves at constant strain rates is presented in this paper. The approach is based on a time based correlation method and works completely without using FEA based optimization procedures like inverse analysis. It only uses data measured in mechanical testing to almost automatically generate true stress/strain-curves at different constant strain rates.

Residual stresses due to foreign object damage in laser-shock peened aerofoils: Simulation and measurement

Foreign object damage (FOD) to the leading edge of aerofoils has been identified as one of the main life-limiting factors for aeroengine compressor blades. Laser-shock peening (LSP) has been proposed as a means of increasing the material’s resistance to such impact damage. In this work, a three-dimensional finite element (FE) model has been developed to simulate the residual stresses due to head on (0°) and 45° impacts by a cuboidal projectile on aerofoil specimens treated with LSP. The Johnson–Cook (JC) material model was employed to describe the strain rate-dependent material behaviour; whilst the Johnson–Cook dynamic failure model was considered in 45° FOD simulation, where significant loss of material occurred. The strain rate sensitivity of the model at selected high strain rates was assessed against the data from the literature. The numerical results from the simulation of head-on impact were compared with the measurements by depth-resolved synchrotron X-ray diffraction on the mid-plane. The models were then used to predict the 3D residual stress distributions due to 0° and 45° FOD impacts, and the results were compared with the strain maps obtained from high-energy synchrotron X-ray diffraction. Good to excellent correlations between the simulations and the measurements have been found.

Macroscopic and mesoscopic modeling based on the concept of generalized stresses for cutting simulation

AbstractBased on the concept of generalized stresses proposed by GURTIN [2] and FOREST et al. [1] macro‐ and meso‐scopic modelling are presented. For the macroscopic modelling we develop a multi‐mechanism model for strain rate and temperature dependent asymmetric plastic material behavior accompanied by phase transformation with consideration of the trip‐strain. Furthermore, we extend the multi‐mechanism model with the gradient of phase fraction, which is considered as an extra degree of freedom. For mesoscopic modelling a phase field model is implemented for describing phase transformations. For the scenario of a cutting process we have a martensite‐austenite‐martensite transformation. A generalized principle of virtual power is postulated involving generalized stresses and used to derive the constitutive equations for both approaches. Furthermore, parameters of the multi‐mechanism model related to visco‐plasticity with SD‐effect and the trip‐strain are identified for the material DIN 100Cr6. In the examples a cutting simulation for testing the multi‐mechanism model and a phase‐transformation simulation are shown. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Constitutive modelling of the rate dependent flow stress of cast high-alloyed metastable austenitic TRIP/TWIP steel

The influence of strain rate and temperature on the resulting mechanical behaviour of a cast metastable austenitic CrMnNi–TRIP/TWIP steel was investigated. At ambient temperature and below, the formation of α′-martensite dominates causing a pronounced strain hardening. Various analytical models are available in literature and are mostly based on rule of mixture concepts (e.g. Ludwigson and Berger [22] and Narutani et al. [25]). These models were developed for commercial metastable alloys with medium stacking fault energy (SFE). However, for the herein-investigated alloy with very low SFE these models were found to be limited in describing the strain rate dependent material behaviour. A new model is presented predicting the flow stress of metastable alloys incorporating strain rate sensitivity, transformation strain, martensite kinetics and adiabatic heating.

The Strain Rate Dependent Material Behavior of S-GFRP Extracted from GLARE

S-Glass fiber reinforced epoxy (S-GFRP) extracted from GLARE has been experimentally characterized at three distinct strain-rates (5 × 10−4 s−1, 10 s−1, and c.a. 2000 s−1) and in four loading directions (0°, 90°, and 45° to the fiber direction and in the through-thickness direction). A novel specimen clamping mechanism was developed and full-field optical strain measurement was applied. With the aid of these techniques, a significant increase in failure-strength and apparent elastic modulus in all loading directions, particularly in fiber direction, was observed with an increased strain-rate; strain to failure increased in the fiber direction and decreased in all other loading directions.

On the numerical handling of fractional viscoelastic material models in a FE analysis

The paper presents the finite element (FE) implementation of linear and nonlinear fractional viscoelasticity models. To this end, a short introduction on fractional calculus is given. In addition to the fractional operators, this includes analytical and numerical solution schemes for selected fractional integral and differential equations. The presented rheological model is based on state of the art approaches and has been adopted to model the strain rate dependent material behavior of polymers. To this end, two approaches with constant and overstress dependent viscous properties resulting in linear and nonlinear evolution equations are discussed. The uniaxial constitutive relations are generalized to the multiaxial case and processed to be implemented in a FE code. The model behavior of both approaches is demonstrated and compared for selected uniaxial and multiaxial load cases.

High strain rate behavior, transformation-induced plasticity and fracture toughness characterization of cast and additionally tempered Fe85Cr4Mo8V2C1 alloy manufactured using a rapid solidification technique

This study focuses on the characterization of the microstructures of an FeCrMoVC alloy in two states (an as-cast and a heat-treated state) as well as the compressive strain rate-dependent material and fracture toughness behavior. Both microstructures consist of martensite, retained austenite and complex carbides. Tempering results in a transformation of retained austenite into martensite, the precipitation of fine alloy carbides, and diffusion processes. High yield stresses, flow and ultimate compressive strength values at a relatively good deformability were measured. The yield and flow stresses at the onset of deformation are higher for the heat-treated state due to higher martensitic phase fractions and fine precipitations of alloy carbides respectively. Compressive deformation causes a strain-induced transformation of retained austenite to α′-martensite. Hence, both high-strength alloys are TRIP-assisted steels (TRansformation-Induced Plasticity). However, the martensitic transformation is more pronounced in the as-cast state due to higher phase fractions of retained austenite already in the initial state. Examinations of strained microstructures showed decreased crystallite sizes with increasing deformation. It is assumed that, during plastic deformation, the amount of low angle grain boundaries increases while the incremental formation of α′-martensite leads to decreased crystallite size. In general, lower microstrains were determined in the heat-treated state as a consequence of stress relaxation during tempering. In comparison to commercially available tool steels, the determined fracture toughness K Ic of both variants revealed relatively high fracture toughness values. It was found that the lower shelf of K Ic is already reached at room temperature. Higher loading rates \( \dot{K} \) resulted in lower dynamic fracture toughness K Id values. Notch fracture toughness K A measurements indicate that the critical notch tip radii of the examined materials are slightly smaller than 0.09 mm.

High Strain-Rate Behavior and Transformation-Induced Plasticity of a High-Strength FeCrMoVWC Alloy Manufactured by Rapid Solidification Technique

By employing the rapid solidification technique and special manufacturing conditions, e.g., using only pure elements, an alloy was produced that exhibits major differences to conventionally produced high-speed steels. Within this study, the strain rate dependent material behavior of the examined alloy was characterized under compressive loading for a strain rate range from 10−3 seconds−1 to 103 seconds−1. The aim was to understand the inherent mechanisms when low and high strain rates are applied. Initially, microstructural observations of the base material, which revealed α’-martensite, retained austenite, and complex carbides, were conducted. The material exhibits extraordinarily high ultimate compression strength of up to 4800 MPa, a high work-hardening behavior, and a good deformability of 15 pct. Moderate strain rate sensitivity was detected. Furthermore, a strain-induced transformation (transformation induced plasticity [TRIP]-effect) from retained austenite to α’-martensite occurred. Interrupted compression tests at different strains and strain rates were carried out to understand the microstructural evolution. The examinations showed that adiabatic heating decreases the transformation rate of retained austenite to α’-martensite and counteracts the work-hardening behavior. For higher strain rates higher α’-martensite contents in the initial deformation region as well as a pronounced saturation behavior of α’-martensite was detected. A hypothesis is given for the strong work-hardening behavior of the alloy.

Application of the time-temperature superposition principle to the mechanical characterization of elastomeric adhesives for crash simulation purposes

In the automotive industry, finite element simulation is widely used to ensure crashworthiness. Mechanical material data over wide strain rate and temperature ranges are required as a basis. This work proposes a method reducing the cost of mechanical material characterization by using the time-temperature superposition principle on elastomeric adhesives. The method is based on the time and temperature interdependence which is characteristic for mechanical properties of polymers. Based on the assumption that polymers behave similarly at high strain rates and at low temperatures, a temperature-dominated test program is suggested, which can be used to deduce strain rate dependent material behavior at different reference temperatures. The temperature shift factor is found by means of dynamic mechanical analysis according to the WLF-equation, named after Williams, Landel and Ferry. The principle is applied to the viscoelastic properties as well as to the failure properties of the polymer. The applicability is validated with high strain rate tests.