Strain Rate Dependence Research Articles

Effects of strain rate and internal hydrogen on tensile properties of Al-10%Mg alloys

Strain rate dependences on tensile properties of the Al-10%Mg alloys containing high (5000H) and low (5000L) internal hydrogen were investigated. The total and uniform elongations increased with decreasing strain rate although the changes of tensile and yield strengths were small in 5000L. On the other hand, the total and uniform elongations also increased with decreasing strain rate whereas the tensile strength slightly increased and yield strength were almost constant in 5000H. The total and uniform elongations of 5000L at low strain rate were high in comparison with those of 5000H. A lot of cracks were observed at the particles consisting of Al-Mg-Mn in both 5000H and 5000L after tensile test. A lot of acoustic emission events (counts) were detected during plastic deformation in 5000H in comparison with those in 5000L. The low total and uniform elongations of 5000H at low strain rate might be attributed to the promotions of void and crack initiation, growth and propagation owing to the acceleration of cracking of particles due to the internal hydrogen which is introduced during casting process.

Dynamic compressive behavior of concrete-filled steel tubes under single and multiple impacts

In this study, the dynamic compression behavior of concrete-filled steel tubes (CFSTs) under single and multiple impacts was investigated using the split Hopkinson pressure bar (SHPB) apparatus. Analyses of the failure patterns, dynamic stress-strain relationship and dynamic compressive strength of CFST members were conducted, and the results for CFSTs were compared with those for plain concrete samples. Moreover, the confinement mechanism of the CFST specimens during the axial impact was investigated, and the influences of strain rate, steel tube thickness, concrete strength and height-to-diameter ratio on the dynamic increase factor of the CFST (DIFCFST) were explored. The experimental results indicate that the CFST specimens had excellent impact resistance under single and multiple impacts, and the dynamic compressive behaviors of CFSTs exhibited significant strain-rate dependence. Larger loading gas pressure can strengthen the confinement from steel tube to concrete, leading to an increase in the dynamic compressive strength of the CFST. Dynamic compressive strength reduction generally occurred during multiple impacts, while the strength enhancement could be observed at lower impact level due to insufficient single impact energy. The DIFCFST decreased with increasing steel tube thickness and concrete strength, while the height-to-diameter ratio had less effect on the DIFCFST. Based on the experimental test data, an empirical formula was proposed for the DIFCFST considering the strain rate, the confinement factor and concrete strength to predict the dynamic compressive strength of CFST members under axial impact.

Dynamic compression behavior of TiZrNbV refractory high-entropy alloys upon ultrahigh strain rate loading

In this study, the dynamic compressive response behavior of a body-centered cubic (BCC) single-phase TiZrNbV refractory high-entropy alloy (RHEA) was investigated under impact at speeds of 313–1584 m s–1 using two-stage, gas-gun-driven, high-speed plate-impact experiments; recovery sample analysis; and theoretical calculations. The strain rate and pressure were approximately 107 s−1 and 5.07–29.37 GPa, respectively. The results showed that the TiZrNbV RHEA had a Hugoniot elastic limit of 4.12–5.86 GPa and a spall strength of 1.84–2.03 GPa. The initial yield strength of the alloy showed a strong strain-rate dependence and could be described by the modified Zerilli–Armstrong model, while the phonon-damping effect was the main reason for its high strain-rate sensitivity. Microstructural analysis showed that the dynamic deformation of the TiZrNbV RHEA was controlled by the dislocation slip, dislocation proliferation, intersection of the deformation bands, and grain refinement. The analysis also showed that the intergranular, transgranular, and mixed-type cracks dominated the spall failure of the material. The dynamic Hall–Petch effect and pinning from the lattice distortion led to high dynamic yield strength. The critical strain rate for the phonon drag effect was positively related to the relative atomic mass and local strain field of the metals. Within the experimental loading range, the RHEA showed good structural stability, and simultaneously, the theoretical calculation method for the equation of state based on a cold-energy mixture could accurately predict its shock-response behavior. The valence-electron concentration (VEC) had a direct effect on the shock-compression properties of the HEAs; higher VEC implied more difficulty in compressing the HEAs. The findings of this study provide insights into understanding the mechanical response characteristics of RHEAs under extreme conditions such as high-speed impact and ultrahigh strain-rate loading.

STRAIN RATE DEPENDENCY OF NEOHOOKEAN MATERIAL USING KELVIN-VOIGT VISCOELASTIC MODEL

This research paper examines the strain rate dependency of a Neo-Hookean material using the Kelvin-Voigt viscoelastic model. The Neo-Hookean model is widely used to describe the mechanical behavior of rubber-like materials, but it fails to consider the timedependent response observed in many materials. To overcome this limitation, the Kelvin-Voigt viscoelastic model, which incorporates a viscosity term into the NeoHookean model, is employed to capture the strain rate dependency. The paper commences by introducing the Neo-Hookean material model and its assumptions. It then elucidates the rationale behind incorporating the Kelvin-Voigt model to account for the time-dependent behavior. To validate the strain rate dependency of the KelvinVoigt model, tensile test is performed using experimental data. The experimental data comprises stress-strain curves, from which the material parameters of both the Neo-Hookean and Kelvin-Voigt models are determined using curve-fitting techniques. The study presents and analyzes the results, with a specific focus on the material's strain rate sensitivity. The stress-strain curves obtained from the Kelvin-Voigt model are compared with the experimental data, and the model's accuracy is evaluated. Additionally, the material parameters obtained from the curve-fitting process are examined to explore the influence of strain rate on the mechanical response of the material.

Strain rate dependency of lightweight hybrid green composite laminate-an experimental study

Strain rate dependency of lightweight hybrid green composite laminate-an experimental study

Highly Stretchable Printed Poly(vinylidene fluoride) Sensors through the Formation of a Continuous Elastomer Phase

Stretchable piezoelectric stress/strain sensing materials have attracted substantial research interest in the fields of wearable health monitoring, motion capturing, and soft robotics. These sensors require operation under dynamic loading conditions with high strain range, changing strain/loading rates, and varying pre-stretch states, which are challenging conditions for existing sensors to produce reliable measurements. To overcome these challenges, an intrinsically stretchable poly(vinylidene fluoride) (PVDF) sensor is developed through the polymer blending of PVDF and acrylonitrile butadiene rubber (NBR). Through precipitation printing and vulcanization, the resulting PVDF/NBR blends exhibit strong β phase PVDF and a blend morphology with submicron-level phase separation, but also strains up to 544%. Both the blend morphology and the mechanical properties indicate that this PVDF/NBR blend can be considered as a continuous elastomer phase above micron scale. After electric poling and adding electrodes, the PVDF/NBR blends have excellent piezoelectric properties to be used as both stretching mode strain sensors and compression mode stress/force sensors. The stretching mode sensors can measure strain up to 70% without strain rate and pre-stretch dependence, while the compression mode sensors have a loading-rate-independent linear voltage-stress relationship up to 4.8 MPa stress and a negligible pre-stretch dependence. Therefore, the PVDF/NBR sensors can provide accurate and reliable stress/strain measurements when attached to soft structures, which paves the way for sensing and calibration of soft robots under dynamic loading conditions.

An Eulerian constitutive model for the inelastic finite strain behaviour of isotropic semi-crystalline polymers

A constitutive model for isotropic, semi-crystalline polymers is proposed. The model is Eulerian in the sense that it is independent of measures of total deformation and plastic/inelastic deformations. It is able to account for such essential phenomena as strain-rate dependence, work hardening, stress relaxation, volumetric inelastic deformations, and damage. The model was applied to uniaxial tension tests performed on polyoxymethylene (POM), which is a semi-crystalline polymer widely used in the industry. Three types of tests were conducted: monotonic tests at different strain rates, stress relaxation tests, and loading-unloading tests. The model was able to reproduce the experimental results well. The proposed model was also implemented as a VUMAT in Abaqus, and the deformation of a 3D geometry was simulated.

Temperature and Strain Rate Dependence on the Tensile Mechanical Properties, Constitutive Equations, and Fracture Mechanisms of MarBN Steel.

The effect of strain rate and temperature on the thermomechanical behavior and microstructure of MarBN steel is studied with the strain rates of 5 × 10-3 and 5 × 10-5 s-1 from room temperature (RT) to 630 °C. At high strain rates of 5 × 10-3 s-1, the Holloman and Ludwigson equations can better predict tensile plastic properties. In contrast, under low strain rates of 5 × 10-5 s-1, coupling of the Voce and Ludwigson equations appears to predict the flow relationship at RT, 430, and 630 °C. However, the deformation microstructures have the same evolution behavior under strain rates and temperatures. Geometrically necessary dislocations appear along the grain boundaries and increase the dislocation density, which results in the formation of the low-angle grain boundaries and a decrease in the number of twinning. The strengthening sources of MarBN steel include grain boundary strengthening, dislocation interactions, and multiplication. The fitted R2 values of these models (JC, KHL, PB, VA, ZA) to plastic flow stress at 5 × 10-5 s-1 are greater than 5 × 10-3 s-1 for MarBN steel. Due to the flexibility and minimum fitting parameters, the phenomenological models of JC (RT and 430 °C) and KHL (630 °C) give the best prediction accuracy under both strain rates.

Effect of Pore Pressure on Strain Rate-Dependency of Coal

Viscoelastic strain rate-dependent behaviour of coal is critical in several subsurface engineering applications especially coal seams gas production. Such rate dependency is controlled by the interaction between coal bulk and gas sorption (a sorbing gas) or gas pressure (a non-sorbing gas). Despite the research conducted to date, the gas pressure effect (non-sorbing) on the viscous behaviour of sediments in particular coal remains unexplored. We, therefore, investigate the strain rate-dependent mechanical behaviour of coal under isotropic loading to specifically explore the effect of gas pressure (Helium) on its rate dependency eliminating the sorption effect. We perform a set of triaxial experiments on coal specimens at dry and pressurised gas (Helium) conditions under different strain rates under isotropic loading. The experimental results show that all coal specimens have viscoelastic strain rate dependency at a dry condition where viscous effect increases with strain rate. As a result, the bulk modulus of the specimens increases with the increase in strain rates. This strain rate dependency response, however, reduces with an increase in pore pressure and vanishes at a certain pore pressure under the same effective stress to that of dry specimens. We further employ X-ray micro-Computed Tomography (XRCT) to 3D scan a coal specimen saturated with Krypton gas undergoing different loading rates to shed light on the micro-mechanisms of gas pressure effect on specimens’ rate dependency. The XRCT results show that gas can be trapped in small-scale fractures and pores during the loading process leading to a localised undrained response that can stiffen the specimen and reduce its ability to show viscous rate dependency. The obtained results are significant in optimizing coal seam gas production and coal seam gas drainage applications.

Fabrication of Li anode metal via bulk mechanical property analysis

Two types of lithium (Li) metals with a different average grain size, i.e., ∼10 μm in orders and above 100 μm, are successfully produced by extrusion process and rapid molding process. The results obtained from nano-indentation tests show that hardness is influenced by grain size, and it decreases with a finer grained structure, which is not the general trend as those of other light-weight pure metals. It is remarkable to observe that these Li metals have a large strain rate dependence (a large m-value) even at room-temperature, irrespective of the grain size. Compared with the Frost-Ashby deformation mechanism map, the dominant deformation mechanism is the dislocation climb. On the contrary, this unusual behavior in the fine-grained Li metal is due to the partial contribution of grain boundary sliding to deformation. This behavior is associated with the enhancement of grain boundary diffusivity and high density of grain boundaries. Concerning the effect of grain size on electrochemical characteristics, similar to the mechanical property, the results obtained from electrodeposition and dissolution tests display that the fine-grained Li metal has much better over-potential of charging and discharging operation as well as voltage response.

Effect of Viscoplasticity on Localization in Saturated Clays and Plastic Silts

A numerical study is presented of the effects of viscoplasticity on localization processes in sensitive, saturated clays and plastic silts. Numerical simulations of laboratory specimens of sensitive, viscoplastic soil subjected to monotonic, undrained, direct simple shear loading were performed using a viscoplastic constitutive model. Parametric analyses evaluated the effects of soil sensitivity, postpeak strain-softening rate, and strain rate dependency, as well as specimen size, mesh discretization, and loading rate. The numerical results showed that the global strain at which a localization forms primarily depends on the strain rate dependency of the soil’s shearing resistance relative to its rate of postpeak strain softening. A regression model is subsequently presented that relates the global strain at the onset of localization to the soil’s strain rate dependency and postpeak strain-softening rate. The results indicate that the inclusion of reasonable levels of viscoplasticity significantly increases the strain that can develop before a localization develops in clays and plastic silts with modest strain-softening rates. The consistency of the numerical results with available laboratory observations is discussed. Implications for practice and future research needs are discussed.

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.

Construction of 2-2 Type Cement-Based Piezoelectric Composites’ Mechanic–Electric Relationship Based on Strain Rate Dependence

It has been found that the mechanic-electric response of cement-based piezoelectric composites under impact loading is nonlinear. Herein, we prepared a 2-2 cement-based piezoelectric composite material using cutting, pouring, and re-cutting. Then, we obtained the stress-strain and stress-electric displacement curves for this piezoelectric composite under impact loading using a modified split Hopkinson pressure bar (SHPB) experimental apparatus and an additional electrical output measurement system. Based on the micromechanics of the composite materials, we assumed that damage occurred only in the cement paste. The mechanical response relationship of the piezoelectric composite was calculated as the product of the viscoelastic constitutive relationship of the cement paste and a constant, where the constant was determined based on the reinforcement properties of the mechanical response of the piezoelectric composite. Using a modified nonlinear viscoelastic Zhu-Wang-Tang (ZWT) model, we characterized the stress-strain curves of the piezoelectric composite with different strain rates. The dynamic sensitivity and stress threshold of the linear response of the samples were calibrated and fitted. Thus, a mechanic-electric response equation was established for the 2-2 type cement-based piezoelectric composite considering the strain rate effects.

Comparison of the Strain Rate Sensitivity in AZ31 and WE43 Magnesium Alloys under Different Loading Conditions

The initial texture effect of strain rate sensitivity response in magnesium alloys was studied using the quasi in situ electron backscatter diffraction technique. The strain accumulations, under uniaxial loading of both tensile and compression along the rolling direction, showed strain rate dependency. For the AZ31 magnesium sheets with strong basal texture (max intensity to 11.2), twinning first occurs at the onset of plastic deformation, resulting in macroscopic strain rate insensitivity. With further loading, the strain rate sensitivity significantly increases (with the strain rate sensitivity coefficient m increased from 0.0025 to 0.012), arising from the initiation of slip. For the WE43 alloy sheets with weak basal texture (max intensity to 2.6), the overall deformation is sensitive to strain rate under both tensile and compression. The twinning growth rate and twinned volume fraction have been used to identify whether the process is twin-dominated or slip-dominated during the plastic deformation of a magnesium alloy.

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.

Specimen geometry design for plasticity and fracture characterization of sheet metal under high testing speed and various stress states

To model a vehicle crash event using the finite element (FE) method, accurate material properties of automotive sheet metals at high strain rates and various stress states need to be known. In this paper, a series of specimen geometries were designed for dynamic tensile tests in a servo-hydraulic tensile machine to get rid of the system ringing effect. These specimen geometries, which consist of different Stress triaxialities and Lode angle parameters, were optimized according to a similar physical principle as that used for the Gen. III specimen of Fang and Grams using FE simulations. Oscillation-free forces were obtained during the high-speed tests in the strain rate range of up to 103 s−1 using specimens that have a novel design. The deformation and local strain fields of the specimens were measured using digital image correlation (DIC) techniques. Furthermore, the deformation and fracture behavior of a micro-alloyed steel (H340) were characterized and analyzed. The determination of the model parameters for plasticity, damage/fracture modeling, and the material’s strain-rate dependency could be conducted more accurately based on the improved oscillation-free force measurements, which resulted in an improved prediction of the plasticity and fracture behavior of the investigated steel.

Numerical investigation on meshing temperature of multicomponent nylon gears by incorporating viscoelasticity

This study concerns a numerical analysis of the meshing temperature for a multicomponent nylon gear by incorporating typical viscoelastic responses of polymers. Firstly, the generalized Maxwell model parameters were calibrated by the dynamic mechanical analysis to capture the viscoelasticity of polyamide 66. Next, the finite element model predicting the meshing temperature was established, including the heat generation analysis model, which calculates the generation of the frictional and hysteretic heat, and the heat propagation analysis model, which simulates the heat transmission. Different material models were used for polyamide 66 to investigate the influences of temperature dependence, strain rate dependence, and hysteretic effect. The effect of the iteration sequence on the meshing temperature calculation was also analyzed, i.e., how the heat generation should be updated as the loading cycles increase. A reasonable iteration scheme was determined by balancing the computational precision and consumption. It is noteworthy that the evolution of the ambient temperature around the gear and the worm within the housing was also considered. Finally, the accuracy of such meshing temperature analysis was validated on a self-developed gear test rig, in terms of the peak temperature evolution on the gear side surface. The experimental results and the simulation with the ambient temperature correction match well and the maximum error is 5 °C.

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.

Identification of Dynamic Behavior Models of Concrete B22.5

We discuss experimental and numerical studies of the deformation and destruction of fine-grained concrete B22.5 under dynamic loading. The experiments were carried out using the Kolsky (or split-Hopkinson pressure bar) method, and its modifications in the strain rate range from 400 to 2000 s-1. The rate dependences of ultimate stresses and fracture energy in tension and compression are obtained. Based on experimental data, the identification of the dynamic component of two models from the LS-DYNA computational complex was carried out: *MAT_CONCRETE_DAMAGE and *MAT_CSCM. The results of a comparative analysis of the identified models based on single-element modeling and comparison with experimental data are presented. It is shown that the obtained experimental strain rate dependences of the fracture characteristics can significantly improve the predictive ability of the model compared to the default parameter set. Information about the rate dependence of the fracture energy in *MAT_CSCM model makes it possible to more realistically simulate the behavior of the material beyond the ultimate stress.

An efficient finite strain constitutive model for amorphous thermoplastics: Fully implicit computational implementation and optimization-based parameter calibration

In this paper, a new visco-elastic visco-plastic (three-dimensional) constitutive model is consistently formulated under isothermal conditions to describe the nonlinear behavior of thermoplastic polymers at finite strains. The constitutive equations include three well-established rheological elements to have well-defined parametric behavior and capture the experimental response. In particular, a visco-elastic generalized Maxwell element, a visco-plastic Eyring dashpot, and a plasticity-induced (nonlinear) hardening element are selected and consistently combined. A fully implicit integration algorithm is derived, and highly efficient implementation is obtained by simplifying the system of equations to a single (scalar) nonlinear residual equation. A new two-stage optimization-based calibration procedure is developed to identify the material parameters in a completely unsupervised way. The constitutive model is validated against results available in the literature for polycarbonate, accounting for temperature and strain rate dependencies. The results show the efficiency of the overall numerical strategy and demonstrate that quadratic convergence rates are attained. Despite the strongly nonlinear finite strain response, it is possible to observe an excellent agreement for all stages of deformation.