Rate-dependent Plastic Deformation Research Articles

Comparison of different elastic strain definitions for largely deformed SEI of chemo-mechanically coupled silicon battery particles

Amorphous silicon is a highly promising anode material for next-generation lithium-ion batteries. Large volume changes of the silicon particle have a critical effect on the surrounding solid-electrolyte interphase (SEI) due to repeated fracture and healing during cycling. Based on a thermodynamically consistent chemo-elasto-plastic continuum model we investigate the stress development inside the particle and the SEI. Using the example of a particle with SEI, we apply a higher order finite element method together with a variable-step, variable-order time integration scheme on a nonlinear system of partial differential equations. Starting from a single silicon particle setting, the surrounding SEI is added in a first step with the typically used elastic Green–St-Venant (GSV) strain definition for a purely elastic deformation. For this type of deformation, the definition of the elastic strain is crucial to get reasonable simulation results. In case of the elastic GSV strain, the simulation aborts. We overcome the simulation failure by using the definition of the logarithmic Hencky strain. However, the particle remains unaffected by the elastic strain definitions in the particle domain. Compared to GSV, plastic deformation with the Hencky strain is straightforward to take into account. For the plastic SEI deformation, a rate-independent and a rate-dependent plastic deformation are newly introduced and numerically compared for three half cycles for the example of a radial symmetric particle.

No yield stress required: Stress-activated flow in simple yield-stress fluids

An elastoviscoplastic constitutive equation is proposed to describe both the elastic and rate-dependent plastic deformation behavior of Carbopol® dispersions, commonly used to study yield-stress fluids. The model, a variant of the nonlinear Maxwell model with stress-dependent relaxation time, eliminates the need for a separate Herschel–Bulkley yield stress. The stress dependence of the viscosity was determined experimentally by evaluating the steady-state flow stress at a constant applied shear rate and by measuring the steady-state creep rate at constant applied shear stress. Experimentally, the viscosity’s stress-dependence was confirmed to follow the Ree–Eyring model. Furthermore, it is shown that the Carbopol® dispersions used here obey time-stress superposition, indicating that all relaxation times experience the same stress dependence. This was demonstrated by building a compliance mastercurve using horizontal shifting on a logarithmic time axis of creep curves measured at different stress levels and by constructing mastercurves of the storage- and loss-modulus curves determined independently by orthogonal superposition measurements at different applied constant shear stresses. Overall, the key feature of the proposed constitutive equation is its incorporation of a nonlinear stress-activated change in relaxation time, which enables a smooth transition from elastic to viscous behavior during start-up flow experiments. This approach bypasses the need for a distinct Herschel–Bulkley yield stress as a separate material characteristic. Additionally, the model successfully replicates the observed steady-state flow stress in transient-flow scenarios and the steady-state flow rate in creep experiments, underlining its effectiveness in capturing the material’s dynamic response. Finally, the one-dimensional description is readily extended to a full three-dimensional finite-strain elastoviscoplastic constitutive equation.

Strain-rate-dependent plasticity of Ta-Cu nanocomposites for therapeutic implants

Recently, Ta/Cu nanocomposites have been widely used in therapeutic medical devices due to their excellent bioactivity and biocompatibility, antimicrobial property, and outstanding corrosion and wear resistance. Since mechanical yielding and any other deformation in the patient's body during treatment are unacceptable in medicine, the characterization of the mechanical behavior of these nanomaterials is of great importance. We focus on the microstructural evolution of Ta/Cu nanocomposite samples under uniaxial tensile loading conditions at different strain rates using a series of molecular dynamics simulations and compare to the reference case of pure Ta. The results show that the increase in dislocation density at lower strain rates leads to the significant weakening of the mechanical properties. The strain rate-dependent plastic deformation mechanism of the samples can be divided into three main categories: phase transitions at the extreme strain rates, dislocation slip/twinning at lower strain rates for coarse-grained samples, and grain-boundary based activities for the finer-grained samples. Finally, we demonstrate that the load transfer from the Ta matrix to the Cu nanoparticles via the interfacial region can significantly affect the plastic deformation of the matrix in all nanocomposite samples. These results will prove useful for the design of therapeutic implants based on Ta/Cu nanocomposites.

Temperature and rate-dependent plastic deformation mechanism of carbon nanotube fiber: Experiments and modeling

High-performance carbon nanotube (CNT) fibers inevitably encounter complicated thermal environments while used in aerospace structures and intelligent actuators. Catastrophic damage is unavoidably induced due to the loss of their mechanical properties. Herein, a modified Hopkinson bar and an in-situ SEM tensile equipment were introduced to study the high-temperature time-dependent mechanical behaviors and microstructure evolution of individual CNT fibers. It was found that the interaction between CNTs was weakened by thermal expansion and defects were introduced into CNTs by thermal oxidation. In addition, the effects of temperature on the viscoplastic strain transition and durability of CNT fibers were studied through a series of relaxation experiments. A shear-lag unit cell and a three-level mathematical model were developed for describing the hierarchical structure evolution of CNT fibers. These models clarified the mechanism of strength loss of CNT fibers at high temperatures and characterized the effect of thermal expansion on their microstructure and mechanical properties. The overlap length and the distance between tubes as a function of temperature were discussed. According to the modeling, an effective strategy was proposed to improve the mechanical properties of CNT fibers at high temperatures by restraining thermal expansion and thermal oxidation. This work would provide crucial theoretical and experimental guidance for the improvement of the thermal dynamic stability of CNT fibers and their composites in extremely high-temperature operating conditions.

Ambient-Temperature Indentation Creep of Shape Memory NiTi Alloys: Additively Manufactured versus Cast

In this study, depth-sensing indentation creep response of cast and additively manufactured (laser powder bed fusion) NiTi alloys in heat-treated conditions have been investigated at ambient temperature. Indentation creep tests were evaluated with the help of a dual-stage approach comprising a loading segment with a subsequent constant load-holding stage and an unloading phase afterward. The investigation was carried out at a maximum load of 50 mN along with a holding time of 600 s. Different creep parameters comprising indentation creep displacement, creep strain rate, creep stress exponent as well as the indentation size effect have been analyzed quantitatively for the employed materials. In addition, microstructural analysis has been performed to ascertain the processing–microstructure–creep property correlations. A substantial indentation size effect was seen for both cast and printed NiTi samples in heat-treated conditions. According to the creep stress exponent measurements, the dominant mechanism of rate-dependent plastic deformation for all NiTi samples at ambient temperature is attributed to the dislocation movement (i.e., glide/climb). The outcome of this investigation will act as a framework to understand the underlying mechanisms of ambient-temperature indentation creep of the cast and printed NiTi alloy in conjunction with heat-treated conditions.

Strength differential effect and anisotropy of Mg–1.9Mn–0.3Ce (wt-%) alloy subjected to high-rate loadings

Tension and compression tests for a rare-earth-containing alloy sheet, Mg–1.9Mn–0.3Ce (wt-%), are performed under quasi-static and high-rate loadings along the rolling, transverse and normal direction, and stress – strain responses exhibit positive strain-rate dependence. Empirically based Johnson-Cook constitutive model is modified to describe the rate-dependent plastic deformation in multiple loading directions. A strong strength differential effect persists, and such effect is shown to be stronger at high strain rates. A weak in-plane anisotropy exists in the initial yielding and subsequent strain hardening behaviour as well as strength differential effect. In contrast, the out-of-plane anisotropy in compression is apparent and is approximately rate insensitive. Microstructural observations indicate that twinning plays the key role for the enhancement of strain-hardening rate under high strain-rate deformation.

Evaluating and modeling rate sensitivity in advanced reactor structural materials: 316H, Gr. 91, and A617

Advanced reactor systems operate at high temperatures to achieve better thermal efficiency. During transients from lower temperatures to high operating temperatures structural metals transition from rate insensitive behavior to rate dependent behavior. In the rate dependent regime creep and plastic deformation are not separable hence requiring a unified treatment with a viscoplastic model. Several bounding design methods in the ASME Boiler and Pressure Vessel Code, Section III, Division 5, Subsection HB, Subpart B assume a decoupled treatment of creep and plasticity so establishing the boundary of the rate insensitive regimes for advanced reactor structural materials is necessary to set limits for the use of these bounding design methods. In the rate sensitive regime new bounding methods or fully inelastic analysis are required for the design of Division 5 Class A components. During temperature transients these components may operate in both the rate insensitive and rate sensitive regions, requiring computational models that can represent both types of behavior. This work establishes criteria for material rate sensitivity and develops a new composite method for modeling constitutive response in both the rate sensitive and rate insensitive regimes for three Division 5, Class A materials: 316H austenitic stainless steel, Grade 91 ferritic-martensitic steel, and Alloy 617, a nickel-based alloy. Both the criteria and new modeling strategy apply the concept of a normalized activation energy for thermally activated mechanisms developed by Kocks, Mecking, and co-workers. This work quantifies the average rate sensitivity of the three materials from an experimental database collected from the literature. Additionally, this work develops rate sensitivity criteria and a complete model for each material that can transition between both deformation regimes and provides several example simulations demonstrating the accuracy of the models and the numerical performance of the composite modeling method.

Rate-dependent plastic deformation of TiZrHfCuNiBe high entropy bulk metallic glass

Rate-dependent plastic deformation behavior of TiZrHfCuNiBe high entropy bulk metallic glass (HE-BMG) is investigated by the nanoindentation and quasi-static compression tests. The experimental results reveal that the pop-in sizes during nanoindentation and the serrations sizes under compression will reduce when the loading/strain increases. The strain rate sensitivity during nanoindentation creep is enhanced as loading rate increases, which represents more homogeneously deformation of TiZrHfCuNiBe HE-BMG at higher loading/strain rate. The average serrations sizes of TiZrHfCuNiBe HE-BMG are significantly smaller than that of traditional bulk metallic glasses. The plastic deformation behavior of the TiZrHfCuNiBe HE-BMG is discussed with respect to the self-organized critical (SOC) state behavior. The results demonstrated that the shear-band interactions of multiple shear bands could affect the SOC behavior and inhomogeneous deformation. Research suggests the shear transformation zone (STZ) sizes become smaller as the loading rate increases based on the statistical analysis. It is ascribed to have a larger shear band density at lower loading/strain rate. The current research is in coincidence with the shear-band patterns shown in microscopic micrographs of specimen surfaces. More shear-banding distributions at the lower loading/strain rate will result in more inhomogeneous deformation.

Depth-sensing time-dependent response of additively manufactured Ti-6Al-4V alloy

Depth-sensing (instrumented) indentation testing technique is a robust, reliable, convenient and non-destructive characterization method to study small-scale mechanical properties and rate-dependent plastic deformation in metals and alloys at ambient and elevated temperatures. In the present paper, depth-sensing indentation creep behavior of an additively manufactured, via laser powder bed fusion (L-PBF) method, Ti-6Al-4V alloy is studied at ambient temperature. Indentation creep tests were performed through a dual-stage scheme (loading followed by a constant load-holding and unloading) at different peak loads of 250 mN, 350 mN, and 450 mN with holding time of 400 s. Creep parameters including creep rate, creep stress exponent, and indentation size effect were analyzed, according to the Oliver and Pharr method, at different additive manufacturing scan directions and scan sizes. To assess processing parameter/ microstructure/ creep property correlations in the additively manufacture Ti-6Al-4V alloy, microstructural quantitative analyses (i.e. optical microscopy and scanning electron microscopy) were performed as well. The findings of this study, according to stress exponent values, showed that the controlling mechanism of the creep at ambient temperature for the examined L-PBF Ti-6Al-4V is mainly glide-controlled dislocation creep. These findings were compared against traditionally processed Ti-6Al-4V as well.

Magnesium nanocomposites: An overview on time-dependent plastic (creep) deformation

Abstract Magnesium (Mg) nanocomposites are created when nano-size particles are embedded into the Mg (or Mg alloy) matrix. The Mg nanocomposites, cited as high-strength energy-saving materials of future, are a group of emerging materials with excellent combination of strength and ductility and superior specific strength property (strength-to-weight ratio). Having said this, Mg nanocomposites are considered as promising replacement for other structural alloys (i.e. aluminum and titanium) wherever low density and high strength are required, i.e. transportation, aerospace, defense, etc. To be able to apply this group of materials for real components, different failure mechanisms at ambient and elevated temperatures under static and dynamic loading condition must be well documented. Compared with other metals and alloys, rate-dependent plastic deformation (creep), at ambient and elevated temperatures, of these novel materials is not yet well studied which seems a tangible lack of knowledge. This is required since the materials in service are often exposed to medium and elevated temperatures and/or static loads for long duration of time and this encourages creep failure on them. To this end, the information and the controlling mechanisms on time/temperature-dependent response of the material need to be developed to be able to predict the response of the Mg nanocomposites where the materials are under creep conditions. This paper aims at providing an overview on (i) creep-resistant Mg alloys (as matrix) and their chemical compositions, and (ii) responses of the Mg nanocomposites at different creep conditions (time and temperature). The controlling mechanisms contributing to the strength and ductility of the Mg nanocomposites due to the presence of the nanoparticles have been reviewed briefly in the present article. In this paper both traditional (uniaxial) and depth-sensing indentation creep of Mg nanocomposites are reviewed. Also, some fundamental questions and possible explanations have been raised on the creep characteristics of Mg nanocomposites and the contribution of microstructural features (i.e. grain boundaries, twins, precipitates, nanoparticles). This overview article provides a comprehensive summary to understand one of the failure modes (creep) at ambient and elevated temperature in the energy saving Mg nanocomposites that would be of interest for those in academia who explore novel nanocomposites.

State parameter-based constitutive modelling of stress strain curves in Al-Mg solid solutions

A novel and comprehensive approach addressing the stress strain response of binary Al-Mg alloys under uniaxial loading over a wide range of temperatures (78 K–650 K), strain rates (10−4–10 s−1) and solute contents (0 wt.%–5 wt.%) is developed and introduced. The model is based on the mechanical threshold Ansatz in combination with a Labusch type solid solution hardening approach and a model for dynamic strain ageing to describe the temperature and strain rate dependence of the yield stress in a thermal activation framework. Strain hardening is modelled on basis of the Kocks-Mecking evolution equations for the average dislocation density and discussed in terms of the temperature-dependence of the initial strain hardening rate and the saturation stress for stage-III hardening. Both, static and dynamic recovery, are fully taken into account. The model predictions are validated on experimental stress-strain curves reported in literature. The results demonstrate that the model successfully reproduces the complex temperature and strain rate dependent plastic deformation characteristics of Al-Mg alloys with a minimum of calibration input parameters.

Indentation-based rate-dependent plastic deformation of polycrystalline pure magnesium

Using a Berkovich pyramidal indenter and an instrumented nanoindentation platform, dual stage nanoindentation creep tests, including loading to a pre-set load and holding at the constant load then unloading, were performed on polycrystalline pure magnesium at 300K. Indentation tests were performed at four indentation loading rates of 0.05, 0.5, 5, and 50mN/s at constant load of 45mN and holding time of 400s. These were performed to assess indentation force-displacement response along with average indentation stress, indentation strain rate sensitivity and ambient temperature rate dependent plastic deformation response of the material. To this end, activation volume, a kinetic characteristic of plastic deformation, and density of mobile dislocations in plastically deforming material in the plastic zone around the indenter are discussed in detail. Uncertainties and sources of error, i.e. indentation size effect, surface roughness, and thermal drift, and pile-up/sink-in measuring creep response through nanoindentation are provided in the current paper as well. The microstructure of the material was also studied through optical and scanning electron microscopy to further investigate the microstructure/property correlations in the tested polycrystalline pure magnesium. The results show the dependency of indentation stress, strain rate sensitivity, and activation volume upon depth and loading rate. According to the creep stress exponent measurements, the dominant mechanism of rate dependent plastic deformation for polycrystalline pure Mg at ambient temperature is attributed to obstacle limited dislocation glide. Finally, the contribution of mechanical twins in the plastic zone around the indenter in the studied polycrystalline pure magnesium is briefly discussed.

Kinetics of length-scale dependent plastic deformation of gold microspheres

Abstract

Testing, characterization and modelling of mechanical behaviour of poly (lactic-acid) and poly (butylene succinate) blends

Abstract Background Significant amount of research, both experimental and numerical, has been conducted to study the mechanical behaviour of biodegradable polymer PL(L)A due to its wide range of applications. However, mechanical brittleness or poor elongation of PL(L)A has limited its applications considerably, particularly in the biomedical field. This study aims to study the potential in improving the ductility of PLA by blending with PBS in varied weight ratios. Methods The preparation of PLA and PBS blends, with various weight ratios, was achieved by melting and mixing technique at high temperature using HAAKE™ Rheomix OS Mixer. Differential Scanning Calorimetry (DSC) was applied to investigate the melting behaviour, crystallization and miscibility of the blends. Small dog-bone specimens, produced by compression moulding, were used to test mechanical properties under uniaxial tension. Moreover, an advanced viscoplastic model with nonlinear hardening variables was applied to simulate rate-dependent plastic deformation of PLA/PBS blends, with model parameters calibrated simultaneously against the tensile test data. Results Optical Microscopy showed that PBS composition aid with the crystallization of PLA. The elongation of PLA/PBS blends increased with the increase of PBS content, but with a compromise of tensile modulus and strength. An increase of strain rate led to enhanced stress response, demonstrating the time-dependent deformation nature of the material. Model simulations of time-dependent plastic deformation for PLA/PBS blends compared well with experimental results. Conclusions The crystallinity of PLA/PBS blends increased with the addition of PBS content. The brittleness of pure PLA can be improved by blending with ductile PBS using mechanical mixing technique, but with a loss of stiffness and strength. The tensile tests at different strain rates confirmed the time-dependent plastic deformation nature of the blends, i.e., viscoplasticity, which can be simulated by the Chaboche viscoplastic model with nonlinear hardening variables.

On room-temperature nanoindentation response of an Al–Li–Cu alloy

Al-Li-Cu alloys are the least dense aluminum series with large applications in aerospace industries where mass plays an important role in calculations. In these applications, ambient- and elevated- temperature creep phenomena are among main failure mechanisms that should be assessed in detail for a safe service. Instrumented nanoindentation approach is a semi-destructive technique that can be well adapted to assess rate-dependent plastic deformation behavior of Al-Li-Cu alloys at room and elevated temperature. In the present paper, therefore, dual stage, constant loading-rate followed by constant-load, pyramidal nanoindentation tests were performed on an Al-Li-Cu alloy to assess time-dependent deformation behavior at room temperature. To this end, indentation size effect, indentation stress/strain rate, dislocations’ activation energy and activation volume and their dependencies upon indenter displacement (indentation depth) were analyzed. The results were used to assess and understand possible transition mechanisms during a dual stage indentation scheme of an Al-Li-Cu alloy.

A molecular dynamics investigation into plastic deformation mechanism of nanocrystalline copper for different nanoscratching rates

The plastic deformation mechanisms of nanoscratching process are investigated through the study of a rigid diamond tip sliding against nanocrystalline Cu using molecular dynamics (MD) simulation. Special attentions are paid to the scratching rate effects, as well as the crystal structural effects from single crystalline, polycrystalline and nanotwinned (NT) polycrystalline. With the increase of scratching rate, scratching force and workpiece temperature increase continuously due to severe plastic deformation and large chip volume, resulting in dislocation slip, GB slip, and twinning/detwinning. Scratching rate also governs the distributions of potential energy and kinetic energy of all the atoms, revealing the rate-dependent plastic deformation. Specifically, the plastic deformation for different scratching rates depends on the competition of scratching force, workpiece temperature and tool–workpiece contacting time that affect dislocation evolution. In addition, the results show that the plastic deformation due to scratching of single crystalline Cu is dominated by the dislocation–dislocation interactions. And the scratching induced plastic deformation of polycrystalline Cu is determined by the dislocation-grain boundary (GB) interactions. As for NT polycrystalline Cu under scratching, it is the dislocation–GB–twin boundary (TB) interactions accompanied with the twinning/detwinning process. While the presented MD simulations and the associated conclusions are based on nanocrystalline Cu, it is believed that the current deformation mechanism could also be applied to other face-centered-cubic nanocrystalline metals.

Rate dependent plastic deformation analysis of creeping short fiber composites using the virtual fiber method in the non-reinforced regions

In this research paper, analysis of time-dependent plastic deformation in non-reinforced regions of creeping short fiber composites is carried out under axial tensile stress using the virtual fiber method. As an important application of the present method, shuttles and spaceships, turbine blades and discs are usually subjected to the creep effects. So, analysis of the creep phenomenon is necessary and important in various industries. The nature of the stress distributions is investigated using the equilibrium and constitutive equations, compatibility relations, and incompressibility condition with various boundary conditions, and geometric relations. Analytical and finite element methods are used to predict the stress distributions in the steady state creep of the short fiber composites. Also, the creep analysis (nodal solution) is done by FEM to predict the possible creep rupture, in which, debonding at the interface of the matrix and fiber may happen due to the maximum tensile axial stress values at the interface. In addition to similarities of the present method and experimental results [34], a good agreement of the stress distributions between the present analytical solutions and the FEM results is found. As a result, the short fiber composites with large non-reinforced regions in the axial direction are proper because it increases the factor of safety for design.

Shape optimization of U-shaped damper for improving its bi-directional performance under cyclic loading

A U-shaped damper typically has a stable and saturated hysteretic performance along the in-plane direction and is usually installed in the isolation layer. However experimental study shows that the conventional U-shaped damper presents an unstable hysteretic performance when it sustains bi-directional deformations. Therefore, shape optimization is needed to improve the hysteretic performance of the U-shaped damper. To obtain an optimal shape for the U-shaped damper, a finite element (FE) model was built using a general FE analysis software called ABAQUS. Comparisons of results obtained from FE models with those obtained from experimental studies demonstrated the effectiveness of the FE models. Optimization of a U-shaped damper was carried out using the FE model. The length and shape of the straight part of the U-shaped damper were treated as optimization parameters and the enlarging the end of the straight part was adopted as the improved approach. The formula for the ratio of the energy dissipated by rate-independent and rate-dependent plastic deformation (ALLPD) to the maximum cumulative equivalent plastic strain (PEEQ) was derived though regression analysis. After four levels of optimization processes the optimal shape of the improved U-shaped damper was obtained, and the bi-directional performance was significantly improved compared to that of a conventional U-shaped damper.

Dislocation Mechanics of High-Rate Deformations

Four topics associated with constitutive equation descriptions of rate-dependent metal plastic deformation behavior are reviewed in honor of previous research accomplished on the same issues by Professor Marc Meyers along with colleagues and students, as follow: (1) increasing strength levels attributed to thermally activated dislocation migration at higher loading rates; (2) inhomogeneous adiabatic shear banding; (3) controlling mechanisms of deformation in shock as compared with shock-less isentropic compression experiments and (4) Hall–Petch-based grain size-dependent strain rate sensitivities exhibited by nanopolycrystalline materials. Experimental results are reviewed on the topics for a wide range of metals.

A three-dimensional sharp interface Cartesian grid method for solving high speed multi-material impact, penetration and fragmentation problems

This work presents a three-dimensional, Eulerian, sharp interface, Cartesian grid technique for simulating the response of elasto-plastic solid materials to hypervelocity impact, shocks and detonations. The mass, momentum and energy equations are solved along with evolution equations for deviatoric stress and plastic strain using a third-order finite difference scheme. Material deformation occurs with accompanying nonlinear stress wave propagation; in the Eulerian framework the boundaries of the deforming material are tracked in a sharp fashion using level-sets and the conditions on the immersed boundaries are applied by suitable modifications of a ghost fluid approach. The dilatational response of the material is modeled using the Mie-Gruneisen equation of state and the Johnson–Cook model is employed to characterize the material response due to rate-dependent plastic deformation. Details are provided on the treatment of the deviatoric stress ghost state so that physically correct boundary conditions can be applied at the material interfaces. An efficient parallel algorithm is used to handle computationally intensive three-dimensional problems. The results demonstrate the ability of the method to simulate high-speed impact, penetration and fragmentation phenomena in three dimensions.