Large Strain Experiments Research Articles

High-rate strength response of tantalum from dynamic hole closure experiments

The science and engineering communities have significant interest in experimental platforms to evaluate and improve models for dynamic material deformation. While well-developed platforms exist, there are still gaps to fill for strain and strain rate conditions accessed during impact and other high-rate loading scenarios. To fill one such gap for strength measurements, a platform was recently developed that accesses high strain rate (≥105/s) and large strain (≥50%) conditions by measuring the transient closure of a cylindrical hole using in situ x-ray imaging. In the work reported here, further refinement of the platform is performed to reduce the potential effects of porosity and anelasticity on the measurement. This helps us to isolate the strength effects that are the focus of the experiment. The updated experimental configuration employs a two-layer flyer design and elongated target to reduce the magnitude of the tensile excursions associated with rarefaction wave interactions. This allows for a more direct assessment of strength models commonly used for dynamic simulations of metals. We apply the new technique to well-characterized tantalum material, allowing for a robust connection to other experimental techniques. Deformation localization can be a concern in large strain experiments, and to help inform future use of the experimental platform, we use simulations with a sub-zone treatment of shear banding to explore potential localization behavior. Overall, we develop and utilize an experimental configuration with improved isolation of strength effects that can be applied to an expanded range of materials.

Physics-based plasticity model incorporating microstructure changes for severe plastic deformation

During machining processes, materials undergo severe deformations that lead to different behavior than in the case of slow deformation. The microstructure changes, as a consequence, affect the materials properties and therefore influence the functionality of the component. Developing material models capable of capturing such changes is therefore critical to better understand the interaction process–materials. In this paper, we introduce a new physics model associating Mechanical Threshold Stress (MTS) with Dislocation Density (DD) models. The modeling and the experimental results of a series of large strain experiments on polycrystalline copper (OFHC) involving sequences of shear deformation and strain rate (varying from quasi-static to dynamic) are very similar to those observed in processes such as machining. The Kocks–Mecking model, using the mechanical threshold stress as an internal state variable, correlates well with experimental results and strain rate jump experiments. This model was compared to the well-known Johnson–Cook model that showed some shortcomings in capturing the stain jump. The results show a high effect of rate sensitivity of strain hardening at large strains. Coupling the mechanical threshold stress dislocation density (MTS–DD), material models were implemented in the Abaqus/Explicit FE code. The model shows potentialities in predicting an increase in dislocation density and a reduction in cell size. It could ideally be used in the modeling of machining processes.

Rheological properties of tough hydrogels based on an associating polymer with permanent and transient crosslinks: Effects of crosslinking density

We studied the rheological and mechanical properties of a series of poly(vinyl alcohol) dual crosslink hydrogels, permanently crosslinked by glutaraldehyde and transiently crosslinked by borate ions, at various crosslinking densities. The contribution of the chemical and physical crosslinks to the dynamic moduli was first determined with linear oscillatory tests, and the additivity of the two contributions was validated. The single relaxation time of the system was interpreted as the physical bond breaking time which can be slowed down by reassociation of the open physical bonds before full relaxation. By comparing the Rouse relaxation time of the strand between two adjacent crosslinks with the healing time of the physical bonds, an increase in the relaxation time with decreasing density of physical crosslinks was explained. In all cases, the extensibility and stress at break of the gels were found to increase with the addition of physical crosslinks, but the extensibility increased the most for the smallest amount of chemical and physical crosslink densities while the stress at break increased the most for the most physically crosslinked system with a low chemical crosslink density. This strongly suggests that the toughening mechanism due to the presence of transient bonds can only be active on a network with a low density of chemical crosslinks. In large strain experiments, the tensile stress could be separated into a strain-dependent and a time-dependent term for all the crosslinking densities studied, and master curves of the reduced stress as a function of time were obtained. This showed that the chemical and physical crosslinks independently and additively contribute to the viscoelasticity of the dual crosslink gel.

Viscoelasticity of cross-linked actin networks: Experimental tests, mechanical modeling and finite-element analysis

Filamentous actin is one of the main constituents of the eukaryotic cytoskeleton. The actin cortex, a densely cross-linked network, resides underneath the lipid bilayer. In the present work we propose a continuum mechanical formulation for describing the viscoelastic properties of in vitro actin networks, which serve as model systems for the cortex, by including the microstructure, i.e. the behavior of a single filament and its spatial arrangement. The modeling of the viscoelastic response in terms of physically interpretable parameters is conducted using a multiscale approach consisting of two steps: modeling of the single filament response of F-actin by a worm-like chain model including the extensibility of the filament, and assembling the three-dimensional biopolymer network by using the microsphere model which accounts for filaments equally distributed in space. The viscoelastic effects of the network are taken into account using a generalized Maxwell model. The Cauchy stress and elasticity tensors are obtained within a continuum mechanics framework and implemented into a finite-element program. The model is validated on the network level using large strain experiments on reconstituted actin gels. Comparisons of the proposed model with rheological experiments recover reasonable values for the material parameters. Finite-element simulations of the indentation of a sphere on a network slab and the aspiration of a droplet in a micropipette allow for further insights of the viscoelastic behavior of actin networks.

The influence of dolomite on the plastic flow of calcite: Rheological, microstructural and chemical evolution during large strain torsion experiments

Aggregates composed of calcite and dolomite have been deformed and annealed at high temperature (700–800 °C) and high pressure (300 MPa) to investigate the mutual effects of deformation and chemical reaction, strain partitioning, fabric development and phase segregation in a polyphase rock. Samples deformed in torsion displayed an almost Newtonian creep with stress exponent of 1.7 ± 0.3. Specimens were deformed up to a maximum shear strain of γ = 10 and developed a clear texture documented by electron back-scatter diffraction measurements in both calcite and dolomite. Both the texture and the foliation created during the large strain experiments display a monoclinic symmetry closely reproducing that of naturally deformed carbonate marbles, with the preferred orientation of the c-axes inclined against the sense of shear. Detailed microstructural investigation shows that grains are internally strain-free and that grain boundaries are preferentially aligned in straight segments, implying that deformation occurred through a combination of grain boundary sliding and diffusion processes accommodated by dislocation activity. Chemical investigations performed on both statically annealed and torsion samples indicate that deformation may have an important influence on the phase equilibrium of a reacting system. Calcite grains deformed with excess of dolomite with respect to the equilibrium were able to incorporate higher amounts of Mg within the calcite lattice than the static samples, as documented by electron probe microanalysis. Moreover, the above analysis documented that reaction rate was faster in torsion than in static experiments at the same conditions of pressure and temperature.

Mechanical behavior of an acrylic elastomer used in dielectric elastomer actuators

The paper reports on extensive experimental work for the characterization of a dielectric elastomer used as base material for electroactive polymer (EAP) actuators. The mechanical behavior of the acrylic elastomer VHB 4910 is characterized using large strain experiments (uniaxial and equibiaxial deformation) under force and displacement controlled loading conditions. Next to tensile and relaxation tests, experiments were conducted also using the so-called circular actuators. Over 40 actuators were produced (with different in-plane pre-strain levels) and activated with voltages between 2000 and 3500 V. The experimental data are useful for determining constitutive model parameters as well as for validating models and simulation procedures for electromechanical coupling in EAP actuators. A novel approach is proposed for finite element analysis of dielectric elastomer actuator, which has been used in the present work for the evaluation of the experimental observations from circular actuators. Material parameters of different visco-hyperelastic models have been determined from a subset of the experimental data and the predictive capabilities of the models evaluated through comparisons with the remaining data. The prediction of the circular actuator behavior was satisfactory so that the proposed models might be useful for actuator design and optimization purposes. Limitations of the proposed constitutive model formulation are presented.

Cross Linking and Rheological Characterization of Adsorbed Protein Layers at the Oil−Water Interface

The dilatational rheological properties of cross-linked protein layers adsorbed at the oil-water interface were investigated with help of a modified drop tensiometer allowing successive replacements of the external phase. This setup enables one to perform cross-linking reactions at the interface only, that is, without any contact between the cross-linking agent and protein molecules in solution, under continuous monitoring of the interfacial tension. The mechanical properties of the resulting interface were investigated with dilatational large strain experiments. Measured rheological properties were related to the expected stability of an emulsion against disproportionation by considering the ratio of the interfacial elasticity to the interfacial tension. In an attempt to increase this ratio to improve the resistance against disproportionation, experiments were performed with densified protein layers obtained via reduction of the droplet area prior to cross linking. To highlight the influence of the protein morphology on the dilatational rheological properties of the cross-linked adsorbed layers, experiments were performed with random coil (beta-casein) as well as globular (beta-lactoglobulin) proteins. Glutaraldehyde was used as a cross-linking agent. Experiments were performed at 55 degrees C and pH 7.0 in 20 mM imidazole buffer for later comparison with enzymatically cross-linked adsorbed protein layers. The present work demonstrated substantial qualitative and quantitative differences in the interfacial rheological properties of cross-linked random coil and globular proteins.

Dynamic recrystallization and strain softening of olivine aggregates in the laboratory and the lithosphere

Abstract The effects of dynamic recrystallization on the deformation mechanisms and rheology of olivine aggregates in the laboratory and the lithosphere are reviewed in this paper. The low-strain rheology of olivine is well documented; however, deformation in the lithosphere often involves large strains. Large strain experiments show that recrystallization can result in both hardening and softening during deformation. Moderate strain softening in experimental shear and torsion can be explained by the operation of dislocation-accommodated grain boundary sliding in bands of fine recrystallized grains. Data on the temperature dependence of recrystallized grain size are needed to extrapolate the effects of dynamic recrystallization to the lithosphere. Theories of dynamic recrystallization suggest that grain size is strongly stress dependent and moderately temperature dependent. A re-analysis of experimental grain size data indicates that the recrystallized grain size is temperature independent for olivine aggregates with low water content (<300 ppm H/Si). Rheological regime maps have been constructed for the lithospheric mantle. The maps suggest that grain size sensitive power law creep, involving both grain boundary sliding and dislocation creep, will produce strong strain softening, greater than found so far in experimental studies, in dry and wet lithosphere shear zones.

Measurement of Lateral Deformation in Natural and High Damping Rubbers in Large Deformation Uniaxial Tests

Abstract In testing the mechanical behavior of rubbers, the incompressibility assumption is used to predict the deformed cross section under loading and thereby to calculate the true stress. There are, however, cases where rubbers can undergo considerable volumetric deformation in large strain experiments. Microstructural investigation through a scanning electron microscope was carried out on a void-filled natural rubber specimen to clarify the effect of voids on the compressibility feature. The microstructure of the natural rubber was observed qualitatively and quantitatively in uniaxial tension and compared to the microstructure in the underformed condition. The existence of the compressibility feature in the void-filled rubber was confirmed from a microstructural viewpoint. The findings indicate the necessity of accurate measurement of the deformed cross section in mechanical tests to obtain the true stress. To this end, an experimental setup capable of measuring the deformed cross section of the rubber specimens subjected to large uniaxial compression is proposed. To do this, the accuracy of laser beams is used for measurement of distance and a mechanical jig is developed to synchronize the movement of the laser transducer with the vertical crosshead of the load cell of a computer-controlled servohydraulic testing machine. Thus the constraints associated with conventional strain gages in measuring large strains are overcome. Finally, two natural rubber specimens and one high damping rubber specimen were tested in the proposed setup to display the adequacy of the developed device in measuring lateral deformation of rubber-like highly deformable solids in large strain uniaxial testing.

Mechanical response of amorphous and semicrystalline poly(ethylene terephthalate) and modelling in frame of quasi point defect theory

The thermomechanical activation of deformation in amorphous and (38%crystalline) semicrystalline poly(ethylene terephthalate) (PET) has been investigated using dynamic mechanical tests and large strain experiments. Activation parameters for both materials are determined in the neighbourhood of the glass transition temperature using stress relaxation experiments. The complete mechanical behaviour of amorphous PET is then analysed in the frame of a molecular model or ‘quasi point defect’ theory. With this aim, a new method is proposed, based on only three isochronal measurements, and leading to the determination of the set parameters. This method makes it possible to reproduce the stress–strain curve over a range of temperatures, as well as the relevant activation parameters. Finally some qualitative explanations are given for the mechanical behaviour of semicrystalline PET.

Simple torsion of isotropic, hyperelastic, incompressible materials with limiting chain extensibility

The purpose of this research is to investigate the simple torsion problem for a solid circular cylinder composed of isotropic hyperelastic incompressible materials with limiting chain extensibil- ity. Three popular models that account for hardening at large deformations are examined. These models involve a strain-energy density which depends only on the first invariant of the Cauchy- Green tensor. In the limit as a polymeric chain extensibility tends to infinity, all of these models reduce to the classical neo-Hookean form. The main mechanical quantities of interest in the torsion problem are obtained in closed form. In this way, it is shown that the torsional response of all three materials is similar. While the predictions of the models agree qualitatively with experimental data, the quantitative agreement is poor as is the case for the neo-Hookean material. In fact, by using a global universal relation, it is shown that the experimental data cannot be predicted quantitatively by any strain-energy density which depends solely on the first invariant. It is shown that a modification of the strain energies to include a term linear in the second invariant can be used to remedy this defect. Whether the modified strain-energies, which reflect material hardening, are a feasible alternative to the classic Mooney-Rivlin model remains an open question which can be resolved only by large strain experiments.

A Clamp-On Strain Transducer for Use on Geologic Materials

Abstract The design, calibration and application of a clamp-on type strain transducer for the simultaneous monitoring of axial and transverse strain under both uniaxial and triaxial test conditions is described The transducer attaches directly to the test specimen and utilizes a number of linear variable differential transformers to provide average strain data. Tests have been carried out on specimens of a number of metallic (steel, brass and aluminum) and geologic materials (granite, limestone and sandstone) at confining pressures of up to 5,000 psi. No difficulties are contemplated in using the psi. No difficulties are contemplated in using the transducer at confining pressures of 10,000 psi and higher. Introduction In order to determine the deformation characteristics of a solid, the requirements are: a suitably shaped test specimen; a system for applying the necessary loads to the test specimen; and a system for monitoring the resulting strains. This paper is concerned with the third requirement and describes the development of a clamp-on strain transducer for the measurement of both axial and transverse strain in specimens of geologic material under both uniaxial and triaxial loading conditions. For studies under uniaxial test conditions several workers have designed transducers for specific research projects. In many cases sufficient time was not available to develop and qualify these transducers for general use. At least one commercial firm manufactures a clamp-on type axial and transverse-strain transducer that utilizes differential transformers and is designed specifically for use on geologic materials. The development of suitable strain transducers for use on geologic materials under triaxial test conditions** has been extremely limited. Several methods have been utilized in which axial specimen strain was determined by external measurement of loading piston displacement. Although such methods have proved more or less satisfactory for experiments where large strains were involved, their use in experiments where small strains (less than 0.5 percent) and small strain increments ( 0.001 percent) are of interest are unsatisfactory due to a percent) are of interest are unsatisfactory due to a number of factors. For example, even with extremely fine polishing of specimen end-surface will compress surface will contain a large number of asperities. Under a compressive load the surface will compress rapidly upon initial loading due to failure or the development of plastic deformation in the individual asperities. Strain values based on deformation measurements made across such a surface would be seriously in error, particularly at low loads. Furthermore, the mechanical stability and accuracy of an external strain measuring system, although not too difficult to achieve in large strain experiments, becomes a major difficulty when small strains are being considered. Bonded resistance-type strain gauges provide one means of conveniently measuring axial and transverse strain in both uniaxial and triaxial tests. These have been used successfully for the investigation of the mechanical behavior of geologic materials. The inability to calibrate directly this type of gauge and the cost of gauges required for any extensive test program suggests that considerable effort should be directed toward the development of a clamp-on type strain transducer that could be utilized under both uniaxial and triaxial test conditions. Besides the transducer described, we are familiar with two other clamp-on transducers designed for use under triaxial test conditions one a purely experimental unit, incorporating bonded resistance strain gauges, being utilized by Mazanti, and the other made by Structural Behavior Engineering Laboratories in Phoenix that utilizes linear differential transformers as sensing elements.