Strain-dependent Part Research Articles

Stiffness and toughness of soft, liquid reinforced composites

Soft composites with a soft solid as the matrix and incompressible liquid inclusions as reinforcements have been synthesised in recent times. These soft composites can be designed to respond to external stimuli and offer the prospect of providing a targeted combination of stiffness and toughness. In fact, counter-intuitively, soft solids, when reinforced with liquid inclusions, can become stiffer than the matrix material. This effect is attributed to liquid like surface stresses at the liquid–solid boundaries and is therefore, accentuated when the inclusions are very small. We perform computational homogenisation on liquid inclusion reinforced soft solids with a view to understand the effect of surface stresses on their overall stiffness and initiation toughness. Especially, we look at the hitherto unexplored effect of the surface strain dependent part of surface stresses on the fracture behaviour of soft solids reinforced with fluid inclusions. Finite deformation based hyperelasticity is the computational framework used. Results indicate that, when surface stresses are sensitive to surface strains, stress concentrations at the microscopic level are alleviated. Also, in pre-cracked composites, though initiation of microcracks from the main crack occurs quite early in the deformation history, the microcracks are deflected off the symmetry plane by the liquid inclusions, indicating a possible significant increase in the propagation toughness of the material.

Behavior characterization of visco-hyperelastic models for rubber-like materials using genetic algorithms

• A nonlinear visco-hyperelastic model is numerically studied. • Genetic algorithms are employed to fully characterize the material. • Single and multi objectives versions are considered. • A benchmarking analysis is performed using a known solution. • Uniaxial, biaxial and shear tests are designed to compare the proposed candidates. Rubber-like materials are widely deployed in industry because of their outstanding properties of elasticity and energy dissipation capacity. In order to analyze and improve the behavior of components made of rubber, suitable models for the material behavior must be formulated before their usage in complex evaluations. The aim of such models is to predict the mechanical response of these materials under external loads, using visco-hyperelastic descriptions. In this paper we are interested in reproducing the nonlinear elastic behavior of rubbers as well as the strain-dependent part (viscoelasticity). Typical viscoelastic models are based on linear assumptions, being the viscous part time-dependent but no strain-dependent. Therefore, nonlinear elasticity and linear viscoelasticity are mixed up in the available models. In our work, we propose a model with both parts described as nonlinear. We use a classical hyperelastic model (Mooney–Rivlin) combined with a nonlinear viscous part including both dependencies in strain and time. We also develop a genetic algorithm for searching (optimizing) the model parameters that describe the behavior of this type of materials. We describe simple and multiple objective genetic algorithms for the optimization based on uniaxial and biaxial stresses . We present benchmarking tests for the algorithms, which reproduce different tests with high accuracy and we also discuss the reliability of the model for different stress sates, strain ranges and strain rates. Finally, a real specimen is tested and studied with the algorithm to define its properties according to the material model developed. The study highlights the capabilities of the model to describe complex stress states based on limited information, and it also shows the possible limitations. The procedure we develop can be used as a design tool that allows implementing any simply analyzed material into a realistic material model for further mechanical evaluations, as it is finite elements or similar.

Superposed nonlinear rheological behavior in filled elastomers

In the present work, the rheological properties of a number of filled elastomers under oscillatory shear conditions are investigated. In both linear and nonlinear regimes, the relationships between moduli (G′ and G″) and strain amplitude (γ0) in response to the frequency change display constant shifts along the vertical direction, leading to a striking superposition of the curves. We show that this superposition via a change of its independent-variables can directly lead to a strain-rate frequency superposition. The underlying principle is that the measured dynamical properties can be separated into a linear viscoelastic frequency-dependent part and a nonlinear strain-dependent part. This frequency-deformation separability is experimentally valid for various rubber compounds that differ widely in the polymer structure, the chemical composition, and the type of the filler as well as the shape, the average size, and the distribution of the particles.

Temperature dependence of work hardening in sparsely twinning zirconium

Fully recrystallized commercial Zirconium plates were subjected to uniaxial tension. Tests were conducted at different temperatures (123 K - 623 K) and along two plate directions. Both directions were nominally unfavorable for deformation twinning. The effect of the working temperature on crystallographic texture and in-grain misorientation development was insignificant. However, systematic variation in work hardening and in the area fraction and morphology of deformation twins was observed with temperature. At all temperatures, twinning was associated with significant near boundary mesoscopic shear, suggesting a possible linkage with twin nucleation. A binary tree based model of the polycrystal, which explicitly accounts for grain boundary accommodation and implements the phenomenological extended Voce hardening law, was implemented. This model could capture the measured stress-strain response and twin volume fractions accurately. Interestingly, slip and twin system hardness evolution permitted multiplicative decomposition into temperature-dependent, and accumulated strain-dependent parts. Furthermore, under conditions of relatively limited deformation twinning, the work hardening of the slip and twin systems followed two phenomenological laws proposed in the literature for non-twinning single-phase face centered cubic materials.

Strain-Induced Formation of Fourfold Symmetric SiGe Quantum Dot Molecules

The strain field distribution at the surface of a multilayer structure with disklike SiGe nanomounds formed by heteroepitaxy is exploited to arrange the symmetric quantum dot molecules typically consisting of four elongated quantum dots ordered along the [010] and [100] directions. The morphological transition from fourfold quantum dot molecules to continuous fortresslike quantum rings with an increasing amount of deposited Ge is revealed. We examine key mechanisms underlying the formation of lateral quantum dot molecules by using scanning tunneling microscopy and numerical calculations of the strain energy distribution on the top of disklike SiGe nanomounds. Experimental data are well described by a simple thermodynamic model based on the accurate evaluation of the strain dependent part of the surface chemical potential. The spatial arrangement of quantum dots inside molecules is attributed to the effect of elastic property anisotropy.

Effect of heat treatment on internal friction in ECAP processed commercial pure Mg

Fine-grained commercial pure Mg was prepared by equal channel angular pressing. Heat treatments were carried out on ECAP processed samples to modify the microstructures, such as the density of dislocation, grain size and grain boundary, and their effects on internal friction at room and elevated temperatures have been studied in detail by dynamic mechanical analyzer (DMA). The ECAP processed pure Mg shows a high value of strain independence of internal friction, which is reduced after heat treatment due to the decrease of mobile dislocations, while the strain dependent part obviously increases owing to the larger grain size. Three internal friction peaks are observed during the measurements of temperature dependence of internal friction. The low temperature peak around 100–200°C is considered to be caused by thermally activated grain boundary relaxation, and it is obviously broadened compared with a Debye peak for a single relaxation time. The changes of activation energy and relaxation time distribution of this peak with an increase in grain size were also studied. The other two peaks at the temperature range of 200–350°C are frequency independent and associated with some irreversible structural transformation, they are considered to be related to the recrystallization.

Improved mechanical property and internal friction of pure Mg processed by ECAP

Equal channel angular pressing was performed on the extruded pure Mg. The elongation to failure of the ECAPed pure Mg is enhanced to 27% without sacrificing the strength, which is mainly resulted from both the effective refinement of grain size and the weakening of the basal plane texture. The internal friction mechanisms of magnesium at room and elevated temperature were studied by dynamic mechanical analyzer (DMA). The strain independent internal friction is increased after ECAP processing, while the strain dependent part is obviously decreased. Three internal friction peaks were observed in the temperature dependent internal friction curves. The activation energy is 105kJ/mol for P1 peak, which may be related to the basal dislocation glide controlled by climb of jogs and diffusion of vacancies along dislocations. The activation energy of P2 peak is in the range from 95 to 181kJ/mol, and this obviously broadened peak is associated with grain boundary relaxation. The P3 peak is related to recrystallization.

Convection and diffusion of polymer network strands

A review of several important constitutive equations is herein conducted with an eye towards determining those most suitable for use in modelling polymer melt processing. General principles are invoked for a priori screening of the equations without needing detailed comparison of the model predictions with experimental data. These principles, which are derived from continuum mechanics, thermodynamics and molecular kinetic theory, and dela with convection and diffusion of entangled polymer strands during flow, are: (1) During sudden deformations, the stress is a unique function of the total strain. (2) The second law of thermodynamics holds for all deformations. (3) The constitutive equation can be derived from a plausible molecular model which describes the convection and diffusion. (4) The model parameters can be determined by a reasonable number of rheometric experiments. Based on these principles, it is concluded that separable free energy models are the most promising. These are either BKZ integral models with a kernel factorable into a time-dependent and a strain-dependent part. or sets of Maxwell-type differential equations that employ a generalized convected derivative, and that are linear in stress in the absence of flow.

Nonlinear shear creep and constrained elastic recovery of a LDPE melt

Shear creep and constrained elastic recovery experiments on a well characterized low-density polyethylene melt are reported. The temperature dependence of the shear strain and the primary normal stress difference is discussed in detail. Comparison is made with predictions of a strain-dependent single integral constitutive equation, which has already been successfully used for the same polymer melt to describe the stress growth after sudden imposition of a constant shear rate flow and stress relaxation after cessation of steady shear flow. It should be emphasized that this constitutive equation contains no adjustable parameters. The linear-viscoelastic part of the memory function is related to the linear-viscoelastic relaxation spectrum, while the nonlinear, strain-dependent part was determined from rapid-strain experiments. In the case of a prescribed shear stress history the resulting integral equation cannot be solved by closed integration but has to be inverted by numerical methods. Agreement between theoretical predictions and experimental data is rather encouraging for shear strain and primary normal stress difference during creep and retardation tests. Within experimental error, the strain and shear rate dependence of the recoverable portion of the total strain can be correctly predicted.

Internal Friction and Critical Stress of Copper Alloys

The effects of strain amplitude on the internal friction and the Young's modulus of polycrystalline specimens of copper alloys (Cu–Zn, Cu–Al, Cu–P) with various concentrations of solute atoms have been investigated. The results are: 1. The critical stress, up to which the internal friction and the Young's modulus are almost independent of strain amplitude, increases with concentration of solute atoms, showing a considerable harmony with the theoretical stress obtained by Mott. 2. The strain-independent part of the internal friction decreases as a power function of concentration of solute atoms, although its numerical value depends largely on the pre-treatment. 3. The strain-dependent part of the internal friction and the fractional change of Young's modulus are represented by two parallel fomulae, as in the theory of Nowick. But the factors of strain-dependencies seem to increase with concentration of solute atoms. 4. The internal friction and the Young's modulus are both almost independent of frequency in the range between 900 and 10,000 cps at at room temperatures.