Uniaxial State Research Articles

Transition from equatorial to whole-shell buckling in embedded spherical shells under axisymmetric far-field loading

Motivated by the need to understand the compression of syntactic foam composites, we solve the canonical problem of buckling of a thin spherical shell embedded in a medium that is much softer than the shell. Syntactic foams comprise shells that usually have diameters in the micron range and are distributed inside a matrix medium that is typically polymeric. Such foams are commonly employed in a range of applications where high stiffness to density ratios are of interest. This can be tailored via choice of shell thickness and type, and filler volume fraction.Embedded glass microspheres fracture under sufficiently high loading, leading to a permanent softening of the syntactic foam. Embedded polymeric Expancel microspheres however are thought to buckle because the associated softening of the foam is recoverable. We determine critical buckling pressures in the practical scenarios of hydrostatic and uniaxial compressive loading states by solving a more general uniaxial loading problem. Critically, we investigate the thin-stiff shell limit, which yields very different results from a standard thin-shell limit under the assumption that the shell and matrix have stiffnesses of the same order. We employ nonlinear shell theory, linear stability analysis and rigorous asymptotics. We present numerical results for the critical buckling pressure over a wide range of shell thickness and contrasts in shell/matrix stiffnesses. Results for hydrostatic loading are compared against existing analytical and semi-analytical models for embedded shells. Under uniaxial loading we note that there are two distinct regions of parameter space, corresponding to equatorial and non-equatorial buckling regimes. The two non-dimensional parameters of critical importance are the shell thickness to radius ratio h/R and the shell to matrix shear modulus ratio μm/μs. By fixing one whilst varying the other we observe and describe the transition between these two regimes.

Ogden material calibration via magnetic resonance cartography, parameter sensitivity and variational system identification.

Contemporary material characterization techniques that leverage deformation fields and the weak form of the equilibrium equations face challenges in the numerical solution procedure of the inverse characterization problem. As material models and descriptions differ, so too must the approaches for identifying parameters and their corresponding mechanisms. The widely used Ogden material model can be comprised of a chosen number of terms of the same mathematical form, which presents challenges of parsimonious representation, interpretability and stability. Robust techniques for system identification of any material model are important to assess and improve experimental design, in addition to their centrality to forward computations. Using fully three-dimensional displacement fields acquired in silicone elastomers with our recently developed magnetic resonance cartography (MR-u) technique on the order of greater than [Formula: see text], we leverage partial differential equation-constrained optimization as the basis of variational system identification of our material parameters. We incorporate the statistical F-test to maintain parsimony of representation. Using a new, local deformation decomposition locally into mixtures of biaxial and uniaxial tensile states, we evaluate experiments based on an analytical sensitivity metric and discuss the implications for experimental design. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

A Damage Model of Concrete including Hysteretic Effect under Cyclic Loading.

A novel damage model for concrete has been developed, which can reflect the complex hysteresis phenomena of concrete under cyclic loading, as well as other nonlinear behaviors such as stress softening, stiffness degradation, and irreversible deformation. The model cleverly transforms the complex multiaxial stress state into a uniaxial state by equivalent strain, with few computational parameters and simple mathematical expression. The uniaxial tensile and compressive stress–strain curves matching the actual characteristics are used to accommodate the high asymmetry of concrete in tension and compression, respectively. Meanwhile, an unloading path and a reloading path that can reflect the hysteresis effect under cyclic loading of concrete are established, in which the adopted expressions for the loading and unloading characteristic points do not depend on the shape of the curve. The proposed model has a concise form that can be easily implemented and also shows strong generality and flexibility. Finally, the reliability and correctness of the model are verified by comparing the numerical results with the three-point bending beam test, cyclic loading test, and a seismic damage simulation of the Koyna gravity dam.

Micro-strains, local stresses, and coherently diffracting domain size in shock compressed Al(100) single crystals

In situ x-ray diffraction (XRD) measurements and their analysis in Al single crystals shock compressed along the [100]-direction were utilized to examine shock wave induced microstructural heterogeneities. High-resolution XRD line profiles for the 200, 400, and 600 Al peaks were measured in uniaxial strain compression states to either 5.6 or 11.7 GPa and partial stress release to 3.5 or 6.6 GPa, respectively. Broadening of the XRD line profiles was analyzed to determine the magnitude of the longitudinal micro-strain distribution (0.195% and 0.28% full width at half maximum for 3.5 and 6.6 GPa stresses, respectively) and the size of coherently diffracting domains (CDDs) (0.125 and 0.07 μm for 3.5 and 6.6 GPa stresses, respectively). From the longitudinal micro-strain distributions, the distribution of local stress differences (or stress deviators) was obtained in the shocked state. The full width at half maximum of this distribution, a measure of the local stress inhomogeneities, is greater than half of the macroscopic stress difference for both 3.5 and 6.6 GPa peak stresses, suggesting considerable variation in local stress deviators. The CDD sizes determined here are comparable to characteristic length scales for defect-free regions determined from defect density measurements in post-shock recovery experiments. The present work represents an important step in understanding material microstructure and inhomogeneities in the shock-compressed state.

Short-term creep strain localization in 12%Cr turbine steel under biaxial stress states at 600 °C via digital image correlation

FV566 martensite steel is an important material for turbine components whose extreme operating conditions potentially give rise to the creep deformation. This paper investigates the short-term creep strain localization of this steel under biaxial stress states at 600 °C. Short-term creep tests utilizing digital image correlation (DIC) were performed on different geometries of specimens with various applied stresses to investigate the strain and damage localization. Using the macroscopic creep data obtained from uniaxial specimens, finite element (FE) models were developed to evaluate stress redistribution and damage evolution. Contrast to the uniaxial state, strain heterogeneities at biaxial states were very similar under different stress levels and the notch tends to extend the creep life. The ‘crack’ growth rate was low during the steady-state creep and increases significantly at the tertiary stage creep, especially close to failure time. Further microstructure characterization involving SEM and EBSD had shown that the formation, growth and coalescence of martensite cracking and microcavities in near fracture frontier area during inelastic deformation are the main creep damage mechanism. By linking DIC, FE and microstructure results, the short-term creep fracture mechanism under biaxial stress states was thoroughly discussed.

Statistical Analysis of the Distribution of the Schmid Factor in As-Built and Annealed Parts Produced by Laser Powder Bed Fusion

This study documents a systematic analysis of the global Schmid factor for different deformation mechanisms in α′/α and β-grains in different forms of direct metal laser sintered (DMLS) Ti6Al4V(ELI) based on EBSD data. A novelty of this study is the use of these data to calculate the values of the Schmid factor and the subsequent determination of their distribution and frequency, which, when compared to the slip systems of crystal structures, helps in determining the favourable slip systems in play. Both retained β-grains and reconstructed prior β-grains were considered in this analysis. The reconstruction of the prior β-grains was executed using the Automatic Reconstruction of Parent Grain for EBSD data (ARPGE) program. The distribution of the global Schmid factor for these Ti6Al4V phases was calculated using the MATLAB-based MTEX toolbox program. This analysis of deformation modes in the α′/α-phase was based on a uniaxial load state acting on the x, y, and z axes, while only the load along the build direction (x-direction) was considered in the analysis of deformation mechanisms in the β-phase of the alloy. The results of this study showed that the DMLS build direction influenced the distribution of the global Schmid factor for the basal slip system of α′/α-grains in as-built specimens and those samples that were heat treated below the α→β transformation temperature.

Analytically predicting the burst pressure of composite rupture discs by considering nonlinear strain path

The composite rupture discs are a safety device that burst at the specified pressure and prevent overpressure and damage to equipment by releasing the fluid at high flow rates. The burst pressure is determined by the bulge formed and then slotted sheet metal. In the hydraulic bulge-forming stage, the sheet is subject to biaxial stress, and after slotting, it is subject to uniaxial tensile stress. Due to the change in the loading type, the sheet has a nonlinear strain path during the bulge-forming and burst test after slotting. In the nonlinear strain paths, the equivalent failure strain changes according to the strain path. In this paper, based on the FEM simulation results and experimental tests, the relationship between plastic failure strain in uniaxial tensile state and the maximum pre-strain due to bulge forming is investigated. According to the results of this paper, when the sheet sufficiently forms under hydraulic pressure, the maximum strain in hydraulic bulge-forming and the equivalent failure strain after slotting are equal. Based on this result, analytical relations were developed to predict the burst pressure of composite rupture discs. This relation estimates the burst pressure of composite rupture discs with an average error of about 13%.

Using the Smith-Watson-Topper Parameter and Its Modifications to Calculate the Fatigue Life of Metals: The State-of-the-Art.

The Smith-Watson-Topper parameter (SWT) in its original form was designed to estimate the fatigue life of metal materials in a uniaxial load state (tension–compression) in the range up to fatigue crack initiation, with non-zero mean values. This parameter is based on the analysis of both stress and strain. Therefore, the stress–strain criterion is the focus, rather than the energy criterion. This paper presents the original SWT model and its numerous modifications. The first part presents different versions of this parameter defined by the normal parameters. Then, it presents versions defined through the tangent parameter and the most promising parameter defined through the tangent and normal parameters. It was noted that the final form of the equivalent value is defined either by stress or by an energy parameter. Therefore, the possible characteristics from which the fatigue life can be determined are also presented.

Ionic Control over Ferroelectricity in 2D Layered van der Waals Capacitors.

The van der Waals layered material CuInP2S6 features interesting functional behavior, including the existence of four uniaxial polarization states, polarization reversal against the electric field through Cu ion migration, a negative-capacitance regime, and reversible extraction of Cu ions. At the heart of these characteristics lies the high mobility of Cu ions, which also determines the spontaneous polarization. Therefore, Cu migration across the lattice results in unusual ferroelectric behavior. Here, we demonstrate how the interplay of polar and ionic properties provides a path to ionically controlled ferroelectric behavior, achieved by applying selected DC voltage pulses and subsequently probing ferroelectric switching during fast triangular voltage sweeps. Using current measurements and theoretical calculations, we observe that increasing DC pulse duration results in higher ionic currents, the buildup of an internal electric field that shifts polarization loops, and an increase in total switchable polarization by ∼50% due to the existence of a high polarization phase which is stabilized by the internal electric field. Apart from tuning ferroelectric behavior by selected square pulses, hysteretic polarization switching can even be entirely deactivated and reactivated, resulting in three-state systems where polarization switching is either inhibited or can be performed in two different directions.

PERIODIC REINFORCEMENT OF TWO PRE-STRESSED STRIPS BY FINISHED SUPPORTING ELEMENTS

The qualitative and quantitative influence of initial (residual) stresses on the law of distribution of contact characteristics at interaction of elastic finished overlays (stringers), at their placement, with two prestressed strips which are clamped by one edge. In general, the research was carried out for the theory of great initial (ultimate) and two variants of the theory of small initial deformations within the framework of linearized theory of elasticity with the elastic potential having arbitrary structure for compressible and incompressible bodies. Fourier integral methods, methods for solving harmonic differential equations, singular integral-differential equations and numerical methods were used too. It is assumed that in the contact area the initial stress state, with a certain degree of accuracy, is considered homogeneous. We make the assumption that the elastic band with initial (residual) stresses is in the conditions of plane deformation. Also, for an elastic lining loaded with both vertical and horizontal forces, the generally accepted model of beam bending in combination with the model of uniaxial stress-strain state of the elastic lining is valid. A singular integral-differential equation with the Gilbert kernel was derived, which allows us to solve this problem. We find the analytical solution of the equation in the form of series from the Jacobi function. Numerical studies were performed for materials with elastic potentials of harmonic type (compressible bodies) and elastic potentials of Bartenev-Khazanovich and Treloar (incompressible bodies). Numerical studies have been performed for materials with elastic potentials of harmonic type (compressible bodies) and elastic potentials of Bartenev-Khazanovich and Treloir (incompressible bodies). We have considered the case when all periodically placed pads that support elastic bands with the initial stresses were loaded with tangential force. Analysis of numerical results shows a significant effect of initial (residual) stresses on the distribution of contact characteristics of periodically reinforced strips with thin reinforcing elements. The results obtained can be used for engineering calculations for the strength and durability of structures, taking into account the initial stresses for a wide range of structural materials.

Hyper‐viscoelastic characterization of highly filled rubber compound: Extending approach for geometrical defect analysis

AbstractThe work provides insight into the hyper‐viscoelastic characterization of highly filled rubber compound with low structured carbon black, further examining geometrical defects using finite element (FE) simulations. The complete force‐extension behavior and stress relaxation (various strain levels [10%–100%]) in a uniaxial state of stress are reported. The extension at break is reduced by more than 42% for geometrically defective specimens. The breakage of filler–filler interaction attains equilibrium at 75% strain in stress relaxation experiment. Beyond this, the relaxation depends majorly on polymer chains. Hyperelastic material models, namely Ogden, Yeoh, and Arruda–Boyce, are chosen for the present investigation. A Prony series is used for capturing the viscoelastic properties of relaxation times. The combined utilization of the Ogden law and the Prony series in FE simulations provides an excellent match in capturing the experimental features. The effect of geometrical defects is illustrated via solving a series of numerical as well as experimental results. The simulated shape/profile changes such as necking and elliptical formation are excellently comparable with experimental results. Strain localization study shows the stress concentration zone and early prediction of failure location. The methodology presented is potentially crucial for understanding and simulating engineering rubber product's complex structures in general.

Methods Development for the Constrained Elastic Modulus Investigation of Organic Material in Natural Soil Conditions.

Compressibility is one of the most important mechanical properties of soil. The parameter that characterizes compressibility is the constrained modulus of elasticity. Knowledge of this is important to calculate the settlement of a structure foundation on peat material. According to soil classification by EN ISO 14688-2, peat is an organic soil that contains min. 20% organic matter. It is a highly organic type of soil. Peat material has large compressibility. The value of the constrained elasticity modulus for peat is ca. 400 kPa, while it may be ca 1.0–1.6 MPa for consolidated peat. Due to the extensive range of the modulus, experimental research in this field is proposed. It is suggested to load the peat material layer with an embankment and to determine its total settlement. Based on this, a program was developed to determine the settlement–strain relationship. The authors propose an approach according to two models: the first is based on constant stress distribution in the soil with an oedometer test. The second considers the variability of stresses in the soil and the influence of the loaded area. Both methods were tested based on numerical simulations, and then an experimental field in Szczecin was used. The formulae for the constrained modulus of elasticity measurement were derived; in practical conditions, a uniaxial deformation state can be used with the combination of the total settlement.

Understanding asteroidal failure through quasi‐static compression testing and 3‐D digital image correlation of the Aba Panu (L3) chondrite

AbstractA comprehensive understanding of the mechanical strength and failure mechanisms of asteroids is essential for the development of hazard mitigation strategies and in situ resource extraction. In this study, the Aba Panu (L3) ordinary chondrite meteorite is investigated to understand its failure response under compressive loading. Compression experiments were conducted on ten 1 cm cubes under quasi‐static conditions in constant displacement control mode at room temperature. Three‐dimensional (3‐D) digital image correlation (DIC) was used to measure the full‐field deformation and strain. These data were used to determine the elastic modulus and local strain distribution, and investigate the effects of the mineralogical and structural heterogeneity on the crack formation and growth sites. Aba Panu exhibits brittle failure during compression with a range of failure strength from 361.7 to 578.0 MPa. Axial splitting and multiple fracturing occur during the uniaxial compressive state of stress. Ultrasonic tests were used to calculate elastic moduli from sound speeds and compared with the results of L‐type ordinary chondrites from the literature. Characterization results from electron microprobe analysis identified different elements and areal distribution of mineral phases and pre‐existing cracks. In general, the DIC results did not show correlations between crack initiation and specific mineralogical or textural components in this meteorite, such as chondrules or metals/sulfide grains, suggesting that the pre‐existing microcracks and porosity control the Aba Panu failure mechanisms.

Polyurethane Treated in Ar/C2H2/Ar Plasma: Towards Deformable Coating with Improved Albumin Adsorption

Plasma modification of soft polymeric surfaces has many prospects in creating biomedical devices. The deformability of the obtained coatings should be studied, as the usage of such materials implies mechanical loads. Polyurethane (a two-phase synthetic polymer) treated in argon/acetylene plasma, with post-treatment in argon plasma, was investigated. A carbon-containing nanocoating (discontinuous mesh-like structures) with structural–mechanical inhomogeneities is formed by the action of Ar/C2H2 plasma. The heterogeneities of the coating are due to the complex structure of the initial substrate and short duration of treatment; as the treatment time increases, the coatings become homogeneous, but their stiffness rises. The treated surfaces in the uniaxial tensile state have micro and/or nanocracks in certain cases of plasma treatment. This is associated with an increased elastic modulus of the coatings. The coatings without cracks have regions with sufficiently alternating stiffness. Post-treatment in argon plasma increases wettability and free surface energy, positively affecting the adsorption of albumin. The stiffness of such coatings increases, becoming more homogeneous, which slightly reduces their crack resistance. Thus, plasma coatings on soft polymers operating under mechanical loads without causing damage should have sufficiently low stiffness, and/or structural-mechanical heterogeneities that provide redistribution of stress.

Study on the mechanical behaviour of Columnar Jointed Rock Mass under uniaxial compression state

The columnar joint is a special type of primary joints which the cross sections are mostly quadrilateral, pentagonal and hexagonal. Intact rock mass is always cut by columnar joints into regular or irregular rock prisms, resulting in poor properties. With the expansion of large-scale engineering activities, a number of hydropower engineering such as Baihetan hydropower station, Xiluodu hydropower station and Ertan hydropower station, have encountered columnar jointed rock mass. The existence of columnar jointed rock mass poses a challenge to the design, construction and safe operation of these projects. To understand the mechanical behaviour of columnar jointed rock mass, uniaxial compression tests were carried out on artificial specimens made from rock-like materials. In the experiments, a self-designed pouring apparatus was used to prepare the columnar jointed rock-like specimens. Based on the experimental results of axial stress–axial strain curves, the strength and deformation of columnar jointed rock mass were investigated. The effect of columnar joint inclination angle on the mechanical behaviour of columnar jointed rock mass was analysed. It is found that the columnar jointed rock masses are characterized by significant anisotropy. The strength of columnar joint plays a significant role on the mechanical response of columnar jointed rock mass. The study Formatting the text

Energy based fracture initiation criterion for strain-crystallizing rubber-like materials with pre-existing cracks

Fracture prediction is indispensable for polymers, like rubbers, which have a broad range of applications mainly due to their high extensibility. The phenomenon known as strain-induced crystallization further contributes to the fracture toughness of certain rubbers. In this study, a criterion based on internal bond energy, incorporating the effects of crystallization, is proposed to predict fracture initiation in rubber-like materials with pre-existing cracks. First, a multi-scale mechanical model is developed for characterizing the behavior of rubber when subjected to both uniaxial and biaxial deformation states. At the microscale, both the amorphous and crystalline chain segments are modeled as elastic in order to consider the energy contribution by the molecular bond distortions. This internal energy is considered along with the entropic and crystalline free energy for each chain. In the chain model, the effects of loading condition and the relative orientation of a chain on its crystallinity are taken into account. At the macroscopic scale, an existing crystallinity distribution function is adapted and a mixed finite element formulation with an augmented Lagrangian multiplier is utilized to impose the incompressibility constraint. A non-affine maximal advance path constraint based homogenization model is utilized for bridging the two scales. Its potential to account for anisotropy in the stretched network compels the model to be preferable due to its physical significance, for the purpose of fracture modeling. The rigidity of the crystallites is accounted for by proposing a crystallite distortion energy in addition to the critical bond dissociation energy, for fracture initiation to occur. The model is validated by comparison with existing experimental results for both crystallizing and non-crystallizing rubbers. In addition to its potential to predict the material behavior when subjected to uniaxial and biaxial loading, the capability of the model to quantitatively estimate the effect of crystallization on fracture initiation is also verified.

Oriented polylactic acid/graphene oxide nanocomposites with high mechanical and thermal properties

Oriented polylactic acid (PLA)/graphene oxide (GO) nanosheets tapes were prepared via uniaxial solid state drawing. The effect of various drawing conditions, including drawing ratio (DR), temperature (DT), and speed (DS) on mechanical, thermal, structural, and barrier properties were studied. Structural studies showed oriented structure for the drawn tapes with aligned polymer chains and GO nanosheets. Differential scanning calorimetry revealed improved glass transition temperature (Tg) and crystallinity (Xc) after drawing. In addition, Tg and Xc were increased more by increasing DR and DT. The highest Tg and Xc were achieved for 3/70/50 tape with values of 73°C and %22, respectively. Higher thermal stabilities and enhanced barrier properties were achieved after drawing, especially at the higher DR. Finally, tensile testing revealed simultaneous improvement in stiffness and toughness due to strain hardening for all the drawn tapes. The strength and elastic modulus were increased after increasing DR, DS, and DT and reached the highest values of 149 MPa and 3.6 GPa for 3/70/50. Overall, the properties were controllable by the processing conditions.

Framework for Predicting Failure in Polymeric Unidirectional Composites through Combined Experimental and Computational Mesoscale Modeling Techniques

As composites continue to be increasingly used, finite element material models that homogenize the composite response become the only logical choice as not only modeling the entire composite microstructure is computationally expensive but obtaining the entire suite of experimental data to characterize deformation and failure may not be possible. The focus of this paper is the development of a modeling framework where plasticity, damage, and failure-related experimental data are obtained for each composite constituent. Mesoscale finite elements models consisting of multiple repeating unit cells are then generated and used to represent a typical carbon fiber/epoxy resin unidirectional composite to generate the complete principal direction stress-strain curves. These models are subjected to various uniaxial states of stress and compared with experimental data. They demonstrate a reasonable match and provide the basic framework to completely define the composite homogenized material model that can be used as a vehicle for failure predictions.

Investigation on Triaxial Dynamic Model Based on the Energy Theory of Bedding Coal Rock under Triaxial Impact Compression

To investigate the dynamic failure characteristics of bedding rocks in depth, a series of dynamic impact compression tests on parallel and vertical bedding coal rocks were conducted by the split Hopkinson pressure bar test system at 10–103 s−1 strain rates and 0, 4, 8, and 12 MPa confining pressures. According to the experiments, the mechanical properties and energy characteristics of bedding coal rock under different confining pressures and strain rates were obtained, and a triaxial dynamic constitutive model of bedding coal rock was established based on the energy theory of rock failure. The results show that the compressive strength, peak strain, incident energy, dissipated energy, and dynamic strength increase factor gradually increase with increase in strain rate, but the increase in peak strain weakens as confining pressure rises. The influence of bedding structure on strength and energy is not obvious in the uniaxial state, while it gradually enhances as confining pressure increases. The obvious difference in DIF and the energy dissipation ratio of bedding coal rocks gets obvious in SHPB tests. Considering the influence of confining pressure, strain rate, and bedding on the dynamic failure characteristics, the dynamic constitutive model of bedding coal rock was established by introducing the comprehensive influence factor K and the DIF. Comparing with test results, the model parameters are almost confirmed, and the correctness of the model is further verified by analysing the law of K value. Meanwhile, the stress-softening characteristics of coal rock in postpeak are well simulated by the dynamic constitutive model. The results can provide reference value for dynamic issues such as high-efficiency rock breaking, prevention of rock burst, and surrounding rock support in deep rock masses.

Elasto-Damage constitutive modelling of recycled aggregate concrete

In this paper, Elasto-Damage model previously proposed by Khan and Zahra for natural aggregates concrete is reformulated to capture the behavior of recycle aggregate concrete (RAC) subjected to uniaxial compressive stress state. The compressive stress-strain relationship was investigated through existing published data for different recycled coarse aggregate (RCA) with replacement percentages of 0%, 30%, 50%, 70% and 100%. Use of recycled aggregate concrete has been advocated widely to be one of the solution for the global issue of depletion of natural resources while fulfilling the needs of material and structural performance required in reinforced-concrete structures. The adoption of RAC in construction industry requires development of appropriate constitutive models that can be implemented in software based on finite element method to predict the reliable results. The proposed model uses four parameters; a, b and r which helps to predict the different behavior of concrete in tension and compression while the fourth parameter critical energy release rate (Rc) controls the damage growth rate. These parameters are defined as a function of concrete compressive strength (fc') and its initial elastic modulus (Eo). The model is validated through existing test results for uniaxial compressive state of stress and it was concluded that it predicts better post cracking and post peak-behaviour of RAC as compared to the commercially available models for the conventional concrete.