Non-elastic Strain Research Articles

Temporal and Spatial Evolution of Non-Elastic Strain Accumulation in Stanstead Granite During Brittle Creep

Temporal and Spatial Evolution of Non-Elastic Strain Accumulation in Stanstead Granite During Brittle Creep

Microstructural mechanisms of hysteresis and transformation width in NiTi alloy from molecular dynamics simulations

Martensitic transformations in shape memory alloys are often accompanied by thermal hysteresis, and engineering this property is of prime scientific interest. The martensitic transformation can be characterized as thermoelastic, where the extent of the transformation is determined by a balance between thermodynamic driving force and stored elastic energy. Here we used molecular dynamics simulations of the NiTi alloy to explore hysteresis-inducing mechanisms and thermoelastic behavior by progressively increasing microstructural constraints from single crystals to bi-crystals to polycrystals. In defect-free single crystals, the austenite-martensite interface moves unimpeded with a high velocity. In bi-crystals, grain boundaries act as significant obstacles to the transformation and produce hysteresis by requiring additional nucleation events. In polycrystals, the transformation is further limited by the thermoelastic balance. The stored elastic energy can be converted to mechanisms of non-elastic strain accommodation, which also produce hysteresis. We further demonstrated that the thermoelastic behavior can be controlled by adjusting microstructural constraints.

A hierarchically correlated flow defect model for metallic glass: Universal understanding of stress relaxation and creep

Due to the structurally disordered arrangement of atoms and deviation from thermodynamic equilibrium, the physical and mechanical properties of metallic glasses can vary with time, temperature and magnitude of strain or stress. The current work provides a theoretical framework based on the hierarchically correlated atomic theory, which allows a quantitative description of the non-elastic deformation in metallic glasses. The defect concentration is adopted as an order parameter, which can evolve with temperature and non-elastic strain owing to correlated atomic movements. Through our hierarchically correlated atomic theory, we derive the characteristic times for local shear events in metallic glasses that entail activation, growth and/or annihilation of flow defects, which however are not accounted for in the previous mean field theories. Finally, we demonstrate that the current theoretical framework can be validated by the stress relaxation and creep experiments on typical La-based metallic glasses, which in turn provides quantitative insights into the non-elastic deformation mechanisms in metallic glasses.

Hellinger–Reissner variational principle for a class of specified stress problems

Abstract Aiming at the problem of the specified stress condition in a partial region of the structure, the Hellinger–Reissner (H–R) variational principle is studied to provide a theoretical basis for the finite element numerical analysis. By introducing the unknown non-elastic strain as an additional unknown quantity to fulfill the specified stress condition, the elastic mechanics governing equations for the specified stress problem are given. Both stress and unknown non-elastic strain are taken as independent variables to establish the complementary energy principle and virtual work equation which are equivalent to the elastic mechanical control equation of the specified stress problem. Based on the conventional H–R variational principle, using displacement, stress and unknown non-elastic strain as independent variables, a H–R variational functional that satisfies the specified stress conditions is established by using Lagrange multiplier method. Also the variational functional with displacement, elastic strain and unknown non-elastic strain as independent variables is deduced by transforming the stress into the elastic strain. The corresponding finite formulae are derived based on an intra-element stress hybridization method. The H–R variational principle for the specified stress problem takes non-elastic strain as an independent variable, so that the stress explicitly appears in the equilibrium equation of the element and structure, which expands the application range and capabilities of the existing variational principle and finite element method. The correctness and accuracy of the theory and algorithm are verified by numerical examples.

Evolution of tensile and shear cracking in crystalline rocks under compression

We performed laboratory-scale unconfined compression experiments on Barre granite specimen with a single pre-existing flaw to study the evolution of tensile and shear cracking that occurs during different stress levels. Moment tensor inversion of acoustic emission (AE) events in combination with the nonelastic strain component obtained through the 2D digital image correlation (DIC) technique are used to track the changes in the source mechanisms of the stress-induced cracks. The mode of deformation computed from the image based strain profiles, enables visual comparison of the nucleation, growth and interaction of the tensile and shear cracks with the microseismic source mechanism observed by moment tensor inversion of the AE events. Comparing the results obtained from the two techniques on the same dataset demonstrates a quantitative correlation between the acoustic and visual observations in terms of the cracking mechanisms obtained at different stages of cracking from crack initiation at the flaw tips to the failure of the rock specimen.

Deep-hole in situ stress measurement method in high-altitude area based on remote sensing technology

In order to improve the understanding of the physical properties of earthquakes and the interior of the earth, a method for measuring deep-hole in situ stress in high-altitude areas based on remote sensing technology is proposed. The area of 2500 m above sea level is selected as the research area of in situ stress measurement in this paper. The digital image of Landsat TM5 (30 m) is used as the main information source, and the spectrum of the visible-shortwave infrared band is 0.38–2.5 um. The information enhancement of TM7-4-2 band is selected to process the clear remote sensing image of the research area. After locating deep boreholes based on remote sensing images, the in situ stress of deep boreholes is measured by the non-elastic strain recovery method. Core samples at five depths of 730 m, 980 m, 1030 m, 1080 m, and 1110 m are extracted and pasted with 18 strain gauges. The principal stress direction is obtained by core orientation, and the stress components are determined by calculating six independent directions of inelastic normal strain and rock’s inelastic strain recovery flexibility. The results are as follows: the direction of maximum horizontal principal stress is 31°~46° and the dominant direction is 36°; the inelastic strain of each strain gauge is positive strain, the curve increases steadily with time, and the initial inelastic strain increases quickly and then slows down, which accords with the law of inelastic strain change. Experiments show that this method can provide a basis for the study of geological conditions at high altitudes.

Force and Shape Control Strategies for Minimum Energy Adaptive Structures

This work presents force and shape control strategies for adaptive structures subjected to quasi-static loading. The adaptive structures are designed using an integrated structure-control optimization method developed in previous work, which produces minimum ‘whole-life energy’ configurations through element sizing and actuator placement optimization. The whole-life energy consists of an embodied part in the material and an operational part for structural adaptation during service. Depending on the layout, actuators are placed in series with the structural elements (internal) and/or at the supports (external). The effect of actuation is to modify the element forces and node positions through length changes of the internal actuators and/or displacements of the active supports. Through active control, the stress is homogenized and the displacements are kept within required limits so that the design is not governed by peak demands. Actuation has been modelled as a controlled non-elastic strain distribution, here referred to as eigenstrain. Any eigenstrain can be decomposed into two parts: an impotent eigenstrain only causes a change of geometry without altering element forces while a nilpotent eigenstrain modify element forces without causing displacements. Four control strategies are formulated: (C1) force and shape control to obtain prescribed changes of forces and node positions; (C2) shape control through impotent eigenstrain when only displacement compensation is required without affecting the forces; (C3) force control through nilpotent eigenstrain when displacement compensation is not required and (C4) force and shape control through operational energy minimization. Closed-form solutions to decouple force and shape control through nilpotent and impotent eigenstrain are given. Simulations on a slender high-rise structure and an arch bridge are carried out to benchmark accuracy and energy requirements for each control strategy and for different actuator configurations that include active elements, active supports and a combination of both.

Influence of temperature- and strain rate-dependent viscoplastic properties of polyoxymethylene on the thermo-mechanical response of a steel-polyoxymethylene spur gear pair

The nonlinear material properties of thermoplastics like polyoxymethylene (POM) can influence the thermo-mechanical response of polymer gears to applied running loads. In the presented study, the non-elastic strain rate- and temperature-dependent mechanical characteristics of POM are examined, along with their influence on the mechanical response of the polymer gear at the tooth root and contact interface, and the resulting heat generation driving the commonly exhibited temperature rise during gear meshing/running. A detailed experimental study of these properties was conducted, employing standardized and partly customized tensile and bending tests. Using a suitable viscoplastic constitutive material model, calibrated based on the obtained experimental results, a numerical structural-contact analysis of the gear meshing process was performed, which could subsequently be used for a more detailed evaluation of the generated frictional heat and resulting temperature rise during gear running. While a significant influence of the viscoplastic material properties on the mechanical contact response and the flash temperature rise on the POM gear was identified, no major impact on the long term nominal temperature rise was recognized.

Influence of the creep ageing process on the fatigue properties of components from V95pchT2 (analog 7175T76) and V95ochT2 (analog 7475) aluminium alloys

Influence of conditions of technological process of forming thick panels of a given geometry on fatigue limit of flat specimens from the V95ochT2 and V95pchT2 (analogues 7475 and 7175T76) alloys (Al-Mg-Cu-Zn) has been analysed. The process has been simulated experimentally on flat samples for temperatures 20, 165 and 420°C. The process includes: non-elastic strain in the range 10-5 - 10-2 s-1 up to 2% of total strain, followed by heat treatment according to T2 mode (quenching and aging). Fatigue life tests were carried out both on solid samples and on samples with a hole. It has been shown that resistance to fatigue of the observed alloys after forming at the annealing temperature (420°C) is comparable to the basic material resistance to fatigue. Meso-structure analysis showed absence of stress in grains. It is established that, on average, the shape of the grains is the same for a series of samples for different temperatures and loading rates. The results of testing samples with a hole showed that fatigue limit slightly decreases in samples which were previously deformed at (420°C), with respect to the durability of samples from the material in basic state. With an increase in rate of pre-strain, the relative number of cycles before destruction occurs increased.

A thermodynamic constitutive model for undrained monotonic and cyclic shear behavior of saturated soils

Based on a non-equilibrium thermodynamic approach, this paper has established a constitutive model for saturated soils different from the classical elasto-plastic model and other thermodynamics-based models. It does not require concepts such as yield surface and flow rule. Instead, through a quantitative description of the energy in the reversible and irreversible processes in materials, the constitutive relations have been obtained theoretically. Using the elastic potential energy function, the stress is expressed as a function of elastic strain. By introducing the granular entropy and locked energy concepts, the non-elastic strain evolution is determined according to the non-equilibrium thermodynamics. The model can describe many basic mechanical properties of saturated soils under monotonic and cyclic shear loadings, such as the stress state boundary, the critical state and especially the cyclic mechanical behavior. Based on this model, the paper simulates the cyclic undrained triaxial shear tests for saturated clays and analyzes the impact of factors that include cyclic stress ratio, OCR value and cyclic stress frequency. The simulation results are compared with experimental results in order to validate the model.

OS1301-376 対称アングルプライCFRP積層板の高温におけるサイクル軟化挙動

Strain-controlled cyclic behavior of angle-ply CFRP laminates [±θ] at high temperature has been studied. Strain-controlled symmetric tension-compression cyclic tests for different strain amplitudes were carried out on coupon specimens with different fiber orientations (θ = 30°, 35° and 45°), respectively. On the basis of the cyclic tests, the changes of stress amplitude, mean stress, non-elastic strain amplitude, maximum and minimum stress levels and loading and unloading tangent moduli with cyclic straining are examined. The experimental results showed that hysteretic stress-strain response to cyclic straining appears, regardless of the fiber orientation. The stress amplitude decreased with increasing number of cycles, and accordingly the non-elastic strain amplitude increased with cyclic straining. These observations reveal that the cyclic softening occurs in the angle-ply CFRP laminates tested in this study. The cyclic softening terminates rapidly in a small number of cycles, and a cyclic saturation stage is reached in all the strain-controlled cyclic tests, except some cases of large strain amplitude or small fiber orientation angle.

Elastically accommodated grain-boundary sliding: New insights from experiment and modeling

Substantial progress is reported towards a reconciliation of experimental observations of high-temperature viscoelastic behaviour of fine-grained materials with the micromechanical theory of grain-boundary sliding. The classic Raj–Ashby theory of grain boundary sliding has recently been revisited – confirming the presence of the following features: (i) at a characteristic period τe much less than the Maxwell relaxation time τd, a dissipation peak of amplitude ∼10−2 and associated shear modulus relaxation resulting from elastically accommodated sliding on grain boundaries of relatively low viscosity; (ii) at intermediate periods, a broad regime of diffusionally-assisted grain-boundary sliding within which the dissipation varies with period as Q-1∼Toα with α∼1/3, sliding being limited by stress concentrations at grain corners, that are progressively eroded with increasing period and diffusion distance; and (iii) for periods longer than the Maxwell relaxation time τd, diffusionally accommodated grain-boundary sliding with Q−1∼To. For periods To≫τe, laboratory dissipation data may be adequately described as a function of a single master variable, namely the normalised period To/τd. However, it is becoming increasingly clear that the lower levels of dissipation measured at shorter periods deviate from such a master curve – consistent with the existence of the two characteristic timescales, τe and τd, for grain-boundary sliding, with distinct grain-size sensitivities. New forced-oscillation data at moderate temperatures (short normalised periods) provide tentative evidence of the dissipation peak of elastically accommodated sliding. Complementary torsional microcreep data indicate that, at seismic periods of 1–1000s, much of the non-elastic strain is recoverable – consistent with substantial contributions from elastically accommodated and diffusionally assisted grain-boundary sliding.

Plastic yielding as a frequency and amplitude independent mechanism of seismic wave attenuation

We have developed a mathematical formulation of two mechanisms of compressional wave attenuation, which can occur within the solid rock frame prestressed up to its yield stress in part of its volume. Energy losses are attributed to two distinct processes: irreversible plastic yielding and formation of radial microfractures around microscopic cavities. Small-amplitude waves propagating through the rocks prestressed at their yield point would cause nonelastic strain to avoid building local stresses above the yield limit and attenuate some fraction of their energy per every loading cycle. New mechanisms of microscale yielding and microfracturing give rise to frequency-independent attenuation due to rate-independence of plasticity formulation. Quality factor [Formula: see text] predicted by the model is independent of strain amplitude for small strains and decreases with increasing amplitude for large strains. We found that attenuation can be high even for small seismic strains [Formula: see text]. Thus, [Formula: see text] is achieved at effective pressures greater than twice the yield strength of the solid matrix for the plastic yielding mechanism and at overpressures exceeding half tensile strength for microfracturing.

Cyclic Deformation Behaviour and Damage Development on Different Hierarchical Levels in Cortical Bone

Bone is a complex natural composite material built of organic and anorganic components and very well adapted to the in vivo loading conditions. The material exhibits an excellent damage resistance under static and fatigue loading conditions. This is partially due to self-healing processes, but to a great extent also to its hierarchical microstructure. The investigation of the deformation behaviour and the damage mechanisms on different length scales gives valuable insight into which level(s) of hierarchy influence the fatigue resistance in which way. In the present work, cyclic deformation tests have been performed on cortical bone specimens. On one hand, stress-strain-hysteresis measurements in different types of tests, such as constant amplitude tests, load increase tests, and combined static and cyclic tests, give information on the active damage mechanisms. For example, changes in the development of the stiffness, non-elastic strain amplitude and non-elastic mean strain as a result of different loading velocities and stress levels allow the discrimination between time and cycle dependent damage mechanisms. These results were correlated with microstructural investigations of the damage development on different hierarchical levels by light and scanning electron microscopy.

Nonlinear Buckling Analysis for Etiological Study of Idiopathic Scoliosis

This paper investigated buckling phenomena of the spine induced by the growth of vertebral bodies that have potential to cause idiopathic scoliosis. In the previous study, we presented a hypothesis that idiopathic scoliosis is a buckling phenomena induced by the growth of vertebral bodies based on the similarity of the clinical single and double-major curves with the results of the fourth and sixth buckling modes, respectively, as analyzed by the finite-elements method using linear buckling theory. However, this theory is valid for infinitesimal deformation and is not applicable to estimation of stability for post-buckling behavior. In this study, we developed a program to analyze deformation histories caused by the growth of vertebral bodies considering the geometrical nonlinearity and investigated buckling phenomena. We assumed that growth represents generation of non-elastic bulk strain. To exclude modes correctable by posture change, we considered constraints at the cervical spine. Using the developed program, we analyzed deformation histories induced by the growth of vertebral bodies and obtained deformation histories including buckling phenomena with side-bending modes similar to clinical curves. However, the magnitudes of deformations were in the sub-millimeter order that is too small for the etiology of idiopathic scoliosis by itself. Based on the results, we suggested that participation of other phenomena, such as bone remodeling caused by the stresses at the side-bending deformations, will be necessary.

Numerical Evaluation of the Surface Displacements due to Soil Grouting and to Tunnel Excavation

The low-pressure grouting with cement mixtures is one of the techniques adopted for improving the mechanical characteristics of granular soils prior to the excavation of underground openings. When applied to shallow subway tunnels, this procedure often induces heaves of the ground surface, which are followed by settlements during the excavation phase. In urban areas, these displacements may lead to appreciable damages of existing buildings. Here, a finite element analysis is presented of the surface displacements recorded during the construction of a subway tunnel in the city of Milan (northern Italy). The critical comparison between numerical and experimental data singles out the limits of an analysis approach used in tunneling practice that simulates the injections through a nonelastic volume strain. To overcome them, an alternative analysis scheme is adopted, based on the application of a neutral pressure within the grouted zone, which seems preferable for estimating the surface displacement caused by the field works.

Anelasticity and Strength in Zirconia Ceramics

Non-elastic strain behavior was investigated for several different zirconia ceramics and a possible mechanism for anelasticity was discussed. Anelastic strain was detected in zirconia ceramics irrespective of the crystallographic phase and its productivity depended on the particular kind of dopant additive. It was found that the anelastic properties could be significantly influenced by the level of oxygen vacancy in the matrix, and that the anelastic strain might be produced by a slight shift of ionic species. In order to investigate the effect of anelasticity on mechanical properties on zirconia ceramics, the tensile strength was investigated for a wide range of strain rates. The obviously unique strain rate dependence was observed only in the materials having anelastic properties. It was assumed that anelasticity could be efficient at improving the tensile strength.

Energy Storage in Cold Non-elastic Deformation of Glassy Polymers

AbstractExperimental results on work W(ε), heat Q(ε) and stored energy U(ε) of deformation for glassy polymers such as linear PS, PC, PMMA, Polyimid, amorphous PET, thermotropic aromatic polyesters, Vectra™ for example, crosslinked epoxy are presented. All the data was obtained by a deformation calorimetry technique. Loading and unloading of samples were performed at room temperature with strain rate έ = 10-2 - 10-4 sec-1 under uniaxial compression up to engineering strains of εdef = 40-50%. During straining all polymers accumulate an excess of the latent energy U(ε). Elastic fraction of the energy is released completely at sample unloading and only residual Ures(ε) energy is conserved in samples. The latent energy Ures(ε) grows up to εdef =20-25% and levels off then. Shapes of the Ures(ε) curves are the same (S-shape) for all polymers. However, the saturation level is different for each polymer. The ratio U(ε)/W(ε) was also measured. It was found that at strains εdef < εy (εy - strain at the yield point) U(ε)/W(ε) ≈100%. I.e. all W is stored by sample in a form of U. The ratio decreases up to 60-30% for different polymers at higher strains. Release of the residual energy Ures (DSC measurements) and strain εres (thermally stimulated strain recovery technique) was measured for deformed and unloaded samples at heating. It was found that about 85-90% of Ures stored by samples is released in glassy state of polymers (below Tg). The Ures is related to a small fraction of εres, only to 7-10%. The rest of Ures and εres are recovered at the softening (devitrification) interval, around Tg. Computer modeling (molecular dynamics) of an isothermal shear deformation was performed for 2-dimentional two component atomic glass containing 500 Lennard-Jones particles of two different diameters. It was found that localized deformation events are of anelastic nature. The εan appears at early deformation stage in a form of localized shear events (transformations). Such events are nucleated in a sample and merged and united at later deformation stages, when concentration of the events becomes high enough. Finally, merged transformations form kind of shear band crossing entire sample. On the basis of experimental data and computer modeling the deformation mechanism for glassy polymers is proposed. The first stage of the process is the nucleation of “the carriers of non-elastic strain”, anelastic shear transformations (ASTs). All these ASTs are energetically excited. The concentration of the ASTs is responsible for the amount of Ures(ε) stored by a sample. It is suggested that such nucleation is the rate-controlling step in non-elastic deformation of any non-covalent glass. Saturation of the stored energy is defined by the reaching the steady state regime in carrier’s concentration. In this regime the rates of nucleation and termination (decrease of the stored local energy by AST) of carriers becomes equal. The termination proceeds spontaneously and easy (fast). The decrease of local energy of ASTs follows by local uncoiling of chains and by an appearance of new, extended chain conformers. However, such uncoiling is not the rate-controlling step for entire deformation process. Suggested mechanism very well describes all existing experimental facts. Deformation mechanisms for glasses seriously differ from that operating in rubbers and crystals.

Analysis of non-elastic strain produced in zirconia ceramics

Abstract Non-elastic strain behavior was investigated in detail for several different zirconia ceramics (Y-TZP, Y-FSZ, Mg-PSZ and Ce-TZP), and a possible mechanism for anelasticity was discussed. Y 2 O 3 -doped zirconia ceramics (Y-TZP and Y-FSZ) exhibited a remarkable degree of anelastic strain, as does Mg-PSZ to a lesser extent. On the other hand, Ce-TZP hardly produced anelastic strain. These results suggest that the anelastic properties depend on the particular dopant additive, irrespective of the crystallographic phase. In Mg-PSZ, besides the anelastic strain, a time-dependent non-recoverable strain is produced under loading. This non-recoverable strain corresponds to the strain caused by a phase transformation. It is suggested that the anelastic properties could be significantly influenced by the level of oxygen vacancy in the matrix, and that the anelastic strain might be produced by a slight shift of ionic species.

Energy storage and strain-recovery processes in highly deformed semicrystalline poly(butylene terephthalate)

Nonelastic deformation of semicrystalline poly(butylene terephtalate) (PBT) was investigated by calorimetric measurements and strain-recovery tests. Differential scanning calorimetry on PBT specimens deformed both below and above their glass-transition temperature (T g 50 °C) showed the presence of a broad exothermal peak whose area represents the energy released for the nonelastic strain recovery. This energy became more and more pronounced as the strain level increased, and it decreased as the deformation temperature increased, even if a significant contribution was detected on specimens deformed at temperatures much higher than T g . For two temperature conditions (21 and 100 °C), strain-recovery master curves were built showing the following two distinct deformation components: one recoverable with time and another one irreversible, this latter one arising from relatively low levels of strain. The recoverable component can be erased by heating the material at temperatures much higher than its T g , close to the onset of the melting process. On the other hand, the irreversible strain component does not recover even if the material is brought close to the onset of the crystals melting. The shift factor for the strain-recovery master curves was compared with the shift factor for the construction of the dynamic storage modulus master curve obtained in the linear viscoelastic regime (small strain).