Loading-unloading Conditions Research Articles

Effects of Thermal Damage on Strain Burst Mechanism for Brittle Rocks Under True-Triaxial Loading Conditions

Strain burst is a common problem encountered in brittle rocks in deep, high-stress mining applications. Limited research focuses on the effects of temperature on the strain burst mechanism and the kinetic energies of rocks. This study aims to investigate the effects of thermal damage on the strain burst characteristics of brittle rocks under true-triaxial loading-unloading conditions using the acoustic emission (AE) and kinetic energy analyses. The time-domain and frequency-domain responses related to strain burst were studied, and the damage evolution was quantified by b-values, cumulative AE energy and events rates. The ejection velocities of the rock fragments from the free face of the granite specimens were used to calculate kinetic energies. The experimental results showed that thermal damage resulted in a delay in bursting but increased the bursting rate at ~ 95% of normalised stress level. This is believed to be due to the micro-cracks induced by temperature exposure, and thus the accumulated AE energy (also supported by cumulative AE counts) at the initial loading stage was reduced, causing a delay in bursting. The strain burst stress, initial rock fragment ejection velocity, and kinetic energy decreased from room temperature (25 °C) to 100 °C, whereas they resulted in a gradual rise from 100 to 150 °C demonstrating more intense strain burst behaviour.

Direct modeling of multi-axial fatigue failure for metals

Innovative elastoplastic J2−flow models with nonlinear combined hardening are proposed for the purpose of simulating multi-axial thermo-coupled fatigue failure for metals and alloys, in a direct sense without involving any usual damage-like variables and any ad hoc failure criteria. As contrasted with usual models, the yield condition and the loading-unloading conditions need not be imposed as extrinsic coercive conditions but may be automatically incorporated into a free, smooth flow rule in a more realistic sense. Novel results in three respects are available directly from model predictions, namely, (i) complex features of thermo-coupled fatigue failure may be automatically represented by simple asymptotic properties of the hardening functions introduced, (ii) critical failure states may be derived with a criterion in unified form, and, in particular, (iii) direct procedures may be established for determining fatigue lives under either stress cycles or thermal cycles. Simulation results in the simplest cases of the proposed model are in good agreement with experimental data.

Size Effect of Concrete Specimens on the Acoustic Emission Characteristics under Uniaxial Compression Conditions

Acoustic emission (AE) experiments under uniaxial compression and cyclic loading-unloading compression conditions were performed using different sizes of cubic concrete specimens. The influences of the loading methods and the concrete sizes on the mechanical parameters and the concrete AE activities were analyzed. The loading method was found to have great impact on the deformation, failure, and energy dissipation of concrete materials. With the increase of the material size, the uniaxial compressive strength of the concrete specimens gradually decreased, while the corresponding strain of peak strength increased first and then decreased. The elasticity modulus fluctuated irregularly. Under the uniaxial compression conditions, five AE patterns corresponding to the deformation and failure of the concrete materials were observed. A significant nonlinear relationship was found between the AE and the stress level. The cumulative AE rings at the peak stress showed nonlinear growth with the increase of the concrete size. Based on an established relationship between the cumulative AE rings and the stress level, the necessary conditions for the existence of the quiet AE period were given. Under the uniaxial cyclic loading-unloading compression conditions, the Felicity ratio decreased first and then increased as the stress increased. The research results have some guiding significance to AE-based monitoring of internal stress evolution of coal, rock, and concrete materials and thereby enable assessment of their stability.

Study of Micro Deformation of Austenitic-Ferrite Duplex Stainless Steel by Nanoindentation Method

Based on the technology of the nanoindentation, the basic mechanical properties and cyclic deformation behavior of the austenite phase and ferrite phase in an austenitic-ferritic duplex stainless steel was studied. Firstly, from the displacement monotonic indentation experiment, the differences between the basic mechanical properties (e.g. hardness and elastic modulus) of austenite phase and ferrite phase are compared. Then, with the incremental load controlled loading-unloading conditions applied, the indentation depth evolution rule and the indentation creep behavior was studied. Finally, with the load controlled cyclic indentation experiments being conducted, the cyclic evolution rule of displacement into surface were observed, and the influence of different load level on the micro cyclic deformation behavior of each phase were discussed.

Wrinkle prediction of seat cover considering cyclic loading-unloading with viscoelastic characteristics

The purpose of this study is to predict the wrinkling of leather seat covers created by repeated loading–unloading conditions and long-term driving conditions. To predict wrinkling, this paper describes a numerical analysis process and material test methods. Viscoelasticity is considered to express the time-dependent deformation of the seat cover and a leather material is selected. To evaluate the viscoelastic behavior of leather seat covers in accordance with time and the number of times being seated, cyclic tests are conducted using leather specimens of a strip type. In the cyclic tests, one cycle consisted of loading–creep–unloading conditions; the viscoelastic (creep) time is 1h, and the total repeated number is 60. To perform the seating simulation, PAM-COMFORT, a commercial software package for seat modeling, is used, and permanent deformation of the seat cover is predicted. It can be difficult to predict viscoelasticity using explicit code. As such, a material modeling and evaluation process is suggested. Test results obtained using a model construct are compared with experimental test results with good agreement. The numerical process is then applied to a seat module with an HPM1 dummy model, and quantitative wrinkle deformation is predicted. The proposed process was used to determine the material properties that had deteriorated due to the viscoelastic characteristics of the seat covers. The viscoelastic effects on wrinkle occurrence were confirmed analytically by applying these properties to the seat modules.

Mechanical characteristics and permeability evolution rule of coal under loading-unloading conditions

Based on the self-made servo-controlled seepage equipment for thermal-hydrological-mechanical coupling of coal and rock, a loading and unloading experimental study was performed by increasing the axial compression and decreasing the confining pressure in consideration of the actual mining method. The mechanical characteristics and permeability evolution rule of coal were analyzed and studied under loading-unloading conditions. The results show that during the process of loading and unloading, the faster the loading rate of axial stress, the longer the platform of the stress-strain curve near the peak, and the larger the peak stress, axial strain and circumferential strain, while the smaller the volume strain. The deformation moduli at different loading and unloading rates exhibit the trend of rapidly decreasing first and then slowly decreasing. When damage occurs, the deformation modulus rapidly decreased and then is nearly constant. Under that condition of the same axial strain, the deformation modulus increases with the decrease of loading and unloading rate. The relations of deviatoric stress and coal permeability with strain can be divided into three stages in the whole test process:initial compaction and elastic stage, yield stage, and post-failure stage. During the process of loading and unloading, the slower the loading and unloading rate is, the larger the coal permeability and volume strain become when the axial stress of coal samples reaches the peak value.

APPLICATION OF AN ELASTOPLASTIC MODEL TO PREDICT BEHAVIORS OF CONCRETE-FACED ROCK-FILL DAM UNDER COMPLEX LOADING CONDITIONS

In this research, a simplified rotational kinematic hardening model with the concept of sub-loading was used to predict behaviors of Concrete-Faced Rock-fill Dam under complex loading conditions. The model can overcome the shortcomings of classic elastoplastic model (i.e. soil behaviors under cyclic loading-unloading can be predicted). Elastoplastic formula of the model was presented in detail. Then this model was verified with test results of coarse grained soils, under both monotonic loading and cyclic loading-unloading conditions. This model was also applied to analyze deformation of Shuibuya rock-fill dam, computed results and in-situ measurements are compared. Results showed that computed results were consistent with in-situ measurements in both construction and operation period. Results also showed that permanent deformation that was caused by fluctuations of the reservoir level can also be predicted by this rotational kinematic hardening model.

Coupled rate-dependent superelastic behavior of shape memory alloy bars induced by combined axial-torsional loading: a semi-analytic modeling

In this article, the coupled thermomechanical response of superelastic shape memory alloy bars and tubes in combined tension and torsion is studied both analytically and experimentally. Using the Gibbs free energy as the thermodynamic potential and choosing appropriate internal state variables, a three-dimensional phenomenological macroscopic constitutive model for shape memory alloys is derived. Taking into account the effect of latent heat during the forward and reverse martensitic phase transformation, the appropriate form of the energy balance relation is obtained. The three-dimensional coupled relations for the energy balance in the presence of the internal heat flux and the constitutive equations are reduced to a two-dimensional form for the tension-torsion case. An explicit finite difference approach is utilized to discretize the governing boundary conditions of bars. An empirical expression for the free heat convection from the surface of a shape memory alloy bar was proposed and experimentally validated. Several sets of experiments were then carried out to evaluate the mechanical and thermal responses of the model for a shape memory alloy tube subjected to uniaxial, pure torsion and non-proportional tension and torsion loading–unloading conditions. The approach could be used in the design of shape memory alloy devices undergoing combined loads with high strain rates or in the fatigue design of shape memory alloy devices subjected to cyclic loading.

IN SITU MULTI-FIELDS INVESTIGATION ON INSTABILITY AND TRANSFORMATION LOCALIZATION OF MARTENSITIC PHASE TRANSFORMATION IN NiTi ALLOYS

When NiTi shape memory alloys thin strips under the uniaxial tensile deforma- tion, the stress-induced martensitic transformation tends to exhibit strain localization and insta- bility, and the sample shows reversible transformation bands evolution on macroscopic. The dis- placement, strain and temperature fields were investigated with in situ optical method, and the full-field strain and temperature information about martensitic localization were quantitatively ob- tained during uniaxial loading-unloading conditions. Strain field is calculated by digital image cor- relation (DIC) method, and the temperature field is captured by infrared thermograph, the thick- ness field and in-plane rotation angle are also calculated by DIC data. The strain, temperature variation, thickness, in-plane rotation both inside and outside of the transformation bands were studied when it nucleation, expansion, combination, reduction and disappear. The results show that transformation strain of the samples are mainly concentrated inside the transformation bands

Evaluation of the prestressing effects on the fatigue life of composite box sections

Fatigue tests were conducted on non-prestressed and prestressed composite box sections. The approach to prestressing of composite structures seeks to eliminate compressive stress excursions under fatigue loading. This approach increased the fatigue life of composite structures; the experimental gains in fatigue life were in agreement with theoretical prediction. The tensile prestress developed in the composite structure mitigate compressive stress excursions under fatigue load, which significantly enhance the fatigue life of composites. Flexural fatigue tests were conducted through repeated application of a constant deformation, with the maximum load level monitored throughout the tests. The repeated (constant) deformation was selected to produce 70% of the ultimate (quasi-static) flexural strength of each of the prestressed and non-prestressed composite box sections. Two prestressed and two non-prestressed specimens were tested under (displacement controlled) fatigue loading–unloading conditions. The fatigue life of non-prestressed composite sections was reached upon local buckling of top flange (which experienced the maximum compressive stress). For both non-prestressed and prestressed composite sections, failure was defined as the number of cycles after which the peak load (at constant repeated deformation) dropped to 70% of the value in the first cycle. The fatigue life of prestressed composite sections was about 100% greater than that of non-prestressed sections. The residual strength of prestressed sections after fatigue loads was, on the average, 56% greater than that of non-prestressed sections. The experimental results indicated that contribution of prestressing to the fatigue life of composite sections was significant.

Comparative studies of yield strength and elastic compressibility between nanocrystalline and bulk cobalt

Comparative studies of yield strength and elastic compressibility between nanocrystalline and bulk cobalt were conducted using synchrotron x-ray diffraction under tri-axial pressure loading-unloading conditions. Relative to micron Co, nano Co exhibits higher flow stress (2.9 GPa compared with 2.1 GPa in micro Co), extra degree of strain-induced peak broadening during loading yet a better strain recoverability after unloading. These observations suggest different deformation mechanisms with intergranular strains dominated in nano Co and intragranular strains in micron Co. The determined bulk modulus for nano Co is 216 GPa, ∼17% higher than that of micron Co (185 GPa). This finding supports a generalized model of nanocrystals with pre-compressed surface layers and indicates that the grain-size induced elastic strengthening and weakening are primarily determined by the nature of internal stress (compressed vs. tensile) present in the surface layer of a nanocrystal.

Modelling finite deformation stress-strain response during loadingunloading of polyethylene over a wide range of crystallinities

Experimental observations are reported on the finite deformation stress-strain response during loading-unloading of polyethylene materials covering the range of crystal volume fractions 0.15–0.72. Hyperelastic-viscoplastic constitutive equations, based on a two-phase interpretation of the microstructure, are derived. It is shown that the constitutive model adequately describes the experimental observations under loading-unloading conditions.

Power modulation based fiber-optic loop-sensor having a dual measurement range

A fiber-optic sensor is investigated in this work for potential applications in structural health monitoring. The sensor, called fiber-loop-sensor, is based on bending an optical fiber beyond a critical radius to obtain intensity losses and calibrating the losses with respect to the applied force or displacement. Additionally, in the present case, the use of single-mode optical fibers allows the appearance of several resonance peaks in the transmitted power-displacement graph. The intensity of one of these resonances can be tracked in a narrow range to obtain high sensitivity. Experimental results show that the resolution of 10−4 N for force and 10−5 m for displacement can be obtained in these sensors. The sensors are calibrated for various loop radii and for various loading rates. They are also tested under loading-unloading conditions for over 104 cycles to observe their fatigue behavior. The sensors show very repeatable response and no degradation in performance under these test conditions. Simple construction and instrumentation, high sensitivity, and low cost are the advantages of these sensors.

Breakage behaviour of spherical granulates by compression

This paper describes the deformation and breakage behaviour of granulates in single particle compression test. Three industrial spherical granulates— γ - Al 2 O 3 , the synthetic zeolite Köstrolith ® and sodium benzoate ( C 6 H 5 COONa ) were used as model materials to study the mechanical behaviour from elastic to plastic range. The elastic compression behaviour of granulates is described by means of force-displacement curves, by application of Hertz–Huber contact theory and continuum mechanics. An elastic–plastic contact model was proposed to describe the deformation behaviour of elastic–plastic granules. The effects of granulate size and stressing velocity on the breakage force and contact stiffness during elastic and elastic–plastic displacement are examined. It is shown that the zeolite granulates with elastic–plastic behaviour have viscous properties as well. Breakage mechanisms of granulates during elastic, elastic–plastic and plastic deformation are also explained. The breakage probability is approximated by Weibull distribution function. The behaviour of the granulate during compression under the repeated loading–unloading conditions was investigated.

Iterative LCP solvers for non‐local loading–unloading conditions

AbstractThis paper deals with the finite element analysis of a certain class of non‐local dissipative constitutive models, where the canonical pointwise backward‐Euler scheme cannot be employed for satisfying the loading–unloading conditions. In the presence of a non‐local dissipation, the admissibility conditions in a point depend on the inelastic strain increment of the surrounding points and can be cast as a linear complementarity problem (LCP) involving all Gauss points of the process zone. In order to actually solve the LCP, the use of iterative algorithms that can be easily embodied into existing FE codes is discussed. The performance of the proposed algorithms is tested in 1D and 2D examples for both elastoplastic and damaging materials. Copyright © 2003 John Wiley & Sons, Ltd.

A finite-strain finite element model for the pseudoelastic behavior of shape memory alloys

This paper presents a finite deformation finite element model for the pseudoelastic response of shape memory alloys under stress loading-unloading conditions at constant temperature. A local multiplicative decomposition of the deformation gradient into volumetricelastic and isochoric—inelastic components is assumed, where the inelastic component is associated with phase transformation and defines an additional intermediate configuration. Strain measure defined on the intermediate configuration is the Hencky strain. The constitutive equations are cast in the framework of generalized plasticity and the two-way phase transformation is modeled via a Kuhn-Tucker type transformation criteria for the rate-independent shape memory behavior. These equations are able to predict the stress-induced phase transformations during complete loading-unloading cycles, and can also predict the correct material behavior when incomplete transformations take place. The resulting nonlinear system of equations is solved for updated stress variables via the radial return algorithm embedded in the Newton-Raphson iteration scheme. Numerical results are presented to show the performance of the model.

Cyclic Behaviors under Thermal and Loading-unloading Conditions in TiNiCu Shape Memory Alloy. Influence of Strains on Cyclic Behaviors under the Constant Heating and Cooling Temperature.

Use of a heat engine of which the working elements consists of a shape memory alloy is a useful method for direct conversion of power from low grade heat. The authors have proposed a reciprocating heat engine using shape memory alloy wires. However, in order to undertake reliable engineering designs and optimum material selection, it is imperative that the cyclic behaviors of the shape memory alloy are well understood. In this paper, the cyclic behaviors of Ti-41.7 at% Ni-8.5 at% Cu are investigated experimentally. Experiments are carried out by repeating the combination of the thermal cycle and the loading-unloading cycle under the constant heating and cooling temperature. The results show that the transformation temperatures of Mf and As almost do not vary with the number of cycles, but Ms and Af temperatures increase gradually with cycles when the number of cycles is greater than about 500. It is also noted that two-way strain and irrecoverable strain increase proportionately with the increase in maximum strain. Furthermore, from results of deformation stress in the martensitic phase, the plastic deformation is recognized in the strain range of boyond 4%.

Analysis of creep and shrinkage in concrete and its application to concrete top layers

Extending a previous method for calculating shrinkage stresses, loading-unloading conditions governing a nonlinear stress-strain behaviour of concrete in tension are presented. The strain-softening part (falling branch) is included in the model. The proposed method is demonstrated by fitting shrinkage test data, and a composite structure which consists of a layer of new concrete on top of an old concrete slab is analysed. For interpretation of these calculations, various risk levels of crackin in the top layer are defined.

Reexamination of the Kolsky Technique for Measuring Dynamic Material Behavior

A one-dimensional wave propagation analysis is carried out to assess the validity of the Kolsky formulas [1] for average stress and strain in a specimen exhibiting bilinear elastic-plastic behavior when subjected to trapezoidal and triangular incident pulses. For this piecewise linear model, the method of characteristics relating stress and particle velocity rates coupled with loading-unloading boundary conditions connecting discontinuities in these same rates proves to be particularly convenient. For a specimen length which allows four complete reflections of the leading edge of the stress pulse before plastic deformation begins, a comparison is made between “reconstituted” stress-strain curves predicted by the Kolsky formulas and the reference bilinear curve. The reconstituted curves exhibit the following features: an underestimate of the initial elastic (primary) modulus; satisfactory agreement with the secondary modulus, particularly for the curve associated with the gentler trapezoidal stress pulse; and realistic “elastic” unloading again associated with the trapezoidal stress pulse. The analysis predicts some separation of the specimen from the bars near the end of the unloading process where influence on the reconstituted curve is small. It is concluded that when one-dimensional effects dominate, by careful selection of design parameters such as specimen length and pulse shape, one may use the Kolsky formulas with confidence in establishing the presence (or absence) of a strain-rate effect in elastic-plastic materials during plastic deformation.