Theoretical Stress-strain Curves Research Articles

A Thermal Damage Constitutive Model for Oil Shale Based on Weibull Statistical Theory

In this work, we first studied the thermal damage to typical rocks, assuming that the strength of thermally damaged rock microelements obeys a Weibull distribution and considering the influence of temperature on rock mechanical parameters; under the condition that microelement failure conforms to the Drucker–Prager criterion, the statistical thermal damage constitutive model of rocks after high‐temperature exposure was established. On this basis, conventional triaxial compression tests were carried out on oil shale specimens heated to different temperatures, and according to the results of these tests, the relationship between the temperature and parameters in the statistical thermal damage constitutive model was determined, and the thermal damage constitutive model for oil shale was established. The results show that the thermal damage in oil shale increases with the increase of temperature; the damage variable is largest at 700°C, reaching 0.636; from room temperature to 700°C, the elastic modulus and Poisson’s ratio decrease by 62.66% and 64.57%, respectively; the theoretical stress‐strain curve obtained from the model is in good agreement with the measured curves; the maximum difference between the two curves before peak strength is only 5 × 10−4; the model accurately reflects the deformation characteristics of oil shale at high temperature. The research results are of practical significance to the underground in situ thermal processing of oil shale.

Nonlinear Biomechanical Characteristics of the Schneiderian Membrane: Experimental Study and Numerical Modeling.

Objective The aim of this study is to quantify the nonlinear mechanical behavior of the Schneiderian membrane. MethodsThirty cadaveric maxillary sinus membrane specimens were divided into the elongation testing group and the perforation testing group. Mechanical experimental measurements were taken via ex vivo experiments. Theoretical curves were compared with experimental findings to assess the effectiveness of the nonlinear mechanical properties. The FE model with nonlinear mechanical properties was used to simulate the detachment of the Schneiderian membrane under loading. Results The mean thickness of the membrane samples was 1.005 mm. The mean tensile strength obtained by testing was 6.81 N/mm2. In membrane perforation testing, the mean tensile strength and the linear elastic modulus were significantly higher than those in membrane elongation testing (P < 0.05). The mean adhesion force between the Schneiderian membrane and the bone was 0.052 N/mm. By FE modeling, the squared correlation coefficients of theoretical stress-strain curves for the nonlinear and linear models were 0.99065 and 0.94656 compared with the experimental data. Conclusions The biomechanical properties of the Schneiderian membrane were implemented into the FE model, which was applied to simulate the mechanical responses of the Schneiderian membrane in sinus floor elevation.

Modelling of microstructure effects on the mechanical behavior of aluminium tubes drawn with different reduction areas

The elastoplastic self-consistent model is one of the effective models to study the initial microstructure effect on the mechanical behavior of bulk materials. However, the use of this micromechanics-based model which only takes into account the Hall–Petch relationship at grain level for predicting the grain size effects on the strength of the deformed materials is not accurate yet. This is because of the fact that the dislocation density also contributes to the strengthening of deformed materials. In this study, a modification made to the Hill-Hutchinson elastoplastic self-consistent model was proposed for investigating the microstructure dependence of the mechanical behavior of deformed materials. Meanwhile, the application of the proposed model for the prediction of mechanical behavior of cold-drawn 6063 aluminium tubes with variable wall thickness was studied. Because of the novel modification, an optimization procedure with two objectives was required to identify the parameters of this micromechanical model. An acceptable agreement between experimental and theoretical stress-strain curves was achieved.

Romanian application of cold‐formed steel beams with screwed corrugated webs

AbstractCold‐formed steel members are used in a wide variety of applications, both residential and industrial, due to their high strength‐to‐weight ratio. This paper introduces an innovative steel structural solution used in a portal frame configuration. The frame is made from cold‐formed steel beams with screwed corrugated web and SHS columns. Very good structural performance was achieved, proved by way of tests on such beams carried out previously at the Technical University of Cluj‐Napoca A finite element analysis was carried out in Abaqus using available, accurate, test‐based calibrated FE models [1]. The same settings, mesh size, contacts, connectors and material definitions were used. Material stress‐strain curves obtained from coupon tests and a theoretical curve were determined; both types were used in the FE analysis for the definition of the material. A monotonic test will be performed on the proposed structural configuration. The paper concludes with advice on how to set up theoretical stress‐strain curves for design assisted by FEA of such kinds of girder. A case study presents one particular proposed structure, analysed by the authors and built for a warehouse application.

Effect of the Solving Method of Parameters on the Description Ability of the Yield Criterion about the Anisotropic Behavior

Two solving methods of Hill48 yield criterion based on stress anisotropy and deformation anisotropy, respectively, are analyzed in detail. The limitation of Hill48 yield criterion is discussed with presenting two kinds of expressions of the solving method of the anisotropic parameters. The uniaxial tensile tests of 5754O aluminum alloy sheet along different directions are carried out. With different solving methods of anisotropic parameters, the theoretical stress-strain curves and the deformation rule during the tension process along different directions are derived. By comparing the theoretical and experimental results, the effect of the solving method on the accuracy of the yield criterion is analyzed. Based on two kinds of solving methods of the parameters the finite element simulations of the deep drawing test of 5754O aluminum alloy sheet are carried out and the accuracy of different solving methods on describing the earing phenomenon is discussed. It is concluded that the solving problem based on stress anisotropy should be used for the research object mainly related to stress anisotropy, while that based on deformation anisotropy should be used for the research objecet mainly related to deformation anisotropy. This research has important reference value for the reasonable application of yield criterion on sheet metal forming.

Tensile mechanics of braided sutures

Sutures are the materials primarily used for closing wounds, and their performance is significantly dependent on their mechanical characteristics. Thus, their tensile property is a key parameter responsible for the success of a suture. In this paper, a simple analytical tensile model of braided sutures has been developed based on braid geometry, braid kinematics, and constituent monofilament properties. The model has accounted for the changes in the braid geometry, including braid angle, diameter, and Poisson’s ratio. The kinematics of the braided suture is analyzed pertaining to monofilament locking or jamming in the braid. The model of jamming state of monofilaments has been presented, and both braid angle and diameter are found to be critical design parameters. The experimental results have been compared to the theoretical stress–strain curves of braided sutures, and an excellent agreement has been observed between them.

Compressive Constitutive Relation for Multi-Layer Corrugated Boards

The investigation into the cushioning properties of multi-layer corrugated boards is a hotspot issue in the packaging field. People one after another investigate into the compressive properties based on experiments. As far as authors' knowledge is concerned, no theoretical research on compressive constitutive relation for multi-layer corrugated boards has ever been reported in literature. Therefore, we investigated into the compressive properties of multi-layer corrugated boards and analyzed their compressive breakage mechanism. The compression curve of multi-layer corrugated boards presents the three sections of linear elasticity, sub-buckling going with local collapse and densification. We constructed the compressive constitutive equation by a subsection function. The equation is standardized by the solid modulus Es of corrugated sandwich materials. Focusing on the structure characteristics, it can express the compression resistance and cushioning properties in the same curve for different basis materials. Comparison between the theory and experiments shows that a good consistency is achieved between theoretical and experimental stress-strain curves. By means of the compressive constitutive equation, the compression resistance and cushioning properties can be evaluated without more experiments, which facilitates the optimization of the structure of the corrugated sandwich structure and the optimized design of the cushioning package.

Non-linear characterization of PP/Twaron laminates based on a model of plasticity with damage

The non-linear stress–strain response of thermoplastic laminates was investigated for a polypropylene matrix composite reinforced with continuous Twaron fibers. Tensile tests were performed on unidirectional composites with a fiber orientation of [0] 5, [24] 5, [33] 5, [45] 5 and [90] 5 and also on a [±45] 2S laminate. The inelastic strains of these materials were described with a modification made to a model of plasticity with damage, originally proposed by Ladeveze (1992). This approach considers the longitudinal plasticity and stiffening behavior of a thermoplastic composite, and models the damaged elastoplastic stress–strain response of the material. The theoretical stress–strain curves and experimental results from the model composites [0] 5, [90] 5 and [±45] 2S were compared, demonstrating that the model can be used as a designing tool for laminated thermoplastic composites.

Comparison between crosslink densities derived from stress–strain data and theoretically data evaluated through the α‐model approach for a polyurethane network system based on hydroxyl terminated polybutadiene and isophorone‐diisocyanate

AbstractThe crosslink density (CLD) for polyurethane elastomeric networks based on hydroxyl terminated polybutadiene and isophorone‐diisocyanate was theoretically calculated with α‐model equations the employing the functionality distribution and extent of reaction as input parameters. The theoretical crosslink density (νt) was compared with the CLD values computed from stress–strain data evaluated at various strain rates. The methods for the calculation of the CLD from stress–strain data were based on the Mooney–Rivlin and Young's modulus approaches. Theoretical stress–strain curves were generated on the basis of νt conforming to both phantom and affine model calculations. The experimental stress–strain plots aligned more closely to the affine model line. The deviation of the experimentally derived stress–strain curves from the theoretical affine curve was probably due to the presence of temporarily trapped physical entanglements. From the stress–strain data, the concentrations of true chemical crosslinks and physical entanglements were estimated individually. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010

Tensile behaviour of thermally bonded nonwoven structures: model description

Nonwovens are complex three-dimensional anisotropic structures and consisting of fibres orientated in certain directions, which are bonded by thermal, chemical, mechanical entanglement or a combination of these techniques. Thermally bonded are further classified in two categories, i.e. through-air and calendared nonwoven structures. In this study, a modified micromechanical model describing the tensile behaviour of thermally bonded nonwovens is proposed by incorporating the effect of fibre re-orientation during the deformation. The anisotropic behaviour of through-air bonded structures is demonstrated through theoretical stress–strain curves and the relationship between the fibre re-orientation and fabric strain is also analysed. Furthermore, the failure criterion of thermally bonded nonwovens is analysed using pull-out behaviour of fibres in the system. A parametric study revealing the dependencies of various structural and geometrical characteristics of fibres on pull-out behaviour of fibres in thermally bonded nonwovens is also discussed.

Rheological Behaviour and Model for Porous Rocks Under Air-Dried and Water-Saturated Conditions

Most rocks exhibit viscoelastic properties or time-dependent behavior during deformation. For example, peak strength and Young's modulus increase with loading rate in uniaxial compression tests. In the creep test, strain increases over time even though stress is maintained at a predetermined value. Such viscoelastic behavior is especially notable in porous rocks such as tuff and weathered rocks. In this study, we first present a brief review of the viscoelastic properties of porous rocks, and then propose a new rheological model based on constitutive equations previously proposed by the authors. The model consists of a spring and a dashpot. We assume that the constitutive equation described in a previous study can be applied to the spring. The viscosity of the dashpot is low prior to loading, and increases gradually with progressive loading. In creep testing at low stress levels, strain of the dashpot corresponds to creep strain because the spring constant does not decrease significantly at low stress levels. Experimental analysis of muddy sandstone, Oya tuff, Tage tuff and Kawazu tuff is compared with theoretical predictions. The measured and theoretical stress-strain curves are in good agreement. The increase in peak strength and Young's modulus with loading rate is well simulated by the model. The most important result of this study is that even at low stress conditions, strain of the dashpot is considerably larger than considered in previous studies. Our model provides a sound simulation of the difference in Young's moduli between air-dried and water-saturated conditions, where the difference is assumed to reflect the partitioning of strain into the dashpot. In water-saturated conditions, strain of the dashpot increases more rapidly than in air-dried conditions, and Young's modulus is consequently relatively small.

Behavior of Concrete Under Nonproportional Biaxial Fatigue Stresses with One Constant

This paper discusses the behavior of concrete subjected to biaxial compression and uniaxial fatigue. Tests are performed on 100 x 100 x 100 mm cube specimens. Within the tests, three lateral stress levels – 0, 0.25, and 0.5 – are performed. The paper also reports on the achievement of experimental stress-strain curves, along with a proposal for using empirical relationships to predict the maximum stress level as a function of lateral stress and fatigue life. Results show that increasing horizontal stress leads to failure mode change and an increase in maximum vertical load-carrying capacity. According to the author, failure modes also indicate that concrete presents similar failure patterns under monotonic and fatigue loadings. From experimental results, the author presents a damage model for predicting the behavior of concrete subjected to biaxial fatigue compression. Good agreement is shown in comparing theoretical stress-strain curves with the experimental data.

Basal-plane slip systems and polymorphic phase transformation inTi2AlC and Ti2AlN: a first-principles study

Deformation modes are studied for two basal-plane slip systems, and , in ternary-layered Ti2AlC and Ti2AlN ceramics using the first-principles plane-wave pseudopotential total energy method. Basedon the theoretical stress–strain curves, the slip system leads to smaller ideal shear strength compared to the mode, implying that the slip system is predominant to the mechanical properties of these ternary-layeredcompounds. Bond-length relaxations are examined for materials strained from elasticity tostructural instability. Interatomic bonds are demonstrated to respond to shear straininhomogeneously because of different bonding strengths. The slips of atomic planes aredetermined by the failure of weak Ti–Al bonds. In addition, we predict a polymorphicphase transformation along the shear deformation path. For the slip system, in contrast, no polymorphic phase transformation is observed because TiCslabs do not hold the original NaCl-type structure and, in addition, Al layers change from ahexagonal to a cubic stacking in the shear deformed lattice. In other words, the structuralunits undergo different atomic configurations from those in the two polymorphs underapplied shear strain.

Constitutive model of rock under static-dynamic coupling loading and experimental investigation

The importance of study on constitutive model of statically loaded rock experiencing dynamic load is set forth, and the studying methods on dynamic constitutive model are classified according to the current studying status. By way of combining statistic damage model and viscoelastic model, uni-axial and multi-axial constitutive models of statically loaded rock experiencing dynamic load (static-dynamic coupling constitutive model) under intermediate strain rate are established. The verification experiment on 2D constitutive model under different static stress and dynamic stress with different frequencies is designed and performed. It is found that there is a good agreement between the experimental stress-strain curves and the theoretical stress-strain curves.

First-principles computations of mechanical properties of Ni2Cr and Ni2Mo

Nickel-based alloys are being considered for use as the outer container of the waste package for the disposal of high-level nuclear waste. During fabrication processes and long-term storage, Ni-based alloy outer containers can undergo microstructural changes due to the formation of Ni2Cr, Ni2Mo, and Ni2(Cr, Mo), which are ordered orthorhombic (oI6) phases whose mechanical properties are unknown because of fabrication difficulties. To circumvent the experimental limitation, a first-principles quantum-mechanical code based on the full-potential linearized augmented plane-wave (FLAPW) method was used to compute the elastic constants and the theoretical stress-strain curves of Ni2Cr and Ni2Mo. The theoretical mechanical properties were then correlated with charge-density distributions of the stressed oI6 unit cell to identify the critical conditions at the onset of fracture. Using first-principles results as material input, the unstable stacking energy and the Peierls-Nabarro (P-N) barrier energy were computed and used to estimate the tensile ductility and fracture toughness of Ni2Cr and Ni2Mo. The influences of the elastic anisotropy and slip vector on dislocation mobility in Ni2Cr and Ni2Mo are identified and contrasted to those in MoSi2 with a tetragonal (tI6) crystal structure.

A pore crack model for the mechanical behaviour of porous granular rocks in the brittle deformation regime

Abstract A model is developed for predicting and simulating the mechanical behaviour and failure mode of brittle porous granular rocks loaded in compression. It is based on a fracture mechanics analysis applied to cracks emanating from the surface of cylindrical pores in two-dimensional, which is well suited to the microstructure of such rocks. It is also consistent with the usual experimental procedure used for biaxial compression tests since the numerical scheme is implemented under the assumption of imposed axial strain. The model takes into account interactions between neighbouring cracks, which grow when their stress intensity factor reaches the fracture toughness of the rock. The simulation of crack growth from cylindrical holes, associated with a failure criterion based on the coalescence of interacting cracks, allows one to calculate the critical stress at rupture and to derive theoretical stress–strain curves. The present model is then used to compare theoretical results with laboratory data obtained on four sandstones with porosity ranging between 13% and 25.5% which were deformed under conventional triaxial compression conditions at confining pressures between 0 and 35 MPa. The comparison shows that by using a small number of parameters (pore size, pore density, fracture toughness, and elastic moduli), the model is able to predict the rock behaviour during the compression tests and the stress level at rupture in a quite accurate way, when the microstructural parameters introduced are consistent with the observations.

Magnetic-field-induced superelasticity of ferromagnetic thermoelastic martensites: Experiment and modeling

The superelastic effect under constant magnetic fields exhibited by the Ni-Mn-Ga ferromagnetic thermoelastic martensites with single-variant and polyvariant microstructure is studied experimentally and theoretically. The formerly proposed statistical model of the magnetostrain effect in the ferromagnetic martensite is modified for the theoretical description of the superelastic stress-strain dependence under magnetic field. The mechanical stress, which is equivalent to the internal stress induced by the magnetic field, is determined by fitting the theoretical stress-strain curves to the experimental results. A quadratic dependence of the field-induced stress on the value of the magnetization of martensite is found. This dependence supports the model assumption that a magnetoelastic interaction causes the magnetostrain effect.

Damage constitutive of concrete under uniaxial alternate tension–compression fatigue loading based on double bounding surfaces

A damage constitutive model for concrete subjected to uniaxial alternate tension–compression fatigue loading is presented. The tension and compression loading and bounding surfaces described in strain-energy release rate are employed to construct the damage-effective tensor in the formulation of the theoretical model. The position of the loading surface in the energy release space between the initial and the bounding surfaces denotes the level of damage state. The varying size of the limit fracture surface for fatigue loading is obtained through establishing the relationship between cumulative damage and the onset of the energy release in a cycle, which simulates the degenerative process of the stiffness of concrete under cyclic loading. Fatigue stress–strain relationship is derived for the investigated loading history. To verify this model an experimental program considering the special mode of loading is developed. Comparisons of the theoretical stress–strain curves and fatigue lives with the experimental data indicate good agreement.

The Numerical Analysis on Superplastic Forming under Plane Strain for 7475 Al-Alloy

The numerical analysis on superplastic forming under plane strain was put in operation. This analytical method is able to account for the strain hardening with regard to strain rate of formed material. The strain rates of each element laid out on the formed material are determined by the combination of stress and strain which are provided by the theoretical equations and stress-strain curve on the tensile test under some strain rates. The experiment was carried out with the condition calculated by the analytical method on the corrugated die for 7475 Al-alloy. The deformation process and variation of thickness on the rectangular pan formed by optimum condition was good agreement with the result predicted by the calculation. By using this analytical method, superplastic forming of the rectangular pan which was controlled the thickness variation to 1: 2 on wall and bottom was planed. The thickness of blank sheet was machined locally according to the design by analysis. It was formed to the rectangular pan successfully. and the formed pan had the thickness distribution which was intended on the forming plan.

軸圧縮を受ける箱形断面短柱の局部座屈領域に関する実験的研究

This paper describes an investigation of local buckling behavior and the local buckling zone of box-section stub-columns subjected to axial compression. In the stub-columns tests, the longitudinal strain of the column is concentrated in the local buckling zone and the strain is not widely distributed along the member axis. In this paper, a series of stub-columns tests is performed to clarify the local buckling behavior of the local buckling zone. The local buckling mode and the length of local buckling zone of the stub-column is measured in detail. Added to this, the theoretical stress-strain curves of stub-columns are derived by plastic hinge analysis. From the experimental and analytical investigation, the length of the local buckling zone of box-section stub-columns is twice as long as the half wave length of the local buckling mode. The deformation capacity of steel member must be estimated considering the local buckling zone.