Complete Stress-strain Curves Research Articles

Flexural capacity predictions of self-compacting concrete beams using stress–strain relationship in axial compression

Due to its unique composition, self-compacting concrete (SCC) may have stress–strain characteristics that are significantly different from those of conventionally vibrated concrete (CVC). An experimental investigation was carried out to generate complete stress–strain curves for SCC in axial compression by testing 162 standard cylindrical specimens of strength 35–70 MPa. The accuracy of analytical models for CVC selected from the literature in predicting the stress–strain behaviour of the SCC mixtures is discussed and their inadequacies are highlighted. A new constitutive model covering a wide range of concrete strengths is proposed for SCC. The equivalent rectangular stress block specified in current design codes for flexural capacity predictions was developed on the basis of tests on CVC; given the observed differences in the stress–strain behaviour of CVC and SCC, its applicability to structural design of SCC members becomes questionable. On the basis of the proposed constitutive model for SCC, a new equivalent rectangular stress block valid for concrete strengths of up to 70 MPa is presented for analysis of flexural capacity. The flexural capacity predictions of the proposed stress block are compared with experimental data from the present work and other investigations reported in the literature, and good agreement was obtained. A simple analytical approach is presented for predictive assessment of the load–deflection behaviour of SCC beams with a reasonable degree of accuracy.

Experimental Study of Different Gases on Permeability of Tectonic Coal

Abstract In order to investigate the change law of different gas permeability of tectonic coal under circumstances of different gas pressure and different stress condition, take the tectonic coal with low permeability and outburst hazard as research object and study on the different gas permeability change law of tectonic coal in complete stress-strain process by using the triaxial servo-controlled seepage equipment for thermo-fluid-solid coupling of coal containing gas. The experimental results show that the complete stress-strain curve of coal containing methane is similar to that of coal containing carbon dioxide, which can be divided into five stages with unique characteristics respectively, and there are the minimum value of permeability corresponding to the neighboring juncture between stage II and phase III in complete stress-strain process. In addition, there are existing Klinkenberg effects not only for absorbing gas, such as methane and carbon dioxide but also for non-absorbing gas such as helium gas in the gas-bearing coal seam. Moreover, the Klinkenberg effect on the methane permeability of coal exists in all the stress condition of coal in complete stress-strain process and that on carbon dioxide permeability of coal only appears in the coal compaction named by phase I. Therefore, occurrence of Klinkenberg effect have something to do with structure of coal mass, but also are related to gas type and stress condition of coal mass.

The complete stress-strain curve of recycled aggregate concrete under uniaxial compression loading

The mechanical performance of recycled aggregate concrete (RAC) is investigated. An experiment on the complete stress-strain curve under uniaxial compression loading of RAC is carried out. The experimental results indicate that the peak stress, peak strain, secant modulus of the peak point and original point increase with the strength grade of RAC enhanced. On the contrary, the residual stress of RAC decreases with the strength grade enhancing, and the failure of RAC is often broken at the interface between the recycled aggregate and the mortar matrix. Finally, the constitutive model of stress-strain model of RAC has been constituted, and the results from the constitutive model of stress-strain meet the experiment results very well.

Improved parameter selection method for mesoscopic numerical simulation test of direct tensile failure of rock and concrete

In order to numerically simulate the failure process of rock and concrete under uniaxial tension, an improved method of selecting the mechanical properties of materials was presented for the random mechanic parameter model based on the mesoscopic damage mechanics. The product of strength and elastic modulus of mesoscale representative volume element was considered to be one of the mechanical property parameters of materials and assumed to conform to specified probability distributions to reflect the heterogeneity of mechanical property in materials. With the improved property parameter selection method, a numerical program was developed and the simulation of the failure process of the rock and concrete specimens under static tensile loading condition was carried out. The failure process and complete stress-strain curves of a class of rock and concrete in stable fracture propagation manner under uniaxial tension were obtained. The simulated macroscopic mechanical behavior was compared with the available laboratory experimental observation, and a reasonable agreement was obtained. Verification shows that the improved parameter selection method is suitable for mesoscopic numerical simulation in the failure process of rock and concrete.

Experimental Study on Influences of Chemical Solutions on Mechanical Properties of Brittle Limestone Under Triaxial Compression

A series of triaxial compression tests on dry and saturated limestone (soaked in water solutions of Na2SO4 and CaCl2 at 0.1 mol / L ionic strengths with varying pH, and distilled water for 240 days) have been carried out. The corresponding complete stress-strain curves are obtained. The influences of chemical solution on rock mechanical behaviors are studied. Results from these tests indicate that: 1) Dry limestone samples have obvious brittle feature. Even if the confining pressure reaching 20MPa, the sample is still ruptured suddenly. After soaked in chemical solutions for 240 days, the deformation and failure behaviours were changed from brittle manner to more ductile. 2) Chemical corrosion is an important reason for the strength deterioration. With the same saturated time and confining pressure, the strength degradation level depends on ionic components and pH value of chemical solutions. Acidic solutions have the most significant influence on samples’ mechanical properties. The study has a good reference to researches of deep rock mechanics, and water-rock interaction.

Maxwell Fluid Model for Generation of Stress–Strain Curves of Viscoelastic Solid Rocket Propellants

AbstractSolid rocket propellants are modeled as Maxwell Fluid with single spring and single dashpot in series. Complete stress–strain curve is generated for case‐bonded composite propellant formulations by taking suitable values of spring constant and damping coefficient. Propellants from same lot are tested at different strain rate. It is observed that change in spring constant, representing elastic part is very small with strain rate but damping constant varies significantly with variation in strain rate. For a typical propellant formulation, when strain rate is varied from 0.00037 to 0.185 per second, spring constant (K) changed from 5.5 to 7.9 MPa, but damping coefficient (D) varied from 1400 to 4 MPas. For all strain rates, stress–strain curve is generated using developed Maxwell model and close matching with actual test curve is observed. This indicates validity of Maxwell fluid model for case‐bonded solid propellant formulations. It is observed that with increases in strain rate, spring constant increases but damping coefficient decreases representing solid rocket propellant as a true viscoelastic material. It is also established that at higher strain rate, damping coefficient becomes negligible as compared to spring constant. It is also observed that variation of spring constant is logarithmic with strain rate and that of damping coefficient follows a power law. The correlation coefficients are introduced to ascertain spring constants and damping coefficients at any strain rate from that at a reference strain rate. Correlation for spring constant needs a coefficient “H,” which is function of propellant formulation alone and not of test conditions and the equation developed is K2=(K1‐H)×{ln(dε2/dt)/ln(dε1/dt)}+H. Similarly for damping coefficient (D) also another constant “S” is introduced and prediction formula is given by D2=D1×{(dε2/dt)/(dε1/dt)}S. Evaluating constants “H” and “S” at different strain rates validate this mathematical formulation for different propellant formulations. Close matching of test and predicted stress–strain curve indicates propellant behavior as viscoelastic Maxwell Fluid. Uniqueness of approach is to predict complete stress–strain curves, which are not attempted by any other researchers.

English

Maxwell fluid model consisting of a spring and a dashpot in series is applied for viscoelastic characterisation of solid rocket propellants. Suitable values of spring constant and damping coefficient wereemployed by least square variation of errors for generation of complete stress-strain curve in uniaxial tensile mode for case-bonded solid propellant formulations. Propellants from the same lot were tested at different strain rates. It was observed that change in spring constant, representing elastic part was very small with strain rate but damping constant varies significantly with variation in strain rate. For a typical propellant formulation, when strain rate was raised from 0.00037/s to 0.185/s, spring constant K changed from 5.5 MPato 7.9 MPa, but damping coefficient D was reduced from 1400 MPa-s to 4 MPa-s. For all strain rates, stress-strain curve was generated using Maxwell model and close matching with actual test curve was observed.This indicates validity of Maxwell fluid model for uniaxial tensile testing curves of case-bonded solid propellant formulations. It was established that at higher strain rate, damping coefficient becomes negligible as compared to spring constant. It was also observed that variation of spring constant is logarithmic with strain rate and that of damping coefficient follows power law. The correlation coefficients were introduced to ascertain spring constants and damping coefficients at any strain rate from that at a reference strain rate. Correlationfor spring constant needs a coefficient H, which is function of propellant formulation alone and not of test conditions and the equation developeds K2 = K1 + H ´ ln{(de2/dt)/(de1/dt)}. Similarly for damping coefficient D also another constant S is introduced and prediction formula is given by D2 = D1 ´ {(de2/dt)/(de1/dt)}S.Evaluating constants H and S at different strain rates validate this mathematical formulation for differentpropellant formulations. Stress-strain curves for solid propellants can be generated at those strain rates atwhich actual testing is not possible. Close matching of test and predicted stress-strain curve indicates propellantbehavior as visco-elastic Maxwell fluid. Defence Science Journal, 2010, 60(4), pp.423-427 , DOI:http://dx.doi.org/10.14429/dsj.60.488

Experimental Investigation on Mechanical Behavior of Coarse Marble Under Six Different Loading Paths

A series of triaxial compression experiments were preformed for the coarse marble samples under different loading paths by the rock mechanics servo-controlled testing system. Based on the experimental results of complete stress-strain curves, the influence of loading path on the strength and deformation failure behavior of coarse marble is made a detailed analysis. Three loading paths (Paths I–III) are put forward to confirm the strength parameters (cohesion and internal friction angle) of coarse marble in accordance with linear Mohr-Coulomb criterion. Compared among the strength parameters, two loading paths (i.e. Path II by stepping up the confining pressure and Path III by reducing the confining pressure after peak strength) are suggested to confirm the triaxial strengths of rock under different confining pressures by only one sample, which is very applicable for a kind of rock that has obvious plastic and ductile deformation behavior (e.g. marble, chalk, mudstone, etc.). In order to investigate re-fracture mechanical behavior of rock material, three loading paths (Paths IV–VI) are also put forward for flawed coarse marble. The peak strength and deformation failure mode of flawed coarse marble are found depending on the loading paths (Paths IV–VI). Under lower confining pressures, the peak strength and Young’s modulus of damage sample (compressed until post-peak stress under higher confining pressure) are all lower compared with that of flawed sample; moreover mechanical parameter of damage sample is lower for the larger compressed post-peak plastic deformation of coarse marble. However under higher confining pressures (e.g. σ 3 = 30 MPa), the axial supporting capacity and elastic modulus of damage coarse marble (compressed until post-peak stress under lower confining pressure) is not related to the loading path, while the deformation modulus and peak strain of damage sample depend on the difference of initial confining pressure and post-peak plastic deformation. The friction among crystal grains determines the strength behavior of flawed coarse marble under various loading paths. In the end, the effect of loading path on failure mode of intact and flawed coarse marble is also investigated. The present research provides increased understanding of the fundamental nature of rock failure under different loading paths.

Modeling Permanent Deformation of Unbound Granular Materials under Repeated Loads

Finite-element analysis on a pavement structure under traffic loads has been a viable option for researchers and designers in highway pavement design and analysis. Most of the constitutive drivers used were nonlinear elastic models defined by empirical resilient modulus equations. Few isotropic/kinematic hardening elastoplastic models were used but applying thousands of repeated load cycles became computationally expensive. In this paper, a cyclic plasticity model based on fuzzy plasticity theory is presented to model the long-term behavior of unbound granular materials under repeated loads. The discussion focuses on the model parameters that control long-term behavior such as elastic shakedown. The performance of the constitutive model is presented by comparing modeled and measured permanent strain at various numbers of load cycles. Calculated resilient modulus from the complete stress-strain curve is also discussed.

Empirical Stress-Strain Model for Unconfined High-Strength Concrete under Uniaxial Compression

In this note, a number of empirical models available in the literature of the complete stress-strain curve for unconfined high-strength concrete under uniaxial compression are reviewed and investigated using the published experimental data. Based on the investigations, a new empirical model with emphasis on the softening branch is proposed to generate the complete stress-strain relationship for high-strength concrete. An application of the new empirical model to published experimental data on normal weight concretes over a wide strength range demonstrates that the present model gives a good representation of the mean behavior of the actual stress-strain response.

Analytical Model for Circular Normal- and High-Strength Concrete Columns Confined with FRP

This paper presents a new incremental stress-strain model for fiber-reinforced polymer (FRP)-confined concrete. The model, able to accommodate concrete with a wide range of strength (25–110 MPa), is based on material properties, force equilibrium, and strain compatibility, and uses newly developed models for constantly confined concrete. An expression is proposed to calculate a FRP jacket rupture strain in columns. Beyond the initiation of rupture, gradual failure of a FRP jacket is modeled to account for the size effect on the FRP-confined concrete columns. This proposed constitutive model is unique in that it accommodates a wide range of concrete strength and uses an analytical rupture strain of a FRP jacket to predict the complete stress-strain curve. Small and large specimens tested by the authors and other researchers are used to validate the proposed model. Very good to excellent agreements have been achieved between the analytical and experimental responses.

Experimental Setup for the Determination of Mechanical Solder Materials Properties at Elevated Temperatures

The fabrication of microelectronic and micromechanical devices leads to the use of only very small amounts of matter, which can behave quite differently than the corresponding bulk. Clearly, the materials will age and it is important to gather information on the (changing) material characteristics. In particular, Young’s modulus, yield stress, and hardness are of great interest. Moreover, a complete stress-strain curve is desirable for a detailed material characterization and simulation of a component, e.g., by Finite Elements (FE). However, since the amount of matter is so small and it is the intention to describe its behavior as realistic as possible, miniature tests are used for measuring the mechanical properties. In this paper two miniature tests are presented for this purpose, a mini-uniaxial-tension-test and a nanoindenter experiment. In the tensile test the axial load is prescribed and the corresponding extension of the specimen length is recorded, both of which determines the stress-strain- curve directly. The stress-strain curves are analyzed by assuming a non-linear relationship between stress and strain of the Ramberg-Osgood type and by fitting the corresponding parameters to the experimental data (obtained for various microelectronic solders) by means of a non-linear optimization routine. For a detailed analysis of very local mechanical properties nanoindentation is used, resulting primarily in load vs. indentation-depth data. According to the procedure of Oliver and Pharr this data can be used to obtain hardness and Young’s modulus but not a complete stress-strain curve, at least not directly. In order to obtain such a stress-strain-curve, the nanoindentation experiment is combined with FE and the coefficients involved in the corresponding constitutive equations for stress and strain are obtained by means of the inverse method. The stress-strain curves from nanoindentation and tensile tests are compared for two mate-rials (aluminum and steel). Differences are explained in terms of the locality of the measurement. Finally, material properties at elevated temperature are of particular interest in order to characterize the materials even more completely. We describe the setup for hot stage nanoindentation tests in context with first results for selected materials.

Extrapolation of flow curves at hot working conditions

Many experimental dynamic recrystallization (DRX) flow curves are incomplete and extrapolating to higher strains is required to construct the complete stress–strain curves. In the present work, the DRX flow curves of a 17-4 PH stainless steel were modeled and generalized using the constitutive equations and Avrami description of DRX. The flow softening was directly related to DRX volume fraction, and the DRX time was determined according to the definition of strain rate. The Avrami kinetics was found to be suitable for extrapolation of flow curves to higher strains. This method is useful to overcome the restrictions of some deformation processes such as hot compression.

Distinct element analysis for Class II behavior of rocks under uniaxial compression

In this study, the radial strain control method for uniaxial compression tests was introduced in the distinct element method (DEM) codes and the Class II behavior of rocks was simulated. The microscopic parameters used in the DEM models were determined based on laboratory uniaxial compression tests and Brazilian tests carried at Äspö Hard Rock Laboratory, Sweden. The numerical simulation results show good agreement with the complete stress–strain curves for Class II obtained from the laboratory experiments. These results suggest that the DEM can reproduce the Class II behavior of the rock successfully. The mechanism of the Class II behavior was also discussed in detail from the microscopic point of view. The loading condition and microscopic structure of rocks will play an important role for the Class II behavior.

Tensile behavior of carbon fiber bundles at different strain rates

Quasi-static and high strain rate tensile tests have been performed on T700 carbon fiber bundles and complete stress–strain curves at the strain rate range of 0.001 s − 1 to 1300 s − 1 were obtained. Results show that strain rate has negligible effect on both ultimate strength and failure strain, and T700 carbon fiber can be regarded as strain rate insensitive materials. On the basis of the fiber bundles model and the statistic theory of fiber strength, a damage constitutive model based on Weibull distribution function has been developed to describe tensile behavior of T700 fiber bundles. And the method to determine the statistic parameters of fibers by tensile tests of fiber bundles is established, too.

Investigation on penetration resistance of foamed concrete

This paper studies the penetration resistance of lightweight foamed concrete subjected to impact by hard projectiles. Experiments were performed to obtain the mechanical properties of the material and the penetration depth. Complete stress–strain curves in compression are presented, based on which several important parameters for the description of the compressive strength and energy absorption of the foamed concrete were determined. The penetration depths of hard projectiles were measured at various impact velocities between 10 m/s and 150 m/s with different types of projectile nose shapes including flat, cone and spherical noses. A simulation model based on rigid body dynamics and a shock resistance function is proposed to predict the penetration depth. Reasonably good agreement between experimental and simulating results is achieved.

Numerical Simulations for Class II Behavior of Rocks under Uniaxial Compression using Distinct Element Method

The brittle fracture is the most studied process in rock mechanics fields, especially the post-failure behavior of rock is one of the key issues for rock mechanical problems. However, even at present, it is still difficult to obtain complete stress-strain curve of brittle rocks in the laboratory experiments. Therefore, a new Distinct Element Method (DEM) code for the uniaxial compression tests with radial strain control was developed and Class II behavior of rock was simulated. The simulation results show good agreement with the complete stress-strain curve obtained from the laboratory experiment with radial strain control. These imply that the DEM simulation may be a strong tool for the analyses of rock failure mechanisms such as class II behavior. The post-failure behavior of rock was discussed in detail by using a newly developed DEM code. The simulation results suggest that the loading control methods strongly affect the failure mechanisms and processes of rocks under uniaxial compression (Class I and II). Moreover, it is also found that the key to understand the Class II behavior of rock is the localized deformation, such as shear band. A clear shear band appears in the axial strain controlled uniaxial compression test, and a significant increase of the axial strain occurs with the crack surface slips along the shear band. As a result, complete stress-strain curve of the entire rock shows the Class I behavior. On the other hand, clear shear band does not appear in the radial strain controlled uniaxial compression tests, because formation of shear band does not grow due to the unloading in a critical state. Since clear shear band is not formed, most local small parts of the rock still keep elastic behavior, and as a result, the complete stress-strain curve of the entire rock shows Class II behavior.

AN IMPROVED ANALYTICAL CONSTITUTIVE RELATION FOR NORMAL WEIGHT HIGH-STRENGTH CONCRETE

In this paper, some available analytical models for the complete stress-strain curve for high-strength concrete (HSC) under uniaxial compression are examined and compared with experimental curves published in the literature. Based on these findings, a new analytical constitutive relation is proposed to generate the complete stress-strain curves for normal weight concrete subjected to uniaxial compression with a strength range of 60-120MPa. To demonstrate the validity of the model, comparisons are made with published experimental data for uniaxial compressive tests on high-strength concrete specimens. The present model is shown to give a quite good representation of mean behavior of the actual stress-strain response.

Stress–strain model for concrete confined with CFRP jackets

Enhancement of strength and ductility is the main reason for the extensive use of FRP jackets to provide external confinement to reinforced concrete columns especially in seismic areas. Therefore, numerous researches have been carried out in order to provide a better description of the behavior of FRP-confined concrete for practical design purposes. Most of the existing models are based on the improved or modified forms of the well known empirical formula of Richart et al. derived from the tests on concrete cylinders. Compressive strength of concrete is predicted without a failure criterion for this modeling approach. There exist only a few models that employ the simplified or modified forms of five-parameter failure criterion proposed by William–Warnke. This paper primarily concentrates on the modeling of FRP-confined concrete using a practical failure surface based on only unconfined compressive strength of concrete. A large comparative analysis is accomplished for the existing test data of 127 cylindrical concrete specimens confined with CFRP jackets. The performance of five existing analytical models for the prediction of the compressive strength of FRP-confined concrete is evaluated leading to the detection of the proposed approach as the most accurate one through this comparative study. Moreover, the complete stress–strain curves of eight concrete cylinders obtained from four different experimental studies are plotted adopting both the stress–strain relation of Saenz and the predictions for compressive strength of the approach. Comparisons between the experimental and analytical results point out that the proposed approach provides satisfactory predictions for both the compressive strength and the stress–strain plots of CFRP-confined concrete.

Verification of post failure behaviour of rock using closed-circuit servo-controlled testing machine

The analysis of the stress-strain curve is a fundamental aspect in the field of rock mechanics. Most rock masses are not intact but have discontinuities. It is important to study the stress-strain curve beyond the peak failure as to assess the characteristic of intact rock against non-intact rock. However, several difficulties arise in obtaining the complete stress-strain curve. Since most rocks exhibit brittle behaviour, they fail violently and uncontrollably when tested on conventional compression machines. In this study, two series of uniaxial compression test were performed on sandstone samples. The first test was conducted using a 2000 kN MaTest conventional compression testing machine and the results were compared with a 3000 kN Tinius Olsen servo-controlled testing machine. Based on the results obtained from sandstone samples, post-peak failure can be achieved by using the servo-controlled testing machine. Comparison between the modes of failure observed from the tests on both types of machines clearly show that violent fracture is not the intrinsic characteristic of the rock but due to the rapid release of strain energy from the loading machine.