Tensile Stress-strain Relationship Research Articles

Experimental study on the physical-mechanical properties of frozen silt

The objective of this study was to investigate the physical-mechanical characteristics of frozen Siberian silt. Unfrozen water content, uniaxial compressive strength and direct-tensile strength of frozen silt samples at different moisture contents were determined in the laboratory. Experimental results revealed that the amount of unfrozen water in the silt decreased with descending temperature and stabilized at temperatures below −10°C. Even at very low temperatures a considerable amount of unfrozen water remained. Mechanical strength test results showed a strong dependence of the stress-strain behavior of the frozen silt on the moisture content and temperature. The strength for compression and tension increased with decreasing temperature and increasing moisture content. At any given temperature and moisture content compressive strength was significantly greater than tensile strength. Based on the compressive and tensile stress-strain relationship at a given temperature and moisture content, approximate values of strength ratio, failure strain ratio and deformation modulus ratio were established.

A softened membrane model for torsion in reinforced concrete members

The Softened Membrane Model (SMM), developed for predicting the behavior of reinforced concrete (RC) membrane elements under shear, is extended to RC members subjected to torsion. This new analytical method, referred to as the Softened Membrane Model for Torsion (SMMT), takes into account the strain gradient of concrete struts in the shear flow zone by making two modifications to the constitutive relationships of concrete. First, in the tensile stress–strain relationship of concrete, the pre-cracking stiffness and the strain at peak stress should each be increased by 45%. Second, the Hsu/Zhu ratio for torsion is taken as 80% of the Hsu/Zhu ratio for shear. Similar to the case of the SMM model for shear, this new SMMT model can predict the entire torque–twist curve, including the ranges before and after cracking, as well as the ascending and descending branches. The theoretical predictions from the SMMT compare very well with the test data on torsion available in the literature.

Predicting the flexural load–deflection response of steel fibre reinforced concrete from strain, crack-width, fibre pull-out and distribution data

A semi-analytical model is presented, based on conventional principles of mechanics, to predict the flexure behaviour of steel fibre reinforced concrete. The model uses a stress-block approach to represent the stresses that develop at a cracked section by three discrete stress zones: (a) a compressive zone; (b) an uncracked tensile zone; and (c) a cracked tensile zone. It is further shown that the stress-block, and hence flexural behaviour, is a function of five principal parameters: compressive stress–strain relation; tensile stress–strain relation; fibre pull-out behaviour; the number and distribution of fibres across the cracked section in terms of their positions, orientations and embedment lengths; and the strain/crack-width profile in relation to the deflection of the beam. An experimental investigation was undertaken on both cast and sprayed specimens to obtain relationships for use in the model. The results of the study showed a reasonable agreement between the model predictions and experimental results. However, the accuracy of the model is probably unacceptable for it to be currently used in design. A subsequent analysis highlighted the single fibre pull-out test and the sensitivity of the strain analysis tests as being the main cause of the discrepancies.

General stress–strain relationship for concrete at elevated temperatures

A general stress–strain relationship for concrete when subjected to fire is needed, as it allows designing concrete structures to specific fire-performance criteria and improves the understanding of the behaviour of these structures during fire events. Existing relationships are developed based on fire tests of unconfined concrete specimens. They provide significantly different predictions because of uniqueness of each relationship and the existence of numerous formulations for calculating the governing parameters. In this paper, available formulations for estimating the parameters affecting the behaviour of unconfined and confined concrete are presented. These parameters are concrete compressive strength, concrete tensile strength, concrete compressive strain at peak stress, initial modulus of elasticity of concrete, transient creep strain, thermal strain, and yield stress and bond strength of reinforcing bars. Recommendations for choosing specific formulations are made based on accuracy, generality, and simplicity. Suitable compressive and tensile stress–strain relationships at elevated temperatures that utilize the recommended formulations are proposed based on well-established relationships for confined concrete at ambient temperature. The proposed relationships are compared to existing ones and to the available experimental data. They can capture changes in the mechanical properties of concrete resulting from temperature and confinement and are found to be superior to existing relationships. However, additional tests are needed to further validate and improve the proposed relationships.

Shock-wave induced tension and spall in a zirconium-based bulk amorphous alloy

Dynamic tensile response and fracture of a Zr-based bulk amorphous alloy (BAA) were examined by subjecting samples to uniaxial tensile strain in plate-impact experiments. Following elastic compressive loading to peak stresses ranging between 3.9 and 6.1 GPa, wave interactions produced tensile loading resulting in spallation in the BAA samples. Rear-surface velocity histories, obtained using laser interferometry, provided a real-time measure of the tensile response including spallation. The initial tensile loading was elastic (loading rates approximately 8×105 s−1) and the data were analyzed to obtain a nonlinear, tensile stress-strain relation. Tensile fracture or spall, observed in all experiments, was initiated at a tensile stress of 3.8±0.3 GPa; this initiation value was independent of the impact stress and is significantly higher than that observed for crystalline metals. A phenomenological tensile fracture model was incorporated into one-dimensional wave propagation simulations to gain insight into the BAA tensile response and damage. Good agreement was obtained between the numerical simulations and the experimental measurements. With increasing impact stress, the BAA samples exhibited a change from ductile to brittle tensile response.

Tensile strength of unidirectional CFRP laminate under high strain rate

The tensile strength of unidirectional carbon fiber reinforced plastics under a high strain rate was experimentally investigated. A high-strain-rate test was performed using the tension-type split Hopkinson bar technique. In order to obtain the tensile stress–strain relations, a special fixture was used for the impact tensile specimen. The experimental results demonstrated that the tensile modulus and strength in the longitudinal direction are independent of the strain rate. In contrast, the tensile properties in the transverse direction and the shear properties increase with the strain rate. Moreover, it was observed that the strain-rate dependence of the shear strength is much stronger than that of the transverse strength. The tensile strength of off-axis specimens was measured using an oblique tab, and the experimental results were compared with the tensile strength predicted based on the Tsai–Hill failure criterion. It was concluded that the tensile strength can be characterized quite well using the above failure criterion under dynamic loading conditions.

Fatigue of Deformed Welded-Wire Reinforcement

Using welded-wire reinforcement (WWR) as an alternative to traditional mild steel reinforcing bars has many advantages. WWR has a higher yield strength and is produced under higher quality control standards. Its use also results in fewer labor costs associated with construction. However, many designers are reluctant to use WWR as an alternative to mild steel reinforcing bars due to the unavailability of fatigue design guidance in the American Association of State Highway and Transportation Officials' AASHTO LRFD Bridge Design Specifications. This paper reports on a fatigue testing program of deformed, high-strength WWR. Based on the results of this testing program, a conservative stress range formula for WWR is presented. This same formula has been adopted for use in the 2007 Interim AASHTO LRFD Bridge Design Specifications. In addition, full monotonic axial tensile stress-strain relationships are presented.

高靱性セメント系複合材料を用いたダンパー部材のせん断耐力と変形能に影響を及ぼす要因に関する実験および解析的検討 : 高靱性セメント系複合材料を用いたダンパー部材のせん断耐力と変形能に関する研究(その1)

High performance fiber reinforced cementitious composite (HPFRCC) shows pseudo strain hardening (PSH) behavior under tensile stress. The purpose of this study is to verify the influencing factors on shear strength and deformation capacity of dampers using HPFRCC. In this study, the structural tests using HPFRCC dampers are conducted to obtain the basic data on shear behavior and investigate the application of FEM analysis to these experiments. On that basis, the shear resistance properties of dampers using HPFRCC are examined based on the results of experiments and analysis. It is concluded that the resistance force of the shear reinforcement and the tensile resistance force of the HPFRCC independently activate in the shear resistance properties of dampers using HPFRCC. In addition, the boundary point between PSH zone and strain softening zone in HPFRCC tensile stress-strain relationship is an important factor to control the brittle failure.

Atomistic deformation modes and intrinsic brittleness ofAl4SiC4: A first-principles investigation

From crystallographic point of view, ${\mathrm{Al}}_{4}\mathrm{Si}{\mathrm{C}}_{4}$ can be described as ${\mathrm{Al}}_{4}{\mathrm{C}}_{3}$-type and hexagonal SiC-type structural units alternatively stacked along [0001] direction. However, relationship between this layered crystal structure and mechanical properties is not fully established for ${\mathrm{Al}}_{4}\mathrm{Si}{\mathrm{C}}_{4}$, except for the reported bulk modulus locating between those of ${\mathrm{Al}}_{4}{\mathrm{C}}_{3}$ and SiC. Based on the first-principles pseudopotential total energy method, we calculated the elastic stiffness of ${\mathrm{Al}}_{4}\mathrm{Si}{\mathrm{C}}_{4}$, and reported on its ideal tensile and shear stress-strain relationships considering different structural deformation modes. Elastic properties of ${\mathrm{Al}}_{4}\mathrm{Si}{\mathrm{C}}_{4}$ are dominated by the ${\mathrm{Al}}_{4}{\mathrm{C}}_{3}$-type structural units and exhibit similar results with those of ${\mathrm{Al}}_{4}{\mathrm{C}}_{3}$. Furthermore, the atomistic deformation modes of ${\mathrm{Al}}_{4}\mathrm{Si}{\mathrm{C}}_{4}$ upon tensile and shear deformations are illustrated and compared with ${\mathrm{Al}}_{4}{\mathrm{C}}_{3}$ as well. Since the tension-induced bond breaking occurs inside the constitutive ${\mathrm{Al}}_{4}{\mathrm{C}}_{3}$-type unit, the ternary carbide has similar ideal tensile strength with ${\mathrm{Al}}_{4}{\mathrm{C}}_{3}$. On the other hand, despite the softening of strong coupling between ${\mathrm{Al}}_{4}{\mathrm{C}}_{3}$- and SiC-type structural units is involved in shear, the shear strength for ${\mathrm{Al}}_{4}\mathrm{Si}{\mathrm{C}}_{4}$ is, however, lower than the tensile strength, since $p$-state involved Al-C bonds respond more readily to the shear deformation than to tension. In addition, based on the comparison of strain energies at the maximum stresses, i.e., ideal strengths, for both tension and shear, we suggest that structural failure occurs in tensile deformation firstly and, thus confirms an intrinsic brittleness of ${\mathrm{Al}}_{4}\mathrm{Si}{\mathrm{C}}_{4}$. For crystal structure arranged in alternatively stacking configuration, such as ${\mathrm{Al}}_{4}\mathrm{Si}{\mathrm{C}}_{4}$, mechanical properties can be traced back to the constituent units, and are also related to the coupling strengths between each constituent unit. The results might provide a computational method to predict ductile or brittle response of a solid to applied deformations.

Initial tensile behaviour of elastomers

At very small strains the tensile stress–strain relationship of elastomers is often fairly linear and therefore might be used for obtaining initial tensile modulus E. In this work we analysed initial tensile data of unfilled and carbon black filled vulcanised SBR samples to test if this is feasible. Strains from mechanical contact extensometer data have shown that the initial stress–strain dependence is nearly linear, as expected, but does not go through the origin, probably because of random initial time lag between force and extension times at crossing the zero point. Initial strains taken from the crosshead position have lower variation coefficients than initial strains from the mechanical contact extensometer data and, consequently, initial tensile modulus from the crosshead position also has lower variation coefficients than initial tensile modulus from the mechanical contact extensometer data.

Experimental method and FE simulation model for evaluation of wafer probing parameters

Wafer probing technology is a critical testing technology that is used in the semiconductor manufacturing and packaging process. A well-designed probing system must enable low and stable contact resistance when each needle-like probe makes contact with the IC chip-bonding pad. Mechanical contact using excessive probe force causes over-sized scrub marks that may damage the die pad and sizably deform the probe tip. In this paper, an experimental setup of a single tungsten needle probe making contact with an Al pad was employed to investigate the relationships between the overdrive, contact force, and scrub mark length. A three-dimensional computational probing simulation model was developed for analyzing dynamic deformations of the contact phenomena during wafer testing. The mechanical tensile strength of the tungsten needle was tested with a micro-tester to examine the tensile stress–strain relationship. The elastoplastic behaviors of the probe and die were taken into account in the simulation model. The resultant scrub lengths from the simulation were verified against the experimental data. Additional critical data, such as data of the scrub mark sinking on the die surface and the maximum Von-Mises stress level location at the probe tips, can be predicted. The experimental and numerical methods presented here can be used as useful performance evaluation tools to support the choice of suitable probe geometry and wafer probe testing parameters.

Monte Carlo simulation on tensile failure process of unidirectional carbon fiber reinforced nano-phased epoxy

This paper presents an analytical approach which combines the modified shear-lag model and Monte Carlo simulation technique to simulate the tensile failure process of unidirectional T700 carbon reinforced composite. Two kinds of matrix were investigated in the present paper, one is neat epoxy and the other one is SiC nano-particle filled epoxy. In the model, the strength of the fiber elements is randomly allocated by the Monte Carlo method, the elastic properties of the matrix elements and the friction after the interfaces breakage are definitely allocated. Using this model, the deformation, damage and failure process of the composite are simulated on the microscopic level, the tensile stress–strain relationship is well predicted. The relationship between mechanical properties of the fiber, matrix and composites was discussed. The analysis also shows that, compared with the neat system, nano-phased composite exhibits 10% improvement in tensile strength, which agrees with the experimental data.

Post-peak response analysis of SFRC columns including spalling and buckling

Standard compression tests of steel fiber reinforced concrete (SFRC) cylinders are conducted to formulate compressive stress versus compressive strain relationship of SFRC. Axial pullout tests of SFRC specimens are also conducted to explore its tensile stress strain relationship. Cover concrete spalling and reinforcement buckling models developed originally for normal reinforced concrete are modified to extend their application to SFRC. Thus obtained monotonic material models of concrete and reinforcing bars in SFRC members are combined with unloading/reloading loops used in the cyclic models of concrete and reinforcing bars in normal reinforced concrete. The resulting path-dependent cyclic material models are then incorporated in a finite-element based fiber analysis program. The applicability of these models at member level is verified by simulating cyclic lateral loading tests of SFRC columns under constant axial compression. The analysis using the proposed SFRC models yield results that are much closer to the experimental results than the analytical results obtained using the normal reinforced concrete models are.

Numerical Simulation for High Strain Rate Failure Process of Unidirectional SiCf-Al Composites

This paper presents an analytical approach which combines the modified shear-lag model and Monte Carlo simulation technique to simulate the high strain rate tensile failure process of unidirectional SiC fiber-reinforced metal matrix composites. In the model, the strength of the fiber elements is randomly allocated by the Monte Carlo method, the elastic-plastic properties of the matrix elements and the friction after the interfaces breakage are definitely allocated. Using this model, the deformation, damage and failure process of the SiCf -Al is simulated on the microscopic level, the tensile stress-strain relationship is well predicted. The relationship between mechanical properties of the composites and the original fiber, in situ fiber, interface strength, and fiber strength distribution is discussed. The analysis also shows that, compared with the experimental results, the simulated results using in situ parameters of fiber arrive at good correlation while those using original parameters have much difference (the predicted strength is obviously higher than the experimental strength).

Fracture Mechanics Model for Analysis of Plain and Reinforced High-Performance Concrete Beams

In developing a one-dimensional analysis and design procedure for reinforced concrete structures, research is generally based on yield phenomena and the plastic flow of steel in tension and concrete in compression. The ability of concrete to resist tension is considered in the form of tension stiffening or is completely disregarded. This procedure does not account for the influence of structural size in changing the failure mode and the stress distribution across the uncracked or cracked ligament. The key factor affecting this stress distribution is found to be the strain-softening modulus. This paper presents an improved model that is based on the fundamental equilibrium equation for the progressive failure of plain concrete beams. The concrete stress-strain relationship in tension is derived by calculating the peak tensile stress and softening modulus for different depths of beams on the basis of the fracture parameters obtained with the size effect law. Thus, the proposed model uses the peak tensile stress and the softening modulus, which vary depending on the size of the beam. To study the effect of the strength of high-performance concrete (HPC) on the concrete tensile stress-strain relationship, the experimental load-deflection plots of different-sized beams are compared with those obtained by using the proposed analytical model for eight different mixes made with locally available fly ash and slag. The model is also extended for lightly reinforced concrete beams, and the results are compared with those in the literature and are found to be in good agreement.

Tension-stiffening model for FRP-strenghened RC concrete two-way slabs

The main focus of this paper is to present a tension-stiffening model that is suitable for finite element analysis (FEA) aimed at investigating the effect of FRP strengthening on the tensile behaviour of concrete slabs. Available experimental results of the FRP-strengthened reinforced concrete slabs are used to calibrate the finite element model based on the ultimate load carrying capacity of the two-way slabs. The proposed tension-stiffening model is implemented into the constitutive concrete model defined in a general-purpose finite element code. Reinforced concrete behaviour in tension can signifcantly be changed due to strengthening. An overall increase in the post-peak stiffness based on the tensile stress-strain relationship is observed. A simplified bilinear model is introduced to define the behaviour of the FRP-strengthened concrete in tension. An expression of the fracture energy density is introduced to define the area under the concrete tensile stress-strain relationship. The tensile stress-strain relationship of concrete is referred to as the tension-stiffening model. It is shown numerically that the ultimate load capacity of two-way slab specimens is sensitive to the fracture energy density. Hence, a distinction has to be made between the definitions of the tension-stiffening model of FRP-strengthened and un-strengthened concrete. This distinction is the focus of this paper.

Interfacial properties in commingled yarn thermoplastic composites. Part II: Influence on crack initiation and propagation

AbstractThe second paper in this series aims to identify the relationship between fiber/matrix interface and cracking phenomena occurring in commingled yarn glass fiber/polypropylene (GF/PP) composites. For this purpose, different interfacial qualities were obtained by a modification of the fiber reinforcement sizing and the matrix coupling. In addition to transverse tensile stress‐strain relationships (Part 1 (17)), mode I interlaminar resistance relationships have been recorded while monitoring acoustic emissions. A mode I mechanical analysis points out the influences of the sizing on the mechanisms contributing to energy absorption, which are protection of fibers against break, creation of an interphase and control of adhesion at the glass fiber surface. Sizing appears as a key parameter governing crack initiation and propagation for these commingled thermoplastic composites. Owing to the relationship between global fiber/matrix adhesion and cracking mechanisms, mode I fracture mechanics is a powerful characterization technique of the interfacial quality of GF/PP composites. Polym. Compos. 25:589–600, 2004. © 2004 Society of Plastics Engineers.

Prediction for initiation of debonding damage and tensile stress–strain relation of glass-bead-filled modified polyphenylene oxide

A three-dimensional finite-element meso-cell model has been designed and constructed to predict initiation of the particle/polymer matrix debonding damage and non-linear stress–strain relation of particulate polymer composites (PPC). The meso-cell model consists of a micro-particle, an interface, and a matrix. The initiation of the debonding damage process has been predicted on the basis of a tensile criterion. An experimental investigation has been made on glass beads reinforced polyphenylene oxides for verification of the meso-cell model and the meso-mechanical finite-element technique. In situ scanning electron microscopy has been adopted to study the particle–matrix debonding process in real time under tensile deformation. The predicted results have been found to be in good agreement with the experimental results. The results of the in situ microscopic test also verify the correctness of the meso-cell model.

Stress-Strain Relationship of Reinforced Concrete Subjected to Biaxial Tension

This paper summarizes results from a research study on the tensile stress-strain relationship of reinforced concrete (RC) membrane elements. Extensive tests of RC panels with varying reinforcement ratios were performed to derive a reasonable constitutive law of the tensile stress-strain relationship of RC. Test results show that concrete carries substantial tensile stress even after initial cracking. The stress-strain relationship of concrete in biaxial tension was derived using the behavior and theory of RC members subjected to uniaxial tension. However, the application of this proposed stress-strain relationship for concrete is limited to cases where the direction of reinforcement coincides with the direction of the applied principal stresses.

New characteristic of tensile stress–strain properties in rubbers

Usually, the tensile stress–strain relationship in rubbers looks like an S-shaped curve. The knee point on a curve for non-crystallized gum is related to limited stretchability of the vulcanization network, hence it is observed for pure-gum and filler-loaded rubbers. The bending occurs when the rubber phase reaches a definite strain (start of developing limited network stretchability), so one may assume that at a knee point the strain in the rubber phase is the same for both pure-gum and filler-loaded rubbers. This assumption enabled normalization of stress–strain curves for pure-gum and filler-loaded rubbers and to use a single curve. Knee-point strain is not a geometrical phenomenon, but a structural characteristic of a rubber, since it is related to vulcanization network density, i.e. to the elastic modulus.