Showing papers on "Stress–strain curve published in 2007"

Dislocation Avalanches, Strain Bursts, and the Problem of Plastic Forming at the Micrometer Scale

Abstract: Under stress, many crystalline materials exhibit irreversible plastic deformation caused by the motion of lattice dislocations. In plastically deformed microcrystals, internal dislocation avalanches lead to jumps in the stress-strain curves (strain bursts), whereas in macroscopic samples plasticity appears as a smooth process. By combining three-dimensional simulations of the dynamics of interacting dislocations with statistical analysis of the corresponding deformation behavior, we determined the distribution of strain changes during dislocation avalanches and established its dependence on microcrystal size. Our results suggest that for sample dimensions on the micrometer and submicrometer scale, large strain fluctuations may make it difficult to control the resulting shape in a plastic-forming process.

Stress-strain model for concrete confined by FRP composites

Abstract: In this paper, a stress–strain model for concrete confined by fiber reinforced polymer (FRP) composites is developed. The model is based on the results of a comprehensive experimental program including large-scale circular, square and rectangular short columns confined by carbon/epoxy and E-glass/epoxy jackets providing a wide range of confinement ratios. Ultimate stress, rupture strain, jacket parameters, and cross-sectional geometry were found to be significant factors affecting the stress–strain behavior of FRP-confined concrete. Such parameters were analyzed statistically based on the experimental data, and equations to theoretically predict these parameters are presented. Experimental results from this study were compared to the proposed semi-empirical model as well as others from the literature.

Molecular dynamics study of the stress–strain behavior of carbon-nanotube reinforced Epon 862 composites

Abstract: Single-walled carbon nanotubes (CNTs) are used to reinforce epoxy Epon 862 matrix. Three periodic systems – a long CNT-reinforced Epon 862 composite, a short CNT-reinforced Epon 862 composite, and the Epon 862 matrix itself – are studied using the molecular dynamics. The stress–strain relations and the elastic Young's moduli along the longitudinal direction (parallel to CNT) are simulated with the results being also compared to those from the rule - of - mixture . Our results show that, with increasing strain in the longitudinal direction, the Young's modulus of CNT increases whilst that of the Epon 862 composite or matrix decreases. Furthermore, a long CNT can greatly improve the Young's modulus of the Epon 862 composite (about 10 times stiffer), which is also consistent with the prediction based on the rule - of - mixture at low strain level. Even a short CNT can also enhance the Young's modulus of the Epon 862 composite, with an increment of 20% being observed as compared to that of the Epon 862 matrix.

Embedded piezoresistive cement-based stress/strain sensor

Abstract: In order to develop one type of embedded piezoresistive cement-based stress/strain sensor (PCSS) to monitor the local compressive stress/strain of concrete structures, we explore the piezoresistivity of cement-based material with carbon fiber and carbon black under single compressive loading and repeated compressive loads at different loading amplitudes, and find it is reversible and stable within the elastic regime. This justifies the use of cement-based material with carbon fiber and carbon black in the manufacture of embedded PCSS. PCSS based on the piezoresistivity of cement-based material with carbon fiber and carbon black is tested with compressive stress/strain in the range 0 MPa (0 μɛ) to 8 MPa (476 μɛ) for performance evaluation. Results indicate that PCSS can be used to achieve a sensitivity of 1.35% MPa−1 (0.0227% μɛ−1, gage factor of 227), linearity of 4.17% (4.16%), repeatability of 4.05% (4.06%) and hysteresis of 3.61% (3.62%), and the relationship between its input (compressive stress/strain) and output (fractional change in electrical resistivity) is Δρ = −1.35σ (Δρ = −0.0227ɛ). These findings suggest that this newly developed sensor can be used as one of the alternatives to monitor the compressive stress/strain of concrete structures.

Calibration of Stress-triaxiality Dependent Crack Formation Criteria: A New Hybrid Experimental–Numerical Method

Abstract: A new experimental technique has been developed to investigate the onset of fracture in metals at low and intermediate stress triaxialities. The gage section of a flat specimen has been designed such that cracks are most likely to initiate within the specimen center, remote from the specimen boundaries. Along with the specimen, a biaxial testing device has been built to apply a well-defined displacement field to the specimen shoulders. The stress state within the specimen is adjusted by changing the biaxial loading angle. Using this new experimental technique, the crack initiation in metals can be studied experimentally for stress triaxialities ranging from 0.0 to 0.6. The stress and strain fields within the specimen gage section are determined from finite element analysis. The reliability of the computational model of the test set-up has been verified by comparing the simulation results with laser speckle-interferometric displacement measurements during testing. Sample experiments have been performed on the Al-7Si-Mg gravity die casting alloy. A three-step hybrid experimental–numerical calibration procedure has been proposed and applied to determine a phenomenological crack formation criterion for the Al-7Si-Mg alloy.

Experimental investigation of cold-formed steel material at elevated temperatures

Abstract: This paper presents the mechanical properties data for cold-formed steel at elevated temperatures. The deterioration of the mechanical properties of yield strength (0.2% proof stress) and elastic modulus are the primary properties in the design and analysis of cold-formed steel structures under fire. However, values of these properties at different temperatures are not well reported. Therefore, both steady and transient tensile coupon tests were conducted at different temperatures ranged approximately from 20 to 1000 °C for obtaining the mechanical properties of cold-formed steel structural material. This study included cold-formed steel grades G550 and G450 with plate thickness of 1.0 and 1.9 mm, respectively. Curves of elastic modulus, yield strength obtained at different strain levels, ultimate strength, ultimate strain and thermal elongation versus different temperatures are plotted and compared with the results obtained from the Australian, British, European standards and the test results predicted by other researchers. A unified equation for yield strength, elastic modulus, ultimate strength and ultimate strain of cold-formed steel at elevated temperatures is proposed in this paper. A full strain range expression up to the ultimate tensile strain for the stress–strain curves of cold-formed carbon steel at elevated temperatures is also proposed in this paper. It is shown that the proposed equation accurately predicted the test results.

Experimental characterization of the stress–strain behaviour of cemented paste backfill in compression

Abstract: It is of great interest for economical and security reasons to understand the compressive properties of underground cemented paste backfill. In this paper, the stress–strain behaviours of cemented paste backfill (CPB) subjected to uniaxial compression and conventional triaxial tests are presented and discussed. The effect of CPB basic components, strength, ageing and confining pressure on the deformation behaviour of CPB are evaluated and discussed. The results show that the stress–strain behaviour of CPB is strongly influenced by the confinement, the age and strength of CPB, and its components. The increase in confining pressure leads to a change in the mode of failure, in the stiffness, and an increase in the strength.

Modulus, Fracture Strength, and Brittle vs. Plastic Response of the Outer Shell of Arc-grown Multi-walled Carbon Nanotubes

Abstract: The fracture strengths and elastic moduli of arc-grown multi-walled carbon nanotubes (MWCNTs) were measured by tensile loading inside of a scanning electron microscope (SEM). Eighteen tensile tests were performed on 14 MWCNTs with three of them being tested multiple times (3×, 2×, and 2×, respectively). All the MWCNTs fractured in the “sword-in-sheath” mode. The diameters of the MWCNTs were measured in a transmission electron microscope (TEM), and the outer diameter with an assumed 0.34 nm shell thickness was used to convert measured load-displacement data to stress and strain values. An unusual yielding before fracture was observed in two tensile loading experiments. The 18 outer shell fracture strength values ranged from 10 to 66 GPa, and the 18 Young's modulus values, obtained from a linear fit of the stress–strain data, ranged from 620 to 1,200 GPa, with a mean of 940 GPa. The possible influence of stress concentration at the clamps is discussed.

Stress-driven Melt Segregation and Strain Partitioning in Partially Molten Rocks: Effects of Stress and Strain

Abstract: The evolution of melt segregation in deforming partially molten olivine-rich rocks has been studied in a series of laboratory experiments. During deformation, melt segregates into networks of anastamosing channels (or ‘bands’) surrounding lenses of melt-depleted material. We quantify the nature of the melt distribution in the samples, including thickness, angle, spacing, volume fraction, and melt fraction of melt-rich bands, to understand the dynamics of melt-network organization. Two series of experiments were designed to isolate the effects of (1) increasing shear strain (at similar stress levels), and (2) varying stress levels (deformed to similar shear strains). Melt-rich bands develop by a shear strain of unity. In samples deformed at varying stress levels, higher stress produces smaller characteristic band spacings. We relate these variations to the compaction length, dc, which varies only as a result of the reduction of matrix viscosity with increasing stress. Simple approaches to scaling from experimental to mantle conditions suggest that stress-driven melt segregation can occur in the asthenosphere; if so, it will significantly affect rheological, transport and seismic properties, with enticing consequences for our understanding of plate^mantle interactions.

Tensile strength of unidirectional CFRP laminate under high strain rate

Abstract: 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 a...

Ensemble averaging stress–strain fields in polycrystalline aggregates with a constrained surface microstructure – Part 2: crystal plasticity

Abstract: The effect of three-dimensional (3D) grain morphology on the deformation at a free surface in polycrystalline aggregates is investigated by means of a large-scale finite element and statistical approach. For a given two-dimensional surface at z = 0 containing 39 grains with given crystal orientations, eight 3D random polycrystalline aggregates are constructed having different 3D grain shapes and orientations except at z = 0, based on an original 3D image analysis procedure. They are subjected to overall tensile loading conditions. The continuum crystal plasticity framework is adopted and the resulting plastic strain fields at the free surface z = 0 are analyzed. Ensemble average and variance maps of the plastic strain field at the observed free surface are computed. In the case of elastoplastic copper grains, fluctuations ranging between 2% and 80% are found in the equivalent plastic slip level at a given material point of the observed surface from one realization of the microstructure to another. The obt...

Shear Strength Behavior of Fiber-Reinforced Sand Considering Triaxial Tests under Distinct Stress Paths

Abstract: The results of drained triaxial tests on fiber reinforced and nonreinforced sand (Osorio sand) specimens are presented in this work, considering effective stresses varying from 20 to 680 kPa and a variety of stress paths. The tests on nonreinforced samples yielded effective strength envelopes that were approximately linear and defined by a friction angle of 32.5° for the Osorio sand, with a cohesion intercept of zero. The failure envelope for sand when reinforced with fibers was distinctly nonlinear, with a well-defined kink point, so that it could be approximated by a bilinear envelope. The failure envelope of the fiber-reinforced sand was found to be independent of the stress path followed by the triaxial tests. The strength parameters for the lower-pressure part of the failure envelope, where failure is governed by both fiber stretching and slippage, were, respectively, a cohesion intercept of about 15 kPa and friction angle of 48.6 deg. The higher-pressure part of the failure envelope, governed by tensile yielding or stretching of the fibers, had a cohesion intercept of 124 kPa, and friction angle of 34.6 deg. No fiber breakage was measured and only fiber extension was observed. It is, therefore, believed that the fibers did not break because they are highly extensible, with a fiber strain at failure of 80%, and the necessary strain to cause fiber breakage was not reached under triaxial conditions at these stress and strain levels.

Simplified Inverse Method for Determining the Tensile Strain Capacity of Strain Hardening Cementitious Composites

Abstract: As emerging advanced construction materials, strain hardening cementitious composites (SHCCs) have seen increasing field applications recently to take advantage of its unique tensile strain hardening behavior, yet existing uniaxial tensile tests are relatively complicated and sometime difficult to implement, particularly for quality control purpose in field applications. This paper presents a new simple inverse method for quality control of tensile strain capacity by conducting beam bending test. It is shown through a theoretical model that the beam deflection from a flexural test can be linearly related to tensile strain capacity. A master curve relating this easily measured structural element property to material tensile strain capacity is constructed from parametric studies of a wide range of material tensile and compressive properties. This proposed method (UM method) has been validated with uniaxial tensile test results with reasonable agreement. In addition, this proposed method is also compared with the Japan Concrete Institute (JCI) method. Comparable accuracy is found, yet the present method is characterized with much simpler experiment setup requirement and data interpretation procedure. Therefore, it is expected that this proposed method can greatly simplify the quality control of SHCCs both in execution and interpretation phases, contributing to the wider acceptance of this type of new material in field applications.

Development of stress-modified fracture strain for ductile failure of API X65 steel

Abstract: The present paper proposes ductile failure criteria in terms of true fracture strain (the equivalent strain to fracture) as a function of the stress triaxiality (defined by the ratio of the hydrostatic stress to the equivalent stress) for the API X65 steel. To determine the stress-modified fracture strain, smooth and notched tensile bars with four different notch radii are tested, from which true fracture strains are determined as a function of the notch radius. Then detailed elastic–plastic, large strain finite element analyses are performed to estimate variations of stress triaxiality in the tensile bars, which leads to true fracture strains as a function of the stress triaxiality, by combining them with experimental results. Two different failure criteria are proposed, one based on local stress and strain information at the site where failure initiation is likely to take place, and the other based on averaged stress and strain information over the ligament where ductile fracture is expected. As a case study, ligament failures of API X65 pipes with a gouge are predicted and compared with experimental data.

High-Resolution Three-Dimensional Computer Simulation of Hominid Cranial Mechanics

Abstract: In vivo data demonstrates that strain is not distributed uniformly on the surface of the primate skull during feeding. However, in vivo studies are unable to identify or track changes in stress and strain throughout the whole structure. Finite element (FE) analysis, a powerful engineering tool long used to predict the performance of man-made devices, has the capacity to track stress/strain in three dimensions (3-D) and, despite the time-consuming nature of model generation, FE has become an increasingly popular analytical device among biomechanists. Here, we apply the finite element method using sophisticated computer models to examine whether 3-D stress and strain distributions are nonuniform throughout the primate skull, as has been strongly suggested by 2-D in vivo strain analyses. Our simulations document steep internal stress/strain gradients, using models comprising up to three million tetrahedral finite elements and 3-D reconstructions of jaw adducting musculature with both cranium and mandible in correct anatomical position. Results are in broad concurrence with the suggestion that few regions of the hominid cranium are clearly optimized for routine feeding and also show that external stress/strain does not necessarily reflect internal distributions. Findings further suggest that the complex heterogeneity of bone in the skull may act to dissipate stress, but that consequently higher strain must be offset by additional strain energy. We hypothesize that, despite energetic costs, this system may lend adaptive advantage through enhancing the organism's ability to modify its behavior before reaching catastrophic failure in bony or dental structures.

Nanotwin formation in copper thin films by stress/strain relaxation in pulse electrodeposition

Abstract: Nanotwinned copper has been shown to greatly improve the yield strength while maintaining good electrical conductivity. It has great potential to be incorporated in the very-large-scale integration of Cu interconnect technology. The influence of stress/strain on nanotwin formation is studied using first principles calculations of the total crystal binding energy. Under biaxial stress, the total energy of strained Cu can be larger than that of strain-relaxed periodic nanotwinned Cu. We propose that, during pulse electrodeposition of Cu films, highly strained Cu can undergo recrystallization and grain growth to relax stress and form strain-relaxed nanotwins.

Ensemble averaging stress–strain fields in polycrystalline aggregates with a constrained surface microstructure – Part 1: anisotropic elastic behaviour

Abstract: The effect of three-dimensional (3D) grain morphology on the deformation at a free surface in polycrystalline aggregates is investigated by means of a large-scale finite element and statistical approach. For a given two-dimensional surface at z = 0 containing 39 grains with given crystal orientations, 17 random 3D polycrystalline aggregates are constructed having different 3D grain shapes and orientations except at z = 0, based on an original 3D image analysis procedure. They are subjected to overall tensile loading conditions. The resulting stress–strain fields at the free surface z = 0 are analyzed. Ensemble average and variance maps of the stress field at the observed surface are computed. In the case of an anisotropic elastic behaviour of the grains, fluctuations ranging between 5% and 60% are found in the equivalent stress level at a given material point of the observed surface from one realization of the microstructure to another. These results have important implications in the way of comparing fin...

A Recruitment Model of Quasi-Linear Power-Law Stress Adaptation in Lung Tissue

Abstract: When lung tissue is subjected to a step in strain, it exhibits a stress adaptation profile that is a power function of time. Furthermore, this power function is independent of the strain, even though the quasi-static stress–strain relationship of the tissue is highly nonlinear. Such behavior is known as quasi-linear viscoelasticity, but its mechanistic basis is unknown. We describe a model of soft tissue rheology based on the sequential recruitment of Maxwell bodies. The model is homogeneous in its elemental constitutive properties, yet predicts both power-law stress relaxation and quasi-linear viscoelasticity even when the stress–strain behavior of the model is nonlinear. The model suggests that stress relaxation in lung tissue could occur via a sequence of micro-rips that cause stresses to be passed from one local stress bearing region to another.