Equivalent Stress-strain Relation Research Articles

A new theoretical method for predicting the elastoplastic behavior of ductile metallic materials

A new theoretical method is proposed to predict the elastoplastic behavior of three ductile metallic materials, including mild steel Q235, high strength low alloy steel HSLA350, and aluminum alloy AL6061. Using this method, only basic experimental parameters are needed for estimating the pre-necking true stress–strain relation. The evolution of the neck profile of a cylindrical tensile specimen is derived based on experimental measurements. The pre-necking model is able to describe the Lüders deformation phenomenon with great precision. It can also provide precise predictions for the pre-necking behavior of structural steels S275, S355, S460, and S690. In addition, the new post-necking model can accurately determine the equivalent stress-strain relation. The complicated analysis of the stress correction factor is avoided in this method. Comparison between our new method and the existing ones is carried out. The accuracy of our prediction is higher than existing methods, e.g., the Hollomon method, the Ludwick method, and the weighted average method (WAM). This work not only provides new insights into the elastoplasticity and fracture of metals, but also holds promise in the design of metal forming.

Critical ductile fracture criterion based on first principal stress and stress triaxiality

A series of quasi-static fracture tests on ten types of specimens for six types of materials were performed to investigate the ductile fracture failure behavior of materials. The full-range equivalent stress-strain relations of materials were obtained by using finite-element-analysis aided testing method. The critical failure behavior was discussed in detail by the analysis of the local stress and strain distributions on the cross-sections of specimens and fractographic observation of specimens. The results show that the first principal stress is the dominant factor of ductile fracture failure. A novel critical fracture criterion of ductile materials represented by the critical first principal stress and critical stress triaxiality is proposed, and the validity of the proposed criterion has been successfully examined.

Local compressive behavior of joint core reinforced with ring beam for connection of polyvinyl chloride fiber‐reinforced polymer confined concrete column and reinforced concrete beam

AbstractIn this paper, seven specimens were designed to study the influence of the height (h), width (b), and reinforcement ratio (ρ) of ring beam on the failure mode, bearing capacity, deformation, and equivalent stress–strain relation of joint core reinforced with ring beam for connection of polyvinyl chloride fiber‐reinforced polymer confined concrete column and reinforced concrete beam. The experimental results indicated that the crushing of concrete in the joint core dominated the failure of specimens. The ultimate, yield bearing capacity and axial strain decreased with the increase of height, while raised with the improvement of width or reinforcement ratio. The growth of the strains of reinforcement and concrete accelerated with the increment of height, while decelerated with the rise of width or reinforcement ratio. Subsequently, based on the local compression theory, confined concrete theory, and the principle of superposition of multiple confinement, considering the influence coefficient of joint height βh and the enhancement coefficient of stirrups αs, a new formula was proposed to estimate the ultimate bearing capacity of specimens under axial local compression. Then, on the basis of Mander's model, taking the correction parameter η into consideration, a new model of equivalent stress–strain relationship was established. Verification results showed that the models proposed in this research agreed well with the experimental results.

Research on the evaluation model of deep foundation pit supporting structures in urban traffic tunnels

In order to improve the building mechanics performance of the foundation pit supporting structure of urban traffic tunnel and guide the engineering design and construction, the evaluation model of the deep foundation pit supporting structure of urban traffic tunnel is proposed based on mechanical anchoring and linear mechanical loading. The mechanical anchoring method is used to load the support structure of deep foundation pit of urban traffic tunnel. The constitutive relation of dynamic node of deep foundation pit supporting structure of urban traffic tunnel under moving load is constructed, and the tangent elastic modulus of supporting structure of deep foundation pit of tunnel is calculated according to equivalent stress-strain relation. Thus, the mechanical evaluation and optimisation design of deep foundation pit supporting structure of urban traffic tunnel are realised. The test results show that the mechanical loading performance of the model is good for the design of the deep foundation pit supporting structure of urban traffic tunnel, and the load capacity of the supporting structure is improved, and the engineering design of the foundation pit supporting structure is optimised.

Effect of Equivalent Stress-Strain Relation and Differential Hardening on Accuracy of Forming Limit Analyses

Multiaxial tube expansion tests (MTETs) were performed to measure the multiaxial plastic deformation behavior of a cold rolled interstitial-free (IF) steel sheet for a range of strain from initial yield to fracture. The testing machine is capable of applying arbitrary principal stress or strain paths to tubular specimens using an electrical, closed-loop servo-control system for an axial force and an internal pressure. Tubular specimens with an inner diameter of 44.6 mm were fabricated from a cold rolled IF steel sheet with a thickness of 0.7 mm by roller bending and laser welding. Many linear stress paths in the first quadrant of stress space were applied to the tubular specimens to measure the forming limit strains and forming limit stresses of the as-received sheet sample, in addition to the contours of plastic work and the directions of the plastic strain rates. It was found that the shapes of the measured work contours changed with increasing plastic work. The observed differential hardening behavior was approximated by changing the material parameters and the exponent of the Yld2000-2d yield function (Barlat et al, 2003) as functions of the reference plastic strain. The hydraulic bulge tests were also conducted to measure the forming limit strain and forming limit stress for equibiaxial tension and to determine the equivalent stress-equivalent plastic strain relation for a larger strain range. The forming limit curve and forming limit stress curve were calculated using the Marciniak-Kuczyński-type approach. The calculated results were in fair agreement with the measurement.

The Influence of Different Stress States on 16MnR Deformation Capacity

16MnR is the typical material of pressure equipment which worked under complex stress state in engineering application. In order to be close to the actual combined tension-shearing stress state and explore the relationship of deformation capacity and different stress state, many groups of combined tension-torsion tests on 16MnR specimens were designed and the equivalent stress-strain relation under different stress state was obtained. The concept of stress triaxiaty (TS value) was cited to characterize the different stress state and the result showed different stress states have a great influence on the material plastic deformation capacity, TS value turns larger, the plastic deformation weakened; 16MnR has a strongest plastic deformation capacity in pure torsion; the level of tensile stress had no significant effect on the maximum stress in the biaxial stress state, but has a significant inverse relationship with the maximum equivalent strain .At last, the mathematical relationship between maximum equivalent-strain and stress triaxiaty could be found. If the stress state of one point in the engineering structures is certain, the maximum equivalent-strain can be estimated.

High Strain Rate Pure Shear and Axial Compressive Response of Porcine Lung Tissue

In this study, both the dynamic shear (torsion) and axial compressive responses of porcine lung tissue were examined using modified Kolsky bar techniques. High-rate compression data were collected using a Kolsky bar with a hollow transmission bar on annular specimens at strain rates between 1000–3000 s−1. The radial deformation of the annular specimen was recorded on a modified single loading Kolsky bar using high-speed imaging capabilities. The collected images and analysis of boundary movement indicated inhomogeneous specimen deformation induced by radial inertia, which significantly altered the desired uniaxial stress state in such high-rate compression test techniques. A novel torsion experimental technique was developed to obtain the dynamic pure shear behavior of lung tissue at shear strain rates above 500 s−1 without inertia effects. The pure shear response was found to be two orders of magnitude weaker than the uniaxial compressive response when compared by equivalent stress–strain relations.

Deriving stress–strain relationships for steel fibre concrete in tension from tests of beams with ordinary reinforcement

One of the most critical points in the theory of steel fibre reinforced concrete (SFRC) is quantifying the residual stresses in tension. Due to concrete interaction with fibres, a cracked section is able to carry a significant portion of tensile stresses, called the residual stresses. Because of a great diversity in the shape and aspect ratio of fibres and, consequently, varying bond characteristics, there are no currently available reliable constitutive models. In present practices, residual stresses needed for strength, deflection and crack width analysis are quantified by means of standard bending tests. However, such tests require relatively sophisticated and expensive equipment based on the displacement-controlled loading. Besides, the test results are highly scattered. This paper investigates an alternative approach for defining the residual stresses. The approach aims at deriving equivalent stress–strain relations of cracked tensile concrete using test moment–curvature relationships of flexural concrete members with ordinary reinforcement and steel fibres. Tests on eight lightly reinforced beams (reinforcement ratio 0.3%) with different contents of steel fibres (0%, 0.5%, 1.0%, and 1.5% by volume) have been carried out. Based on the proposed technique, equivalent stress–strain relations were defined for each of the beams and further used for curvature and crack width analyses.

THE INFLUENCE OF STRAIN PATH ON BIAXIAL COMPRESSIVE BEHAVIOR OF AZ31 MAGNESIUM ALLOY

The strain path dependence of the compressive flow behavior of cast AZ31 magnesium alloy was investigated. Biaxial compression tests with linear strain paths were conducted using a unique biaxial compression device. It was found that the equivalent stress-strain relations varied according to the strain paths. The work contour for linear strain paths was well described by the Logan-Hosford yield criterion. Biaxial compressions with abrupt strain path change were also carried out to investigate the influences of the prestrain amplitude and angular relation of the sequential strain paths on the flow behavior. Rapid increase in the equivalent stress was observed just after the abrupt strain path change. These specific flow behaviors were discussed with regard to the plastic anisotropy, which showed rapid evolution in the early stage of the biaxial compressions.

Finite Element Modeling of Concrete-Filled Steel Tubular Column after Exposure to Fire

A computational model, in which the effects of high temperature on steel and concrete’s properties and the composite action and interfacial properties between steel tube and concrete core were considered, was developed using ABAQUS program. Based on a damage model of concrete at ambient condition and tested stress versus strain curves of fire-damaged concrete, a new damage model of concrete after exposure to high temperatures was developed to consider the influence of high temperatures on the damage of concrete. By introducing the damage model of fire-damaged concrete, the reasonable equivalent stress-strain relations of confined concrete and a modified steel tube-concrete interface model into the ABAQUS FE model, the mechanical behaviors of the fire-damaged CFT columns and connections were simulated precisely and verified by some relative test results.

Theoretical statistical solution and numerical simulation of heterogeneous brittle materials

The analytical stress-strain relation with heterogeneous parameters is derived for the heterogeneous brittle materials under a uniaxial extensional load, in which the distributions of the elastic modulus and the failure strength are assumed to be statistically independent. This theoretical solution gives an approximate estimate of the equivalent stress-strain relations for 3-D heterogeneous materials. In one-dimensional cases it may provide comparatively accurate results. The theoretical solution can help us to explain how the heterogeneity influences the mechanical behaviors. Further, a numerical approach is developed to model the non-linear behavior of three-dimensional heterogeneous brittle materials. The lattice approach and statistical techniques are applied to simulate the initial heterogeneity of heterogeneous materials. The load increment in each loading stage is adaptively determined so that the better approximation of the failure process can be realized. When the maximum tensile principal strain exceeds the failure strain, the elements are considered to be broken, which can be carried out by replacing its Young's modulus with a very small value. A 3-D heterogeneous brittle material specimen is simulated during a full failure process. The numerical results are in good agreement with the analytical solutions and experimental data.

Nonlinear Finite-Element Analysis of RC Shear Panels and Walls

In the assessment of existing reinforced concrete structures, finite-element analysis plays an important role, particularly in regard to the evaluation of critical regions, regions with special detailing, or regions of stress concentration. A popular class of concrete model uses an orthotropic constitutive relation in which the directions of orthotropy are the principal directions of total strain. Since these directions change during the load-displacement response, such an approach is known as a rotating crack model. The models proposed to date differ in the description of the biaxial failure envelope, the uniaxial equivalent stress-strain relation, Poisson ratio, and the tension-compression behavior. This paper describes the implementation of an orthotropic concrete constitutive model in the finite-element analysis of reinforced concrete members. The emphasis of the paper is on the evaluation of the effect of orthotropic model parameters on the monotonic load-displacement relation of shear panels and walls under different stress states. The ability of the orthotropic concrete material model to assess failure mode, ultimate strength, and load-deformation behavior of this type of structural element is evaluated by correlation studies with available experimental data.

Failure by fracture or yielding in strain hardening materials according to the t-criterion

An attempt is described to develop an improved theoretical approach for the failure of materials, being initially either precracked or uncracked. As a guide for this an idealized approach to the fundamental reaction of solids during state transitions is employed. By setting an upper limit T v,0 of mechanical energy for volume change and another one T D,0 for distortion, beyond which the material transits to either brittle fracture or general rupture by yielding, a closed limiting failure surface is obtained. The necessity of considering the constitutive relation between hydrostatic pressure, p, and unit volume change, θ, in addition to the equivalent stress-strain relation ( \\ ̄ gs- \\ ̄ ge) is emphasized. Finally conclusions are made concerning the experimental evaluation of T v,0 and T D,0 and the application of the present failure criterion in the case of precracked materials. Predictions obtained from this criterion agree well those of McClintock's criterion based on void coalescence, and are clearly supported by the classical experiments performed by Bridgman.

An experimental study of large finite plastic deformation in annealed 1100 aluminum during proportional and nonproportional biaxial compression

A new nonproportional biaxial compression experiment has been developed where a rectangular block first undergoes uniaxial compression and then, after finite deformation, it is subjected to large deformations (up to 45% strain) under biaxial compression. Experimental results on rectangular specimens of annealed 1100 aluminum subjected to uniaxial and biaxial compressive loadings are presented. The experiments include proportional and nonproportional loading paths. Stress and strain measures, directional changes of plastic strain increment, and existence of the von Mises equivalent stress-strain relation at large finite strains are discussed. Small volume changes were computed from the measured strains; however, density measurements after unloading indicate negligible change in density or volume. The classical Prandtl-Reuss equations are shown to predict acceptable results when the true or logarithmic strain loading paths are approximately proportional; however, many constitutive models can predict the experimental results during proportional loading paths. On the other hand, during sharp directional changes in loading paths, the predictions using Prandtl-Reuss equations in terms of deviatoric stress ratios and incremental strain ratios do not agree with experimental data for nonproportional loading paths, especially in the neighborhood of loading path change.

On the Dynamic Yield Condition under Combined Loading of Dynamic Torsion and Static Tension : In the Case of S45C and SS41

In this paper we devised a test device for applying dynamic torsion and static tension to a specimen. Using this device, some experiments were performed on mild steels (S45C and SS41) to examine dynamic yield condition. In addition the relations between stress and strain during plastic flow were studied on the basis of a plastic flow theory including a potential function. Consequently the following were obtained. Yield stresses of S45C and SS41 under the high strain rate of 50/s ∼90/s agreed with those by Mises' condition. Equivalent stress-strain relations under dynamic combined stresses also agreed with those under compressive stresses. The relations between Lode's parameter μ and ν seemed to be μ=ν. Consequently the above theory including a potential function seemed to be valid.