Real Stress-strain Curves Research Articles

Microstructural evolution and dynamic recrystallization model of extruded homogenized AZ31 magnesium alloy during hot deformation

Abstract Using a thermal simulation testing machine, hot compression experiments were carried out on extruded homogenized AZ31 magnesium alloy, and the hot deformation behavior was analyzed. Based on this, the constitutive equation of the alloy is constructed to explore the evolution law of microstructure during hot deformation of the alloy, which could provide theoretical guidance for the reasonable selection of parameter ranges during hot compression of extruded homogenized AZ31 magnesium alloy. The experimental result indicated that the flow stress of the alloy during the hot deformation decreases with increasing temperature, increases with the strain rate increasing, and the real stress–strain curves during deformation show dynamic recrystallization curves. According to the experimental results, the deformation activation energy Q is 126.882 kJ mol−1 and the stress exponent n is 4.36 calculated by the constitutive equation under the given parameters, which confirmed that the glide and climb of dislocations in the climb-controlled regime is the deformation mechanism in this work. Decreasing the compression temperature and increasing the strain rate are helpful to reduce the Zener–Hollomon parameter, control the dynamic recrystallization occurring, and refine grain size to improve the mechanical properties effectively. Moreover, the dynamic recrystallization model of the alloy was constructed using the work hardening rate method and regression method, including dynamic recrystallization critical condition model, dynamic model and grain size model.

Study on Dynamic Impact Response and Optimal Constitutive Model of Al-Mg-Si Aluminum Alloy.

Al-Mg-Si series aluminum alloy is a heat-treatment-strengthened alloy. Research on the impact resistance of Al-Mg-Si series aluminum alloy is of great significance to expand its application in engineering. Taking 6082-T6 aluminum alloy as the concrete research object, using the split Hopkinson pressure bar (SHPB) device, the dynamic mechanical response of the material under different temperatures and average strain rates was studied, and the service performance of the material under extreme conditions was determined. The absolute temperature rise was introduced to optimize the existing constitutive model. The results show that when the environment temperature is 298.15~473.15 K under high-speed impact, the internal thermal softening effect of the material is dominant in the competition with the work hardening, resulting in a decrease in the flow stress of the material. Through the analysis of the real stress-strain curve, it was found that the elastic modulus of the material was negatively correlated with the strain rate, negatively correlated with the temperature, and showed an obvious temperature-softening effect. Yield strength was negatively correlated with temperature and positively correlated with strain rate, which showed an obvious strain rate hardening effect. Based on SEM microscopic analysis, it was found that under given conditions, adiabatic shear bands appeared in some samples, and their internal structures demonstrated obvious change. It was judged that when high-speed impact occurs, cracks are induced at the shear bands, and the cracks will continue to develop along the adiabatic shear bands, resulting in many oblique cracks which will gradually become larger and eventually lead to material failure. Finally, based on the model, the strain rate and temperature softening terms were improved, and a rise in adiabatic temperature rise was introduced. The improved model can better describe the strain rate effect of the material and accurately describe its flow stress. It provides a theoretical basis for the engineering application of materials.

Investigation of dynamic mechanical properties and constitutive model of (010) plane of gallium oxide crystals under shock loading

In this study, ultraprecision processing performance of new-generation optoelectronic gallium oxide crystals is investigated. Based on material mechanics, Hopkinson rod test is carried out on (010) crystal plane of gallium oxide crystal. The destruction process of gallium oxide crystals was observed by high-speed photography and three-dimensional topography. Through this experiment, the dynamic mechanical properties of the (010) crystal plane of the gallium oxide crystal were tested, and the real stress-strain curves at different rates were obtained.The formation mechanism of fracture after crystal crushing was analyzed. It was found that the compressive strength and yield strength of gallium oxide crystals showed a significant plastic increase with the increase of the impact speed, while the plastic failure strain decreased with the increase of the impact speed. Furthermore, dynamic mechanical properties of (010) crystal plane of gallium oxide crystal are tested, and actual stress-strain curves are obtained. The fracture process of gallium oxide crystals is observed via high-speed photography. Formation mechanism of fractures is analyzed using three-dimensional topography. AlongsideCombined with the quasistatic indentation test, a set of Holmquist–Johnson–Cook constitutive models suitable for gallium oxide crystals is established. Based on obtained parameters, finite element software ABAQUS is used to numerically simulate nanoindentation test of gallium oxide crystals. By comparing numerically and experimentally obtained load-displacement curve data, validity of parameters of constitutive model is verified. It provides a certain guiding significance for the subsequent ultra-precision machining of gallium oxide crystals.

Finite Element Analysis for the High Pressure Rotary Cylinder Block

As a pneumatic actuator, high pressure rotary cylinder has been successfully used in some ships, which can provide large torque output and is small and easy to install. The finite element method is used to calculate the cylinder block of high pressure rotary cylinder, and the stress and deformation of the cylinder block are analyzed by using the real stress-strain curve of metal materials. The distribution of stress and deformation is obtained. Moreover, the influence of 1 ~ 7MPa gas pressure on stress and deformation of the cylinder block is investigated. The maximum stress and deformation of the cylinder block under different pressure loads are obtained. The analysis results provide a basis for the design and operation of high pressure rotary cylinder.

Effect of Sintering Factors on Properties of Al-Rich PTFE/Al/TiH2 Active Materials.

Sintering process is an important part of the specimen preparation process, which directly affects the properties of materials. In order to obtain the best sintering control factors of Al-rich PTFE/Al/TiH2 active materials, Al-rich PTFE/Al/TiH2 active specimens with different sintering control factors were prepared using a mold pressing sintering method. A quasi-static compression experiment was carried out on a universal material testing machine, and a real stress-strain curve was obtained. The effects of sintering control factors on the properties of Al-rich PTFE/Al/TiH2 active materials were analyzed by means of mechanical parameters such as compressive strength, failure strain and toughness. SEM and XRD were used to analyze the microstructure and phase of the sintered samples. The results show that: (1) With the increase of cooling rate, the density, yield strength, strain hardening modulus, compressive strength and toughness of Al-rich Al/PTFE/TiH2 specimens decrease gradually, while the failure strain and pores of the specimens increase gradually. (2) With the increase of sintering temperature, the density, maximum true strain and toughness of the specimens first increase and then decrease, and the failure strain of the specimens gradually increases. When the sintering temperature is 360 °C, the PTFE matrix and particles inside the specimen are closely combined, a small number of particles are exposed on the PTFE matrix and there are a small number of voids. (3) With the increase of holding time at 360 °C, the strength and toughness of the material first decrease and then increase. When the holding time is 6 h, the interface between particles and matrix inside the specimen is the strongest, and the crack propagation inside the specimen is less. (4) When the sintering time increased from 1 h to 4 h at 315 °C, the compressive strength of the specimen increased by 1.62%, the toughness of the specimen decreased by 0.55% and the failure strain of the specimen decreased by 0.54%. The interface between PTFE matrix and particles is the strongest and the crack propagation is less in the specimen with a holding time of 4 h. (5) Above all, the optimum sintering parameters of Al-rich Al/PTFE/TiH2 materials are cooling rate of 25 °C/h, sintering temperature of 360 °C, holding time of 6 h and holding time of 4 h at 315 °C. (6) The reactivity of Al-rich Al/PTFE/TiH2 specimens with 10% content of TiH2 under static compression is not significantly affected by sintering parameters.

A numerical study of the constitutive characterization of thermoplastic materials submitted to finite strain

The mechanical characterization of thermoplastics submitted to finite strain is a non-trivial procedure since they may present necking and cold-drawing. These phenomena are associated with heterogeneous strain fields that may mask the real stress–strain curve and lead to mistaken conclusions about the capability of constitutive models to represent the material mechanical response. Aiming to shed light on this issue, this paper presents a numerical study based on a Finite Element Method Updating (FEMU) technique to obtain the true stress–strain curve of a thermoplastic specimen. FEMU technique is employed to characterize three elastoplastic models with different mathematical frameworks. Inverse problems are constructed considering force response and displacement data of a heterogeneous strain field on the specimen due to the necking and neck propagation kinematics. Results shown that even a very simple multilinear elastoplastic model, available in commercial software, is capable of representing force response of a tensile test when only experimental force data is considered. However, when the necking kinematics is taken into account, the studied models present different results and poor mechanical behavior representation, indicating that only the force data obtained from a tensile test is not enough to establish conclusions about the performance of a constitutive model when heterogeneous strain field occurs. Since none of the models was capable of accurately reproduce the experimental force and kinematics data, to evaluate which model performs better, it is proposed a multi-objective analysis of Pareto front results.

Influence of Process Parameters on Forming Load of Variable-Section Thin-Walled Conical Parts in Spinning

Thin-walled conical parts with variable-section are usually made of superalloy material, with poor plasticity and complex forces, which are difficult to form and control. In this research, a thin-walled conical casing of superalloy GH1140 with variable-section is studied; the real stress–strain curve of the material is fitted and the load-displacement curves of superalloy GH1140 are obtained through a universal testing machine. To clarify the equivalent stress distribution on the upper surface of the thin-walled casing during the forming process and after unloading the rotary wheel, the finite element model of the thin-walled conical casing during the spinning forming process is established with the Simufact Forming finite element analysis software. The effects of processing parameters, such as the mandrel rotational speed ω, the roller feed ratio f and the gap deviation rate δ between the roller and mandrel, on the spinning forming load were obtained. The distribution and numerical trend of the tangential residual stress after forming were detected by X-ray diffraction, and the causes of defects such as flange instability were analyzed. The results of the forming test and the test of residual stress conform well with the simulation, which verifies the stability of the model. The research provides a theoretical basis for improving the forming quality of thin-walled parts with variable-section.

Modeling constitutive relationship of sulfate-attacked concrete

Sulfate attack is one of the most common factors responsible for the performance deterioration of concrete exposed to aggressive environment. The transport of sulfate in concrete is a gradual process causing a gradient sulfate attack in concrete. Nominal stress-strain relationship which is directly based on the whole cross-sectional area is not applicable in practical engineering because of its dependence on geometrical dimensions. In this paper, a method is developed to obtain a real constitutive model for sulfate-attacked concrete. To investigate the transport behavior of sulfate ion in concrete, 16 cubic specimens were immersed in 10% sodium sulfate solution for eight immersion durations. Based on the development of sulfate ion content distribution, a modified diffusion model was developed to simulate the transport of sulfate ion in concrete. To clarify the effects of sulfate attack on mechanical properties of concrete, 24 prism specimens were immersed in 10% sodium sulfate solution, and another 24 specimens were immersed in pure water as control group to compensate the influence of further hydration. Based on the sulfate ion content distribution and nominal stress-strain curve for concrete in different immersion durations, real stress-strain curves of concrete with different sulfate ion contents were obtained by an innovative method. After analyzing the effects of sulfate ion content on the mechanical properties of concrete, a real constitutive model was proposed, which can well predict the structural performance of sulfate-attacked concrete members. With the increase of sulfate immersion duration, the peak stress and elastic modulus increase first and then decrease, while the peak strain decreases first and then increase.

Study on Hydroforming of Magnesium Alloy Tube under Temperature Condition

First of all, under 100 °C, 150 °C, 200 °C, 250 °C, 300 °C and 350 °C, respectively do the test of magnesium alloy AZ31B temperature tensile and the fracture of SEM electron microscopic scanning, studying the plastic forming ability under six different temperature. Secondly, observe and study the real stress-strain curves and fracture topography. Through observation and research can concluded that with the increase of temperature, the yield strength and tensile strength of AZ31B was increased, and the elongation rate and the plastic deformation capacity are increased obviously. Taking into account the actual production, energy consumption, and mold temperature resistance, 250 °Cwas the best molding temperature. Finally, under the temperature condition of 250 °C, the finite element simulation and simulation of magnesium alloy profiled tube were carried out by Dynaform, and the special wall and forming limit diagram of magnesium alloy were obtained. According to the forming wall thickness and forming limit diagram, the molding experiment can be optimized continuously.

ANALYSIS OF STABILITY OF A TRUSS MODEL WITH HARD NODES BASED ON VARIOUS STRESS-STRAIN CURVES

The stability of the equilibrium of rod systems is studied numerically taking into account the geometric nonlinearity using as an example a truss with rigid nodes. Various material models are used: linear elastic and elastoplastic with Prandtl and real stress-strain curves. The features of the loss of equilibrium stability are shown

A new approach to investigate real flow stress in micro-extrusion

The friction effect is very important in micro-forming process and differs from the usual forming process. A new method of evaluating the friction factor in tests by combining micro-compression was presented. The friction behavior and the flow stress were investigated in micro-expression by theory analysis and experiment. To investigate the effects of specimen size on the flow stress, a series of compression tests were carried out for specimens with different diameters. The results show that with the decrease of specimen size, the flow stress shows a gradually downward trend. The bulging value increases with increasing the friction factor. Combining the bulging method and theory analysis, the experimental friction factor was obtained and the flow stress was calibrated without friction. Thus, the real stress—strain curve was obtained, which provides the accurate material model for the subsequent finite element simulation on micro-forming.

Study on Deformation Resistance of Bi-Based Superconducting Composite Tapes

The deformation resistance of composite tapes was measured through compression tests. At room temperature, composite tapes were compressed and shaped at different deformation rates to different extents, and the real stress-strain curve of the composite superconducting tapes was obtained. Regression analysis was carried out on the curve using the Nonlinear Least Square Fitting (NLSF) method to acquire the parameters and coefficients regarding the curve, and a mathematical model for the deformation resistance of the composite superconducting tapes was built.

Investigation on the influence of combined shear loads on the forming limit for high strength steels

The knowledge of material behaviour under certain load conditions, occurring in metal-forming processes, urgently calls for the development of robust production processes. For characterisation of materials behaviour in metal forming processes in the automotive industry, Forming Limit Diagrams (FLD) are mainly used to characterise formability under certain in-plane load conditions . But in industrial forming processes not only in-plane- loads, but a mixture of in-plane, bending, pure-shear and combined shear-and tensions loads can occur. But today there is a lack in testing equipment for those combined load conditions because with conventional testing set-ups no superposed shear rates can be realized. For this purpose three novel sample geometries are presented in this article. Further first experimental results show the application of the specimen geometries. On the one hand maximal achievable strains under combined shear and tension loads are measured and on the other hand a first approach to get real stress-strain curves is shown.

Load-sharing and Monte Carlo models of defects in a bundle of fibres

Two methods for modelling and random simulation of progressive deformation and breaks in a bundle of parallel fibres are proposed. First, a stochastic load-sharing reliability model of a parallel system and of its resistance against a stress is utilized. The method of its statistical analysis is presented, too. In order to improve certain limitations of such model, a complementary method based on the Monte Carlo simulation is introduced. The bundle of fibres is modelled as a grid consisting of a set of nodes and connecting arcs. The deformation and breaks are caused by an external load stretching the grid. The first objective is to find an optimal, stabilized, states of the grid corresponding to each load level. Optimal configuration is found with the help of Markov Chain Monte Carlo (MCMC) procedures. In order to model the breaking process, the load is increased sequentially. It is shown that the model is applicable also to other structures, namely to the plain weave fabric and its defects simulation. The results with bundle of fibres are compared with real stress–strain curves. The parameters for simulation were selected in such a way that obtained stress–strain curve corresponds to a real experiment with carbon fibres.

Characterization of material behavior under pure shear condition

In the last decades the design of sheet metal manufacturing processes and products has been mainly influenced by modern tools, e.g. the large field of numerical simulations based on the finite element (FE-) method. Since the modeling of the material behavior is essential for the quality of the calculated results both the determination of characteristic material data and the transformation of these into material models are of high relevance for the whole process-chain. New materials, e.g. light weight sheet metals often show anisotropic and sometimes also some special forming behavior like the twinning effect of magnesium alloys. Furthermore, car body components become more and more complex concerning the geometry and that leads to a mixture of different stress conditions during forming, e.g. deep drawing, stretching and shearing. As a consequence of these reasons also the material models have to be enhanced and therefore especially the yield locus diagram and the real stress-strain curve must include the relevant material characteristics and data. Nevertheless, the forming behavior of sheet metal under pure shearing condition is not sufficient described. In 1984 Miyauchi proposed a new kind of shear test that is characterized by a symmetrical loading of the specimen and homogenous areas of shearing. In this paper a new tool and a new specimen’s geometry are introduced with which shear tests have been done in the style of Miyauchi for different materials. The forming behavior is analyzed using an optical strain measurement system, in order to obtain detailed information on the onset of plastification as well as the homogeneity of the plastification itself. It can be shown that the two shear zones are constant and homogenous during the forming process. Basing on the experimental investigations the real stress-strain curves and the yield loci under pure shear conditions are obtained.

A note on the inadequacy of dislocation theory (disbonding theory)

A model (conventional dislocation theory) was required to explain the extremely low shear strength of real metals in comparison with their theoretical strength. However, dislocation theory based on conventional metallic bonding cannot produce a real stress–strain curve. Disbonding theory based on the crystallizing π-bonding of atoms, can easily explain the real stress–strain curve. Many π-far infrared rays emerge from the crystal lattices at the disbonding, and are used in the rebonding for plastic deformation and strain-hardening. Anelastic behavior, the hysterisis effect, the Bauschinger effect, and slip banding in fatigue can be easily explained by the π-far infrared rays and crystallizing π-bondings.

金屬の柔性的の變形とそれに及ぼす温度の影響に就て

(1) Compression tests were made on seven pure metals. "Real stress-strain curves" were found and the "plastic deformation" was defined. (2) In the plastic deformation, the following relations hold : P/α′=Constant. Pl′=Constant. (3) The variation due to the dimension of specimen or the process of londing was examined. The "stress of the plastic deformation" is almost constant and the "range of the plastic deformation" is larger as the shape of specimen is shortor or the rate of loading is slower. (4) As a rule, the stress of the plastic deformation is small but the range is large for a metal whose melting point is low. (5) The effect of temperature was investigated, the temperature ranged between 0° to 560℃. The stress decreases with the rise of temperature and the range increases, but slightly. (6) For each metal, the stress vanishes at melting point and the relation between the stress and temperature can be expressed as follows : (P/α′)=A(M-t)^m or (P/α′)/(P/α)_2=(M-t_1/M-t_2)^m. (7) There exists a definite relation between the constants A or m and melting points, and in general the value of A is larger or m is smaller as the melting point is lower. (8) Each relation makes two series according as metals are hot short or not, or according as their molecular structures are hexagonal or cubic form.