True Stress Strain Research Articles

Microstructural, Corrosion, and Mechanical Characterization of Friction Stir Welded Al 6022-to-ZEK100 Mg Joints

Friction stir welded (FSW) aluminum–magnesium lightweight vehicle joints have gained significant interest due to their high strength-to-weight ratio. In this work, the corrosion resistance of this material is analyzed through electrochemical tests, which include open circuit potential (OCP) inspection and potentiodynamic polarization (PD) scanning. Weight loss measurements tested the corrosion rate of the FSW weld through cyclic corrosion testing (CCT) according to the standard SAEJ 2334. Mechanical properties were also investigated, including lap-shear strength, micro- and nano-hardness mapping, and true stress–strain curves as a function of local processing history. The electrochemical results indicate that the center weld zone’s corrosion property stays between the two base alloys. Indentation-based testing demonstrated that the weld zone behaves differently from base alloys. Lap shear strength surprisingly did not drop much even after eight weeks of cyclic corrosion tests, indicating that the joint did not allow any ingress of the electrolyte.

Using surround DIC to extract true stress–strain curve from uniaxial tension experiments

The exact stress–strain curve can be directly identified from uniaxial tension experiments up to the point of onset of diffuse necking. To gain insight into the post-necking hardening response of metals, other experimental methods such as the bulge, compression or torsion experiments are typically employed. Here, we introduce the idea of using surround DIC to obtain accurate specimen shape measurements of tensile specimens with rectangular gage section. Based on the results from a series of detailed three-dimensional finite element simulations of ASTM E8 type of uniaxial tension experiments on a wide spectrum of steel and aluminum behaviors, it is proposed to combine the history of the axial strain on the surface at the specimen center with the average axial stress to extract the stress–strain curve for strains of up to axial true strain of 1. The estimation uncertainty of this stress–strain curve estimation procedure is of the same order as that of the associated experimental uncertainties. This result is validated through an additional computational study for more than 100 distinct hardening behaviors. Furthermore, a surround DIC system composed of four stereo DIC systems is built and used to determine the stress–strain curve for a 1.5 mm thick DP780 steel. In addition, bulge experiments are performed on the same material revealing a good agreement of the post-necking hardening behavior determined through uniaxial and bulge testing.

Thermomechanical Treatment Performance and Flow Stress Model of a Fe–Mn–Al–C Low‐Density Steel

The flow stress curves of Fe‐31.7Mn‐11.5Al‐0.9C low‐density steel are obtained by a hot‐compression test with a Gleeble‐3500 thermomechanical simulator. It is shown in the results that the dynamic recovery and dynamic recrystallization (DRX) of δ‐ferrite occur preferentially under the same deformation condition, inducing a “yield point‐like” phenomenon in the true stress–strain curves. The Zener–Hollomon parameter is introduced to fit the characteristic parameters used to establish the flow stress model according to Arrhenius hyperbolic sine relationship and Avrami equation, and the DRX activation energy of austenite is 414.12 KJ mol−1. The hot‐processing maps at different true strains are simulated based on the dynamic material model to determine the suitable hot‐rolling process and the optimal hot‐working process selection of high strain rate and high deformation temperature combination, 1100–950 °C/1–0.2 s−1, is recommended.

A New Approach for Evaluation True Stress-Strain Curve from Tensile Specimens for DC04 Steel with Vision Measurement in the Post-Necking Phases.

The paper presents an experimental evaluation of deformation of flat samples during uniaxial tensile testing, including uniform deformation and post-necking phases. The authors recommend a specially designed vision extensometer and simplified image processing method for analytical correction of triaxial test results for extended stress-strain curve estimation. A modified correction model is proposed, based on the application of Gaussian functions, to determine the neck geometry of the tested sample. The vision extensometer can monitor a specimen's elongation using two fibre-optic gauges inserted into the material. Measurements taken from the vision extensometer are compared with readings from analogue gauges within the range of uniform deformation. The analytical correction model's ability to correctly assess the extended true stress-strain curve in the post-necking phase was investigated. Image processing forms the basis of an efficient method for identifying the contour of the specimen's neck. Digital image correlation (DIC) was used to verify the proposed solutions and assess the results obtained for the uniform and post-neck deformation phases. The change in thickness of the sample was experimentally measured throughout the tensile test with a digital gauge sensor and compared with the results of the digital image correlation.

Experimental evaluation of bio medical titanium alloy stabilized with niobium

Niobium stabilized titanium alloy has very less cytotoxicity effect compared to commercially pure titanium alloy (Ti-6Al-4 V). Flow behavior of the metals during hot deformation depends mainly on the strain rate and temperature. Such parameter plays a major role in understanding, and enhancing the workability of metals alloys in real life applications. When bio medical metal alloys are considered where, complex shapes of bio implants are major concern for which mechanical properties are analyzed experimentally. Further allows to optimizing those parameters for hot forging process based on required geometrical modelling. Experimental analysis can make reliable and precise prediction of flow behavior in real time industrial forming process. In this experiment, tensile test on bio medical titanium alloy specimen carried out at two different elevated temperatures ranging from 300℃ and 400℃ at strain rate of 10-3. Experiment carried out shows us flow stress, relation between engineering stress vs strain and true stress vs true strain. Along with this tensile fracture behavior of titanium alloy is examined with electron microscope (SEM) over a range of magnification. Micro hardness and microstructure are observed on the specimen appear to show how dislocation density changes increases with increasing strain rate, but decreases with increasing temperature. Deliberate outcomes manifest the yield and ultimate tensile strength continuously decreased with increase in temperature, and ductility (% elongation) increased with rise in temperature.

Optical Strain Measurement and Microfractography of the Fractures of Armstal 550 Steel after Temperature Tensile Tests.

A material strength investigation along with a detailed microfractography analysis of fractures formed during static tensile tests of steel Armstal 550 was performed. The tests in this research were conducted in a temperature range of 298 to 973 K. In addition, during tensile tests at ambient temperature, optical measurements of strain maps and the curvature of the neck were performed. The minimum cross-sectional diameter and the radius of the neck curvature during tensile tests were obtained. The data can be directly used to obtain the true stress-strain curve. The material property analysis confirmed the high strength of the Armstal 550 alloy. The ultimate strength at room temperature equals 2.14 GPa, whereas the yield point equals 1.65 GPa. A decrease in the strength parameters along with an increase in temperature was noted. This is a typical phenomenon related to a change in the density and thermal expansion of steel under the influence of the temperature increase. For example, at a temperature of 500 °C, the ultimate strength is more than 50% less than at room temperature. An in-depth analysis of the metallography and microfractography of fractures resulting from static tensile tests showed the formation of atypical nano- and microstructures with an elongated shape. Local nano- and microstructures were observed at different levels of intensity for different temperatures. The largest clusters of nanoparticles were present on the surfaces of the specimens examined at a temperature of 973 K. Scanning microscopy analysis confirmed the presence of molybdenum oxides.

Computer Simulation of Composite Materials Behavior under Pressing.

Composite materials have a wide range of functional properties, which is ensured by using various technological methods of obtaining both the matrix or fillers and the composition as a whole. A special place belongs to the composition formation technology, which ensures the necessary structure and properties of the composite. In this work, a computer simulation was carried out to identify the main dependencies of the behavior of composite materials in the process of the main technological operations of their production: pressing and subsequent sintering. A polymer matrix randomly reinforced with two types of fillers: spherical and short cylindrical inclusions, was used to construct the finite element models of the structure of composites. The ANSYS Workbench package was used as a calculation simulation platform. The true stress-strain curves for tension, Poisson's ratios, and ultimate stresses for composite materials were obtained using the finite element method based on the micromechanical approach at the first stage. These values were calculated based on the stretching diagrams of the matrix and fillers and the condition of the ideality of their joint operation. At the second stage, the processes of mechanical pressing of composite materials were modelled based on their elastic-plastic characteristics from the first stage. The result is an assessment of the accumulation of residual strains at the stage before sintering. The degree of increase in total strain capability of composite materials after sintering was shown.

Investigation of Low Cycle Fatigue Behaviors of Inertia-Friction-Welded Joints of the TC21 Titanium Alloy

As a new highly damage-tolerant structural material, the TC21 titanium alloy has been widely used in aerospace applications. Inertial friction welding (IFW) is a form of pressure welding technology with less welding parameters and high welding joint performance, which is especially suitable for the connection of rotors of aero-compressors and engines. In this paper, inertia friction welding of TC21 titanium alloys was successfully carried out, and the microhardness, tensile properties and low cycle fatigue (LCF) behaviors of IFW joints were studied. Based on the mechanical parametric results of the tensile test, the true stress–strain curves of the IFW joint of TC21 titanium alloys are obtained by further calculation. Based on the LCF test results under different strain amplitudes, life prediction of IFW joints was investigated. The results of the LCF test show that there is no obvious cyclic hardening and cyclic softening of the IFW joints. Moreover, the fracture morphology of LCF samples under high strain amplitude (0.9%) and low strain amplitude (0.6%) was observed. The results show that the fatigue cracks initiate and propagate at multiple points in the LCF samples, and the transient fracture zone is larger under high strain amplitude. However, under low strain amplitude, a fatigue crack nucleates and propagates at a single point, and the crack propagation zone is larger.

Mechanical properties of Q235∼Q460 mild steels at low temperatures

Mechanical properties of mild steels (MSs) at varying temperatures are fundamental to structural design and numerical analysis. This paper studied mechanical properties of Q235∼Q460 mild steels used for the cold-region infrastructures and LNG tanks. To investigate the mechanical properties of mild steels at low temperatures, standard tensile tests on 12 Q235, 16 Q355 and 12 Q460 mild steel coupons in a cooling chamber were carried out at low temperatures of 20 ∼ -165℃. Test results showed that the yield and ultimate strength of mild steels increased with the decreasing temperatures. In addition, the ductility of MS was not compromised, and ductile failure occurred to MS at low temperatures. Furthermore, prediction equations on mechanical properties of MS at low temperatures were established by regression analyses. Finally, based on the predicted mechanical indexes, two- and three-stage constitutive models were proposed to describe the true stress–strain laws of Q355, Q460 and Q235 mild steels at 20 ∼ -165℃, respectively. Validations showed that the proposed constitutive model reasonably estimated the stress–strain behaviours of Q235 ∼ Q460 mild steels at low temperatures.

Rate-dependent constitutive model of high-strength reinforcing steel HTRB600E in tension

High-strength reinforcing steel HTRB600E has significant potential application in reinforced concrete (RC) structures because of its high strength and ductility. Under the risk that structures with HTRB600E are subjected to severe dynamic loadings, the rate-dependent behavior and constitutive model of HTRB600E need to be investigated to provide a basis for the structural analysis. A series of tension tests were carried out to acquire the engineering stress–strain curves of HTRB600E in the strain rate range from 0.00025 to 590 s−1. Moreover, a hybrid experimental–numerical converse method was used to obtain the true stress–strain curves beyond the necking of HTRB600E at different strain rates. The test results indicate that the strain rate significantly affects the mechanical properties of HTRB600E. The effect of strain rate on yield and ultimate tensile strength, uniform elongation, and yield to tensile ratio of HTRB600E was discussed. Three commonly-used models were calibrated or modified to predict the dynamic increase factors (DIFs) for yield and ultimate tensile strength of HTRB600E. A rate-dependent constitutive model for the engineering stress–strain curves modified from the Mander model was presented for the structure's analytical model based on the section analysis technique. A new rate-dependent constitutive model for the true stress-plastic strain relationship with necking behavior was proposed for the structure's nonlinear finite element analysis model. The formulations of DIFs and constitutive models agree with the test results well.

Annealing process optimization of 3D coil core based on annealing simulation experiment and thermal mechanical coupling model

Annealing is necessary to reduce the residual stress and no-load loss of 3D coil core. In production, because monitoring the changes in temperature and stress of 3D coil core in real time is impossible, the trial and error method is usually used to formulate the annealing process parameters. The annealing simulation experiment of grain-oriented electrical steel (GOES) is carried out to explore the influence of soaking time on iron loss and magnetic flux density. The mechanical properties of GOES are tested, and the true stress–strain curves at different temperatures are obtained. Based on the existing research and experimental results, an anisotropic thermal mechanical coupling model of 3D coil core is established. An optimization scheme of 3D coil core annealing process is obtained, considering the temperature difference, stress and strain. According to the onsite measured parameters, the annealing process is simulated and optimized by the coupling model. Results show that the total annealing time is shortened by about 18.7% without increasing the stress and strain.

Experimental study on the constitutive model of optically clear adhesive films under rapid loading

AbstractThe mechanical properties of optically clear adhesive (OCA) films can be anisotropy and viscoelasticity, and they are distinguished from conventional linear elasticity and hyper‐elasticity. These properties should be considered to analyze the interfacial stress, which plays an important role in evaluating the failure of a structure containing OCA. Based on well‐designed systematical experiments in the material's principal axes, a phenomenological constitutive model of OCA has been proposed in a transversely isotropic and rate‐dependent form. For the application to large deformation cases, the constitutive model was developed by using true stress and true strain. Results show that the well‐known assumption of volume‐incompressibility is not appropriate for OCA, and Poisson's ratio can vary with the loading rate and the current strain. Considering that the mono‐axial mechanical behaviors along the material's principal axes present strong non‐linearity, an incremental three‐dimensional constitutive model has been developed for finite element method (FEM) implementation. By comparing with traditional isotropic elastic and hyperelastic models, numerical examination results show that the proposed constitutive model can give a more accurate description of experimental stress–strain curves.

True Stress-Strain Behavior of Al-based Cast Automotive Alloy Under Different Ageing Conditions and the Effect of Trace Zr

A thorough investigation has been carried out on the Al-12Si-1Mg-1Cu-1Ni automotive alloy considering different properties, specially mechanical properties associated with true stress and true strain with Zr addition of trace amount. A commercially available piston is melted to produce the alloy, and trace amount of Zr is added to make another. The base alloy along with the Zr added alloy had been applied to homogenization, solution treatment, quenching, and ageing in order to get the age-hardening response. The alloys have been heat-treated at 25 ºC, 200 ºC, and 300 ºC, respectively, for four hours for attaining the under, peak and over-aged states, respectively. During ageing, Al2Cu and Mg2Si phases are formed in the aluminium matrix leading to peak-aged strength, which is reduced at over-aged state because of coarsening of precipitation and recrystallizing, shown by the tensile and hardness properties. When Zr is added to the alloy, Al3Zr phases appear while casting and heat-treatment, resisting the drop of strength at over-aged state. It is visible in the stress-strain diagram that at over-aged conditions, the alloy with trace Zr shows improved strength and ductility. In the micrographs of Zr added alloy, finer distributed grains are visible through the grain refinement of Zr, which also prevents recrystallization at over-aged conditions. The homogeneity of the grains as a result of the Zr addition's microstructural change was further confirmed by fractography. It is clear that adding Zr to such alloys does not greatly increase their strength, but it does restrict the declining of strength by preventing the production of thermally stable Al3Zr precipitates, which coarsens the resisting behavior of various intermetallics in the thermally damaged alloy.

Hydraulic-based testing and material modelling to investigate uniaxial compression of thermoset and thermoplastic polymers in quasistatic-to-dynamic regime

The strain rate dependence of thermoplastics and thermosets in the range 10-3–102 s−1 is still unclear due to experimental difficulties. This interval cannot be fully treated using a quasistatic-based electromechanical machine nor a high-speed test relying on the Kolsky bar method. This paper presents a uniaxial compression test set-up to cover the aforementioned range providing robust stress–strain measurements up to 100 s−1. This set-up is assessed at room temperature with a semi-crystalline polymer (SCP) polyether-ether-ketone (PEEK) KT880-NT and a toughened thermoset epoxy PR520. High-speed 3D stereo digital image correlation (DIC) and an infra-red camera are used for data acquisition. The macroscopical true stress–strain curves demonstrate the importance of the thermal softening effect taking place in this range, accompanied with a temperature rise. In terms of characterization, an advanced unified SCP (USCP) model is employed to quantify the rate- and temperature-dependence for both polymers. A straightforward FEM-based parameter identification procedure is proposed requiring only two compressive stress–strain curves. The USCP model is further applied to PEEK 450G from literature to highlight the features of SCPs. The comparison of PEEK and PR520 is discussed pointing out the characterization challenges due to the transitional quasistatic-to-dynamic testing regime.

Evaluation of Fracture Properties of Two Metallic Materials under Hydrogen Gas Conditions by Using XFEM

Interest in hydrogen energy is increasing due to its eco-friendliness and ease of use. Research is being conducted to produce and use hydrogen in various fields such as hydrogen vehicles and nuclear power plants. However, considering the purity requirements and the need for containment, experiments with hydrogen have several constraints, such as accounting for the charging and purging time. In this study, the effects of hydrogen gas on the fracture properties of T6 heat-treated 6061 aluminum alloy (Al6061-T6) and Chromium-molybdenum steel (SA372) were investigated using the extended finite element method (XFEM). First, numerical analyses for smooth and notched slow strain rate tensile test specimens under air and hydrogen gas conditions were conducted using a multi-island genetic algorithm and XFEM to derive true stress–strain data and damage parameters of the two materials based on experimental results. Second, the fracture resistance curves of ½T-compact tension (CT) specimens made of SA372 steel were determined by crack growth analyses using the calibrated parameters. The estimated JQ values were compared with those from experiments to validate the method, of which differences were less than 20%. Finally, the fracture properties of Al6061-T6 alloy were predicted using the same method with ½T-CT specimens.

Hot Deformation Behavior and Processing Maps of ZnSnO3/Cu Composites.

In this work, we designed ternary ZnSnO3 particle-reinforced Cu matrix composites and evaluated the hot deformation behavior of ZnSnO3/Cu composites. The hot deformation characteristics of typical dynamic recrystallization were probed by the resulting true stress–strain curves of ZnSnO3/Cu composites. The influences of deformation conditions, including temperatures (650–850 °C) and strain rates (0.01–5 s−1), on the flow stress of the designed composites were investigated. This revealed that the peak stress increased with the increasing of strain rate and decreasing of temperature. Additionally, the activation energy was calculated to be 237.05 kJ/mol and followed by yielding a constitutive equation for low-stress ZnSnO3/Cu composites. The processing maps established by dynamic materials model theory indicated that the designed composites possessed excellent hot workability, and then the processing parameters (790–850 °C and 0.01–0.04 s−1) of the ZnSnO3/Cu composites were determined for practical industrial production. Our work discloses the deformation behavior of ZnSnO3/Cu matrix composites and extends the rational process design for ternary ceramic/metal materials with excellent hot workability.

Hot deformation behavior, microstructure evolution and slip system of Mg-2Zn-0.5Mn-0.2Ca alloy

The hot deformation behavior of as-cast Mg-2Zn-0.5Mn-0.2Ca alloys was investigated by hot compression tests conducted at 250–400 °C with strain rates of 0.001–1 s−1. The true stress–strain curves showed that flow stress increased with the increase of strain rates and decrease of temperatures. The constitutive equation was obtained, and the calculated average activation energy is 196.79 kJ mol−1. The processing map is developed. Combined with the analyses of microstructural and processing map, the optimal processing parameter is determined at 350 °C and 0.001–0.1 s−1. Based on EBSD analysis, the microstructures of the instability areas and the stable areas are quite different, yet both have a <0001>//CD texture. The slip system in deformed grains was determined by the in-grain misorientation axis (IGMA) analysis. Typical discontinuous dynamic recrystallization (DDRX) mechanism is the main dynamic recrystallization (DRX) mechanism. As the decrease of the strain rates and the increase of the deformation temperatures, the DRX fraction gradually increased, meanwhile, the behavior of DRX has an obvious weakening effect on texture strength.

A Forward Identification Method for High-Temperature Stress–Strain Curves of 7075 Aluminum Alloy Sheet Considering the Necking Stage

The necking phenomenon of metal sheet under high temperatures is serious and continues over a longer duration. It is difficult to describe the high-temperature mechanical properties of materials only on the basis of hardening behavior before necking. To obtain the high-temperature stress–strain curve considering diffuse necking stage, a forward identification method based on strain measurement is proposed in this study. Here, the strain field of the minimum cross-section in the necking region of the specimen is obtained using a DIC (digital image correlation) measurement technique, and the average axial true stress–strain curve is calculated. Then, the average axial true stress–strain curve is modified using the modified Bridgeman formula. Taking 7075 aluminum alloy as an example, the high temperature equivalent stress–strain curve considering the diffuse necking stage is obtained. Compared with the traditional method, the maximum effective strain range is expanded from 0.05 to 0.8 due to the consideration of the necking stage. The obtained curve is characterized by a coupled viscoplastic–damage constitutive model and embedded in ABAQUS through the user subroutine VUMAT to simulate the hot tensile process. The relative error of force–displacement between the simulation and the experiment was 2.4%, validating the ability of the presented method. This study provides theoretical guidance and a scientific basis for the application and forming control of hot stamping processes.

Numerical simulation of strain-softening behavior of glass-filled polymer composites: Comparison of two-dimensional and three-dimensional analyses using Arruda-Boyce and Three-Network viscoplastic models

Most polymers and stiff-filler reinforced polymer composites exhibit post-yield strain-softening characteristics under large deformation mechanical loading. Singh et al. [Polymer Composites, 40 (12), pp. 4726–4741, 2019] conducted compression tests on glass-filled epoxy composites, altering the shape and volume percent of the glass fillers, and observed a dominant strain-softening tendency immediately after the yield stress values. This study aims to capture the post-yield strain-softening characteristics of glass-filled epoxy composites reported by Singh et al. using finite element analysis (FEA). Arruda - Boyce (AB) and Three Network (TN) viscoplastic constitutive material models are used as matrix behavior to perform numerical simulations on two-dimensional and three-dimensional representative volume elements (RVEs), where spherical (circular in 2D) and milled/cylindrical (rectangular in 2D) fillers are randomly positioned and oriented inside. When the calibrated AB and TN models were used to simulate the stress-strain response of the pristine matrix, both models numerically converged and were in good agreement with the experimental results. However, when filler-reinforced polymer composites are considered, the simulations using the AB model become unstable and fail to converge soon after the yield stress (at small strain values) is reached. Whereas simulations using the TN model take a short period to converge to large strain values compared to the former model. The existence of an extra elastic-viscoplastic network in the TN model improves stability in the model's strain-softening zone, allowing for faster numerical convergence. Therefore, the TN model can be used to simulate the strain-softening behavior of both pristine and stiff-filler-reinforced polymer composites under large deformations. The true stress versus true strain data retrieved from the FEA of the two-dimensional and three-dimensional simulations using the TN model were compared with experimental data. When the TN constitutive model was used in three-dimensional simulations instead of the AB viscoplastic model, the elastic modulus, yield stress, and post-yield strain-softening characteristics of the spherical particle and milled fibre epoxy composites were shown to predict the experimental data rather well.

Influence of Loading Rate and Temperature on the Energy Absorption of 3D-Printed Polymeric Origami Tubes under Quasi-Static Loading.

Owing to deformation in the form of the diamond mode with high-energy absorption capacity, origami thin-walled tubes have attracted considerable attention in recent years. Stamping and welding are mainly employed to produce different types of origami thin-walled tubes. The processing defects and geometric asymmetry may be caused by the manufacturing process, which changes the collapsed mode and decreases the energy-absorbing capacity. In this study, fused filament fabrication (FFF) 3D printing is used to fabricate the origami-ending tube (OET) by integrated formation. Experiments and numerical simulations were conducted to study the influence of loading rate and temperature on the energy absorption of polymeric origami tubes under quasi-static loading. The experiments showed that different constitutive models are needed to capture the complex true stress–strain behavior of 3D printing polylactic acid (PLA) material at different temperatures. The damage model is established and then applied to the numerical simulations, which could predict the collapsed mode and the damage behavior of the OET tubes under different loading rates at 30 °C, 40 °C, and 50 °C. Based on the experiments and the validated numerical model, the influence of loading rate and temperature on the crashworthiness performance of the OET tubes is analyzed.