Engineering Stress Strain Curves Research Articles

Stress wave effects and their mechanisms on stress-strain curves in the elastic phase of SHPB tests

In Split Hopkinson Pressure Bar (SHPB) tests, the stress wave effects during the elastic phase of the stress-strain curve and their influence mechanisms are crucial. Due to the extremely short duration of the elastic deformation phase, the stress wave effects on the specimen during this stage cannot be ignored. This leads to significant errors in the obtained elastic stress-strain curves. However, the dynamic compressive elastic stress-strain relationship forms the basis for studying the viscoelastic behavior of materials. Accurate determination of elastic yield stress and yield strain is also essential for deriving accurate plastic stress-strain relationships. Quantitative research on the stress wave effects during the elastic compression phase of SHPB tests is fundamental for decoupling and obtaining accurate material elastic curves. This paper conducts a quantitative theoretical analysis of the structural effects caused by stress wave evolution during the elastic compression phase, based on the assumption of plane waves. It studies the deviation characteristics and main factors of the phenomenological engineering stress-strain curves of the specimen compared to the actual material stress-strain curves under different conditions, revealing the influence rules and mechanisms of this deviation. The maximum stress deviation value and its corresponding dimensionless time, as well as the variation trend of the maximum stress deviation value within different fluctuation intervals, are calculated. Additionally, the study investigates the cases where the incident wave is arc-shaped or a combination of arc and linear waves. The findings provide theoretical references for the precise design and accurate data processing of SHPB tests.

Kinking induced plasticity in a novel refractory high-entropy alloy

A novel Ti41V27Hf13Nb13Zr6 refractory high-entropy alloy (RHEA) with an excellent fracture elongation of 30 % at a high strength level of 986 MPa was successfully fabricated. We discovered that kinking induced plasticity, involving successive stages of dislocation arrangement, pre-kinking, and the coalescence of multiple kink bands. The soft character of kinking originated from the degraded dislocation density within the kink bands. As such, the interplay between strain hardening caused by dislocation accumulation and the softening effect due to kink bands led to a plateau-type engineering stress-strain curve to large strains. These findings provide a novel design pathway to achieve ductile RHEAs via deformation kinking.

Dynamic tensile behavior and constitutive model of a novel high-strength and high-toughness plate steel

The dynamic tensile behavior of a novel-developed plate steel with high strength and toughness is investigated. Uniaxial tensile tests are conducted at various strain rates varying from 0.1 s−1 to 1000 s−1, and then scanning electron microscope and electron backscattered diffraction analyses are performed on tensile specimens at failure. A large and homogeneous deformation is demonstrated during the tension and small necking is observed at failure; all test results reveal the strain rate dependency of this novel plate steel: with an increase in strain rate, the yield strength, ultimate tensile strength, and total elongation increase, whereas the uniform elongation decreases. Microstructure analyses find dimple fracture surface and considerable deformation twins and dislocations, confirming the high strength and high ductility of the novel plate steel. The density of twins and dislocations demonstrates a positive correlation with the increasing strain rate, aligning with the variations observed in the mechanical properties. Engineering stress–strain curves exhibit a necking lag effect at high strain rates, and this effect is considered when solving the true stress–strain relationships by a developed hybrid experimental–numerical method. A modified Johnson-Cook model considering the power law strain rate effect and thermal softening effect caused by adiabatic temperature rise is finally proposed and verified. This work explores the dynamic mechanical behavior of the novel plate steel at different strain rates, promoting its application in aseismic design and impact resistance engineering.

Experimental research on mechanical, material, and metallurgical properties of Inconel 600: Application in elevated temperature environment

Experimental research on mechanical, material, and metallurgical properties of Inconel 600: Application in elevated temperature environment

Role of Ti and Cr on microstructure and hydrogen embrittlement of welded joint of low-alloy steel used for armor layer

Welded joints suffer from hydrogen embrittlement (HE) owing to the internal stress generated during welding. Alloying elements play a vital role in the metallurgical behavior of welded joints. In this study, the influence of chromium (Cr) and titanium (Ti) on the HE behavior of welded joints in low-alloy steel was investigated by examining the microstructural morphology, grain characteristics, precipitate particles, engineering stress–strain curves, and fracture modes. The experimental results indicated that, compared with the addition of Cr, the addition of Ti promoted the formation of acicular ferrite in the lower fusion zone (FZ) via Ti-bearing oxides, and refined the grains of the FZ. The strength and elongation of the Ti joint were superior to those of the Cr joint in both air- and hydrogen-containing environments. Furthermore, compared with the addition of Cr, the addition of Ti improved the HE sensitivity. The fracture modes of both the Cr and Ti welded joints changed from ductile to brittle when the prepared joints were exposed to an H-containing environment.

Experimental and theoretical investigation of aortic wall tissue in tensile tests.

Understanding the mechanical properties of aortic tissue is essential for developing numerical computation tools and assessing the risk of aortic aneurysm fractures. Tensile tests using aortic wall specimens allow for the determination of stress and strain depending on the location and direction of the sample. The aim of this study was to perform a mechanical tensile test using canine aorta samples and create a numerical model of aortic tissue tension from the processed data. Dogbone-shaped samples were dissected from canine aortic segments. The initial measurements were made at zero tension and the tensile tests were conducted at 10 mm/min until rupture. Force and stretch data were used to obtain engineering and true stress-strain curves. The true stress-strain curves were taken until the maximum strength was obtained, after which they were smoothed and fitted using a logistic function with three coefficients. These curves were then used as material mechanical properties for a numerical model of the aortic tissue tension. A simplified rectangle form was used to mimic the middle of the dogbone-shaped portion of the tissue specimen. Experimental displacement data were collected for the boundary conditions of the finite element 3D model. The experimental data processing revealed that the logistic function described the nonlinear behaviour of the aorta soft tissue with an accuracy of 95% from the start of the tension to the media layer rupture. By applying numerical simulations, we obtained a correspondence of the load curve with an RMSE = 0.069 for the theoretical and experimental external tension data. The numerical investigation confirmed that the non-linear soft tissue was validated by applying a logistic function approach to the mechanical properties of the aortic wall.

Orientation selected micro-pillar compression behavior of heavy-ions irradiated RAFMs

The present study aimed to investigate the mechanical property of heavy ions irradiated Reduced Activation Ferrite/Martensitic (RAFM) steels. The CLF-1 steel was irradiated by 33.5 MeV Fe ions at room temperature, resulting a peak displacement damage of 20 displacements per atom (dpa). Experimental analysis was conducted using Electron Backscatter Diffraction (EBSD) mapping-assisted Focused Ion Beam (FIB) technique to prepare micro-pillars oriented along crystal directions <0 0 1>. Subsequently, these fabricated micro-pillars underwent compression tests utilizing a flat indenter within the Nano-indentation setup. Engineering Stress-strain curves were generated for specimens both un-irradiated and irradiated. The yield strength of the un-irradiated and irradiated specimens in the <0 0 1> directions was determined by using the engineering stress-strain curves. In addition, the critical resolved shear stress (CRSS) of the un-irradiated and irradiated specimens was calculated. Microstructural analysis revealed that the formation of dense and fine dislocation loops were appeared in the material after irradiation. By combining the results of microstructure analysis with the dispersion barrier hardening model, the changes in CRSS caused by irradiation were calculated. Furthermore, the number of dislocation lines participating in deformation at a strain of 20 % was quantified, with the irradiated specimen exhibiting an increase of 33 % in comparison to the un-irradiated specimen.

Towards Determining an Engineering Stress-Strain Curve and Damage of the Cylindrical Lithium-Ion Battery Using the Cylindrical Indentation Test

Mechanical internal short circuit (ISC) is one of the significant safety issues in lithium-ion battery design. As a result, it is possible to subject LIB cells to thorough mechanical abuse tests to determine when and why failure may occur. The indentation test is a recommended loading condition for evaluating mechanical damage and ISC. In this study, 18,650 cylindrical battery cells underwent indentation tests and a voltage reduction following the peak force identified by the ISC. Due to the complexity of the contact surface shape between two cylinders (LIB cell and indenter), a new phenomenological analytical model is proposed to measure the projected contact area, which the FEM model confirms. Moreover, the stress-strain curve and Young’s modulus reduction were calculated from the load-depth data. In contrast to previously published models, the model developed in this paper assumes anisotropic hyperelasticity (the transversely isotropic case) and predicts the growing load-carrying capacity (scalar damage), whose variation is regulated by the Caputo-Almeida fractional derivative.

Experimental Investigation of the Mechanical Behavior of Corroded Q345 and Q420 Structural Steels

This study investigated the residual mechanical behavior of Q345 and Q420 structural steels after corrosion. Firstly, the tensile specimens were corroded in an acid solution until the weight loss rate reached 20%, 30%, and 40%. The corroded specimens were then subjected to axial tensile experiments to observe the tensile fracture behavior and obtain the engineering stress–strain curves. The effects of corrosion on stress–strain curves, failure modes, tensile strength, and ductility were analyzed and discussed. The strength and ductility of Q345 and Q420 structural steel dropped sharply after corrosion. In addition, a constitutive model of Q345 and Q420 structural steels with different mass loss rates was established. Based on the test data, empirical equations were proposed to predict the residual strength and ductility of corroded Q345 and Q420 structural steels.

Damping and Mechanical Properties of Epoxy/316L Metallic Lattice Composites

The lattice structure was prepared by selective laser melting of 316L metal powder, and the epoxy was naturally infiltrated into the pores of the 316L metallic lattice structure. The epoxy/316L metallic lattice composites with integrated structure and function were prepared. Scanning electron microscopy was used to observe the microstructure of the epoxy/316L metallic lattice composites. The damping performance of the epoxy/316L metallic lattice composites were studied by modal measurement method. At the same time, the engineering stress-strain curve was obtained by a quasi-static compression experiment on a universal testing machine. The results show that the interface of epoxy and 316L metallic lattice is well bonded, and there are a few bubbles in the epoxy. The epoxy/316L metallic lattice composites have high damping characteristics with damping ratio over 10%. The energy absorption of epoxy/316L metallic lattice composites is as high as 68.32 MJ/m3, showing high energy absorption characteristics.

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.

Study on the Fracture Mechanisms of a Grade 91 Steel at 600°C via Interrupted Miniature Tensile Testing

Abstract The study of the deformation and fracture mechanisms of power plant materials at elevated service temperature is of utmost importance in structural integrity assessment. In this work, interrupted miniature uniaxial tensile tests (MUTT) have been conducted to investigate the fracture evolution mechanisms for a Grade 91 steel at 600°C. The engineering stress–strain curves of the MUTT can be divided into six different stages, including the elastic stage, strain hardening stage, homogeneous plastic deformation stage, necking across the transverse and thickness direction stage, and finally, the fracture propagation stage. In addition to full history tests, MUTT were interrupted in each of the different stages to study the entire failure process evolution from the uniform deformation, necking to specimen separation, using optical microscopy and Scanning Electron Microscope (SEM). It has been shown that the necking of the interrupted testing specimens appears at Stage IV across the width direction prior to the thickness direction at Stage V. The thickness direction necking would lead to fracture rapidly. The void coalescence directly caused by damage has been observed in Stage VI.

Correction of the stress–strain curve for 2024 aluminum alloy after necking using the new surface strain method

Nowadays, many studies concerning plasticity and numerical simulations indicate that the true stress–strain curve plays a prominent role in the analysis of metal deformation. Hence, a new method is considered to correct the stress–strain curve based on image processing. Since the axial stress mainly becomes triaxial in the neck zone, the relationship obtained from the engineering stress–strain curve is not reliable in terms of authenticity and accuracy. Accordingly, correcting this relationship is highly advantageous and necessary. Due to the triaxial state of stress in the plastic area, longitudinal and surface strains are calculated through image processing and the correction coefficient of the stress–strain curve is obtained based on them. The equation of the stress–strain curve is based on the Hollowman relation until the onset of necking and then becomes almost linear. The finite element method (FEM) is employed for validating the obtained results. Since the corrected stress and strain equation is linear, the objective function of optimization is considered. This optimization is based on minimizing the difference between the three diameters values of the specimen, which are observed through experiment and FEM. Besides, a statistical method with the help of the genetic algorithm is employed to minimize this difference. As a result, an optimal equation is predicted for the 2024 aluminum based on the stress–strain curve of the error rate. Finally, a comparison is made between the results obtained from the surface strain method and the results obtained from the classical methods of Bridgman and Davidenkov, and a good agreement is observed between them.

Response to Comment on “Cryoforged nanotwinned titanium with ultrahigh strength and ductility”

We address the three main points of Guo et al . They claim that we should have used the engineering stress versus engineering strain curves to infer the mechanical properties of our nanotwinned titanium, question our sample design on the basis of a finite-element analysis, and doubt the immobility of some preexisting grain/twin boundaries in our electron backscatter diffraction micrographs. We find their analysis to be groundless and to contain many inconsistencies.

Predicting stress–strain curves using transfer learning: Knowledge transfer across polymer composites

The engineering stress–strain curve of a material allows one to determine mechanical properties such as elastic modulus, strength, and toughness. While machine learning has recently been used to predict stress–strain curves, large volumes of experimental data are required to achieve high prediction accuracy. More importantly, conventional machine learning models are not generalizable from one material to another. To address this issue, a novel transfer learning approach is introduced to predict stress–strain curves across different fiber reinforced polymer (FRP) composites fabricated via additive manufacturing. Optimal transport (OT) is integrated with the transfer learning approach by mapping the source label space to the target label space, which further improves knowledge transferability across different FRP composites. The stress–strain curves of the additively manufactured FRP composites are generated under flexural loading conditions. Experimental results show that the OT-integrated transfer learning approach can predict the complex stress–strain curves of FRP composites with small training data. The predictive model achieved a mean absolute percentage error (MAPE) of less than 10%. The extracted modulus and strength from the predicted stress–strain curves achieved MAPEs of less than 5% and 10%, respectively. This work demonstrates that transfer learning has the potential to transform how stress–strain curves are generated.

Inverse Approach of Parameter Optimization for Nonlinear Meta-Model Using Finite Element Simulation

Accurate and efficient estimation and prediction of the nonlinear behavior of materials during plastic working is a major issue in academic and industrial settings. Studies on property meta-models are being conducted to estimate and predict plastic working results. However, accurately representing strong nonlinear properties using power-law and exponential models, which are typical meta-models, is difficult. The combination meta-model can be used to solve this problem, but the possible number of parameters increases. This causes a cost problem when using FE simulation. In this study, the accuracy of the nonlinear properties of materials and the number of iterations were compared for three typical meta-models and the proposed advanced meta-models considering stress–strain properties. A material property test was conducted using ASTM E8/E8M, and the meta-model was initialized using ASTM E646 and MATLAB Curve Fitting Toolbox. A finite element (FE) simulation was conducted for the meta-models, and the test and simulation results were compared in terms of the engineering stress–strain curve and the root-mean-square error (RMSE). In addition, an inverse method was applied for the FE simulation to estimate the true stress–strain properties, and the results were analyzed in terms of the RMSE and the number of iterations and simulations. Finally, the need for an advanced meta-model that exhibits strong nonlinearity was suggested.

A modified version of MATLAB application window for predicting the weld bead profile and stress–strain plot of AA5052 CMT weldment using ER4043

The present study deals with the extended version of our previous research work. In this article, for predicting the entire weld bead geometry and engineering stress–strain curve of the cold metal transfer (CMT) weldment, a MATLAB based application window (second version) is developed with certain modifications. In the first version, for predicting the entire weld bead geometry, apart from weld bead characteristics, x and y coordinates (24 from each) of the extracted points are considered. Finally, in the first version, 53 output values (five for weld bead characteristics and 48 for x and y coordinates) are predicted using both multiple regression analysis (MRA) and adaptive neuro fuzzy inference system (ANFIS) technique to get an idea related to the complete weld bead geometry without performing the actual welding process. The obtained weld bead shapes using both the techniques are compared with the experimentally obtained bead shapes. Based on the results obtained from the first version and the knowledge acquired from literature, the complete shape of weld bead obtained using ANFIS is in good agreement with the experimentally obtained weld bead shape. This motivated us to adopt a hybrid technique known as ANFIS (combined artificial neural network and fuzzy features) alone in this paper for predicting the weld bead shape and engineering stress–strain curve of the welded joint. In the present study, an attempt is made to evaluate the accuracy of the prediction when the number of trials is reduced to half and increasing the number of data points from the macrograph to twice. Complete weld bead geometry and the engineering stress–strain curves were predicted against the input welding parameters (welding current and welding speed), fed by the user in the MATLAB application window. Finally, the entire weld bead geometries were predicted by both the first and the second version are compared and validated with the experimentally obtained weld bead shapes. The similar procedure was followed for predicting the engineering stress–strain curve to compare with experimental outcomes.

One-Pot Synthesis of Supertough, Sustainable Polyester Thermoplastic Elastomers Using Block-Like, Gradient Copolymer as Soft Midblock

It remains challenging to synthesize supertough thermoplastic elastomers (TPEs) since the stretchability and tensile strength are mutually exclusive. Here, we report a one-pot strategy for the prep...

Synthesis of High-Performance Lignin-Based Inverse Thermoplastic Vulcanizates with Tailored Morphology and Properties

We report synthesis of a high-strength renewable phenolic composition with linear large deformation strain without a thermoplastic-like yielding while retaining thermal processability. Small molecule carboxylic acid derivatives with varying molecular architectures act as esterifying crosslinkers in an equal mass mixture of lignin and acrylonitrile–butadiene copolymers in a highly scalable, solvent-free process. These “inverse thermoplastic vulcanizates” (iTPVs)─unique in their approach of crosslinking the rigid lignin phase rather than the soft phase─exhibit ordered self-assembly, tunable nanoscale morphology, and processability. The first of its kind iTPV compositions exhibit engineering stress–strain curves with two- to sixfold linear extensibility, a twofold rise in strength, and an order of magnitude enhanced modulus compared to a simple lignin-rubber blend. Viscoelastic properties correlate well with crosslinker architecture and the resulting morphology, allowing competing properties of toughness and stiffness to be tuned. This research finds a path for identifying the potential of lignin as a sustainable feedstock.

Microstructural Evolutions, Hot Deformation and Work Hardening Behaviour of Novel Al–Zn Binary Alloys Processed by Squeezing and Hot Extrusion

The main goals of this work were to manufacture novel Al–Zn extruded alloys by varying the Zn content (0, 10, 20, 30 wt%), investigate the microstructural evolutions, hot deformation, and work hardening behaviour by hot compression test at different temperatures (25 °C, 75 °C, 150 °C, 225 °C, 300 °C). Al–20Zn alloy microstructure revealed α-Al and uniform distribution of (α + η) phases, coherent (α + η) crystals in GBs with casting defect-free surfaces, and effective interactions of pinning dislocations which led to improve mechanical performance of Al–20Zn alloy, as compared to the other alloys. The observed engineering stress–strain curve results revealed the decrease of stress with increasing of temperature due to flow softening, dynamic recovery and dynamic recrystallization. These results displayed also an increase of stress value with increasing of Zn content due to the precipitation of high density (α + η) phase in the matrix and GBs, increasing of forest and mobile dislocations density with strain fields, and the formation of fine dendrites. Work hardening rate (WHR) of extruded samples displayed three stages: stage I, WHR decreased slightly with increasing of temperature up to 75 °C and decreased drastically from 75 °C to 300 °C due to softening; stage II, WHR maintained constant due to balance between dislocation generations and dislocation annihilation; stage III, WHR slightly increased due to strain hardening of (α + η) phase. WHR was observed to increase considerably with increasing of Zn content due to the formation and dispersion of high density of (α + η) phase in the Al matrix and GBs. Deformation micro-localization in terms of different characteristics was examined and reported on the deformed samples after hot-compression test through SEM micrographs.