Stress-strain Curve Of Material 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.

Sound Characteristics and Mechanical Properties of Metal Powder Chamber Structures Composite Materials Formed by Laser Powder Bed Fusion

Granular damping technology is a widely used method in aerospace and other industries to reduce vibration and noise. However, the technique still faces challenges such as secondary processing, additional structure, single structure, and residual stress. This article introduces a new composite material, the metal powder chamber structure (MPCS), formed through the laser powder bed fusion technology. The article explores the effects of factors like arrangement mode, volume fraction, and powder chamber diameter on the sound and mechanical properties of MPCS. The study shows that MPCS improves the sound insulation effect of the material and defies the mass law of sound insulation. The sample 4B40 using a body‐centered cubic arrangement has a sound insulation coefficient of 52 dB. The sound absorption efficiency curve presents a double peak, and the sample 6F60 exhibits the highest sound absorption efficiency of 0.76. MPCS changes the deformation stage of the material stress–strain curve, and different MPCS also alters the compression deformation mode of the composite material. By studying the effects of MPCS on sound and mechanical properties, it is hoped to provide a better and more sustainable solution for vibration and noise reduction.

Extraction of Equivalent Stress Versus Equivalent Plastic Strain Curve of Necking Material in Tensile Test Without Assuming Constitutive Model

Abstract An algorithm for extracting the equivalent stress versus equivalent plastic strain curve of a necking material in tensile test is proposed (the curve is called here the equivalent-plastic (EP) stress–strain (SS) curve). The presented algorithm traces the force–elongation curve via iterative finite element (FE) simulations without assuming a constitutive model and is suitable for a general-purpose FE solver available to a general audience. In the FE simulation and experiment, a slightly tapered geometry was employed around the specimen center to stably initiate necking there. The proposed algorithm and mentioned necking initiation method have been applied to extracting the EP SS curve of a high-strength steel material using an axisymmetric specimen. Because necking was initiated stably in simulation at the specimen center for a range of mesh sizes, the convergence of the extracted EP SS curve with the mesh size could be successfully verified. The EP SS curve of the tested material was extracted up to an EP strain of 0.85 with average strain intervals of approximately 2.5 mili-strain. The error values were less than 0.2 and 0.1% after four and seven FE simulations, respectively. The presented algorithm and necking initiation method in simulation can also be used for simultaneously quantifying the fracture EP strain of a necking material in the tensile test.

Material characterization of A356-T6 aluminum alloy and correlation of wheel impact test results using finite element analysis

This paper focuses on the material characterization of the A356-T6 aluminum alloy wheel, which is mandatory when an experimental correlation is required with respect to the finite element analysis performed. There is always a chance that the finite element analysis results differ from experimental results if the material properties used for analysis are not developed from the component due to variation in the manufacturing processes and chemical compositions. Hence, the procedure for developing material data is presented, and the respective applicable standards are mentioned. The method of generating a stress–strain curve from the specimens extracted from the alloy wheel is presented. Finite element analysis is performed for impact loads using the developed material stress–strain curve and reference material of the same composition and heat treatment process. The finite element results for both the materials are compared to study the variations.

Neural network modeling of titanium alloy composition-microstructure-property relationships based on multimodal data

The composition and microstructure of metallic materials determine their mechanical properties. Establishing quantitative “composition-microstructure-property” relationships is essential for material design and optimization. However, materials data are complex and heterogeneous, often containing multi-modal information such as “point-image-curve”. Traditional mathematical models and simulations can no longer meet the needs of advanced applications. Big data technology provides a new approach to materials research, and machine learning tools can offer high-dimensional information in a low-order form. In this study, a neural network-based titanium alloy microstructure identification model and a performance prediction model have been designed. A model for heterogeneous data of titanium alloy composition (data), microstructure (image), and performance (curve) has been established through the fusion of the two models. The cross-dimensional prediction of the material stress-strain curve using composition and microstructure image data has been successfully achieved. A four-step workflow of dataset preparation, pre-processing, model building, and fusion is determined. The task of identifying 1215 images of 14 titanium alloys and predicting 604 performance curves has been completed. This work demonstrates the process of establishing the “composition-microstructure-property” relationship of materials by big data technology.

Determination of the parameters of material models using dynamic indentation test and artificial neural network

Stress-strain curves of materials normally change with strain rate and temperature and are normally defined by material models. In this study, a new technique was developed for determining the constants of material models. This technique was based on dynamic indentation test, numerical simulation using Ls-dyna code and artificial neural network. An indenter of tapered shape was shot against the materials as the target by a gas gun. The experiments were carried out for four strain rates and four temperatures. The target was made of pure copper. The penetration depth-time and load-time histories were captured by a LVDT and a piezoelectric load-cell, respectively and the load-penetration depth curve (P-h) was obtained. This curve is characterized by five parameters which are determined for each indentation test. On the other hand, the indentation test was simulated using Ls-dyna hydrocode. From the simulations, the P-h curves were obtained using Johnson-Cook (J-C) and Zerilli-Armstrong (Z-A) material models and the characterizing parameters of the numerical P-h curves were also identified. Finally, an artificial neural network (ANN) was trained by the numerical P-h curves parameters as the input and the constants of J-C and Z-A models as the output. The trained neural network was then tested by the experimental p-h curves parameters as the input and the constants of J-C and Z-A models as the output. Moreover, a number of dynamic compression tests were performed using the well-known Split Hopkinson Bar at the same strain rates and temperatures used for indentation tests and the stress-strain curves of material were obtained. A reasonable agreement was observed between the stress-strain curves predicted by neural network and the Split Hopkinson Bar. The proposed method does not need sophisticated instrumentation and in fact, the load-time and indentation depth-time histories are directly converted to stress-strain of material using an artificial neural network.

Analysis of the limiting states of cylindrical elastic-plastic shells under tension and combined loading by internal pressure and tension

The elastic-plastic deformation, limiting states and supercritical behavior of cylindrical shells under tension and combined loading by internal pressure and tension to failure are studied theoretically and experimentally. This problem is characterized by the occurrence of large strains, shape changes and, as a result, an inhomogeneous stress-strain state. In the numerical solution of such problems, the problem arises of constructing true stress-strain curves of materials. In this regard, to study the deformation and strength properties of materials, it is important to use an experimental-computational approach, which makes it possible to take into account the non-uniaxiality and inhomogeneous of the stress-strain state without accepting simplifying hypotheses. The paper presents a new efficient algorithm for constructing a true stress-strain curve, which is based on the procedure of nonlinear extrapolation of the curve. Such an algorithm, in the process of direct numerical solution of the problem, consistently constructs a stress-strain curve without using repeated direct calculations, which significantly (at times) increases its efficiency. Based on the experimental-computational approach, the true stress-strain curves for solid rods and shells made of 10KhSND and 10G2FBYu steels were determined under tension and combined loading by internal pressure and tension to failure. The failure of shells under tension occurs at lower (at times) values of true strain than solid rods. Significant differences in true stresses and strains at the moment of failure are due to different localization of deformation of solid rods and shells after the loss of stability of plastic deformation in tension. It is shown numerically and experimentally that after loss of stability of plastic deformation according to Considerer in tension, the cylindrical shell contains two forms of loss of stability until the moment of failure. The first form of loss of stability, as in solid rods, is characterized by localization of deformations along the diameter of the sample in the form of a neck, and the second form is characterized by localization of deformations along the thickness of the sample, which determines the final stage of failure. Under the action of internal pressure on the shell, the first form of loss of stability of plastic deformation degenerates with the formation of a neck inside the shell, and only the form of loss of stability is observed, caused by the localization of deformations along the thickness of the shell.

Dimensionless Analysis to Determine Elastoplastic Properties of Thin Films by Indentation

By assuming the elastoplastic properties of thin-film materials, a reverse analysis method is proposed by deriving a dimensionless function for the indentation process. The substrate effect is taken into account by assuming a perfect interface between thin-film and substrate materials. In order to obtain the applied load–penetration depth (P-h) curves, the indentation process is numerically modeled as an axisymmetric problem with a rigid-body Berkovich indenter on the semi-infinite substrate when performing finite element (FE) simulations. As a typical soft film/hard substrate problem, the elastic substrate is assumed and the power–law model is used to describe the constitutive properties of thin-film materials. Varying elastic modulus (10–50 GPa), yield strength (60–300 MPa), and hardening exponent (0.1–0.5) characterize different elastoplastic mechanical properties of thin-film materials with film thickness of 10–30 μm. Owing to the good trending P-h curves with the maximum indentation depth up to the 2/3 film thickness for different elastoplastic thin-film materials, a dimensionless function is derived and validated based on the predictions by reliable FE simulations. The proposed dimensionless function elegantly elucidates the essential relationship between the elastoplastic mechanical properties of the thin-film material and indentation responses (e.g., loading and unloading variables). The elastoplastic constitutive curves predicted by the proposed reverse method are confirmed to be in good agreement with the stress-strain curves of materials by FE simulations with the randomly selected elastoplastic mechanical properties and film thicknesses. This study provides a theoretical guidance to understand the explicit relationship between elastoplastic mechanical properties of the thin-film material and indentation responses.

Experimental and numerical tests of cold-formed square and rectangular hollow columns

This paper summarizes the results of experimental tests and finite element simulations aimed at investigating the buckling response of cold-formed square and rectangular hollow columns. The material stress–strain curves of the tested columns have been derived from testing 83 coupons sampled from the flat and corner parts of the cross-sections, along with coupons containing the weld in both longitudinal and perpendicular directions. The experimental stress–strain parameters have been statistically processed to calibrate the parameters of Ramberg-Osgood and Giuffrè-Menegotto-Pinto material models. The cross-sectional geometry and geometric imperfections have been also measured for all tested profiles. The buckling resistance of 21 different pin-ended columns has been experimentally measured in order to examine the influence of the steel grade (both S275 and S355), the normalized slenderness and the shape of cross-section. Finite element simulations of the tested members have been carried out to investigate the influence of residual stresses and out-of-straightness imperfections on the buckling resistance of hollow profiles. The buckling resistance evaluated on the basis of current EN1993-1–1 and the measured properties of the members are in very good agreement with the tested buckling resistances, even though slightly underestimating the resistance of stocky columns. The partial safety factor for flexural buckling has been evaluated using the method given by Annex D of EN 1990 and the results show that the computed average partial safety factor of curve “c” of EN1993-1–1 for cold-formed square and rectangular hollow columns is 0.92.

Portable universal tensile testing machine for studying mechanical properties of superelastic biomaterials

A portable universal tensile testing machine for single and cyclic loading of superelastic biomaterials is presented. It’s an alternative to large-sized stationary universal testing machines. The machine is designed to obtain uniaxial cyclic tension stress-strain curves of materials with a low elastic modulus, including biological tissues. Its portability allows using it in various conditions: classrooms, production laboratories, and in the field. An interface has been developed to connect it to a computer. Computer output of experimental data allows recording and displaying load-displacement curves, setting the number of cycles, limits, and rate of cyclic deformation. Several examples of testing various biomaterials are presented. The functional advantage of the device is the wide tensile testing speed range of 0.01–10 mm s−1 and cyclic loading, which allow capturing viscoelastic and superelastic behavior of biomaterials.

Molecular dynamics simulation of edge crack propagation in single crystalline alpha quartz

Edge crack propagation of single-crystalline alpha quartz under mode I loading condition was investigated using a molecular dynamics simulation. Five different crack lengths are used to analyze the effects of crack length on each sample's crack growth behavior. The effect of crack length was studied in terms of the material's stress-strain curve, strain energy, fracture toughness, atomic analysis of crack propagation, and crack opening deformation. The results revealed that during tensile loading, the pre-cracked crystalline quartz samples are fractured in a brittle approach. The fracture stress in the pre-cracked sample (40 Å length) is dropped about 70% compared to pristine quartz. Moreover, the effect of loading velocity on the mechanical properties is investigated. According to the findings, maximum stress rises by enhancing the loading velocity, and fracture toughness improves. The fracture surface energy of the single crystalline alpha quartz is calculated, and based on the results, there is a good agreement with experimental data.

Modeling the Stress-Strain Curve of Elastic-Plastic Materials

The work is devoted to the formulation of mathematical models of plastic materials without hardening. A functional is proposed, the requirement of stationarity of which made it possible to formulate the differential equation of stress as a function of deformation. On the linear deformation section, a second-order functional is proposed; on the non-linear deformation section, a fourth-order functional is proposed. A range of boundary value problems is formulated, that ensure the continuity of the function at the boundary of the linear and non-linear sections of the deformation curve. The theoretical strain curve was compared with the samples of experimental points for materials: St3sp steel, steel 35, steel 20HGR, steel 08Kh18N10, titanium alloy VT6, aluminum alloy D16, steel 30KhGSN2A, steel 40Kh2N2MA, and showed a good agreement with the experiment. Thus, a variational model is constructed, that allows one to construct curve deformations of various physically non-linear materials, which will allow one to construct further mathematical models of the resource of such materials.

A parametric study on the effect of uniformly-induced curvature on the deformational capacity of steel onshore pipelines based on a novel material characterization procedure

Onshore pipelines are generally required to transport various hydrocarbon fluids and other liquid consumables over considerably long distances. In many cases, pipe segments are unavoidably installed across geotechnically unstable environments, making them prone to significant ground deformation-induced stresses and strains which may lead to local buckling or pipe wrinkling, and possible rupture of the pipe wall. Current practice idealizes the typical deformation induced in a pipeline by movement of the surrounding or supporting soil medium as a displacement-controlled loading phenomenon characterized by monotonically-increasing uniform curvature, with or without internal pressurization and/or net-section axial stress. This idealization is adopted in this study to investigate the moment vs. curvature response of unpressurized and pressurized pipelines, with no axial stress, subjected to uniform bending deformation; with a view to develop a set of constitutive design equations for predicting the critical values of the average strain, measured over a 2D (two times pipe diameter) gauge length, that coincides with the maximum attainable bending moment. The shortcomings of existing equations, which is related to inadequate characterization of the shape of the material stress–strain curve, is effectively tackled by employing a novel stress–strain model, referred to as the ‘Ndubuaku model’, for accurately parametrizing the shape of stress–strain curves, including curves with a distinct yield point and extended yield plateau. Other relevant parameters investigated include the D/t (diameter-to-thickness) ratio, the internal pressure, and the material grade. A parametric study, comprising about 720 numerical simulations, is implemented herein using finite element methodology. Two semi-empirical equations are developed based on a material curve classification approach that distinguishes between ‘yield-plateau’ stress–strain curve materials and ‘round-house’ stress–strain curve materials. The predictions of the developed models are compared to results of previous experiments on pipe segments subjected to uniform bending, and a good agreement is obtained.

Construction of True Stress-Strain Curve of Metallic Material by Artificial Neural Network and Small Punch Test

Small punch test (SPT) is used to evaluate mechanical properties of metallic materials by a miniature specimen. A method combining SPT and artificial backpropagation neural network for determining the true stress-strain curve of metallic materials is proposed. The load-displacement curves of different hypothetical materials were obtained by the finite element model of SPT with considering Gurson-Tvergaard-Needleman (GTN) damage parameters and used to train a backpropagation neural network. The relationship between the load-displacement curve of SPT and the true stress-strain curve of the conventional uniaxial tensile test was established based on the trained neural network, which is validated by the experimental results of X80 pipeline steel. The results demonstrate that the established relationship can be used to predict the true stress-strain curve of the metallic materials and then to determine their elastoplastic properties by SPT.

Construction of 6061-T6 aluminum alloy constitutive model based on hot bulging test and study on the non-isothermal hydroforming process

Due to the high requirements of drawing equipment and process, it is relatively rare in the field of aluminum alloy sheet forming to introduce soft or sticky fluid medias as soft mold into the course of hydroforming with a non-isothermal condition that maintaining the temperature of high pressure liquid differs to the ones of molds. Consequently, in this paper, the material stress-strain curve in the temperature range is obtained by the bidirectional tensile hot bulging test which contains compress to sheet’s thickness, and can best meet the characteristics of non-isothermal hydroforming in mechanics compared with unidirectional hot stretching. Based on analysis of stress-strain of 6061-T6 aluminum alloy, its constitutive equation on the basis of an original model of processing hardening rate is established for finite elements numerical simulation, and a highly accurate setting range of forming temperature can be confirmed to provide guidance for practical manufacturing accordingly. Result of the study suggests, by applying the constitutive model mentioned above, simulation on non-isothermal hydroforming can reach a desirable effect; The non-isothermal condition set reasonably causes an enhance to the junction of straight wall and round corner, and a deduce of thickness reduction rate simultaneously, limit height increases as a result. Besides, the fluency of blank located in the flange improves to a great extent when its temperature is well set. The position of the 1 mm wall thickness constant line of the workpiece is further reduced, so that the forming quality of the workpiece is remarkably improved.

Meso-mechanics and damage evolution of AA5182-O aluminum alloy sheet Based on the GTN model

According to meso-damage mechanics, the evolution of the volume of micro-voids is an important factor that contributes to damage and fracture. Improving the prediction accuracy of plastic deformation of aluminum alloy sheet is an important endeavor for studying the influence of various factors on plastic meso-damage evolution. Based on the GTN (Gurson-Tvergaard-Needleman) model, the meso-mechanics and damage evolution of AA5182-O rolled aluminum alloy sheet were studied in this paper. The mechanical properties were obtained through uniaxial tensile tests for studying the effect of the strain rate and sampling direction on each GTN damage parameter. Using the response surface method, the GTN model of each strain rate specimen at R00° was calibrated by the finite element method, and the influence of each damage parameter on the stress–strain and void volume evolution curves are studied. The results show that the strain rate has no effect on the initial void volume fraction and critical void volume fraction but has a significant effect on nucleation void volume fraction and fracture void volume fraction. An increase in the initial void volume fraction will cause the fracture point of the material stress–strain curve to occur earlier but has no obvious effect on the slope of the void volume evolution. As the void nucleation volume fraction increases, the highest point of the true stress–strain curve will decrease, the fracture point will advance, and the slope of the curve will increase in the uniform deformation stage of the void volume evolution. However, increasing the critical void volume fraction and fracture void volume fraction will delay the fracture point of the stress–strain curve.

Study of plastically deformed region underneath the ball in indentation tests and evaluation of mechanical properties of materials through finite element simulation and a hybrid algorithm

Ball indentation technique has been studied extensively in literature and it has been widely applied to determine mechanical properties of different materials because of simplicity and minimal requirement of material for the tests. Originally, the material deformation was represented in terms of a representative strain, which is a non-dimensional form of indentation diameter and a representative stress, which again is the instantaneous mean pressure multiplied by some empirical factors. It is known that the state of deformation as well as stress beneath the ball is multiaxial in nature in a ball indentation test. In this work, a new hybrid algorithm for estimation of equivalent stress and equivalent plastic strain during the process of indentation in the most stressed location beneath the ball has been developed. The algorithms uses experimental load–indentation data as well as the multiaxial stress and strain parameters obtained from 2D axisymmetric elastic-plastic finite element simulations. The stress and strain multiaxial parameters are functions of applied load, material yield stress and strain hardening exponents. The algorithm is iterative in nature and uses suitable initial guess values for material yield stress and strain hardening exponents and it converges very quickly. This method can be applied to determine the material stress–strain curve for a wide range of equivalent plastic strain, yield stress as well as plastic strain hardening exponent of the engineering materials. The data points of load vs. indentation depth as obtained directly from the ball indentation tests can be used in the new algorithm without the need for conducting unloading during the test. To illustrate the new scheme, two case studies have been presented where the results from the proposed new method have been compared with those of the existing method in literature and tensile test data to check the accuracy.

Estimation of elastic‐plastic strain response at two‐dimensional notches

AbstractIt is widely recognized that the accuracy of notch fatigue calculations can be improved significantly when those calculations are based on the elastic‐plastic response strain at the notch root, as opposed to the remotely applied loads or stresses. Two of the most widely used approximations for this response are Neuber's rule and Glinka's equivalent strain energy density method. In the present work, a survey of some of the many published evaluations of these methods was first conducted, and then, additional detailed comparisons with elastic‐plastic finite element analyses for a series of semicircular and V‐shaped notch configurations were performed. Based on the observed limitations of both the Neuber and Glinka approaches, and with the guidance of the elastic‐plastic finite element results, a new (and more robust) approach for the estimation of notch response strains is proposed. This approach calls for the definition of a generalized notch response curve (GNRC), which is dependent on both the material stress–strain curve and the notch geometry. Once defined, the GNRC allows the determination of the response strain for any applied stress.

Mechanical behavior and microstructures of aluminum processed by low strain amplitude multi-directional confined forging

Severe Plastic Deformation (SPD) leads to grain refinement and strengthening of metals. Among the many SPD processing methods, Multi-Directional Forging (MDF) is the only one where in-situ material stress–strain curves can be obtained. These are adequate only for specimens re-machined after each compression step, thus avoiding problems connected to specimen shape distortions; re-machining involves complex, expensive and time consuming procedures. This difficulty has been circumvented using confined plane strain compressions, where the strain path, however, differs from that in simple, unconfined free compression. A new processing method involving, for each processing step, an initial free simple compression followed by a confined compression (Multi-Directional Confined Forging – MDCF) is proposed, eliminating the specimen re-machining. Strengthening by MDF depends on strain amplitude; low strain amplitude MDF (LSA-MDF) leads to lower work hardening of the material than high strain amplitude MDF, as well as to limited softening and to an increase in the residual work hardening capacity of material previously deformed monotonically or in successive deformation steps with high strain amplitudes. This supplies a highly desired enhanced uniform elongation of the material after SPD. It is shown that Low Strain Amplitude Multi-Directional Confined Forging (LSA-MDCF) of aluminum leads to adequate stress–strain curves up to the contact of the specimen with the confining die walls, as well as to microstructures very similar to those obtained using free compressions with re-machined specimens. This processing route is simpler, faster and cheaper than LSA-MDF with re-machined samples, and thus emerges as a more practical MDF route.

Refined Model for the Stress-Strain Curve of Austenitic Stainless-Steel Materials at Elevated Temperatures

AbstractBased on the room-temperature and high-temperature test method (steady state and transient state), a series of mechanical property tensile tests was carried out on S30408 (AISI304) austenit...