Stress-strain Curve Of Material Research Articles

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...

An experimental and theoretical study on constitutive model of Al-2024T4 for sheet metal incremental forming

Incremental sheet metal forming (ISF) is well known as a die less and flexible forming method and is widely used for prototype part fabrication. It can extremely improve the forming limit of sheet metal. But how to get the stress-strain curve of material with improved strain limit to be used for analysis of incremental forming process? Comparing with classic global forming method, sheet metal incremental forming is local forming method. It means that any time only a small zone of entire component is deforming and moving correspondingly with the forming tool head and is undergoing a complex loading history during the forming process. Based on these characteristics, in the present study, a constitutive model is proposed to describe the stress-strain curve of material and to research the mechanism of high forming limit phenomena in ISF experimentally and theoretically.Three aspects are focused on: firstly, a constitutive model is proposed to describe the stress-strain curve of material and to adapt to the complex loading history and to analysis the mechanism of high forming limit. Secondly, an incremental forming paradigm with truncated conical shape is conducted with geometrical relationship between tool and sheet metal to calculate the strain path of sheet metal around the tool head. Thirdly, the mechanical properties are gained by tension test before and after truncated conical component made by incremental forming. The forming limit diagram is obtained by measuring and calculating the grids printed on the surface of truncate conical component.The calculation algorithm with the proposed constitutive model is programmed to calculate the plastic forming strain and stress of truncated conical component during incremental forming process. The proposed constitutive model is compared with experimental results and can be used to analysis forming limit of incremental sheet metal forming.

Determination of Johnson-Cook material model for weldment of mild steel

The material behavior of mild steel is determined after the material experiences weld induced heating effect. The mild steel, when subjected to high-speed large deformation, is subjected to high temperatures and strain rate. The material behavior is modeled using the Johnson-Cook (JC) model to incorporate the effect of strain, strain rate, and temperature. The material experiences significant metallurgical changes due to the involvement of heat during the welding process. It is thought that the material in the weld zone and the base metal may have different flow stress due to the application of such diverse heat distribution. The mild steel plates of 6 mm thickness are welded using the shielded metal arc welding process. The weld metal pieces are subjected to tensile testing at different strain rates. The JC Parameter for flow stress and strain rate is determined using non-linear regression. The JC parameter for temperature dependence is determined through the heat equation obtained through quasi-static deformation and the data values for the strain rate. The increase of 97 MPa in the initial yield point is observed for the materials in the heat-affected zone (HAZ). The prominent effect is observed in the strain hardening parameter from 0.005 for base metal to 0.06 for HAZ. Later, the tensile test using the finite element model under quasi-static and medium strain rate is simulated incorporating the Johnson-Cook material model for base metal and HAZ of metal. The comparison of tensile load history and material stress–strain curve indicates that the results are in good confirmation with the experimental results for base metal and HAZ.

Experimental evaluation of orientation and temperature dependent material stress-strain curves of Zr2.5%Nb Indian pressure tube material and development of a suitable anisotropic material model

Because of their hexagonal close-packed (HCP) structure and easy prismatic slip, the tensile properties of Zirconium based alloys show strong texture dependence and hence, anisotropy. The type of texture, microstructure and hence, the mechanical properties depend upon the sequence of manufacturing process followed in fabrication of components, such as pressure tubes (PT) in pressurized heavy water type reactors. Due to small wall thickness (i.e., 3.75 mm) of the pressure tubes, designing and machining of specimens in all the three directions, especially in the radial direction, is a challenge and this explains the reason for scarcity of work in this area in research literature. In this work, different types of specimens have been machined from transverse, longitudinal and radial orientations of the Zr2.5%Nb Indian PT following a novel design in order to study the anisotropy in the plastic deformation and hardening properties. In addition, shear specimens have been extracted from longitudinal-transverse plane to study the plastic deformation in shear. Tests on tensile and shear specimens have been carried out at room temperature (25), 100, 200 and 300 °C respectively. Using the experimental data, the parameters of Hill’s anisotropic yield function have been evaluated. In addition to evaluating the parameters at initial yield point, the nature of variation of these parameters with equivalent plastic strain, has also been established. This new material model where the anisotropic parameters evolve with plastic strain, shall be useful for design (by analysis) and integrity assessment of the pressure tubes for different types of postulated loading conditions.

The use of neural networks and nonlinear finite element models to simulate the temperature-dependent stress response of thermoplastic elastomers

In this study, a methodology that combines artificial neural networks and nonlinear hyperelastic finite element modeling to simulate the temperature-dependent stress response of elastomer solids is presented. The methodology is verified by a discrete model of a tensile test specimen, which is used to generate stress–strain pairs of existent experimental data. The proposed method is also tested with a benchmark problem of a rubber-like cylinder under compression. Three grades of an elastomer used for diverse engineering applications are used throughout the study. On this basis, three neural network architecture with 10 hidden neurons are implemented as constitutive models to reproduce the experimental data of the materials. The validation results show that the proposed methodology can reproduce tensile tests with an error of 5% of less than regarding experimental data for elastomers that present no yielding point. The benchmark problem results were at the range expected for the elastomer materials with no yielding, where it was possible to derive force temperature-dependent responses. These results suggest that the methodology helps the prediction of the material response when only material stress–strain curves at different temperatures exist. Therefore, the presented approach in this contribution helps to simulate the temperature-dependent stress responses of elastomeric solids with no defined yielding point.

Research on the composite curling characteristic of plastic film reinforced pliable veneer of teak

In order to study the curling deformation characteristic of plastic film reinforced pliable decorative sliced veneers of teak (teak PRPDSV for short, a kind of green product with mechanical meshing structure by the permeation of plastic film into the pliable decorative sliced veneer through high-temperature hot pressing and fusion), which is unlike other veneer species, this paper established a constitutive model between reinforcing plastic films and veneers under different temperatures on the basis of stress-strain testing. Different hot-press temperatures and material thickness have been applied in the model to verify the experimentally obtained curling degrees of a teak PRPDSV. The study results show that: curling deformations obtained in the elastoplastic mechanical model, into which a material stress-strain curve has been introduced, for a plastic film and a teak veneer through high temperature hot-press composite processing, is highly accurate and scientific, and the model is up to be used for prediction in practical production; the material’s thickness are quite different against other decorative veneer species.

Effective factors in achieving an accurate finite element simulation of shear links

PurposeDuring severe earthquakes, the inelastic energy dissipation of eccentrically braced frame system depends on shear links performance. A finite element model can predict links behavior appropriately if the factors causing large discrepancies are recognized and modified. The paper aims to discuss this issue.Design/methodology/approachIn order to achieve this, the present paper discusses the cyclic response of five types of shear links constructed of various steel grades that ranged from 100 to 485 MPa yield strength. Finite element models are verified by experimental results. As these links have substantial differences in strain hardening of steel materials, different amplitudes of material stress‒strain curve loops are used to specify the level of strain hardening in finite element models.FindingsThe solid and shell elements in ABAQUS element factory can predict local buckling perfectly, and the computation cost of the former is significantly more than the latter. However, one of the solid elements can predict plastic deformation accurately if no local buckling emerges. The axial constraint of test setup equipment can cause excessive plastic deformation in comparison to the link plastic rotation capacity. Furthermore, some shear links with middle stiffeners can reach inaccurate high plastic rotations due to lack of defining fracture criteria in finite element models.Originality/valueIn this study, some resources of discrepancies between experimental results and finite element models are mentioned to ensure the reliable use of finite element models.

Tendon tissue microdamage and the limits of intrinsic repair

The transmission of mechanical muscle force to bone for musculoskeletal stability and movement is one of the most important functions of tendon. The load-bearing tendon core is composed of highly aligned collagen-rich fascicles interspersed with stromal cells (tenocytes). Despite being built to bear very high mechanical stresses, supra-physiological/repetitive mechanical overloading leads to tendon microdamage in fascicles, and potentially to tendon disease and rupture. To date, it is unclear to what extent intrinsic healing mechanisms of the tendon core compartment can repair microdamage. In the present study, we investigated the healing capacity of the tendon core compartment in an ex vivo tissue explant model. To do so, we isolated rat tail tendon fascicles, damaged them by applying a single stretch to various degrees of sub-rupture damage and longitudinally assessed downstream functional and structural changes over a period of several days. Functional damage was assessed by changes in the elastic modulus of the material stress-strain curves, and biological viability of the resident tenocytes. Structural damage was quantified using a fluorescent collagen hybridizing peptide (CHP) to label mechanically disrupted collagen structures. While we observed functional mechanical damage for strains above 2% of the initial fascicle length, structural collagen damage was only detectable for 6% strain and beyond. Minimally loaded/damaged fascicles (2–4% strain) progressively lost elastic modulus over the course of tissue culture, despite their collagen structures remaining intact with high degree of maintained cell viability. In contrast, more severely overloaded fascicles (6–8% strain) with damage at the molecular/collagen level showed no further loss of the elastic modulus but markedly decreased cell viability. Surprisingly, in these heavily damaged fascicles the elastic modulus partially recovered, an effect also seen in further experiments on devitalized fascicles, implying the possibility of a non-cellular but matrix-driven mechanism of molecular repair. Overall, our findings indicate that the tendon core has very little capacity for self-repair of microdamage. We conclude that stromal tenocytes likely do not play a major role in anabolic repair of tendon matrix microdamage, but rather mediate catabolic matrix breakdown and communication with extrinsic cells that are able to effect tissue repair.

Assessment of Different Steel Material Characteristics on Shear Links Performance

The inelastic behavior of shear links depends on their material ductility. In order to investigate the effect of cyclic characteristics of steel on shear links behavior, five experimental links constructed of various steel grades are modeled by finite element approach. These models are verified using experimental shear links results. Moreover, cyclic stress-strain material curve is used for simulating links behavior and the models can simulate strength degradation of flange and web local buckling appropriately. The overstrength and plastic rotation of the links are modified due to the influence of test setup configuration once the buckling occurs. It can be concluded that the links material characteristics can affect the overstrength and plastic rotation. In this study, the various strain hardening of different grades of steel are evaluated and the amplitudes of strain which can simulate strain hardening of links are determined for five materials.

Ballistic limit predictions for perforation of aluminium armour plates by rigid nose-pointed projectiles

We start with a derivation of a new formula for the spherical cavitation yield stress of aluminium targets with Ludwik power-hardening response. As part of this analysis we have suggested simple and accurate formulae for spherical and Mises plane-strain cylindrical cavitation pressures. These algebraic relations simplify the well-known integral expressions for quasi-static cavitation pressures in a material exhibiting Ludwik work hardening. A comprehensive comparison with experimental data has clearly demonstrated that the ratio between ballistic limits of targets with thicknesses kh and h, against the same threat, is higher than the commonly accepted value of k. A new integral formulation of the specific cavitation energy, which directly depends on target material stress-strain curve, reveals the coupling between hole slenderness ratio and hardening characteristics of the target. This formulation is shown to be more accurate than currently existing models for perforation resistance, and has led to an efficient and accurate ballistic limit formula. While a general integral formulation is valid for arbitrary stress-strain relations, further simplifications are given for linear, power and Voce hardening laws in terms of classical functions from mathematical physics. Extensive comparison with about 200 available experimental results for perforation of different aluminium alloys by several armour-piercing bullets and nose-pointed projectiles is provided in support of main findings. The aluminium alloys response is mostly modelled by Ludwik stress-strain curve and also by the Voce hardening model, and the vast majority of ballistic limit predictions represent deviations of up to ± 5% from experimental data. A few comparisons are made for Weldox steel alloys to demonstrate the accuracy of the specific formula for linear hardening response of material target.

Low-velocity penetration of a rigid, hemispherical nose projectile in incompressible, elastoplastic, strain-hardening Mises media

A core-cavity model for steady, low-velocity penetration of a rigid, hemispherical nose projectile in elastoplastic, strain-hardening Mises media is presented. The target response is modelled by two distinct regions. The first region is an incompressible, elastoplastic flow field core around the projectile nose. The second region, outside the plastic core, is an incompressible, elastoplastic material response, which is induced by an internally pressurized spherical cavity. The analytical analysis has led to a closed-form expression for the penetration resisting pressure, for an arbitrary target material stress-strain curve with a definite yield point, which depends on the extent of the plastic core. This expression reduces to the quasi-static spherical cavitation pressure when a plastic core does not exist and it matches with well-known results for the resisting pressure of a perfectly-plastic Mises solid. The strain hardening effect on the penetration resisting pressure is found to be significant when compared to elastic/perfectly-plastic target response. Comparison with available numerical results has revealed that a relatively large flow field core, with the outer boundary at the elastic region, should exist around the hemispherical nose. By further comparison to penetration depth experiments, the core outer boundary location is found to be identical to the elastic/plastic interface location of a quasi-static cylindrical cavitation in incompressible Mises media under plane-strain conditions.

Experimental study of cold-drawn duplex stainless steel circular tubes under axial compression

Cold-drawing is one of the typical cold-forming techniques in producing stainless steel circular hollow sections (CHS). Compared with cold-rolling, cold-drawing can produce large scale stainless steel tubes which have wide applications in highly corrosive environment. Nevertheless, few researches have been carried out on the duplex stainless steel CHS columns. In this paper, cold-drawn duplex S22053 stainless steel CHS of three types of cross-sections were tested, including 8 material tensile coupon tests, 6 axially compressed stub column tests and 7 axially compressed long column tests. The material stress-strain curves of the cold-drawn CHS tubes, ultimate loads and failure modes of the stub and long columns were obtained. It has been revealed that material properties of cold-drawn stainless steel CHS tubes are close to those of the virgin plate in the annealed state. Moreover, all the stub columns show local buckling in “elephant foot” mode, while all the long columns undergo overall flexural buckling, among which a long column specimen with the nominal length of 700 mm（CHS-700） shows local buckling after the peak load due to the interaction of axial compression and second-order bending moment. Furthermore, comparing the test values with the predicted values based on the European, American, Australian/New Zealand and Chinese design codes, and the calculation methods available in literatures, it is concluded that the predicted values of the stub columns and the long columns with relatively large member slenderness are all lower than the test values, while the predicted values using the design methods except that in the Chinese design code are higher than the test values for the long columns with relatively small member slenderness. Chinese design code could provide safety predictions for cold-drawn duplex stainless steel CHS columns.

Experimental determination of strain distribution on Printed Circuit Boards using Digital image correlation

The paper investigates the use of digital image correlation (DIC) for strain measurement on Printed Board Circuits (PCBs). Digital Image Correlation (DIC) is a full-field contactless optical method for measuring displacements and strain in experimental testing, based on the correlation of the digital images taken during test. This method is used to measure strain of the surfaces of materials and structures subjected to various stresses (such as mechanical stresses or thermal stresses).So, this method is used according to the documentation for a variety of applications such as: large deformation measurements, crack analysis, stress strain curves (σ-ε) for new materials, constructions - to evaluate certain displacements and cracks, measurement of strain caused by temperature variations.Circuit boards (PCBs) are designed to mechanically support and electrically connect an electronic component assembly. Due to screw assemblies, the surface level differences on which the PCB is placed, the process of assembling the electronic components induces a certain state of stress and deformation in the PCB. The main components affected are microprocessors due to the way they are glued to PCBs with BGA - Ball grid arrays (BGA).To determine the strain on PCBs, the actual measurement method uses strain gages. This method allows determining the strain only at certain points. The Digital Image Correlation method provides full field strain field. The experimental setup is realized with Dantec Q-400 system used for image capture and Istra 4D software for image correlations and data analyses. The maximum level of the obtained strain is compared with the allowable limit.

Experimental complexes for investigation of behavior of materials at a strain rate of 5·102÷105 s-1

A description of experimental complexes, methodological and hardware means for determining the mechanical properties of materials under high-speed deformation and fracture is given in the report. Determination of mechanical properties in the strain rate range 5•102÷103 s-1 is the first direction of work in the laboratory of “Dynamic Materials Testing”. These tests are done using automated complexes based on the Kolsky method and its modifications for compression, tension and shearing. It is also possible to determine the fracture toughness, the characteristics of dynamic crack resistance, as well as to obtain stressstrain curves of low-density materials under uniaxial strain. Original gas guns with a caliber of 10, 20 and 57 mm are used for creation a dynamic load. The study of the behavior of materials at strain rates of 105 s-1 and higher is the second direction of work. In this case, the methods of a planewave shock experiment based on gas guns of 57 and 85 mm caliber are used. Manganine and dielectric pressure sensors, as well as laser interferometry are used for measuring the parameters of elastoplastic waves and for determining such important characteristics as impact compressibility, Hugoniot yield strength, spall strength.

Experimental and numerical analyses of the ultimate compressive strength of perforated offshore tubular members

Tubular steel members are widely used as structural elements in offshore units. The strength capacity and design formulas for intact members, subject to axial compressive forces, have been thoroughly investigated. However, there are few studies on the behavior of perforated tubular members from offshore aged units and on their remaining load capacity assessment. Perforation damage leads to deterioration of strength capacity and life-time shortening of the structures. The aim of this paper is to present an experimental campaign and a numerical finite element model to obtain the ultimate strength of tubular structures with circular perforated damage subjected to axial compression. In the experimental program fifteen tubular scaled specimens are tested and results are compared with the ones from geometrical and material non-linear finite element model considering reconstructed geometries, variable thickness distribution and actual material stress-strain curves. Shell elements are used and the finite element meshes are obtained from detailed external wall 3D laser scanning of the experimental samples and ultrasonic thickness measurements in several cross-sections. Spatial thickness interpolation is performed to define the thickness in all meshed nodes. Results from numerical model analyses demonstrate considerable accuracy and good agreement with those directly measured from experimental perforated tubular member's samples in terms of axial load-displacement and strains. From the results, it has been concluded that the perforation size is the most important variable in determining the extent of the compressive strength degradation.

Elastic modulus in the selection of interbody implants.

The modulus of elasticity of an assortment of materials used in spinal surgery, as well as cortical and cancellous bones, is determined by direct measurements and plotting of the appropriate curves. When utilized in spine surgery, the stiffness of a surgical implant can affect its material characteristics. The modulus of elasticity, or Young's modulus, measures the stiffness of a material by calculating the slope of the material's stress-strain curve. While many papers and presentations refer to the modulus of elasticity as a reason for the choice of a particular spinal implant, no peer-reviewed surgical journal article has previously been published where the Young's modulus values of interbody implants have been measured. Materials were tested under pure compression at the rate of 2 mm/min. A maximum of 45 kilonewtons (kN) compressive force was applied. Stress-strain characteristics under compressive force were plotted and this plot was used to calculate the elastic modulus. The elastic modulus calculated for metals was more than 50 Gigapascals (GPa) and had significantly higher modulus values compared to poly-ether-ether-ketone (PEEK) materials and allograft bone. The data generated in this paper may facilitate surgeons to make informed decisions on their choices of interbody implants with specific attention to the stiffness of the implant chosen.

Finite element simulation of twist forming process to study twist springback pattern

Springback is one of the most common defects found in the metal forming of automotive parts. There are three conditions which can be considered as springback i.e. flange angle change, sidewall curl and twist springback and among them, twist springback is the most complicated problem. This study will focuses on the development of finite element simulation model of the twist forming process. The main aim of this project is to investigate the parameters that may affect the twist springback. Few parameters including twist angle, hardening constant and thickness are explored using finite element (FE) software ANSYS Workbench (16.0). The rectangular mild strips are used to form the twist forming. The standard material properties and stress-strain curve of mild steel had been used to get the springback prediction. The results of springback were measured by the difference of the bending angles before and after unloading process. The results were then be validated with the research made of Dwivedi et al., (2002). The results show that the springback angle reduces as the thickness of strips are increased and also as the angle of twist increases.

Design Aspects of a Ring Tension Test Setup and Evaluation of Transverse Material Stress-Strain Curve of Tubular Components Using FE Analysis

Abstract Ring tensile specimens are often used to determine the transverse properties of tubular components due to ease in fabrication and handling. Due to the presence of combined tension, bending, lateral pressure, and friction stresses in the ring tension test setup, it is essential to employ a computational tool in order to evaluate the transverse mechanical properties of these tubes accurately. On the other hand, choice of suitable loading mandrel and loading geometry may facilitate estimation of mechanical properties directly from the tests. In this work, the effect of various types of mandrel design and loading geometries on the load-displacement response of a ring specimen were studied. Finite element analysis with material, geometric, and contact nonlinearities were used in order to simulate the plastic deformation behavior of the specimen in ring tension setup and a novel algorithm was employed to extract the material stress-strain curve from experimental data. In addition, it was observed that a 3-piece mandrel with gage length oriented perpendicular to loading axis produced data which closely fits with the results from finite element analysis.