True Stress-strain Relationship Research Articles

Strength and Fracture Toughness of TIG- and Laser-Welded Joints of Low Carbon Ferritic Steels.

This paper presents the results of experimental testing of joints welded using conventional TIG and laser methods. The welded components were sheets of the low-carbon steels 13CrMo4-5 and 16Mo3. Welded joints were made using different levels of linear welding energy. In the case of laser welding, a bifocal beam with longitudinal positioning of the focal lengths in relation to the welding direction was used. Experimental tests on welded joints included a bending test and determination of hardness distribution, mechanical properties, and fracture toughness, as well as microstructural research in the material of the various joint zones. Based on the determined strength characteristics, the true stress-strain relationships were defined, and a numerical model of the laser joints was developed in Abaqus 6.12-3. The modelled joint was subjected to loading to determine the most stressed areas of the joints. The numerical results were compared with those obtained using GOM's Aramis 3D 5M digital image correlation system. The system used made it possible to record displacements on the surface of the analysed joints in real time. Good agreement was obtained between the strain fields calculated numerically and those recorded using the Aramis 3D 5M video system. The numerical calculations provided information on the strains and stresses occurring inside the analysed joint during loading. It was found that the welded joints were characterised by increased hardness and high strength properties in relation to the base material. The bending test of the laser-welded joints gave a positive result-no cracks were observed on the face or root of the weld. The fracture toughness of the joint zones is slightly lower in relation to that of the base material, but no brittle fracture was observed.

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.

Plasticity and ductile fracture of high-strength bolt materials under monotonic tension

The plasticity and fracture properties of high-strength bolts are crucial to the mechanical behaviours of bolted connections subjected to extreme loadings. However, the material properties of high-strength bolts have not been comprehensively studied. This paper presents a collaborative experimental and numerical investigation to characterise the material plasticity and fracture properties of normal high-strength bolts (NBs) and weathering high-strength bolts (WBs) under monotonic tension. Eighteen cylindrical tensile coupons, cut from M20, M24 and M30 grade 10.9 NBs and WBs, are tested to capture the full-range engineering stress-strain relationships. The combined Swift-Voce weighting model is modified to describe and calibrate the material true stress-strain relationship of NBs and WBs. Then, a void-growth model (VGM) incorporated with the calibrated true stress-strain relationship is used to simulate the ductile fracture of tensile coupons. The calibration process collaborating experimental results and finite element (FE) simulations to obtain material parameters of high-strength bolts is demonstrated in detail. This collaborating method is further employed to simulate the plasticity and fracture properties of normal bolts with various grades under tension, as well as grade 10.9 high-strength bolts subjected to monotonic tension at elevated temperatures in literature. FE simulation results show a high accuracy with experimental results across all specimens, proving the rationality of the proposed method for material plasticity and fracture properties of high-strength bolts.

Quantification and assessment of the error associated with engineering stress-strain analysis in stress accelerated creep tests in 316H stainless steel

ABSTRACT Historically, reduction of area has been neglected during uniaxial creep tests, and engineering rather than true stress-strain and strain rate have been considered. In high load accelerated tests, there is an increasing error associated with the engineering stress and strain, hence this assumption is no longer valid. In this work, uniaxial creep tests on Type 316H austenitic stainless steel at 480–550 °C have been analysed for both engineering and true stress–strain and strain rate. Significantly higher stresses and lower minimum strain rates were determined from true stress-strain rate relationships for as-received 316H. These differences diminish as the material is strain hardened, limiting plastic loading strains and reducing creep ductility. The true stress-strain rate analysis method is shown to be more accurate, however, the engineering stress-strain analysis predicts higher creep strain rates for a given stress and is the more conservative measure for component lifetime assessments.

A compact system for accurate measurement of true stress-strain curves in transparent materials subject to extensive deformation

Accurate quantification of the true stress-strain curve over an extensive strain range is pivotal for elucidating material mechanical properties and simulating non-linear plastic deformation. A novel experimental approach was developed to directly measure true stress-strain behavior in transparent materials. Our setup featured a single 3CCD camera and mirrors, capturing images of both specimen surfaces with bicolored fluorescent speckle patterns. Initially, we determined and corrected the specimen’s refractive index using a point-by-point least squares method. Subsequently, we used multispectral dual 3D digital image correlation (DIC) to reconstruct surface profiles and correct refractive distortions. This allowed precise computation of the deformed cross-sectional area over an expansive strain range. True stress was calculated from the measured engineering stress and computed deformed area. Validity was confirmed by deforming a fluorescent elastomer, and results aligned with the theoretical predictions. This compact experimental setup effectively evaluates true stress-strain relationships in transparent materials under extensive deformation.

Research on the constitutive relation of different material zones of weathering steel Q355GNHB

To research the mechanical properties and low cycle fatigue performance of Q355B structural steel and Q355GNHB weathering steel, this study performs monotonic and cyclic tests on the base metal, welded metal and heat-affected zone (HAZ) of Q355GNHB welded connections and Q355B. The monotone and cyclic constitutive model parameters are calibrated using the true stress-strain relationship and the Chaboche hybrid strengthening model, and their accuracy is verified by ABAQUS. To streamline the calibration process, a simplified calibration method is established for the Chaboche combined hardening model. Compared to the traditional calibration method, the proposed method uses the stress-strain data obtained from the monotonic tests. The applicability of the calibrated model is verified by simulating the tests via ABAQUS. The research results show that both Q355B structural steel and Q355GNHB weathering steel have excellent bearing capacity and plastic deformation capacity. The Q355GNHB weathering steel has better ductility, while the Q355B structural steel has higher bearing capacity and stronger strength reserve capacity. The strength of Q355GNHB varies according to different zones: the yield strength of the base metal material is the lowest, while the tensile strength and the plastic deformation capacity of the welded metal material is the lowest. Besides, the Chaboche combined hardening model and simplified combined hardening model can capture the cyclic fatigue performance of Q355B and Q355GNHB steel. The research results provide effective data support for the in-depth study of the constitutive relations and mechanical properties of weathering steel materials and the accurate simulation of the properties of weathering steel structures.

A novel method for determining the stress-strain constitutive relationship of high-grade pipeline weld zone material

As a typical welding structure, the girth weld of high-grade pipelines has obvious heterogeneity. Therefore, the axial mechanical properties of girth weld materials cannot be accurately tested, and the safety evaluation of the girth weld of the pipeline is seriously affected. Based on MATLAB-PYTHON-ABAQUS co-simulation, an optimization inversion method of the material stress-strain constitutive relationship in the weld zone of the high-grade pipeline is proposed in this paper. Four groups of uniaxial tensile tests with different notch sizes are carried out, and the load-displacement curves of each specimen are obtained. The true stress-strain constitutive relationship of the weld zone material is obtained by the Bayesian regularization back propagation (BRBP) neural network and the Grey wolf optimizer (GWO). The accuracy of the constitutive relationship is fully verified by the test data, and the relative error is less than 1%. In addition, taking the weld material of the oil and gas pipeline as an example, this paper proposes a universal design method of specimen size with a notch, which is convenient for researchers in different fields to measure the stress-strain constitutive relationship of different materials. The proposed inversion method can provide an accurate stress-strain constitutive relationship for the safety evaluation of girth welds of high-grade pipelines.

Microstructure evolution, tensile properties and internal structure transformation study on Ti6Al4V–5Cu anti-bacterial alloy during uniaxial tensile straining at low forming temperature

The tensile behavior of Ti6Al4V–5Cu alloy studied in the temperature range of 450–550 °C at the strain rate interval of 10−3-10−1 s−1. Alloy deformation behavior, microstructure evolution, and its relative internal structure changes due to deformation were investigated. The tensile behavior of the alloy had elucidated in terms of change in true stress-strain relationship. At 450 °C, the alloy showed the decrease of peak stress at the strain rate interval of 10−3-10−2 s−1, which suggests Ti6Al4V–5Cu plastic flow behavior, was quite different. The alloy exhibited an elongation (El) of 28% at 450 °C in a strain rate of 10−3 s−1. At 10−3 s−1, the El of the alloy decreased with the increase of forming temperature. However, at 10−2 s−1 and 10−1 s−1, the El increased with the rising of temperature. Scanning electron microscope (SEM) was used to investigate the microstructure of Ti6Al4V–5Cu alloy. The alloy grain boundaries (GBs) were found as continuous and discontinuous structural features, especially the high angle grain boundaries (HAGBs). The GB feature has contributed to the initiation of micro-cracks because of the creation of weakest regions in the material during deformation. The nature of GB geometry has also a tremendous contribution to the workability of Ti6Al4V–5Cu alloy at low forming temperatures. The presence of a high amount (%) LAGBs and the serrated nature of HAGBs structures determined the pull to grain pieces. The deformation mechanism of the Ti6Al4V–5Cu alloy at low forming temperatures was accomplished initially by boundary serration phenomenon due to strain-induced GB migration related to heat treatment at low strain condition, then by initiation of recrystallized grains-triggered by the plasticity behavior of strain induced sub-boundaries, and finally by the development of deformed grains generated by the reduction in corrugation propensity of GBs due to high strain condition.

Microstructure development in warm upset AM Ti64

As AM Ti alloys generally contain porosity, for demanding applications it must be eliminated. HIP was reported, but it is expensive; accordingly forging by upsetting of EBM Ti6Al4V at 900?C was investigated. Strain rates of 0.01-1 s-1 were employed. In contrast to the as-printed material, porosity was not detected. From the plastometric tests the stress-true strain relationships were obtained and peak stresses were determined. Using the Simufact simulation program, details of the distribution of equivalent strains and temperatures were obtained. Comparison with wrought cast and printed materials is reported. The eventual microstructure consisted of alpha lamellae ranging in width from 1.81 to 2.34 ?m, depending on strain rate and deformation, and beta formed in the interlamellar space during cooling in air. The hardness of the fully processed material was in the range of 293-304 HV1, independently of strain rate. This is to be compared with EBM Ti64, 316-360 HV0.3, and similarly processed cast wrought material, 350-365 HV0.3.

Ductile fracture modelling of steel plates under tensile and shear dominated states

The prediction of ductile fracture is highly related to the stress and strain states in the plastic stage. For steel plates in the engineering structure, despite many stress-strain equations based on the von Mises criterion developed, it is found that the finite element (FE) analysis using true stress-strain relation calibrated by the uniaxial tensile tests cannot properly describe the shear behaviour of steel plates. In this paper, the combined linear and power stress-strain law with a shear plastic factor is proposed to characterize the mechanical behaviour of steel plates under shear dominated state. Then, Bao-Wierzbicki (BW) criterion, an uncoupled damage model, is adopted to predict the tensile and shear dominated fracture of steel plates. The uniaxial tensile and shear tests of steel plates are carried out to calibrate relevant parameters in the true stress-strain relation and ductile fracture model. Furthermore, single-bolt connections subjected to tensile and shear dominated states are designed and tested. Parallel FE simulations are performed to validate the ductile fracture model with the calibrated stress-strain relations. FE results regarding these specimens show a good agreement with the corresponding experimental results. The uncoupled damage model integrated with the proposed stress-strain relation is verified to be suitable to simulate the ductile fracture of steel plates under tensile and shear dominated states.

Determination of the true stress-strain relations of high-grade pipeline steels based on small punch test correlation method

The small punch test (SPT) has been widely used to evaluate the mechanical properties of small regions in pipeline steels. However, its application has thus far been limited to the determination of elastoplastic mechanical properties such as the ultimate tensile strength, and few works on estimating he true stress-strain curves. This paper aims to propose a new method for determining the true stress-strain relations of high-grade pipeline steels based on the SPT results, and apply it to the welded joints of X80 grade pipeline steel where the traditional mechanical characterizations cannot be carried out. Mechanical properties of several high-grade pipeline steels were obtained by empirical formulas that were determined by the correlation relationships between the conventional tensile tests and SPT results. Then the Ramberg-Osgood(R–O) power law which can describe the stress-strain relations of high-grade pipeline steels was simplified and expressed by four determined mechanical property parameters so that the true stress-strain curves could be generated using these parameters. Meanwhile, the SPT correlation method was used to estimate the true stress-strain curves of the heat-affected zones and weld zones of the welded joints of X80 steel and the accuracy was verified by numerical simulations. The results demonstrate that the true stress-strain curves determined by the SPT correlation method are in good agreement with the uniaxial tensile results for base materials of high-grade pipeline steels and the predicted results of different areas of the welded joints of X80 steel are reliable.

A method for determining the constitutive model of the heat-affected zone using digital image correlation

The heat-affected zone (HAZ) is an unmelted region of a welded joint that has changed in material properties because of high temperatures during the welding process. HAZ has a lower strength than the base (parent) material (BM) and the weld metal (WM). The lower material strength is more significant if BM is made of high strength steel and the undermatching filler metal is used. Therefore, the constitutive model of HAZ is essential for predicting the mechanical behaviour of the welded joint. In this paper, a method for determining the true stress–strain relationship of HAZ is proposed. The effect of the transverse constraint on the longitudinal deformation of HAZ imposed by BM and/or WM is eliminated by a linear modification factor correlating to the true strain. Standard tensile coupon tests were used to obtain the constitutive model of HAZ using digital image correlation (DIC). The modification factor proposed for reducing the true stress is calibrated based on finite element analysis (FEA). The modified constitutive model of HAZ is validated against the experimental results obtained by DIC. The validated HAZ material property can be used in advanced numerical simulation of welded joints.

True Stress–True Strain Relationship up to the Plastic Deformation Limit in Ferrite–Pearlite Steel at Various Temperatures

True Stress–True Strain Relationship up to the Plastic Deformation Limit in Ferrite–Pearlite Steel at Various Temperatures

Development of a portable Universal Testing Machine (UTM) compatible with 3D laser-confocal microscope for thin materials

The tensile test always delivers an in-depth understanding of true stress-strain relationship. However, it is not easy for the researchers to understand and evaluate the tensile properties of micro-specimens. This paper presents a research work aiming at the design and manufacturing of a small universal test machine (UTM) for measuring the mechanical properties of the miniaturised samples. The newly developed machine is sensitive to small loads and permits to obtain the stress-strain curves for thin materials. This portable UTM consists of a stepper motor, a load cell, a linear variable differential transformer (LVDT), a load cell amplifier and a data acquisition system. Copper based small and thin (50 μm) tensile test samples were tested on this machine at room temperature, and the calculated results were compared with the test results derived from a commercial UTM (METEX - 1 kN) to justify the validation of the developed apparatus. The obtained mechanical properties are in good agreement with the values obtained from a commercial UTM. To confirm the possibility of in-situ micro-observation, the surface roughness analysis has been conducted on the developed apparatus for pure copper foils under 3D laser-confocal microscope. Finally, it is concluded that this kind of testing apparatus could be manufactured within a manageable budget.

Prediction of Cutting Force and Chip Formation from the True Stress-Strain Relation Using an Explicit FEM for Polymer Machining.

In the present work, an explicit finite element (FE) model was developed for predicting cutting forces and chip morphologies of polymers from the true stress–strain curve. A dual fracture process was used to simulate the cutting chip formation, incorporating both the shear damage failure criterion and the yield failure criterion, and considering the strain rate effect based on the Johnson–Cook formulation. The frictional behaviour between the cutting tool and specimen was defined by Coulomb’s law. Further, the estimated cutting forces and chip thicknesses at different nominal cutting depths were utilized to determine the fracture toughness of the polymer, using an existing mechanics method. It was found that the fracture toughness, cutting forces, and chip morphologies predicted by the FE model were consistent with the experimental results, which proved that the present FE model could effectively reflect the cutting process. In addition, a parametrical analysis was performed to investigate the effects of cutting depth, rake angle, and friction coefficient on the cutting force and chip formation, which found that, among these parameters, the friction coefficient had the greatest effect on cutting force.

Creep of particle and short fibre reinforced polyurethane rubber

Tensile stress–strain testing and creep testing have been carried out on a polyurethane rubber, at three temperatures, with and without either particulate or short fibre alumina reinforcement. A previous paper reported concerning composites with particulate reinforcement and the present work is focused on the effect of the fibres. The samples were made via a blending and extrusion process that produced a certain degree of fibre alignment (along the direction of loading). Prior milling procedures were used to produce fibres with two different ranges of aspect ratio (with averages about 10 and 16). When expressed as true stress–strain relationships, all materials exhibit approximately linear responses. The dependence of stiffness on the volume fraction and aspect ratio of the reinforcement was found to conform well to the Eshelby model predictions. Moreover, the creep behaviour of all of the materials can be captured well by a Miller–Norton formulation, using the average matrix stress predicted by the Eshelby model. A striking conclusion is that it is both predicted and observed that short fibres are much more effective in reducing the creep rate than is the case with particles.

Validation and application of bearing and block tearing resistance; background to prEN1993-1-8:2021

An investigation of bolted connections with a specific geometry and bolt arrangement that require high local ductility to achieve the predicted resistances according to the design rules of the new prEN 1993-1-8 is presented. The experimental campaign includes tensile and shear tests on mild steel coupons to calibrate the parameters used for the true stress-strain relationship, damage initiation criterion and fracture evolution, while a numerical model for the high strength steel grade S690 was selected from the literature. The FEA results were satisfactorily validated by experiments on bolted connections for which the rules of the new prEN 1993-1-8:2021 were used to predict the resistance and deformation behaviour. The deformation behaviour was predicted by applying the new analytical model to calculate the deformation at the bolt hole due to the bearing action. The resistances of the tested connections were also predicted using EN 1993-1-8:2005. It is clearly shown that the new design formulae predict the experimental results significantly better than the results obtained according to EN 1993-1-8:2005. The FEA of a bolt group in bending, representing a high web splice, provides new proof for an analytical model for the distribution of forces between the bolts in the elastic stage and at ultimate resistance. Furthermore, the new Eurocode approach for predicting the bearing deformation behaviour at the bolt hole agreed well with the experimental and numerical results.

A Constitutive Stress–Strain Law for Metals with Sigmoidal Curves

A formulation is proposed for true stress–true strain relationships in the plastic regime that exhibit sigmoidal shapes, such as those of certain metastable austenitic stainless steels (MASS). It contains two terms, broadly accounting for contributions to hardening from conventional plasticity and from mechanical stimulation of martensite formation. It is a continuous function, designed to cover the plastic strain range from zero up to several tens of percent. It is shown that it is suitable for capture of a range of curve shapes of this type—experimental data from tensile testing of a MASS alloy over a range of temperature, with good fidelity. The formulation incorporates six independent parameters, although there may be scope for limiting the range of values that they can have, facilitating convergence operations. Information is presented about how convergence is obtained. The equation is thus expected to be suitable for use in finite element method (FEM) models for simulation of plastic deformation in various scenarios, including indentation. Future work will involve exploration of the details of this.

Profilometry‐Based Inverse Finite Element Method Indentation Plastometry

This is a review of the current state‐of‐the‐art regarding a particular approach to extraction of the (quasistatic) stress–strain relationship of a metallic sample from an indentation experiment. It is based on the application of a relatively high load (kN range) to the sample via a large spherical indenter (≈1 mm radius), followed by measurement of the indent profile. This profile is then used as the target outcome for inverse finite element method (FEM) modeling of the test, aimed at converging on the best fit set of parameter values in a constitutive plasticity law (true stress–true strain relationship). This can then be used to simulate any specified loading configuration, including a conventional tensile test. Commercial products are now available in which the indentation, profilometry, and convergence operations are all automated and completed within a few minutes. The review covers the various conceptual and practical issues involved in implementation and optimization of these procedures, including both those related to the measurement system (experimental and FEM simulation) and those associated with the sample (such as anisotropy, inhomogeneities, and residual stresses). An attempt is made to convey an impression of the expected levels of reliability and also the scope for obtaining insights that are not readily obtainable using other types of test.

A new theoretical method for predicting the elastoplastic behavior of ductile metallic materials

A new theoretical method is proposed to predict the elastoplastic behavior of three ductile metallic materials, including mild steel Q235, high strength low alloy steel HSLA350, and aluminum alloy AL6061. Using this method, only basic experimental parameters are needed for estimating the pre-necking true stress–strain relation. The evolution of the neck profile of a cylindrical tensile specimen is derived based on experimental measurements. The pre-necking model is able to describe the Lüders deformation phenomenon with great precision. It can also provide precise predictions for the pre-necking behavior of structural steels S275, S355, S460, and S690. In addition, the new post-necking model can accurately determine the equivalent stress-strain relation. The complicated analysis of the stress correction factor is avoided in this method. Comparison between our new method and the existing ones is carried out. The accuracy of our prediction is higher than existing methods, e.g., the Hollomon method, the Ludwick method, and the weighted average method (WAM). This work not only provides new insights into the elastoplasticity and fracture of metals, but also holds promise in the design of metal forming.