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Modeling of temperature-dependent ultimate tensile strength for metallic materials
Abstract
Quantitative evaluation of temperature effect on the mechanical properties of materials has always been the core issue concern. In this study, based on the Force-Heat Equivalence Energy Density Principle, a method to model the temperature-dependent ultimate tensile strength (UTS) for metallic materials was proposed. The critical plastic instability energy density related to the onset of plastic instability was put forward which is composed of the elastic-plastic strain energy and the corresponding heat energy. Subsequently, two temperature-dependent UTS models considering the effect of strain hardening behavior were theoretically derived. The models do not contain meaningless adjustable fitting parameters and each parameter has clear physical meanings. The intrinsic quantitative relationships between temperature, UTS, strain hardening exponent, strength coefficient, and specific heat capacity are revealed. Model predictions achieved good agreement with 31 groups of accessible metallic materials, including structural steels, high-strength steels, cold-formed steels, zirconium alloys, and aluminum alloys, which are commonly used in engineering. Especially, the models achieved a better agreement with the results of uniaxial tensile tests compared with the current indentation method. Furthermore, the quantitative influence of the strain hardening exponent and the strength coefficient on UTS at different temperatures was analyzed. This work will contribute to the evaluation of the properties of materials at elevated temperatures and the fire design of structures.
... Based on the proposed force-heat equivalence energy density principle, we have developed a series of novel theoretical characterization models of materials; for example, temperature-dependent models of yield strength, ultimate tensile strength, and fatigue strength for metallic materials. [28][29][30] Furthermore, the proposed force-heat equivalence energy density principle has been successfully extended to the theoretical characterization of the physical properties of materials, such as the temperature-dependent anti-phase boundary energy, vacancy formation energy, surface energy, grain boundary slip energy and dislocation climbing energy of the metallic materials, [31][32][33][34][35] and the temperature-dependent band gap, refractive index and Raman frequency of semiconductor materials. [36][37][38] These models offer a quantitative description of the properties affected by temperature due to the change in heat energy. ...
Based on the force–heat equivalence energy density principle, a theoretical model for magnetic metallic materials is developed, which characterizes the temperature-dependent magnetic anisotropy energy by considering the equivalent relationship between magnetic anisotropy energy and heat energy; then the relationship between the magnetic anisotropy constant and saturation magnetization is considered. Finally, we formulate a temperature-dependent model for saturation magnetization, revealing the inherent relationship between temperature and saturation magnetization. Our model predicts the saturation magnetization for nine different magnetic metallic materials at different temperatures, exhibiting satisfactory agreement with experimental data. Additionally, the experimental data used as reference points are at or near room temperature. Compared to other phenomenological theoretical models, this model is considerably more accessible than the data required at 0 K. The index included in our model is set to a constant value, which is equal to 10/3 for materials other than Fe, Co, and Ni. For transition metals (Fe, Co, and Ni in this paper), the index is 6 in the range of 0 K to 0.65Tcr (Tcr is the critical temperature), and 3 in the range of 0.65Tcr to Tcr, unlike other models where the adjustable parameters vary according to each material. In addition, our model provides a new way to design and evaluate magnetic metallic materials with superior magnetic properties over a wide range of temperatures.
... Compared to traditional methods for predicting UTS, such as empirical model [66] and physical model, [67] the multimodal fusion learning method based on composition and microstructure images proposed in this work has wider applicability. The limitation of the empirical model is that it can only be applied to certain materials or under certain conditions, while for physical model, some model parameters are difficult to obtain, and the simplification and assumptions of the physical model limit the scope of the model. ...
Exploring the “composition‐microstructure‐property” relationship is a long‐standing theme in materials science. However, complex interactions make this area of research challenging. Based on the image processing and machine learning techniques, this paper proposes a multimodal fusion learning framework that comprehensively considers both composition and microstructure in prediction of the ultimate tensile strength (UTS) of Al‐Si alloys. Firstly, the composition and image information are collected from the literature and supplementary experiments, followed by the image segmentation and quantitative analysis of eutectic Si images. Subsequently, the quantitative analysis results are combined with other features for three‐step feature screening, and 12 key features are obtained. Finally, four machine‐learning models (i.e., decision tree, random forest, adaptive boosting, and extreme gradient boosting [XGBoost]) are used to predict the UTS of Al‐Si alloys. The results show that the quantitative analysis method proposed in this paper is superior to Image‐Pro Plus (IPP) software in some aspects. The XGBoost model has the best prediction performance with R² = 0.94. Furthermore, five mixed features and their critical values that significantly affect UTS are identified. Our study provides enlightenment for the prediction of UTS of Al‐Si alloys from composition and microstructure, and would be applicable to other alloys.
... En la actualidad, el material estructural más utilizado en el campo de la ingeniería, esto se debe a que los materiales metálicos se utilizan en diversas aplicaciones, que van desde la construcción de edificios de gran altura, como soporte estructural de centrales eléctricas, solventar reactores nucleares, construcción de motores de turbinas de gas y otros campos como la construcción de máquinas herramientas en donde se ha convertido en el material fundamental de este tipo de aplicación (He et al., 2022). ISSN: 2773-7330 Vol. 5 No. 3. pp. ...
Introducción: Los materiales metálicos han utilizado durante muchos años, en una diversa gama de aplicaciones a nivel industrial, esto debido a que poseen excelentes propiedades físicas y mecánicas. Los materiales metálicos son elementos producidos mediante varios cambios de manufactura, para desarrollar aleaciones con mejores propiedades, como mayor resistencia y tenacidad. En la industria, es importante conocer los procesos que se encuentran en disposición para la selección de una mejor opción y optimización en el consumo del material, así obteniendo un aumento en la eficiencia de la producción. Metodología: Este artículo indaga los avances de los materiales metálicos y su relevancia en la industria actual, analizando sus características químicas y mecánicas, y su influencia en diversas aplicaciones en sus aleaciones con compuestos de Hierro-Carbono, a bajas conductividad con distintos elementos en su composición. Resultados: Se resalta la importancia de mantenerse informado en este campo para utilizar al máximo las ventajas que ofrecen estos materiales en un entorno industrial competitivo. Es fundamental chequear investigaciones previas y estudios científicos para la mejor comprensión de los materiales metálicos, así como presentar ejemplos de aplicaciones industriales para resaltar sus beneficios y desafíos. El entendimiento de los procesos de manufactura y la elección adecuada de materiales son elementos importantes para mejorar la eficiencia y reducir el desecho de recursos en la producción industrial. Conclusión: los materiales metálicos continúan siendo esenciales para la industria debido a sus propiedades avanzadas y su capacidad para satisfacer diversas necesidades de aplicación. Área de estudio general: ciencia de los materiales, Área de estudio específica: resistencia de los materiales, Tipo de estudio: revisión bibliográfica.
... Based on this hypothesis, we have developed a series of temperature-dependent theoretical models without fitted parameters for advanced ceramics and their composites, polymers and their composites, concrete materials, deep rock materials, and other brittle materials, as well as temperature-dependent yield strength models for metallic materials. Furthermore, this principle has been successfully extended to a wider range of theoretical characterization of temperature-dependent mechanical/physical properties of various material systems [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Therefore, in the present work, we followed the way of the linear assumptions of the previous work. ...
In this study, a temperature-dependent fatigue failure criterion was proposed. A maximum energy density related to the fatigue failure of the material which is comprised of the strain energy and its equivalent heat energy was put forward at different temperatures. Two temperature-dependent fatigue strength models without fitting parameters were developed. The quantitative relationship between temperature, fatigue strength, Young's modulus, and melting point was established by the models. The model predictions were in good agreement with all the available experimental data for 17 metallic materials. A fast and simple non-destructive method for predicting temperature-dependent fatigue strength is realized in this work.
In this work, based on the force-heat equivalence energy density principle and the theory of dislocation kinetics, a dislocation-based theoretical model of temperature-dependent ultimate tensile strength without fitting parameters is developed. The novelty of this model is that the theoretical characterization of the temperature-dependent dislocation annihilation energy barrier is implemented, and the new temperature-dependent expressions of the dislocation annihilation term and the dislocation storage term in the dislocation kinetics approach are derived. The model is well validated by comparing against available experimental results of pure face-centered cubic metals in a wide temperature range with the lowest temperature close to absolute temperature 0 K and the highest temperature close to melting point. Furthermore, the analysis results of the model show that increasing the dislocation storage coefficient and reducing the dislocation annihilation coefficient are effective measures to improve the ultimate tensile strength of metal materials, particularly at lower temperatures. The theoretical model provides a clear and profound physical basis for understanding the evolution of ultimate tensile strength at different temperatures.
Nanoprecipitate-strengthened face-centered cubic high entropy alloys (NSFCC-HEAs) have huge potential for engineering applications due to their outstanding mechanical performance at extremely cryogenic temperatures. In this work, a temperature-dependent yield strength predictive theoretical model of NSFCC-HEAs was established by considering the evolution of main influence mechanisms with temperature, such as lattice friction stress, grain boundary strengthening, and precipitation strengthening. Only requiring some physical parameters at room temperature, the model can achieve good predictions of yield strength of NSFCC-HEAs at different temperatures, especially at extremely cryogenic temperatures, as verified by available experimental results. Furthermore, the contribution evolutions of each mechanism with temperature were quantitively analyzed by using the present model. It revealed theoretically that lattice friction and short-range order strengthening are the main mechanisms determining the temperature dependence of NSFCC-HEAs. In addition, the influences of grain size, precipitate size, and precipitate volume fraction were analyzed. The scope of applicability of the model was discussed. The model can provide a method to help save time and resources by reducing cryogenic temperature testing, and deepening the understanding of the relationship between microstructure and yield strength of NSFCC-HEAs at different temperatures. More importantly, the customized cryogenic-temperature strength of NSFCC-HEAs is expected to be achieved through a priori theoretical prediction by selecting the basic material parameters and the corresponding processing technology.Graphical abstract
Ultra-high-temperature materials have applications in aerospace and nuclear industry. They are usually subjected to complex thermal environments during service. The mechanical properties of materials in ultra-high-temperature environments have been attracted increasing attentions. However, the characterization and evaluation of ultra-high-temperature mechanical properties of materials are still challenging work. This article presents a review on the mechanical properties of materials at elevated temperatures. The experimental results and techniques on the ultra-high-temperature mechanical properties of materials are reviewed. The constitutive models of materials at elevated temperatures are discussed. The recent research progress on the quantitative theoretical characterization models for the temperature-dependent fracture strength of advanced ceramics and their composites is also given, and the emphasis is placed on the applications of the force-heat equivalence energy density principle. The thermal–mechanical-oxygen coupled computational mechanics of materials are discussed. Furthermore, the outlook and concluding remarks are highlighted.
Aluminum alloys are attractive for a number of applications due to their high specific strength, and developing new compositions is a major goal in the structural materials community. Here, we investigate the Al-Zn-Mg-Cu alloy system (7xxx series) by machine learning-based composition and process optimization. The discovered optimized alloy is compositionally lean with a high ultimate tensile strength of 952 MPa and 6.3% elongation following a cost-effective processing route. We find that the Al8Cu4Y phase in wrought 7xxx-T6 alloys exists in the form of a nanoscale network structure along sub-grain boundaries besides the common irregular-shaped particles. Our study demonstrates the feasibility of using machine learning to search for 7xxx alloys with good mechanical performance.
This work compares different measurement and analysis protocols of spherical nanoindentation tests performed at different temperatures on a ferritic/martensitic P91 grade steel, in order to derive meaningful indentation stress−strain curves (ISSC) and estimate material parameters such as indentation modulus, yield strength, work hardening exponent and ultimate tensile strength. Quasi-static multi-cycle and dynamic continuous stiffness measurement indentation using a spherical indenter with a tip radius of 20 μm has been carried out from room temperature to 600 °C in vacuum in a set-up where thermal drift has been minimised by an active surface referencing system and accurate temperature stabilization in the contact area. The methodology used to determine the contact radius is critical to achieve consistent results. The application of different combinations of definitions of contact radius and indentation-induced strain to nanoindentation data obtained by the quasi-static and dynamic measurements reveals that Tabor's approach combined with a geometrically determined contact radius best represents the ISSC relationship for the P91 characterized. This method is then extended to predict the high temperature tensile properties of the steel from nanoindentation results.
Tensile deformation and fracture behaviour of AISI 431 martensitic stainless steel, over the temperature range of 300-823 K, has been examined. Yield and ultimate tensile strength values decreased gradually from room temperature to intermediate temperatures, followed by a rapid decrease at high temperatures. At the intermediate temperatures (523-673 K), the steel exhibited jerky/serrated flow and anomalous variations in terms of a plateau in flow stress/strength and work hardening parameters and minima in ductility. These manifestations were identified to be the signatures of dynamic strain ageing, operating at these temperatures. At high temperatures, a rapid decrease in flow stress/strength values and increase in ductility with increasing temperature indicated the dominance of dynamic recovery. The fracture remained transgranular ductile at all temperatures. Work hardening relations that best described the flow behaviour of AISI 431 steel were identified. Variations of the work hardening parameters with temperature were consistent with the variations exhibited by strength and ductility values.
Aluminium alloys are being used widely in multiple engineering applications. However, the material properties of aluminium alloys could change significantly at high temperatures. This paper studied the mechanical properties of normal strength aluminium alloy 6063-T5 and high strength aluminium alloy 6061-T6 at elevated temperatures. Tensile tests were conducted at room temperature (24 °C) and high temperatures up to 600 °C. Both steady temperature state tests and transient temperature state tests were used. The yield stress (i.e., 0.2% proof stress), the ultimate stress, the Young's modulus, and the ultimate strain were determined from tests. The measured material properties at different temperatures are compared with the predictions by the American and European specifications. A series of unified equations for calculating the reduction factors of the material properties at high temperatures are proposed herein; they are found to yield more accurate reduction factors for aluminium alloys.
In this paper, the development of the industrial forming process of drawpieces is investigated experimentally and numerically. The drawing process presented in this work was achieved with a form of 17-4PH stainless steel sheet with a sheet thickness of 1 mm. Due to the high ratio of yield stress to ultimate tensile strength and large amount of springback of the formed material, to ensure that the shape and dimensions of drawpiece are suitably accurate, the forming process is divided into two stages: forming of the drawpiece using a rubber punch and calibration of the drawpiece at elevated temperature. A 3D finite element (FE) coupled thermo-mechanical model was built using the commercial FE-package eta/DynaForm 5.9.3. This package allows physical models of real processes to be analysed, placing special emphasis on non-linear material behaviour, large deformations, and complex friction phenomena. The distribution of the drawpiece shape error obtained by the GOM ATOS system and thickening measurements confirmed that the developed methodology is suitable for industrial manufacture of bearing housings for aircraft fan engines.
For conical indentation, the strain energy is a function of the semi-vertical cone angle, the indentation depth and the stress-strain relation. According to equivalent energy principle of representative volume elements (RVE) and the classical cavity assumption for material deformation region, the function with dual-parameters about volume and deformation is theoretically derived in the present study. This original equivalent-energy indentation model (EIM) is capable of forward-predicting load-depth relation and reverse-predicting uniaxial stress-strain relation for ductile materials only based on loading part of indentation. Further analyses show that the forward and reverse predicted results from EIM method are in excellent agreement with those by finite element analyses (FEA). Macro conical indentation experiments on five types of metals have been conducted using conventional indenters which are similar to Rockwell sclerometer. Consequently, the stress-strain relations predicted by EIM are quite close to those from standard tensile tests.
Solid state joining techniques are increasingly employed in joining duplex stainless steel materials due to their high integrity. Continuous drive friction welding is a solid state welding technique which is used to join similar and dissimilar materials. This joining technique is characterized by short cycle time, low heat input and narrow heat affected zones. The simulation becomes an important tool in friction welding because of short welding cycle. In the present work, a three dimensional non-linear finite element model was developed. The thermal history and axial shortening profiles were predicted using ANSYS, a software tool. This numerical model was validated using experimental results. The results show that the frictional heating stage of the process has more influence on temperature and upsetting stage has more impact on axial shortening. The knowledge of these parameters would lead to optimization of input parameters and improvement of design and machine tools.
Austenitic Stainless Steel grade 304L and 316L are very important alloys used in various high temperature applications, which make it important to study their mechanical properties at elevated temperatures. In this work, the mechanical properties such as ultimate tensile strength (UTS), yield strength (YS), % elongation, strain hardening exponent (n) and strength coefficient (K) are evaluated based on the experimental data obtained from the uniaxial isothermal tensile tests performed at an interval of 50 °C from 50 °C to 650 °C and at three different strain rates (0.0001, 0.001 and 0.01 s−1). Artificial Neural Networks (ANN) are trained to predict these mechanical properties. The trained ANN model gives an excellent correlation coefficient and the error values are also significantly low, which represents a good accuracy of the model. The accuracy of the developed ANN model also conforms to the results of mean paired t-test, F-test and Levene's test.
The effect of normalizing and tempering temperatures on mechanical properties of P92 steel has been investigated using tensile tests and ball indentation techniques (BI) at several test temperatures in the range of 300-923 K. A silicon nitride indenter having 0.762 mm diameter was used for BI testing. The material deformation behaviour underneath the indenter has been investigated by optical microscopy, scanning electron microscopy and profilometry. Strength of the material decreased and its tendency to form pile up increased for higher test and tempering temperatures. The effect of tempering temperature was more dominant than that of normalizing temperature over tensile properties of the steel. The decrease in yield and ultimate tensile strength with increase in tempering temperature has been attributed to increase in M23C6 precipitate size, lath width and dynamic recovery. The tensile properties obtained from BI technique were in good agreement with that obtained from conventional tensile tests.
A brief description is given for a field indentation microprobe (FIM) apparatus which was developed to evaluate, nondestructively in situ, the integrity of metallic structures. The FIM consists of an automated ball indentation (ABI) unit for determining the mechanical properties (yield strength, flow properties, fracture toughness, etc.) and a nondestructive evaluation (NDE) unit (consisting of ultrasonic transducers and a video camera) for determining the physical properties such as crack size, material pile-up around indentation, and residual stress presence and orientation. The laboratory version used here performs only ABI testing. Results of the laboratory version of the FIM tests on unirradiated and irradiated A212 grade B pressure vessel steel are discussed in this paper. Excellent agreement was obtained between yield strength and flow properties (true-stress/true-plastic-strain curve) measured by the ABI tests and those of uniaxial tensile tests.
The design of thin-walled steel plate girder cross-sections is considerably governed by the web instabilities driven by the phenomenon called shear buckling. Change of web geometry due to the partial loss of material in the form of local corrosion of web panels or the loss of mechanical properties caused by elevated temperature amplifies the shear buckling behaviour of girders leading to the loss of ultimate shear capacity significantly. Moreover, steel plate girders with low fire resistance due to their high thermal conductivity and thermal expansion are equally vulnerable to corrosion when exposed to detrimental environmental conditions. This research investigated how the standard fire resistance and elevated temperature buckling resistance of steel plate girders can be affected by the corrosion induced structural deterioration. An advanced Finite Element (FE) modelling procedure was used to evaluate the behaviour of steel plate girders shear behaviour. Some commonly encountered corrosion patterns reported in the literature were simulated. Results revealed both the position and the severity of damage is important for the fire resistance degradation resulting from the reduction in the shear capacity of thin-walled steel girders. Results were also compared with the EN 1993-1-5 design guidelines to achieve a modified formulation. This comparison revealed that depending upon the position and the extent of the corrosion level, the web contribution factor to the shear buckling resistance of a steel plate girder can fall below the Eurocode design guidelines.
There has been a growing shift towards the use of fire-resistant steel (FRS) in the construction industry as a replacement for conventional structural steel (CSS). However, only limited research has been undertaken in the past on the structural properties of cold-formed FRS, especially at elevated temperatures. This paper presents the results of an experimental investigation on key mechanical properties of FRS after subjecting to elevated temperatures. The steady-state tensile tests were performed on two different types of FRS and a CSS at different elevated temperatures ranging from 100° to 800 °C with a holding time of 60 min. A total number of 99 tensile coupon test specimens were tested in this study, both at room and elevated temperatures. Important observations have been made in the paper about the performance of FRS at elevated temperatures in terms of stress-strain relationships, mechanical properties, and deformability parameters. The test results indicate the better performance of FRS compared to CSS at elevated temperature greater than 400 °C suggesting a possible application of FRS in steel structures liable to be exposed to fire conditions. Constitutive modeling for steels is also proposed for strength and stiffness properties.
Stainless steel bolts have an underlying use in bolted connections, as they possess more significant material properties and resistance than high-strength bolts under fire and/or corrosion conditions. Appropriate estimation for fire safety design of these connections depends largely on the ability to accurately predict the fundamental material response at elevated temperatures. Currently, although residual properties of different stainless steels have been excessively investigated using experimental and analytical methods at elevated temperatures, the mechanical behaviour of stainless steel bolts exposed to fire is much less attentively scrutinized than that of high-strength steel bolts. Thus an elevated temperature experimental investigation was conducted to exhibit discrete reduction factors and continuous stress–strain response for A2-70 stainless steel bolts. Test results indicated that the currently available reduction factors or equations of A2-70 base materials (EN1.4301 equivalent to SUS304) are incapable of providing a more accurate representation of residual properties for A2-70 stainless steel bolts subjected to the cold-forging effect. Hence, for A2-70 residual properties of Young’s modulus, yield strength, ultimate strength, ultimate strain and strain-hardening exponent, their regression-based reduction equations were developed to accommodate test data, respectively. Hereafter, in conjunction with five proposed reduction equations, the full-range measured stress–strain curves of A2-70 stainless steel bolts were evaluated using five ambient temperature mechanical parameters based on a modified material model with a necking stage at elevated temperatures, thus the predicted stress–strain curve up to the ultimate stress can correlate well with stress–strain curves of replicate tests at a given temperature, while the necking segment can be predicted approximately and quantitatively after the peak stress.
Mechanical properties of steel at elevated temperatures are critical to the fire-resistant analysis and the fire safety design of steel structures. Thus, one solution for improving the fire resistance is use of high-performance (HP) steel, such as fire-resistant (FR) steel. However, practical use of the FR steel in steel structures implies requirements of sufficient fire resistance for the high-strength (HS) bolts as well, so that the loading capacities of bolted connections commonly used in steel structures can be guaranteed in case of fire. In this paper, material properties of grade 10.9 HP bolts recently developed in China, possessing both fire resistance and corrosion resistance, are tested at various elevated temperatures. Their stress-strain curves, modulus of elasticity, yield strength, ultimate tensile strength (UTS), and elongation percentage after fracture are obtained. These results are compared with that of conventional HS bolts and with reduction factors given in national standards. Constitutive models and prediction equations of the HP bolts at elevated temperatures are proposed. Besides, the relationship between degradation in macro mechanical properties and change in microstructure is clarified. The research outcomes may provide essential bases for the fire response analysis of steel structures applying the FR steel and the HP bolts.
Based on the experimental investigations on compressive buckling behavior of fire-resistant steel columns subjected to elevated temperatures, the numerical analysis models were established and validated by the experimental results of 12 fire-resistant steel columns and 15 conventional steel columns. The parametric analysis was performed to examine the influence of cross-section types, axial load ratios, normalized slenderness ratios, initial imperfections, residual stress and temperature elevation procedure on critical temperatures of fire-resistant steel columns. The parametric analysis indicated that: (1) The critical temperatures increased with decreasing axial load ratios and slenderness ratios; (2) The fire resistance of column with higher axial load ratios and middle slenderness ratios were more sensitive to the residual stress and initial imperfections; (3) Cross-section size and temperature elevation curve variations had less influence on critical temperatures. Furthermore, a total of 1674 numerical simulations were compared with the results determined from the current standards. It was found that provisions in Chinese GB 51249 and European EC 3 tended to overestimate the compressive buckling coefficient while underestimate the critical temperature, when applied to fire-resistant steel columns. Based on Perry-Robertson formula and EC 3 critical temperature formula, the fire resistance determination methods were proposed to facilitate the engineering application of the fire-resistant steel. The proposed methods were proved to meet both safety and economic requirements of structural design.
Dislocation transmission across grain boundary (GB) and activation of dislocation source in adjacent grains are considered common features of dislocation-GB interactions in regulating mechanical properties and behaviors of metallic materials and structures. However, it is currently unclear which of dislocation transmission and dislocation source activation plays the dominant role in regulating dislocation-GB interaction. To study the competition between dislocation transmission and dislocation source activation, a theoretical framework is established based on a dislocation pile-up model. It is found that both dislocation transmission and dislocation source activation exhibit strong dependence on the GB misorientation angle. The critical transmission stress derived based on an energy method also depends on the grain size in a scaling form similar to the Hall-Petch relation. The outgoing slip systems during dislocation transmission are successfully predicted and agree with experimental observations. Regarding the dislocation source activation, the critical activation stress is investigated by examining the local stress fields generated by single and multiple slip dislocation pile-ups. It is found that compared with single slip dislocation pile-up, the result of multiple slip dislocation pile-ups displays lower critical activation stresses and exhibits feature of sensitivity to loading direction, interpreting the reported results of dislocation source activation in polycrystals. Further comparison between dislocation transmission and dislocation source activation for <100> tilt GBs indicates that the dislocation transmission prevails at low angle GB, while dislocation source activation is prone to occur at high angle GB. Our theoretical studies quantify the dislocation-GB interaction induced by dislocation pile-ups, shed light on the competition between dislocation transmission and dislocation source activation, and might provide essential guidance for high-performance metallic material design.
In this study, a theoretical model is developed to characterize the quantitative effect of temperature on the hardness of pure FCC and HCP metals. The model is verified by comparison with the available experimental results of Cu, Al, Zn, Mg, Be, Zr, Ni, Ir, Rh, and Ti at different temperatures. Compared with the widely quoted Westbrook model and Ito–Shishokin model which need piecewise fitting to describe experimental values, the present model merely needs two hardness values at different temperatures to predict the experimental results, reducing reliance on conducting lots of experiments. This work provides a convenient method to predict temperature-dependent hardness of pure metals, and it is worth noting that it can be applied to a wide temperature range from absolute zero to melting point.
Elastic modulus is one of the key elemental material parameters. Its variation with temperature has long been concerned by researchers. In this study, a new temperature-dependent elastic modulus model without phenomenological fitting parameters for metallic bulk materials is developed. The model is capable of predicting the Young's modulus, elastic constant, and shear modulus at different temperatures. Good agreement is obtained between values predicted by the model and available experimental data of body-centered-cubic metals, faced-centered-cubic metals, wrought superalloys, and cast superalloys. The inherent relationships between temperature-dependent elastic modulus, coefficient of expansion, heat capacity (or Debye temperature), and melting point of metallic materials are uncovered by the model. Additionally, the model also provides a new method to predict elastic moduli: the elastic moduli at extremely high and low temperatures, which are difficult to obtain through experiments, can be predicted by the model with reference of an easy-to-access elastic modulus.
Reliable constitutive models are necessary for the precise design and manufacture of complicated components. This study is devoted to developing a modified constitutive model to capture the effects of prior fatigue loading on subsequent tensile deformation of 9%Cr steel. In the proposed model, a strain hardening rule combined with a defined fatigue damage parameter was introduced to represent prior fatigue damage. The defined fatigue damage parameter based on the inelastic strain range of each cycle is capable of describing the evolution of tensile strength, recovery of martensite laths and decline of dislocation density, regardless of the variation in fatigue loading conditions. To validate the predictive capacity of the proposed model, experimental tensile results at different strain amplitudes, lifetime fractions and hold times of prior fatigue loading were compared with the predicted results. Good agreement between experimental and predicted results indicates that the proposed model is robust in describing the tensile behaviour under prior fatigue loading. Moreover, few determined material parameters are required, which makes the proposed model convenient for practical applications.
Selective Laser Melting (SLM) is a promising additive manufacturing technology for the production of complex and highly individual parts on short lead time request. Key aspects for the competitiveness of the SLM process are stability and reproducibility. Poorly optimized pre-processing may lead to deviations in structural properties and geometrical accuracy which results in cost and time consuming iterations. Pre-processing assisted by numerical simulations can reduce defects which occur during construction and hence increase the quality of the parts and the efficiency of this technology.
This research work aims to describe a method for a non-linear macroscale finite element method simulation (FEM) to predict a detailed temperature history of the material as well as residual stresses and distortions for medium-sized parts. An advanced calculation procedure is introduced to reduce the calculation effort significantly. It offers an alternative for experimental calibration of faster linear simulation methods (Keller and Ploshikhin, 2016). Specimens have been fabricated via SLM and subjected to distortion measurements for the validation of the developed simulation technique. One austenitic and two martensitic stainless steels are included in the investigated materials. Numerical simulations with consideration of the material specific phase transformations properties have been performed, which show a good agreement with experimental measurements. Significant influence of phase transformations for the residual stresses and distortions is observed.
Type 316LN stainless steel (SS) is the principal structural material for the components of sodium cooled fast reactors operating under elevated temperature conditions. In order to assess the degradation in strength of service exposed components using a small specimen testing technique such as automated ball indentation (ABI), it is necessary to carry out prior detailed ABI studies on the virgin material. In this investigation, the tensile behaviour of as-received 316LN SS were investigated at several temperatures in the range 298–973 K using ABI technique. The load-depth of indentation data measured from ABI tests was analyzed using semi-empirical relationships to obtain the tensile properties. The yield stress and the flow curves were determined by correlating ABI results with corresponding uniaxial tensile test results. Trend curve for tensile strength with temperature, as estimated from ABI tests, exhibited a plateau region in the temperature around 823 K, similar to uniaxial tensile tests. The variations of strength coefficient, strain hardening exponent, yield ratio, hardness and uniform ductility with temperature were evaluated from ABI tests. The ABI technique was found to estimate the influence of temperature on tensile properties sensitively.
This study reports new temperature-dependent yield strength models for solid solution strengthening binary and multi-component alloys. The models take into account the contributions of base metal, solid solution strengthening, and grain boundary strengthening at different temperatures. Comparisons for different Nickel-based alloys are made between experimental and predicted data with all parameters obtaining from literatures and handbooks and they are in good agreement in a wide range of temperature. This study points out that the yield strength of solid solution strengthening alloys is very sensitive to the lattice misfit. It is not suitable to cursorily estimate the lattice misfit by the atomic radius of solute and solvent. In addition, the variation with temperature of the contribution of each mechanism to the yield strength of solid solution strengthening Nickel-based alloys is firstly made in this study. The study also provides some useful suggestions to improve the temperature-dependent yield strength of solid solution strengthening Nickel-based alloys in the manufacturing.
The nickel interlayer improved the laser weldability of Zr-2.5Nb to AISI 410 stainless steel. The fusion zone contained a large amount of refined and tough dendritic γ-Ni(Fe, Cr) solid solution (182 ∼ 268 HV), while the brittle Zr(Fe, Cr)2 intermetallic compound (1171 ∼ 1460 HV), which was the main phase as the result of direct welding of Zr-2.5Nb to SS410 as well as the source responsible for the welding cracks, disappeared. Only limited quantities of Zr2(Ni, Fe), Zr7Ni10 (and/or Zr2Ni7) intermetallics were present mainly in the form of thin layers (less than 200 μm thick in total) near the fusion interface with Zr-2.5Nb. Those Zr-Ni based intermetallics showed relatively higher toughness and lower hardness (301 ∼ 497 HV) than the brittle Zr(Fe, Cr)2, which reduced the overall cracking sensitivity of the laser-weld.
A model of temperature dependent shear modulus and Young's modulus in bulk metallic glasses is established. The inherent relationship between the glass transition temperatures, the Debye temperature and shear modulus of bulk metallic glasses is revealed. The temperature dependent shear modulus can be predicted by our model without any fitting parameter. The model is presented based on a critical energy density criterion for plastic yielding which is derived from fundamental thermodynamics. This critical energy density consists of two parts: the heat added to the system and the input of mechanical energy, which are not completely equivalent. The agreement between theoretical results and experimental results is striking. And it is found that the temperature dependent Young's modulus could also be predicted pretty well by our model.
The particulate-reinforced ultra-high temperature ceramics (pUHTCs) have been particularly developed for fabricating the leading edge and nose cap of hypersonic vehicles. They have drawn intensive attention of scientific community for their superior fracture strength at high temperatures. However, there is no proper model for predicting the fracture strength of the ceramic composites and its dependency on temperature. In order to account for the effect of temperature on the fracture strength, we proposed a concept called energy storage capacity, by which we derived a new model for depicting the temperature dependent fracture toughness of the composites. This model gives a quantitative relationship between the fracture toughness and temperature. Based on this temperature dependent fracture toughness model and Griffith criterion, we developed a new fracture strength model for predicting the temperature dependent fracture strength of pUHTCs at different temperatures. The model takes into account the effects of temperature, flaw size and residual stress without any fitting parameters. The predictions of the fracture strength of pUHTCs in argon or air agreed well with the experimental measurements. Additionally, our model offers a mechanism of monitoring the strength of materials at different temperatures by testing the change of flaw size. This study provides a quantitative tool for design, evaluation and monitoring of the fracture properties of pUHTCs at high temperatures.
A novel temperature-dependent fracture strength model for ceramic materials is developed, based on a critical fracture energy density associated with material fracture comprising strain energy, the corresponding equivalent potential energy, and kinetic energy of atoms per unit volume. It relates the fracture strength at high temperatures to that at the reference temperature, the temperature-dependent Young’s modulus, the temperature, and the melting point. The model is verified by comparison with experimental data of ceramic materials. The model predictions and the experimental data are in excellent agreement with each other. As the Young’s modulus can easily be obtained by experiments and the melting point can easily be obtained by materials handbook, the model can easily predict the fracture strength of ceramic materials at arbitrary temperatures.
This paper presents the material properties of cold-formed high strength steel at elevated temperatures. Material properties at elevated temperatures have a crucial role in fire resistance design of steel structures. The fire resistances of steel structures in the existing international standards are mainly based on experimental data of hot-rolled mild steel. However, investigation of high strength steel at elevated temperatures is limited. Therefore, a test program has been carried out to investigate the material properties of cold-formed high strength steel at elevated temperatures. The coupon specimens were extracted from cold-formed high strength steel square and rectangular hollow sections with nominal yield stresses of 700 and 900 MPa at ambient temperature. The coupon tests were carried out through both steady and transient state test methods for temperatures up to 1000 °C. Material properties including thermal elongation, elastic modulus, yield stress, ultimate strength, ultimate strain and fracture strain were obtained from the tests. The test results were compared with the design values in the European, American, Australian and British standards. The comparison results revealed the necessity of proposing specified design rules for material properties of cold-formed high strength steel at elevated temperatures. New design curves to determine the deterioration of material properties of cold-formed high strength steel at elevated temperatures are proposed. It is shown that the proposed design curves are suitable for high strength steel materials with nominal yield stresses ranged from 690 to 960 MPa at ambient temperature.
In this work, we proposed a novel temperature dependent yield strength model for metallic materials which has no fitting parameters. The temperature dependent yield strength at arbitrary temperatures can be predicted. And a critical yield energy density with material yield is introduced, which comprises the distortional strain energy, potential energy and kinetic energy of atomic motion. A kind of quantitative relationship between the yield strength, temperature, elastic modulus and Poisson’s ratio is presented. The agreement between theory and experiment is of good satisfaction. Moreover, a temperature dependent yield strength model considering the precipitation strengthening is introduced to predict the yield stress of precipitation strengthened superalloy. Based on the proposed temperature dependent model, a new temperature and strain rate dependent yield strength is established. The good agreement between theory and experiment is found at the temperatures and strain rates considered.
Differential Thermal Analysis (DTA) and high frequency (HF) coil measurement were carried out in present work in order to measure the liquidus temperature of some austenitic and duplex stainless steel samples made by different steel companies in Sweden. A good agreement between the measured and thermal calculated values using Thermo-Calc software (Appendix 1) was found. The liquidus model used 1986 shows a lower value for most of these alloys. When the nitrogen gas used as an inert gas, the nitrogen content increased in the alloys because of the increasing of nitrogen solubility at high temperature. On the other hand, the nitrogen content decreased in the alloys when the argon used as an inert atmosphere because of the different partial pressure of nitrogen between the liquid alloy and the atmosphere. This changing has an effect on the microstructure and liquidus values especially in high nitrogen content alloys.
Tensile properties of autoclaved Zr-2.5Nb pressure tube material containing hydrogen isotope between 5 and 200 wppm were evaluated between 25 and 300°C using specimens with its axis oriented along longitudinal direction of the tube. Analysis of tensile test results showed that both YS and UTS of this alloy decreased linearly with increasing test temperature. The uniform and total plastic strain decreased marginally with increase in test temperature. At all test temperatures, before necking tensile properties were unaffected by hydrogen isotope concentration whereas hydrogen isotope had clear effect on post-necking tensile properties especially at 25 and 100°C. Post-necking ductility showed a transition behavior at 25 and 100 °C and it was able to capture the effect of hydride embrittlement in this material.
Effects of natural aging and test temperature on the tensile behaviors have been studied for a high-performance cast aluminum alloy Al–10Si–1.2Cu–0.7Mn. Based on self-strengthening mechanism and spheroidization microstructures, the alloy tested at room temperature (RT) exhibits higher 0.2% proof stress (YS) of 206 MPa, the ultimate tensile strength (UTS) of 331 MPa and elongation of 10%. Increasing aging time improves the YS and UTS and reduces the ductility of the alloy. Further increasing aging time beyond 72 h does not significantly increase the tensile strengths. Increasing test temperature significantly decreases the tensile strengths and increases the ductility of the alloy. The UTS of the alloy can be estimated by using the hardness. The Portevin-Le Chatelier effect occurs at RT due to the interactions between solid solution atoms and dislocations. Similar behaviors occurring at 250 °C are attributed to dynamic strain aging mechanism. Increasing aging time leads to decrease in the strain-hardening exponent (n) value and increase in the strain-hardening coefficient (k) value. Increasing test temperature apparently decreases the n and k values. Eutectic phase particles cracking and debonding determine the fracture mechanism of the alloy. Final failure of the alloy mainly depends on the global instability (high temperature, necking) and local instability (RT, shearing). Different tensile behaviors of the alloy are mainly attributed to different matrix strengths, phase particles strengths and damage rate.
The tensile properties and flow behavior of modified 9Cr-1Mo steel clad tube have been investigated in the framework of various constitutive equations for a wide range of temperatures (300-923 K) and strain rates (3 x 10(-3) s(-1),3 x 10(-4) s(-1) and 3 x 10(-5) s-1). The tensile flow behavior of modified 9Cr-1Mo steel clad tube was most accurately described by Voce equation. The variation of instantaneous work hardening rate (theta = d sigma/d epsilon) and sigma theta with stress (sigma) indicated two stage behavior characterized by rapid decrease at low stresses (transient stage) followed by a gradual decrease in high stresses (Stage III). The variation of work hardening parameters and work hardening rate in terms of theta vs. sigma and sigma theta vs. sigma with temperature exhibited three distinct regimes. Rapid decrease in flow stress and work hardening parameters and rapid shift of theta vs. sigma and sigma theta vs. sigma towards low stresses with increase in temperature indicated dynamic recovery at high temperatures. Tensile properties of the material have been best predicted from Voce equation.
The titanium modified 14Cr-15Ni austenitic stainless steel is used as clad and wrapper material for fast breeder nuclear reactor. Thermo-mechanical treatments consisting of solution annealing at two different temperatures of 1273 and 1373 K followed by cold-work and thermal ageing have been imparted to the steel to tailor its microstructure for enhancing strength. Tensile tests have been carried out on the thermo-mechanically treated steel at nominal strain rate of 1.6 x 10(-4) s(-1) over a temperature range of 298-1073 K. The yield stress and the ultimate tensile strength of the steel increased with increase in solution treatment temperature and this has been attributed to the fine and higher density of Ti(C, N) precipitate. Tensile flow behaviour of the steel has been analysed using Ludwigson and Voce constitutive equations. The steel heat treated at higher solution temperature exhibited earlier onset of cross slip during tensile deformation. The rate of recovery at higher test temperatures was also influenced by variations in solution heat treatment temperature. In addition, dynamic recrystallization during tensile deformation at higher temperatures was profound for steel solution heat-treated at lower temperature. The differences in flow behaviour and softening mechanisms during tensile testing of the steel after different heat treated conditions have been attributed to the nature of Ti(C, N) precipitation.
IN recent papers, O'Neill,' Vivian,= and Zener and Hollomon3 have reviewed some of the information concerning the relations between stress and strain during plastic deformation. Since further information has been obtained since these reviews were published, this paper attempts to further coordinate and amplify the knowledge concerning the plastic deformation of metals in simple tension. Ordinarily the results of tensile tests of metals are presented as graphs in which the load divided by the original area is plotted as a function of thc percentage of elongation measured over some specified gauge length. The interpretation of graphs of this sort is limited, since the stress required to deform the metal at any stage of the deformation is actually the load divided by the instantaneous rather than the original area. Furthermore, each increment of the deformation is performed on metal that has been previously dc-formed, and, as pointed out by L ~ d r n i k , ~ the strain could be more effectively defined: $ For large strains, the change in dimensions due t o the change in volume accompanying elastic deformation will be small compared with the change in dimensions arising from plastic flow. If the actual area under load has been measured, the plastic strain is equal to A In $ -zu(S/E). where A is the area under where e is the strain and AO and A are, respectively, the original and instantaneous areas. The results of the tensile tests can be more effectively presented and interpreted if the stress* (load divided by actual area) is lotted as a function of the strain . . as defined above. A schematic curve of this type is presented as Fig. I . In a previous paper,6 the concept of Ludwik7 concerning the flow and fracture of metals was successfully employed to explain some of the puzzling results of notched-bar impact tests of steel. I t appears that the use of this concept ii; very fruitful and should be kept in mind in any study of the deformation charac-tcristics of metals. I,udn.ik considered that a flow stress-strain curve of a metal was essentially a locus of points that described the stress required for plastic flow of an infinite numbcr of specimens, each with a different strain history determined by the preceding part of the flow curve Each of these specimens can also be con-sidered to have a fracture strength. Uniortunatcly (or fortunately depending upon the point of view), all the specimens, except the one deformed to the fracture strain, flow and do not fracture. Even though the metals do not fracture, the concept of a fracture-strength curve seems 1 References are a t the end of the paper.
Under a postulated accident scenario of loss of cooling medium in an Indian Pressurised Heavy Water Reactor (IPHWR), temperature of the pressure tubes can rise and lead to large deformations. In order to investigate the modes of deformation of pressure tube – calandria tube assembly, material property data defining the flow behaviour over a temperature range from room temperature (RT) to 800 ̊C are needed. It is of practical importance to formulate mathematical equations to describe the stress–strain relationships of a material for a variety of reasons, such as the analysis of forming operations and the assessment of component's performance in service. A number of constitutive relations of empirical nature have been proposed and they have been found very suitable to describe the behaviour of a material. Although these relations are of empirical nature, various metallurgical factors appear to decide applicability of each of these relations. For example, grain size influences mainly the friction stress while the strain hardening is governed by dislocation density. In a recent work, tensile deformation behaviour of pressure tube material of IPHWR has been carried out over a range of temperature and strain rates (Dureja et al., 2011). It has been found that the strength parameters (yield and ultimate tensile strength) vary along the length of the tube with higher strength at the trailing end as compared to the leading end. This stems from cooling of the billet during the extrusion process which results in the variation of microstructure, texture and dislocation density from the leading to the trailing end. In addition, the variation in metallurgical parameters is also expected to influence the work hardening behaviour, which is known to control the plastic instability (related to uniform strain).
In the present investigation, the tensile flow and work-hardening behaviour of a cold worked Zr–2.5Nb pressure tube material of IPHWRs has been studied over the temperature range of 30–600 ̊C. The stress strain data have been analysed in terms of stress–strain relations proposed by Hollomon (1945), Voce (1948) and Ramberg–Osgood (RO) (Ramberg and Osgood, 1943). The relative efficacies of these relations has been examined by fitting the appropriate equation to the experimentally obtained true stress–true strain data. The quality of fit of these empirical relations is quantified using square root of co-efficient of determination, i.e. R value (in %). The results have been discussed in terms of the correlation coefficient and in error in the estimation of UTS and uniform strain. Of the various relations employed, the Voce's relation has been found to describe the stress–strain behaviour most precisely up to 300 ̊C. Hollomon's relation describes the strain–stress behaviour of the material over the entire temperature range but with over-estimation of UTS. RO relation does not fit well in the initial stage but satisfactorily models the uniform elongation regime till UTS for temperatures up to 500 ̊C.
A computational methodology combining models of precipitation and dispersion strengthening with grain growth and grain boundary hardening has been produced to provide a predictive capability of the microstructure and yield strength of nickel-base superalloys subjected to arbitrary thermal cycles. This methodology has been applied to optimise the post-forging heat treatment of the advanced polycrystalline nickel-base superalloy, RR1000, to provide an improved proof stress. The temperature dependent antiphase boundary energies required were obtained using thermodynamic data and temperature dependent lattice parameters obtained via in situ synchrotron X-ray diffraction. Optimal yield strength properties between 600 and 700 °C were predicted with precipitates in the range of 34–57 nm. The precipitation modelling software, PrecipiCalc was used to optimise the solution and ageing heat treatments to maximise the volume fraction of intragranular γ′γ′ precipitates within the target precipitate size range, whilst maintaining a critical minimum volume fraction of primary γ′γ′ to give a grain size of 7 μm. The optimal yield strength of the material was predicted following a heat treatment consisting of 4 h at 1105 °C; cooling to ambient at 40 °C s−1, and ageing for 16 h at 798 °C. Tensile testing at 650 °C of samples subjected to this heat treatment showed a 125 MPa increase in yield strength over RR1000 in the conventional microstructural condition. However, this was accompanied by a significant loss of ductility.
We have conducted a detailed series of tensile tests on one heat of annealed 2¹/â Cr-1 Mo steel over the range 25 to 593°C (75 to 1100°F) and at nominal strain rates of 0.4, 0.04, 0.004, and 0.0004/min. To determine an empirical relationship to represent the flow behavior, we fitted the true-stress true-strain data from these tests to several proposed models. The models fit were those proposed by Holloman, Ludwik, Ludwigson, and Voce. From a comparison of the standard error of estimate, the Voce equation was concluded to be the best mathematical description of the data under most test conditions and the best single representation over the wide range of test conditions.
Thermo-mechanical fatigue (TMF) tests of 304L stainless steel were performed in the temperature range in which creep and oxidation effects can be considered negligible. Four different phase angles between mechanical strain and temperature cycles (in-phase (IP), out-of-phase (OP), clockwise-diamond-phase (CD), and counter-clockwise-diamond-phase (CCD)) with three different mechanical strains were performed to elucidate the effects of the mechanical strain and phase angle on the fatigue life. IP and CD induce longer life in general compared to OP and CCD, which could be related to the difference of the mean stress in each condition. Ultimate tensile strength values from tensile tests were used to consider the effect of varying temperature during a TMF cycle on the fatigue damage and material resistance. The effects of specimen geometry (solid versus hollow) on the fatigue life were considered. A simple life prediction model that utilizes the plastic strain energy density, ultimate tensile strength, and mean stress is suggested; this model can predict the TMF fatigue life within a 2× scatter band and explain the difference between different phase angles. The model used one new term to consider the mean stress effect, in addition to the two parameters that are used in the conventional Morrow's model.
High bainite dual phase steel has been subjected to tension test at different temperatures from 25 to 500°C with strain rate of 4.6×10−4s−1 to investigate the effect of temperature on its mechanical properties. Stress–strain curves of steels showed serration flow at temperature range of 200–350°C and smooth flow at the other temperatures. In agreement with previous studies on some steels, peaks in the variations of yield strength (YS) and ultimate tensile strength (UTS) and minima in ductility were observed at temperature range of 200–350°C which are various manifestations of dynamic strain aging (DSA). It has been also found that ferrite volume fraction has no effect on the temperature range of serrated flow but work hardening decreased slightly with increasing ferrite volume fraction.The tensile test data were also analyzed in term of Hollomon equation and it was found that this steel has two work hardening stages. In this study the effects of temperature on Hollomon equation parameters and onset strain of stage II hardening were investigated. The observed peaks/plateaus in the variation of Hollomon equation parameters with temperature at the intermediate temperature range have been identified as the other manifestation of dynamic strain aging. The work hardening analysis of flow stress data revealed that, in the DSA region, the onset strain of stage II work hardening is athermal.
The deformation mechanism map of 2.25Cr—1Mo steel was examined by creep data obtained over a wide range of creep rates down to 10−11s−1. The stress dependence of minimum creep rates of the steel is similar to that of particle strengthened materials: low, high, and low stress exponent, respectively, in high (H), intermediate (I), and low (L) stress regions. The stress exponent and activation energy for creep rate suggest dislocation creep controlled by lattice diffusion as the deformation mechanism in regions I and L, including service conditions of the steel. Transition to diffusion creep occurs at a lower creep rate than what is expected in the deformation mechanism maps. Region H appears above athermal yield stress. During loading in this region, athermal plastic deformation takes place by dislocation glide mechanism, and then dislocation creep starts. The dislocation creep in region H is different from the one in regions I and L due to the plastic deformation during loading. A modified creep mechanism map of 2.25Cr—1Mo steel is proposed on the basis of the experimental results.
An understanding of the strain hardening behaviour of discontinued reinforced aluminium alloys is essential in optimising the parameters for deformation processes of these materials. The 2124 aluminium alloy reinforced with SiC particles has been studied in T4 condition in order to determine the stress–strain response at different temperatures. The strain hardening exponent, n, decreases with the temperature. A non-linear value of the exponent n with the strain has been observed, and two regions are clearly characterised for each temperature.
The tensile properties of Zr-1 wt% Nb alloy were determined in the
temperature interval 295 to 773 K. A phenomenological description of the
tensile behaviour of the alloy is derived in terms of the Holloman
equation and the activation area and enthalpy for deformation. The
strain-hardening exponent of the Holloman equation reaches a maximum
value of $˜0.23 for deformation at 573 K and this is associated
with the occurrence of dynamic stain-ageing. The apparent activation
energy for this process is 51 ± 15 kcal/mole which is in
agreement with that for lattice diffusion of oxygen in α-Zr. The
strain-rate sensitivity, activation area and enthalpy values obtained
for the deformation of the alloy compare favourably with those reported
for Zr- O alloys. The occurrence of an athermal region in the
deformation at 6˜00 K is rationalised in terms of the
superposition of two mechanisms: (i) dynamic strain-ageing due to Snoek
ordering of solute atom pairs and (ii) thermally activated overcoming of
oxygen atom clusters.
Dynamic strain ageing (DSA) behavior of a 20% prior cold worked titanium modified austenitic stainless steel (Alloy D9) was investigated in the temperature range 300–1023 K at a constant (nominal) strain rate of 1.33 × 10−3 s−1. Serrated plastic flow was observed in a narrow temperature region of 773–873 K. Anomalies characteristic of DSA were observed in the variations of strength, ductility, and strain hardening parameters with temperature. Specifically, the difference between ultimate tensile stress and yield stress indicated that a single DSA mechanism is operative over the range of observations. Plastic strain energy density for uniform deformation showed a peak in the DSA temperature range, suggesting that in this material, DSA should enhance the ductile fracture resistance.
Pressure tube material of Indian Heavy Water Reactors is 20% cold-worked and stress relieved Zr–2.5Nb alloy. Inherent variability in the process parameters during the fabrication stages of pressure tube and also along the length of component have their effect on micro-structural and texture properties of the material, which in turn affect its strength parameters (yield strength and ultimate tensile strength) and flow characteristics. Data of tensile tests carried out in the temperature range from room temperature to 800 °C using the samples taken out from a single pressure tube have been used to develop correlations for characterizing the strength parameters’ variation as a function of axial location along length of the tube and the test temperature. Applicability of Ramberg–Osgood, Holloman and Voce’s correlations for defining the post yield behaviour of the material has been investigated. Effect of strain rate change on the deformation behaviour has also been studied.