Stress Curves Research Articles

Analysis of dynamic features on local fatigue cracks in steel bridges

In steel bridges with orthotropic decks, a common and important engineering structure, fatigue cracks can appear under long-term operation. Existing artificial detection is the main approach to detecting fatigue cracks in steel bridges, in addition to some non-destructive testing or image processing methods, and unmanned aerial vehicle are applied to improve accuracy and efficiency. However, the detection of fatigue cracks in steel bridges based on the variation of dynamic responses or dynamic parameters is another attractive idea, which is still rarely mentioned and investigated in the international literature. The reason is that local cracks usually have negligible effect on the global dynamic characteristics of steel bridges, resulting in the insensitivity to dynamic indexes to fatigue cracks. On this occasion, this study numerically explores and establishes two sensitive damage features to local damage, i.e., the crack in the vertical rib, based on the fatigue cracks found on the Türr Istvan bridge over the Danube River in Hungary. The local vibrations of the bridge are excited through the local impact on the structural details, i.e., the vertical rib, and then the high-order frequencies of the entire bridge are examined. The obtained high-order frequencies are proved to be more sensitive to the fatigue cracks on vertical ribs and increased with the crack depths. On the other hand, the correlation of the stress curves on opposite sides of the crack is sensitive to the depth of the crack. If fatigue cracks are found, the development degree of the fatigue cracks can be monitored more accurately by focusing on the correlation of local stresses near the crack. These two damage features are numerically proven to have feasibility and are expected to break through the insensitivity of the existing dynamic detection methods.

Numerical and experimental study for process improvement of cross-wedge rolling of bearing steel balls

The uniaxial compression experiments were conducted on GCr15 bearing steel to obtain the flow stress curves under hot deformation conditions. Based on the results of uniaxial compression experiments, finite element modeling was conducted on the cross wedge rolling (CWR) of GCr15 bearing steel balls, and numerical simulation was conducted using Simufact Forming 16.0. The results show that the distribution of effective strain of existing CWR steel balls is uneven, which may lead to uneven quality of steel balls. In addition, the three principal stresses at the center of the steel balls are all tensile stresses, and the effective stress at the center of the middle ball is relatively large, which can easily induce central defects. Moreover, different diameter billets were used for steel balls rolling experiments. It can be seen that when the die cavity is underfilled with billet, the rolled steel balls have no central defects. When the die cavity is fulfilled with billet, there is central piercing appearing at the middle ball, while the side balls have no obvious central defects. Finally, the paper proposes the method of even numbered ball rolling (ENBR) which starts from the middle connector to improve the CWR process of steel balls.

Prediction of rock loading stages using average infrared radiation temperature under shear and uniaxial loading

Accurately predicting geologically rock loading phases under varying water levels is crucial to prevent rock engineering operations from severe geological hazards. Acoustic emission (AE) traditionally determines these phases, but machinery in rock projects can disrupt AE sensors, leading to imprecise data and potential accidents. To address this, our study tested a novel approaches using AE, Average Infrared Radiation Temperature (AIRT), Critical Slow Down Theory (CSDT), and Convolutional Neural Networks (CNNs) to predict rock loading phases accurately under different water conditions. The research findings are: (1) AE analysis divides the stress–strain curve into four phases: crack closure, elastic deformation, and stable and unstable crack propagations. Each phase exhibits distinct characteristics in terms of AE signal behavior. (2) AIRT analysis reveals specific patterns during different loading phases. The AIRT and cumulative AIRT have distinct trends in different phases. (3) The AIRT sequence's fractal dimension shows distinct trends during loading phases: it initially rises during the elastic phase and then declines. Fractal dimensions for crack closure, elastic deformation, and stable crack propagation increase, while that for unstable crack propagation decreases with water content. 4) The stress–strain curve phases were successfully predicted by using AIRT and CSDT, demonstrating a strong correlation with actual stress levels. Notably, this marks the first-time prediction of phases through non-destructive tests (IR and CSDT), where CSDT fluctuations at each stage can serve as early indicators of rock failure.5) The proposed CNNR model achieves high accuracy (98%) in predicting different phases of the stress curve using AIRT. It particularly performs well in the elastic deformation and stable crack propagation phases, with only a few instances of false negative predictions. The model shows promising potential for effective and safe geological projects, especially under varying water conditions. The findings contribute to the understanding of rock behavior and offer insights for the design of safer and more efficient rock engineering projects.

Artificial neural network and YUKI algorithm for notch depth prediction in X70 steel specimens

The presence of notches directly influences the material's degree of resistance to fracture, as each notch is defined by its size and location in the structure. In this study, we present a methodology using an optimization technique that allows us to predict the notch depths based on one of the most important mechanical parameters, namely the maximum stress for each notch depth. This study starts with the experiments of standard pipe specimens, which have notches with different depths. A numerical model, using GTN parameters, is created based on the experimental model and its results are presented in form of stress and strain curves of API X70 steel specimens under uniaxial tensile tests. The high-performance numerical models used to simulate the experimental model consider a considerable number of different cases. The study is concluded by choosing the best optimization technique among different proposed algorithms, namely NN-YUKI, NN-JAYA, and NN-EJAYA. The validation of models and their accuracy is determined by comparing the outputs of NN-YUKI, NN-JAYA, and NN-EJAYA with experimental and numerical data. The obtained results using NN-YUKI determine the best optimization parameters and provide a good prediction of notch depth. This methodology gives an insight into the notch size under different loading conditions and is applicable to large structures like pipes under various loadings.

Fracture Prediction of Aluminum Alloy Sheet AA2024-T3 Using Analytical Stress and Experimental Strain Based Failure Criteria

In this work, the fracture prediction of aluminium alloy sheet, grade AA2024-T3 was investigated using the Fracture Forming Limit Curve (FFLC) and Analytical Fracture Forming Limit Stress Curve (FFLSC) as failure criteria. Initially, the FFLC was experimentally achieved by means of the Nakajima Stretch forming test coupled with GOM strain measurement system, providing the Digital Image Correlation (DIC) technique. Subsequently, the analytical FFLSC was plastically computed using experimental FFLC data combination with Swift hardening model and anisotropic Hill’48 yield model for representing anisotropic plastic deformation behaviour on examined sheet. Finally, Fukui stretch drawing and Three point bending tests were conducted both experiment and numerical simulation to evaluate the fracture state and verifying an applicability of obtained FFLC and FFLSC. In the simulation, the ABAQUS 2017 element deletion function was employed for directly implementing the fracture criteria regarding the FFLC and FFLSC. It was concluded that the analytical FFLSC could more realistically predict fracture behaviour better than the FFLC based on strain. In term of percentage error, the analytical FFLSC generated an error less than the FFLC.

On the Application of some Plasticity Laws

Three main rheological laws are found in the literature to describe the strain hardening of materials at high temperatures. The choice of the most suited law to describe a flow stress curve is often discussed as a function of the nature of the material; but it still remains difficult to choose the most appropriate one. These semi-empirical laws systematically comprise two main terms linked either to the dislocations generation or their annihilation.The objective of this paper is to determine by an inverse method which law appears to be the most suited. It is finally demonstrated that the application of one law is mostly equivalent to another. The various laws are overall equivalent and do not help to describe some peculiar physical mechanism of plasticity.

Experimental and numerical studies of the multi-tube assembled buckling-restrained braces

In this paper, the multi-tube assembled bolt-connected buckling-restrained brace (MT-BRB) with four internally restrained rectangular steel tubes and one externally restrained square steel tube is experimentally analyzed. This study conducted cyclic loading tests on five specimens with different parameters to investigate the effects of different loading directions of the core plate, the presence or absence of unbonded materials, the gap-to-width ratio and the width-to-thickness ratio on the mechanical properties, seismic performance and failure mode of MT-BRB. The experimental results indicated that the MT-BRB specimens made of unbonded materials had stable cyclic performance and energy dissipation capacity. Subsequently, the same numerical model as the experimental specimen was established, and the hysteresis and stress curves extracted from the finite element model were compared with the experimental results. The simulation had ideal agreement with the experiment result, demonstrating that the model was effective for performance predictions. Based on this, the working mechanism of MT-BRB was further explored through finite element analysis. Finally, parameter analysis was conducted on the constraint ratio and constraint length ratio to further investigate the energy dissipation performance of MT-BRB. This study is beneficial for promoting the application of MT-BRB in energy dissipation and vibration reduction engineering.

An improved cellular automaton model of dynamic recrystallization and the constitutive model coupled with dynamic recrystallization kinetics for microalloyed high strength steels

This study analyzed the deformation behavior of Nb–Ti microalloyed high strength steel at strain rates of 0.001–0.1 s−1 and deformation temperatures of 1050–1150 °C using hot compression tests. The deformation activation energy of 321.1 kJ/mol was calculated based on the stress-strain curve, and the characteristic points on the flow stress curve were extracted. In contrast, the relationship equation between the characteristic points and the Zener-Hollomon parameter was established. A modified dynamic recrystallization (DRX) kinetics model was proposed based on the stress-strain data, considering the strain rate and deformation temperature. A high-precision constitutive model was established based on the dislocation density evolution phenomenological model, which couples with the modified DRX kinetics model. Furthermore, an improved DRX cellular automaton (CA) model was constructed, which comprehensively took into account a series of processes such as dislocation density evolution, recrystallization nucleation, and grain growth. Notably, the model also embedded the pinning effect of second phase (SP) particles on the DRX process. The improved CA model can control the pinning force by adjusting the size and volume fraction of SP particles and can accurately predict the evolution characteristics of DRX and the average austenite grain size of Nb–Ti microalloyed high strength steels during thermal deformation. The development of an improved CA model can be extended to apply to the DRX evolution of other microalloyed steels, and the model provides a powerful tool and method for understanding the thermal deformation behavior and microstructural evolution of microalloyed steels.

Study on Dynamic Parameters and Energy Dissipation Characteristics of Coal Samples under Dynamic Load and Temperature

Coal and rock dynamic disasters such as rock burst and outburst seriously threaten the sustainable development of the coal mining industry, which are intimately correlated with the nonlinear dynamic response process of the deep coal and rock mass. This study conducts coal dynamic experiments under vibration load from room temperature to 60 °C by using the split Hopkinson bar (SHPB) with a temperature real-time control system and analyzes the variation in stress and strain and the energy dissipation characteristics of coal during the dynamic load process. The expression equation of dissipated energy of coal at different scales is established, and the judgment conditions of the macroscopic mechanical behavior of coal are analyzed theoretically. The stress curves show a multi-stress peak phenomenon when the coal samples are subjected to different temperatures and dynamic loads, and the coal’s dynamic stress and temperature show a polynomial fitting relationship at different stages. When the coal sample is subjected to temperature and dynamic load, the macroscopic changes in incident energy, reflected energy, and dissipated energy are consistent; that is, various energies gradually increase to a fixed value and tend to stabilize with the time of stress wave action. The transmission energy exhibits a rising trend in correlation with the duration of the dynamic load action, but the value is less than 0.1 J. The growth gradients of the different energies, in descending order, are: the growth gradient of incident energy, reflection energy, dissipation energy, and transmission energy. The energy inflection point appears at 60 °C. Based on the linear elastic fracture mechanics and damage mechanics theories, the expression for coal energy dissipation from the nanoscale to the microscale is established, and the relationship between energy dissipation and macroscopic mechanical behavior response of the coal samples is analyzed. The main physical components of the coal sample are calcite and kaolinite. Within the temperature range of 18–60 °C, the macroscopic failure form of the coal is horizontal tensile failure. The study results are introduced into dynamic disaster prevention and control and the surrounding rock system stability evaluation in deep mines.

A parametric study into the influence of Taylor-type scale-bridging artifacts on accuracy of multi-level crystal plasticity finite element models for Mg alloys

Meshing grain structures explicitly to incorporate microstructure dependent material behavior in modeling tools for metal forming processes and structural components is unfeasible. Grain-to-polycrystal meso-level homogenization theories are employed to embed polycrystal plasticity constitutive laws in finite element (FE) frameworks, which hence relate the meso-scale to the macro-scale response. A Taylor-type polycrystal plasticity (T-CP) theory is often used at the meso-scale within FE frameworks (T-CPFE) owing to its simplicity and computational efficiency. The theory relies on the iso-strain constraint imposed over constituent grains at each integration point. The constraint can be relaxed by spreading orientation distributions over finite elements in a mesh. This work seeks to establish an optimal number of crystal orientations to spread over integration points for accurate modeling of Mg alloys. Quasi-static and high strain-rates simulations of tension, compression, simple-shear, and plane strain deformation conditions are performed and post-processed to reveal the differences in predicted mechanical fields between T-CPFE and an explicit polycrystalline grain microstructure of an AZ31 Mg alloy. Moreover, several flow stress curves of the alloy are simulated and compared with measured data. A range of meshes with variable degree of relaxed constraints at integration points are suitably designed and used in the simulations. The performance of the six crystals per integration point is established to be an optimum in smoothing local deformation while allowing heterogenous deformation over the mesh. As such, the relaxed Taylor homogenization can provide tractable part level simulations of Mg alloys.

Experimental study on the mechanical behavior and energy absorption capacity of coral sand at high strain rates

This study investigated and compared the compression responses and energy absorption capacities of coral sand and silica sand at a strain rate of approximately 1000 s−1. To this end, the effects of the relative density and particle size distribution on the abovementioned properties were analyzed, and the stress–strain curves, yield stresses, compressibilities, energy absorption curves, and energy absorption ratios were obtained. The experimental results showed that coral sand had a significantly higher energy absorption capacity than silica sand owing to its higher compressibility. The energy absorption curve for sand was primarily influenced by the yield stress and energy absorption ratio. The lower relative density of coral sand contributed to its higher compressibility and energy absorption capacity compared to silica sand. For coral and silica sands with different particle sizes, the intersection of the stress–strain and energy absorption curves was observed and analyzed. Formulas for predicting the yield stress, compressibility, and energy absorption curve of coral sand were derived, considering the variations in the relative density and particle size. The study findings reveal that using poorly graded coral sand with large particle sizes can improve the energy absorption capacity of coral sand.

Study on Hot Deformation Behavior and Dynamic Recrystallization Mechanism of Cu‐Ti‐Fe Alloy

Hot compression experiments with the deformation temperatures of 750–950 °C and the strain rates of 0.01–10 s−1 are carried out on a Gleeble‐3500 thermal‐mechanical simulator. The flow behavior and dynamic recrystallization (DRX) mechanism of the Cu‐Ti‐Fe alloy are systematically studied under different hot deformation conditions. According to the curves of flow stress and work hardening rate, the DRX critical condition of the alloy is obtained, and the critical stress value of DRX is small under high‐temperature and low‐strain rate. After fitting, the logarithmic values of the critical stress and critical strain have a linear relationship with lnZ, which indicates that the alloy is more prone to DRX at high temperatures and low‐strain rates. The Arrhenius constitutive model of the alloy is established, the linear correlation coefficient (R2) is 0.984. Combined with the microstructure of Cu‐Ti‐Fe alloy, the microstructure evolution characteristics and DRX mechanism are elucidated. The dominant mechanism of the alloy under the deformation temperature of 750–950 °C is the DRX mechanism. The low‐angle grain boundaries (LAGBs) transform into high‐angle grain boundaries (HAGBs) and continuous dynamic recrystallization (CDRX) grains form. Abundant dislocations gather near the HAGBs, causing grain boundaries to protrude. High‐temperature conditions make the dislocations disappear, forming discontinuous dynamic recrystallization (DDRX) grains.

Micropillar compression using discrete dislocation dynamics and machine learning

Discrete dislocation dynamics (DDD) simulations reveal the evolution of dislocation structures and the interaction of dislocations. This study investigated the compression behavior of single-crystal copper micropillars using few-shot machine learning with data provided by DDD simulations. Two types of features are considered: external features comprising specimen size and loading orientation and internal features involving dislocation source length, Schmid factor, the orientation of the most easily activated dislocations and their distance from the free boundary. The yielding stress and stress-strain curves of single-crystal copper micropillar are predicted well by incorporating both external and internal features of the sample as separate or combined inputs. It is found that the machine learning accuracy predictions for single-crystal micropillar compression can be improved by incorporating easily activated dislocation features with external features. However, the effect of easily activated dislocation on yielding is less important compared to the effects of specimen size and Schmid factor which includes information of orientation but becomes more evident in small-sized micropillars. Overall, incorporating internal features, especially the information of most easily activated dislocations, improves predictive capabilities across diverse sample sizes and orientations.

Viscoelastic-damage constitutive model and mechanical characterisations of Aluminium/polytetrafluoroethylene under impact loading

As a typical structural energy-containing material, aluminium/polytetrafluoroethylene (Al/PTFE) exhibits excellent mechanical properties under conventional conditions and releases large amounts of energy through chemical reactions under impact loading. In this research, a viscoelastic-damage constitutive model suitable for polymer-based reactive materials was developed, which consisted of an elastic element, two Maxwell elements, and a SCRAM damage element. The effect of damage on the stress–strain relationship was obtained by analysing the crack evolution process and deformation field. A modified Split Hopkinson pressure bar experiment investigated the mechanical characteristics of aluminium/polytetrafluoroethylene under uniaxial/multiaxial impact loading. The results indicated that the viscoelastic-damage constitutive model could describe the effects of the initial crack size and initial crack density on the mechanical properties of aluminium/polytetrafluoroethylene. With the decrease in initial crack length and density, the damage to the aluminium/polytetrafluoroethylene under impact loading was limited, which caused the dynamic mechanical properties to increase. When the pre-stress increases from 0 MPa to 10 MPa, the dynamic ultimate compressive stress of aluminium/polytetrafluoroethylene increases from 77.2 MPa to 89.8 MPa at 2910 s−1 strain rate. A comparison of the experimental and calculated strain–stress curves shows that the established constitutive model is feasible to predicting the mechanical behaviour of aluminium/polytetrafluoroethylene.

Determining Hot Deformation Behavior and Rheology Laws of Selected Austenitic Stainless Steels

Due to their versatile properties, austenitic stainless steels have a wide application potential, including in specific fields, such as the nuclear power industry. ChN35VT steel is a chromium–nickel–tungsten type of steel stabilized by titanium, and it is suitable for parts subjected to considerable mechanical stress at elevated temperatures. However, the available data on its deformation behavior at elevated/high temperatures is scarce. The core of the presented research was thus the experimental characterization of the deformation behavior of the ChN35VT steel under hot conditions via the determination of flow stress curves, and their correlation with microstructure development. The obtained data was further compared with data acquired for 08Ch18N10T steel, which is also known for its applicability in the nuclear power industry. The experimental results were subsequently used to determine the Hensel-Spittel rheology laws for both the steels. The ChN35VT steel exhibited notably higher flow stress values in comparison with the 08Ch18N10T steel. This difference was more significant the lower the temperature and the higher the strain rate. Considering the peak stress values, the lowest difference was ~8 MPa (1250 °C and 0.01 s−1), and the highest was ~150 MPa (850 °C and 10 s−1). These findings also corresponded to the microstructure developments—the higher the deformation temperature, the more negligible the observed differences as regards the grain size and morphology.

Temperature-dependent behavior of CP-Ti interpreted via self-consistent crystal plasticity simulation

A commercially-pure titanium sample was investigated using an elasto-visco-plastic self-consistent polycrystal model. Temperature-dependent plastic deformation behavior was described by a dislocation density-based hardening model. The model reasonably reproduced various experimental behaviors, including stress vs. strain curves, diffraction lattice strains, twin volume fraction, and crystallographic texture. The temperature-dependent behavior was interpreted based on the dislocation evolution rules comprised of dislocation generation and recombination in accordance with the Kocks-Mecking rule. The modeling results successfully provided an in-depth interpretation of mechanical behavior of α-titanium under a wide range of temperatures.

Compressive performance of paper honeycomb core layer with double-hole in cell walls

The perforated paper honeycomb structure with double-hole in cell walls is one kind of innovative sandwich structure also to improve drying process of traditional honeycomb paperboard. Based on the analytical calculation, experiment inspection and finite element analysis, this paper is focus on the paper honeycomb core layer with double-hole in cell walls, and especially studies the bending and folding deformation and the compressive strength under out-of-plane quasi-static compression for different humidity. The structure first appears elastic buckling and folds near the circular holes in the cell wall, and goes on buckling, folding and crushing until to the densification with the continuously increase of compression set. Its quasi-static compressive stress and strain curve mainly shows four kinds of compression deformation processes, such as linear elastic stage, elastic yielding stage, plastic collapse stage, and densification stage. The critical stress and plateau stress of the structure slowly decrease with the increase of humidity and aperture, and the multiple linear regression analysis result illustrates that the relative humidity has much more influence on the critical stress and plateau stress. For different humidity and aperture, the analytical calculation result is close to the experiment result. However, the finite element simulation result greatly deviates from the above two results, especially for relative humidity 50% and 60% cases.

Influence of vacancies on the stability and mechanical properties of V2AlC: Guidelines for etching MAX phases via ab initio calculations

This study focuses on the ideal etching of defective MAX phases in a mechanical exfoliation process to produce vanadium-based MXenes. Two-dimensional MXenes exhibit high structural stability and excellent electrical conductivity, and can be applied as electrode materials. Mechanical exfoliation can be facilitated by modifying the vacancy in the V2AlC MAX phase, which makes etching challenging. We report the effects of M (vanadium), A (aluminum), and X (carbon) vacancies on the mechanical behavior of V2AlC via ab initio calculations. To this end, the anisotropic mechanical properties and strain–stress curves were calculated for MAX phases with different vacancies (x = 0.08, which corresponds to 8.33 at.%). The presence of vanadium vacancies significantly deteriorated the structural and mechanical properties compared to those of aluminum and carbon vacancies. Thus, it was confirmed that vanadium vacancies had a significant effect on the mechanical exfoliation of the MAX phases. These findings provide further insights into the design of MXenes.

Optimizing process parameters for hot forging of Ti-6242 alloy: A machine learning and FEM simulation approach

In this study, we investigated the hot deformation behavior of Ti–6Al–2Sn–4Zr–2Mo (Ti-6242) alloy and propose a method to derive optimal hot process parameters for grain refinement and avoidance of flow instability. Microstructural Risk Index (MRI) was introduced as a microstructural evaluation index consisting of grain size, standard deviation of grain size, and flow instability. The initial temperature of the material and the stroke speed of the die were selected as design variables. Finite element analysis (FEA) was used to calculate grain size and flow instability and determine MRI of the forgings. The grain size model coefficient and flow instability were calculated based on the flow stress curve and verified with optical microscope (OM) and electron backscatter diffraction (EBSD) analysis results. The Deep Neural Network (DNN) model was used to determine the optimal process parameters for the forging process. The MRI prediction accuracy of the trained DNN models showed excellent performance at 97.01 %. The MRI of the optimized process variables was improved by 7.95 % compared to the minimum MRI of the training data set. Optimized process parameters can improve the quality of forgings through grain refinement and avoidance of flow instability regions.

Microstructure evolution and constitutive analysis of nuclear grade AISI-316H austenitic stainless steel during thermal deformation

Compression experiments were performed on AISI-316H austenitic stainless steel using Gleeble-3800 at temperatures ranging from 900 °C and 1200 °C and strain rates ranging from 0.01 and 10 s−1, up to the actual strain of 0.69. The tests aimed to examine the material’s microstructure evolution and flow stress behavior. Based on OM and EBSD studies, it was found that thermal deformation mostly induces discontinuous dynamic recrystallization (DDRX). The proportion of recrystallization nucleation increases steadily with increasing deformation temperature, while the impact of strain rate on recrystallization is complex. At the same deformation temperature, the recrystallization volume fraction initially declines and rises as the strain rate rises. In low strain rate regime, the longer (deformation) time available for grain boundary migration, the higher recrystallization volume fraction. In high strain rate regime, the higher stored energy (and thus the increased boundary velocity) raises the probability of nucleation events, stimulating twin formation. As a result, the twin promotes a dynamic recrystallization (DRX) process. An abundance of Σ3 twins was notably observed in uniformly refined recrystallized grains at a true strain of 0.69, at a temperature of 1200 °C, and a strain rate of 10 s−1. As a result, it was discovered that DRX occurs at higher strain rates and deformation temperatures. In addition, the flow stress curves were modified to account for adiabatic heating at strain rates exceeding 1 s−1. The findings demonstrated that adiabatic heating increased when strain level and strain rate increased and deformation temperature decreased. The strain compensation Arrhenius model is developed following the given stress–strain curve while considering strain. The model exhibits high accuracy, with a correlation value of 0.986. According to a kinetic study, the average activation energy for hot deformation of the tested steel was 444.994 kJ/mol. These findings provide fundamental insights into the microstructure control technology and the outstanding mechanical properties of the austenitic stainless steel AISI-316H.