Effect Of Stress Gradient Research Articles

Model for predicting type Ι fatigue crack growth rate in RKE field considering stress gradient

Based on the stress–strain field at the crack tip of Rice-Kujawski-Ellyin (RKE) and considering the stress gradient effect near the crack tip of type I, a fatigue crack growth rate prediction model L-SG (RKE) for type I is proposed in this paper. Firstly, the stress gradient change value of 1 % at the crack tip is considered as the characteristic distance (stress gradient influence range), and the ratio of the equivalent stress to the far-field stress in the stress gradient influence range is defined as the stress gradient influence coefficient ρ; Secondly, the new model L-SG (RKE) is proposed to quantitatively describe the fatigue crack growth behavior by using the stress–strain field at the crack tip of RKE, and the stress gradient influence coefficient ρ is introduced, and then the crack tip passivation radius rp is defined to eliminate the crack tip singularity, and the plastic strain energy failure criterion is combined.; Finally, the prediction effect of the L-SG (RKE) model is verified by 6 metal materials and the fatigue crack growth rate test results of 2 groups of 45 steel CT specimens, and compared with the SHI-CAI (RKE) model. At the same time, based on the R2 fitting effect and the different requirements of the three stages of fatigue crack propagation, the prediction effect of the two prediction models is analyzed, and comprehensive evaluation from two aspects of safety and accuracy. The results show that the L-SG (RKE) prediction model can better reflect the actual fatigue crack propagation behavior, and can meet the requirements of practical engineering for the accuracy and safety of the prediction model. Especially, the prediction results of physical cracks in 45 steel shaft parts by this model agrees well with the experimental data.

Nanoscale stress and microstructure gradients across a buckled Mo-Cu bilayer: Cu self-annealing triggered by interface delamination

Residual stresses in thin film structures significantly impact their mechanical properties and affect interface delamination. Highly compressively stressed thin films buckling is the predominant interfacial failure mode due to strain energy release. In the present study the effect of cross-sectional stress and microstructural gradients of thin films on the buckling behavior are explored in a model material system consisting of a thin Cu film sputtered onto glass and a highly compressively stressed 500 nm thick Mo overlayer causing buckling delamination at the Cu-glass interface. Employing synchrotron cross-sectional X-ray nano-diffraction, multiaxial X-ray elastic strain and microstructure distributions were explored across the cross-section of the adhering and buckled bilayer, respectively. In the adhering state, a gradual thickness evolution of columnar microstructure and residual stress was found for Mo, while in Cu, no microstructure changes and only minimal stress variations were detected along the film thickness. After delamination, diffraction peak broadening and changes in unstrained lattice parameters in the Cu sublayer indicated structural defect annihilation and grain coarsening. These microstructural changes were further validated via cross-sectional transmission electron microscopy. The evaluated residual stress distributions across the two sublayers of the pristine and buckled bilayer were used to quantify the released strain energy per unit area due to buckling, amounting to 0.61 J/m². Further cross-validation of experimental stress results with finite element simulations strengthened the experimental findings, providing a comprehensive understanding of the stress distribution across the buckled bilayer.

Effect of strain gradient and interface engineering on the high-temperature energy storage capacitors

The miniaturization and high integration of electronic devices pose new requirements for the energy storage density and high-temperature performance of dielectric capacitors. For thin film materials, internal stress and the interface layer often show a significant impact on their energy storage performance. Therefore, the capacitors with different stress gradient sequences and different periods were designed by BaHf0.17Ti0.83O3 (BHTO17), BaHf0.25Ti0.75O3 (BHTO25), and BaHf0.32Ti0.68O3 (BHTO32) to investigate the effect of stress gradient and interface engineering on the energy storage characteristics. Dielectric thin film structures with upward gradient, downward gradient, and periodic upward gradient (4N) were constructed. The study found that the upward gradient structure had higher breakdown field strength than the downward gradient structure. This is because the upward gradient structure can effectively extend the ending electric field of the Ohmic conduction mechanism and delay the activation electric field of the F–N tunneling mechanism. The 4N structure had a slightly higher breakdown field strength (reaching 9.22 MV/cm) compared to the pure upward gradient structure. The 4N structure thin film also exhibited higher energy storage density (115.44 J/cm3) and wide temperature (−100 to 400 °C) characteristics. These findings provide important guidance and application value for improving the energy storage characteristics of dielectric capacitors at high temperatures through structural design.

Predicting fatigue failure in five‐axis machined ball‐end milled components through FKM local stress approach

AbstractComponents created with five‐axis machining show a multi‐scale surface character due to cusps created on the surface and feed and tool marks within the cusps. Therefore, it becomes difficult to incorporate the effects of surface character on fatigue life for such components. In this work, an Forschungskuratorium Maschinenbau (FKM) guideline is adapted to develop a fatigue prediction model which considers cusps as notches and marks within the cusps as surface roughness (characterized by parameter R10z). The assessment uses stresses obtained from an finite element analysis model to predict the fatigue life of components whilst considering stress concentration, stress gradient, mean stress, and surface roughness effects. When cusps are regarded as surface roughness within the conventional FKM approach, fatigue life is considerably underestimated. In comparison, fatigue life predictions that take into consideration the roughness within cusps and treat cusps as stress‐raising notches are closer to experimental life.

Lower-order mechanism-based strain gradient plastic model considering stress gradient effect

Lower-order mechanism-based strain gradient plastic model considering stress gradient effect

The effect of stress gradient on the formation of topologically close packed phases in a Ni-based single crystal superalloy at 1050 °C

The formation of topologically close packed (TCP) phases is detrimental to the mechanical properties of Ni-based single crystal (SX) superalloys, which are used in harsh environments with high temperature and gradient stress caused by centrifugal force during service. In order to study the precipitation behavior of TCP phases in coupling with temperature and stress gradient, a third generation Ni-based SX superalloy is selected to conduct force holding experiments at 1050 °C for 8 hours. Stress gradient can be realized under constant load by designing tensile samples with cross-sectional area continuously changed. The results indicate that the area fraction of TCP phases varies at different positions of the sample, where the effective tensile stress is different. The area fraction of TCP phases decreases at the thinner region of the sample, which means that the amount of TCP phases decreases as applied stress increases. At the thinnest position, where the stress is estimated to be 400 MPa, almost no TCP was observed. The inhibition of stress on the formation of TCP phase may be due to the reduction of Re concentration in the γ matrix, because of the segregation of Re at γ/γ′ phase interfacial dislocation cores and the dissolving of γ′ phase.

Stress–diffusion coupling. Application to interstitial diffusion

A numerical study of the stress–diffusion coupling theory based on the Cahn–Larché method is presented in the case of interstitial diffusion. Indeed, the interaction between diffusion and stress fields has been widely studied in the past. Most of the studies focused on the effect of chemical stress due to mass transport on diffusion. The majority of the studies have been focusing on the coupling between external mechanical and chemical stresses with diffusion. In this study, the effect of stress/strain on mobility and stress gradient mobility and driving forces are presented, based on the model of Voorhees and Larché. The analytical solutions are detailed, from general equations (interstitial diffusion, elastic material) to a macroscopic model (interstitial diffusion, isotropic elastic material, infinite dilute solution, 2D axisymmetric). Numerical simulations for different samples thickness and β parameter helped to better understand and then experimentally identify the prevailing effect of stress on mobility or diffusion driving forces. These studies demonstrated the impact of constant compressive and tensile stress on diffusion kinetics through the mobility term of the equation, as well as the effects of negative and positive stress gradients via the Nernstian term. The results show that constant compressive stress and negative stress gradient hinder the diffusion. On the contrary, tensile stress and positive stress gradient promote the diffusion. This work also demonstrates the importance of coupling between mobility and Nernstian effect on the diffusion promotion.

Kinetics of voids evolution during diffusion bonding of dissimilar metals on consideration of the realistic surface morphology: Modeling and experiments

A comprehensive model for analyzing the kinetics of void evolution and shrinkage during dissimilar diffusion bonding is proposed based on the sinusoidal profile. The model incorporates atom accumulation at void tip to determine the curvature radius of void neck, and integrates the local effect of surface diffusion to quantify the contribution of surface diffusion, thus avoiding the unrealistic void evolution observed in previous models. Furthermore, the model utilizes a combined diffusion coefficient for multicomponent alloys under the effect of stress and concentration gradients, to determine the interfacial diffusion coefficient for dissimilar joints. In contrast to previous models, the current model demonstrates significant improvements in predicted accuracy, efficiently depicting the realistic void evolution and interpreting the formation of various interfacial voids, which can be applied in various bonding cases, including for the dissimilar base metals with different surface conditions. Simulation results from bonding between austenitic steel and ferritic steel with different surface roughness reveal that interfacial voids predominantly form on the side of the base metal with the rougher bonding surface. Additionally, as surface roughness decreases, the prevailing surface source diffusion and interface source diffusion mechanisms promote void evolution and shrinkage, resulting in a significant reduction of the final bonding time. To achieve a high-quality bonding joint, it's suggested to place the smoother bonding surface on the higher creep-resistant base metal, which can accelerate the void closure process.

Composite effects of residual stress and hardness gradient on contact fatigue performance of rough tooth surfaces and optimization design of detailed characteristic parameters

Residual stress and hardness gradient significantly affect the contact fatigue failure process of rough tooth surfaces, and the meticulous design of their characteristic parameters can help improve the fatigue resistance of gears. In this paper, an efficient computational method for rough tooth surface contact is established based on the reconstruction modeling of asperities and mixed lubrication analysis. By comprehensively considering the effects of residual stress and hardness gradient, the Dangvan multiaxial fatigue criterion is adopted to predict and analyze the contact fatigue life of the gear surface. The correlation between the surface residual stress, maximum residual stress depth, surface hardness, and effective hardening layer depth, among other characteristic parameters, and the contact fatigue performance of tooth surfaces is established. The results show that: (1) Increasing the magnitude of surface residual compressive stress and surface hardness can significantly reduce the risk of fatigue failure in the near-surface layer of the gear. To achieve the same fatigue performance, there is a linear negative correlation between the design values of the two parameters. (2) Affected by the double stress peaks in the rough tooth surface stress field, the maximum residual stress depth significantly affects the depth at which the highest failure risk occurs. With changes in roughness, the optimal design value of the maximum residual compressive stress depth changes from about 0.5 times the Hertzian contact half-width depth in the subsurface layer (Sa < 0.2 μm) to about 15 μm in the near-surface layer (Sa > 0.4 μm). (3) Considering both process cost and gear surface fatigue resistance, the design threshold for the effective hardening layer depth should be greater than the Hertzian contact half-width. This paper establishes a composite correlation between the meticulous characteristic parameters of residual stress, hardness gradient, and the contact fatigue performance of tooth surfaces, providing theoretical support for optimal design of tooth surface anti-fatigue performance.

Numerical Simulation Study on the Mechanics and Pore Characteristics of Tectonically Deformed Coal under Multi-Level and Multi-Cycle Loading and Unloading Conditions

Horizontal well cavern completion and stress release is considered a potential technique for efficient development of coalbed methane in tectonically deformed coal (TDC). Pulsating loading and unloading is a key technique for the controlled expansion of caverns and broader stress release within the reservoir. However, current understanding of the mechanical characteristics and pore network structure evolution of TDC under cyclic loading and unloading conditions is still limited. This paper employs numerical simulation methods to study the mechanical behavior and damage characteristics of TDC under cyclic loading and unloading. After obtaining a set of micromechanical parameters reflecting the behavior of TDC samples under triaxial compression in high-stress states, the effects of different stress gradients and cyclic amplitudes on the stress–strain curve, porosity changes, and crack propagation in TDC samples were analyzed. The study results indicate that under various cyclic loading and unloading conditions, the mechanical response characteristics of TDC samples are broadly similar, primarily divided into compression, slow expansion, and accelerated expansion phases. Under low unloading level conditions, the volume expansion of TDC samples is minimal. Also, at the same unloading level, the strain increment decreases with an increasing number of cycles. Correspondingly, under these conditions, the porosity and microcrack expansion in TDC are less than in high-stress gradient scenarios. Under the same unloading level but different amplitudes, the volume expansion rate at 50% unloading amplitude is higher than at 1 MPa unloading amplitude for TDC, with an increased number of crack expansions. Therefore, under cyclic loading conditions, the sensitivity of crack propagation within TDC samples to amplitude is greater than that to unloading level. Under actual pulsating excitation conditions, a low-amplitude, low-stress gradient pulsation method should be used to maintain the stability of horizontal well caverns, and gradually increase the cyclic amplitude to achieve the efficient extraction of coalbed methane in TDC reservoirs. The findings of this study can serve as an important reference for optimizing process parameters in cyclic pulsating stress release engineering for TDC.

Roles of chain stretch and concentration gradients in capillary thinning of polymer solutions

Abstract Polymers inhibit the breakup of a liquid filament thinning under surface tension. The coupling of elasticity, capillarity and inertia leads to the well-known beads-on-a-string (BOAS) formation. Additionally, under different conditions, smaller satellite drops can form along the liquid bridge between the main beads. The development of BOAS and satellite drops is controlled by the rheology of the polymer solution. In this study, we consider the roles played by finite extensibility and anisotropic drag on the formation of satellite beads. In particular, we show that the more stretching a polymer chain can undergo, satellite beads are suppressed. The latter stages of capillary thinning has been shown to result in a phase separation resulting in what is referred to as a blistering pattern. We thus also conduct simulations of an inhomogeneous dilute polymer model that considers the competing effects of diffusion and stress gradients. We show that polymer is pulled axially towards the region connecting string and bead. This simple model does not predict a phase separation, but does reveal that pinchoff could be inhibited by the buildup of polymer concentration.

Coexistence of Ambrosia chamissonis and Ammophila arenaria in coastal dunes in the Ñuble Region, Chile

Coastal dunes are unique ecosystems distributed worldwide. They share coastline-to-inland abiotic stress gradients determining their plant´s spatial distribution and biological interactions. Ambrosia chamissonis and Ammophila arenaria dominate coastal dunes in Chile, but there is scarce ecological information about their interactions and spatial distribution. The aim of this study was to characterize the coexistence of these two species and to evaluate the effect of stress gradients on their spatial distribution and performance. The study was carried out in three coastal dunes of the Ñuble Region, Chile; two dunes in which each species dominates and one in which they coexist. In each dune, sampling sites were defined along study transects perpendicular to the coast, where both soil characteristics (pH, salinity, contents of water, organic matter, nitrogen, phosphorus, and potassium) and biological variables of each species (cover, height, water content, content of foliar macronutrients) were measured. Variation of each abiotic variable with the distance from the high tide level was correlated to determine environmental stress gradients. A Canonical Correspondence Analysis (CCA) was performed to determine soils characteristics that better explained changes in plant abundance. The Relative Interaction Intensity index was calculated from biological variables and compared intraspecifically to determine dominant interactions along the dunes. Our results showed two soil stress gradients (soil salinity and available potassium) which decreased inland and may define in part, the spatial distribution of the species, as shown by the CCA. Our results support the idea that dune plants do not always follow the stress gradient hypothesis suggesting a modification of the hypothesis.

Design of aluminum alloy channel sections bent about the minor axis

Aluminum alloy extruded channel sections are often used as rafters for light roofs, columns in framed buildings and chords of roof trusses. In this paper, a numerical study is carried out on the response of aluminum alloy channel sections under minor axis bending. Numerical models were developed and validated based on the experimental data of aluminum alloy channel sections under minor-axis bending. Subsequently, parametric studies covering various cross-sectional geometries were performed to expand the numerical data. The results were used to assess the applicability of Eurocode 9 slenderness limits, revealing that the Class 2 and Class 3 limits for outstand flanges under stress gradient with peak compression at tip are too conservative. Moreover, Eurocode 9 underestimates the predicted bending strengths of slender cross-sections due to the lack of consideration of the effect of stress gradient. The equivalent stress gradient factor applied in the effective thickness approach was proposed based on the buckling coefficient of BS 5950. For channel sections bent about minor-axis with the web in compression, flanges exhibit pronounced inelastic behavior even when the web locally buckles. An alternative design method based on the ultimate shape factor of a rectangular plate is proposed for semi-compact and slender channel sections in minor-axis bending (producing compression in the web), which leads to more favorable and less scattered capacity predictions.

Nonlocal approach to fatigue analysis of a welded bicycle frame joint

AbstractThe paper attempts to predict the probabilistic fatigue strength scatter bands of a welded bicycle frame joint. The experimental data of the base material and the weld material were approximated by a nonlinear probabilistic model of the Weibull distribution. The fatigue strength for the material at the fatigue crack location was estimated considering the mean stress, residual stress, fatigue notch factor, and hardness profile. The output finite element numerical data of the real welded joint were compared with a nonlocal multiaxial fatigue criterion. The implementation of the volumetric method takes into account the stress gradient effect in the three‐dimensional geometry of the weld toe. The comparative localization of the minimum stress and the real crack indicates the validity of the numerical model. The predicted fatigue strength determines the possible failure of a welded joint at 5·105 cycles.

Numerical modelling of microstructure inhomogeneity to reproduce experimentally observed scatter in fretting fatigue lifetimes

Experimental fretting fatigue lives exhibit large degree of scatter. One of the aspects behind this is the microstructural inhomogeneity which affects the stresses in the material. Variance in stress values can greatly impact crack initiation speed, leading to changes in fretting fatigue lifetimes, as well as the crack propagation behaviour. This research aims to study this issue in more detail and recreate the experimentally observed scatter using numerical modelling. In this work, Voronoi tessellation is used to simulate microstructural topologies of low carbon steel, where each grain is assigned elasto-plastic properties at random, from a predetermined range. In total, 60 finite element models are created and the effect of microstructural inhomogeneity on fretting fatigue lifetime dispersion is evaluated using a Continuum Damage Mechanics approach. Additionally, crack propagation is studied with XFEM combined with Smith-Watson-Topper fatigue parameter to determine crack path under multiaxial, non-proportional loading conditions. For both crack initiation and propagation investigation, the Theory of Critical Distances is applied to overcome the effect of high stress gradients. Simulation results show that microstructural inhomogeneity has significant impact on the contact stress distributions and subsurface stress and strain fields. Scatter observed in the predicted lifetimes matches well with that observed in practical experiments and is used to propose a design curve for the studied material. The applied crack path prediction approach captures the variance in crack paths originating from microstructural inhomogeneity and shows good correlation with reference experimental results at low bulk stress levels.

Gigacycle Fatigue Properties of Wrought Aluminum Alloys

Fatigue data sheets of the National Institute for Materials Science disclose the results of gigacycle fatigue tests conducted on wrought aluminum alloys. The materials tested were hot-rolled plates and extruded round bars of A5083P-O (two heats), A7075-T6 (three heats), and A6061-T6 (three heats). The fatigue testing methods were rotating-bending at 100 Hz, ultrasonic at 20 kHz, and uniaxial at 100 Hz. The rotating-bending fatigue tests were conducted for 3 years to reach 1010 cycles. The ultrasonic and uniaxial fatigue tests were also conducted at high stress ratios. This study analyzed the fatigue life data, clarifying frequency effects, presence or absence of fatigue limits, and stress ratio effects. The three types of fatigue tests revealed equivalent results, meaning that frequency effects and stress gradient effects were negligible in the wrought aluminum alloys. Frequency effects were visible in several cast aluminum alloys owing to the influence of humidity, but the wrought aluminum alloys were observed to be insensitive to humidity. Many specimens were fractured at >107 cycles, whereas the degradation of fatigue strength after 107 cycles was very small in A5083P-O but large in A7075-T6 and A6061-T6. A5083P-O revealed fatigue limits at around 107 cycles. The heat treatment effects determined the presence or absence of fatigue limits because the equivalent tensile strengths between A6061-T6 and A5083P-O excluded the possibility of tensile strength effects. The stress ratio effects on gigacycle fatigue strengths of the wrought aluminum alloys are reasonable and can be estimated in conventional ways.

Notch Fatigue Life Prediction Model Considering Stress Gradient Influence Depth and Weight Function

Notch characteristics significantly affect the fatigue performance of engineered components, for which the stress gradient effect is worth careful consideration. The traditional stress gradient analysis method based on the Coffin–Manson equation does not take into account the stress gradient influence range regarding the definition of the stress gradient correction factor, nor the high-stress gradient region, which has a greater influence on fatigue life. To address the aforementioned problems, a new notch fatigue life model is proposed in this paper. First, the stress–strain field at the root of the notch is analyzed to define the depth of stress gradient influence, following which the influence of the low-stress gradient region is reduced by a weighting function in the calculation of the stress gradient correction factor. Finally, to validate the method, three sets of experimental data, including TC4, GH4169, and EN8B, were used and compared with three other models. The results demonstrate that the predicted lifetimes of the new model are all within a 2-fold dispersion band, and the prediction ability is better than that of the other three models.

Toward tunable shape memory effect of NiTi alloy by grain size engineering: A phase field study

The inelastic deformations of shape memory alloys (SMAs) always show poor controllability due to the avalanche-like martensite transformation, and the effective control for the deformation of precision devices has been not yet mature. In this work, the phase field method was used to investigate the shape memory effects (SMEs) of NiTi SMAs undergoing grain size (GS) engineering, to obtain tunable one-way and stress-assisted two-way SMEs (OWSME and SATWSME). The OWSME and SATWSME of the systems with various gradient-nanograin structures and bimodal grain structure, as well as that with geometric gradients were simulated. The simulated results indicate that due to the GS dependences of martensite transformation and reorientation, the occurrence and expansion of martensite reorientation, martensite transformation and its reverse can be efficaciously controlled via the GS engineering. When combining the GS engineering and geometric gradient design, since the effects of GS and stress gradient can be superimposed or competing, and the responses of martensite reorientation, martensite transformation and its reverse to this are different, the OWSME and SATWSME of the geometrically graded systems with various nanograin structures can exhibit different improvements in controllability. In short, the reorientation hardening modulus during OWSME is increased and the transformation temperature window during SATWSME is widened by GS engineering, indicating the improved controllability of SMEs. The optimal GS engineering schemes revealed in this work provide the basic reference and guidance for designing tunable SMEs and producing NiTi-based driving devices catering to desired functional performance in various engineering fields.

Nonlinear Dynamical Instability Characteristics of FG Piezoelectric Microshells Incorporating Nonlocality and Strain Gradient Size Dependencies

In the present exploration, the nonlocal stress and strain gradient microscale effects are adopted on the nonlinear dynamical instability feature of functionally graded (FG) piezoelectric microshells under a combination of axial compression, electric actuation, and temperature. To perform this objective, a unified unconventional shell model based on the nonlocal strain gradient continuum elasticity is established to capture the size effects as well as the influence of the geometrical nonlinearity together with the shear deformation along with the transverse direction on the dynamic stability curves. With the aid of an efficient numerical strategy incorporating the generalized differential quadrature strategy and pseudo arc-length continuation technique, the extracted unconventional nonlinear differential equations in conjunction with the associated edge supports are discretized and solved to trace the dynamic stability paths of FG piezoelectric microshells. It is revealed that the nonlocal stress and strain gradient effects result in, respectively, higher and lower values of the nonlinear frequency ratio in comparison with the conventional one due to the stiffening and softening characters associated with the nonlocality and strain gradient size dependency, respectively. In addition, it is observed that within the prebuckling territory, the softening character of nonlocality is somehow more than the stiffening character of strain gradient microsize dependency, while by switching to the postbuckling domain, this pattern becomes vice versa.

Stress gradient effect in metal fatigue: Review and solutions

Under external loadings, notched components always show varying degrees of stress concentration. Accordingly, different kinds of approaches have been presented to characterize notch fatigue behaviours under complex loading histories. Among them, the considering of the stress gradient effect is a popular perspective, together with the fatigue damage zone and critical distance concepts. This work systematically reviews recent advances on notch fatigue analysis considering the stress gradient effect. Specifically, four approaches are summarized and explored, namely the local stress/strain-based approaches, critical distance-based approaches, critical plane-based approaches, and weighting control parameters-based approaches. This review aims to provide a systematic review and comparison on these methods, therefore to offer a reference for subsequent research on notch fatigue.