High Stress Gradients Research Articles

Influence of abnormal stress under a residual bearing coal pillar on the stability of a mine entry

Mine entries close to residual bearing coal pillars (RBCPs) will suffer large deformation that may cause rock burst. To better understand the deformation mechanism and develop safe and practical guidelines for entry design, most studies focus on the absolute size of the stress field in and around the pillar. In this paper, we present a new approach to analyze the abnormal stress field close to a RBCP that uses the stress concentration coefficient (SCC), stress gradient (SG), and coefficient of lateral pressure (CLP) to describe the stress state induced by the RBCP. Based on elastic theory and a mathematical model for the abutment stress in the RBCP, an analytical solution for the abnormal stress in the strata below the RBCP was derived and the characteristics of the abnormal stress for a case study of a coal mine in China were analyzed. The results show that the abnormal stress field around the pillar is characterized by four distinct zones: a zone of high SCC, high SG, and CLP less than 1, a zone of high SCC, low SG, and CLP less than 1, a zone of low SCC, SG close to 0, and CLP greater than 1, and a zone of SCC close to 1, SC close to 0, and CLP close to 1. Based on this zoning pattern, a numerical model was established to study the combined effects of the abnormal stress on the stability of the entry. The most stable zone was determined based on a model of the Xinrui coal mine and verified by field measurements at the mine. Our conclusions can be used as guidelines for designing safe entry layouts in similar geological and mining settings.

Integrating coupled magnetoelastic sensors onto a flexible hernia mesh for high dynamic range strain measurements.

Despite better performance over primary repairs, tension-free ventral hernia repairs with mesh still suffer from a high recurrence rate. High stress gradients in the mesh are thought to contribute to hernia recurrence. We propose a postoperative monitoring system based on a coupled pair of magnetoelastic strain sensors to enable patients and physicians to non-invasively measure and track the strain distribution across the hernia mesh. Our design combines an encased resonator with a spring-loaded transducer to achieve high signal amplitude with a wide dynamic range. We also demonstrate a fabrication protocol to integrate the resonant strain sensors with a commercial polypropylene mesh. The packaged sensor is capable of detecting up to 37.5 millistrain, an order of magnitude greater than previously demonstrated.

High resolution residual stress gradient characterization in W/TiN-stack on Si(100): Correlating in-plane stress and grain size distributions in W sublayer

Residual stress gradient characterization by the ion beam layer removal method (ILR), using a milling step of 10nm, was applied to W/TiN stacks processed on thermal SiO2-insulated standard silicon wafers. The stress profiles indicate a pronounced stress gradient with high tensile, as well as compressive stress concentrations in polycrystalline W and amorphous TiN sublayers ranging between 3.5 and −4GPa. Electron backscatter diffraction shows that the W sublayer exhibits zone T microstructure with nano-sized crystallites in the nucleation region at the interface to TiN and above that columnar or V-shaped grain morphology typical for competitive grain growth. In the W sublayer, the stress distributions correlate well with this in-plane crystallite size distribution on the base of a Hall-Petch mechanism, reaching a tensile maximum in the transition region between the nucleation layer and the region with columnar microstructure.

Stress gradient due to incremental forming of bonded metallic laminates

ABSTRACTThe residual stress and associated gradient can affect the performance of a material/component during service. Sheet-metal in incremental sheet forming (ISF) due to missing back support may experience high stress gradient across the thickness. The current work is aimed at experimentally analyzing the through-thickness stress gradient in the Cu/steel bonded laminates after ISF deformation. It is found that ISF induces compressive stress gradient, which can be a way greater (about 18 times) than that the rolling process induces in the parent laminates while bonding, specifically when the deformation angle is high. Further, the tool imposes more stress gradient (1–50% depending on the forming conditions) in its motion direction than that in the transverse (or stretching) direction. Moreover, un-strained Cu/steel laminated sheet experiences higher (25%–68%) gradient than that the pre-strained/rolled sheet endures. Regarding the role of technological parameters, high angle, small tool, average step-size and spindle rotation, and low flow-stress induce high stress gradient. The tension tests of the ISFed samples reveal that the post-ISF tensile strength of laminated sheet increases as the stress gradient increases, thus showing a direct relationship between stress gradient and strain hardening in ISF. Finally, models are proposed to predict the stress gradient in the ISFed Cu/steel components.

Finite Element Model for Analysis of the Spatial Interfacial Debonding of FRP from Concrete

The debonding of the FRP plate from concrete and crack-propagation processes are complex and the current research studies regarding this debonding mechanism are insufficient and not comprehensive. This work proposes a plane stress model along with equal width and different width FRP to concrete models to simulate the debonding and crack-propagation processes are presented. The longitudinal and horizontal stress distributions were analysed and the FRP to concrete width effect and FRP thickness parameters were also studied by means of the proposed three-dimensional finite element model. The results show that the different width 3D model is optimal for analysing the spatial interfacial debonding of FRP from concrete. The concrete surface horizontal stress distribution along the length of the concrete substrate could judge the effective bond length. Both the normal stress and shear stress are mainly divided into the following two small central stress regions under the PRP plate: a high stress gradient region near the FRP plate edge and a stress-free region near the concrete edge. The debonding strength and the stiffness of the bonding interface increase with the width of the FRP plate and the FRP plate thickness. The stress range and magnitude are strongly dependent on the width of the FRP plate. Debonding begins at the FRP plate edge; the thicker FRP plate more easily exhibits debonding.

Artificial neural network for correction of effects of plasticity in equibiaxial residual stress profiles measured by hole drilling

The hole drilling method is a widely known technique for the determination of non-uniform residual stresses in metallic structures by measuring strain relaxations at the material surface caused through the stress redistribution during drilling of the hole. The integral method is a popular procedure for solving the inverse problem of determining the residual stresses from the measured surface strain. It assumes that the residual stress can be approximated by step-wise constant values, and the material behaves elastically so that the superposition principle can be applied. Required calibration data are obtained from finite element simulations, assuming linear elastic material behavior. That limits the method to the measurement of residual stresses well below the yield strength. There is a lack of research regarding effects caused by residual stresses approaching the yield strength and high through-thickness stress gradients as well as the correction of the resulting errors. However, such high residual stresses are often introduced in various materials by processes such as laser shock peening, for example, to obtain life extension of safety relevant components. The aim of this work is to investigate the limitations of the hole drilling method related to the effects of plasticity and to develop an applicable and efficient method for stress correction, capable of covering a wide range of stress levels. For this reason, an axisymmetric model was used for simulating the hole drilling process in ABAQUS involving plasticity. Afterward, the integral method was applied to the relaxation strain data for determining the equibiaxial stress field. An artificial neural network has been used for solving the inverse problem of stress profile correction. Finally, AA2024-T3 specimens were laser peened and the measured stress fields were corrected by means of the trained network. To quantify the stress overestimation in the hole drilling measurement, an error evaluation has been conducted.

Numerical study to indicate the vulnerability of plaques using an idealized 2D plaque model based on plaque classification in the human coronary artery.

Atherosclerosis is one of the leading causes of death in the world. In this study, an idealized 2D plaque model based on plaque classification in the coronary artery is developed. When creating the idealized 2D model for each plaque type (fibrocalcic, FC; fibrofatty, FT; calcified fibroatheroma, CaFA; fibroatheroma, FA; calcified thin-cap fibroatheroma, CaTCFA; thin-cap fibroatheroma, TCFA), the cap thickness and stenosis by diameter were set as variables. In order to establish the correlation between each plaque type and plaque rupture, a numerical simulation was performed and the stress and stress gradient were reviewed to analyze the mechanical behavior. Results show that both the TCFA and CaTCFA plaque types, which have the smallest cap thicknesses of the different types of plaque, showed relatively high stress values in the thin membrane when compared with the FT type. The FT type is considered to be relatively stable since it does not have necrotic core or a thin membrane. With a stenosis rate of 50% and a cap thickness of 60μm, the TCFA and CaTCFA types showed approximately 11 and 110% higher stress values, respectively, and 679 and 1568% higher negative stress gradient values, respectively. In other words, the plaque types with thin caps, which have weak load-bearing capacities, showed high stress values and high negative stress gradients in the radial direction. It is understood that this result could indicate the possibility of plaque rupture.

Early cracking orientation under high stress gradients: The fretting case

Many fretting contacts experience a rapid variation of the magnitude and relative contribution of the stress components away from the surface. This feature of the fretting problem poses an additional difficulty for the modeling of the early cracking orientation. In this work, critical plane approaches associated with a process zone are evaluated by taking into account the fretting crack behavior observed in two different steels. The results show that the conventional approaches may provide inconsistent cracking directions. A new method for early cracking orientation prediction is developed by employing the average values of the normal and shear stresses along a critical direction. This method is simpler to implement and improves the estimates when compared to the other approaches.

Strategy for refinement of nodal densities and integration cells in EFG technique

MeshFree methods have become popular owing to the ease with which high stress gradients can be identified and node density distribution can be reformulated to accomplish faster convergence. This paper presents a strategy for nodal density refinement with strain energy as basis in Element-Free Galerkin MeshFree technique. Two popular flat plate problems are considered for the demonstration of the proposed strategies. Issue of integration errors introduced during nodal density refinement have been addressed by suggesting integration cell refinement. High stress effects around two symmetrical semi-circular notches under in-plane axial load have been addressed in the first problem. The second considers crack propagation under mode I and mode II fracture loading by the way of introducing high stress intensity through line crack. The computational efficacy of the adaptive refinement strategies proposed has been highlighted.

Mixed Lagrangian formulation for size‐dependent couple stress elastodynamic and natural frequency analyses

SummaryCouple stress formulations have been given much attention lately because of the possibility to explain cases, when the classical theory of elasticity fails to describe adequately the mechanical behavior. Such cases may include size‐dependent stiffness, high stress gradients, and the response of materials with microstructure. Here, a new mixed Lagrangian formulation is developed for elastodynamic response within consistent size‐dependent skew‐symmetric couple stress theory. With a specific choice of mixed variables, the formulation can be written with only C0 continuity requirements, without the need to introduce a Lagrange multiplier or penalty method. Furthermore, this formulation permits, for the first time, the determination of natural frequencies within the consistent couple stress theory. Details for the strong form of the equilibrium equations, constitutive model relations, boundary conditions, and the corresponding weak form are provided. In addition, the discrete forms are also discussed with two approaches for reducing variables. Several simple two‐dimensional computational example problems are then examined, along with a brief investigation of the effect of couple stress on natural frequencies, which exhibit size‐dependence for most, but not all, modes. Copyright © 2016 John Wiley & Sons, Ltd.

Stress-induced trench narrowing in Cu interconnect of sub-20 nm node: FEM simulation

The trench narrowing at sub-20nm BEOL process has been reproduced using a FEM simulation. The trench narrowing can be observed under the conditions of both the high intrinsic stress of a hard mask and the specific design of metal line patterns with the length difference between center and side trenches. As the center trench length increases, a trench displacement takes place because trench walls have a high compressive stress gradient from the side trench surface to the center one in the direction parallel to the trench lines. The displacement also decreases with decreasing the width of the trench while increasing with decreasing the width of the low-k wall. The high pattern density of metal or dummy lines around the trenches decreases the displacement of the low-k dielectric walls. Considering the distribution of pattern densities at left and right sides of the trenches, a symmetrical pattern density deforms the trench wall more largely than an asymmetrical one. Young's modulus of SiOCH is not a sensitive factor on the trench narrowing. Our displacement analysis may be used in predicting hot spots of void defects in the Cu interconnect of real Si wafers.

Thermal stress singularity analysis for V-notches by natural boundary element method

The accuracy of thermal stresses at internal points by the conventional boundary element method becomes deteriorate when the points are approaching to the boundary due to the inaccuracy of the calculation of nearly singular integrals by the Gaussian integration. Herein, a thermal stress natural boundary integral equation is proposed, in which the nearly hyper-strongly singular integral is reduced to a nearly strongly singular one and then dealt by the regularization method. Thus, it can be applied to model the high stress gradient in the vicinity very close to the V-notch vertex. The stress method is subsequently introduced to calculate the stress singularity orders and thermal stress intensity factors once the thermal stresses along the bisector and very close to the notch tip are yielded. The mathematical and physical singularity difficulties, i.e., the evaluation of nearly singular integrals and singular stress fields, are both overcome in this paper. After a benchmark model being given out to verify the efficiency of the present method, the thermal stress singularities for a symmetrical V-notch and an inclined one are respectively analyzed. The benchmark example manifests that the thermal stress nature boundary integral equation can be successfully used to calculate the thermal stresses much closer to the boundary by the comparison with the conventional thermal stress boundary integral equation. The accuracy of the stress singularity orders and thermal stress intensity factors by the present method is confirmed and the computational effort is dramatically decreased by comparing with the finite element method.

A non-local approach based on the hypothesis of damage dissipation potential equivalence to the effect of stress gradient in fretting fatigue

A non-local approach based on continuum damage mechanics is proposed to take into account the stress gradient effect on fatigue crack initiation in fretting fatigue. The concept of subRVE (sub Representative Volume Element) is introduced as a smaller constituent unit of RVE (Representative Volume Element) and with the dimension of material average grain size for the purpose of considering the heterogeneous damage in the RVE. The fatigue damage in the subRVE is regarded as uniform, while the stress of subRVE is not uniform due to the effect of stress gradient. The fatigue damage evolution of each subRVE is derived by the hypothesis of damage dissipation potential equivalence with consideration of stress heterogeneity in the subRVE. Fretting fatigue is analyzed using this approach due to a zone of high stress gradient exists in the contact area. The predicted result from the proposed non-local model is better than that from local model by comparing with the experimental data. The interaction between wear and effect of stress gradient is also investigated.

Numerical Investigation on Atomic Migration Effect on Thermal Conductivity of Al/Cu Interface Structures in Electronic Interconnection Packaging

At present, MEMS and micro/nano electronic packaging technology have an exhaustive range of applications in the field of mass-produced commercial products, such as cell phones, computer, automobiles, and pedometers, which cause a strong demand for the reliability of heat transfer in nano or micro scales. Wire bonding process has been widely used in the MEMS or devices packaging approach to create high aspect interconnection structures [1], hence, the thermal analysis, thermal design, and thermal management become more and more important for microelectronic system or microelectronic devices. The interfacial structures of dissimilar materials are suffering the high stress gradients due to the thermal and stiffness mismatches of the different materials [2, 3]. The interface structures of dissimilar materials are very prone to crack initiations under the heat flow effect. The heat transfer across the interface is a critical consideration for the thermal design in the IC or devices manufacturing. Here we reveal the relationship between the atomic migration and thermal conductivity of Al/Cu interface in nanoscale heat transfer by using non-equilibrium molecular dynamics method. To create the Al/Cu interface, the modified Embedded-atom method (EAM) for alloy is used to describe the interatomic interactions between Cu/Cu, and Al/Cu interface. The results show that the interfacial diffusion is enhanced with the increase of the temperature from 400K-600K. The thermal conductivity of the Al/Cu interface, first increases, and then decreases. When the temperature is over 600K, it reaches the recrystallization temperature of Al. which makes to Al atoms recrystallization. The recrystallization of Al atoms may reduce the heat transfer efficiency of the Al/Cu diffusion region. That is to say, it reduces the thermal conductivity of Al/Cu interface when the temperature is over 600K. This means that we can enhance the interfacial heat transfer efficiency of Al/Cu interface and the cooling efficiency of IC by heat treatment in advance on interface structures. This investigation is helpful for understanding the interfacial heat transfer mechanism of the interface structures in the IC, which is helpful for the design of the interface in micro/nano manufacturing and benefit for the estimate the reliability of the IC manufacturing. Figure 1

A Chemomechanical Model for Stress Evolution and Distribution in the Viscoplastic Oxide Scale During Oxidation

Using the location-dependent growth strain, a chemomechanical model is developed for the analysis of the stress evolution and distribution in the viscoplastic oxide scale during high-temperature oxidation. The problem of oxidizing a semi-infinite substrate is formulated and solved. The numerical results reveal high compressive stress and significant stress gradient. The maximum stress is at the oxide/substrate interface and the minimum stress at the oxygen/oxide interface in short oxidation time, while the maximum stress is no longer at the oxide/substrate interface in long oxidation time. The stress evolutions at different locations are also presented. The predicted results agree well with the experimental data.

Viscoelastic viscoplastic model for aeronautical thermoplastic laminates at high temperature: Validation on high stress gradient structures

This study was aimed at validating a numerical model accounting for the influence of time-dependent effects of thermoplastic PolyPhenyleneSulfide (PPS) matrix on the behavior of carbon woven fiber reinforced PPS laminates at temperatures exceeding its Tg, when matrix viscoelasticity and viscoplasticity are prominent. This model combines a linear spectral viscoelastic model and a generalized Norton-type viscoplastic model, and was implemented into the Finite Element code Cast3m. From the macroscopic response standpoint, the validation of the model has been achieved by means of tests on high gradient structures at T > Tg (perforated with a central hole, single-edge notched, asymmetric double-edge notched specimens). Lastly, a full-field measurement technique (Digital Image Correlation) has been used at high temperature to test the model's ability to qualitatively and quantitatively predict the surface strains distribution of TP composites in high gradient structures.

Microstructural Modeling of Coupled Electromagnetic-Thermo-Mechanical Response of Energetic Aggregates to Infrared Laser Radiation and Dynamic Fracture

ABSTRACTA dislocation-density based crystalline plasticity, a finite viscoelasticity, and a nonlinear finite-element formulation were used to study the high strain-rate failure of energetic crystalline aggregates. The energetic crystals of RDX (cyclotrimethylene trinitramine) with a polymer binder were subjected to high strain-rate tensile loading, and the predictions indicate that high localized stresses and stress gradients develop due to mismatches along crystalline-crystalline and crystalline-amorphous interfaces. These high-stress interfaces are sites for crack nucleation and propagation, and the predictions are used to show how the cracks nucleate and propagate.

Influence of Size Effect and Stress Gradient on the High-cycle Fatigue Strength of a 1.4542 Steel

Nowadays technical applications require very small components which leads to the question of how to handle fatigue strength data gained from tests carried out on specimen which are even larger than the component itself. Previous high-cycle-fatigue (HCF) tests have outlined the negative influence of increasing “risk volumes” due to enlargement of the specimen size. Additional to the effect of “risk volumes” the influence of stress gradient may not be neglected as the gradient changes as well due to the enlargement of the specimen size. Especially thin profiles could be affected by high stress gradients which results in high and low stress loaded profile areas. The fatigue strength of an hourglass shaped specimen with a standardized diameter of 7.5 mm tends to have higher fatigue strength than a specimen with a larger diameter. In this work rotating bending tests were carried out on specimens with a diameter of 4 and 7.5 mm. Lifetime simulations with different specimen diameters (D2.5, D4 and D7.5) were carried out by a common simulation tool FEMFAT and simultaneous testing of D4 and D7.5 specimens was performed to compare the results. An outlook is given on how such influences can be estimated and an appropriate method can be derived for damage calculations.

Creep behavior and life assessment of anisotropic bicrystals with a void and without void in different kinds of grain boundaries

Based on crystallographic theory, a creep constitutive relationship and a life predictive model have been presented. The crystallographic creep constitutive relationship has been implemented as a user subroutine ’CRPLAW' to MACR. Bicrystal models containing a void in the grain boundary and bicrystal model without void have been studied by the finite element method. Different loading direction has been studied in order to show the influence of relative direction of loading to grain boundary on the creep behavior of the bicrystals. The numerical results of bicrystal models show that there are a high stress gradient and stress concentration near the void and grain boundary. The existing of the void has strong influence on creep durability life of the crystal. The stress distribution and creep strain characterization are dependent on the crystallographic orientations of the two crystals and the grain boundary direction as well as the existing of the void and loading directions. It is shown that the bicrystal model of the loading direction perpendicular to the grain boundary has the highest creep strain and creep damage, while that model of the of the loading direction parallel to the grain boundary has the minimum. This above conclusion is also same to the growth of void.

Association of Hemodynamic Factors With Intracranial Aneurysm Formation and Rupture: Systematic Review and Meta-analysis.

Recent evidence suggests a link between the magnitude and distribution of hemodynamic factors and the formation and rupture of intracranial aneurysms. However, there are many conflicting results. To quantify the effect of hemodynamic factors on aneurysm formation and their association with ruptured aneurysms. We performed a systematic review and meta-analysis through October 2014. Analysis of the effects of hemodynamic factors on aneurysm formation was performed by pooling the results of studies that compared geometrical models of intracranial aneurysms and "preaneurysm" models where the aneurysm was artificially removed. Furthermore, we calculated pooled standardized mean differences between ruptured and unruptured aneurysms to quantify the association of hemodynamic factors with ruptured aneurysms. Standard PRISMA guidelines were followed. The hemodynamic factors that showed high positive correlations with location of aneurysm formation were high wall shear stress (WSS) and high gradient oscillatory number, with pooled proportions of 78.8% and 85.7%, respectively. Positive correlations were largely seen in bifurcation aneurysms, whereas negative correlations were seen in sidewall aneurysms. Mean and normalized WSS were significantly lower and low shear area significantly higher in ruptured aneurysms. Pooled analyses of computational fluid dynamics models suggest that an increase in WSS and gradient oscillatory number may contribute to aneurysm formation, whereas low WSS is associated with ruptured aneurysms. The location of the aneurysm at the bifurcation or sidewall may influence the correlation of these hemodynamic factors.