Hydrostatic Stress Research Articles

The crucial role of periodontal ligament's Poisson's ratio and tension-compression asymmetric moduli on the evaluation of tooth displacement and stress state of periodontal ligament

The hydrostatic stress in the periodontal ligament (PDL) evaluated by finite element analysis is considered an important indicator for determining an appropriate orthodontic force. The computed result of the hydrostatic stress strongly depends on the PDL material model used in the orthodontic simulation. This study aims to investigate the effects of PDL Poisson's ratio and tension-compression asymmetric moduli on both the simulated tooth displacement and the PDL hydrostatic stress. Three tension-compression symmetric and two asymmetric PDL constitutive models were selected to simulate the tensile and compressive behavior of a PDL specimen under uniaxial loading, and the resulting numerical results were compared with the in-vitro PDL experimental results reported in the literature. Subsequently, a tooth model was established, and the selected constitutive models and parameters were employed to assess the hydrostatic stress state in the PDL under two distinct loading conditions. The simulated results indicate that PDL Poisson's ratio and tension-compression asymmetry exert substantial influences on the simulated PDL hydrostatic stress. Conversely, the elastic modulus exhibits minimal impact on the PDL stress state under the identical loading conditions. Furthermore, the PDL models with tension-compression asymmetric moduli and appropriate Poisson's ratio yield more realistic hydrostatic stress. Hence, it is imperative to employ suitable Poisson's ratio and tension-compression asymmetric moduli for the purpose of characterizing the biomechanical response of the PDL in orthodontic simulations.

Impacts of nanofiller shapes on the interface confinement effect in polymer nanocomposites

Shape effect of nanofillers (NFs) on the properties of nanocomposites has attracted considerable attention in recent research. The present study aims to examine how NF shapes influence the confinement effect of polymer-NF interface on the physical properties of nearby polymer (the interphase). Herein molecular dynamics simulations are performed to capture the shift of interphase properties when NFs change from nanosphere to nanocylinder and nanofilm geometry. A stress analysis is then carried out in the interphase to identify a key parameter for characterizing the stress-property coupling and revealing the pathway of the NF shapes to impact the interphase properties. It is shown that the peak hydrostatic stress σhyd quantifies the effect of internal stresses on the properties of the interphase. Specifically, the shape transition considered can substantially enhance the peak σhyd by flattening the stress space in the interphase without largely affecting the polymer-NF interaction. Increased peak σhyd in turn upshifts the interphase properties and thus, leads to the coupling between the NF shapes and interface confinement effect.

Significant mobilization of REE from calc-alkaline melt into fluid during fluid exsolution: Insights from magmatic amphibole composition from Tieshan skarn Fe-Cu deposit (Hubei Province, China)

Hydrothermal fluids associated with carbonatites and peralkaline silicate rocks typically exhibit high REE content, but this is generally not the case for calc-alkaline rocks. However, the Tieshan skarn Fe-Cu deposit in the Edong district of Hubei Province in China demonstrates economic REE mineralization potential linked to calc-alkaline rocks. To investigate the presence of REE enrichment in the fluid, we present textural and compositional data of rock-forming mineral amphibole from the quartz diorite in the Tieshan deposit. Three distinct types of amphibole are identified in the Tieshan quartz diorite, namely Early amphibole, Main-stage amphibole, and Late amphibole, following the crystallization sequence. Early amphibole (813–864 °C, 115–152 MPa) crystallized when the magma was emplaced at a depth of approximately 4.8 km. Main-stage amphibole (741–806 °C, 58–103 MPa) crystallized at a depth of roughly 3 km. Between the early and main-stage amphibole crystallization, the magma experienced fractional crystallization of pyroxene, amphibole, and plagioclase, resulting in a REE enrichment in the residual melt. Late amphibole crystallized subsequent to the transition from lithostatic to hydrostatic stress states (656–729 °C, 27–52 MPa). Significantly, the transport of REE from the magma system initiated towards the end of Main-stage amphibole crystallization. A comparison with the Tonglvshan granitic rocks in the same district indicates an elevated F content and extended fractional crystallization history in the Tieshan magma, contributing to REE enrichment in its melt. Furthermore, the high F content lowered the solidus temperature of the Tieshan magma, thereby facilitating the more efficient removal of REE into the fluid. The assimilation of evaporate into the magma possibly led to heightened sulfur and chlorine levels in the fluid, enabling the transport of a significant amount of REE.

Interaction between an edge dislocation and a circular incompressible liquid inclusion

We use Muskhelishvili’s complex variable formulation to study the interaction problem associated with a circular incompressible liquid inclusion embedded in an infinite isotropic elastic matrix subjected to the action of an edge dislocation at an arbitrary position. A closed-form solution to the problem is derived largely with the aid of analytic continuation. We obtain, in explicit form, expressions for the internal uniform hydrostatic stresses, nonuniform strains and nonuniform rigid body rotation within the liquid inclusion; the hoop stress along the liquid-solid interface on the matrix side and the image force acting on the edge dislocation. We observe that (1) the internal strains and rigid body rotation within the liquid inclusion are independent of the elastic property of the matrix; (2) the internal hydrostatic stress field within the liquid inclusion is unaffected by Poisson’s ratio of the matrix and is proportional to the shear modulus of the matrix; and (3) an unstable equilibrium position always exists for a climbing dislocation.

Effect of Tensile Loading and Temperature on the Hydrogen Solubility of Steels at High Gas Pressure

The hydrogen solubility in ferritic and martensitic steels is affected by hydrostatic stress, pressure, and temperature. In general, compressive stresses decrease but tensile stresses increase the hydrogen solubility. This important aspect must be considered when qualifying materials for high‐pressure hydrogen applications (e.g., for pipelines or tanks) by using autoclave systems. In this work, a pressure equivalent for compensating the effect of compressive stresses on the hydrogen solubility inside of closed autoclaves is proposed to achieve solubilities that are equivalent to those in pipelines and tanks subjected to tensile stresses. Moreover, it is shown that the temperature effect becomes critical at low temperatures (e.g., under cryogenic conditions for storing liquid hydrogen). Trapping of hydrogen in the microstructure can increase the hydrogen solubility with decreasing temperature, having a solubility minimum at about room temperature. To demonstrate this effect, the generalized law of the hydrogen solubility is parameterized for different steels using measured contents of gaseous hydrogen. The constant parameter sets are verified and critically discussed with respect to the high‐pressure hydrogen experiments.

Void nucleation at dislocation boundaries aided by the synergy of multiple dislocation pile-ups

Void nucleation is of great significance in understanding ductile fracture. Recent experiments have shown that voids are nucleated via vacancy condensation and dislocation boundaries are the main nucleation sites. However, it is unclear what role is played exactly by dislocation boundaries in promoting void nucleation. Here we propose a new mechanism for dislocation boundary-induced void nucleation and develop a corresponding model based on the classical nucleation theory and vacancy diffusion theory. The model suggests that void nucleation is mainly influenced by hydrostatic stress, temperature, and relative vacancy concentration, whose contributions are systematically studied. It is also suggested that the vacancy formation energy and the interaction energy of hydrostatic stress and vacancy, which are absent in the previous models and introduced in ours, exhibit a clear tendency to lower the activation free energy barrier. Analysis of the nucleation kinetic suggests that the growth rate of void depends on the vacancy diffusion coefficient and vacancy concentration; the higher the values of these parameters, the faster the growth rate of the void. The kinetic feasibility of the newly proposed mechanism is examined using three-dimensional discrete dislocation dynamics simulations. The results predict that the size of incipient voids nucleated at the dislocation boundary is ∼35 nm, which is consistent with the experimental characterization value of ∼50 nm. Finally, when the relaxation of the dislocation boundary is considered, the synergistic effect is weakened.

Effective contribution ratio of the molar during sequential distalization using clear aligners and micro-implant anchorage: a finite element study

IntroductionThis study aims to investigate the biomechanical effects of anchorage reinforcement using clear aligners (CAs) with microimplants during molar distalization. And also explores potential clinical strategies for enhancing anchorage in the sequential distalization process.MethodsFinite element models were established to simulate the CAs, microimplants, upper dentition, periodontal ligament (PDL), and alveolar bone. In group set I, the 2nd molars underwent a distal movement of 0.25 mm in group set II, the 1st molars were distalized by 0.25 mm after the 2nd molars had been placed to a target position. Each group set consisted of three models: Model A served as the control model, Model B simulated the use of microimplants attached to the aligner through precision cuts, and Model C simulated the use of microimplants attached by buttons. Models B and C were subjected to a series of traction forces. We analyzed the effective contribution ratios of molar distalization, PDL hydrostatic stress, and von Mises stress of alveolar bone.ResultsThe distalization of the 2nd molars accounted for a mere 52.86% of the 0.25-mm step distance without any reinforcement of anchorage. The remaining percentage was attributed to the mesial movement of anchorage teeth and other undesired movements. Models B and C exhibited an increased effective contribution ratio of molar distalization and a decreased loss of anchorage. However, there was a slight increase in the undesired movement of molar tipping and rotation. In group set II, the 2nd molar displayed a phenomenon of mesial relapse due to the reciprocal force produced by the 1st molar distalization. Moreover, the efficacy of molar distalization in terms of contribution ratio was found to be positively correlated with the magnitude of force applied. In cases where stronger anchorage reinforcement is required, precision cuts is the superior method.ConclusionsThe utilization of microimplants in conjunction with CAs can facilitate the effective contribution ratio of molar distalization. However, it is important to note that complete elimination of anchorage loss is not achievable. To mitigate undesired movement, careful planning of anchorage preparation and overcorrection is recommended.

The effects of abrasive moving speed and motion mode on the thinning mechanism of SiC in three-body contact

Three-body contact is the main contact type in polishing process and leads to a different thinning mechanism than the two-body contact. Molecular dynamics simulation is employed to investigate the thinning mechanism of 3C-SiC substrate in three-body contact. The thinning mechanisms of 3C-SiC under different moving speeds and motion modes of diamond abrasive are compared. Through the analysis of force, temperature, potential energy, stress distribution and atomic flow field, the causes of different thinning mechanisms are explained. It is found that the influence of moving speed is mainly reflected in the temperature rise of substrate when the motion mode of abrasives is the same. The changes of motion mode will significantly alter the stress distribution, which is closely related to the damage depth and atomic flow field. When the feed speed is the same, increasing the self-rotation speed of abrasives can reduce concentration zone of hydrostatic stress and then reduce the damage depth. The self-rotation of abrasives will also change the distribution of von Mises stress, resulting in the different displacement directions of 3C-SiC atoms. Dislocations are more easily generated when the displacement direction of SiC atoms is the same. The moving speed of abrasive is found to have little effect on the thinning mechanism, while the motion mode of abrasive will significantly change the thinning mechanism.

Unstable stress-triaxiality development and contrasting weakening in two types of high-strength transformation-induced plasticity(TRIP) steels: Insights from a new compact tensile testing method

The impact of high stress triaxiality on work hardening in transformation-induced plasticity (TRIP) steel has been widely acknowledged, particularly through measurements of the austenite fraction. Understanding this TRIP behavior is crucial for predicting material fracture in press-forming processes. However, the actual flow stresses under high-stress-triaxiality conditions remain largely undetermined. To address this gap, we developed a new tensile testing method using tiny notched round bars to investigate stress-triaxiality-induced work hardening in TRIP steels. The specimens were analyzed using two-dimensional micrometry to allow finite element analyses to identify the flow stress. Additionally, we conducted in situ tensile tests in which their crystal lattice stresses were monitored using synchrotron X-ray diffraction (XRD) to realize mechanism analyses of the unexpected work-hardening behavior identified by the developed tensile testing method. Our combined approach revealed a mutual, unstable increase in the flow stress and stress triaxiality in the TRIP-aided bainitic ferrite steel, which reduced the hardening exponent coefficients and thus induced a higher stress triaxiality. In contrast, the TRIP-aided martensitic steel exhibited a weakening behavior, characterized by a significant decrease in the hardening exponent coefficients in the case of the sharpest notch. XRD analyses showed that microstructural heterogeneity led to an extraordinarily high hydrostatic stress in the austenite phase, accounting for these contrasting behaviors. This finding challenges the established consensus on TRIP steels and suggests the need for a revised framework for their application in press-forming, taking into account stress-triaxiality conditions.

Optimization procedure for the Strut-and-Tie method considering the stiffness of concrete in compression

An optimization procedure is proposed for finding an optimal truss for the Strut-and-Tie method used to design the steel reinforcement in concrete structural elements. The basis of the procedure is to maximize the global stiffness of the element by optimizing the reinforcement layout but considering the stiffness of concrete in the compressed zones of the element. The hydrostatic stress is used to determine those zones, which changes along the maximization.Three examples from the literature are used to test the procedure, finding very good results in terms of higher ratios of ultimate load over the weight of steel, and also in terms of spreading more evenly the cracks in the damaged zones of the element.

Comparison of Isothermal and Adiabatic Elasticity Characteristics of the Single Crystal Nickel-Based Superalloy CMSX-4 in the Temperature Range Between Room Temperature and 1300°C

Based on the results of performed thermophysical measurements and available experimental data for adiabatic elastic stiffnesses, isothermal elastic characteristics of the single crystal nickel-based superalloy CMSX-4 have been calculated for a wide temperature range, from room temperature to 1300°C. According to the results obtained, the adiabatic and isothermal values of such elastic characteristics as elastic stiffnesses {{c}_{{11}}}, {{c}_{{12}}} and bulk modulus of elasticity B differ significantly at high temperatures. The reasons for this are significant changes in the thermophysical properties of the alloy with temperature and a temperature increase of its Poisson’s ratio approaching the limiting value for cubic crystals, equal to 0.5. It is shown that the use of adiabatic elastic constants instead of isothermal ones in engineering calculations affects the relationship between the volumetric strain and hydrostatic stress, and this effect is similar to introducing a field of thermal dilatation into the analyzed object. At low temperatures, this effect is small, but at high temperatures, typical for the service conditions of the blade material of aircraft gas turbine engines, it increases many times.

Calibration and efficient evaluation of electromigration lifetime for interconnect wire sizing of multi-port networks

A canonical form of the hydrostatic stress equations for electromigration is proposed to determine the minimum number of parameters to calibrate the model. An efficient probabilistic lifetime checker is developed to determine the wire sizing of interconnect segments. Large networks can be checked on a segment-by-segment basis. To enable efficient evaluation of lifetime, multivariate models are constructed by precomputing the results for all possible interconnect segment geometries, model parameters, and current densities.

Numerical Investigation of the Influence of Nonmetallic Inclusions on the Local Hydrogen Concentration under Consideration of Residual Stress Fields

Hydrogen as an energy carrier is politically supported and essential for the planned energy turnaround, but requires infrastructure for transport and storage of hydrogen on a large scale, which in turn requires the development of steels resistant to hydrogen‐induced damage. Since the experimental characterization of local hydrogen concentration is nearly impossible, but microstructure level effects are significant for damage initiation, it becomes essential to further develop accompanying numerical evaluation methods. These have to be able to quantitatively describe the effect of nonmetallic inclusions on the local hydrogen concentration as the detrimental effect of nonmetallic inclusions governs the resistance against hydrogen‐induced cracking. To capture this influence, the modeling approaches available in the literature are extended and made usable for tetrahedral elements. Validation is performed using numerical studies with specimens of different stress states. Submodels are exposed to a virtual cooling and then to a hydrogen loading. Based on the resulting residual stress fields, the local hydrogen concentrations around nonmetallic inclusions with different chemical compositions and geometry are investigated and evaluated. Herein, it can be shown that especially the hydrostatic stress has a large influence on the development of the local hydrogen concentration and that the influence is particularly strong for Al2O3‐inclusions.

Structural and optical properties of micro-diamonds with SiV− color centers

Isolated, micro-metre sized diamonds are grown by micro-wave plasma chemical vapour deposition technique on Si(001) substrates. Each diamond is uniquely identified by markers milled in the Si substrate by Ga+ focused ion beam. The morphology and micro-grain structure analysis, indicates that the diamonds are icosahedral or bi-crystals. Icosahedral diamonds have higher (up to = 2.3 GPa), and wider distribution ( = 4.47 GPa) of hydrostatic stress built up at the micro-crystal grain boundaries, compared to the other crystals. The number and spectral shape of SiV− colour centres incorporated in the micro-diamonds (MDs) is analysed, and estimated by means of temperature dependent photoluminescence measurements, and Monte Carlo simulations. The Monte Carlo simulations indicates that the number of SiV− colour centres is a few thousand per MD.

Numerical Study of the Hydride Embrittlement in Zirconium Alloy using XFEM

A numerical model for hydride embrittlement in Zirconium alloy (Zr–2.5Nb) is developed utilizing the extended finite element method (XFEM). Hydride embrittlement reduces the ductility and failure time of a metal/alloy. During hydride embrittlement, stress-directed hydrogen diffusion, metal-hydride phase transformation, mechanical deformation, and hydride precipitation occur simultaneously. The present model incorporates all these processes and is able to predict the hydrogen concentration and the hydride fraction distribution under any externally applied stress field. In this work, both the steady and transient hydrogen diffusion cases are evaluated. Further, the XFEM is utilized to develop a model of hydride embrittlement in the presence of a crack. The first step of the hydride embrittlement process is the diffusion of hydrogen. According to Fick’s law of diffusion, hydrogen diffusion is directly dependent on hydrostatic stresses and hydrogen concentration gradient under external stresses. The next step is the hydride precipitation in hydride embrittlement, where the expansion of material takes place that changes the hydrostatic stress field. Thus, studying the effect of precipitation of hydride on hydrostatic stresses is essential. Moreover, the process of hydride embrittlement is highly influenced by residual stresses in the structure. Hence, the effect of residual stress present in the zirconium alloy pressure tube (PT) is also evaluated. The results indicate that the residual tensile stresses contribute to the growth of hydride, which will reduce the material failure time.

The microstructural evolution of sputtered ZnO epitaxial films to stress-relaxed nanorods

Epitaxial ZnO thin films and nanorods were grown on c-sapphire substrate by reactive sputtering of Zn in Ar-O2 atmosphere at substrate temperatures ranging from near room temperature to 700 °C. Scanning electron microscopy showed that with increase in substrate temperature, the morphology transformed from columnar films to vertically aligned ZnO nanorods. High resolution x-ray diffraction revealed improvement in crystalline and epitaxial quality with increase in substrate temperature, along with the decrease of edge dislocation density from 5 × 1012 cm−2 to 8 × 1010 cm−2. The films grown near room temperature showed large hydrostatic strain (∼6 × 10−3) and compressive intrinsic biaxial stress (-0.8 GPa), which decreased substantially with increase in substrate temperature, due to the desorption of excess oxygen and reduction in edge dislocation density. Above the substrate temperature of 500 °C, the intrinsic biaxial stress reversed from compressive to mildly tensile in the case of nanorods, due to the intrinsic tensile stress, originating from crystallite coalescence. Raman measurements correlate well with the changes in biaxial stress and confirm the improvements in crystallinity and epitaxial quality of nanorods grown at higher temperatures. Room temperature photoluminescence of the ZnO films showed weak near-band-edge emission, which enhanced drastically in the case of nanorods due to their superior microstructure and epitaxial quality.

Effects of Confining Stress on Blast-Induced Damage Distribution of Rock with Discontinuity

Discontinuous rock mass, such as joints and fractures, have a great influence on the blasting quality and sometimes induce additional damage at the discontinuity. In deep rock engineering, high in situ stress makes the damage mechanism of rock with discontinuity under blasting loading more complicated. Quantitative analysis of blast-induced damage in discontinuous rock under high in situ stress is of great importance in guiding the fine blast design. In this paper, a series of numerical models have been established to quantitatively investigate the effect of confining stress and inclination angle on blast-induced damage of rock with discontinuity. The numerical results show that the discontinuity obviously changes the distribution mode of blast-induced damage, and there is more damage near the discontinuity. The blast-induced damage crack length of discontinuous rock decreases as hydrostatic stress rises. Under non-hydrostatic stress, the damage crack propagation appears to have a higher tendency in the higher confining stress direction. In addition, the inclination angle of discontinuity will affect the damage distribution of rock with discontinuity. The fragmentation degree is greatest when the discontinuity is perpendicular to the direction of higher confining stress. Due to the presence of discontinuity, the guiding effect of higher confining stress on damaged cracks is weakened. The results provide a reference for the tunnel fine-blasting design of rock with discontinuity.

A Mechanical Approach to the Growth Plate Behaviour and Chondrocytes Columns Organization

This study aims to explore the behaviour of mechanical stimuli and their effect on growth plate shape under different physiological scenarios and loading conditions. A linear elastic, isotropic, and homogeneous model was implemented to model the epiphyseal progressive ossification and the development of the secondary ossification centre. Results shed light on the role of mechanical stimulus, suggesting that maximum shear stress, hydrostatic stress, and von Mises Stress may contribute to the morphological changes of the growth plate. This model is a useful tool to improve orthopaedic therapies focused on pathologies that imply abnormal bone growth under abnormal mechanical conditions.

Actual contribution ratio of maxillary and mandibular molars for total molar relationship correction during maxillary molar sequential distalization using clear aligners with Class II elastics: A finite element analysis

Class II elastics, in combination with clear aligners (CA), are efficient for molar distalization. However, the effects of this combination on intermaxillary molar relationship correction have yet to be investigated. This study aimed to investigate the actual contribution ratio of the maxillary and mandibular molars for total molar relationship correction during maxillary molar distalization using Class II elastics with CA and further explore therapeutic recommendations for clinical practice. Finite element models (FEMs) were established, including the distalization of the second molars (Set I), followed by the distalization of the first molars (Set II). Model A simulated elastics attached by precision cutting, whereas Model B simulated elastics attached to buttons. Force magnitudes of 100 g, 150 g, and 200 g of force were applied. We recorded the contribution ratio of the maxillary and mandibular molars for total molar relationship correction, effective distalizing distance in 0.25 mm step distance, tipping and rotation angles, and the hydrostatic stress in the periodontal ligament. During maxillary molar distalization, mesialization of the mandibular molar had a notable contribution ratio for molar relationship correction. The mandibular first molar was mesialized with mesiolingual rotation tendency. Approximately half of the 0.25 mm step distance was occupied by maxillary molar distalization; the remainder was occupied by anchorage teeth mesialization and tipping or rotation. When traction forces increased, the total molar relationship correction and effective distalization increased; the mandibular molars mesialization contribution ratio also increased, as did rotation and inclination tendency. Precision cutting had a higher total molar relationship correction and more effective distalization than a button but also had a larger contribution ratio of mandibular molar mesialization and inclination or rotation. Mandibular molar mesialization should be considered when correcting the molar relationship using CA with intermaxillary elastics during maxillary molar distalization. It is also important to consider the anchorage teeth mesialization and undesired tipping or rotation.

A hydrogen diffusion model considering grain boundary characters based on crystal plasticity framework

The influence of grain boundaries (GBs) on hydrogen transportation is a crucial factor in understanding the mechanisms of hydrogen embrittlement (HE) in polycrystalline alloys. Crystal plasticity models have the advantages in simulating the effect of grain microstructure on hydrogen diffusion in polycrystals, but they have not yet been coupled with hydrogen diffusion models that can take into account GB characters. In this study, a hydrogen diffusion model that considers the effect of GBs on the transportation of hydrogen was developed to study the local hydrogen diffusion behavior in bi-crystalline and polycrystalline alloys. The simulation results showed the capability of the model in describing the influence of hydrogen on the material deformation. In addition, this study found that the hydrostatic stress determined the hydrogen concentration in the far-GB region, whereas the GB energy played a control role in and near the GB regions. Notably, hydrogen exhibits a preference for localization near high-angle grain boundaries (HAGBs) and triple junctions. In alloys with medium grain size, hydrogen typically had low average concentration with a more uniform distribution. Furthermore, the hydrogen-assisted crack growth mechanism was analyzed as the continuous coalescence of primary and secondary cracks along GBs. This work presents a hydrogen diffusion model that considers GB effects, and the proposed model has advantages in predicting the deformation and fracture of polycrystalline alloys in hydrogen environments.