Critical Stress Distribution Research Articles

A Multisubstructure-Based Method for the Assessment of Displacement and Stress in a Fluid–Structure Interaction Framework

A multisubstructure-based method for assessing the deformation and stress of a fine-meshed model according to a coarse model was proposed. Integrating boundary conditions in a local fine-meshed model, a displacement mapping matrix from the coarse model to the fine-meshed model was constructed. The method was verified by a three-level panel in a fluid–structure interaction (FSI) framework by integrating the steady vortex lattice method (VLM). A comparison between the inner deformation distribution of the coarse model and that of the global fine-meshed model obtained from MSC.Nastran was carried out, and the results showed that the coarse model failed to demonstrate reliable strains and stresses. In contrast, the proposed method in this paper can effectively depict the inner deformation and critical stress distribution. The deformation error was lower than 8%, meeting engineering requirements. Moreover, the results of different working conditions can achieve a similar relative error of displacement for an identical position. The easy storage of the displacement mapping matrix and the convenience of the boundary information transformation among all substructure levels are prominent aspects. As a result, there is a solid foundation for addressing the time-dependent problem in spite of the simultaneity and region.

Large-volume and swift magmatic response to Late Cenozoic segmentation of the subducted Neotethyan oceanic slab: evidence from the Galatian Volcanic Province, northwestern Turkey

ABSTRACT The Miocene Galatian Volcanic Province (GVP) is one of the largest volcanic provinces in central-western Anatolia, with an extent of ~ 8,900 km2. The volcanic activity is extended from 22.5 to 7.5 Ma. The volcanic compositions straddle the alkaline-subalkaline fields, from basic to acid compositions and mostly transitional to sodic affinity. Major oxides show good correlation with SiO2 indicating prolonged effects of fractional crystallization. Primitive mantle-normalized multi-element patterns indicate overall similarities among the different samples of the three geographic sectors, sharing strong negative anomalies in Nb–Ta–Ti, strong positive peaks at Cs and K, coupled with a common, albeit not always present, positive anomaly at Pb. Mineral-melt geothermobarometric estimates indicates ~1070–1235°C and ~7–19 kbar for melting conditions of basaltic compositions and ~1000–1150°C and ~3–12 kbar for andesitic-dacitic rocks. The absence of correlation between radiogenic isotopes and SiO2 and MgO is here interpreted as consequence of assimilation-fractional-crystalization processes involving lower continental crust as contaminant. The GVP parental magmas are generated from ~2% to 10% partial melting of a lherzolitic mantle with high spinel/garnet ratio based on intra-REE fractionation constraints. The subduction-related metasomatism inferred for the GVP mantle sources based on their chemistry is interpreted to be linked to the northward subduction of the northern branch of the Neo-Tethys slab. Successive slab retreat resulted in extension for the critical stress distribution through the Cyprus slab, favouring magma propagation for the GVP volcanic region. The eventual break-off of the slab after the continent-continent collision of Arabian and Eurasian plates could have caused a toroidal mantle flow, favouring the widely distributed 15–16 Ma alkaline magmatism in the eastern GVP, associated with passive hot asthenospheric upwelling imaged by teleseismic P-wave tomography.

Phase-field models of floe fracture in sea ice

Abstract. We develop a phase-field model of brittle fracture to model fracture in sea ice floes. Phase fields allow for a variational formulation of fracture by using an energy functional that combines a linear elastic energy with a term modeling the energetic cost of fracture. We study the fracture strength of ice floes with stochastic thickness variations under boundary forcings or displacements. Our approach models refrozen cracks or other linear ice impurities with stochastic models for thickness profiles. We find that the orientation of thickness variations is an important factor for the strength of ice floes, and we study the distribution of critical stresses leading to fracture. Potential applications to discrete element method (DEM) simulations and field data from the ICEX 2018 campaign are discussed.

Extended finite element simulation on Tensile, fracture toughness and fatigue crack growth behaviour of additively manufactured Ti6Al4V alloy

The mechanical properties such as tensile, fracture toughness, and fatigue properties of Additive Manufacturing (AM) fabricated Ti6Al4V alloy is critically crucial for structural applications. The in-house developed MATLAB-based extended finite elements method (XFEM) model has been utilized to analyse experimental results of fatigue, fracture, and tensile properties of AM fabricated Ti6Al4V alloy, to avoid expensive and destructive mechanical characterisation. The XFEM model was first used to validate the single edge cracked sample of laser powder bed fusion (LPBF) processed Ti6Al4V alloy for fatigue crack growth rate (FCGR). The XFEM simulation study was further extended to analyse fatigue life of center and double-side cracked specimens, as well as for evaluating fracture toughness KIC upon accounting potential crack initiation site. The model has also been developed to predict FCGR of edge cracked specimen under mixed-mode loading conditions. The critical stress intensity factor (SIF) and stress distribution map in the crack vicinity of the C(T) specimen were modelled through FEA Abaqus package to estimate the fracture toughness of Ti alloy. A similar XFEM approach was used to analyse the tensile properties of Ti alloy to predict its fracture behaviour through the center cracked specimen taken at the tensile gauge section. The strengthening mechanisms contributing to Ti alloy's static and dynamic properties are elucidated through microstructural characteristics of LPBF processed Ti6Al4V alloy reported in the literature.

The lateral femoral wall thickness on the risk of post-operative lateral wall fracture in intertrochanteric fracture after DHS fixation: A finite element analysis

BackgroundPatients with a lateral femoral wall (LFW) fracture were reported to have high rates of re-operation and complication. Although the LFW thickness was a reliable predictor of post-operative or intra-operative LFW fracture, there was a paucity of literature evaluating the critical stress distributions on the femur and screws of intertrochanteric fractures treated with dynamic hip screw (DHS). This study aimed to investigate the biomechanical performance of intertrochanteric fractures with different LFW thickness treated with DHS device. MethodsA three-dimensional model of the proximal femur was established by computed tomography images. The intertrochanteric fracture model with three different LFW thickness (10 mm, 20.5 mm and 30 mm, respectively) was created, which was fixed by DHS. The von Mises stress on the proximal femur, lateral femoral wall, DHS and the total displacement of the device components were evaluated and compared for three different LFW thickness model. ResultsThe maximum von Mises stress in the proximal fragment of the 10 and 20.5 mm model increased by 80.56% and 57.97% when compared with the 30 mm model. The peek von Mises stress around the blade entry point of the 10 mm and 20.5 mm model increased by 89.26% and 66.39% when compared with the 30 mm model. The peek von Mises in the DHS located near the junction of the barrel and side plate of each model and the 30 mm model had the smallest von Mises stress compared with the other two models. Furthermore, the maximum displacement in the 30 mm model was much smaller than that in the10mm model and 20 mm model. ConclusionsThe intertrochanteric fracture with a thinner LFW tended to have a higher risk of LFW fracture stabilized by a DHS device. Thus, the intertrochanteric fractures with a thinner LFW should not be treated by DHS alone and the intramedullary nail or an addition of trochanteric stabilization plate(TSP) was recommended.

Structural responses of energy storage pile foundations under thermal-mechanical loadings

Recently studies have investigated feasibilities to configure pile foundations as energy storage media using a small-scale compressed air energy storage technology. These studies consider that storage temperatures of compressed air can be lowered entirely down to ambient temperatures through a cooling process. This assumption may not be feasible and economical due to the efficiency of the cooling process. As an alternative option, a higher storage temperature can be allowed by reducing the cooling time, which can cause additional thermal-mechanical loadings to the pile foundation. This paper investigates structural responses of reinforced concrete pile foundations subjected to combined structural, compressed air pressure, and thermal-mechanical loadings through nonlinear dynamic heat transfer and thermal-mechanical analyses. Several parameters were studied, including pile spacing, pile inner diameters, and concrete grades. Analysis results show that thermal-mechanical loading can reduce critical tensile stresses and change stress distributions in the pile section originated from compressed air pressure. Design recommendations were made to determine an optimal storage temperature and an allowable loading cycle for the energy storage pile foundation.

A Semianalytical Solution for a Griffith Crack Nonuniformly Pressurized By Internal Fluid

Unintentional variations of fluid pressure within a hydraulic fracture will disturb the surrounding stress state, affect the stability of fracture propagation and complicate the fracture intersections during the process of hydraulic fracturing. However, little attention has been paid to the effect of nonuniform fluid pressure inside the hydraulic fracture. This paper presents a semianalytical solution for a Griffith crack nonuniformly pressurized by internal fluid in an impermeable elastic plane. The fluid pressure is hypothetically designated as a general polynomial with respect to the location of the fluid, such that the effect of an arbitrary form of fluid pressure distribution can be explored by polynomial fitting. The semianalytical solution is capable of being degenerated into constant pressure forms which confirms that the solution is an extension of classic constant pressure. In addition, the critical propagation conditions and stress distributions (e.g., σxx) under constant and nonuniform pressures are compared and discussed. The comparison results indicate that the effect of nonuniform fluid pressure accumulated by the number of polynomial terms increases the magnitude of stress (or displacement) but does not change its distribution. Subsequently, the semianalytical solution is validated by comparing the fracture intersection predicted by the semianalytical solution with the laboratory experimental observations and published predictions under constant fluid pressure. Good agreement with the experiments and sufficient advantages over previous predictions are observed. Finally, a sensitivity analysis of existing parameters in the semianalytical solution, including crack length, initial pressure, number of terms and number of subintervals, is conducted to evaluate their influence on surrounding stresses and critical propagation conditions, which further demonstrates the applicability and reliability of the presented semianalytical solution. The new solution enriches hydraulic fracturing theory by considering the nonuniform fluid pressure effect and provides important reference for fracture network design during hydraulic fracturing.

Study on identification of critical Weibull stress distribution by using miniature specimen

Study on identification of critical Weibull stress distribution by using miniature specimen

Finite element study of effect of parameters on stress distribution of steel shim in elastomeric bearings

Elastomeric bearings are widely used in various structures as a type of seismic isolation device, and accurately assessing the state of their stress is an essential step in the design of elastomeric bearings. This article aims to better understand the influencing factors of stress distribution on the steel shims and the effect of steel shim thickness on the critical behaviour of elastomeric bearings. First, theoretical analysis is conducted for investigating the influencing factors of the bearing’s critical load capacity and stress distribution on the steel shim thickness. Then, a series of finite element models is employed to study the influence of steel shim thickness on the global performance of bearings, the stress distribution on steel shims at different locations and the effect of steel shim thickness on stress distribution. Combining the results of theoretical analysis and finite element analysis, we conclude that steel shim thickness has little obvious effect on the mechanical properties of the bearing under normal working conditions, but it has a significant influence on the distribution and change of the local stress. Especially, when the vertical load and the horizontal displacement of the bearing increases, the growth rate of stress on the upper steel shims is very fast and may enter the yield state first or even resulting in local damage.

Influence of the Homogenization Pressure on the Rheology of Biopolymer-Stabilized Emulsions Formulated with Thyme Oil

Different continuous phases formulated with ecofriendly ingredients such as AMIDET® N, an ecological surfactant, as well as welan and rhamsan gums were developed. An experimental design strategy was been in order to study the influence of the ratio of these two polysaccharides and the homogenization pressure applied in a microfluidizer on the critical shear stress for the continuous phases developed. A pure rhamsan gum solution was selected as the starting point for further study based on the production of thyme oil-in-water emulsions. The effect of the homogenization pressure on the physical stability, critical shear stress and droplet size distribution was analyzed for emulsions with optimized values of the rhamsan–welan ratio. These bioactive thyme oil-in-water emulgels could be considered as delivery systems with potential applications in the food industry.

Deformation behavior of saddle surface part during multi-point forming under normally full constraint condition

In order to solve the problem of wrinkling in traditional multi-point forming (MPF), a new multi-point forming process, namely multi-point forming with individually controlled force-displacement (MPF-ICFD), was proposed. The core idea of this process is to impose a full-area normal constraint on the sheet metal during the whole forming process. Therefore, the deformation sequence of the sheet metal is changed from the local constraint and the whole deformation in the traditional MPF to the whole constraint and the local deformation so as to completely eliminate the noncontact region and avoid wrinkling. In this paper, the saddle surface part was taken as the research object. The influence of normal restraint on critical wrinkle stress is studied by mechanical analysis, and the wrinkle restraint mechanism under normal restraint is revealed. The deformation behavior of saddle surface parts was studied by forming experiments, and the wrinkling law of saddle surface parts under different constraints is obtained. The deformation characteristics of saddle surface parts were analyzed by numerical simulation, and the critical stress distribution rules of the sheet metal were given. It is shown that the critical wrinkling stress of the sheet metal is significantly increased in MPF-ICFD compared with that in traditional MPF, and the increased value is proportional to the magnitude of normal constrained force. Besides, the wrinkling phenomenon of saddle surface parts is significantly suppressed, and the surface quality of workpiece is obviously improved. In addition, the stress state change from compressive stress to tensile stress in the core region of the sheet metal was prone to wrinkle.

Effective and internal stresses in 713LC and Rene 41 superalloys using analysis of the hysteresis loop shape

Strain controlled cyclic straining with constant strain amplitude and a single strain rate has been applied to cylindrical specimens of 713LC and Rene 41 superalloys and hysteresis loops were digitally recorded. The shape of hysteresis loops was analyzed using the statistical theory of the hysteresis loop. First and second derivatives of half-loops were calculated. From these data effective elastic modulus, effective stress component and probability density distribution of internal critical stresses were evaluated. The stress-strain response and its evolution have been discussed in relation to the internal structure and its development during cyclic plastic straining.

Design and Simulation Analysis of Lightweight HDPE Milk Bottle

A lightweight design is proposed for a 2800 ml HDPE milk bottle. In designing the bottle, a three-dimensional elastic-plastic dynamic finite element model is first constructed to explore the effect of the bottle thickness on the critical load and stress distribution. The validity of the proposed model is confirmed by comparing the numerical results for the load-displacement response of the bottle with the experimental results. A parametric analysis is then performed to examine the effects of the body thickness and bottom thickness on the critical load and weight of the HDPE bottle. The results show that the critical load increases with an increasing body thickness, but is insensitive to the bottom thickness. Finally, a lightweight design is proposed in which the structural shape of the original bottle is retained, but the thickness is varied in different regions of the body in order to reduce the weight. It is shown that the redesigned bottle achieves the same maximum top-load 315 N, but reduces the weight by 21.4% compared to the reference design obtained in the parametric analysis.

The stress statistics of the first pop-in or discrete plastic event in crystal plasticity

The stress at which the first discrete plastic event occurs is investigated using extreme value statistics. It is found that the average of this critical stress is inversely related to the deforming volume, via an exponentially truncated power-law. This is demonstrated for the first pop–in event observed in experimental nano-indentation data as a function of the indenter volume, and for the first discrete plastic event seen in a dislocation dynamics simulation. When the underlying master distribution of critical stresses is assumed to be a power-law, it becomes possible to extract the density of discrete plastic events available to the crystal, and to understand the exponential truncation as a break-down of the asymptotic Weibull limit.

An innovative tooth root profile for spur gears and its effect on service life

An innovative approach to the design of the gear-tooth root-profile, and its effects on the service life is reported in this paper. In comparison with the widely used trochoidal and the recently proposed circular-filleted root profiles, the optimum profile proposed here is a $$G^2$$ -continuous curve that blends smoothly with both the involute of the tooth profile and the dedendum circle. Following the AGMA and ISO standards for fatigue loading, the von Mises stress at the critical section and stress distribution along the gear tooth root are studied. The process leading to gear-tooth failure is composed of the crack initiation phase, in number of cycles $$N_i$$ , and the crack propagation phase, in $$N_p$$ cycles. The strain-life ( $$\epsilon$$ -N) method is employed to determine $$N_i$$ , where the crack is assumed to initiate at the critical section. Based on the ANSYS crack-analysis module, the effects of $$G^2$$ -continuous blending on the stress intensity factor (SIF) are investigated for different crack sizes. Paris’ law, within the framework of Linear Elastic Fracture Mechanics, is used to correlate the SIF with crack size and, further, to determine $$N_p$$ . The optimum profile provides a significant reduction in SIF and improvement in both $$N_i$$ and $$N_p$$ . Spur gears are made of high-strength steel alloy 42CrMo4, the effects of its properties and surface treatment on service life improvement not being included in this study.

A Nano-Cantilever Method for Crack Initiation at the Free Edge of the Cu/Si Interface in Nanoscale Components

Straight and Bent nano-cantilever specimens are respectively proposed to investigate the single-mode and mixed-mode crack initiation at the Cu/Si interface edge in nanoscale components. With a minute loading apparatus, all nanoscale samples are in situ loaded and observed. Numerical analysis is employed to acquire the critical interfacial stress distributions during crack initiation. The stress concentration regions near the edge of Cu/Si interface in all specimens are within the scale of 100 nm, and the critical normal and shear stresses have a circular relation in nanoscale components, which represents the fracture criterion of the interface in nanoscale components.

Brittle fracture assessment of embedded flaw in heat-affected zone based on Weibull stress criterion

This paper presents a method for estimating the condition for the brittle fracture limit of a welded joint with an embedded flaw in the heat-affected zone (HAZ) based on the Weibull stress criterion. A welded joint with an embedded flaw generated by cold cracking was subjected to a wide plate (WP) tension test, and a welded joint with a fatigue crack was subjected to three-point bending (3PB) tests; both tests were conducted at −30 °C. Brittle fractures occurred in all specimens, and the microstructure of the fracture initiation point for the WP specimen in the coarse-grained HAZ (CGHAZ) was upper bainite with M-A constituents. The critical Weibull stress distribution of the CGHAZ was calculated by finite element analyses for the 3PB specimens. The predicted fracture load and global displacement of the WP specimen at the brittle fracture obtained by the critical Weibull stress distribution were in agreement with experimental results from the WP tensile test. This confirmed that the brittle fracture limit of a welded joint with an embedded flaw could be predicted from the Weibull stress criterion.

Interfacial fracture strength property of micro-scale SiN/Cu components

The strength against fracture nucleation from an interface free-edge of silicon-nitride (SiN)/copper (Cu) micro-components is evaluated. A special technique that combines a nano-indenter specimen holder and an environmental transmission electron microscope (E-TEM) is employed. The critical load at the onset of fracture nucleation from a wedge-shaped free-edge (opening angle: 90°) is measured both in a vacuum and in a hydrogen (H2) environment, and the critical stress distribution is evaluated by the finite element method (FEM). It is found that the fracture nucleation is dominated by the near-edge elastic singular stress field that extends about a few tens of nanometers from the edge. The fracture nucleation strength expressed in terms of the stress intensity factor (K) is found to be eminently reduced in a H2 environment.

Interfacial Fracture Strength of Micro-Scale Si/Cu Components with Different Free-Edge Shape

The strength against interfacial fracture initiation from a free-edge of Si/Cu micro-components was evaluated. The micro-scale cantilever specimens containing dissimilar interfaces were fabricated with a focused-ion-beam (FIB) technique, and they were loaded with a quantitative nanoindenter holder operated in a transmission electron microscope (TEM). The specimens were successfully fractured along the Si/Cu interface, and the critical loads at fracture were measured. The critical stress distribution near the free-edge was evaluated with the finite element method (FEM). The near-edge stress distributions of 90°/90°-shaped specimens were scattered while those of 135°/135°-shaped specimens were in good agreement despite the difference in specimen dimensions. Such a difference was discussed in terms of the relation between the magnitude of stress singularity and the microstructures of material.

Universal power-law strengthening in metals?

The strength of most metals scales with either an internal or external length scale. Motivated by the wide applicability of this phenomenon to material type and microstructure, we develop a model which gives quantitative insight into the scaling exponent using the known universal properties of a dislocation network and the leading order stress dependence of an underlying critical stress distribution. The approach is found to be equally valid for both Hall–Petch strengthening and the smaller-is-stronger paradigm of small scale plasticity.