Von Mises Equivalent Stress Research Articles

Cellular Automata in Topology Optimization of Continuum Structures

In this paper, an optimization algorithm based on cellular automata (CA) is developed for topology optimization of continuum structures with shear and flexural behavior. The design domain is divided into small triangle elements and each cell is considered as a finite element. The stress analysis is performed by the Constant Strain Triangles (CST) finite elements method. The thicknesses of the individual cells are taken as the design variables, while the weight of the structure and the ratio of the Von Mises equivalent stress to the yield stress in each cell are considered as the two objective functions to minimize. Using the weighted sum method, the multi-objective optimization problem (MOOP) is converted to the single-objective optimization problem (SOOP) and then the optimization problem is solved by the developed method. The paper reports the results of several design experiments, comparing with the existing reported results.

Experimental Analysis of the Influence of Hydrostatic Stress on the Behaviour of an Adhesive Using a Pressure Vessel

The modelling of the non-linear behaviour of ductile adhesives requires a large experimental database in order to represent accurately the strains which are strongly dependent on the tensile-shear loading combination. Various pressure-dependent constitutive models can be found in the literature, but only a few experimental results are available, for instance, to represent accurately the initial yield surface taking into account the two stress invariants, hydrostatic stress, and von Mises equivalent stress. This paper presents the possibility of combining the use of tests on bulk specimens and tests on bonded assemblies, which strongly limit the influence of the edge effects, with a pressure vessel especially designed to study the influence of hydrostatic stress. The latter allows pressures up to 100 MPa to be applied during mechanical testing. For a given strain rate of the adhesive, experimental results using various stress paths are presented in order to analyse the influence of the hydrostatic stress on the mechanical behaviour of an adhesive. The analysis of the results focuses herein on the modelling of the initial yield surface, but such results are also useful for the development of the flow rules in the case of 3D pressure-dependent models.

Geometrical optimization of notches under multi-axial fatigue loading

Geometrical optimization of notched parts under multi-axial fatigue loadings is the object of the present paper. By considering that usual structural optimization criteria based on the Von-Mises equivalent stress are strictly applicable to static loading, and that their application to fatigue loading is questionable, particularly when the applied loads are out-of-phase, an approach based on Computer Aided Optimization proposed by Mattheck in the ‘90s of the last century is proposed. The original CAO method is modified by introducing the Liu–Zenner fatigue criterion. A numerical routine is developed that, by means of an interface to ABAQUS FE code, is able to lead to an optimized geometry of notched details under general multi-axial loading. Obtained results demonstrate the dependency of optimized geometry on relative phase of the applied loads.

The Biomechanics of Erections: Two- Versus One-Compartment Pressurized Vessel Modeling of the Penis

Previous biomechanical models of the penis simulated penile erections utilizing 2D geometry, simplified 3D geometry or made inaccurate assumptions altogether. These models designed the shaft of the penis as a one-compartment pressurized vessel fixed at one end when in reality it is a two-compartment pressurized vessel in which the compartments diverge as they enter the body and are fixed at two separate anatomic sites. This study utilizes the more anatomically correct two-compartment penile model to investigate erectile function. Simplified 2D and 3D models of the erect penis were developed using the finite element method with varying anatomical considerations for analyzing structural stresses, axial buckling, and lateral deformation. This study then validated the results by building and testing corresponding physical models. Finally, a more complex and anatomically accurate model of the penis was designed and analyzed. When subject to a lateral force of 0.5 N, the peak equivalent von Mises (EVM) stress in the two-compartment model increased by about 31.62%, while in the one-compartment model, the peak EVM stress increased by as high as 70.11%. The peak EVM stress was 149 kPa in the more complex and anatomically accurate penile model. When the perforated septum was removed, the peak EVM stress increased to 455 kPa. This study verified that there is significant difference between modeling the penis as a two- versus a one-compartment pressurized vessel. When subjected to external forces, a significant advantage was exhibited by two corporal based cavernosal bodies separated by a perforated septum as opposed to one corporal body. This is due to better structural integrity of the tunica albuginea when subjected to external forces.

Influence of Different Sliding Velocity on the Thermo-Mechanical Coupling of the Rough Surface Contact

Sliding velocity has a direct impact on friction heat and contact situation. Frictional heating and associated temperature seriously affects the material chemical and physical - mechanical properties, and is one of the direct factors on the wear mechanism. To analyze the influence of the sliding speed on the maximum contact temperature, contact pressure, stress, etc, a 3D thermo-mechanical coupling model for the rough surface frictional sliding is established. The rough surface is characterized based on fractal theory. The model considers friction contact between an elastic flat plane and an elasto-plastic rough surface. Also, the model integrates the heat flux coupling between the sliding surfaces and allows the analysis of the effects of elastic-plastic deformation of rough body and the interplay among asperities. The numerical results from the analysis and simulation show that the maximum contact temperature increases with the increasing of the sliding velocity. But the maximum VonMises equivalent stress and the maximum contact pressure have few relationships with sliding speed. They may increase or reduce with the sliding velocity increasing. Some results are validated by research’s results available in the literature.

Influences of inner pressure and tube thickness on process responses of hydroforming copper tubes without axial force

Tube hydroforming is a metal forming technique which has attracted the attention of several industries because of its ability to produce complex parts with high strength and low weight in low expense and time. In this process, a piece of tube attains the shape of the die under the pressure of inner fluid and exerted axial force. This process is able to produce a unified part in a single-step process. In order to achieve these advantages and an appropriate process, it is necessary to select convenient process and part parameters. Therefore, the present research focused on the effects of two important tube hydroforming process parameters, inner pressure and tube thickness, on process responses during the hydroforming of copper tubes without axial force. In the analytical investigation, the relationships for calculating pressures in three steps of tube hydroforming, i.e. yield pressure, ultimate plastic pressure, and calibration pressure, were developed. By using the derived pressures from these relationships, finite element investigations using a dynamic explicit code and experimental tests using tube hydroforming experimental facilities were performed. These investigations were accomplished on seamless copper tubes of four different thicknesses (0.5, 0.63, 0.9, and 1,mm) under different pressures. The results of these investigations showed that by increasing inner pressure, the thickness strain, bulging height, and von Mises equivalent plastic stress increase along with the length of the part. Also, higher tube thickness results in both higher required forming pressures in all forming steps and more capacity of enduring thickness strain and equivalent plastic stress. The results of these three different investigations showed good agreement with each other.

Stresses around a miniscrew. 3-D analysis with the finite element method (FEM)

Abstract Background Miniscrews used for absolute anchorage may induce stresses in the surrounding tissues that are dependent on their proximity to the miniscrew. Aims To determine the stresses in the buccal walls of the sockets of lower molars adjacent to a miniscrew under load when the position and angulation of the miniscrew are changed. Methods Five 3-D FEM models containing the first and second lower molars, their periodontal ligaments and the surrounding spongy and cortical bone, were modelled in SolidWorks 2006 (SolidWorks, Concord, MA, USA) and transferred to the ANSYS Workbench (ANSYS Inc., Southpointe, Canonsburg, PA, USA). A tensile force of 2 N, decomposed in 3-D space, was applied to a miniscrew inserted between the lower first and second molars. The von Mises (equivalent) stresses along the buccal walls of the sockets of the first and second molars were derived following changes in miniscrew position and angulation. No direct force was applied to the molars. Results When the miniscrew was inserted at right angles to the bone and midway between the molars the stress in the crestal area was 0.093 MPa. This stress increased proportionally in the first molar socket as the miniscrew was moved towards the first molar and declined when the miniscrew was tipped towards the second molar. Stresses also decreased in the crestal area of the second molar as the miniscrew was moved towards the first molar, but increased when it was tipped towards the second molar. A 30–55 per cent increase in crestal stress in the first molar socket was detected. Conclusion Stress occurred in the tissues surrounding a miniscrew subjected to a force vector. Changes in the position or angulation of a miniscrew can affect the stress in the socket walls of adjacent teeth.

The Effect of Stress Amplitude on Multi-Axial High-Cycle Fatigue Failure under Constant Amplitude Loading

Studies about the effect of stress characteristics on multi-axial high-cycle fatigue of metals are still insufficient. Up to now, little work about the effect of different ratio of stress amplitude has been done on multi-axial fatigue under the same equivalent stress. In this paper, the effect of ratio of stress amplitude, under the same Von-Mises equivalent stress is studied from theory and experiment. The results show that the main factor of multi-axial high-cycle fatigue failure is the maximum principal stress. For proportional loading, fatigue life raises when ratio of stress amplitude increase. The variety of fatigue life is not obvious when is larger than a certain value and its value closes to that of pure torsion. For non-proportional loading, when ratio of stress amplitude increases, fatigue life raise at first, then has an inflection point. The value of at the inflection point changes with phase difference and its value is 0.5 while phase angle is 90º. Fatigue life of uniaxial tension was lower than that of pure torsion.

Elastic–plastic contact analysis of an ellipsoid and a rigid flat

The work presents a finite element model (FEM) of the equivalent von-Mises stress and displacements that are formed for the different ellipticity contact of an ellipsoid with a rigid flat. The material is modeled as elastic perfectly plastic and follows the von-Mises yield criterion. The smaller the ellipticity of the ellipsoid is, the larger the depth of the first yield point from the ellipsoid tip happens. The FEM produces contours for the normalized normal and radial displacement as functions of the different interference depths. The evolution of plastic region in the asperity tip for a sphere (ke=1) and an ellipsoid with different ellipticities (ke=12and15) is shown with increasing interferences. It is interesting to note the behavior of the evolution of the plastic region in the ellipsoid tip for different ellipticities, ke, is different. The developments of the plastic region on the contact surface are shown in more details in Fig. 7. When the dimensionless contact pressure is up to 2.5, the uniform contact pressure distribution is almost prevailing in the entire contact area. It can be observed clearly that the normalized contact pressure ascends slowly from the center to the edge of the contact area for a sphere (ke=1), almost has uniform distribution prevailing the entire contact area for an ellipsoid (ke=12), and descends slowly from the center to the edge of the contact area for an ellipsoid (ke=15).

A FEM Study on Thermal Stress in Laminated Composite

The 3-D elasto-plastic finite element method (FEM) was used to analyze the thermal stress in the laminated composite (SiC/6061Al) under the condition of a temperature cycling of 200 0C-30 0C- 200 0C-30 0C. The results from the FEM analysis showed that the hysteretic peak value of the von Mises equivalent stress in the substrate 6061Al was increased significantly as the temperature loading cycles processed on but it was nearly the same after the first cycle in the interface layer SiC of the laminated composite. The elastic strain in the substrate 6061Al varied within the range of -0.15% to 0.15% and the maximum plastic deformation was equal to about 0.26 %. The results also showed that the maximum normal stress Sx was increased from 32.8 MPa to 87.9 MPa after ten cycles and the work-hardening of the substrate 6061Al occurred during the stress and strain hysteresis loop.

인공우주물체 추적/관측을 위한 다중 광학계 탑재용 가대 설계 및 구조해석

인공우주물체는 출현 시간이 비교적 짧고 운동 특성이 고정적이지 않기 때문에 한 번의 관측으로 측광 및 분광 데이터를 획득하기 어렵다. 따라서 인공우주물체의 측광 및 분광 동시 관측을 위해서 경희대학교 인공위성 추적 및 관측시스템에 다중 광학계를 탑재할 수 있는 가대를 설계하였다. 이 연구에서는 구조해석을 통해 다중 광학계 탑재 시에 개조된 가대의 변형을 계산하고 인공 우주물체 추적 및 관측 시 발생할 수 있는 가대의 지향오차를 추론하여 관측시야에서 인공우주물체를 안정적으로 추적할 수 있음을 보였다. 또한 등가응력 해석을 수행하여 가대의 구조적 안전성을 확인하였다. Since artificial space objects are observable only in a short period of time and the characteristics of their motion is not exactly predictable, it is difficult to obtain both photometric and spectroscopic data by a set of observations. We have, therefore, designed a mount to load multi-optical instruments on the Kyung Hee University (KHU) satellite tracking and observation system for both photometric and spectroscopic observations of artificial space objects. In this paper, we have calculated the deformation of the remodeled mount using structural analyses for the loading of the multi-optical instruments. We have also deduced pointing errors of the mount occurring at tracking and observing artificial space objects. we have derived tracking reliably artificial space objects in our field of view and confirmed structural safety test of mount utilizing equivalent (von-mises) stress distribution.

Theoretical and finite-element modeling of autofrettage process in strain-hardening thick-walled cylinders

The optimum autofrettage pressure and the optimum radius of the elastic–plastic boundary of strain-hardening cylinders in plane strain and plane stress have been studied theoretically and by finite-element modeling. Equivalent von-Mises stress is used as yield criterion. Comparison of the results of the two methods shows good agreement. Although there is no explicit expression for the optimum autofrettage pressure in plane stress, the equation for plane strain can be used with good accuracy. It has also been observed that the optimum autofrettage pressure is not a constant value but depends on working pressure.

Three-dimensional finite element analysis of strain and stress distributions in endodontically treated maxillary central incisors restored with diferent post, core and crown materials

Objectives The present comparative analysis aimed at evaluating which combination of restorative materials resulted in the most homogeneous stress and strain distributions. Methods A three-dimensional finite element analysis was performed. All the nodes on the external surface of the root were constrained in all directions. Eighteen experimental models with different material properties and configurations were simulated. An arbitrary load of 10 N was applied at 60° angle with tooth longitudinal axis on the palatal surface of the crown. Von Mises (equivalent stresses) energetic criterion was chosen. Results In all the models the values of both strain and stress recorded at the middle third of the buccal aspect of the root surface were at their maxima. On the contrary, the minimum values were noticed at level of both the apical portion of the post and the root apex. The maximum stresses were evidenced at level of the cemento–enamel junction (CEJ) on both the buccal and palatal aspects of root cement and dentin. Stress progressively decreased from the outer to the inner part of the root and from the CEJ towards the incisal margin of the crown as well. Significance The results of the present study would allow clinicians to make an informed choice from among available materials to restore endodontically treated teeth.

Three-dimensional modeling of ductile crack growth: Cohesive zone parameters and crack tip triaxiality

For 10 mm thick smooth-sided compact tension specimens made of a pressure vessel steel 20MnMoNi55, the interrelations between the cohesive zone parameters (the cohesive strength, T max, and the separation energy, Γ) and the crack tip triaxiality are investigated. The slant shear-lip fracture near the side-surfaces is modeled as a normal fracture along the symmetry plane of the specimen. The cohesive zone parameters are determined by fitting the simulated crack extensions to the experimental data of a multi-specimen test. It is found that for constant cohesive zone parameters, the simulated crack extension curves show a strong tunneling effect. For a good fit between simulated and experimental crack growth, both the cohesive strength and the separation energy near the side-surface should be considerably lower than near the midsection. When the same cohesive zone parameters are applied to the 3D model and a plane strain model, the stress triaxiality in the midsection of the 3D model is much lower, the von-Mises equivalent stress is distinctly higher, and the crack growth rate is significantly lower than in the plane strain model. Therefore, the specimen must be considered as a thin specimen. The stress triaxiality varies dramatically during the initial stages of crack growth, but varies only smoothly during the subsequent stable crack growth. In the midsection region, the decrease of the cohesive strength results in a decrease of the stress triaxiality, while the decrease of the separation energy results in an increase of the triaxiality.

20705 ダマシン構造におけるvia部最大応力の有限要素法解析(機械工学が支援する半導体製造技術(I),OS13 機械工学が支援する半導体薄膜製造技術)

This paper shows analysis of stress in inter-connected structures made by dual-damascene method during planarizing processes by CMP (Chemical Mechanical Polishing). Mechanical properties and dimensions in the future generations of inter-connected structures are analyzed. Von Mises equivalent stresses are calculated by Finite Element Method under down-forces and frictions of CMP processes. The results of analysis show that maximum stress is observed at the intermediate positions of vias and depends on the Young's modulus of the Low-k material. However, the maximum stress in vias at the 32 nm-node is only three times as large as the stress at the 90 nm-node.

647 荷重条件が骨梁のリモデリング刺激量に与える影響

Distribution function of mechanical quantities at single trabecular level as remodeling stimuli was obtained by using digital image-based finite element models of normal vertebral body of rat. When a linear rate equation was assumed, integration of strain energy density (SED), von Mises equivalent stress, and local stress nonuniformity were more candidate stimuli of trabecular bone remodeling near remodeling equilibrium than SED. The sensitivity of distribution function of stress nonuniformity to change in physiological loading condition was the smallest in the four mechanical quantities.

Contact mechanics of surfaces with various models of roughness descriptions

In this paper, the differences among various models of rough surface descriptions on the stress analysis of head–disk interface are examined. Besides the commonly used fractal geometry, simpler polynomials and Fourier series are used for describing the surface height variation. Elastic–plastic contact analyses for the head–disk interface (HDI) are then performed using ABAQUS. By incorporating various rough surface characterizations into the finite element model of the disk medium, the corresponding finite element analyses are carried out to demonstrate the variation and distribution of the contact pressure. Simulation results for Von Mises equivalent stress, equivalent plastic strain, and maximum tensile stress, are examined for various maximum interference distances.

Mechanical Properties of Al Thin Films as Measured by Bulge Testing

AbstractFree-standing rectangular Al thin films have been fabricated using sputter deposition and standard micromachining techniques. Mechanical properties and residual stresses of both asdeposited and annealed Al films were measured by bulge testing. The films were loaded into the plastic deformation regime, and then unloaded and reloaded several times. The pressure and deflection of the thin films were recorded and used to generate stress-strain curves. The planestrain elastic modulus, flow stress and plastic behavior of the Al thin films were used to characterize the mechanical response of these films. The Al films were measured to have a plane-strain modulus that is slightly lower than the literature values for a {111} textured film. The Von-Mises equivalent yield stress was measured to be higher in the annealed films but much more significant strain hardening was observed in the as-deposited films. A plastic hysteresis was observed on unloading and reloading stress-strain curves of the as-deposited Al films but not the annealed films.

Semi-Analytical Modeling of Crack Initiation Dominant Contact Fatigue Life for Roller Bearings

The fatigue test of a needle roller bearing suggests that the dominant failure mechanism is subsurface crack initiation and propagation. Therefore, a new semi-analytical contact fatigue model is derived from a micromechanics based crack initiation model. The analysis indicates that in the life calculation the selection of the critical stress, such as the maximum orthogonal shear stress, maximum shear stress, octahedral shear stress, or von Mises equivalent stress, becomes arbitrary under the nonfrictional Hertzian line contact condition. The fatigue life of roller bearings under the pure rolling condition can be predicted by simply knowing the Hertzian contact pressure and the contact width, which avoids complicated calculation of the subsurface stresses. The film thickness, roughness, and the material hardness effects on contact fatigue are also included in the new model. The comparisons with different models and the experimental data indicate that the new model makes similar life predictions as the Ioannides-Harris model, but the new model is much simpler to use. The Lundberg-Palmgren model does not fit with the experiment data.

Deformation Twinning and Grain Size Aspects of Numerical Simulations of Plastic Flow

AbstractThe dependence of the twinning stress on grain size is similar to the dependence of the athermal part of the flow stress on grain size. Previous numerical simulations included a twinning effect based upon the premise that twinning refines the grain size and gives additional Hall-Petch strengthening. If a grain reaches the stress level given by σT = σT0+ kT ∓-1/2, it is considered twinned and a constant increment is added to the flow stress. Once twinned, the new twinning threshold stress is much higher than the original and so further twinning is unlikely to occur. The twinning model used in this work is based on the idea that enough twinning will occur in a grain to accommodate the excess by which the Von Mises equivalent stress exceeds the twinning threshold stress. The previous twinning model required knowledge of the number of twins per grain produced. With this model, the parameters for iron are known a priori (σT0 = 330 MPa and kT = 2.8 MPa m1/2) and numerical simulations of Taylor cylinder impacts produced good agreement with experimental results. For titanium and zirconium, σT0 and kT were determined by matching the computed and experimental shapes. The results here indicate that twinning hardens these metals by effectively changing the material grain size and the microstructure within the grains.