An Innovative Yield Criterion Considering Strain Rates Based on Von Mises Stress

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Jingwei Yu ◽  
Qingguo Fei ◽  
Peiwei Zhang ◽  
Yanbin Li ◽  
Dahai Zhang ◽  
...  
Keyword(s):  
Energy Density ◽  
Yield Strength ◽  
Constitutive Model ◽  
Strain Rate ◽  
Dynamic Load ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Yield Criterion ◽  
Von Mises Stress ◽  
Von Mises

Abstract An innovative yield criterion based on von Mises stress is proposed to represent the strain rate-dependent behavior under dynamic load. Considering the strain rate in the constitutive model, the distortional strain energy density is derived and the yield criterion is established. A plot of yield strength for a range of strain rate reveals that despite the differences in material properties and test methods, the yield strength rise can be represented by a unified criterion. The overall yield behavior of the material under dynamic load can be explained by introducing the strain rate into the constitutive model and threshold distortional strain energy density. This criterion is in a simple form that may be widely applied.

Experimentally determined microcracking around a circular hole in a flat plate of bone: comparison with predicted stresses

1995 ◽  
Vol 347 (1322) ◽  
pp. 383-396 ◽  
Keyword(s):  
Energy Density ◽  
Circular Hole ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Bone Remodelling ◽  
Von Mises Stress ◽  
Analysis Model ◽  
Material Interfaces ◽  
Empirical Examination ◽  
Von Mises

We examined the microcracking (damage) in the vicinity of a circular hole in bovine femoral bone specimens. The stresses near the hole were derived by a finite element analysis model using the bone’s elastic constants and yield stresses, which were determined from a series of mechanical tests specifically for the type of bone under examination. The spatial occurrence and distribution of microcracking was compared to the patterns of the predicted maximum principal stress, the von Mises stress, and the strain energy density function (all implicated by various workers as stimuli for bone remodelling) and to the predictions derived by the use of two engineering criteria for anisotropic yield under mixed mode of stress. The predictions for stresses and the strain energy density were all very similar, making it impossible to claim that any of them is superior to the others. However, empirical examination of the results of the Hencky-von Mises and Tsai-Wu anisotropic yield criteria showed that the Tsai-Wu criterion approximated reasonably the pattern of microcracking around the hole. We suggest that, in the light of the considerable damage observed in the vicinity of stress concentrators, similar damage in irregular material interfaces (i.e. near orthopaedic implants) would require the re-examination of the theories concerning bone remodelling so as to account for the possibility of occurrence of damage and the quantification of its magnitude and likely effect. The presence of considerable microdamage in bone long before it fails suggests that damage-based criteria are more likely to be successful predictors of bone remodelling behaviour than would stress or strain-based criteria.

Microstructure Evolution and Analysis of a Single Crystal Nickel-Based Superalloy during Tensile Creep

2011 ◽  
Vol 689 ◽  
pp. 154-158 ◽  
Author(s):  
Shu Zhang ◽  
Su Gui Tian ◽  
Yong Su ◽  
Ben Jiang Qian
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Lattice Misfit ◽  
Tensile Creep ◽  
Von Mises Stress ◽  
Stress Axis ◽  
Directional Growth ◽  
Misfit Stress ◽  
Von Mises

By means of the finite element method (FEM) for calculating the von Mises stress and strain energy density in the cubic γ/γ′ phases, the regularity of γ′ phase directional growth is investigated. Results show that the change of the strain energy density in the different planes of the cubical γ′ phase occurs during tensile creep of alloy, the cubical γ′ phase is directionally grown, along the crystal plane with bigger strain energy, to transform into the mesh-like rafted structure along the direction perpendicular to the applied stress axis. The change of the atomic potential energy, interfacial energy and lattice misfit stress is thought to be the driving force for promoting the elements diffusion and directional growth of γ′ phase.

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

Use of Strain Energy Density W and Qo as Quality Indices for Rating the Quality of Cast Aluminium Alloy354 as a Function of Processing Parameters

2013 ◽  
Vol 704 ◽  
pp. 189-194 ◽  
Author(s):  
Prateek Sibal ◽  
G. Dinesh Babu ◽  
M. Nageswara Rao
Keyword(s):  
Energy Density ◽  
Yield Strength ◽  
Aluminium Alloy ◽  
Aging Temperature ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Artificial Aging ◽  
Heat Treatments ◽  
Cast Aluminium

Cast aluminium alloy 354 has found widespread application in the automotive industry for its excellent mechanical properties and good castability. The stringent emission norms and demands for improved fuel economy have pushed automobile technology to new frontiers. This has led to efforts to reduce weight while maintaining higher vehicle performance. Cast aluminium alloy 354 is a material that performs with reasonable effectiveness in the high stress automobile environment. The present study looks at the use of strain energy density W and the quality index Qo to determine the effect of process parameters like aging temperature and modification on the quality of the alloy 354 and also to monitor the effect of interrupted heat treatments T6I4 and T6I6 on the quality of the material. The strain energy density W calculated for the interrupted heat treatments on alloy 354 show a broad inverse relation with yield strength Rp. An improvement in the yield strength and the strain energy density of the alloy is observed when the alloy is subjected to modification. At artificial aging temperatures lower than the artificial aging temperature adopted in standard aging treatment an improvement in the Qo and W quality of the alloy 354 have been observed.

scholarly journals IMPACT TESTING OF ORDNANCE GELATINE UNDER MODERATE STRAIN RATE CONDITIONS

2018 ◽  
Vol 18 ◽  
pp. 44
Author(s):  
Tomáš Doktor ◽  
Petr Zlámal ◽  
Jan Šleichrt ◽  
Tomáš Fíla ◽  
Daniel Kytýř
Keyword(s):  
Energy Density ◽  
Strain Rate ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Deformation Behaviour ◽  
Rate Sensitivity ◽  
Impact Testing ◽  
Static Compression ◽  
Static Conditions ◽  
The Impact

An experimental study on energy absorption capabilities and strain rate sensitivity of ordnance gelatine was performed. Strain energy density under quasi static compression and moderate strain rate impact tests was compared. In the study two types of material were tested, bulk ordnance gelatine and polymeric open-cell meshwork filled with ordnance gelatine. From the results a significant strain-rate effect was observed in terms of ultimate compressive strength and strain energy density. In comparison of the deformation behaviour under quasi static conditions and drop weight test the difference was very significant, however slight increase in both strength and strain energy density was observed even between different impact energies and velocities during the impact testing. The peak acceleration was significantly reduced in polymer meshwork filled by gelatine in comparison to the bulk gelatine.

scholarly journals Creep-Fatigue Behaviours of Sn-Ag-Cu Solder Joints in Microelectronics Applications

2021 ◽  
Author(s):  
Joshua A. Depiver ◽  
Sabuj Mallik ◽  
Yiling Lu ◽  
Emeka H. Amalu
Keyword(s):  
Energy Density ◽  
Thermal Cycling ◽  
Strain Rate ◽  
Deformation Rate ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Solder Joints ◽  
Creep Fatigue ◽  
Accelerated Thermal Cycling ◽  
Isothermal Ageing

Electronic manufacturing is one of the dynamic industries in the world in terms of leading technological advancements. Electronic assembly’s heart lies the ‘soldering technology’ and the ‘solder joints’ between electronic components and substrate. During the operation of electronic products, solder joints experience harsh environmental conditions in terms of cyclic change of temperature and vibration and exposure to moisture and chemicals. Due to the cyclic application of loads and higher operational temperature, solder joints fail primarily through creep and fatigue failures. This paper presents the creep-fatigue behaviours of solder joints in a ball grid array (BGA) soldered on a printed circuit board (PCB). Using finite element (FE) simulation, the solder joints were subjected to thermal cycling and isothermal ageing. Accelerated thermal cycling (ATC) was carried out using a temperate range from 40°C to 150°C, and isothermal ageing was done at −40, 25, 75 and 150°C temperatures for 45 days (64,800 mins). The solders studied are lead-based eutectic Sn63Pb37 and lead-free SAC305, SAC387, SAC396 and SAC405. The results were analysed using the failure criterion of equivalent stress, strain rate, deformation rate, and the solders’ strain energy density. The SAC405 and SAC396 have the least stress magnitude, strain rate, deformation rate, and strain energy density damage than the lead-based eutectic Sn63Pb37 solder; they have the highest fatigue lives based on the damage mechanisms. This research provides a technique for determining the preventive maintenance time of BGA components in mission-critical systems. Furthermore, it proposes developing a new life prediction model based on a combination of the damage parameters for improved prediction.

scholarly journals The role of PDL-cementum enthesis in protecting PDL under masticatory loading: A finite element investigation

2021 ◽  
Author(s):  
Hossein Jokar ◽  
Gholamreza Rouhi ◽  
Nabiollah Abolfathi
Keyword(s):  
Computed Tomography ◽  
Finite Element ◽  
Periodontal Ligament ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Alveolar Bone ◽  
Von Mises Stress ◽  
Mechanical Stimuli ◽  
Von Mises

Abstract PURPOSE. Function of periodontal ligament-cementum enthesis (PCE) in transferring mechanical stimuli within tooth-periodontium (PDT)-bone complex was not made clear yet. This study aimed to evaluate the effects of PCE on the mechanical stimuli distribution within the PDL and alveolar bone in the tooth-PDT-bone complex under occlusal forces using finite element method (FEM). METHODS. A computed tomography (CT) based model of alveolar bone and 2nd premolar of mandible was constructed, in which the PDT was considered at the interface of alveolar bone and tooth. Under a 3MPa distributed occluso-apical masticatory load, applied over the uppermost surface of crown, the von Mises strain (vMST) and strain energy density (SED) within PDL, and von Mises stress (vMSR) and SED within alveolar bone were calculated in two situations: 1. When the PCE was absent; and 2. When the PCE was present between the PDL and cementum. RESULTS. PCE levels-off the SED and vMST within PDL by maximum values of 92 kPa and 0.04 mm/mm, respectively, compared to the model without PCE. Moreover, it increased the alveolar bone SEDs and vMSR by maximum values of 0.36 kPa and 0.63 MPa, respectively, compared to the without PCE model.CONCLUSION. By including PCE in the tooth-PDT-bone model, the mechanical stimuli shift from PDL to its surrounding alveolar bone. Thus, it can be speculated that the tooth-PDT-bone complex has the capability of, through shifting excess mechanical stimuli from PDL toward the alveolar bone, reducing the risk of PDL damage.

NUMERICAL/GRAPHICAL IMPLEMENTATION OF MAXIMUM STRAIN ENERGY DENSITY CRITERION

1992 ◽  
Vol 16 (1) ◽  
pp. 33-46
Author(s):  
F. Taheri ◽  
A.A. Mufti
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Graphical Method ◽  
Crack Tip ◽  
Material Constant ◽  
Critical Distance ◽  
Fracture Load ◽  
The Finite Element Method ◽  
Von Mises

In this paper a numerical/graphical method is developed to establish the initial angle of crack propagation and the associated fracture load for a crack in a mixed mode. This method incorporates the maximum dilatational strain energy density criterion (SED). The resultant stresses, obtained by the finite element method (FEM) are used to establish the distribution of the distortional component of SED (i.e: Von-Mises elastic-plastic boundary) around the crack tip. The angle at which the crack propagates is the angle where the dilatational component of SED attains a maximum. It is also postulated that the fracture will occur if the distance from the crack tip to the point of the maximum dilatational SED exceeds a critical distance, with the critical distance being a material constant. The predicted results are compared to the measured results (both experimental, and analytical) of other researchers.

Determination of Pipeline Yielding Occurred in Hydrostatic Pressure Testing

2019 ◽  
Author(s):  
Xian-Kui Zhu
Keyword(s):  
Hydrostatic Pressure ◽  
Yield Strength ◽  
Yield Criterion ◽  
Limit Load ◽  
Von Mises Stress ◽  
Classical Solutions ◽  
Line Pipe ◽  
Pressure Testing ◽  
Offset Yield Strength ◽  
Von Mises

Abstract The pipeline industry has traditionally utilized the “double stroke” concept to define line pipe yielding for limiting plastic deformation of the pipeline during hydrostatic pressure testing. Practice showed that double stroke may define a nominal yield point lying between the elastic limit and the offset yield strength. Recently, a set of field hydrostatic tests were conducted on an X70 pipeline at Enterprise Products, and the test pressure at double stroke was as high as 129% of SMYS, but the von Mises stress was less than the actual yield strength. The entire pipeline was thought in the elastic conditions at double stroke during the hydrostatic testing. It is well recognized that the classical Tresca and von Mises yield criteria determines a lower and an upper bound of the limit load at yielding, and a newly proposed Zhu-Leis yield criterion determines a medium result of the two classical solutions. Extensive full-scale tests have confirmed that the Zhu-Leis yield solution is the best prediction of experimental data on average. This paper attempts to use the more accurate Zhu-Leis yield criterion to reanalyze the real-world hydrostatic tests of the X70 pipeline to see if pipe yielding occurs and to determine pipe diameter expansion at double stroke during the hydrostatic pressure testing.

scholarly journals Biomechanical investigation of extragraft bone formation influences on the operated motion segment after anterior cervical spinal discectomy and fusion

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Won Man Park ◽  
Yong Jun Jin
Keyword(s):  
Energy Density ◽  
Bone Formation ◽  
Trabecular Bone ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Rotation Angle ◽  
Von Mises Stress ◽  
Stress And Strain ◽  
Mechanical Stimuli ◽  
Motion Segment

AbstractAlthough the clinical importance of extragraft bone formation (ExGBF) and bridging (ExGBB) has been reported, few studies have investigated the biomechanical influences of ExGBF on the motion segment. In this study, ExGBF was simulated at the C5-C6 motion segment after anterior cervical discectomy and fusion using a developed finite element model and a sequential bone-remodelling algorithm in flexion and extension. The computer simulation results showed that extragraft bone was primarily formed in the extension motion and grew to form ExGBB. A stepwise decrease in the intersegmental rotation angle, maximum von Mises stress and strain energy density on the trabecular bone with ExGBF were predicted in extension. When ExGBB was formed in the trabecular bone region, the intersegmental rotation angle slightly decreased with additional bone formation. However, the stress and strain energy density on the trabecular bone region decreased until ExGBB reached the peripheral cortical margin. The results offer a rationale supporting the hypothesis that mechanical stimuli influence ExGBF. ExGBF was helpful in increasing the stability of the motion segment and decreasing the fracture risk of trabecular bones, even in cases in which ExGBB was not formed. ExGBB can be classified as either soft or hard bridging based on a biomechanical point of view.

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