An equivalent von Mises stress and corresponding equivalent plastic strain for elastic–plastic ordinary peridynamics

Aims The material and design of knee components can have a considerable effect on the contact characteristics of the tibial post. This study aimed to analyze the stress distribution on the tibial post when using different grades of polyethylene for the tibial inserts. In addition, the contact properties of fixed-bearing and mobile-bearing inserts were evaluated. Methods Three different grades of polyethylene were compared in this study; conventional ultra high molecular weight polyethylene (UHMWPE), highly cross-linked polyethylene (HXLPE), and vitamin E-stabilized polyethylene (VEPE). In addition, tibial baseplates with a fixed-bearing and a mobile-bearing insert were evaluated to understand differences in the contact properties. The inserts were implanted in neutral alignment and with a 10° internal malrotation. The contact stress, von Mises stress, and equivalent plastic strain (PEEQ) on the tibial posts were extracted for comparison. Results The stress and strain on the tibial post for the three polyethylenes greatly increased when the insert was placed in malrotation, showing a 38% to 56% increase in von Mises stress and a 335% to 434% increase in PEEQ. The VEPE insert had the lowest PEEQ among the three materials. The mobile-bearing design exhibited a lower increase in stress and strain around the tibial posts than the fixed-bearing design. Conclusion Using VEPE for the tibial component potentially eliminates the risk of material permanent deformation. The mobile-bearing insert can help to avoid a dramatic increase in plastic strain around the tibial post in cases of malrotation. The mobility allows the pressure to be distributed on the tibial post and demonstrated lower stresses with all three polyethylenes simulated. Cite this article: Bone Joint Res 2020;9(11):768–777.

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Predicting Plastic Flow Behaviour, Failure Mechanisms and Severe Deformation Localisation of Dual-Phase Steel using RVE Simulation

International Journal of Automotive and Mechanical Engineering ◽

10.15282/ijame.18.1.2021.19.0654 ◽

2021 ◽

Vol 18 (1) ◽

pp. 8601-8611

Author(s):

A. K. Rana ◽

P. P. Dey

Keyword(s):

Plastic Strain ◽

Failure Modes ◽

Volume Fraction ◽

Ferrite Matrix ◽

Martensite Phase ◽

Von Mises Stress ◽

Dual Phase ◽

Strain Partitioning ◽

Deformation Inhomogeneity ◽

Von Mises

In this work, the von Mises stress and plastic strain distribution of Ferrite-Martensite–Dual-Phase (FMDP) steels are predicted at various stages of deformation. The failure modes and volume fraction effect are identified based on Representative Volume Element (RVE). FMDP steel consists of a typical ferrite-matrix phase, in which martensite-islands are dispersed. Recently FMDP steels are increasingly used to the various car parts in demand. 2D-RVEs are also utilised to predict the orientations effect of the martensite phase in the FMDP steels. Based on the position of the element, the boundary conditions (BC) are given in the RVE of FMDP steel microstructures. The failure modes are examined in the form of severe plastic strain localisation. While the distribution of islands in the microstructure varies, as a result, the deformation inhomogeneity increases with a rise of martensite fraction. The results of numerical computation and the trend of experimental failure shown in the literature are compared. This is signifying that the overall macro-behaviour of FMDP steel, as a consequence of stress-strain partitioning and influence of martensite-island volume fractions (MVFs), can be predicted by the finite element (FE) based 2D-RVE modelling.

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Elasto-plastic analysis of the contact region between a rigid ellipsoid and a semi-flat surface

Advances in Mechanical Engineering ◽

10.1177/1687814018797397 ◽

2018 ◽

Vol 10 (9) ◽

pp. 168781401879739 ◽

Cited By ~ 1

Author(s):

Pengyang Li ◽

Lingxia Zhou ◽

Fangyuan Cui ◽

Quandai Wang ◽

Meiling Guo ◽

...

Keyword(s):

Residual Stress ◽

Plastic Deformation ◽

Plastic Strain ◽

Contact Pressure ◽

Contact Region ◽

Three Dimensional ◽

Von Mises Stress ◽

Effective Plastic Strain ◽

Normal Forces ◽

Von Mises

When the load acting on a mechanical structure is greater than the yield strength of the material, the contact surface will undergo plastic deformation. Cumulative plastic deformation has an important influence on the lifespan of mechanical parts. This article presents a three-dimensional semi-analytical model based on the conjugate gradient method and fast Fourier transform algorithm, with the aim of studying the characteristic parameters of the contact region between a rigid ellipsoid and elasto-plastic half-space. Moreover, normal forces and tangential traction were considered, as well as the contact pressure resulting from various sliding speeds and friction coefficients. The contact pressure, effective plastic strain, von Mises stress, and residual stress were measured and shown to increase with increasing sliding velocity. Finally, when the friction coefficient, contact pressure, and effective plastic strain are increased, the von Mises stress is also shown to increase, whereas the residual stress decreases.

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Numerical Study on Elastic-Plastic Stress Field Near the Cooling Holes of Nickel-Based Single Crystal Air-Cooled Blades

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.324-325.563 ◽

2006 ◽

Vol 324-325 ◽

pp. 563-566 ◽

Cited By ~ 1

Author(s):

Qing Min Yu ◽

Zhu Feng Yue ◽

Yong Shou Liu

Keyword(s):

Shear Stress ◽

Stress Field ◽

Numerical Study ◽

Von Mises Stress ◽

Shear Stresses ◽

Slip Systems ◽

Stress Distributions ◽

Elastic Plastic ◽

Von Mises ◽

Plastic Stress

In this paper, a plate containing a central hole was used to simulate gas turbine blade with cooling hole. Numerical calculations based on crystal plasticity theory have been performed to study the elastic-plastic stress field near the hole under tension. Two crystallographic orientations [001] and [111] were considered. The distributions of resolved shear stresses and strains of the octahedral slip systems {110}<112> were calculated. The results show that the crystallographic orientation has remarkable influence on both von Mises stress and resolved shear stress distributions. The resolved shear stress distributions around the hole are different between the two orientations, which lead to the different activated slip systems. So the deformed shape of the hole in [001] orientation differs from that in [111] orientation.

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Chest Deflection vs. Chest Acceleration as Injury Indicator in Front Impact Simulations Using Full Human Body Finite Element Model

Volume 13: New Developments in Simulation Methods and Software for Engineering Applications; Safety Engineering, Risk Analysis and Reliability Methods; Transportation Systems ◽

10.1115/imece2009-11088 ◽

2009 ◽

Cited By ~ 1

Author(s):

Raed E. El-Jawahri ◽

Jesse S. Ruan ◽

Stephen W. Rouhana ◽

Saeed D. Barbat

Keyword(s):

Finite Element ◽

Plastic Strain ◽

Finite Element Model ◽

Human Body ◽

Element Model ◽

Von Mises Stress ◽

Head Acceleration ◽

Blunt Impact ◽

Von Mises ◽

Impact Simulations

The Ford Motor Company Human Body Finite Element Model (FHBM) was validated against rib dynamic tension and 3-point bending tests. The stress-strain and moment-strain data from the tension and bending simulations respectively were compared with human rib specimen test data. The model used represented a 50th percentile adult male. It was used to compare chest deflection and chest acceleration as thoracic injury indicator in blunt impact and belted occupants in front sled impact simulations. A 150 mm diameter of 23.4 kg impactor was used in the blunt impact simulations with impact speeds of 2, 4, and 8 m/s. In the Front sled impact simulations, single-step acceleration pulses with peaks of 10, 20, and 30 g were used. The occupants were restrained by 3-point belt system, however neither pretensioner nor shoulder belt force limiter were used. The external force, head acceleration, chest deflection, chest acceleration, and the maximum values of Von Mises stress and plastic strain were the model outputs. The results showed that the external contact force, head acceleration, chest deflection, and chest acceleration in the blunt impact simulations varied between 1.5–7 kN, 5–28 g, 18–80 mm, and 8–40 g respectively. The same responses varied between 7–24 kN, 13–40 g, 15–50 mm, and 16–46 g respectively in the front sled impact simulations. The maximum Von Mises stress and plastic strain were 50–127 MPa, and 0.04–2% respectively in the blunt impact simulations and 72–134 MPa, and 0.13–3% respectively in the sled impact simulations.

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Investigation on Yield Behavior of 7075-T6 Aluminum Alloy at Elevated Temperatures

10.21203/rs.3.rs-30462/v2 ◽

2020 ◽

Author(s):

Jianping Lin ◽

Xingyu Bao ◽

Yong Hou ◽

Junying Min ◽

Xinlei Qu ◽

...

Keyword(s):

Aluminum Alloy ◽

Aluminum Alloys ◽

Plastic Strain ◽

Elevated Temperatures ◽

Equivalent Plastic Strain ◽

Yield Behavior ◽

State Dependency ◽

Yield Criteria ◽

Yield Loci ◽

Von Mises

Abstract Aluminum alloys have drawn considerable attention in the area of automotive lightweight. High strength aluminum alloys are usually deformed at elevated temperatures due to their poor formability at room temperature. In this work, the yield behavior of 7075 aluminum alloy in T6 temper (AA7075-T6) within the temperature ranging from 25 ℃ to 230 ℃ was investigated. Uniaxial and biaxial tensile tests with the aid of induction heating system were performed to determine the stress vs. strain curves and the yield loci of AA7075-T6 at elevated temperatures, respectively. Von Mises, Hill48 and Yld2000-2d yield criteria were applied to predicting yield loci which were compared with experimentally measured yield loci of the AA7075-T6. Results show that yield stress corresponding to the same equivalent plastic strain decreases with increasing temperature within the investigated temperature range and the shape of yield loci evolves nearly negligibly. The experimental yield locus expands with an increase of equivalent plastic strain at the same temperature and the work hardening rate of AA7075-T6 exhibits obvious stress-state-dependency. The non-quadratic Yld2000-2d yield criterion describes the yield surfaces of AA7075-T6 more accurately than the quadratic von Mises and Hill48 yield criteria, and an exponent of 14 in the Yld2000-2d yield function gives the optimal predictions for the AA7075-T6 at all investigated temperatures.

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Qualitative Behaviour of Elastic-Plastic Solutions for a Class of Damage Mechanics Models Near Bimaterial Interfaces: A Simple Analytical Example

Mathematical Problems in Engineering ◽

10.1155/2013/197632 ◽

2013 ◽

Vol 2013 ◽

pp. 1-5

Author(s):

Sergei Alexandrov ◽

Yusof Mustafa

Keyword(s):

Plastic Strain ◽

Boundary Value Problem ◽

Damage Mechanics ◽

Boundary Value ◽

Equivalent Plastic Strain ◽

Damage Parameter ◽

Bimaterial Interface ◽

Hard Material ◽

Qualitative Behaviour ◽

Elastic Plastic

The paper presents an exact analytic solution for a class of elastic-plastic models with damage evolution. The boundary value problem consists of a planar deformation comprising the simultaneous shearing and expansion of a hollow cylindrical specimen of material and involves a bimaterial interface at which the materials stick to each other. With no loss of generality for understanding the qualitative behaviour of the solution near the bimaterial interface, an extreme case when the hard material is rigid is considered. The solution is reduced to a transcendental equation for the value of the equivalent plastic strain at the bimaterial interface. This equation predicts that the equivalent plastic strain attains a maximum under certain conditions. The existence of the solution of the boundary value problem depends on the value of the damage parameter at fracture, which is a material constant. In particular, if this value is larger than the value of the damage parameter at the bimaterial interface corresponding to the maximum possible value of the equivalent strain at this interface, then no solution exists. Experimental data available in the literature are used to assess whether Lemaitre’s model is applicable.

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Effects of Local Peak Stress Distribution on the Ratchet Limit

Pressure Vessel and Piping Codes and Standards ◽

10.1115/pvp2002-1216 ◽

2002 ◽

Author(s):

Nobuyoshi Yanagida ◽

Masaaki Tanaka ◽

Norimichi Yamashita ◽

Yukinori Yamamoto

Keyword(s):

Finite Element ◽

Stress Distribution ◽

Plastic Strain ◽

Equivalent Stress ◽

Equivalent Plastic Strain ◽

Peak Stress ◽

Element Analysis ◽

Stress Evaluation ◽

Elastic Plastic ◽

Plastic Analysis

Alternative stress evaluation criteria suitable for Finite Element Analysis (FEA) proposed by Okamoto et al. [1],[2] have been studied by the Committee on Three Dimensional Finite Element Stress Evaluation (C-TDF) in Japan. Thermal stress ratchet criteria in plastic FEA are now under consideration. Two criteria are proposed: (1) Evaluating variations in plastic strain increments, and (2) Evaluating the width of the area in which Mises equivalent stress exceeds 3Sm. To verify of these criteria, we selected notched cylindrical vessel models as prime elements. To evaluate the effect of the local peak stress distribution on these criteria, cylindrical vessels with a semicircular notch on the outer surface were selected for this analysis. We used two notch configurations for our analysis, and the stress concentration factor for the notches was set to 1.5 and 2.0. We conducted elastic-plastic analysis to evaluate the ratchet limit. Sustained pressure and alternating enforced longitudinal displacements which causes secondary stress were used as parameters for the elastic-plastic analysis. We found that when no ratchet was observed, the equivalent plastic strain increments decreased and the area in which Mises equivalent stress exceeds 3Sm are below the certain range.

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Dislocation Densities and Velocities within the γ Channels of an SX Superalloy during In Situ High-Temperature Creep Tests

Materials ◽

10.3390/ma11091527 ◽

2018 ◽

Vol 11 (9) ◽

pp. 1527 ◽

Cited By ~ 2

Author(s):

Thomas Schenk ◽

Roxane Trehorel ◽

Laura Dirand ◽

Alain Jacques

Keyword(s):

High Temperature ◽

Plastic Strain ◽

Applied Stress ◽

Load Transfer ◽

Von Mises Stress ◽

High Temperature Creep ◽

Creep Tests ◽

Temperature Creep ◽

Von Mises

The high-temperature creep behavior of a rafted [001] oriented AM1 Ni-based single crystal superalloy was investigated during in situ creep tests on synchrotrons. Experiments were performed at constant temperatures under variable applied stress in order to study the response (plastic strain, load transfer) to stress jumps. Using two different diffraction techniques in transmission (Laue) geometry, it was possible to measure the average lattice parameters of both the γ matrix and the γ ′ rafts in the [100] direction at intervals shorter than 300 s. The absolute precision with both diffraction techniques of the constrained transverse mismatch (in the rafts’ plane) is about 10−5. After stress jumps, special attention is given to the evolution of plastic strain within the γ channels. The relaxation of the Von Mises stress at leveled applied stress shows evidence of dislocation multiplication within the γ channels. From the analysis, we showed an interaction between plastic stress and dislocation density of the γ phase.

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SIMULATION STUDIES ON CHIP FORMATION PROCESS IN HIGH SPEED MILLING OF ALUMINIUM ALLOY

Vietnam Journal of Science and Technology ◽

10.15625/2525-2518/54/5a/12075 ◽

2018 ◽

Vol 54 (5A) ◽

pp. 174

Author(s):

Pham Thi Hoa

Keyword(s):

Finite Element ◽

Aluminium Alloy ◽

High Speed ◽

Equivalent Plastic Strain ◽

Cutting Parameters ◽

Element Model ◽

Von Mises Stress ◽

High Speed Milling ◽

Von Mises ◽

Cutting Processes

Simulations of chip formulation mechanism and phenomenon ccurred in cutting processes can help to reduce time and cost comparing with experiment. Finite element method (FEM) is an effective and accurate technique, which can be used for simulation of cutting process. In this paper, chip formulation process in high-speed milling of A6061 aluminium alloy is investigated using FEM based on the Johnson-Cook (J-C) and Bao-Wierzbicki (B-W) fracture models. The Von-Mises stress distribution and equivalent plastic strain (PEEQ) during cutting are then investigated. Finally, the evolution of cutting forces in cutting was examined. The presented Finite element model in this study proved to be useful in determination of cutting parameters, especially in high-speed machining.

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