Elastoplastic Plane Strain Analysis of Stresses and Strains at the Notch Root

1988 ◽  
Vol 110 (3) ◽  
pp. 195-204 ◽  
Author(s):  
G. Glinka ◽  
W. Ott ◽  
H. Nowack
Keyword(s):  
Energy Density ◽  
Plane Strain ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Notch Root ◽  
Equivalent Strain ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Energy Concept ◽  
Notch Tip

For the evaluation of the local elastoplastic strains and stresses at the notch root suitable approximation formulas of sufficient accuracy are often used. In the present study the “equivalent strain energy density” concept for elastic-plastic notch strain-stress analysis has been developed. It was found that the evaluation of the strain energy density in the notch tip plastic zones does not require any input data other than the material stress-strain relation and the elastic stress concentration factor. The concept was verified on the basis of the results obtained from plane strain elastic-plastic finite element analysis using the material model after Mro´z. Comparison of the two sets of results revealed satisfactory accuracy of the equivalent strain energy concept. It was also shown that all stress and strain components in the notch tip can be calculated by complementing the method with Hencky’s equations. Neuber-based calculations were also included in the study. It was found that the energy concept was superior to Neuber’s rule, especially in the presence of high inelastic strains in the notch tip.

Thermal Fatigue Prediction for Leadless Solder Joint of TFBGA

2006 ◽  
Author(s):  
Chia-Lung Chang ◽  
Tzu-Jen Lin ◽  
Chih-Hao Lai
Keyword(s):  
Energy Density ◽  
Solder Joint ◽  
Creep Strain ◽  
Thermal Fatigue ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Creep Property ◽  
Inelastic Strain ◽  
Temperature Cycling ◽  
Element Analysis

Nonlinear finite element analysis was performed to predict the thermal fatigue for leadless solder joint of TFBGA Package under accelerated TCT (Temperature Cycling Test). The solder joint was subjected to the inelastic strain that was generated during TCT due to the thermal expansion mismatch between the package and PCB. The solder was modeled with elastic-plastic-creep property to simulate the inelastic deformation under TCT. The creep strain rate of solder was described by double power law. The furthest solder away from the package center induced the highest strain during TCT was considered as the critical solder ball to be most likely damaged. The effects of solder meshing on the damage parameters of inelastic strain range, accumulated creep strain and creep strain energy density were compared to assure the accuracy of the simulation. The life prediction equation based on the accumulated creep strain and creep strain energy density proposed by Syed was used to predict the thermal fatigue life in this study. The agreement between the prediction life and experimental mean life is within 25 per cent. The effect of die thickness and material properties of substrate on the life of solder was also discussed.

Peridynamic Modeling of Hyperelastic Membrane Deformation

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
D. J. Bang ◽  
E. Madenci
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Equations Of Motion ◽  
Uniaxial Loading ◽  
Density Functions ◽  
Loading Conditions ◽  
Element Analysis ◽  
Material Parameters ◽  
Loading Case

This study concerns the development of peridynamic (PD) strain energy density functions for a Neo-Hookean type membrane under equibiaxial, planar, and uniaxial loading conditions. The material parameters for each loading case are determined by equating the PD strain energy density to that of the classical continuum mechanics. The PD equations of motion are derived based on the Neo-Hookean model under the assumption of incompressibility. Numerical results concern the deformation of a membrane with a defect in the form of a hole, a crack, and a rigid inclusion under equibiaxial, planar, and uniaxial loading conditions. The PD predictions are verified by comparison with those of finite element analysis.

scholarly journals Strain Energy Density as Failure Criterion for Quasi-Static Uni-axial Tensile Loading

2021 ◽  
Vol 15 (57) ◽  
pp. 331-349
Author(s):  
Andrea Kusch ◽  
Simone Salamina ◽  
Daniele Crivelli ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Notch Root ◽  
Tensile Load ◽  
Strain Curve ◽  
Material Behavior ◽  
Uniaxial Tensile ◽  
Notched Specimens ◽  
Nonlinear Stress

Strain energy density is successfully used as criterion for failure assessment of brittle and quasi-brittle material behavior. This work investigates the possibility to use this method to predict the strength of V-notched specimens made of PMMA under static uniaxial tensile load. Samples are characterized by a variability of notch root radii and notch opening angles. Notched specimens fail with a quasi-brittle behavior, albeit PMMA has a nonlinear stress strain curve at room temperature. The notch root radius has most influence on the strength of the specimen, whereas the angle is less relevant. The value of the strain energy density is computed by means of finite element analysis, the material is considered as linear elastic. Failure prediction, based on the critical value of the strain energy density in a well-defined volume surrounding the notch tip, show very good agreement (error <15%) with experimental data.

Elastic-plastic finite element analysis for oblique cutting with a discontinuous chip of 6-4 brass

2001 ◽  
Vol 36 (6) ◽  
pp. 579-594 ◽  
Author(s):  
Z-C Lin ◽  
Y-Y Lin
Keyword(s):  
Finite Element ◽  
Energy Density ◽  
Crack Growth ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Equivalent Stress ◽  
Initial Crack ◽  
Chip Surface ◽  
Oblique Cutting ◽  
Elastic Plastic

If the workpiece material experiences tremendous strain during the chip formation process or brittle material undergoes fracture in the primary deformation zone when the chip is only partly formed, the segmented chip formed under the above conditions is called a discontinuous chip. With the introduction of the tool inclination angle geometry, an elastic-plastic finite element model is developed for oblique cutting of discontinuous chip. The tool is P20 while the workpiece is made of 6-4 brass. The initial crack location, the direction of crack growth and variations of discrete chips are examined under the condition of a low cutting speed. These predictions are made possible by application of the strain energy density theory. The initial crack was formed in the (d W/d V)maxmin region (i.e. the maximum region among many of the strain energy density minima) of the chip surface and grew progressively along the stationary values of the strain energy density function. The direction of crack growth was based on the maximum strain energy density curve along the surface. The fracture process on the other chip layers was identical with that on the chip surface and occurred in sequence until it reached the chip free surface. The plastic deformation and friction result in a high equivalent stress on the chip surface above the tool tip, especially at the place of crack formation. As more residual stress is present after cutting, degradation of the workpiece prevails and should be accounted for.

A Coupled Finite Element Model of Thermo-Elastic-Plastic Large Deformation for Orthogonal Cutting

1992 ◽  
Vol 114 (2) ◽  
pp. 218-226 ◽  
Author(s):  
Z. C. Lin ◽  
S. Y. Lin
Keyword(s):  
Finite Element ◽  
Energy Density ◽  
Large Deformation ◽  
Chip Formation ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Metal Cutting ◽  
Orthogonal Cutting ◽  
Elastic Plastic ◽  
Chip Separation

In this paper, a coupled model of the thermo-elastic-plastic material under large deformation for orthogonal cutting is constructed. A chip separation criterion based on the critical value of the strain energy density is introduced into the analytical model. A scheme of twin node processing and a concept of loading/unloading are also presented for chip formation. The flow stress is taken as a function of strain, strain rate and temperature in order to reflect realistic behavior in metal cutting. The cutting tool is incrementally advanced forward from an incipient stage of tool-workpiece engagement to a steady state of chip formation. The finite difference method is adopted to determine the temperature distribution within the chip and tool, and a finite element method, which is based on the thermo-elastic-plastic large deformation model, is used to simulate the entire metal cutting process. Finally, the chip geometry, residual stresses in the machined surface, temperature distributions within the chip and tool, and tool forces are obtained by simulation. The calculated cutting forces agree quite well with the experimental results. It has also been verified that the chip separation criterion value based on the strain energy density is a material constant and is independent of uncut chip thickness.

scholarly journals Peridynamic model for visco-hyperelastic material deformation in different strain rates

2019 ◽  
Author(s):  
Yunke Huang ◽  
Selda Oterkus ◽  
Hong Hou ◽  
Erkan Oterkus ◽  
Zhengyu Wei ◽  
...  
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Surface Defects ◽  
Force Density ◽  
Strain Rates ◽  
Element Analysis ◽  
Material Parameters ◽  
Peridynamic Model

AbstractThis study presents a peridynamic (PD) constitutive model for visco-hyperelastic materials under homogenous deformation. The constitutive visco-hyperelastic model is developed in terms of Yeoh strain energy density function and Prony series. The material parameters in the model are identified by optimizing the classical stress–strain relation and tension test data for different strain rates. The peridynamic visco-hyperelastic force density function is proposed in terms of the peridynamic integral and the Yeoh strain energy density. The time-dependent behaviour for different strain rates is captured by numerical time integration representing the material parameters. The explicit form of peridynamic equation of motion is then constructed to analyse the deformation of visco-hyperelastic membranes. The numerical results concern the deformation and damage prediction for a polyurea membrane and membrane-type acoustic metamaterial with inclusions under homogenous loading. Different surface defects are considered in the simulation. The peridynamic predictions are verified by comparing with finite element analysis results.

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