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.

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 Large-Deformation Finite-Element Analysis for Multilayer Elastomeric Bearings

1987 ◽  
Vol 60 (5) ◽  
pp. 856-869 ◽  
Author(s):  
Wataru Seki ◽  
Yoshihide Fukahori ◽  
Yutaka Iseda ◽  
Tsutomu Matsunaga
Keyword(s):  
Finite Element ◽  
Energy Density ◽  
Density Function ◽  
Large Deformation ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Biaxial Testing ◽  
Element Analysis ◽  
Elastomeric Bearings ◽  
Strain Energy Density Function

Abstract Finite element methods are applied for multilayer elastomeric bearings under large deformation. The method is capable of handling nonlinear elasticity and incompressibility of rubber-like materials. The strain energy density function which determines elastic properties of the materials is obtained empirically through strip biaxial testing. The computation using the strain energy density function is conducted to analyze the stress and strain distribution and the performance characteristics of multilayer elastomeric bearings, which is in good agreement with the results of actual experiments.

Finite Element Modeling of Grain Aspect Ratio and Strain Energy Density in a Textured Copper Thin Film

1996 ◽  
Vol 436 ◽  
Author(s):  
R. P. Vinci ◽  
J. C. Bravman
Keyword(s):  
Finite Element ◽  
Energy Density ◽  
Aspect Ratio ◽  
Finite Element Modeling ◽  
Strain Energy Density ◽  
Driving Force ◽  
Strain Energy ◽  
Interface Energy ◽  
Element Modeling ◽  
Grain Aspect Ratio

AbstractWe have modeled the effects of grain aspect ratio on strain energy density in (100)-oriented grains in a (111)-textured Cu film on a Si substrate. Minimization of surface energy, interface energy, and strain energy density (SED) drives preferential growth of grains of certain crystallographic orientations in thin films. Under conditions in which the SED driving force exceeds the surface- and interface-energy driving forces, Cu films develop abnormally large (100) oriented grains during annealing. In the elastic regime the SED differences between the (100) grains and the film average arise from elastic anisotropy. Previous analyses indicate that several factors (e.g. elimination of grain boundaries during grain growth) may alter the magnitude of the SED driving force. We demonstrate, using finite element modeling of a single columnar (100) grain in a (111) film, that changes in grain aspect ratio can significantly affect the SED driving force. A minimum SED driving force is found for (100) Cu grains with diameters on the order of the film thickness. In the absence of other stagnation mechanisms, such behavior could cause small grains to grow abnormally and then stagnate while large grains continue to grow. This would lead to a bimodal grain size distribution in the (100) grains preferred by the SED minimization.

Large Deformation Analysis of the Arterial Cross Section

1971 ◽  
Vol 93 (2) ◽  
pp. 138-145 ◽  
Author(s):  
B. R. Simon ◽  
A. S. Kobayashi ◽  
D. E. Strandness ◽  
C. A. Wiederhielm
Keyword(s):  
Finite Element ◽  
Energy Density ◽  
Numerical Integration ◽  
Density Function ◽  
Cross Section ◽  
Finite Deformation ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Exponential Form ◽  
Strain Energy Density Function

Possible relations between arterial wall stresses and deformations and mechanisms contributing to atherosclerosis are discussed. Necessary material properties are determined experimentally and from available data in the literature by assuming the arterial response to be a static finite deformation of a thick-walled cylinder constrained in a state of plane strain and composed of an incompressible, nonlinear elastic, transversely isotropic material. Experimental justification from the literature and supporting theoretical considerations are presented for each assumption. The partial derivative of the strain energy density function δW1/δI , necessary for in-plane stress calculation, is determined to be of exponential form using in situ biaxial test results from the canine abdominal aorta. An axisymmetric numerical integration solution is developed and used as a check for finite element results. The large deformation finite element theory of Oden is modified to include aortic material nonlinearity and directional properties and is used for a structural analysis of the aortic cross section. Results of this investigation are: (a) Fung’s exponential form for the strain energy density function of soft tissues is found to be valid for the aorta in the biaxial states considered; (b) finite deformation analyses by the finite element method and numerical integration solution reveal that significant tangential stress gradients are present in arteries commonly assumed to be “thin-walled” tubes using linear theory.

Creep Analysis and Thermal-Fatigue Life Prediction of the Lead-Free Solder Sealing Ring of a Photonic Switch

2002 ◽  
Vol 124 (4) ◽  
pp. 403-410 ◽  
Author(s):  
J. Lau ◽  
Z. Mei ◽  
S. Pang ◽  
C. Amsden ◽  
J. Rayner ◽  
...  
Keyword(s):  
Finite Element ◽  
Fatigue Life ◽  
Energy Density ◽  
Thermal Fatigue ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Constitutive Law ◽  
Isothermal Fatigue ◽  
Thermal Fatigue Life ◽  
Sealing Ring

Thermal reliability of the solder sealing ring of Agilent Technologies’ bubble-actuated photonic cross-connect switches has been investigated in this paper. Emphasis is placed on the determination of the thermal-fatigue life of the solder sealing ring under shipping/storing/handling conditions. The solder ring is assumed to obey the Garofalo-Arrhenius creep constitutive law. The nonlinear responses such as the deflections, stresses, creep strains, and creep strain energy density of the 3-D photonic package have been determined with a commercial finite element code. In addition, isothermal fatigue tests have been performed to obtain the relationship between the number of cycle-to-failure and the strain energy density. Thus, by combining the finite element results and the isothermal fatigue test results, the average thermal-fatigue life of the solder sealing ring is readily determined and is found to be more than adequate for shipping/storing/handling the photonic switches.

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.

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