On the Plane Stress to Plane Strain Transition Across the Shear Zone in Metal Cutting

1988 ◽  
Vol 110 (4) ◽  
pp. 322-325 ◽  
Author(s):  
B. E. Klamecki ◽  
S. Kim
Keyword(s):  
Plane Strain ◽  
Shear Zone ◽  
Plane Stress ◽  
Central Region ◽  
Chip Formation ◽  
Metal Cutting ◽  
High Strain ◽  
Surface Characteristics ◽  
Workpiece Material ◽  
Element Analysis

The effects of the stress state transition from plane stress at the workpiece surface to plane strain in the central region of the chip formation zone were studied. A finite element analysis of the incipient chip formation process was performed. The model included heat generation and temperature induced workpiece material property changes. The primary result is that the unique high strain, high strain rate, large free surface characteristics of the metal cutting process can result in qualitatively different deformation behavior across the shear zone. Temperatures are higher in the regions near the surface of the workpiece than in the central region. In extreme cases, this will result in strain hardening behavior in the plain strain regions and thermal softening of the work material near the surface.

scholarly journals Elastic soil

1971 ◽  
Vol 4 (2) ◽  
pp. 258-269
Author(s):  
A. J. Carr ◽  
P. J. Moss
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Soil Structure ◽  
Soil Structure Interaction ◽  
Mode Shapes ◽  
Element Analysis ◽  
Structure Interaction ◽  
Stiffness Properties ◽  
Acceleration History ◽  
Elastic Soil

This paper presents a refined finite element analysis for the analysis of two-dimensional plane stress and plane strain structures with particular emphasis being placed on the ability to solve problems of soil-structure interaction under earthquake loadings. The structure and
the soil are idealized as an assemblage of quadrilateral plane stress and plane strain elements having a cubic variation in displacement enabling a more accurate representation of the stiffness properties of the system than that previously available. The response of the system to the earthquake acceleration history is achieved by a superposition of normal mode responses and the methods of obtaining the mode shapes and frequencies are outlined. Examples are presented to illustrate the capability of this approach.

Numerical Investigation of Heat Partition in the Primary Shear Zone in Metal Cutting

2005 ◽  
Author(s):  
Vasant Pednekar ◽  
Vis Madhavan ◽  
Amir H. Adibi-Sedeh
Keyword(s):  
Partition Coefficient ◽  
Strain Rate ◽  
Shear Zone ◽  
Metal Cutting ◽  
Plastic Material ◽  
Shear Plane ◽  
Analytical Models ◽  
Machined Surface ◽  
Element Analysis ◽  
Heat Partition

The fraction of heat generated in the primary shear zone that is conducted into the workpiece is a key factor in the calculation of the shear plane temperature and in calculating the cutting forces based on material flow stress. Accurate analytical, numerical, or experimental determination of this heat partition coefficient is not available to date. This study utilizes a new approach to obtain the heat partition coefficient for the primary shear zone using results for strain, strain rate, and temperature distribution obtained from a coupled thermo-mechanical finite element analysis of machining. Different approaches, using strain rate and equivalent strain, are used for calculating the total plastic power in the primary shear zone and the heat generated by plastic deformation below the plane of the machined surface. The heat carried away by the workpiece is obtained by calculating the heat flow by convection in regions where the conduction is expected to be small. We have used an elastic perfectly plastic material model and constant thermal properties to mimic the assumptions used in analytical models. The fraction of the total heat generated in the primary shear zone that is conducted into the machined workpiece is found and compared to the prediction of different analytical models. It is found that for most of the cutting conditions, the values of heat partition coefficient are closest to those provided by Weiner’s model.

Cruciform specimens for biaxial fatigue tests: An investigation using finite-element analysis and photoelastic-coating techniques

1971 ◽  
Vol 6 (1) ◽  
pp. 27-37 ◽  
Author(s):  
I H Wilson ◽  
D J White
Keyword(s):  
Finite Element ◽  
Central Region ◽  
High Strain ◽  
Fatigue Tests ◽  
Surface Strain ◽  
Element Analysis ◽  
Biaxial Fatigue ◽  
Photoelastic Coating ◽  
Endurance Range ◽  
Transition Radius

The results are presented of investigations made on four cruciform biaxial fatigue specimens, each of which had a differently designed central region. This central region consisted of a reduced section of uniform thickness t over a circular area of diameter d which was connected by a transition radius to the full thickness of the cruciform. Equal tensile and compressive forces were applied alternately along one pair of arms only and the distribution of surface strain was studied by photoelastic-coating techniques after elastic cycling and then plastic cycling. To assess the fatigue performance of the specimens further cycling was carried out until cracks developed. Under elastic conditions, strains uniform over the thickness were calculated by finite-element techniques. For conventional fatigue tests in the high-endurance range the specimen with d/t = 12.5 is recommended. For high-strain low-endurance fatigue investigations the specimen with d/t = 5 is preferred. The recommended designs are free from problems of buckling and are such that an area of uniform strain is produced at the centre of the specimen.

New Development in the Theory of the Metal-Cutting Process: Part II—The Theory of Chip Formation

1961 ◽  
Vol 83 (4) ◽  
pp. 557-568 ◽  
Author(s):  
P. Albrecht
Keyword(s):  
Shear Zone ◽  
Tool Life ◽  
Chip Formation ◽  
Metal Cutting ◽  
Cutting Speed ◽  
Shear Plane ◽  
Cutting Process ◽  
Chip Formation Mechanism ◽  
Bending Stresses ◽  
Set Up

Introduction of the concept of ploughing into the metal-cutting process lead to the abandoning of the assumption of collinearity of the resultant force on tool face and on the shear plane. With this understanding the tool face force is found to produce a bending effect causing bending stresses in the shear zone. Study of the chip formation mechanism when varying cutting speed showed that increased bending action reduces the shear angle and vice versa. A set-up for the development of an analytical model of the chip formation process based on the combined effect of shear and bending stresses in the shear zone has been given. Application of the gained insight to the design of the cutting tool for maximum tool life by controlling of the chip-tool contact was suggested. Brief introduction to the study of cyclic events in chip formation and their relation to the tool life is presented.

A Plasticity Problem Involving Plane Strain and Plane Stress Simultaneously: Groove Formation in the Machining of High-Temperature Alloys

1966 ◽  
Vol 88 (2) ◽  
pp. 142-146 ◽  
Author(s):  
M. C. Shaw ◽  
A. L. Thurman ◽  
H. J. Ahlgren
Keyword(s):  
High Temperature ◽  
Plane Strain ◽  
Plane Stress ◽  
Metal Cutting ◽  
Unit Volume ◽  
High Temperature Alloys ◽  
Plastic Analysis ◽  
Plasticity Problem ◽  
Cutting Problem ◽  
Free Edges

Although a plane strain plastic analysis represents a good approximation for the central portion of a metal-cutting chip, plane stress better approximates conditions at the free edges of the chip. Therefore the metal-cutting problem is reexamined using both plane strain and plane stress simultaneously. The analysis indicates that the material at the edges of the chip will become plastic at a lower value of stress than will be required by the central constrained region and that the energy per unit volume at the edges of the chip will be greater than at the center. The consequence of these results is discussed in terms of the wear groove frequently observed on a tool under the free edges of the chip, which is particularly troublesome when machining high-temperature alloys.

scholarly journals An An Analysis of Strain Rate Distribution Using Streamline Model and A Quick Stop Device in Metal Cutting

2019 ◽  
Vol 22 (2) ◽  
pp. 136-142
Author(s):  
Osama Ali Kadhim ◽  
Fathi A. Alshamma
Keyword(s):  
Strain Rate ◽  
Chip Formation ◽  
Metal Cutting ◽  
Equivalent Strain ◽  
Element Analysis ◽  
Rate Distribution ◽  
Equivalent Strain Rate ◽  
Cumulative Plastic Strain ◽  
Cutting Speeds ◽  
Strain Rate Distribution

In this paper, a quick stop device technique and the streamline model were employed to study the chip formation in metal cutting. The behavior of chip deformation at the primary shear zone was described by this model. Orthogonal test of turning process over a workpiece of the 6061-T6 aluminum alloy at different cutting speeds was carried out. The results of the equivalent strain rate and cumulative plastic strain were used to describe the complexity of chip formation. Finite element analysis by ABAQUS/explicit package was also employed to verify the streamline model. Some behavior of formation and strain rate distribution differs from the experimental results, but the overall trend and maximum results are approximately close. In addition, the quick stop device technique is described in detail. Which could be used in other kinds of studies, such as the metallurgical observation.

scholarly journals Semi-Analytical Prediction of Flank Tool Wear in Orthogonal Cutting of Aluminum

2020 ◽  
Vol 26 (5) ◽  
pp. 38-46
Author(s):  
Osama Ali Kadhim ◽  
Fathi Alshamma
Keyword(s):  
Metal Cutting ◽  
Cutting Tool ◽  
Orthogonal Cutting ◽  
Prediction Equation ◽  
Analytical Prediction ◽  
Wear Coefficient ◽  
Workpiece Material ◽  
Element Analysis ◽  
Cutting Test ◽  
The Given

This study aims to model the flank wear prediction equation in metal cutting, depending on the workpiece material properties and almost cutting conditions. A new method of energy transferred solution between the cutting tool and workpiece was introduced through the flow stress of chip formation by using the Johnson-Cook model. To investigate this model, an orthogonal cutting test coupled with finite element analysis was carried out to solve this model and finding a wear coefficient of cutting 6061-T6 aluminum and the given carbide tool.

Investigation of the Transition From Plane Strain to Plane Stress in Orthogonal Metal Cutting

2004 ◽  
Author(s):  
Vasant Pednekar ◽  
Vis Madhavan ◽  
Amir H. Adibi-Sedeh
Keyword(s):  
Strain Rate ◽  
Plane Strain ◽  
Plane Stress ◽  
Metal Cutting ◽  
Chip Thickness ◽  
Cutting Conditions ◽  
Depth Of Cut ◽  
Orthogonal Machining ◽  
Strain And Strain Rate ◽  
Plane Strain Deformation

It is widely known that in practical orthogonal machining experiments, interior sections of the deforming material undergo plane strain deformation whereas material near the side faces of the workpiece undergoes plane stress deformation. This study is aimed at investigating the plane strain to plane stress transition using 3D coupled thermo-mechanical finite element analysis of orthogonal machining. The temperature, stress, strain and strain-rate distributions along different planes of the workpiece are analyzed to obtain estimates of the fraction of material undergoing plane strain deformation for different widths of cut. While it is found that the deformation in the mid-section of the workpiece is close to that observed in 2D plane strain simulations, the deformation along the side faces is quite different from that observed in 2D plane stress simulations, due to the constraint imposed upon the material along the sides by the material in the middle. Though the chip thickness along the sides is smaller than the chip thickness in the middle, the strain, strain-rate, and temperature fields along the side face and mid-section are quite similar. This study confirms that accurate maps of temperature, strain and strain-rate in plane strain deformation can be obtained by observing the side faces. It is found that for the cutting conditions used, a width to depth-of-cut ratio of twenty (not ten, as is commonly assumed) results in a close approximation to plane strain deformation through more than 90% of the width of the work material. For a width to depth-of-cut ratio of ten, significant deviations are observed in the stresses, with respect to their corresponding values in plane strain. Recommendations for the width of cut to depth of cut ratio to be used in experiments for other cutting conditions can be developed based upon similar studies.

scholarly journals Comparison of theoretical approaches to determine the stresses in surface mounted permanent magnet rotors for high speed electric machines

2021 ◽  
pp. 030932472110076
Author(s):  
Levi Mallin ◽  
Simon Barrans
Keyword(s):  
Permanent Magnet ◽  
Plane Strain ◽  
Plane Stress ◽  
High Speed ◽  
Electric Machines ◽  
Mechanical Transmission ◽  
Element Analysis ◽  
Theoretical Approaches ◽  
Rotor Design ◽  
Stress Plane

High-speed electrical machines (HSEMs) are becoming more popular in applications such as air handling devices. Using surface-mounted permanent magnet (PM) rotors manufactured from rare earth metals, they provide benefits over their mechanical transmission counterparts. However, these PMs have low tensile strength and are prone to failure under large centrifugal loads when rotating. Therefore, retaining sleeves are used to hold the PMs in compression to eliminate tensile stress and reduce failure risk. The magnets are also often held on a back iron or carrier, forming an assembly of three cylinders. The ability to predict these stresses is extremely important to rotor design. Current published work shows a lack of exploration of analytical methods of calculating these stresses for three-cylinder assemblies. This paper shows the development of plane stress, plane strain and generalised plane strain (GPS) theories for three cylinders. For a range of rotor designs, these theories are compared with finite element analysis (FEA). GPS is shown to be more accurate than plane stress or plane strain for the central region of long cylinders. For short cylinders and for the ends of cylinders, all three theories give poor results.

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