13. The Ideal Work Method for the Analysis of Forming Processes ME 612 Metal Forming and Theory of Plasticity 13. The Ideal Work Method for the Analysis of Forming Processes Assoc.Prof.Dr. Ahmet Zafer Şenalp e-mail: azsenalp@gmail.com Mechanical Engineering Department Gebze Technical University

Mechanical Engineering Department, GTU 13. The Ideal Work Method for the Analysis of Forming Processes In general the prediction of external forces needed to cause metal flow is needed. Such prediction is difficult due to uncertainties introduced from frictional effects and non-homogeneous deformation as well as from not knowing the true manner of strain hardening. Each solution method is based on several assumptions. The easiest method is the ideal work method. The work required for deforming the workpiece is equated to the external work. The process is considered ideal in the sense that the external work is completely utilized to cause deformation only. Friction and non-homogeneous deformation are neglected. Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.1. Axisymmetric Extrusion and Drawing 13. The Ideal Work Method for the Analysis of Forming Processes Figure 13.1 Illustration of direct or forward extrusion assuming ideal deformation. Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.1. Axisymmetric Extrusion and Drawing 13. The Ideal Work Method for the Analysis of Forming Processes Let us consider axisymmetric extrusion (Fig 13.1) where the diametral area is reduced from A0 to Af . The ideal work is Here and r is the percent area reduction: The final axial strain is usually called the homogeneous strain and denoted as Assuming we finally can write: (13.1) (13.2) Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.1. Axisymmetric Extrusion and Drawing 13. The Ideal Work Method for the Analysis of Forming Processes Note that if there is no hardening (n = 0 and ), The external work (actual work) applied; or per unit volume: Where Pe is the applied extrusion pressure. For an ideal process: In reality: (13.3) (13.4) (13.5) (13.6) Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

13.1. Axisymmetric Extrusion and Drawing 13. The Ideal Work Method for the Analysis of Forming Processes Similar results can be obtained for rod or wire drawing (Figure 13.2). The external work/volume in drawing is and so in general we have: Where is the applied drawing stress. (13.7) Figure 13.2. Illustration of rod or wire drawing. Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.2. Friction, Redundant Work and Efficiency 13. The Ideal Work Method for the Analysis of Forming Processes The actual work: and are usually combined. We define the mechanical efficiency as follows: The efficiency is a function of the die, lubrication, reduction rate, etc; , Usually (13.8) Figure 13.3. Comparison of ideal and actual deformation to illustrate the meaning of redundant deformation. Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.2. Friction, Redundant Work and Efficiency 13. The Ideal Work Method for the Analysis of Forming Processes Generalizing the formulas given above for the extrusion pressure and drawing stress, we can write the following: (13.9) (13.10) Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.2. Friction, Redundant Work and Efficiency 13. The Ideal Work Method for the Analysis of Forming Processes Figure 13.4. The stress-strain behavior is depicted in (c), the metal obeying is to be considered as the true stress needed to reduce to ( is the corresponding true strain). Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU Example: 13. The Ideal Work Method for the Analysis of Forming Processes As shown in Fig 13.4.(a) A round rod of initial diameter, can be reduced to diameter by pulling through a conical die with a necessary load, as shown in sketch 13.4(a). A similar result can occur by applying a uniaxial tensile load, as shown in sketch 13.4(b). Using the ideal-work method for both the drawing and tensile operations, compare the load Fd with the load F1 (or the “drawing stress” with the tensile stress ) needed to produce equivalent reductions. For drawing we showed that: For tension: From the two equations above: (13.11) (13.12) (13.13) Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU Example: 13. The Ideal Work Method for the Analysis of Forming Processes But, (strain at ultimate load – max strain to avoid necking). So finally: Also, Then, (13.14) (13.15) Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.3. Maximum Drawing Reduction in Axisymmetric Drawing 13. The Ideal Work Method for the Analysis of Forming Processes Figure 13.5. The tensile stress-strain curve and the drawing stress-strain behavior for two levels of deformation efficiency. The intersection points, , are the limit strains in drawing. Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.3. Maximum Drawing Reduction in Axisymmetric Drawing 13. The Ideal Work Method for the Analysis of Forming Processes With greater reduction the drawing stress; increases. Its value can’t be higher than the yield stress of the material at the exit. From the previous analysis The maximum possible value of is , where we denote as the final axial strain corresponding to maximum reduction. From the above equations From here with (13.16) (13.17) Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.3. Maximum Drawing Reduction in Axisymmetric Drawing 13. The Ideal Work Method for the Analysis of Forming Processes and maximum reduction per pass: For (perfect drawing) the maximum reduction is given as and for n=0 (perfectly plastic material – no hardening) we have that: (13.18) Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.3. Maximum Drawing Reduction in Axisymmetric Drawing 13. The Ideal Work Method for the Analysis of Forming Processes Figure 13.6. Influence of semi-die angle on the actual work; during drawing where the individual contributions of ideal , frictional, and redundant work are shown Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.3. Maximum Drawing Reduction in Axisymmetric Drawing 13. The Ideal Work Method for the Analysis of Forming Processes Figure 13.7. Effect of semi-die angle on drawing efficiency for various reductions; note the change in the optimal die angle, Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

13.4. Plane Strain Extrusion And Drawing 13. The Ideal Work Method for the Analysis of Forming Processes The calculations and previous definitions are applicable to plane strain problems with only minor modifications. The differences arise from the new form of the yield condition and the new expression for the equivalent strain. They are as follows: Yield condition: where Y.S. is the yield stress of the material at any location in the deformation zone. Figure 13.8. Plane strain drawing. Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.4. Plane Strain Extrusion And Drawing 13. The Ideal Work Method for the Analysis of Forming Processes Equivalent strain: The above changes will modify the final results as follows: Plane strain extrusion: Extrusion Pressure: where, with the homogeneous strain (13.19) Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.4. Plane Strain Extrusion And Drawing 13. The Ideal Work Method for the Analysis of Forming Processes For (rigid plastic material): For (power law hardening): Plane strain drawing: Drawing Stress: (13.20) Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.4. Plane Strain Extrusion And Drawing 13. The Ideal Work Method for the Analysis of Forming Processes where, with the homogeneous strain (x-strain) For (rigid plastic material): For (power law hardening): Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU

Mechanical Engineering Department, GTU 13.4. Plane Strain Extrusion And Drawing 13. The Ideal Work Method for the Analysis of Forming Processes For max reduction: from which we finally conclude that: Note that the max reduction is the same for both plane strain and axially symmetric problems. (yield stress at exit) (13.21) (13.22) Dr. Ahmet Zafer Şenalp ME 612 Mechanical Engineering Department, GTU