1. 9. Methods of Determining Work Hardening Characteristics
ME 612 Metal Forming and Theory of Plasticity
9. Methods of Determining Work Hardening Characteristics
Assoc.Prof.Dr. Ahmet Zafer Şenalp
Mechanical Engineering Department
Gebze Technical University

2. Mechanical Engineering Department, GTU
9. Methods of Determining
Work Hardening Characteristics
It is necessary to make experiments in order to determine the work hardening characteristics of materials. The type of experiment should be determined by considering the actual size of the material in operation and the type of the operation. In this section some experiments and related formulations are presented.
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

3. 9.1. Simple Tension Test 9. Methods of Determining
Work Hardening Characteristics
Simple tension test was described in chapter 2.
Here assumptions about simple tension test are given and as a result equivalent stress and equivalent strain terms are expressed in terms of parameters along the tension direction.
Figure 9.1. Directions in simple tension test
As shown in figure 9.1 tension direction is defined as direction 1. These directions are at the same time principal directions.
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

4. 9.1. Simple Tension Test 9. Methods of Determining
Work Hardening Characteristics
Figure 9.2. Load-extension and true stress-true strain diagrams
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

5. Mechanical Engineering Department, GTU
9.1. Simple Tension Test
9. Methods of Determining
Work Hardening Characteristics
At first step stress and strain states in tension test should be determined:
(9.1)
(9.2)
(9.3)
(9.4)
(9.5)
(9.6)
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

6. Mechanical Engineering Department, GTU
9.1. Simple Tension Test
9. Methods of Determining
Work Hardening Characteristics
Then using Levy-Mises equations stress and strain should be related: If Eq (9.2) and (9.3) are placed in Levy-Mises equations:
(9.7)
(9.6)
(9.9)
(9.10)
(9.11)
(9.12)
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

7. Mechanical Engineering Department, GTU
9.1. Simple Tension Test
9. Methods of Determining
Work Hardening Characteristics
From here: is obtained. The above equalities are placed in the equivalent stress equation: As a result: is obtained.
(9.13)
(9.14)
(9.15)
(9.18)
(9.19)
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

8. Mechanical Engineering Department, GTU
9.1. Simple Tension Test
9. Methods of Determining
Work Hardening Characteristics
To find equivalent strain the above equalities are placed into the equivalent strain equation: As a result: is obtained. Using the above equalities statement is reached. From constancy of volume: And from here; is obtained.
(9.20)
(9.21)
(9.22)
(9.23)
(9.24)
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

9. Mechanical Engineering Department, GTU
9.1. Simple Tension Test
9. Methods of Determining
Work Hardening Characteristics
Hence by using the above equations İs obtained. The results obtained in the above equations show that for tension test equivalent stress is equal to the stress in tension direction and equivalent strain is equal to the strain in tension direction. By using the data obtained in the test equivalent stress equivalent strain diagram should be plotted. By using this drawn diagram and operation conditions one of the work hardening models described in chapter 3 should be selected and by using the method described in chapter 3.9. the parameters of the work hardening law should be determined.
(9.25)
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

10. Mechanical Engineering Department, GTU
9.2. Direct CompressionTest
9. Methods of Determining
Work Hardening Characteristics
In spite of the fact that in most forming applications there are compresive forces direct compression test is not widely used as tension test. Barrelling (Figure 9.3) due to friction and interactions of compression surfaces makes the calculations about compression operation difficult. Thus stresses and strains are not uniform. In this test the load is applied to a right circular specimen of original height and diameter of h0 and d0 respectively, the height beccomes smaller and the area larger. Streess and strain terms at any point: This method is first worked by Cook and Larke and then developped by Watts and Ford. This test is good for obtaining stress and strain datas.
(9.26)
(9.27)
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

11. Mechanical Engineering Department, GTU
9.2. Direct CompressionTest
9. Methods of Determining
Work Hardening Characteristics
In this method workpieces with equal diameter but different heights are used. The rule for diameter and height is;
Figure 9.3. Direct compression showing the formation of dead-metal zones and barrelling
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

12. Mechanical Engineering Department, GTU
9.2. Direct CompressionTest
9. Methods of Determining
Work Hardening Characteristics
The test procedure is:
Cylinders have equal diameter but different heights.
The ends of the parts are lubricated.
Load is applied up to certain level.
Load is removed and height is measured.
The things mentioned above are applied again with increasing load.
Reduction of height at certain load (r) is plotted against for each workpiece.
Line passing through points are elongated until In figure 9.4. the experiment results of this kind is given. Horizontal axis is used for r which is the reduction of height. The relation between strain and r is:
By using certain amount of points equivalent stress equivalent strain graph is plotted ( ) .
(9.28)
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

13. Mechanical Engineering Department, GTU
9.2. Direct CompressionTest
9. Methods of Determining
Work Hardening Characteristics
Figure 9.4. Watt and Ford method to correct for the end effects in compressive loading.
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

14. Mechanical Engineering Department, GTU
9.2. Direct CompressionTest
9. Methods of Determining
Work Hardening Characteristics
In most of the metals tensile and compressive equivalent stress equivalent strain curves are practically the same. If they are not the same then there is Baushinger effect. In compressive operations higher strains are obtained.
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

15. 9.3. Plane Strain Compression Test
9. Methods of Determining
Work Hardening Characteristics
This test is applied to relatively thin materails (plate). Special dies are used. Schematic views of dies used and directions choosen are given in Figure 9.5. To apply this test and conditions (plane strain) should be satisfied.
Figure 9.5. Details of plane strain comppression test
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

16. Mechanical Engineering Department, GTU
9.3. Plane Strain Compression Test
9. Methods of Determining
Work Hardening Characteristics
At first step stress and strain state should be determined: Using constancy of volume is obtained.
(9.29)
(assumed for narrow dies)
(9.30)
(9.31)
( plane strain assumption)
(9.32)
(9.33)
(9.34)
(9.35)
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

17. Mechanical Engineering Department, GTU
9.3. Plane Strain Compression Test
9. Methods of Determining
Work Hardening Characteristics
Then using Levy-Mises equations stress and strain should be related: Eq (9.30) is placed in Levy-Mises equations: is obtained.
(9.36)
(9.37)
(9.38)
(9.39)
(9.40)
(9.41)
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

18. Mechanical Engineering Department, GTU
9.3. Plane Strain Compression Test
9. Methods of Determining
Work Hardening Characteristics
From Eq (9.37) is obtained. The value obtained in Eq (9.42) is placed into (9.39) and (9.40) and then: is obtained. Eq (9.30) and (9.42) are placed into equivalent stress equation: As a result: is obtained.
(9.42)
(9.43)
(9.44)
(9.45)
(9.46)
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

19. Mechanical Engineering Department, GTU
9.3. Plane Strain Compression Test
9. Methods of Determining
Work Hardening Characteristics
To find equivalent strain Eq (9.32) and (9.44) are placed into equivalent strain equation: As a result: is obtained. Using Eq (9.29) and (9.46): is obtained. Using Eq (9.31) and (9.48) is obtained.
(9.47)
(9.48)
(9.49)
(9.50)
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

20. Mechanical Engineering Department, GTU
9.3. Plane Strain Compression Test
9. Methods of Determining
Work Hardening Characteristics
The results obtained from above equations relate equivalent stress and equivalent strain values to the parameters in compression direction. By using the data obtained in the test equivalent stress equivalent strain diagram should be plotted. By using this drawn diagram and operation conditions one of the work hardening models described in chapter 3 should be selected and by using the method described in chapter 3.9. the parameters of the work hardening law should be determined.
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

21. Mechanical Engineering Department, GTU
9.4. TorsionTest
9. Methods of Determining
Work Hardening Characteristics
Although not as widely used as the previous methods, torsion of thin-walled tubes and solid bars has been studied in connection with work-hardening behavior. We include this short qualitative discussion for completeness. The general approach is to convert torque-angular twist data into shear stress-shear strain data. Then using pertinent assumptions, the equivalence with s -e curve follows. Detailed discussions on procedures may be found in reference [1]. Torsional studies do find use in certain hot-working operations where very high strains may be induced. For determining strain-hardening behavior caused by cold working, the tensile test is the simplest to conduct, and for that reason has found the widest application.
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

22. Mechanical Engineering Department, GTU
9.5. Hydrolic Bulging Test
9. Methods of Determining
Work Hardening Characteristics
In the bulge test, a thin disc of sheet metal is clamped around its periphery and then subjected to an increasing fluid pressure applied to one side as shown in Fig 9.6, As the sheet bulges, the region in the vicinity of the dome becomes nearly spherical in shape.
Figure 9.6. Schematic of a bulge test showing equivalent stress states.
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

23. Mechanical Engineering Department, GTU
9.5. Hydrolic Bulging Test
9. Methods of Determining
Work Hardening Characteristics
At first step stess and strain states should be determined: If Eq (9.51) and (9.52) is placed in Levy-Mises equations:
(9.51)
(9.52)
(9.53)
(9.54)
(9.55)
(9.56)
(9.57)
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

24. Mechanical Engineering Department, GTU
9.5. Hydrolic Bulging Test
9. Methods of Determining
Work Hardening Characteristics
is obtained. From above equations is obtained. Equations (9.51) and (9.52) are placed into equivalent stress equation: As a result: is obtained. To find equivalent strain Eq (9.58) is placed into the equivalent strain equation: is obtained.
(9.58)
(9.59)
(9.60)
(9.61)
(9.62)
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU

25. Mechanical Engineering Department, GTU
9.5. Hydrolic Bulging Test
9. Methods of Determining
Work Hardening Characteristics
Using Eq (9.51) and (9.60) : term is obtained. Using Eq (9.53) and (9.62) is obtained. Eqivalent stress and equivalent strain are calculated from datas obtained from the test. Then eqivalent stress versus equivalent strain diagram is plotted.
(9.63)
(9.64)
Dr. Ahmet Zafer Şenalp ME 612
Mechanical Engineering Department, GTU