In metal forming, particularly in hot forming many metallurgical processes may take place concurrently. These include strain hardening, recovery, re-crystallization, etc. All these factors affect the yield strength. Therefore, it is important to know the extent of effect of each of these factors.
The yield strength of a metal or alloy is affected by following factors:
(i) Strain hardening.
(ii) Strain rate.
(iii) Temperature of metal and microstructure.
(iv) Hydrostatic pressure.
To understand the effect of strain hardening let us again consider the tension test curve shown below in Fig. 1.9.
In this figure the test piece is loaded beyond the yield point up to a point P. The test piece is then unloaded. The elastic deformation recovers via the unloading curve PR which is more or less parallel to AO. It is generally taken that there is no change in Young’s modulus during plastic deformation. The line PR depicts elastic recovery. Out of the total strain OS corresponding to the point P, the part RS is the elastic recovery. The part OR which is not recovered is the plastic strain suffered by the test specimen.
Now if we reload the same test piece, it nearly follows the line RP. There is, however, some deviation due to hysteresis which is very small, and the yielding now occurs at the point P. Further loading of the test piece beyond P gives the same stress-strain curve as we would have obtained if there were no unloading. This shows that after suffering a plastic strain represented by OR, the yield strength of metal has increased from point B to point P (or σo1 to σo2). This is called strain hardening or work hardening.
Now consider another experiment for which the test curve is shown in Fig. 1.10. In this test, the specimen has been loaded in tension up to a point P beyond the yield point B (yield strength = σot), then unloaded to point R and again loaded in reverse direction, i.e. compressed.
In compression the test piece yields at the point Q where yield strength is equal to σoc which is smaller in magnitude than σot. This shows that the yield strength in compression has decreased due to the previous plastic strain in tension. Similarly the yield strength in tension would decrease with previous compressive plastic strain. This is known as Bauschinger Effect (BE).
In fact due to plastic strain the material develops anisotropy. Its properties are no longer the same in different directions. Bauschinger Effect (BE) is observed in many metals and alloys.
BE may be reduced by thermal treatment. Complete removal is possible only by re- crystallization of strained material. However, it may be reduced by stress aging which is a process of heating the material to a certain temperature while it is subjected to suitable value of stress. By this process BE may be reduced at a low temperatures (less than 200°C).
For the sake of simplification in analysis it is taken that there are two factors in strain hardening. One is isotropic strain hardening, in which the strain hardening effect is same in all directions, i.e. yield strength increases equally in all the directions.
The second is kinematic strain hardening in which the yield strength does not increase in magnitude but whole of the yield diagram shifts in the direction of plastic strain thus showing Bauschinger effect. Metals exhibit both these effects together, however, for sake of simplicity isotropic strain hardening is generally adapted in various analyses of metal forming problems.
Some expressions developed for the flow stress (σf) by different researchers are as follows:
where σ0, B, n and C are material parameters. The ‘n’ is called strain hardening index or exponent, ԑ is true strain. Equations (1.6a to 1.6c) are generally used for small strains, while Eqn. (1.6d) is used for large strains for alloys which show a decreasing rate of work hardening or exhibit work hardening saturation.
One of the methods to determine n for Eqn. (1.6a) is given below. Let V be the volume, a the area of cross section and l the length of the specimen, then
Equation (1.9) gives a method of determining the exponent n. Even for other strain hardening rules there is close relationship between n and ԑu. The data obtained by Narayanasamy and Sowerby on three steels, shows that n is nearly equal to the true strain at maximum strength. According to them these steel conform to hardening law σf = K (ԑ0 + ԑ)n.
Determine the percent increase in yield strength of annealed aluminum bar if it is elongated from 200 mm to 250 mm.
The yield strength of annealed aluminum is given by,
You-Min Huang et al., have given the following data for low carbon steel, copper and aluminum.
A cylindrical test specimen of diameter 10 mm and gauge length 50 mm is extended to 65 mm. determine the true strain. Neglect the elastic deformation. If the ultimate strength occurs at a force of 25000 N and at an extension of 70 mm, determine the strain hardening exponent n and ultimate strength of the material.
Work Done During Plastic Deformation:
Let a bar of area of cross-section ‘a’ and length ‘l0’ be elongated to length l. The work (W) done during elongation is given by
For the other strain hardening laws discussed above, the expressions for work done may be obtained similarly. Thus if the strain hardening law is σf = A (B + C ԑ)n the amount of work done for plastic strain 0 to ԑ becomes
The yield strength of brass is given by σf = 300 (1 + 15 ԑ)0.3 MPa. A bar of this material having area of cross-section 200 mm2 and length 200 mm is extended to 250 mm. Determine the value of the yield strength of the material of bar after extension. Also determine the work done during the elongation.
Another factor that increases load on forming equipment is the rate at which the forming process is carried out. At higher rates of strain the flow stress of material increases leading to higher loads on the equipment. The effect of strain rate on yield strength for an alloy is illustrated in Fig. 1.11.
The factors described above influence the forming processes to varying degrees depending upon the temperatures at which the processes are carried out. If a forming process is carried out at a temperature less than the re-crystallization temperature and at a slow rate, such a case may be taken as an isothermal process, i.e. the effect of temperature change during the process may be neglected and we may consider only the effect of strain hardening.
When a forming process is carried out in hot state the re-crystallization is also present along with strain hardening and strain rate effect. The strain hardening may be nullified by re- crystallization. Therefore, in hot working we may only consider the effect of temperature and strain rate on the yield strength of metal. The effect of strain rate may be written as given below-
Where σf is the flow stress, ԑ̇ is the plastic strain rate, m and σ0 are material parameters. Since the effects of strain rate and strain hardening may vary at different temperatures, this presents a major problem of testing each metal and alloy at different temperatures, at different strain rates and to different extents of strain. The problem of testing becomes more difficult because most of the work done on the metal body for plastic deformation reappears as heat and raises the temperature of the test specimen.
At low strain rates the flow stress increases with increase in strain rate. At higher strain rates it still increases but at a slower rate because of the softening effect due to temperature rise in the material. Stout and Follanshee have determined the following expression for strain rate sensitivity in stainless steel 304L at strain rates of the order of 103 s-1 and above.
Factor # 3. Effect of Temperature:
Recovery and Re-Crystallization:
Figure 1.12(a) shows initial structure of an under formed metal piece. Figure 1.12(b) shows the structure after it has been compressed along its height. The grains get elongated in the direction normal to the direction of applied force, i.e. in the lateral direction. The material gets strain hardened, i.e. its yield strength, UTM and hardness increase while ductility decreases.
The strain hardening occurs because the dislocation density increases due to cold deformation. With increase in temperature the movement of dislocations gets easier and they readjust due to stresses locked in the lattice. Some dislocations having opposite sign may annihilate each other. This is called recovery process in which the residual stresses are reduced, however, the enhanced properties due to cold working are only little affected.
Now if the compressed metal piece is heated to certain higher temperature (0.4 to 0.6. Tmelt), new grains will start emerging at the boundaries of old grains and at sites of other defects. If this temperature is maintained for some time the new grains will grow to cover the entire structure. This is called primary re-crystallization.
Re-crystallization removes the strain hardening effect and hence reduces strength but increases ductility. However, the process does not stop there. Some grains start growing at the expense of other grains till the complete structure is covered by bigger grains. This is called secondary re-crystallization and grain growth.
The mechanical properties like yield strength depend upon the grain size. The relationship between grain size and flow stress is given by the Hall-Petch formula (Eqn. 1.14).
σf = σ0 + λ d-1/2 ……… (1.14)
Where σf is the flow stress of material, d is the average grain size and σ0 and λ are material parameters. The parameters σ0 and λ are not absolute constants but are functions of strain, strain rate and temperature.
During hot working the processes of strain hardening and subsequent stress relieving/ recovery and re-crystallization may occur depending upon the temperature and strain. It has been found that in ferrous alloys at 780°C a three stage softening may take place after hot deformation to a certain minimum true strain which may vary between 0.08 to 0.15.
Several attempts have been made to determine single expression for yield strength, which includes the effect of strain, strain rate, temperature, grain size and re-crystallization. Bonnavand, Bramley and Mynores have employed the following formulation for the effect of these factors for calculations related to backward extrusion process.
where K is material constant in stress units, ԑ = equivalent strain, n = strain hardening exponent, m = strain-rate-effect exponent, T = temperature (Kelvin) and β = material parameter. Values of these parameters for some metals are given in Table 1.4.
Metal forming processes may be carried out in hot as well as in cold state. Temperature of re-crystallization is the boundary between the two.
Hot Forming or Hot Working:
It is defined as forming at temperatures above the re-crystallization temperature of the metal. In fact the actual temperatures are much higher than the re- crystallization temperature. High temperatures reduce the flow stress of metals, which results in low deforming forces.
Cold Forming or Cold Working:
It refers to forming at temperatures below the re-crystallization temperature of the metal. The strain hardening during the process improves the mechanical properties of the product. Also close dimensional tolerances can be obtained in cold forming.
(i) At high temperatures, the metals become soft, its yield strength decreases (Fig. 1.13) and hence low forces are required for forming. This reduces the cost of equipment needed for the process.
(ii) Metals are more ductile at higher temperatures and their formability in hot state is higher than in cold state. Therefore, large deformations may be given in hot working.
(iii) The casting defects in ingots like internal shrinkage cavities (not those in contact with atmosphere) and blow holes get welded during hot working. The structure becomes more homogeneous resulting in better mechanical properties.
(iv) Due to low flow stresses at high temperatures, very large components may be made by plastic deformation.
(i) The products have low surface quality due to oxidation of surface layer.
(ii) The components formed have low dimensional accuracy.
(iii) There is little improvement in mechanical properties.
(iv) The forming tools also get heated up due to contact with hot metal and wear of tools is rapid.
(i) Good surface finish of the product.
(ii) High dimensional accuracy.
(iii) Superior mechanical properties, e.g. hardness and strength increase due to strain hardening.
(iv) Strain hardening may eliminate the surface hardening heat treatment required in some components such as cold rolled gears.
(v) The material develops anisotropy which may be used to advantage in subsequent forming processes. For instance, the anisotropy developed in cold rolled sheet metal helps in getting deeper draws.
(i) High loads on the equipment require it to have high strength and rigidity. This increases the cost of machines.
(ii) With strain hardening the material becomes less ductile.
Of recent, ‘warm forming’ has come to be used in order to gain the advantages of hot as well as cold forming, though to a lesser extent. Warm forming is carried out at a temperature higher than room temperature but lower than the re-crystallization temperature.
Since yield strength decreases with increase in temperature, the load on the equipment in warm forming is lower than in cold forming. Also the temperatures are not that high that the surface layer damage can occur. Therefore, the advantages of cold forming are achieved, that is, better surface quality, better dimensional accuracy and better mechanical properties than in hot forming.
Because of reduced forces, the tools wear is less and the equipment is also less expensive. Temperatures for warm forming should be chosen such that the ductility of metal is high at that temperature.
In a forming process, metal blank has to come in contact with dies or tools which are generally massive compared to the metal blank being processed and hence there is considerable heat transfer from work piece to the tools in hot forming. This makes the temperature of metal blank itself non-uniform, i.e. reduces temperatures near contact zones.
The testing also becomes more complicated because of phase changes in metals and alloys due to temperature and strain. It is difficult to have a clear cut relationship between yield strength, temperature, strain and strain rate because of complex behavior of metals, however, there are quite a few attempts to empirically describe the yield strength of certain metals as a function of these variables in specific temperature ranges.
Hydrostatic pressure may affect the following properties of metals and hence their formability:
(ii) Yield strength or flow stress.
(iii) Strain hardening index and strain rate index.
Experiments of Bridgeman have shown that hydrostatic pressure does not lead to plastic deformation. However, hydrostatic pressure increases the ductility and formability of metals and alloys. The phenomenon of increased ductility with hydrostatic pressure is also called pressure induced ductility.
Even brittle materials may be plastically deformed under suitable hydrostatic pressures. Materials in which the plastic deformation leads to change in volume, the yield strength may be affected by hydrostatic pressure. Spitzig et al. have shown that yield strength of quenched and tempered AISI 4310 and 4330 steels is affected by hydrostatic pressure.
Figure 1.14 shows the effect of hydrostatic pressure on the yield strength of 4330 steel. Both the steels show increase in volume during plastic deformation as well as increase in yield strength under hydrostatic pressure. Very few researchers have attempted to determine the effect of hydrostatic pressure on strain hardening and strain rate effect indices. According to Spitzig et al., there is no effect of hydrostatic pressure on the strain hardening index (n).
These steel also show a constant difference in the values of yield strength in tension and in compression. The yield strength in compression is higher than that in tension and the difference between the two yield strengths is not affected by hydrostatic pressure.