4. Poor surface finish and loss of precise gauge control result from the lack of adequate lubrication, oxide scales, and roughened tools.
5. The lack of work hardening is undesirable where the strength level of a cold-worked product is needed.
Because of these limitations, it is common to hot roll steel to about 0.10-in thickness to take advantage of the decreased flow stress at high temperature. The hot-rolled product is then pickled to remove scale, and further rolling is done cold to ensure good surface finish and optimum mechanical properties.
5.9 TEMPERATURE RISE DURING DEFORMATION
The temperature of the metal rises during plastic deformation because of the heat generated by mechanical work. The mechanical energy per volume, w, expended in deformation is equal to the area under the stress–strain curve:
w= ¯ε
0
σ¯d¯ε. (5.23)
Only a small fraction of this energy is stored (principally as dislocations and vacancies). This fraction drops from about 5% initially to 1 or 2% at high strains.
The rest is released as heat. If the deformation is adiabatic (no heat transfer to the surroundings) the temperature rise is given by
T = α σ¯d¯ε
ρC = ασ¯aε¯
ρC , (5.24)
where ¯σais the average value ofσ over the strain interval 0 toε,ρis the density,Cis the mass heat capacity, andαis the fraction of energy stored as heat (∼0.98).
EXAMPLE 5.1: Calculate the temperature rise in a high-strength steel that is adiabat- ically deformed to a strain of 1.0. Pertinent data areρ=7.87×103 kg/m3,σa=800 MPa,C=0.46×103J/kg◦C.
SOLUTION: Substituting in equation5.24and takingα=1, T = 800×106×1.0
7.87×103×0.46×103 =221◦C.
Although bothσaandεwere high in this example, it illustrates the possibility of large temperature rises during plastic deformation. Any temperature increase causes the flow stress to drop. One effect is that at low strain rates, where heat can be transferred to surroundings, there is less thermal softening than at high strain rates. This partially compensates for the strain-rate effect on flow stress and can lead to an apparent decrease in the strain-rate sensitivity at high strains, whenmis derived by comparing continuous stress–strain curves.
Another effect of the thermal softening is that it can act to localize flow in nar- row bands. If one region or band deforms more than another, the greater heating may lower the flow stress in this region, causing even more concentration of flow and more local heating in this region. An example of this is shown in Figure 5.27,
5.27.Flow pattern and microstructure of a bolt head of quenched and tempered 8640 steel after cold upsetting at a high velocity. The light bands of untempered martensite show a higher hardness, as indicated by the Knoop indentations at the right. From F. W. Boulger,op. cit.
where in the upsetting of a steel bolt head, localized flow along narrow bands raised the temperature sufficiently to cause the bands to transform to austenite. After the deformation, these bands were quenched to martensite by the surrounding material.
Similar localized heating, reported in punching holes in armor plate, can lead to sudden drops in the punching force. Such extreme localization is encouraged by conditions of high flow stresses and strains which increases T, low rates of work hardening and work-piece tool geometry that encourages deformation along certain discrete planes.
NOTES OF INTEREST
Svante August Arrhenius (1859–1927) was a Swedish physical chemist. He stud- ied at Uppsala where he obtained his doctorate in 1884. It is noteworthy that his thesis on electrolytes was given a fourth (lowest) level pass because his commit- tee was skeptical of its validity. From 1886 to 1890 he worked with several noted scientists in Germany who did appreciate his work. In 1887, he suggested that a very wide range of rate processes follow what is now known as the Arrhenius equa- tion. For years his work was recognized throughout the world, except in his native Sweden.
Count Rumford (Benjamin Thompson) was the first person to measure the mechan- ical equivalent of heat. He was born in Woburn, Massachusetts in 1753, studied at Harvard. At the outbreak of the American Revolution, after been denied a commission by Washington, he was commissioned by the British. When the British evacuated Boston in 1776, he left for England, where he made a number of experiments on heat.
After being suspected of selling British naval secrets to the French, he went to Bavaria.
In the Bavarian army he eventually became Minister of War and eventually Prime Minister. While inspecting a canon factory, he observed a large increase in temperature during the machining of bronze canons. He measured the temperature rise and, with the known heat capacity of the bronze, he calculated the heat generated by machining.
By equating this to the mechanical work done in machining, he was able to deduce the mechanical equivalent of heat.
PROBLEMS 73
REFERENCES
W. A. Backofen,Deformation Processing, Addison-Wesley, 1972.
W. F. Hosford,Mechanical Behavior of Materials, Cambridge University Press, 2005.
PROBLEMS
5.1. Low-carbon steel is being replaced by HSLA steels in automobiles to save weight because the higher strengths of HSLA steels permit use of thinner gauges. In laboratory tests at a strain rate of about 10−3s−1, one grade of HSLA steel has a yield strength of 420 MPa with a strain-rate exponentm=0.005, while for a low-carbon steel,Y=240 MPa andm=0.015. Calculate the percent weight saving possible for the same panel strength assuming
a) a strain rate of 10−3s−1,
b) crash conditions with a strain rate of 10+4s−1.
5.2. The thickness of a sheet varies from 8.00 mm to 8.01 mm depending on location so tensile specimens cut from a sheet have different thicknesses.
a) For a material withn=0.15 andm=0, what will be the strain in the thicker region when the thinner region necks?
b) Ifn=0 andm=0.05, find the strain in the thicker region when the strain in the thinner region is 0.5 and∞.
5.3. a) Find the % elongation in the diagonal ligaments in Figure5.5, assuming that the ligaments make an angle of 75◦with the horizontal.
b) Assuming that f = 0.98 and n = 0, what value of m is required for the variation of thickness along the ligaments be held to 20%? (The thickness of the thinnest region is 0.80 times the thickness of the thickest region.) 5.4. Find the value of min equation5.12that best fits the data in Figure5.28.
200 400 600 800
MPa
0.05
0.04
0.03
0.02
0.01
00
Strain rate exponent, m
40 80 120
Static flow stress, ksi
5.28.Effect of stress level on the strain-rate sensitivity of steel. Adapted from A. Saxena and D. A. Chatfield,SAE Paper 760209(1976).
5.5. From the data in Figure5.23, estimateQin equation5.15andmin equation5.1 for aluminum at 400◦C.
5.6. Estimate the total elongation in a tensile bar if a) f=0.98,m=0.5, andn=0
b) f=0.75,m=0.8, andn=0.
5.7. Estimate the shear strain necessary in the shear bands of Figure5.27necessary to explain the formation of untempered martensite if the tensile strength level was 1.75 GPa,n=0, and adiabatic conditions prevailed.
5.8. During superplastic forming it is often necessary to maintain a constant strain rate.
a) Describe qualitatively how the gas pressure should be varied to form a hemispherical dome by bulging a sheet clamped over a circular hole with gas pressure.
b) Compare the gas pressure required to form a hemispherical dome of 5 cm diameter with the pressure for a 0.5-m diameter dome.
5.9. a) During a creep experiment under constant stress, the strain rate was found to double when the temperature was suddenly increases from 290◦C to 300◦C.
What is the apparent activation energy for creep?
b) The stress level in a tension test increased by 1.8% when the strain rate was increased by a factor of 8. Find the value ofm.
5.10. Figure5.29gives data for high-temperature creep ofα-zirconium. In this range of temperatures, the strain rate is independent of strain.
a) Determine the value ofmthat best describes the data at 780◦C.
10 12 14 16 18 20
10−2
10−3
10−4
10−5
10−6
Strain rate, sec−1
Stress, MPa
810°C 780°C 700°C
5.29.Strain rate vs. stress forα-zirconium at several temperatures.
PROBLEMS 75
b) Determine the activation energyQin the temperature range 700◦C to 810◦C at about 14 MPa.
5.11. Tension tests were made in two different labs on two different materials. In both the strain hardening exponent was found to be 0.20, but the post-uniform elongations were quite different. Offer two plausible explanations.
6 Work Balance
This chapter introduces the work or energy balance, which is a very simple method of estimating the forces and energy involved in some metal forming operations. It does not, however, permit predictions of the resulting properties. The energy to complete an operation can be divided into the ideal work,wi, that would be required for the shape change in the absence of friction and inhomogeneous flow, the work against friction, wf, and the redundant work,wr.