Chapter 7: Strain-Rate and Temperature Dependence of

Flow Stress

Prof. Wenjea J. Tseng (曾文甲)Department of Materials Engineering

National Chung Hsing Universitywenjea@dragon.nchu.edu.tw

Reference: W. F. Hosford (Cambridge, 2010)

Mechanical Properties of Materials

OHP 1

Introduction• For most materials, an increase of strain rate raises flow

stress. The effect of strain rate to the flow stress is mostly negligible near room temperature (e.g., ca. only 1 or 2% increase), but becomes pronounced at elevated temperatures (e.g., becomes 10-50% increase in flow stress).

• Strain localization occurs in materials that have a high strain-rate dependence. For superplastic materials, tensile elongation can be as large as 1000% when coupling between strain rate and temperature can be fine tuned.

Strain-Rate Dependence of Flow Stress• The average strain rate during most tensile tests is in

the range of 10-3 to 10-2/s, which correspond to time of 30s to 5min to reach a strain of 0.3.

• When temperature is held constant, stress and strain rate relation can be described by a power-lawexpression,

where m is called the strain-rate sensitivity. Typical values of m at room temperature is given here.

mC

Strain-Rate Dependence of Flow Stress• The relative levels of stress at two strain rates

measured at the same total strain are given by

If 2 is not much greater than 1, i.e., is small, then

)/ln(/)/ln( 1212 m

m)/(/ 1212

Dependence of flow stress on strain rate for several values of the strain-rate sensitivity, m, at room temperature. The increase of flow stress, / is small unless either m or ratio is high.

12 /

Strain-Rate Dependence of Flow Stress• Example problems 7.1 and 7.2 (“old” text).

Experimental Determination of m• The strain-rate sensitivity, m, can be experimentally

determined. One method is to run two continuous tensile tests at different strain rates and compares the levels of stress at the same strain. The other way is to change the strain rate suddenly during a test and compare the levels of stress immediately before and after the change. The two methods may give somewhat different values of m.

Effect of Temperature on m• The increase of m with temperature is quite rapid

above half of the melting temperature (T Tm/2) on an absolute temperature scale.

Al alloy

Superplasticity• If the rate sensitivity, m, is 0.5 or higher, the material

will behave superplasticity, exhibiting very high tensile elongations. The high elongation occurs because the neck is extremely gradual. The conditions for superplasticity are(1) Temperatures equal to or above 0.5Tm

(2) Slow strain rates (typically 10-3/s or slower)(3) Very fine grain size (typically less than a few m)

Under superplastic condition, very high elongation (>1000%) is possible, allowing metal forming/forging into complex shapes and deep parts.

Both induce grain growth

Mostly are multi-phasic structures or with dispersion of insoluble particles.

Superplasticity Mechanisms• Two main mechanisms contributing to the

superplasticity. One is a net diffusional flux under stress of atoms from grain boundaries parallel to the tensile axis to grain boundaries normal to the tensile axis, causing a tensile elongation (i.e., diffusional creep). The other is grain boundary sliding. Accommodation of the triple junction of the grain structure needs to occur either by slip or by diffusion.

Superplasticity Mechanisms• For the creep model, creep occurs by diffusion

between grain boundaries. As atoms diffuse from lateral boundaries to boundaries normal to the tensile stress, the grain elongates and contracts laterally (since vacancies move at a direction counter to that of the atomic diffusion)

Atoms

Vacancies

Superplasticity Mechanisms• By observing the relative positions of grain centers as

grains deform, it is apparent that in order to accommodate the shape change without opening up voids at the grain junctions (i.e., causing cavitation) the grains must slide with respect to one another.

Strain-rate Sensitivity• There are two possible effects of strain rate on

stress-strain flow curves. On the left, the difference in flow stress, , is proportional to . On the right, is independent of

Strain-rate Sensitivity for FCC and BCC metals

• The underlying figures show stress-strain flow curves for copper (FCC) and iron (BCC) metals at 25oC.

Copper Iron

= f() f()

Summary• When temperature is held constant, stress and strain rate

relation can be described by a power-law expression

where m is called the strain-rate sensitivity.• The relative levels of stress at two strain rates measured

at the same total strain are given by

m)/(/ 1212

mC