This article describes strainhardening exponent and strength coefficient, materials constants which are used in calculations for stressstrain behaviour in work hardening, and their application in some of the most commonly used formulas, such as Ludwig equation.
The flow curve of many metals in the region of uniform plastic deformation can be expressed by the simple power curve relation


(10) 
where n is the strainhardening exponent and K is the strength coefficient. A loglog plot of true stress and true strain up to maximum load will result in a straightline if Eq. (10) is satisfied by the data (Fig. 1).
The linear slope of this line is n and K is the true stress at e = 1.0 (corresponds to q = 0.63). The strainhardening exponent may have values from n = 0 (perfectly plastic solid) to n = 1 (elastic solid), see Fig. 2. For most metals n has values between 0.10 and 0.50, see Table 1.
It is important to note that the rate of strain hardening
ds /de, is not identical with the strainhardening exponent. From the definition of n
or

(11) 
Figure 2. Log/log plot of true stressstrain curve
Figure 3. Various forms of power curve
s=K*
e
^{n}
Table 1. Values for n and K for metals at room temperature
Metal

Condition

n

K, psi

0,05% C steel

Annealed

0,26

77000

SAE 4340 steel

Annealed

0,15

93000

0,60% C steel

Quenched and tempered 1000^{o}F

0,10

228000

0,60% C steel

Quenched and tempered 1300^{o}F

0,19

178000

Copper

Annealed

0,54

46400

70/30 brass

Annealed

0,49

130000

There is nothing basic about Eq. (10) and deviations from this relationship frequently are observed, often at low strains (10
^{3}) or high strains (
e»1,0).
One common type of deviation is for a loglog plot of Eq. (10) to result in two straight lines with different slopes. Sometimes data which do not plot according to Eq. (10) will yield a straight line according to the relationship

(12) 
Datsko has shown how
e_{0}, can be considered to be the amount of strain hardening that the material received prior to the tension test.
Another common variation on Eq. (10) is the Ludwig equation

(13) 
where
s_{0} is the yield stress
and K and n are the same constants as in Eq. (10). This equation may be
more satisfying than Eq. (10) since the latter implies that at zero true
strain the stress is zero.
Morrison has shown that
s_{0} can be obtained from the
intercept of the strainhardening point of the stressstrain curve and the elastic modulus line by
The truestresstruestrain curve of metals such as austenitic stainless steel, which deviate markedly from Eq. (10) at low strains, can be expressed by
where e
^{K} is approximately equal to the proportional limit and n1 is the slope of the deviation of stress from Eq. (10) plotted against
e. Still other expressions for the flow curve have been discussed in the literature.
The true strain term in Eqs.(10) to (13) properly should be the
plastic strain
e_{p}=
e_{total}
e_{E}=
e_{total}
s/E