How To Calculate True Stress

True Stress - True Strain Curve: Role Four

Abstract:

This article describes strain-hardening exponent and forcefulness coefficient, materials constants which are used in calculations for stress-strain behaviour in work hardening, and their application in some of the well-nigh commonly used formulas, such as Ludwig equation.

The catamenia curve of many metals in the region of uniform plastic deformation tin exist expressed by the simple power curve relation

(10)

where n is the strain-hardening exponent and Thou is the strength coefficient. A log-log plot of true stress and truthful strain up to maximum load will effect in a straight-line if Eq. (x) is satisfied past the data (Fig. 1).

The linear gradient of this line is n and Thousand is the true stress at

due east = ane.0 (corresponds to q = 0.63). The strain-hardening exponent may have values from n = 0 (perfectly plastic solid) to n = 1 (elastic solid), come across Fig. 2. For most metals n has values between 0.10 and 0.l, see Tabular array ane.

It is of import to note that the rate of strain hardening d

south /deastward, is not identical with the strain-hardening exponent. From the definition of northward

(11)

Figure 2. Log/log plot of truthful stress-strain curve

Figure 3. Various forms of power bend southward=One thousand* e ⁿ

Table ane. 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 one thousand^oF	0,ten	228000
0,sixty% C steel	Quenched and tempered 1300^oF	0,19	178000
Copper	Annealed	0,54	46400
70/xxx brass	Annealed	0,49	130000

There is nothing bones about Eq. (10) and deviations from this human relationship oft are observed, frequently at low strains (ten^-3) or loftier strains (

e»ane,0).

One mutual type of departure is for a log-log plot of Eq. (ten) to result in ii directly lines with different slopes. Sometimes data which practice not plot according to Eq. (10) will yield a directly line co-ordinate to the relationship

(12)

Datsko has shown how e ₀, can be considered to be the amount of strain hardening that the cloth received prior to the tension test.

Some other common variation on Eq. (10) is the Ludwig equation

(xiii)

where s ₀ is the yield stress and K and n are the same constants as in Eq. (10). This equation may be more than satisfying than Eq. (10) since the latter implies that at zip truthful strain the stress is zero.

Morrison has shown that

s ₀ tin be obtained from the intercept of the strain-hardening point of the stress-strain curve and the elastic modulus line past

The true-stress-truthful-strain curve of metals such equally austenitic stainless steel, which deviate markedly from Eq. (10) at depression strains, can be expressed by

where due east^Chiliad is approximately equal to the proportional limit and n1 is the slope of the difference of stress from Eq. (10) plotted against e. Notwithstanding other expressions for the menses curve have been discussed in the literature.

The truthful strain term in Eqs.(ten) to (13) properly should be the plastic strain

e _p= e _total- e _E= eastward _total- south/E

Date Published: Aug-2010

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