Calculate strength coefficient - true stress and true strain, Mechanical Engineering

Calculate strength coefficient:

A copper specimen of 64 mm gauge length and 12.80 mm dia. was tested in tension. Following two diameters were recorded in the plastic range of deformation.

Load = 25.75 kN, d1 = 12.176 mm

Load = 24.25 kN, d2 = 8.581 mm

Calculate strength coefficient and strain hardening exponent.

Solution

Original area of cross-section,

1685_Calculate strength coefficient.png

A0  = 128.6144 mm2

Area of cross-section at 25.75 kN

1046_Calculate strength coefficient1.png

A1  = 116.3802  mm2

Area of cross-section at 24.25 kn

825_Calculate strength coefficient2.png

A2  = 57.8023 mm2

∴          True stress at 25.75 kN,

1195_Calculate strength coefficient3.png

True stress at 24.25 kN,

792_Calculate strength coefficient4.png

Note from Eq. (1.15) true strain ε′ = ln A0

5_Calculate strength coefficient5.png

And

2236_Calculate strength coefficient6.png

Thus two pairs of values are obtained. Use these values of σ′ and ε′ in Eq. (1.15), i.e. ln σ′ = ln k + n ln ε′

∴          ln 221.25 = ln k + n ln 0.0999 and     

             ln 419.53 = ln k + n ln 0.7998

Subtract first equation from second

6.039 - 5.399 = n (- 0.2234) - n (- 2.3036)

i.e.       0.64 = 2.0802 n

or, n =   0.64 /2.0802= 0.3077 ------------ (i)

Using this value in one of above equations

5.399 = ln k + 0.3077 (- 2.3036)

∴          ln k = 5.399 + 0.7088 = 6.1078

k = 449.35 N/mm2       ---------------- (ii)

∴          True stress-true strain relationship for copper is

σ′ = 449.35 ε′0.3077 ------------(iii)

Posted Date: 1/23/2013 2:44:19 AM | Location : United States







Related Discussions:- Calculate strength coefficient - true stress and true strain, Assignment Help, Ask Question on Calculate strength coefficient - true stress and true strain, Get Answer, Expert's Help, Calculate strength coefficient - true stress and true strain Discussions

Write discussion on Calculate strength coefficient - true stress and true strain
Your posts are moderated
Related Questions
how to e solve motion of followers in simple harmonic motion. what is the angle thita?

Comparison of Disc and Drum type Brakes Drum Brake Disc Brake Drum brakes have cooling problem because the friction occurs at internal surfaces,

In case of welded vessels why is stress relieving in the form of post-weld treatment necessary? When a metal is welded together the point at which two surfaces are joined are s

Evaluate the stream function at point (2, 3) for a two dimensional flow given by U = 5x 3           v = - 15x 2 y Evaluate the velocity potential function for a two dimension




defference between rankine and cornot cycle

we have to design crane we did already with calculation remaining is process planning

ELECTRON BEAM WELDING In this process fusion is achieved by focusing a high power density beam of electrons on the area to be joined. Upon striking the metal, the kinetic ener