REVERSED STRESS & DESIGN:FINITE & INFINITE LIFE

STRESSES AND DESIGN ANALYSIS: HOW THE PROCESS OCCURS?????????

Reversed stresses : Those stresses which have same magnitude of stresses but in opposite sense (i.e σ_{1 =} -σ₂).

Here, σ_m=0 & σ_{v =} σ₁ or σ₂

Fluctuating stresses : Those stresses which have different magnitude of stresses and also induces in a specific direction.

σ_m= σ₁ +σ₂/2 & σ_{v =} σ₁ – σ₂/2 where , σ₁= maximum stress σ₂= minimum stress

In fatigue design , we deal with two types are problems:

1) Components subjected to completely reversed stresses

2) Components subjected to fluctuating loading stresses

For reversed stresses ,since the Mean stress value is zero.

Therefore tensile stresses occupy the first half and Compressive stresses occupy the second half of the stress distribution.

Whereas, for fluctuating loading stresses, there comes a definite non zero mean stress value.

Therefore, the stresses here can be purely tensile, purely compressive or Mix of both tensile and compressive.

DESIGN STRATEGY FOR REVERSED STRESS PROBLEMS:

For designing a component subjected to completely reversed stresses, there are further 2 sub conditions under which study is done.

1) DESIGN FOR INFINITE LIFE

2) DESIGN FOR FINITE LIFE

DESIGN FOR INFINITE LIFE

When a component has to be designed for infinite life, the ENDURANCE LIMIT becomes the failure criteria. Here, the stress amplitude (σ_f) should be less than the Endurance Limit (σ_e) to withstand infinite no. of cycles.

These equations are mainly used in this type of design analysis:

σ_a=S_e / FOS        τ_a  = S_se / FOS         

Where ;

σ_a = Stress amplitude in component (due to bending)

S_e =  Corrected Endurance Limit in reversed bending

τ_a  = Stress amplitude in component (due to torsion)

S_se=  Corrected Endurance Limit in reversed bending

DESIGN FOR FINITE LIFE

When a component has to be designed for finite life, the S N CURVE becomes the failure criteria. Here, the stress amplitude (σ_f) is usually greater than the Endurance Limit (σ_e). It mostly finds applications in steels.

PLOTTING TECHNIQUE OF S N CURVE :

THE S N CURVE drawn here is a Straight Line AB drawn from (0.9 S_ut) at 10³ cycles to S_e at 10⁶ cycles on a LOG-LOG graph paper.

PLOTTING PROCEDURE :

1. Locate point A with coordinates {log₁₀(10³),log₁₀(0.9 S_ut)}= {3, log₁₀(0.9 S_ut)} .

2. Locate point B with coordinates {log₁₀(10⁶),log₁₀(S_e)}= {6, log₁₀(S_e)} .

3.Join AB . This is the criterion for failure for Finite life problems.

4. Depending upon the Value of the life N given to us, draw a vertical line passing through log₁₀N on the abscissa, which further intersects AB at point F.

5. Draw a line FE parallel to abscissa. The ordinate at point E i.e log₁₀Sf gives the fatigue strength corresponding to N cycles.