1

1

Endurance Strength,

Stress Transformation

and Prediction of Failure

Revision and Summary

2

Estimating Fatigue Failure Criteria

Fatigue is progressive failure that occurs due to

dynamic and fluctuating stresses.

Almost 90% of the metallic failures are due to

fatigue

Fatigue failures can occur at stress levels far below

the ultimate or yield strengths of a material.

To estimate the fatigue life, Endurance strength/

fatigue strength is necessary to be determined.

2

3

Endurance Strength

Endurance strength is a materials ability to

withstand the fatigue loading.

Several factors that could affect the

endurance strength.

4

Factors Affecting Endurance strength

1. Type of selected material

2. Type of stress on a component

3. Size of a part

4. Surface treatments

5. Reliability

3

5

Estimating actual endurance strength

Actual endurance strength, Sn

where Sn = modified endurance strength (depend on surface

treatment)

Cm = material factor,

Cst = type of stress factor,

CR = reliability factor, and

Cs = size factor

))()()(('

sRstmnn CCCCss =

6

Try Example Problem 5-2

Estimating actual endurance strength

4

7

Stress Transformation

Refer to Stress Transformation.pdf

Examples (refer to Example Stress

Transformation.pdf)

8

Static Failure Theories

Static failure occurs due to the stresses

applied to a part exceed the materials

allowable stress.

Therefore, it is necessary to ensure the

operation stress subjected to a component is

less the allowable stress.

Machine components are always subjected to

uncertain load and varies of material

behavior.

5

9

A design factor, N (factor of safety) should

introduce to design of component to ensure it

is safe to use under a specific operation

condition.

Designer must determine a reasonable value

of design factor for a component to avoid

overdesign.

Static Failure Theories

10

Guidelines to select appropriate Design Factor, N

(proposed by Robert L. Mott)

For ductile materials:

N = 1.25 to 2.0: Design of structures under static loads for which

there is a high level of confidence in all design data.

N = 2.0 to 2.5: Design of machine elements under dynamic

loading with average confidence in all design data.

N = 2.5 to 4.0: Design of static structures or machine elements

under dynamic loading with uncertainty about loads, material

properties, stress analysis or the environment.

N = 4.0 or higher: Desire to provide extra safety to critical

components.

Static Failure Theories

6

11

Several theories have been formulated to

predict failure of ductile materials

1. The maximum normal-stress theory

2. Maximum normal-strain theory

3. Total strain-energy theory

4. The distortion-energy (von-Mises) theory

5. Maximum shear stress theory

Static Failure Theories

Good predictor, most accurate and

commonly used in failure investigation

12

Distortion Energy Theory

Refer to Distortion energy theory.pdf

Examples (refer to Example Distortion energy

theory.pdf)

7

13

Shear stress due to torque

J

Tc=

T = Torque, Nm

c = radius distance from center to point of interest, m

J = Polar moment of Inertia, m4

r) toequal always c , (For max

Exercise

Compute the torsional shear stress in a circular shaft with a diameter of

50mm that is subjected to a torque of 800 N.m.

14

Normal stress due to Bending (Bending stress)

I

Mc=

M = moment, Nm

c = distance from center to point of interest, m

I = moment of Inertia, m4

Exercise

A circular shaft has diameter of 40mm

is subjected to forces as shown in the

figure. Calculate the maximum bending

stress at point B