Post on 05-Oct-2015
description
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Endurance Strength,
Stress Transformation
and Prediction of Failure
Revision and Summary
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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.
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Endurance Strength
Endurance strength is a materials ability to
withstand the fatigue loading.
Several factors that could affect the
endurance strength.
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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
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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 =
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Try Example Problem 5-2
Estimating actual endurance strength
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Stress Transformation
Refer to Stress Transformation.pdf
Examples (refer to Example Stress
Transformation.pdf)
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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.
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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
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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
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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
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Distortion Energy Theory
Refer to Distortion energy theory.pdf
Examples (refer to Example Distortion energy
theory.pdf)
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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.
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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