Chapter 5 – Design for Different Types of Loading

• Part 1 – Types of stress and loading, stress ratio, endurance strength, design factors

• Part 2 – Failure theories

• E. R. Evans, Jr./ R. Michael• MET 210W

Static Load

Time

F and P are applied and remain constant

Stress Ratio, R = 1.0

Dynamic Stress:• Loads that vary during normal service of the product produce

dynamic stress.• Dynamic stress can be cyclic or random.• High cycle fatigue – part subject to millions of stress cycles.

Examples: Parts subject to dynamic stress?

Cyclic loads produce cyclic stress which can lead to mechanical fatigue failure:

Mechanical Fatigue = The progressive and localized structural damage that occurs when a material is subjected to cyclic loading. The cyclic stress is well below tensile, Su and yield, Sy , strengths!

Types of Cyclic Stress:

1.Repeated and Reversed (i.e. RR Moore, rotating shafts, etc.) – mean stress = 0.

2.Fluctuating stress (mean stress not zero):a.Tensile mean stress (can cycle between

tension and compression or all tension)b.Compressive mean stress (can cycle

between tension and compression or all compression)

c. Repeated, one-direction stress

Definitions:

22minmax

a

2minmax

m

max

min

R = R value:

R = 0, repeated and one direction, i.e. stress cycles from 0 to max value.

R =-1, Fully reversed (R-R Moore)

= Alternating stress

= Mean stress

1.Repeated & Reversed Stress• an element subjected to a repeated and

alternating tensile and compressive stresses.

Demo: Switch to Excel

Continuous total load reversal over time

1.Repeated and Reversed Stress

The average or mean stress is zero.

1max

min

R

Cyclic loading. (a) Very low amplitude acoustic vibration. (b) High-cycle fatigue: cycling well

below general yield, y. (c) Low cycle fatigue: cycling abovegeneral yield (but below the tensile strength ts).

All stresses above are repeated and reversed (R = -1)

Fatigue Testing• Bending tests

– R-R More = Spinning bending elements – most common.

• Fast, cost effective, pure bending stress• See: http://www.instron.co.uk/wa/solutions/rotating_beam_fatigue.aspx

Fatigue Testing• Bending tests

– Sontag = Constant stress cantilever beams• Good for flat stock (sheets)• Get shear stress in addition to bending stress.

Top View

Specimen

Fatigue Testing

Number of Cycles to Failure, N

Str

ess,

(

ksi)

Data from R. B. Englund, 2/5/93

Test Data

Endurance• Endurance strength is the stress level that a

material can survive for a given number of load cycles.

• Endurance limit is the stress level that a material can survive for an infinite number of load cycles.

• Estimate for Wrought Steel:

Endurance Strength = 0.50(Su)

• Most nonferrous metals (aluminum) do not have an endurance limit.

Representative Endurance Strengths

Estimated endurance strength of steel is about 0.50 * Su

2. Fluctuating Stress

• When an element experiences alternating stress, but the mean stress is NOT zero.

Load varies between P and Q over time

2.Fluctuating Stress Example

Valve Spring Force

Valve Spring ForceValve Open

Valve Closed

Valve Closed

Valve Open

• Bending of Rocker Arm

• Tension in Valve Stem

Adapted from R. B. Englund

RBE 2/1/91

Types of Fluctuating Stress:

Tensile Stress w/ Tensile Mean• Case 1:

2minmax

m

2minmax

a

Partially Reversed w/ Tensile Mean• Case 2:

2minmax

m

2minmax

a

max is tensile and min is compressive

Partially Reversed w/ Compressive Mean• Case 3:

2minmax

m

2minmax

a

max is tensile and min is compressive

Compressive Stress w/ Compressive Mean• Case 4:

2minmax

m

2minmax

a

max and min are both compressive

Repeated – One Direction Stress• Case 5:

Example of the Effect of Stress Ratio on Endurance Strength of a Material

Mott, Fig. 5-11, Pg. 180

Stages of Fatigue:

1. Micro structural changes – nucleation of permanent damage (m)

2. Creation of microscopic cracks (mm)3. Growth and coalescence of cracks into

dominant crack (striations).4. Stable crack growth (Beach marks)5. Instability and rapid failure (area goes down,

stress goes up eventually exceeding tensile strength).

Stages of Fatigue:

1. Micro structural changes – nucleation of permanent damage (m)

2. Creation of microscopic cracks (mm)

These two steps = crack initiation = 99% of the total life!!!!!!!!!!!!!!!!!!!

Key: prevent cracks from forming at surface!!!!!!!!!!

B

A

Crack nucleation and Growth

Instantaneuos Fast Fracture!

The endurance limit plotted against the tensile strength. Almost all materials

fail in fatigue at stresses well below the tensile strength.

Design Factor

• Analysis

• Design

ySN:Example

StressApplied

StrengthFailureSafetyofFactor

N

S:Example

FactorDesign

StrengthFailureStressAllowable

yALLOW

Factors Effecting Design Factor

• Application• Environment• Loads• Types of Stresses• Material• Confidence

Factors Effecting Design Factor

• Application• Environment• Loads• Types of Stresses• Material• Confidence

• How many will be produced?

• What manufacturing methods will be used?

• What are the consequences of failure?

•Danger to people•Cost

• Size and weight important?

• What is the life of the component?

• Justify design expense?

Factors Effecting Design Factor

• Application

• Environment• Loads• Types of Stresses• Material• Confidence

• Temperature range.

• Exposure to electrical voltage or current.

• Susceptible to corrosion

• Is noise control important?

• Is vibration control important?

• Will the component be protected?•Guard•Housing

Factors Effecting Design Factor

• Application• Environment

• Loads• Types of Stresses• Material• Confidence

• Nature of the load considering all modes of operation:

•Startup, shutdown, normal operation, any foreseeable overloads

• Load characteristic•Static, repeated & reversed,

fluctuating, shock or impact

• Variations of loads over time.

• Magnitudes•Maximum, minimum, mean

Factors Effecting Design Factor

• Application• Environment• Loads

• Types of Stresses• Material• Confidence

• What kind of stress?•Direct tension or compression•Direct shear•Bending•Torsional shear

• Application•Uniaxial•Biaxial•Triaxial

Factors Effecting Design Factor

• Application• Environment• Loads• Types of Stresses

• Material• Confidence

• Material properties

• Ultimate strength, yield strength, endurance strength,

• Ductility•Ductile: %E 5%•Brittle: %E < 5%

• Ductile materials are preferred for fatigue, shock or impact loads.

Factors Effecting Design Factor

• Application• Environment• Loads• Types of Stresses• Material

• Confidence

• Reliability of data for•Loads•Material properties•Stress calculations

• How good is manufacturing quality control

• Will subsequent handling, use and environmental conditions affect the safety or life of the component?

Recommended Design Factors

Confidence in material properties, analysis, loads, the environment, etc.

See Mott, pages 185 - 186

Design Factor