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**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

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**Static Load Stress Stress Ratio, R = 1.0**

F and P are applied and remain constant Stress Stress Ratio, R = 1.0 Time

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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?

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**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!

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**Types of Cyclic Stress:**

Repeated and Reversed (i.e. RR Moore, rotating shafts, etc.) – mean stress = 0. Fluctuating stress (mean stress not zero): Tensile mean stress (can cycle between tension and compression or all tension) Compressive mean stress (can cycle between tension and compression or all compression) Repeated, one-direction stress

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**Definitions: = Alternating stress = Mean stress = R value:**

R = 0, repeated and one direction, i.e. stress cycles from 0 to max value. R =-1, Fully reversed (R-R Moore)

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**1.Repeated & Reversed Stress**

an element subjected to a repeated and alternating tensile and compressive stresses. Continuous total load reversal over time Demo: Switch to Excel

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**1.Repeated and Reversed Stress**

The average or mean stress is zero.

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

Cyclic loading. (a) Very low amplitude acoustic vibration. (b) High-cycle fatigue: cycling well below general yield, sy. (c) Low cycle fatigue: cycling abovegeneral yield (but below the tensile strength sts). All stresses above are repeated and reversed (R = -1)

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**Fatigue Testing Bending tests**

R-R More = Spinning bending elements – most common. Fast, cost effective, pure bending stress See:

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**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

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**Fatigue Testing Test Data Stress, s (ksi)**

Number of Cycles to Failure, N Data from R. B. Englund, 2/5/93

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**Endurance Strength = 0.50(Su)**

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.

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**Representative Endurance Strengths**

Estimated endurance strength of steel is about 0.50 * Su

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2. Fluctuating Stress When an element experiences alternating stress, but the mean stress is NOT zero. Load varies between P and Q over time

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**2.Fluctuating Stress Example**

Bending of Rocker Arm Valve Spring Force Valve Open Valve Closed Tension in Valve Stem Valve Closed Valve Spring Force Valve Open RBE 2/1/91 Adapted from R. B. Englund

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**Types of Fluctuating Stress:**

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**Tensile Stress w/ Tensile Mean**

Case 1:

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**Partially Reversed w/ Tensile Mean**

Case 2: smax is tensile and smin is compressive

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**Partially Reversed w/ Compressive Mean**

Case 3: smax is tensile and smin is compressive

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**Compressive Stress w/ Compressive Mean**

Case 4: smax and smin are both compressive

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**Repeated – One Direction Stress**

Case 5:

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

Reversed is the worst case and is the case used to determine the endurance strength of materials (RR Moore, etc) Fluctuating stress has less effect on endurance strength than reversed Mott, Fig. 5-11, Pg. 180

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Stages of Fatigue: Micro structural changes – nucleation of permanent damage (mm) Creation of microscopic cracks (mm) Growth and coalescence of cracks into dominant crack (striations). Stable crack growth (Beach marks) Instability and rapid failure (area goes down, stress goes up eventually exceeding tensile strength).

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Stages of Fatigue: Micro structural changes – nucleation of permanent damage (mm) Creation of microscopic cracks (mm) These two steps = crack initiation = 99% of the total life!!!!!!!!!!!!!!!!!!! Key: prevent cracks from forming at surface!!!!!!!!!!

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B Instantaneuos Fast Fracture! A Crack nucleation and Growth

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**fail in fatigue at stresses well below the tensile strength.**

The endurance limit plotted against the tensile strength. Almost all materials fail in fatigue at stresses well below the tensile strength.

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Design Factor Analysis Design

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**Factors Effecting Design Factor**

Application Environment Loads Types of Stresses Material Confidence

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**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?

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**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

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**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

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**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

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**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.

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**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?

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**Recommended Design Factors**

Confidence in material properties, analysis, loads, the environment, etc. See Mott, pages

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Design Factor

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