Chapter 5 Design for Different Types of LoadingPart 1 Types of stress and loading, stress ratio, endurance strength, design factorsPart 2 Failure theoriesE. R. Evans, Jr./ R. MichaelMET 210W

Static LoadTimeF and P are applied and remain constantStress 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: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

Definitions:= 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 Stressan element subjected to a repeated and alternating tensile and compressive stresses.Demo: Switch to ExcelContinuous total load reversal over time

1.Repeated and Reversed StressThe average or mean stress is zero.

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

Fatigue TestingBending testsR-R More = Spinning bending elements most common.Fast, cost effective, pure bending stressSee: http://www.instron.co.uk/wa/solutions/rotating_beam_fatigue.aspx

Fatigue TestingBending testsSontag = Constant stress cantilever beamsGood for flat stock (sheets)Get shear stress in addition to bending stress.Top ViewSpecimen

Fatigue TestingNumber of Cycles to Failure, NStress, s (ksi)Data from R. B. Englund, 2/5/93Test Data

EnduranceEndurance 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 StrengthsEstimated endurance strength of steel is about 0.50 * Su

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

2.Fluctuating Stress ExampleValve Spring ForceValve Spring ForceValve OpenValve ClosedValve ClosedValve Open Bending of Rocker Arm Tension in Valve StemAdapted from R. B. EnglundRBE 2/1/91

Types of Fluctuating Stress:

Tensile Stress w/ Tensile MeanCase 1:

Partially Reversed w/ Tensile MeanCase 2:smax is tensile and smin is compressive

Partially Reversed w/ Compressive MeanCase 3:smax is tensile and smin is compressive

Compressive Stress w/ Compressive MeanCase 4:smax and smin are both compressive

Repeated One Direction StressCase 5:

Example of the Effect of Stress Ratio on Endurance Strength of a MaterialMott, Fig. 5-11, Pg. 180

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).

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!!!!!!!!!!

BACrack nucleation and GrowthInstantaneuos Fast Fracture!

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

Design FactorAnalysis

Design

Factors Effecting Design FactorApplicationEnvironmentLoadsTypes of StressesMaterialConfidence

Factors Effecting Design FactorApplicationEnvironmentLoadsTypes of StressesMaterialConfidenceHow many will be produced?What manufacturing methods will be used?What are the consequences of failure?Danger to peopleCostSize and weight important?What is the life of the component?Justify design expense?

Factors Effecting Design FactorApplicationEnvironmentLoadsTypes of StressesMaterialConfidenceTemperature range.Exposure to electrical voltage or current.Susceptible to corrosionIs noise control important?Is vibration control important?Will the component be protected?GuardHousing

Factors Effecting Design FactorApplicationEnvironmentLoadsTypes of StressesMaterialConfidenceNature of the load considering all modes of operation:Startup, shutdown, normal operation, any foreseeable overloadsLoad characteristicStatic, repeated & reversed, fluctuating, shock or impactVariations of loads over time.MagnitudesMaximum, minimum, mean

Factors Effecting Design FactorApplicationEnvironmentLoadsTypes of StressesMaterialConfidenceWhat kind of stress?Direct tension or compressionDirect shearBendingTorsional shearApplicationUniaxialBiaxialTriaxial

Factors Effecting Design FactorApplicationEnvironmentLoadsTypes of StressesMaterialConfidenceMaterial propertiesUltimate strength, yield strength, endurance strength, DuctilityDuctile: %E 5%Brittle:%E < 5%Ductile materials are preferred for fatigue, shock or impact loads.

Factors Effecting Design FactorApplicationEnvironmentLoadsTypes of StressesMaterialConfidenceReliability of data forLoadsMaterial propertiesStress calculationsHow good is manufacturing quality controlWill subsequent handling, use and environmental conditions affect the safety or life of the component?

Recommended Design FactorsConfidence in material properties, analysis, loads, the environment, etc.See Mott, pages 185 - 186

Design Factor

*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

*