Design against Fluctuating LoadGanesh Mandpe

mandpeganesh2@gmail.com

What we will cover:Stress ConcentrationNotch SensitivityFatigue FailureEndurance LimitGoodman, soderberg diagramsModified Goodman diagramsFatigue design under Combined stresses

Stress

Axial Load on Plate with HolePlate with cross-sectional planeHalf of plate with stress distribution.

FEA analysis of 2D plate with circular hole using ANSYS

Stress ConcentrationStress Concentration is defined as the loacalization of high stresses due to the irregularities present in the component and abrupt changes of the cross-section.

Stress Concentration Factor (Kt)

Causes of Stress ConcentrationVariation in Properties of MaterialsLoad ApplicationAbrupt changes in sectionDiscontinuities in componentMachining Scratches

Variation in Properties of Materials

Internal cracks and flaws like blow holes

Cavities in weldsAir holes in steel components

Nonmetallic or foreign inclusions

Load Application

Abrupt changes in sectionIn order to mount gears, sprockets,pulleys and ball bearings in a transmission shaft, steps are cut on the shaft and shoulders and provided from assembly considerations.

This results in stress concentration

Discontinuities in the componentCertain features of machine components such as oil holes or oil grooves, keyways and splines and screw threads result in discontinuities in the cross-section of component.

There is stress concentration

Machining ScratchesMachining scratches,stamp marks or inspection marks are surface irregularities which cause stress concentration.

STRESS CONCENTRATION FACTORSStress concentration factors are determinded by two methods,Mathematical method based on theory of elasticityExperimental methods like photo-elasticityAt present, FEA packeges are used to find out the stress concentration factor for any geometric shape.

Charts for Kt for different geometric shapes and conditions of loading were developed by RE PetersonStress concentration factor for rectangular plate with central hole.EX: A 50mm wide and5mm high rectangularplate has a 5mmdiameter central hole.Allowable stress is 300MPa. Find the max.tensile force that canbe applied.Ans: d/b = 0.1; Kt=2.7A = (50-5)5P = 25 kN

EX: AssumeH=45mm,h=25mm, andfillet radiusr=5mm. Findstressconcentrationfactor.Ans: ~1.8Stress concentration factor under axial load for rectangular plate with fillet

Gap between linesdecrease withincrease in r/d ratio.Stress concentration factor under axial load for round bar with fillet

Stress concentration factor under bending for round bar with fillet

REDUCTION OF STRESS CONCENTRATIONAlthough It is not possible to completely eliminate effect of stress concentrationThis is achieved by providing a specific geometric shape to the component

Additional Notches and Holes in Tension Member

Fillet Radius,Undercutting and Notch for Member in Bending

Drilling Additional Holes for shaftAn empirical relationship developed By HF Moore for the ratio C of torsional Strength of shaft having a keyway to torsional Strength of same sized shaft without a keyway

Reduction of Stress Concentration in Threaded Members

Guidelines for DesignerDuctile Materials Under Static Load

Under a static load, ductile materials are not affected by stress concentration ,to the extent that photo-elastic analysis might indicate.

Ductile Materials under Fluctuating LoadHowever, when the load is fluctuating, the stress at the discontinuities may exceed endurance limit and in that case, the component may fail by fatigue.Endurance limit of the components made of ductile materials is greatly reduced due to stress concentration.This accounts for the use of stress concentration factors for ductile materials.

Brittle MaterialsThe effect of stress concentration is more severe in case of brittle materials, due to their inability of plastic deformation.Brittle materials do not yield locally and there is no adjustment of stresses at the discontinuities.Stress concentration factors are used for components made of brittle materials subjected to both static as well as fluctuating load.

NOTCH SENSITIVITY

Fatigue Stress Concentration Factor (Kf)Some materials are more sensitive than others to stress raising notches under fluctuating load.To account for this effect, a parameter called notch sensitivity factor is found for each material.The notch sensitivity factor is used to modify the theoretical stress concentration factor.

Is defined as the ratio of the actual maximum stress in component to the nominal stress at the same section.

The term notch sensitivity is used to relate the fatigue stress concentration factor with theoretical stress concentration factor.

It indicates the sensitivity of the material to notches or discontinuities.

NOTCH SENSITIVITYIs defined as the degree to which the theoretical expected effect of stress concentration is actually reached.