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d - E21 - Technische Universität München

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1. Introduction3 types of Residual Stressdepending on the length scale●Type I (macrostresses): misfitsgenerated by manufacturingprocesses or in-service loading.●Type II (microstresses): usuallypresent in polycristalline andmulti-phase materials as aconsequence of materialprocessing and service loading.●Type III (atomic scale stresses):due to point defects anddislocations.Schematic illustration of different length scalesfor axial stress components for a pipe butt weld


1. IntroductionResidual Stress superimposed toapplied stresses during service lifeCan affect to mechanicalbehaviour of a componentEvaluation of Residual Stress is fundamental


2. Measurement typesThere are several ways of measuring Residual Stresses (STRAIN)2.1 Destructive methods- Sectioning- Hole drilling- Slotting methods- Contour method- Microscale stress measurement for microdevicesand coatings- etc.


2. Measurement typesSometimes it is not interesting to destroy the piece of study.There is a need for non-destructive methods.2.2 Non-destructive methods- Diffraction methods: the crystalline lattice is used like an atomic strain gauge.- Other methods: there exist many other methods due to properties related tothe stress such Photoluminiscence, Magnetoelasticity, Acoustoelasticity,Photoelasticity, Thermoelasticity, etc. that are portable and cheap but may beconfounded by factors such texture, inhomogeneity and plastic deformation.


3. Diffraction methodsMethod → measurement of small changes in lattices spacing


3. Diffraction methodsStrainε = (d – d o ) / d od: space between lattice planes with residual stressd o : space between lattice planes with no applied stressThe Stiffness tensor (E) allows to determine the Stress tensor (σ) from theStrain tensor (ε)σ = E ε


3. Diffraction methodsTo obtain d and d o valuesBragg's Law2 d sin θ = λθ: half of the scattering angle(scattering angle: ϕ=2θ)λ: wavelength


3. Diffraction methodsNo stress situationThere is a shift in the Bragg peakStress situation


3. Diffraction methods3.1 X-ray diffraction2D imageNear surfaceMust be combined with layer removal methodsMaterial lossLost of information


3. Diffraction methods3.2 Synchrotron X-ray diffractionLess sensitive to textural changesHigh energy X-raysShort wavelengthsMore penetrating than X-raysSmall diffraction anglesLimitation


3. Diffraction methods3.3 Neutron diffractionThermal neutron beamsVery penetrating3D ImageSamples can be studiedunder complexenvironmental conditions


3. Diffraction methods3.3 Neutron diffractionVery penetrating3D Image


4. Neutron DiffractionNeutrons Chargeless particles Low absorption More penetrationPenetration of neutronsin different materials


4. Neutron DiffractionNo sample preparation is requiredCan be used on irregular shaped samplesLimitation → sample must be brougth to a neutron source (limited dimensions)


4. Neutron Diffraction2 cases (depending on the source of neutrons)1) Reactor λ is constantBragg's lawDifferentiatingBragg's law:2 d sin θ=λ2[∆ d sin θ+d cosθ ∆θ]=∆ λλ is constant ∆ λ=0∆ d sin θ+d cosθ ∆ θ=0∆ d sin θ= d cosθ∆θ∆ d /d= (cosθ/sin θ)∆θ∆ d /d= cotθ∆θε=∆ d /dε= cotθ∆θ


4. Neutron Diffraction1) Reactor λ is constant(Diffraction angle is varied to collect data)ε=(d d 0)/d 0=∆ d /d 0= cot θ∆ θSmall lattice strain will giverise to a change (SHIFT) in ϕ∆ ϕ=2 ∆θ= 2εtan θε can be determined


4. Neutron Diffraction1) ReactorDirection of εDirection of Q (scattering vector)SampleQ= Ki - KfKi: incident beamKf: final beamIt is required to measure strains in at least 6 directionsto obtain the strain tensor.


4. Neutron Diffraction2) Spallation source θ is constant ε=(d d 0)/d 0=∆ d /d 0=∆ λ /λ=∆ t/tWhere t = L/v = (λm/h)/Lt: time taken for aneutron to traverse apath length Lwith a mass mand velocity vh: Planck's constantT.O.F.ISIS Spallation Source


4. Neutron Diffraction2) Spallation sourceAssumptionIsotropic materialYoung's modulus (E) and Poisson's number (ν)Hooke's lawσ i=[ε i+(ε 1+ε 2+ε 3)ν/(1 2 ν)]E /(1+ν) i = 1, 2, 3


4. Neutron DiffractionGauge volumeVolume of the material sampledCross section of the incoming and outgoing neutron beams on the sampleStress mapping over theentire sample is done bymoving the sample.Gauge volume = 1~100 mm³


4. Neutron DiffractionExperimentBar treated for 1 hour at 550ºC to remove any initialresidual stressApplying a force in the elastic rangeNeutron diffractionAnalyse internal stress


5. InstrumentsNuclear reactor


5. InstrumentsSpallation source


5. InstrumentsMonochromator(For nuclear reactors)Used to obtain a constant wavelengthDifferent reflection directions fordifferent wavelengthsMonochromatic beam in onedirectionMost used materials: pyroliticgraphite (PG), Cu and hotpressedGe.


5. InstrumentsCollimatorsDEFINE GAUGE VOLUME (before and after the sample)Collimators


5. InstrumentsCollimatorsDEFINE GAUGE VOLUME (before and after the sample)Narrow the beam from ~4 cm wide to a few milimeters.Collimator and detector bank fora spallation source


5. InstrumentsDetectorsConvert the neutron impacts into an electronic signal●●●Standard He³-detectorsPosition sensitive detectorsShielding detectorsTime-Of-FlightNecessary in spallation source to know λ


6. Areas of study & Applications●Strain mapping●●Near-surface stress measurementShot peeningMechanical surface treatment toimprove fatigue performanceResidual stress under plasticcallydeformed layerImportant to know depth of shooting


6. Areas of study & Applications●Composite materials2 phasesOne almost no strainedOther very strainedNeutron difraction●Neutron residual stress measurement in welds●Etc.


7. Summary (Neutron Diffraction)Non-destructive methodBragg's law → d-spacing → strain (→stress)Neutrons are very penetrating → gauge volume ~1-100 mm³3D imageNo sample preparation requiredAny shaped sample can be studied


8. ReferencesNeutron diffraction methods for the study of residual stress fieldsAllen et al.The Appropiateness of Residual Stress Length Scales in Structural IntegrityBouchard et al.Residual stress and its role in failureP. J. WithersNeutron strain measurementA. D. KrawitzAnalysis of Residual Stress by Diffraction using Neutron and Synchrotron RadiationE. Fitzpatrick and A. LodiniStrain and Stress Analysis by Neutron DiffractionM. CerettiMaterials Research at the High Flux Neutron Source FRM IIChr. MorkelResidual-stress Measurement by the Sectioning MethodN. Tebedge et al.Measurement of Residual Stresses by the Hole-Drilling Strain Gage MethodVishay Precision GroupGeneral Chemistry: Principles, Patterns and ApplocationsB. Averill and P. EldredgeHyper Physics Quantum PhysicsR. Nave


Thank youRafael Cabello

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