XRD残余应力测试课件.ppt

BSSM WorkshopPART IIThe sin2 Method Using Laboratory X-RaysJudith ShackletonSchool of Materials, University of Manchester,The sin2 Method What are We Measuring?,We measure the ELASTIC Strain. We can determineMagnitude of the stress,Its directionIts natureCompressive or tensileWe use the planes of the crystal lattice as an atomic scale “strain gauge”,The sin2 Method How Does it Work?,We measure STRAIN () not STRESS ()We CALCULTE STRESS from the STRAIN & the ELASTIC CONSTANTSWe use the planes dhkl , of the crystal lattice as a strain gaugeWe can measure the change in d-spacing, dStrain = = d/d,Changes in d-spacing with Stress,Consider a bar which is in tensionThe d-spacings of the planes normal to the applied stress increase, as the stress is tensileThe d-spacings of the planes parallel to the applied stress decrease, due to Poisson strain,Measuring Elastic & InelasticStrain,Primarily we are measuring macro stressesThis is a uniform displacement of the lattice planesThese cause a VERY SMALL shift in the position, the Bragg angle 2, of the reflection & we can measure this (Only Just!)Inelastic stresses cause peak broadening, which can be measured. This is an extensive subject, not covered here.,Which Materials Can We Measure?,Works on any poly-crystalline solid which gives a high angle Bragg reflectionMetalsCeramics (not easy!)Multi-phase materials Not usually applied to polymers, as no suitable reflections, can add a metallic powder, reported in the literature,Why use the sin2 MethodThe Advantages,Most ImportantA stress free d-spacing is NOT required for the bi-axial case which is almost always usedOther advantagesLow cost (compared with neutrons & synchrotrons, but not hole drilling)Non-destructive, unlike hole drillingEasy to do & fairly fool proof (if you are careful!),Disadvantages,Most ImportantSurface method only, X-ray beam penetration depth 10 to 20 microns, at bestFor depth profiling must electro-polish, gives 1-1.5mmOther DisadvantagesAffected by grain size, texture (preferred orientation) & surface roughnessDoesnt work on amorphous materials (obviously!),Basic Theory,Consider a unit cube (quite a big one!) embedded in a componentNotation, (ij) the stress component acting on face i in direction (parallel to axis) j,Basic Theory,The normal stresses act normal to the cube faces & the two subscripts are the same e.g. (22)The shear stresses (twisting forces) act parallel to the cube faces & the two subscripts are different e.g. (31) or in the general case (ij)We measure normal stresses & shear stresses, but thats not what we want, we dont get all of the information! Why?,Basic TheoryNormal Stresses,From elastic theory of isotropic materials, the 3 normal strains are given by,11 = 1 11 - (22 + 33) E22 = 1 22 - (33 + 11) E33 = 1 33 - (11 + 22) EThe strain in any direction is a function of the stress in the others!. Ideally, we should measure more than one direction,Principal Stresses,We should measure more than one direction to get a complete picture of the stress in the component If we measure 3 directions or more we can calculate the PRINCIPAL STRESSESS, these are the directions on which no shear stress actsWe do this by rotating the sample through an angle , in its own plane, exact details & diagrams later,How the Sin2 Method WorksSample in “Bragg Condition”,Diffraction vector, normal to sample surface,dn,We measure the d-spacing with the angle of incidence () & the angle of reflection of the X-ray beam (with respect to the sample surface) equal. These planes are parallel to the free surface & unstressed, but not unstrained,Also called focussed geometry,How the Sin2 Method Works,Diffraction vector, titled with respect to sample surface,Tilt the sample through an angle and measure the d-spacing again. These planes are not parallel to the free surface. Their d-spacing is changed by the stress in the sample.,d,Defocused geometry,How the Sin2 Method Works,We tilt the sample through an angle psi, to measure magnitude the normal & shear stressesWe use a range of values of (called offsets) for example, from 0 to 45 in steps of 5 NEVER use the “Double Exposure Method” which uses just one offsets. Not enough data points!We rotate the the sample through an angle, to determine the directions of the principle stresses,No Stress Free d-Spacing Needed The Approximation,The depth of penetration of the X-ray beam in the sample is small, typically 20We can say that there is no stress component perpendicular to the sample surface, that is 33 = 0We can use the d-spacing measured at = 0 as the stress free d-spacingThis is the d-spacing of the planes parallel to the sample surfaceA reasonable approximation! The error is 2%, certainly less than trying to make a stress free standard!,The Equation for the sin2 Method,The simplest form of the equation is, = E d - dn (1 + ) sin2 dnWere = Stress in direction E = Youngs modulus (GPa) = Poissons ratio = Tilt angle (degrees)d = d-spacing measured at tilt angle, ()dn = The “stress free d-spacing” from our approximation measured at = 0 (),Strain Term,The sin2 Plot : The Results!,dn is obtained by extrapolating a plot of d (or strain) against sin2 to = 0Stress is obtained from the gradient, m of the sin2 plot = E m (1 + )If the d-spacing decreases, the stress is compressive (planes pushed together)If the d-spacing increases the stress is tensile (planes pulled apart),The sin2 Plot : Example,We can plot STRAIN against sin2 & obtain the STRESS from the gradient,The sin2 Plot : Example,Also, we can plot dhkl against sin2 & obtain the stress from the gradient, which is the same on both plots,General: Stress Diffractometers,Basically adapted powder diffractometers Can accommodate larger, heavier samplesMaximum accessible 2 angle is largerUsually about 165 2 (check this if you buy one!)More axes of rotation than a standard powder diffractometer, omega and 2 can move independently,There are Two Basic Types,Laboratory Based SystemsFixed locationCan usually be used for other applications, for example phase identificationPortable systemsDesigned specifically for residual stress measurementsCan carried and fixed to a large component (aircraft!),Diffraction Angles used in Stress Analysis,Diffraction GeometrySummary of the Angles Used in Residual Stress Analysis,Two-theta (2) The Bragg angle, angle between the incident (transmitted) and diffracted X-ray beams.Omega () The angle between the incidence X-ray beam and the sample surface. Both omega and two-theta rotate in the same plane.Phi () The angle of rotation of the sample about its surface normal.Psi () Angles through which the sample is rotated, in the sin2 method. We start at psi=0, where omega is half of two-theta and add (or subtract) successive psi offsets, for example, 10, 20, 30 and 40Chi () Angle of rotation about the axis of the incident beam. Chi rotates in the plane normal to that containing omega and two-theta. This angle is also sometimes (confusingly) referred to as ,InstrumentationThe Omega Method Portable Systems,Instrumentation an Example of a Portable System, Manchesters Proto i-XRD,Deciding What to do?,We need to decide how to make our measurements, we need to make some choices,Which X-ray tube to use?Which crystallographic plane do we choose?The best thing to do is copy what someone else has done!Your results will be comparable with those made by other workersMany Industries have “set” methods,Radiation SelectionChoice of X-Ray Tube (Wavelength!),ALWAYS check what other people have done in the past as, generally measurements on different planes with different wavelengths are not comparable3 Considerations(1) Dispersion(2) Fluorescence(3) Choice of crystallographic plane,Radiation SelectionChoice of X-Ray Tube (Wavelength!),We can measure the stress in a variety of materials (i.e. ferrite, austenite, nickel, aluminium, corundum etc) using the same diffractometer, by changing the X-ray tube & consequently the wavelength of the X-rays.Most residual stress diffractometers will have a selection of X-ray tubes availableHow do we choose?,Choice of X-Ray Tube(1) Dispersion,We need a 2 angle, ideally 140 2The change in d-spacing, due to strain, is very small, typically in the third decimal placeThe dispersion of the diffraction pattern is much greater at high 2 angles. The small changes in d-spacing can only be detected at angles 125 2,Choice of X-Ray Tube(1) DispersionAn Example,If we have a reflection from ferrite 211 at 156 2. Using radiation from a chromium anode X-ray tube of wavelength 2.2897If we introduce a stress of 200 MPa, given Youngs modulus of 220 GPa, what is the change in the 2 angle?Answer, the new 2 angleis155.51The difference is 0.48 NOT MUCH!,Choice of X-Ray Tube(2) Sample Fluorescence,If the K-1 component of the incident X-ray beam causes the sample emit its own fluorescent X-rays, DO NOT USE ITX-ray penetration depth will be very small 5 microns & NOT representative of the bulkPeak to background ratio will be terribleMay damage sensitive detectors,Choice of X-Ray Tube(3) Choice of Crystallographic Plane,For accurate comparison with other peoples data CHECK which planes have been used historically!Measurements made on planes with different Miller hkl indices are not usually comparable.If the sample is textured (preferred orientation) select a set of planes with a high multiplicity,Choice of Measurement Conditions: Summary,Ask someone who has experience with that particular materialDont re-invent the wheelChoose radiation type carefullyAvoid X-ray tubes which cause K -1 fluorescenceLots of “tricks of the trade” see the NPL Good Practice Guide for Residual Stress Measurements using the sin2 Method,Data CollectionPositioning the Sample,Sample must be centre of rotation of the goniometer, most instruments have depth gauge or a pointerBe careful that the sample is as flat as possible, bent samples will give artificial shear stressesFor curved and uneven samples restrict the irradiated areaHoop direction, Spot size R/4, where R= radius of curvatureAxial direction, Spot size R/2,Data Collection,Make sure that you collect data over a sufficient 2 range! Include the background on both sides of the peak. Can be difficult as inelastic is usually present & this causes peak broadening. Peaks can be up to 10 2Count for a sufficient time to ensure adequate statistics, need 1000 count at the top of the peak if possible,Data Processing,ALWAYS CHECK THIS STAGENeed a program with good graphicsStages in the data processingBackground strippingK-2 stripping (only if K-2 peak is visible)Lorentz Polarisation CorrectionPeak fitting to locate maximumCritical Stage, check the results on the screen. A variety of peak models are available most of which will work. Usually use Gaussian, dont use parabolaGood quality data can be fitted with most models, this is a good test!,How Precise are the Results,Generally theres a lot of scatter on sin2 plots!The error bars printed out by most PCs are just the standard deviation of the points from the fitted line and tend under estimate the errorsLarge error bars are not necessarily unacceptable and are due to,Texture, large grain size, poor peak fitting etcFor example, 200 50MPa is quite normalCheck the peaks on the screen!Values of less than 50MPa, can usually be thought of as zero, this depends on the instrument To confirm such low readings make several measurements & see if they all come out with the same sign (i.e. all compressive),Instrument Misalignment,- Omega-2 misalignments-Omega- misalignments (side inclination method)Instrument misalignment causes, Shifts in the positions of the reflections and incorrect stress valuesThe positive and negative measurements give different peak positions, this is called splittingWe must measure at least two standards to verify that the machine is working correctly,Instrument Misalignment,- Recommended StandardsA stress free powderNot an easy thing to makeBeware stresses due to filing and oxidationCan be combined with resin for ease of useA stressed standardBe careful, always measure in the same directionShot peened samples are goodUsually verified by Round-Robin tests No certified standards (?)One set for each tube anode,A typical Example of a Stress Profile in a Shot Peened Sample,A shot peened surface, depth profiled by Electro-polishing,Problems!,Good one, the material has a small grain size ( 100) is isotropic, rather than textured & theres no shear stress. Ideal!,Texture, the “wiggle” Our sample is not isotropic,Shear Stress, the positive & negative plots split,Shear Stressessin2 Splitting,Positive and negative give different results when a shear stress is present (or sample is not correctly positioned, always check!)Function of the direction of the measurement,Conclusions,The sin2 method works well if you are carefulCheck to see whats been done by othersDont reinvent the wheelChoose you X-ray tube with carePosition the sample carefullyThink about the directions you wish to measureMeasure a sufficient range of 2 & count for a sufficient timeCheck you peak fittingDo the results make sense?,Thank You & Happy Landings!,