XRD-殘余應(yīng)力測(cè)試課件

1、BSSM WorkshopPART IIThe sin2 Method Using Laboratory X-RaysJudith ShackletonSchool of Materials, University of ManchesterThe 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

2、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/dChange

3、s in d-spacing with StressConsider 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 strainMeasuring Elastic & InelasticStrainPrimarily we are measu

4、ring 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 her

5、e.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 literatureWhy use the sin2 MethodThe A

6、dvantagesMost 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!)Disadvantage

7、sMost 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 TheoryCon

8、sider a unit cube (quite a big one!) embedded in a componentNotation, (ij) the stress component acting on face i in direction (parallel to axis) jBasic TheoryThe normal stresses act normal to the cube faces & the two subscripts are the same e.g. (22)The shear stresses (twisting forces) act parallel

9、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 StressesFrom elastic theory of isotropic materials, the 3 normal strains are g

10、iven 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 directionPrincipal StressesWe should measure more than one direction to get a complete picture of the stress i

11、n 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 laterHow the Sin2 Method WorksSample in “Bragg Condition”

12、Diffraction vector, normal to sample surfacednWe 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 unstrainedAlso called focussed geometryHow

13、 the Sin2 Method WorksDiffraction vector, titled with respect to sample surfaceTilt 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.dDefocused geometryHow the Sin2 Method WorksWe ti

14、lt 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 angl

15、e, to determine the directions of the principle stressesNo Stress Free d-Spacing Needed The ApproximationThe 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-spa

16、cing 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 140 2The change in d-spacing, due to strain, is very small, typically in the third decimal placeThe dispersion of the diffraction pattern is muc

17、h greater at high 2 angles. The small changes in d-spacing can only be detected at angles 125 2Choice of X-Ray Tube(1) DispersionAn ExampleIf 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, give

18、n 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 FluorescenceIf 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 d

19、epth will be very small 5 microns & NOT representative of the bulkPeak to background ratio will be terribleMay damage sensitive detectorsChoice of X-Ray Tube(3) Choice of Crystallographic PlaneFor accurate comparison with other peoples data CHECK which planes have been used historically!Measurements

20、 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 multiplicityChoice of Measurement Conditions: SummaryAsk someone who has experience with that particular materialDont re-invent the wheelC

21、hoose 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 MethodData CollectionPositioning the SampleSample must be centre of rotation of the goniometer, most instruments

22、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 1000 count at the top of the

23、 peak if possibleData ProcessingALWAYS 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

24、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 ResultsGenerally theres a lot of scatter on sin2 plots!The error bars printed out by most PCs are just the standard d

25、eviation 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

26、 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,

27、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 correctlyInstrument 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