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DRSA Inreach
Internal Stresses in Aluminum Engines
Data
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Introduction of research project Solidification of casting alloys Stresses and strains Crystal lattices Diffraction Neutrons Experimental design Data Analysis of data
Measuring Residual Stresses
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FCC Aluminum Diffraction Pattern
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Experimental Geometry
Detectors
Engine Head
Beam Aperture
Transmitted Neutron Beam
Scattered Neutrons
Monochromator
Sampling Volume
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Experimental Geometry
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Count scattered neutrons as a function of scattering angle for the Al (311)
For a neutron wavelength of 0.154906 nm the Al (311) peak is at 2θ of about 79 degrees
Plot counts against angle to map out the peak
Diffraction Peaks
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Peaks
77 77.5 78 78.5 79 79.5 80 80.50
500
1000
1500
2000
2500
Aluminum (311)
Scattering Angle (degrees)
Neu
tron
Cou
nts
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Goal is to measure strains and ultimately stresses Strain is measured relative to unstressed sample Therefore, repeat all measurements on
unstressed samples◦Made by cutting up the engine and re-measuring the
samples removed from the engine◦Removing the samples from engine relieves stresses
Reference Peak Positions
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Bragg’s Law has a Direction
IncidentBeam Scattered
Beam
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Look at three directions around the valve ports
Stress Components
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Stress Components
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Stress Components
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In 1-D, law was σ=Eε, where:◦ σ is stress,◦ E is Young’s Modulus and◦ ε is strain
More complicated in 3-D:
Where:◦ σ R,A,H is the Radial, Axial or Hoop stress (pick one) ◦ ε R,A,H is the Radial, Axial or Hoop Strain (pick one)◦ ν is Poisson’s Ratio
Hook’s Law in 3-D
),,,, (
211 HARHARHARE
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Al (311) Scattering Angle
Depth (mm) Radial Axial Hoop
0 78.7291° 78.8203° 78.7864°
6 78.7701° 78.7942° 78.7632°
12 78.6396° 78.7036° 78.6999°
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From the peak angles, calculate the “d” spacings From the “d” spacings, calculate the strains using:◦Strain ε = (d-d0)/d0 , for Al (311) do = 0.122082 nm
From Young’s Modulus (E) and Poisson’s ratio (ν), calculate components of stress using:
Al E=68.9 GPa, ν=0.33 For R,A,H pick one component each time and
recalculate
Data Analysis
),,,, (
211 HARHARHARE
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Next week: Analysis of Data
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Poisson’s Ratio
Isotropic MaterialStrain in x-direction is εx = ΔL/LStrain in transverse (y and z) direction is εT = ΔL’/LPoisson’s Ratio is ν = - εT/εx