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Internal Stresses in Aluminum Engines
Data
Introduction of research project Solidification of casting alloys Stresses and strains Crystal lattices Diffraction Neutrons Experimental design Data Analysis of data
Measuring Residual Stresses
FCC Aluminum Diffraction Pattern
Experimental Geometry
Detectors
Engine Head
Beam Aperture
Transmitted Neutron Beam
Scattered Neutrons
Monochromator
Sampling Volume
Experimental Geometry
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
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
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
Bragg’s Law has a Direction
IncidentBeam Scattered
Beam
Look at three directions around the valve ports
Stress Components
Stress Components
Stress Components
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
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°
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
Next week: Analysis of Data
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