Introduction of research project Solidification of casting alloys Stresses and strains Crystal lattices Diffraction Neutrons Experimental.

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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)

Ne

utr

on

Co

un

ts

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 HARHARHAR

E

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 HARHARHAR

E

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