Abstract of Residual Stress Measurement using Neutron Diffraction

This lab report analyzes experimental results obtained using Neutron diffraction method and compares them with theoretically calculated values. Neutron diffraction method here is used to measure residual stress distributions in two sample. Strain from neutron diffraction of samples is measured in axial and transverse with error values. Error values are obtained from estimating uncertainty from the peak fitting process and then will be combined using weighting average method. Some properties and characteristics of material are needed to perform calculations. Dog bones will be used to measure the required properties from tensile test of small samples. Residual stress distributions form experiment results will be compared with expected distributions base on elastoplastic beam theory. Moreover, possible error and significance of error will also be discussed in this report.

 

 

Table of content

•         Introduction and Background

•            Diffraction principle-the Bragg law

•            Strain Measurement using Neutron

•         Experiment Details

•            Sample Preparation

•              Sample Descriptions

•              4-Point Bending

•            Mechanical Testing and Material Properties (Dog bone)

•            Strain Measurement using Neutron

•         Results and Data Analysis

•            Material Properties from dog bone sample

•            Residual Stress Distributions from elastoplastic beam theory

•            Residual Stress Distributions using neutron Diffraction

•        Discussion: Theory compare with results from experiment

•         Conclusion

•            Possible errors and significant of error

•         Reference

Introduction and Background of Residual Stress Measurement using Neutron Diffraction

Stress that stays in material after manufacture and processing in the absence of external forces or thermal gradients can be defined as residual stress. Most of techniques that are used for measurement of residual stress first measure the strain and then utilizing Young’s modulus and Poisson’s ratio, residual stresses is calculated in material.

 

Residual stress that originates form manufacturing process may become reason for yielding and plastic deformation that can lead to failure or cracking in materials. They can be categorized as Mechanical, Thermal and Chemical.

 

there are many techniques to measure the residual stress. Two of them are main techniques. First is destructive or mechanical strain release technique and second is diffraction technique. destructive strain technique actually disturbs the state of residual stress equilibrium and release stress. It then records the deformations of strain or material and  then calculates original residual stress. Hole drilling is one of examples that make use of this technique. While in diffraction technique, material is not deformed because it will be tested for crystallographic properties or physical properties of material. Rather it measures variations that are caused due to stress, in the lattice spacing of polycrystalline materials. X-ray is one of such examples that make use of this technique.

 

Neutron Diffraction is one of such methods that uses diffraction techniques. It has many advantages that make this technique very useful. Its ability to work with up to 60mm depths in steel and 100mm in aluminum, to measure residual stress in Tri-axial and to measure residual stress in macro and micro are some of uses that make this technique a useful choice.

 

 1.1 Diffraction principle-the Bragg law of Residual Stress Measurement using Neutron Diffraction

            Radiation interaction with crystalline materials can be cause of occurrence of diffraction phenomena. Diffraction principle is applicable when wavelength is non varying and then the pattern of constructive and destructive interference will likely occur. For a crystalline material, it is tested by utilizing neutron beam with geometry shown below and hence can be expressed by Bragg law.

Figure1: Bragg law theory

where λ = wavelength of neutron beam,

           d = inter-planer spacing and

           2θ = point where diffraction peaks appear and each diffraction peak

                   corresponds to a single lattice spacing

           θ = the incident angle and

           n = an integer.

The Neutron beam generated from the reactor reflects with Monochromator and it defines the direction by a slit or Collimator. The detector then counts the number of neutrons that pass through it. The gauge volume is the intersection of incident and scattered beam. The gauge volume can be moved in different direction to distribute stress in sample and measure in different directions.

 

 

 

2. Experiment Details of Residual Stress Measurement using Neutron Diffraction

            Neutron diffraction method is use to measur residual stress distributions can in two samples of plastically deformed aluminum bars. The diffractometer that was used for calculating strain using neutron was KOWARI. All properties of the samples were calculated through the use of the tensile test.

 

•           Sample Preparation

2.1.1 Sample Descriptions of Residual Stress Measurement using Neutron Diffraction

          Two samples used in this experiment were rectangular shaped bars of hardened aluminum alloy. One sample was 6061-T6 and other sample was 7075-T6. Larger rolled plates were used in cutting and were obtained from a supplier in Sydney. The dimensions used in cutting process are shown in the table1.

 

Sample	Dimensions(mm)
6061-T6	40 x 44.45 x 300
7075-T6	40 x 38.1 x 300

Table1:Dimensions of the two aluminum bars

 

2.1.2 4-Point Bending of Residual Stress Measurement using Neutron Diffraction

            Two sample were deformed in 4-point bending apparatus that was available in University’s mechanical testing machine. The process continued until they yield and become plastic with permanent deformation, hence giving us a plastically deformed aluminum bar. The position of bending is shown in figure 4.

7075-T6

179

7

2.1

 

Table2:Maximun loads and deformation from 4-point bending of sample

After bending, the sample were cut. In this process centre 100mm was taken from strain measurement using neutron for further use in our experiment.

 

 

 

 

 

•        Mechanical Testing and Material Properties of Residual Stress Measurement using Neutron Diffraction

Sample	Rupture stress	Rupture Strain
6061-T6	270	0.2
7075-T6	540	0.18

 

Different properties and characteristic of each sample were determined. To do so, new small plates were prepared from each sample to test in the university’s mechanical testing machine. Deformation of the materials was measured using standard tensile test at the time when force was applied to sample. For accuracy in the small elongation measurement, clip-gauge were used at the midpoint of the sample. The test continued until yielding and then ultimate load and final strain were recorded in the table3. All measured data of each sample was recorded for analysis.

 

were used in this axial and transverse measurement. All measured data for each sample during the test was recorded for analysis in table4.

3.1 Material Properties from dog bone sample of Residual Stress Measurement using Neutron Diffraction

            Dataset obtained from tensile test comprises of of 6061-T6 and 7075-T6 aluminum bar. It has been analyzed to determine their properties where units of force are in kN and units of clip gauge length are in mm . In both obtained datasets of samples, the force and clip gauge length were not recorded from start. Therefore it can be seen that force is zero with initial clip gauge length. Maximum force was applied up to 19kN for 6061-T6 and 36 kN for 7075-T6 sample. The graphs for both sample are shown in figure 8 and figure 9 present in Appendix 1.

 

Due to slip of clip gauge at the beginning of test, period must be ignored and the initial clip gauge length was unknown. The initial length of clip gauge can be determined. For that purpose, straight line trendline were drawn along the straight line part because of elastic deformation to find interception when force is equal to zero. Same thing was done to both samples 6061-T6 and 7075-T6. The trend line with the line equation were shown for both sample in figure 10 and 11 in Appendix 4.

 

 

 

 

Table5: Initial clip gauge length

 

Using force and clip gauge length as a base, strain and stress can be measured. For this purpose, we would make use of initial clip guage length that was measured from trendline equation and area of mid-section of dog-bone which is 62.5mm2 . Figure 12 and Figure13 in Appendix 2 shown are graphs of stress and strain that were calculated from tensile test of each sample. It can be clearly seen that the stress of 6061-T6 sample increased up to around 300MPa and stress of 7075-T6 sample increased up to 580MPa. In Elastic zone, the stress is lower than approximately 270 for 6061-T6 sample and 550 for 7075-T6 sample. These calculations were just an estimation. To determine the exact value, proper analysis of graphs is required.

 

Value of Young’s modulus can be determined from graphs shown in figure 14 and figure 15 in Appendix 3. It can be done from the slope of the the elastic zone. Yield stress can be determined by drawing the line 0.2% offset to find the interception. The result of the graph gives the value of Young’s modulus of 74401MPa and yield stress of 295MPa for 6061-T6 sample and Young’s modulus of 71191MPa and yield stress 540MPa for 7075-T6 sample.

 

 

Sample	E(MPa)	Yield Stress(MPa)
6061-T6	74401	295
7075-T6	71191	540

Table6: Material properties from tensile test

 

3.2 Residual Stress from elastoplastic beam theory.

  

     Figure17: Theoretical residual stress distribution of 7075-T6

 

3.3 Residual Stress Distributions using neutron Diffraction

The purpose of experiment for each sample was the measurement of axial and transverse d-spacing with error. Two values were required so that final value for each point could be obtained by combining them. For this purpose, using weighted mean as base, Error propagation was helpful in estimating the value. Formula is shown below. After that strain formula and Hooke’s law were apllied to acquire stress at each point. the plots of the residual stress distributions of each sample were shown in figure18 and figure19.

 

Figure18: Residual stress distribution using neutron diffraction of 6061-T6

 

Figure19: Residual stress distribution using neutron diffraction of 7075-T6

 

4. Discussion: Theory compare with results from experiment

            Results of residual stress distribution were obtained from both experiment as well as theoretical calculation. They were shown in the graphs above. It can be critically analyzed and observed that they were similar to some extent. Additionally, an outcome that is different from theory was also observed.

A slip from the clip gauge can be seen in tensile test and this data leads to the properties of the material . Those properties are yield stress and Young’s modulus of each sample. Any errors in this test can also result in error in theoretical calculation that is further used to compare with the experiment using neutron diffraction.

            The residual stress in both sample along the vertical axis is not straight line that makes angle when the stress change like theoretical calculation. Gradual change in direction of line of residual sress using neutron can be seen clearly whereas in theoretical calculations, the line turns to other direction at that point. The location turns out to precise for both sample when stress is zero at intersecting points.

Experiment values of 6061-T6 do not seem to be as expected or accurate or we can say that there might be something wrong with the data. The lack of smoothness in grapg of residual stress distribution is because of those unexpected values in dataset of 60661-T6. There can be many possible errors for the lack of accuracy. Out of many, one can be the chosen method that is used to combine the axial and transverse d value. As there are many ways to be chosen so there are many possible outcomes depending on the chosen method. Also from the given value with error of d0, the 6061-T6 sample gives more rough estimate than 7075-T6 for uncertainty of 8x10^-6 as compared to 5x10^-6. This may also be of reasons that might lead us to the error of the result.

As a whole, it can be concluded that the value of residual measured from experiment at every point is smaller than the calculated theoretical values. This becomes more visible at the maximum value in compression and tensile stress (negative and positive values). Additionally it can also b e seen that the value of stress at the surface including top and bottom, are very large in calculated theoretical values but as a results of experiment, they are smaller than the value of stress inside the bars.

 

5. Conclusion of Residual Stress Measurement using Neutron Diffraction

          The results of the experiment using Neutron diffraction method have been analyzed from the data recorded during the experiment. The results were in form of graphs and diagrams so that they must be clearer and easier to make a comparison. Axial and transverse d spacing value with error values from estimating uncertainty were combined using weighted mean method and Hook’s law was applied. Theoretical residual distribution was calculated from its properties from tensile test of dog bones and compared with the experimental result.

            To sum up, the experiment results of neutron diffraction method obey the theory in some part for both samples. The data of 7075-T6 seem to be more accurate that 6061-T6 sample in terms of result that came out quite similar to the theoretical calculation but not for 6061-T6 that seem to have some error in the data.

 

5.1Possible errors and significant of error of Residual Stress Measurement using Neutron Diffraction

            Experiments of physical quantities dont give 100 percent accurate measurements. There are always chances of error in experiment that makes the result erroneous so uncertainties must be concerned in every measurement. The smaller range of uncertainty will result into the more precise the measurement. Significant of the error is the significant of the digit. Example of the values with uncertainties is d0, d spacing, and the entire bars dimension. Apart from these, there also be many chances of some error from machine or environment where the experiment is being performed.

 

6. Reference of Residual Stress Measurement using Neutron Diffraction

Aerospace aluminum distributor supplier. Retrieved August 2, 2016, from https://www.aerospacemetals.com/aluminum-distributor.html

 

ASM material data sheet. Retrieved August 2, 2016, from http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061T6

 

ASM material data sheet. Retrieved August 2, 2016, from http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA7075T6

 

M. T. Hutchings (1991). Measurement of Residual and Applied Stress Using Neutron Diffraction. United Kingdom: Oxford.

 

Measurement of residual stress in materials using neutrons. Retrieved August 2, 2016, from http://www-pub.iaea.org/MTCD/publications/PDF/te_1457_web.pdf

 

Neutron diffraction study of the deformation behaviour of deformation processed copper/chromium composites. Retrieved August 2, 2016, from http://www.isis.stfc.ac.uk/instruments/engin-x/publications/neutron-diffraction-study-of-the-deformation-behaviour-of-deformation-processed-6512.pdf

Neutron Diffraction Technique. Retrieved August 2, 2016, from http://www.veqter.co.uk/assets/files/RSM%20techniques/Neutron%20Diffraction%20flyer%20v1.pdf

 

Neutron strain scanning on Kowari. Retrieved August 2, 2016, from http://www.ece.rochester.edu/courses/ECE111/error_uncertainty.pdf

 

Preuss, M. Engineering Advanced diffraction techniques for Residual Stress determination. Retrieved August 2, 2016, from http://www.oxfordneutronschool.org/2011/lectures/Engineering_lecture_Michael%20Preuss.pdf

Residual stress info. Retrieved August 2, 2016, from http://www.protoxrd.com/residual-stress-info.html

 

Something to Bragg about: One Hundred years of Bragg’s law - royal institution of Australia (2015). Retrieved August 2, 2016, from http://riaus.org.au/articles/something-to-bragg-about-one-hundred-years-of-braggs-law/

 

Using fracture mechanics for determining residual stress fields in diverse geometries (2012).Ingeniería e Investigación, 32(3), 19–26. Retrieved from http://www.scielo.org.co/scielo.php?script=sci_arttext HYPERLINK "http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-56092012000300005"& HYPERLINK "http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-56092012000300005"pid=S0120-56092012000300005

 

Veqter. (2016). An overview of residual stress measurement. Retrieved August 2, 2016, from http://www.veqter.co.uk/residual-stress-measurement/overview

 

Veqter. (2016). Measuring residual stress using the neutron diffraction technique. Retrieved August 2, 2016, from http://www.veqter.co.uk/residual-stress-measurement/neutron-diffraction

 

Wensrich, C. M. (2012). Measurement and analysis of the stress distribution during die compaction using neutron diffraction. Granular Matter, 14(6), 671–680. doi:10.1007/s10035-012-0366-8

 

Withers, P. J., Holden, T. M., & Lorentzen, T. (2005). Introduction to the characterization of residual stress by neutron diffraction. United Kingdom: Taylor & Francis.

7. Appendix

Appendix 1