Stress Analysis of the Bi-Metallic Coins – a Potential Shrink Fit Ring & Plug Standard

The “Shrink-fit ring and plug” system is known in the residual stress neutron community mostly due to the VAMAS Round Robin specimens, that were measured by most of the neutron residual stress instruments worldwide. This standard, however, can be challenging for some low flux instruments and considerable beamtime and efforts are required to accomplish measurements accordingly to the measurement protocol. Theoretically, the residual stress distribution is not simple, being neither plain stress nor plain strain, and essentially it is a 3D distribution with a large gradient toward the flat cut, especially for the axial component. Another “shrink-fit ring-and-plug” system is being considered, namely bi-metallic coins. With an easier zero plane stress state, they represent another potential candidate for a standard. Bi-metallic coins are in current circulation in many countries of the world. In the given study we report on an assessment of the residual stress state of 7 different bi-metallic coins measured by means of neutron diffraction to reconstruct the full stress state. The magnitudes of the stresses in the specimens were different obviously due to differences in the coinage process and materials in use. While in some cases residual stresses are weak and therefore difficult to measure accurately, in some cases stresses reach ~100 MPa. Although question in variability of the coinage process through years and within series is still debatable, tight standards and tolerances of the mint industry suggest the probability of consistency in the residual stress state making bi-metallic coin an interesting alternative to the VAMAS ring-and plug standard.. Introduction The so-called VAMAS shrink-fit “ring-and-plug” sample [1] has been used over the last decade as a standard round-robin sample by the neutron community for the purpose of standardization and instrument calibration. The idea was so successful that all existing, newly built, or upgraded stress scanners made measurements of this sample, usually during commissioning. Collected data is commonly among the very first results, as in the case of residual stress diffractometer KOWARI at ANSTO [2]. Despite this success, there were few drawbacks with this approach: o There were only two samples made and although they can become available within reasonable time, the associated logistics and mailing samples around the world without risk of losing them is problematic. o Although aluminium barely activates during a normal neutron diffraction experiment (transmission tomography can be different!) moving samples that have been irradiated across borders can be problematic. o The samples were produced in one single and unrepeated process, there is a seriously challenging problem if someone wishes to reproduce them exactly; there were some unsuccessful attempts in the past to make copies. There are also problems of a scientific nature and related to the experimental process: o The samples are made of aluminium alloy AA7050. Although this has the advantage of providing high penetration and low stiffness, both good for neutron strain measurements, aluminium is a weak scatterer, therefore for some residual stress diffractometers with moderate performance it is a challenging task to carry out the prescribed measurement programme in full. As a consequence Residual Stresses 2016: ICRS-10 Materials Research Forum LLC Materials Research Proceedings 2 (2016) 31-36 doi: http://dx.doi.org/10.21741/9781945291173-6 32 incomplete data sets were collected on some instruments, while on other beamlines spatial resolution or accuracy was sacrificed to have measurements done within reasonable experimental time. o Another drawback of AA7050 alloy is that it is anisotropic and special efforts must be made to keep it under control and separate measurements of a specially made d0 sample (a stand-alone plug sample) should be performed slowing down the overall experiment. o With overall dimensions 50 mm diameter and 50 mm height, the residual stress state is not simple, neither plane-strain state, nor plane stress state. In general, a gradient along the axis of the cylinder is present for strains and stresses. It is especially pronounced for the axial stress component which changes from a maximum value in the mid-height to exact zero at the top and bottom surfaces. Thus, results of the measurements, in principle, depend on the experimental setup and how measurements were executed, e.g. on the exact shape and size of the gauge volume In an attempt to overcome these drawbacks, a much simpler standard sample can be envisaged. It should be made of a better neutron scatterer, still with sufficiently low stiffness and it should have a highly symmetric shape, like the VAMAS sample, cylindrical. If the sample is to comply with the plane stress condition, then to have a 2D shrink ring-and-plug system made of copper (or steel), a few mm in thickness and 30-40 mm in diameter would be a good candidate. Such systems are available in mass-production and they are bi-metallic coins. They are produced in almost all countries around the world from similar materials in similar size, though technologies of their production are expected to be different and undisclosed. The aim of this study is to investigate residual stress in bi-metallic coins, using several easily obtainable candidates, and to assess how reasonably they can be used as standard specimens. The issues to investigate are o How strong are the residual stresses in the coins? It is difficult to measure weak stresses since very small strain/stress error bars should be experimentally achieved. o Is the material very anisotropic and should a special d0 be a part of the measuring programme? o How uniform is the material? Since stamping of the surface image (relief) is not uniform, it can potentially induce non-uniformity in the stress state that should be avoided. o Although there are expectations of tight standards and tolerances in the mint industry, can the consistency of minting technology and variability in the residual stress state (through years of minting and within the same year) be addressed and satisfactorily resolved in an experimental manner? This is a first of the kind study on bi-metallic coin residual stress since no experimental results are available up to now. Beyond the particular consideration of bi-metallic coins as a stress standard, this work brings a new characterisation of these every-day objects. Principles of bi-metal coin production (minting) The production process starts with punching coin blanks to be the ring and core/plug. A hole is also punched through a blank to produce a ring, whose diameter is accurately sized to fit inside the ring. The blank of the plug is also treated specially by adding a groove all the way around the edge e.g. by milling. The stamping (or double stamping) finally fixes the two parts of the assembly together and the force of the stamping plunger is adjusted to provide conditions for material of the inside edge of the ring to be pressed into the groove, locking the two parts into place (Fig. 1). The different materials with different elastic and plastic properties, different sizes of ring and plug, different groove designs and tolerances are Fig. 1. Structure of a generic bi-metallic coin. A variable groove design is shown in two options. Residual Stresses 2016: ICRS-10 Materials Research Forum LLC Materials Research Proceedings 2 (2016) 31-36 doi: http://dx.doi.org/10.21741/9781945291173-6 33 reflected in different accumulated stresses. Although the locking mechanism by groove is partially responsible for the integrity of a bi-metallic coin, the residual stress should be generally present and also play a role. Samples and materials A number of bi-metallic coins were selected for the current study of the residual stresses and their details are given in Table 1. All selected coins are made from copper alloy of a certain kind (with few exceptions for the ring material) and all fall into a very narrow interval of sizes: 26 – 28 mm diameter. Experimental: principles Due to the plane stress condition the stress state of a bi-metallic coin with outer radius b and inner Table 1. Bi-metallic coins and their characteristics (data collected from multiple sources)


Introduction
The so-called VAMAS shrink-fit "ring-and-plug" sample [1] has been used over the last decade as a standard round-robin sample by the neutron community for the purpose of standardization and instrument calibration.The idea was so successful that all existing, newly built, or upgraded stress scanners made measurements of this sample, usually during commissioning.Collected data is commonly among the very first results, as in the case of residual stress diffractometer KOWARI at ANSTO [2].Despite this success, there were few drawbacks with this approach: o There were only two samples made and although they can become available within reasonable time, the associated logistics and mailing samples around the world without risk of losing them is problematic.o Although aluminium barely activates during a normal neutron diffraction experiment (transmission tomography can be different!)moving samples that have been irradiated across borders can be problematic.o The samples were produced in one single and unrepeated process, there is a seriously challenging problem if someone wishes to reproduce them exactly; there were some unsuccessful attempts in the past to make copies.There are also problems of a scientific nature and related to the experimental process: o The samples are made of aluminium alloy AA7050.Although this has the advantage of providing high penetration and low stiffness, both good for neutron strain measurements, aluminium is a weak scatterer, therefore for some residual stress diffractometers with moderate performance it is a challenging task to carry out the prescribed measurement programme in full.As a consequence incomplete data sets were collected on some instruments, while on other beamlines spatial resolution or accuracy was sacrificed to have measurements done within reasonable experimental time.o Another drawback of AA7050 alloy is that it is anisotropic and special efforts must be made to keep it under control and separate measurements of a specially made d 0 sample (a stand-alone plug sample) should be performed slowing down the overall experiment.o With overall dimensions 50 mm diameter and 50 mm height, the residual stress state is not simple, neither plane-strain state, nor plane stress state.In general, a gradient along the axis of the cylinder is present for strains and stresses.It is especially pronounced for the axial stress component which changes from a maximum value in the mid-height to exact zero at the top and bottom surfaces.Thus, results of the measurements, in principle, depend on the experimental setup and how measurements were executed, e.g. on the exact shape and size of the gauge volume In an attempt to overcome these drawbacks, a much simpler standard sample can be envisaged.It should be made of a better neutron scatterer, still with sufficiently low stiffness and it should have a highly symmetric shape, like the VAMAS sample, cylindrical.If the sample is to comply with the plane stress condition, then to have a 2D shrink ring-and-plug system made of copper (or steel), a few mm in thickness and 30-40 mm in diameter would be a good candidate.Such systems are available in mass-production and they are bi-metallic coins.They are produced in almost all countries around the world from similar materials in similar size, though technologies of their production are expected to be different and undisclosed.
The aim of this study is to investigate residual stress in bi-metallic coins, using several easily obtainable candidates, and to assess how reasonably they can be used as standard specimens.The issues to investigate are o How strong are the residual stresses in the coins?It is difficult to measure weak stresses since very small strain/stress error bars should be experimentally achieved.o Is the material very anisotropic and should a special d 0 be a part of the measuring programme?o How uniform is the material?Since stamping of the surface image (relief) is not uniform, it can potentially induce non-uniformity in the stress state that should be avoided.o Although there are expectations of tight standards and tolerances in the mint industry, can the consistency of minting technology and variability in the residual stress state (through years of minting and within the same year) be addressed and satisfactorily resolved in an experimental manner?This is a first of the kind study on bi-metallic coin residual stress since no experimental results are available up to now.Beyond the particular consideration of bi-metallic coins as a stress standard, this work brings a new characterisation of these every-day objects.

Principles of bi-metal coin production (minting)
The production process starts with punching coin blanks to be the ring and core/plug.A hole is also punched through a blank to produce a ring, whose diameter is accurately sized to fit inside the ring.The blank of the plug is also treated specially by adding a groove all the way around the edge e.g. by milling.The stamping (or double stamping) finally fixes the two parts of the assembly together and the force of the stamping plunger is adjusted to provide conditions for material of the inside edge of the ring to be pressed into the groove, locking the two parts into place (Fig. 1).
The different materials with different elastic and plastic properties, different sizes of ring and plug, different groove designs and tolerances are

Fig. 1. Structure of a generic bi-metallic coin. A variable groove design is shown in two options.
reflected in different accumulated stresses.Although the locking mechanism by groove is partially responsible for the integrity of a bi-metallic coin, the residual stress should be generally present and also play a role.

Samples and materials
A number of bi-metallic coins were selected for the current study of the residual stresses and their details are given in Table 1.All selected coins are made from copper alloy of a certain kind (with few exceptions for the ring material) and all fall into a very narrow interval of sizes: 26 -28 mm diameter.

Experimental: principles
where K =b/a and apart from the geometric dimensions is characterized by only one parameter p, a pressure on the plug.Stress-strain relationships are also simplified to (3) In principle, for full reconstruction of the stress state, the stress measurement of the inner core is sufficient.Experimentally, the measurement programme might vary depending on assumption regarding d 0 anisotropy: (EXP1) If a d 0 isotropy assumption is made, the experiment can be carried out non-destructively.The measurements of the central core involve detection of the two principal directions, hoop/radial and axial, from which by applying the condition of the axial component to be zero, the hoop/radial stress component and d 0 can be resolved.
(EXP2) If, however, d 0 is assumed to be anisotropic, the stresses can be resolved only in a destructive way.The experimental programme of the central core then involves detection of the two principal directions, hoop/radial and axial, each measured in loaded (intact coin) and unloaded (the central core is removed from the ring).Thus two principal elastic strains can be derived from the pair of measurement and the hoop/radial stress component can be calculated.
In both cases, due to the uniform stress state in the plug (Eq. 1, no radial dependence, only uniform pressure p), measurements with an elongated gauge volume can be used reducing overall measurement time in this way and/or improving counting statistics.With the thickness range of the coins of 1.75 to 2.6 mm, and core diameters at least 15mm, a gauge volume with dimensions 1×1×10 mm 3 seems the most adequate.Thus, measurements of the two directions (in transmission and reflection geometry) are easily possible, even for moderate performance neutron stress scanners.

Experimental: neutron diffraction setup
Neutron residual stress measurements of bi-metallic coins were performed on the KOWARI neutron diffractometer at OPAL research reactor at ANSTO [2].For all coins the Cu(311) reflection was used at 90°-geometry employing a neutron wavelength of λ = 1.54 Å.Because different alloys had slightly different lattice spacings, there was a natural variation in the exact position of the diffraction peak, but all of them they were within range of ±1°.
A gauge volume with size of 1×1×10 mm 3 was consistently used since it could be positioned within each and every coin central core.Not just one, but 5 locations (exact centre, ±3 mm, ±6 mm) were systematically measured for each coin to assess uniformity and statistical variations of the material of the plug with measurement times of 3 minutes.The high flux of KOWARI, optimised for this wavelength, yielded 50 -60 µstrain accuracy on average or ~7-8 MPa in terms of calculated stresses.

Experimental: results and data analysis
The study has been performed in several steps: First, the attempt was made to conduct a non-destructive experiment (EXP1), i.e. the inner core part was measured in two directions, hoop/radial and axial, to assess elastic strain anisotropy.The experimental results are presented in Fig. 2. As can be seen from the diagram, three out of seven coins demonstrate tension of the core.As this is a non-physical result, but rather an artefact of the data treatment, the assumption of isotropic d 0 is not viable for the majority (if not all) of the coins.
Secondly, a full, but destructive analysis (EXP2) was performed next.The two principal directions, hoop/radial and axial, were measured in two states, intact and free, where the central core is removed from the ring.Stresses were calculated with properly measured d 0 and are shown in Fig. 3.They are quite different from those shown in Fig. 2: with d 0 taken correctly into account, all stresses are compressive, as expected.
Due to the significant anisotropy in coin UK2, additional measurements were made on it to assess in-plane anisotropy, uniformity and reproducibility.The dependence of the lattice d-spacing on the in-plane direction is shown in Fig. 4 (left) and indicates no in-plane anisotropy and non-uniformity, thus the cylindrical symmetry of coin is confirmed for this specimen.In comparison, the aluminium alloy AA7050 exhibits much larger degree of in-plane d0 anisotropy presented in Fig. 4 (right) inherited from the plate rolling process.To address the question of reproducibility, two UK2 coins were compared in intact conditions, from minting years 2002 and 2008, and within error bars they provided the same result.However, this coin is not the best sample to be used to check reproducibility of stress since the magnitude of stress turned out to be close to zero.

Fig. 2 .
Fig.2.Measure of the appeared anisotropy in strain and stress scale for seven bi-metal coins.