A finite-element study of sapphire anvils for increased ...

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A finite-element study of sapphire anvils for increased sample volumes a

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C.J. Ridley , M.K. Jacobsen & K.V. Kamenev

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The School of Engineering and the Centre for Science at Extreme Conditions, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK Published online: 19 Feb 2015.

Click for updates To cite this article: C.J. Ridley, M.K. Jacobsen & K.V. Kamenev (2015): A finite-element study of sapphire anvils for increased sample volumes, High Pressure Research: An International Journal, DOI: 10.1080/08957959.2015.1009454 To link to this article: http://dx.doi.org/10.1080/08957959.2015.1009454

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A finite-element study of sapphire anvils for increased sample volumes Downloaded by [The University of Edinburgh] at 03:18 03 March 2015

C.J. Ridley ∗ , M.K. Jacobsen† and K.V. Kamenev The School of Engineering and the Centre for Science at Extreme Conditions, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK (Received 10 July 2014; final version received 15 January 2015) Diamond anvil cells enable over Mbar sample pressures to be generated, but remain unsuitable for many measurements due to the limited sample volume available. Larger sapphire anvils have enabled approximately an order of magnitude increase in sample volume, but fail to reach similar pressures due to the mechanical differences between sapphire and diamond, and the difficulties in containing larger sample volumes under pressure. To understand the origin of these limitations, finite element analyses of large sapphire anvils have been performed and compared with experimental loading data. Keywords: finite element analysis; sapphire anvils; shape optimisation; opposed anvil pressure cells

Introduction Opposed anvil cells are used for a wide variety of pressure measurements over extensive temperature ranges. Single-crystal diamond is the most commonly used anvil material due to its high compressive strength, optical transparency, and excellent thermal properties, but commercially available diamond anvils are limited in size, and can only contain sample volumes ∼ 0.1 mm3 . Techniques such as neutron diffraction, and other applications such as high pressure material synthesis, require much larger sample volumes,[1] achieved through using large volume presses (∼ 100 mm3 ) such as multi-anvil devices [2] or the Paris-Edinburgh cell.[3] The increased support required by these devices makes low-temperature work difficult, as the thermal mass of the cell increases and the large composite anvils (typically WC) do not easily allow for optical access to the sample. This has motivated the development of more compact gem-anvil devices capable of pressurising sample volumes between 1 and 5 mm3 . Sapphire is a hard material (σc ∼ 3 GPa1 , σt ∼ 350 MPa), although not as strong as diamond (σc ∼ 8GPa, σt ∼ 1.2 GPa), it has the advantage that it can be mass produced in much larger dimensions, with high purity at significantly lower cost. Sapphire anvils with sample volumes large enough for neutron studies have been reported elsewhere,[4–9] though remain limited to pressures below ∼ 15 GPa. It has been reported that sapphire performs most reliably when used with ‘softer’ gasket materials (Al or Cu),[10] with stainless steel being the hardest material suitable.[4] This intrinsically *Corresponding author. Email: [email protected] † Current address: Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA. © 2015 Taylor & Francis

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limits the use of sapphires, since softer gaskets are not able to contain the same pressures as rhenium or Inconel, as commonly used in diamond anvil cell (DAC) experiments. Modelling the anvil/gasket under pressure provides an insight into how sapphire is limited in this way, and into how the pressure limit on larger sample volumes may be increased. Analytical modelling of the system becomes inaccurate due to the large plastic deformations involved, and the resulting complex pressure distribution. Numerical modelling using finite element analysis (FEA) has been performed to overcome these limitations. Through controlling the parameters of the model, and comparing the results to reported data, suggestions for the cause of anvil failure are reported, forming the basis for possible improvements.

Finite element analysis The nonlinear behaviour of the gasket, and the complex onset of support provided between it and the anvil, makes the ab initio calculation of full stress patterns challenging. Previous studies have looked for analytical solutions to the problem of anvil optimisation,[9,11,12] though the results tend to underestimate the capabilities of the anvils. FEA is used to numerically analyse stress patterns in objects with complex geometries under non-trivial loading scenarios. Separating the system into elements (‘meshing’) allows for a large yet finite number of stress and strain tensors to be evaluated fully at any stage of the simulated experiment. Realistic modelling requires extensive material data, and the input of some poorly characterised parameters, such as friction coefficients, which limits the accuracy of the results. To verify the models, and identify the cause for failure of the system, the calculated stress distributions must be compared with experimental data. Studying the process of pressure generation in a gasketed anvil cell complicates FEA for several reasons: (1) the large pressures under the anvil quickly cause plastic deformation in the gasket, requiring longer computation times, and the use of simplified models of plasticity, since the properties of highly deformed gasket materials at high pressure are generally unknown. (2) The interaction between components requires unknown contact parameters to be defined. (3) The material properties of hard, brittle materials are poorly defined as measurements are highly dependent on less controllable parameters, such as surface finish or purity which alters the mechanical properties. Previous FEA studies Previous FEA studies of opposed anvil systems have avoided some of these complications through artificially generating the pressure distribution from the gasket, instead of modelling the full anvil/gasket assembly. This type of model has helped in identifying the cause for large levels of basal tension in diamond anvils,[13] leading to anvil seat optimisation.[14] However, it fails to distinguish the complex onset of support provided between the anvil and the gasket, and neglects the effects of gasket deformation on stresses in the culet. Existing studies that include the gasket are concerned with DACs, with small culets and thin gaskets.[15–19] The present study is unique in that it considers sapphire, a far more compressible anvil material, with larger dimensions than those typically used for the DAC construction, and the gaskets used are thicker, and undergo significantly larger deformations. Present model The simulations were performed using the ANSYSTM Mechanical Workbench, static structural module. If isotropic elasticity is assumed, the rotational symmetry of an opposed anvil system


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Figure 1. (left) Geometry of the sapphire anvil/gasket assembly with key parameters labelled; (right) reduced model for stress analysis. The contact between the sapphire and the anvil is assumed to be frictional. The typical values for the geometry of this anvil were chosen using the experimental data from [4–6].

allows for the model to be reduced to a two-dimensional representation, which may then be further reduced through plane symmetry to 25% of the original model (Figure 1). These reductions of the model significantly reduce simulation times, compensating for the increased computation times required for modelling the plasticity of the gasket. The isotropic assumption is acceptable for the gasket, as the grain structure of most metallic alloys means they behave approximately isotropically prior to deformation, but is a simplification for single-crystal sapphire. This approximation has also been used in previous FEA studies of diamond, since inclusion of anisotropy is computationally expensive, whilst the key features of the stress patterns at pressures much less than 100 GPa are present in both scenarios. One further assumption made by the model is that no plastic deformation of the sapphire occurs prior to failure. This is justifiable since brittle fracture is the main mode of failure in sapphire (at room temperature or lower) [20], meaning that plastic strain is significantly smaller than the elastic strain sustained prior to failure. The material properties used in this study are listed in Table 1. These materials were chosen due to their use in previously reported results with sapphire anvils. Several different gasket materials were chosen, covering a range of hardnesses. The Poisson ratio was chosen as ν = 0.3 for all material models. The contact between the sapphire and the gasket was assumed to be frictional throughout the study, with a coefficient of 0.3. The results were found to be independent of this value between 0.2 and 0.4, consistent with the finding that the pressure generated is independent of contact friction between the anvil and gasket.[9] To approximate the plastic behaviour of the gasket a bilinear model is used, where the form of the stress/strain beyond the elastic limit is approximated as linear. The yield strengths and tangent moduli chosen in each case were calibrated against experimental loading, and tensile testing data (using a standard tensiometer). The loading data were achieved through gradually loading the gasket (without a sample) between two anvils, and measuring the change in gasket

4 Table 1.

C.J. Ridley et al. Material properties used in FEA.

Sapphire (isotropic) [21] NaCl sample (powder) Cu alloy Aluminium 6061 (I) Aluminium 7075 (II) BeCu25 (H) (I) BeCu25 (AT) (II) BeCu25 (HT) (III)

Elastic modulus (GPa)

Yield strength : tangent modulus

Density (g cm−3 )

350 35 110 75 75 123 123 123

n/a 150 MPa: 500 MPa 280 MPa: 1.15 GPa 350 MPa: 500 MPa 500 MPa: 500 MPa 800 MPa: 1 GPa 1 GPa: 2 GPa 1.4 GPa: 2 GPa

3.98 2.17 8.30 2.84 2.84 8.24 8.24 8.24


Note: Values from the literature are referenced where applicable, other values were determined in the present study using tensile testing, and calibration with load testing.

thickness for a known load. This procedure was then replicated in the FEA. Through comparing the behaviour of the model to the experimental data, the elastic and plastic moduli were altered so as to match the thickness/load curve to within 10% (this procedure is similar to that reported by Fang et al [22]). The results found from the loading curve differed slightly from the tensiometer measurements, ascribed to differences between the compressive and tensile behaviour of the materials. Once the parameters of the gasket were fixed, a sample of powdered NaCl was then included, and the sample properties were determined through comparing experimental sample pressure versus load. Failure criteria The failure criterion of a system consists of identifying critical stress states in the system where failure is initiated. There is no single method for determining the nature of this stress state, it being highly dependent on the material being studied, and the nature of the problem. For ductile metals under simple compression or tension, the level of deviatoric strain in the material (represented by the Von Mises strain) gives an accurate indication of the maximum loads it may support. For brittle materials, which behave very differently in compression and tension, and may differ depending on surface properties, there is no single accurate metric for failure.[20] The main challenge in predicting failure in sapphire anvils is that the strength of the material is not known accurately; see Table 2. These reported strengths do not give an objective measure of the intrinsic strength of a sapphire anvil, since they strongly depend on the testing method used. However, the disparity between different axis alignments, and sapphire’s weakness in tension suggest that regions of high tension may initiate failure. This has been verified through the work of Shipway and Hutchings,[31] who found that the high axial tensile stress, in a sapphire sphere under compression between two platens, is the most likely cause of failure. It was also found

Table 2.

Single-crystal sapphire strengths – the compressive strength is highly dependent on surface finish.

Yield strength

Room temperature, atmospheric pressure value (MPa)

Compressive Flexural Shear Tensile

2420–3390 [23], 2000–2900 [21], 2400 [24] 689 (c-axis) [25], 320 [26], 420 [27], 680 [27,28], 1030 (c-axis) & 1540 (⊥c-axis) [21] 4320 [29], 2247 (c-axis), 1723–5970 (a-axis) [30] 300 (a-axis), 450 (c-axis) [23], 410 [24]

Notes: The flexural strength data were taken using 4-point flexural test or biaxial flexure. The alignment of the sapphire test piece axis, if specified, is given. The shear stress result is averaged over random orientations, under uniaxial compression between various platens. The huge variation in results for the critical shear stresses is due to the orientation of the prismatic plane.



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that for large contact areas, surface tension (rather than bulk tension) becomes more dominant, and may lead to premature failure due to surface imperfections. The conclusion that compressive failure is initiated through tensile fracture is also supported elsewhere.[32] However, the data for flexural strength and shear strength indicate that shearing may also be important in the initiation of failure. Shear gives a measure of off-axis distortion in the sapphire, and the difference between the maximum and minimum principal stresses in the system (τmax = |σmax − σmin |/2). If a region of the anvil is found to be under both very high tensile and compressive stresses then this will show as the region of high shear, where brittle materials are more prone to failure. This is supported by Bruno and Dunn,[15] who suggested that large octahedral shear at the edge of the culet area leads to chipping of the culet, motivating the use of additional bevel angles. In a complex loading scenario, tension can most easily be identified through considering the maximum, middle and minimum principal stresses in the system (σ1 , σ2 , and σ3 , respectively). The maximum principal strain (1 ) of the system may be derived from the principal stresses as 1 = (1/E)(σ1 − ν(σ2 + σ3 )), where E is the isotropic modulus of elasticity. Where 1 > 0 the system is under some form of tensile deformation, this may be achieved with different stress states, depending on the sign of the principal stresses. In a simple tensile test, σ2,3 are generally small, so when σ1 > 0 the system is in uniaxial tension. In a more complex compressive loading, it is possible that σ1,2,3 < 0, whilst 1 > 0. For this reason, this study considers the strains of the system rather than the stresses. Sapphire anvils have been tested using the sapphire anvil device described in the work of Jacobsen et al.[5] The failure of the anvils in this system was the initial motivation for the finite element study, such that the relative dimensions of the system, gasket materials used, and applied loads match those used in the models. The sample used in these tests was polycrystalline NaCl (without additional pressure medium). From the experimental observation, the anvil either (a)

(b)

Figure 2. Two failure mechanisms seen in sapphire anvils. (a) No distinguishable origin of failure, complete compressive failure of the culet. (A) top view of the culet and tapered section and (B) side view of the failed anvil. Scale bar approximately 4.8 mm across. Softened BeCu gasket, 1 mm thick, with a 1 mm diameter sample hole, no pre-indent. (b) Damage contained to the culet area. Small chips caused by gasket rupture. TiZr gasket, 1 mm thick, with a 1 mm sample hole. Pre-indentation to 0.75 mm, maximum pressure 5.2 GPa. Final thickness 0.3 mm. Smaller ring cracks possibly indicative of tensile failure due to a cupping of the 3 mm diameter culet.

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demonstrates total or partial failure (Figure 2). Total failure of the sapphire results in cracks and fractures extending through the bulk of the anvil, and is the most commonly witnessed mode of failure, whereas partial failure is confined to the culet area. It is possible that partial failure is the precursor to total failure, suggesting that failure may always originate from the culet region, though experimentally it is difficult to rule out failure originating in the bulk or along the conical face of the anvil.

Results


Effects of gasket hardness Since it has been previously suggested that the cause for failure may be due to either bulk tension or surface tension in the anvil, this study focusses on three key regions of interest in the anvil; the central portion of the anvil (bulk region), the culet surface region, and the surface of the conical face (pavilion) of the anvil. To compare the form of tensile strains between each model, paths are taken through each of these three regions as indicated in Figure 1. Initially, the effects of gasket hardness were considered. The anvil parameters as described by Furuno et al.,[6] were used, whilst the material properties of the gasket were varied as noted in Table 1. The parameters that determine material hardness (defined as resistance to plastic deformation by indentation) are the yield strength and the tangent modulus of the bilinear model, but are dominated by the former, such that the gasket materials are listed in an approximate order of increasing hardness. Figure 3 shows a compilation of the results obtained from the models, all taken at a normalised sample pressure (determined as the average of normal stresses in the sample) of 9.5 GPa, the applied load required to reach this pressure was typically 10 kN on a 1 mm diameter culet. This pressure was chosen as it is achievable experimentally with sapphire anvils, and is below the observed failure pressure. For comparison, the calculated strain distributions for an anvil with a compressibility similar to diamond (E ≈ 1220 GPa) are shown for the hardest gasket material (BeCu III) considered. The data from culet region indicate that a harder gasket material increases the tension and shear within the anvil at the edge of the sample hole, whilst reducing tensile strain at the edge of the culet which gains more support. A similar trend is seen along the path of the pavilion, showing that the critical region is the point where the anvil and gasket depart from contact. A harder gasket material results in a large transition from compression to tension resulting in large shear strains. If the path through the central region of the anvil is considered, it is found that neither the maximum shear nor the maximum tensile strain is increased with increased gasket hardness, but their distributions are broadened, suggesting that the anvil is more evenly strained. This is consistent with the expectation that the pressure distribution along the culet is also broadened for a harder gasket material. The gasket may be said to behave as a ‘thick’ or ‘thin’ gasket, referring to the behaviour of the sample hole under axial load.[33] Thin gaskets show a large inward intrusion of the surrounding gasket material into the sample hole, whereas thick gaskets are less stable, and the sample hole tends to expand. The transition between these two regimes is determined by the relative properties of the sample and gasket, the initial thickness of the gasket, and the ratio of the culet diameter to the sample hole diameter. Figure 4 shows the evolution of the maximum principal strain profiles for the Cu gasket and the BeCu (HT) gasket. For the harder gasket, the sample region of the culet is under a larger compressive strain as the gasket hole intrudes inwards, whereas the soft gasket sample hole initially remains approximately unchanged, before than expanding. At higher loads the soft gasket becomes thinner, and eventually starts to act as a thin gasket, shown by the



(a)

(c)

(e)

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(b)

(d)

(f)

Figure 3. Strain distributions along the three paths considered for different gasket hardnesses. (left) maximum principal strain, (right) maximum shear strain. The blue dotted line in each plot is the strain distribution for a diamond anvil in the same loading scenario with the BeCu III gasket. The model parameters used for this comparison are φc = 1 mm, φs = 0.4 mm, t0 = 0.3 mm, φg = 3 mm, and θ = 18◦ .

eventual increase in compressive strain. The origin of the growth of the maximum principal strain at the edge of the sample region is the compressibility of the anvil. The pressure distribution over the culet causes it to cup, and this effect is slightly more pronounced for harder gasket materials, though is largely determined by the sample pressure. Cupping has been measured in diamond anvils approaching mega-bar pressures.[17]

Anvil profile Altering the geometry of the anvil is restricted by difficulties in machining hard ceramics, and particularly gem stones. The easiest parameter to control is the pavilion angle, or inclusion of

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(a)

(b)

Figure 4. Evolution of maximum principal strain along culet path with increasing pressure for the Cu gasket (left) and BeCu III gasket (right). φc = 1 mm, φs = 0.4 mm, t0 = 0.3 mm, φg = 3 mm, and θ = 18◦ .

additional cone angles, which may be polished using conventional techniques. The cone/pavilion angle used for sapphire anvils varies in the literature between 2◦ and 30◦ . Furuno et al. [6] found that 18◦ worked reliably, though no attempt was made to optimise the angle. Taking the geometry of this system again as the basis of study the pavilion angle was varied, and the resulting stress distributions are shown in Figure 5. The strain profile behind the culet is not significantly different between 18◦ and 30◦ , but changes more significantly when further decreased to 8◦ . It is also seen that the central region of the anvil is less strained as the angle is increased, whilst the edge of the culet becomes increasingly strained. The growth of strain at the culet edge suggests that there is little benefit from sharpening the angle beyond 18◦ . To counteract this strain an additional angle may be added to the anvil (a bevel angle) to relieve stress at the edge of the culet. A sharper pavilion angle also provides the benefit of increased pressure/load performance. Relative culet/gasket dimensions The ratio of the culet diameter to the thickness of the gasket, and to the diameter of the sample hole, determines the form of the pressure distribution within the gasket, affecting the stresses in the anvil. Decreasing the size of the sample hole in relation to the size of the culet leads to a change in the strain profile behind the culet (Figure 6). A larger sample hole relative to the culet

(a)

(b)

Figure 5. (left) Maximum principal strain along the culet path and (right) maximum shear strain along the pavilion path for differing pavilion angles. The discontinuities along the pavilion path at approximately 0.2 , 0.3, and 0.7 mm correspond to the point where the gasket and anvil lose contact. φc = 1 mm, φs = 0.4 mm, t0 = 0.3 mm, and φg = 3 mm.


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results in a more even pressure distribution, less cupping, and lower tension and shear. Whilst all sample volumes require the same relative volume reduction for a given pressure, the smaller samples require a smaller absolute volume reduction, resulting in a decrease in compressive strain caused by the gasket intrusion. If the ratio of culet diameter to gasket thickness is considered, it was found that a lower ratio reduces the maximum shear in the central region of the anvil, whilst leading to an increase in strain both behind the culet, and along the pavilion (Figure 7).


Composite gasket design The requirement for the gaskets to be soft means they must initially be thinner to contain the highest pressures before the sample hole becomes unstable, reducing the sample volume which can be used with sapphire anvils. Composite gaskets made from soft–hard–soft laminated gaskets have been shown to allow the sample volume to be increased by approximately 40%, though still with small absolute sample volumes (∼ 0.05 mm3 ).[7] The process for choosing the dimensions of the composite gasket are not discussed in the study, but the present model can be used to examine how the relative thicknesses of the components affect the anvil. The data show that the inclusion of a laminate layer reduces the tension and shear introduced at the edge of the sample hole due to the differences in material compressibility, likewise at the point of gasket/anvil departure. However, as with the case where the gasket hardness was varied, the levels of tension are increased at the culet edge. It is found that the thicker the laminate layer used, the larger the increase in strain at this vulnerable region of the culet. The thickness of the laminate layer appears optimal at the point where the increase in culet tension is minimal for a maximal decrease in shear at the edge of the sample hole, see Figure 8. The optimal ratio appears between 2 < tgasket /tlaminate < 5.5. Tapered gasket design An alternative gasket design is reported by Kuhs et al.,[34] with similar designs reported elsewhere,[35–37] whereby the gasket is machined with a conical hole to either fit, or slightly misfit, to the conical form of the anvil. Kitagawa et al. and Okuchi et al. report that a profiled gasket improves the performance of the cell.

(a)

(b)

Figure 6. (left) Maximum principal strain and (right) maximum shear strain along culet path for different ratios of culet diameter to sample hole diameter. The distribution along the pavilion and through the centre of the anvil did not change. φc = 1 mm, t0 = 0.3 mm, φg = 3 mm, and θ = 18◦ .

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(a)

(b)

(c)

Figure 7. Maximum principal strain distribution along the three paths showing the effects of changing the ratio of culet diameter to gasket thickness. The discontinuity in along the pavilion path corresponds to the region where the anvil and gasket lose contact. φc = 1 mm, φs = 0.4 mm, φg = 3 mm, and θ = 18◦ .

A conical gasket profile provides additional support to the sample hole, increasing the stability of the gasket. Pressure/load efficiency in the cell may be retained by increasing the size of the gasket cone in relation to the anvil profile, such that the contact surface between the cones is achieved progressively, and is maximised under maximum applied load. FEA reveals that the tapered design is also beneficial to the anvil. The tapered section of the gasket gradually provides more support to the flanks of the anvil as the gasket deforms further. This additional support reduces cupping in the culet, and the tension associated with it. The choice of gasket tapering angle, and the diameter at which to the taper starts, will determine the level of support provided. To achieve maximum support, the taper angle should be chosen to match the pavilion angle of the anvil, the inner diameter of the taper should then be chosen to be slightly larger than the diameter of the culet, such that the gasket is fully engaged at the maximum sample pressure. Figure 9 gives an overview of the benefits of tapering the gasket. The results suggest that tapering the gasket leads to a reduction in tension and shear behind the culet region, but does not improve the strain profile in the pavilion region of the anvil. As the gasket deforms, the profile will change, such that the conical shape of the anvil does not engage fully. This can be improved through the inclusion of a laminate layer, which allows the anvil to engage fully with the harder gasket material.



(a)

(b)

(c)

(d)

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Figure 8. (top) Maximum principal strain and maximum shear strain along culet, and (bottom) along pavilion. Effects of changing the relative thickness of the soft laminate layer and hard central layer. φc = 1 mm, φs = 0.4 mm, t0 = 0.3 mm, φg = 3 mm, and θ = 18◦ .

Scaling An important consideration, if sample volumes are to be increased, is how upscaling the anvil parameters affects the strain profile. If the system is scaled in such a way so as to maintain the ratio of certain parameters (such as the ratio of anvil diameters to the thickness of the gasket material, and the size of the sample hole), and the load is scaled as the square of this, then the form and magnitude of the strain distribution should be unchanged, whilst the extent of the distribution scales with the parameter scaling. The basis of failure theories relies on measured critical stresses; ceramics typically contain flaws that may greatly vary in form and extent such that measurements are found to be dependent on the testing method, the condition of the stressed surface and the volume of the region that is stressed. A larger stressed area contains more flaws than a smaller one, and so the probability of failure increases accordingly. In fracture mechanics, Weibull statistics can be used to predict the form of the failure probability distribution.[38] The key result to consider is that the probability of failure in sapphire increases with a larger stressed region.

Conclusions A series of finite element studies were performed to understand how sapphire anvils are mechanically limited in pressure range, and to provide an insight into how it may be improved.


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(a)

(b)

(c)

(d)

Figure 9. Maximum principal and maximum shear strain profiles comparing a BeCu (HT) gasket which is not tapered, tapered to match the pavilion angle, or tapered to match the pavilion angle with the inclusion of a soft Al laminate layer. The culet diameter is 1 mm and the taper starts at a 1.5 mm diameter.

Discussions from the literature and analysis of the FEA results suggest that sapphire anvils fail due to: (1) (2) (3) (4)

Shear, induced by the relative compressibility of the sample and gasket. Tension in the surface of the culet due to the flow of the gasket material. Tension caused by cupping of the culet at high sample pressures. Surface shear and tensile strain at the point of gasket/anvil contact departure along the pavilion.

By altering the properties of the gasket material, the profile of the anvil, and the relative dimensions of the anvil and gasket, it has been shown how sapphire anvils are limited to use with softer gasket materials. It has been demonstrated that the inclusion of a soft laminate layer acts to improve the stresses in the pavilion region of the anvil, though not to the extent that the effects of using a hard gasket are completely removed. Techniques using a conical gasket profile have been shown to drastically reduce the tension in the culet region, due to the increased support they provide to the edge of the culet, and the sample region, which is promising for increasing the given pressure range for a given sample volume. If the size of the sapphire anvils is increased further, then methods for augmenting the tensile strength of sapphire must be implemented due to size effects, with particular focus given to the quality of the surface of the sapphire, such as chemical etching of the surfaces to reduce surface roughness, or surface coatings to preclude crack propagation.[39]


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Disclosure statement No potential conflict of interest was reported by the authors.

Funding The authors would like to thank the EPSRC and STFC funding bodies for supporting this work.


Note 1. Compressive yield stress, σc ; tensile yield stress, σt .

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