Indentation plastometry

Abstract

A method of performing profilometry-based indentation plastometry, including: a measuring step of scanning a surface of a sample, the surface having an indentation formed therein, using a profilometer to obtain scanned data representing the shape of the scanned surface, a curvature correction step of correcting the scanned data by applying a transform function to obtain corrected data in which a curvature of the scanned surface represented in the scanned data is reduced in a first surface direction, and a determining step of determining a material characteristic of the sample using the corrected data. Also provided is: an apparatus for performing profilometry-based indentation plastometry; a computer program comprising code which, when the code is executed on a computer, causes the computer to execute a curvature correction process of correcting scanned data obtained from a profilometer; a computer readable medium storing the computer program; and a computer programmed to execute the computer program.

Description

[0001] INDENTATION PLASTOMETRY

[0002] This application claims priority from GB2304493.6 filed 28 March 2023, the contents and elements of which are herein incorporated by reference for all purposes.

[0003] Field of the Invention

[0004] The present invention relates to indentation plastometry.

[0005] Background

[0006] It is essential to assess the structural integrity of a building or structural component on a regular basis, to ensure that the component can withstand a certain load or pressure. In some circumstances, the failure of a structural component can have devastating consequences. According to a report published by the Pipeline and Hazardous Materials Safety Administration (PHMSA) of the US Department of Transportation, there were 12,781 pipeline incidents in the US between 2003 and 2022 [1]. These incidents resulted in 274 fatalities and cost approximately $10.7 billion [1],

[0007] The structural integrity assessment relies on accurate and reliable data concerning the inelastic mechanical properties of the material(s) of the component. Inelastic mechanical properties of materials are conventionally obtained via uniaxial (tensile or compressive) tests. In contrast, indentation plastometry characterises the inelastic mechanical properties of materials by penetrating an indenter into the sample of the material, removing the indenter, measuring the residual indent profile, and then performing iterative numerical modelling of the indentation process.

[0008] Iterative numerical modelling of the indentation process generally involves using a Finite Element Method (FEM), with the plastic deformation of the material being captured in the form of a constitutive law containing adjustable parameters, and repeated comparisons being made between experimental and modelled outcomes A number of papers [3-11] have been published regarding various details of such methodologies. Several of these have highlighted the advantages of using the indent profile (rather than conventional load-displacement curves). The performance of indentation, profilometry and iterative numerical modelling procedure is termed PIP (Profilometry-based Inverse FEM Indentation Plastometry).

[0009] Use of an indentation-based technique brings important advantages. These include a reduction in the size and shape requirements for the sample. Also, the fact that properties are being measured in a relatively small region allows local variations in properties to be examined over the surface of a component.

[0010] However, known indentation plastometry techniques are particularly constrained by the flatness of the sample surface relative to the size of the indenter. Typically, a (small) flat plate is measured to determine its material characteristics, such as ultimate tensile strength (UTS) and yield strength (YS), with a high degree of accuracy. However, there are many circumstances in which it is impractical to obtain a flat sample surface of a structural or building component. A primary example is an excavated pipeline, particularly a pipe having a small radius and thus a high curvature. Flattening the curved surface of the sample is likely to affect the mechanical properties of the material [12-14] and may lead to inaccurate measurements of material characteristics of the sample.

[0011] Therefore, it is desirable to provide a method of performing indentation plastometry which can be performed with accuracy, reliability, and time-efficiency on curved surfaces.

[0012] The present invention has been devised in light of the above considerations.

[0013] Summary of the Invention

[0014] According to a first aspect of the present invention, there is provided a method of performing profilometry- based indentation plastometry, including: a measuring step of scanning a surface of a sample, the surface having an indentation formed therein, using a profilometer to obtain scanned data representing the shape of the scanned surface, a curvature correction step of correcting the scanned data by applying a transform function to obtain corrected data in which a curvature of the scanned surface represented in the scanned data is reduced in a first surface direction, and a determining step of determining a material characteristic of the sample using the corrected data.

[0015] The method of the first aspect differs from known methods for performing indentation plastometry in that the material characteristics of the surface of the sample can be measured to an appropriate degree of accuracy without flattening the sample. In particular, by applying a curvature correction step, a material characteristic value may be obtained from a curved sample surface with an accuracy comparable to that of a material characteristic value obtained by testing a flat surface. The correction may also be quicker and easier than carrying out additional inverse FEM to model the indentation of the curved surface, because the corrected data can be used as if it was scanned (raw) data representing a flat surface. For example, methods according to the present invention can allow for the determining step to be performed by applying a 2D radially symmetric model of the indentation based on the corrected data, in a similar manner as used for modelling indentations on flat surfaces. In other words, use of methods according to the present invention may allow the step of determining a material characteristic of a curved sample to be computationally simpler, with suitable accuracy, as compared with alternative methods of performing indentation plastometry on curved surfaces.

[0016] Methods according to the present invention may find particular utility in testing of samples which belong to a structural component for which the mechanical properties will be altered by physically flattening its surface or completely removing the sample to be flattened separately from the structural component. The material characteristic may include a stress-strain curve, preferably a true stress-true strain curve, such curves generally exhibiting regions of plastic deformation which are indicative of inelastic mechanical properties of materials. The material characteristic may include at least one characteristic selected from the ultimate tensile strength (UTS) and the yield strength (YS) of the sample.

[0017] The curvature correction step may include reducing the curvature of the scanned surface represented in the scanned data in the first surface direction to substantially zero, or zero.

[0018] The curvature may be a concave curvature, a convex curvature, or concave in one direction and convex in another direction (saddle-shaped).

[0019] The transform function may be derived by calculating a function of curvature in the first surface direction and converting the function to a linear form.

[0020] The specific form of the function may be selected based on the curvature of the scanned surface in the first surface direction. Suitably, the function of curvature may define a circle. Many curved surfaces can be suitably modelled by approximating the curvature of the surface in the first surface direction to a circle, and this can allow for a computationally simple manner of correcting for curvature of the surface in this direction. However, it is also contemplated that more complex functions of curvature may be defined. For example, in some cases, the function of curvature may define an ellipse or a quadratic curve, or may define a complex curvature.

[0021] The function of curvature may be a function calculated by fitting a best-fit curve to the scanned data in the first surface direction. Alternatively, the function of curvature may be a function calculated by fitting a best-fit curve to additional scanned data in the first surface direction, said additional scanned data being obtained by an additional measuring step of scanning the surface of the sample to obtain additional scanned data. The additional measuring step may be performed at any suitable time. In some methods, the additional measuring step may be performed prior to formation of the indentation in the surface of the sample.

[0022] The scanned data may comprise an array of points associated with a set of coordinates corresponding to the shape of the scanned surface. Where additional scanned data is used, the additional scanned data may comprise an additional array of points associated with a respective set of coordinates corresponding to the shape of the scanned surface (i.e. scanned in the additional measuring step).

[0023] The scanned data and / or additional scanned data may correspond to a scanned image or model in which the array of points is provided by a 2D array of pixels, with a height in the third dimension defined for each pixel. Each pixel may be identified by its 2D coordinates with respect to the scanned image. The set of coordinates may therefore consist of the height values associated with the respective pixels in the scanned image, and the 2D coordinates intrinsically defined by the pixels, i.e. may consist of 3 coordinates corresponding to the position of each pixel along first, second and third orthogonal measurement axes in 3D space. These first second and third orthogonal measurement axes may correspond to first and second surface directions, and a height / depth direction.

[0024] The curvature correction step may include applying the derived transform function to each point of the array of points to obtain an updated array of points associated with a corrected set of coordinates. In some embodiments, the corrected set of coordinates for each point in the array may differ from the original set of coordinates by a change in the position of the point along at least one of the first, second and third orthogonal measurement axes. Suitably, the corrected set of coordinates for each point in the array may differ from the original set of coordinates by a change in the position of the point in a depth direction, which may be a direction parallel to a penetration direction / indentation extension direction of the indentation formed in the sample surface. By correcting the depth of each point in the array using the derived transform function, the curvature of the scanned surface represented in the scanned data can accordingly be reduced in a first surface direction (which is a direction orthogonal to the depth direction).

[0025] When the transform function is a function derived by calculating a best-fit curve of the curvature in the first surface direction and converting the best-fit curve to a linear form, the curvature correction step may further include selecting a sub-set of points from the array of points and calculating the best-fit curve based on the coordinates associated with the sub-set of points. Where the transform function is derived from additional scanned data, the curvature correction step may include selecting a sub-set from the additional array of points and calculating the best-fit curve based on the coordinates associated with the sub-set of points. In some embodiments, the sub-set of points comprises a row of points extending in the first surface direction. However, in preferred embodiments, the sub-set of points may comprise a region of the scanned data representing 5% or less of the scan width, e.g. 4% or less, 3% or less, 2% or less, or 1% or less of the scan width. Determining the best-fit curve based on a sub-set of points in this manner may be preferable to determining the best-fit curve based on a row of points, because it can smooth out the effect of noise in measurement of individual pixels. The sub-set of points may be selected from one continuous region of the scanned data. Alternatively, the sub-set of points may be selected from two or more non-continuous regions of the scanned data - e.g. from opposing edge regions of the scanned data. In one suitable arrangement, the sub-set of points is selected as a region that represents 0.5% of the scan width at opposing edges of the scan. For a 5 mm x 5 mm, 1024 pixel square scan, this corresponds to a 0.025mm border region at each edge, containing 5 rows of pixels.

[0026] The sub-set of points may be selected from an edge region of the scanned data representing the shape of the scanned surface. The edge region may include two areas on opposing edges of the scanned area.

[0027] The edge region may be defined in terms of its smallest distance to the centre of the indentation as represented in the scanned data. For example, the smallest distance between the edge region and the centre of the indentation may be not less than 2 times the width of the indentation, e.g. not less than 2.5 times, e.g. not less than 3 times, e.g. not less than 4 times the width of the indentation. The width of an indentation is determined as the maximum measurable width across the indentation in any direction. The term "edge region" is used above in view of the fact that scanned data will typically include an indent at an approximately central region of the scanned data (e.g. within a distance of ±0.5mm of the centre of the scan), and accordingly, regions of the data fulfilling the above distance criteria will typically be located in a region that would be considered to lie at or near the edge of the scanned data. However, it is contemplated that in some cases, for example, where the indent is off-set from centre, it may be possible to select the sub-set of points from a region that may be considered to be a generally central region of the data. Accordingly, in some embodiments, the sub-set of points may be selected from any region of the data which fulfils the above distance criteria (i.e. which lies not less than 2, 2.5, 3, 4 times the width of the indentation from the centre of the indentation as represented in the scanned data). Selecting the sub-set of points to be at this distance from the indentation can ensure suitable accuracy in determination of the derived material properties. In particular, by selecting the points to be at least 2, 2.5, 3 or 4 times the width of the indentation from the centre of the indentation as represented in the scanned data, the effect of residual deformation on determination of the derived material properties can be reduced or avoided. Whilst it is contemplated that the most efficient way of performing the curvature correction may be to determine the transform function based on scanned data or additional scanned data as discussed above, it is also contemplated that the transform function may be derived by calculating the function of curvature based on a physical measurement of the sample body, e.g. based on a known or measured diameter of the sample body.

[0028] In some embodiments, the curvature correction step may be repeated for a second surface direction perpendicular to the first surface direction to obtain corrected data in which the curvature of the scanned surface represented in the scanned data is also reduced in the second surface direction.

[0029] The second curvature correction step may include reducing the curvature of the scanned surface represented in the scanned data in the second surface direction to substantially zero, or zero.

[0030] The second curvature correction step may include deriving a second transform function by calculating a second best-fit curve of the curvature in the second surface direction and converting the second best-fit curve to a linear form and applying the second transform function to the updated array of pixels.

[0031] Alternatively, the second curvature correction step may include combining the first transform function and the second transform function to derive a combined transform function and applying the combined transform function to the scanned data to obtain corrected data in which a curvature of the scanned surface represented in the scanned data is reduced in both a first surface direction and in a second surface direction.

[0032] The second transform function may be derived using the scanned data or the additional scanned data, in a similar manner as discussed above in relation to derivation of the first transform function for correcting curvature in the first surface direction.

[0033] The sample may comprise a substantially cylindrical body, e.g. a pipe. It is contemplated that methods according to the present invention may find utility in determining material characteristics of cylindrical bodies of all diameters, however, may be particularly advantageous for bodies having a diameter of 600 mm or less, e.g. 500 mm or les, 400 mm or less, 300 mm or less, 200 mm or les, 150 mm or less, 100 mm or less, 75 mm or less, or 37.5 mm or less in view of the potential for large discrepancies in measured material characteristics resulting from sample curvature, when performing PIP on a curved surface of such bodies.

[0034] The first surface direction may be a circumferential direction or an axial direction of the substantially cylindrical body. The second surface direction may therefore be the other of the circumferential direction or the axial direction.

[0035] The indentation may be formed using an indenter having a contact surface by applying a load to press the contact surface of the indenter into the surface of the sample. The contact surface of the indenter may lie on a sphere having a radius, r. For example, the indenter may simply be a sphere. A penetration depth of the indenter may be not less than 10% of r, e.g. not less than 25% of r.

[0036] The profilometer may be a contact profilometer, e.g. a stylus, which moves a probe along the sample surface to acquire the local surface height.

[0037] Alternatively, the profilometer may be a non-contact profilometer, e.g. an optical profilometer, which maps the sample surface using light reflected by the sample surface.

[0038] According to a second aspect of the present invention, there is provided an apparatus for performing profilometry-based indentation plastometry, the apparatus including: a profilometer for scanning a surface of a sample to obtain scanned data representing the shape of the scanned surface, a computer system programmed to: execute a curvature correction process of correcting the scanned data by applying a transform function to obtain corrected data in which a curvature of the scanned surface represented in the scanned data is reduced in a first surface direction, and determine a material characteristic of the sample using the corrected data.

[0039] According to a third aspect of the present invention, there is provided a computer program comprising code which, when the code is executed on a computer, causes the computer to execute a curvature correction process of correcting scanned data obtained from a profilometer for scanning a surface of a sample to obtain scanned data representing the shape of the scanned surface and input to the computer by applying a transform function to obtain corrected data in which a curvature of the scanned surface represented in the scanned data is reduced in a first surface direction.

[0040] The computer program may be configured such that, when the code is executed on a computer, it additionally causes the computer to determine a material characteristic of the sample using the corrected data. The material characteristic may include a stress-strain curve, preferably a true stress-true strain curve, such curves generally exhibiting regions of plastic deformation which are indicative of inelastic mechanical properties of materials. The material characteristic may include at least one characteristic selected from the ultimate tensile strength (UTS) and the yield strength (YS) of the sample

[0041] According to a fourth aspect of the present invention, there is provided a computer readable medium storing the computer program according to the third aspect.

[0042] According to a fifth aspect of the present invention, there is provided a computer programmed to execute the computer program according to the third aspect.

[0043] The invention includes the combination of the aspects and preferred features described except where such a combination is clearly impermissible or expressly avoided.

[0044] Summary of the Figures

[0045] Embodiments and experiments illustrating the principles of the invention will now be discussed with reference to the accompanying figures in which:

[0046] Figure 1 shows PIP-determined Ultimate Tensile Strength (UTS) and Yield Strength (YS) measurements of a pipe as a function of the inverse of the pipe radius, said data being obtained by a method not incorporating a curvature correction step as used in the present invention;

[0047] Figure 2 is a block diagram showing steps of an exemplary method of performing indentation plastometry according to the present invention;

[0048] Figure 3 is a block diagram showing steps of an exemplary method of deriving a transform function for use in a method according to the present invention;

[0049] Figure 4 is a block diagram showing steps of an exemplary method of applying a transform function to scanned data to perform a curvature correction step as used in a method according to the present invention;

[0050] Figure 5 shows a graphical representation of scanned data obtained following the measuring step of the exemplary method; and

[0051] Figure 6 shows a graphical representation of corrected scanned data obtained following the curvature correction step of the exemplary method.

[0052] Figure 7 shows schematically selection of a sub-set of pixels at the edge of the scan which are used to carry out curvature correction in the circumferential (C) direction following the curvature correction step of the exemplary method.

[0053] Figure 8 shows the y and z coordinates of all the pixels selected from both edges of the scan as shown in Fig. 7, and the best fit circle to these data. Detailed Description of the Invention

[0054] Further background to the present invention, and aspects and embodiments of the present invention will now be discussed with reference to the accompanying figures. Further aspects and embodiments will be apparent to those skilled in the art. All documents mentioned in this text are incorporated herein by reference.

[0055] Figure 1 shows a graph of (Ultimate Tensile Strength) UTS values and Yield Strength (YS) / ’SigmaY’ values for various pipe samples comprising mild steel, derived using PIP to obtain an average indentation profile without correcting for any curvature of the respective pipe surfaces. The UTS and YS measurements were obtained for six pipes each having a different radius, R, as well as for a flat sample having a curvature 1 / R = 0. The UTS data points are represented in Figure 1 by solid circles while the YS (or SigmaY) data points are represented by hollow circles. The data points are presented in the X-axis in terms of 1 / R, i.e. in terms of pipe curvature. The UTS value of 631 MPa and the YS value of 445 Mpa for the flat surface are deemed to be representative of the ‘true’ UTS and YS value for this material.

[0056] Excluding the flat surface measurements, the data points from left to right in Figure 1 correspond to pipe radius values of 1200 mm, 600 mm, 300 mm, 150 mm, 75 mm, and 37.5 mm. Therefore, the corresponding 1 / R values represented in the X-axis, respectively, are 0.83 nr1, 1 .67 nr1, 3.33 nr1, 6.67 nr1, 13.3 rrr1, and 26.7 nr1.

[0057] The graph in Figure 1 illustrates that for a radius lower than 75 mm (1 / R = 13.3 nr1) the derived material properties are significantly different as compared with those measured from a flat sample. However, a noticeable difference in measurement as compared with the flat samples is seen even for larger radius / lower curvature pipes having a curvature of 3.33 nr1or more (corresponding to a diameter of 300 mm). This indicates that for PIP testing the surfaces of pipes with radii less than or equal to 300 mm, it is necessary to either prepare a flattened surface on the outside of the pipe or to carry out a correction for the curvature when deriving the mechanical properties from the measured indentation profiles in order to accurately determine the material properties of the sample using PIP.

[0058] The present invention therefore provides a convenient method for performing PIP with suitable accuracy on samples which are curved in at least a first surface direction.

[0059] Figure 2 is a block diagram illustrating the steps of an exemplary method of performing indentation plastometry according to the present invention. At step S1 , a sample having a surface with an indentation formed therein is provided. When the sample is a pipe the indentation is formed e.g. on the curved outer surface of the pipe. The curvature is therefore convex in the circumferential direction of the pipe, which may also be referred to as a first surface direction, with an axial direction of the pipe being referred to as a second surface direction.

[0060] The indentation may be formed in a conventional manner e.g. using an indenter, by applying a load to press a contact surface of the indenter into the surface of the sample. The indenter may have a spherical shape and may be made from a material that is significantly harder than the sample material under the conditions of the plastometry testing to ensure that the indenter does not deform when forming the indentation, e.g. a ceramic material. The compressive force of the indenter forms a “crater” which is circumscribed by a “pile-up” area. The “pile-up” area is raised above the height of the original surface of the sample.

[0061] At step S2, the surface of the sample is scanned using a profilometer to capture the shape of the indentation. Specifically, the profilometer scans the residual indentation including the “crater” and the surrounding “pile-up” area. The profilometer may be a contact profilometer, e.g. a stylus, which moves a probe along the sample surface to acquire the local surface height. Typically, a feedback loop monitors the force from the sample pushing up against the probe as it scans along the surface. Alternatively, the profilometer may be a non-contact profilometer, e.g. an optical profilometer, which maps the sample surface using light reflected off the sample surface.

[0062] At step S3, scanned data representing the shape of the scanned surface is obtained from the profilometer. The scanned data is raw data comprising information about the height variation (also referred to as depth variation) across the scanned surface, relative to the profilometer. Said height / depth variation can be attributed to the indentation as well as any pre-existing curvature of the sample surface.

[0063] Conveniently, the scanned data comprises an array of points associated with a set of coordinates corresponding to the shape of the scanned surface. Preferably, the coordinates are 3D-coordinates and include coordinates corresponding to the position of each point along first, second and third orthogonal array axes in 3D space, said axes corresponding to first and second surface directions, and a depth direction - see below discussion of Fig. 5. When the sample is a pipe or other cylindrical body, the first surface direction may be selected to correspond to the circumferential direction, while the second surface direction may be selected to correspond to the axial direction (perpendicular to the circumferential direction).

[0064] Step S4 includes deriving a transform function. The transform function may be derived by calculating a function of curvature in the first surface direction and converting the function to a linear form.

[0065] For example, if a set of co-ordinates, (yi,Zi) are used to assess the curvature in the circumferential (y) direction, and the best fit circle to these co-ordinates is given by the equation: r2= (z - ze)2+ (y - ycy

[0066] Which can be written in the form (for a convex surface where zcis negative): z = ze+ 7r2- (y — ycy

[0067] Then the transform function that should be used to convert all the measured co-ordinates, (ym,zm), to flattened coordinates, (yt.zt), is (+ for concave, - for convex): yf = ym

[0068] When the sample is the pipe and the first surface direction is the circumferential direction, the function of curvature may be calculated based on a physical measurement of a transverse cross-section of the pipe. For example, the measurement may be a measurement of the pipe radius or diameter, and the function of curvature may be a circle calculated from said measured radius or diameter. However preferably, the function of curvature is calculated as a best-fit curve derived by fitting a curve to the scanned data in the first surface direction - this may provide for a more accurate determination of the surface curvature in the scanned region than using a function calculated based on physical measurements of the entire sample.

[0069] Figure 3 is a block diagram illustrating the steps of a method of deriving the transform function using a best-fit curve:

[0070] Step S41 requires the provision of the array of points discussed above, which are associated with a set of coordinates corresponding to the shape of the scanned surface.

[0071] Step S42 includes selecting a sub-set of points from the array of points. The sub-set is conveniently selected to be near the edge of the scan and elongated in the first surface direction. Where the indent represented in the scanned data is located close to the centre of the scan, this can ensure that any residual deformation in the region from which the sub-set of points is selected has a relatively small / substantially no effect on the curvature measurement. The region may include two areas from opposite edges of the scan, both elongated in the first surface direction.

[0072] The coordinates of each point in the sub-set of points lie close to a single 2D plane - conveniently, the sub-set of points is selected from a region representing 0.5% of the scan width at each edge. For a 5mmx5mm, 1024 pixel square scan, this corresponds to a 0.025mm border region at each edge, containing 5 rows of pixels. When the first surface direction is the circumferential direction of the pipe, the 2D plane is a transverse cross-section of the pipe.

[0073] The sub-set of points may be selected from an edge region of the scanned data. The edge region may be defined in terms of its smallest distance to the centre of the indentation. In other words, it is preferable to select the sub-set of points from a region far away from the indentation, e.g. clear of the “pile-up” area. This may be defined in terms of the smallest distance between the edge region and the centre of the indentation.

[0074] The smallest distance, measured from the centre of the indentation, is preferably not less than 2 times the width of the indentation. The width of the indentation is the maximum width of a boundary between the “crater” and the “pile-up” area. It is deemed that the pile-up height is sufficiently reduced at a distance greater than or equal to twice the width of the indentation from the centre of the indentation.

[0075] As shown in step S43, calculating the best-fit curve may include calculating the best-fit curve based on the coordinates associated with the points in the defined sub-set.

[0076] Finally, in step S44, the transform function is obtained based on converting the best-fit curve to a linear form.

[0077] Turning back to Figure 2, the method may in some embodiments include an additional measuring step S2’ (not shown) of scanning the surface of the sample to obtain additional scanned data. The additional measuring step S2’ may occur before or after forming the indentation, i.e. before or after step S1 . Instead of step S4, the method may include a step S4’ (not shown), which is identical to step S4 except that the transform function is derived using the additional scanned data instead of the scanned data obtained in S3. For example, the function of curvature may be a best-fit curve calculated by fitting a curve to the additional scanned data in the first surface direction. Also, the additional scanned data may comprise an additional array of points associated with a respective set of coordinates corresponding to the shape of the scanned surface in the additional measuring step S2’. Step S4’ may therefore include selecting the sub-set of points from the additional array of points in the first surface direction.

[0078] Step S5 includes applying the derived transform function to the scanned data.

[0079] Figure 4 is a block diagram illustrating the steps of a method of applying the transform function to the scanned data:

[0080] Step S51 requires the provision of the array of points discussed above, which are associated with a set of coordinates corresponding to the shape of the scanned surface.

[0081] At step S52, the transform function is applied to each point of the array of points.

[0082] Finally, in step S53, an updated array of points associated with a corrected set of coordinates is obtained.

[0083] Turning again to Figure 2, at step S6 (see Figure 2), corrected data in which a curvature of the scanned surface represented in the scanned data is reduced in a first surface direction is obtained (i.e. as a result of applying the transform function to the scanned data). The corrected data may comprise the updated array of points associated with the corrected set of coordinates. Preferably, in the corrected data, the curvature of the scanned surface represented in the scanned data in the first surface direction is reduced to substantially zero or zero. For example, this is achieved when the transform function converts the function of curvature to a linear form - see here the below discussion comparing Fig. 5 and Fig. 6 which are images representing scanned data before and after a curvature correction step is performed.

[0084] In some embodiments, steps S4, S5 and S6, or S4’, S5 and S6, may be repeated for the second surface direction. This is optional, as the sample may have substantially no curvature in the second surface direction: e.g. where the sample is a pipe or other cylindrical body, it may have substantially no curvature in an axial direction, in which case it is not necessary to perform the curvature correction for this second direction. However, such a step may be appropriate where the sample for testing includes a curvature in the second surface direction, e.g. where the sample is a spherical body, or where a surface curvature is present in an axial direction of a substantially cylindrical body e.g. as a result of surface preparation techniques which have been applied to the pipe surface. Therefore, in a repeated step RS6 (not shown) further corrected data in which the curvature of the scanned surface represented in the scanned data is also reduced in the second surface direction may be obtained.

[0085] The repeated steps may include step S4’ instead of S4, even if step S4 was performed instead of S4’ previously. Likewise, the repeated steps may include step S4 instead of S4’, even if step S4’ was performed instead of S4 previously. Preferably, the repeated steps include reducing the curvature of the scanned surface represented in the scanned data in the second surface direction to substantially zero or zero. When the curvature is reduced to substantially zero or zero in both the first surface direction and the second surface direction, the further corrected data represents the shape of a flat surface having an indentation formed therein.

[0086] In repeated steps RS4 (not shown) or RS4’ (not shown), a second transform function may be derived by calculating a function of curvature in the second surface direction and converting the function to a linear form.

[0087] The second transform function may be applied to the corrected data obtained in step S6.

[0088] Alternatively, the first transform function and the second transform function may be combined to derive a combined transform function which is applied to the scanned data obtained in step S3.

[0089] At step S7 (see Figure 2), the corrected data or further corrected data is used to determine a material characteristic of the sample. In other words, the corrected data is treated as if it is raw data (equivalent to the scanned data). As such, the corrected data may be used as an input for iterative numerical modelling of the indentation, e.g. using a conventional FEM method as disclosed in references [5]-

[0011] .

[0090] Figure 5 shows scanned data plotted on a first surface mesh grid 1 . The scanned data represents the shape of a scanned surface of a pipe having an indentation 2 formed therein. The minimum height of the scanned surface is at the centre 4 of the indentation 2. Figure 5 illustrates a curvature of the pipe in the circumferential direction C (corresponding to the first surface direction), perpendicular to the axial direction A (corresponding to the second surface direction). The curvature is most easily seen at the edge region 6 of the plotted scanned data, away from the indentation 2.

[0091] Figure 7 shows the regions of pixels at the edge of the scan, under the black dashed lines, which are used to carry out curvature correction in the circumferential (C) direction. Figure 8 shows the y and z coordinates of all the pixels selected from both edges of the scan, and the best fit circle to these data. The y and z coordinates of the centre of the circle are 2.52mm and -132.4mm respectively, and the radius of the circle (convex) is 132.4mm. The transform applied to all the measured data (xm, ym, zm) to generate flattened data (xt, yt, zt) correcting for the curvature in the circumferential (C) direction is: yf = ymzf= zm+ 132.4 - 7132.42- (ym- 2.52)2

[0092] Figure 6 shows corrected data plotted on a second surface mesh grid 10. The corrected data is obtained from the scanned data by applying the curvature correction step described above. It can be seen that as a result of applying the transform function as discussed above, each point in the array has a corrected set of coordinates which may differ from the original set of coordinates by a change in the position of each point at least in a depth direction D. By correcting the depth of each point in the array using the derived transform function, the curvature of the scanned surface represented in the scanned data is accordingly reduced in the first surface direction (here, in the circumferential direction C), such that the curvature is reduced to substantially zero to derive a profile of an equivalent indentation 12 formed in a flat surface 16. The correction is clearly visible at the edge region 18 of the corrected data, which is substantially planar. However, the transform function is applied to the whole surface represented by the scanned data.

[0093] Therefore, the profile of the corrected indentation 12 represented in the corrected data is changed with respect to the profile of the actual indentation 2 as represented in the original scanned data.

[0094] The corrected profile of the indentation 12 can be analysed to determine a material characteristic of the sample using the corrected data. For example, an average 2D radial profile can be obtained by averaging the profile of the corrected indentation 12 in a 2D plane extending radially outward from the centre 14 of the “crater” for a range of angles up to 360°. This averaged 2D radial profile may be used to determine one or more material characteristics of the sample, such as UTS or YS, in a similar manner as known for PIP on flat samples as per conventional methods.

[0095] The features disclosed in the foregoing description, or in the following claims, or in the accompanying drawings, expressed in their specific forms or in terms of a means for performing the disclosed function, or a method or process for obtaining the disclosed results, as appropriate, may, separately, or in any combination of such features, be utilised for realising the invention in diverse forms thereof.

[0096] While the invention has been described in conjunction with the exemplary embodiments described above, many equivalent modifications and variations will be apparent to those skilled in the art when given this disclosure. Accordingly, the exemplary embodiments of the invention set forth above are considered to be illustrative and not limiting. Various changes to the described embodiments may be made without departing from the spirit and scope of the invention.

[0097] For the avoidance of any doubt, any theoretical explanations provided herein are provided for the purposes of improving the understanding of a reader. The inventors do not wish to be bound by any of these theoretical explanations.

[0098] Any section headings used herein are for organizational purposes only and are not to be construed as limiting the subject matter described.

[0099] Throughout this specification, including the claims which follow, unless the context requires otherwise, the word “comprise” and “include”, and variations such as “comprises”, “comprising”, and “including” will be understood to imply the inclusion of a stated integer or step or group of integers or steps but not the exclusion of any other integer or step or group of integers or steps.

[0100] It must be noted that, as used in the specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another embodiment includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by the use of the antecedent “about,” it will be understood that the particular value forms another embodiment. The term “about” in relation to a numerical value is optional and means for example + / - 10%. References

[0101] A number of publications are cited above in order to describe and disclose the invention and the state of the art to which the invention pertains more fully. Full citations for these references are provided below. The entirety of each of these references is incorporated herein.

[0102] [1] Pipeline & Hazardous Materials Safety Administration, “ALL REPORTTED INCIDENT 20 YEAR TREND”, 2023. https: / / www.phmsa.dot.gov / data-and-statistics / pipeline / pipeline-incident-20-year-trends (accessed 07 February 2023)

[0103] [2] Pipeline & Hazardous Materials Safety Administration, “Factsheet: Corrosion”, 2018. https : / / pri mis. phmsa.dot.gov / comm / FactSheets / FSCorrosion. htm?nocache=9090 (accessed 07 February 2023)

[0104] [3] J Dean, JM Wheeler & TW Clyne, Use of Quasi-Static Nanoindentation Data to Obtain Stress- Strain Characteristics for Metallic Materials, Acta Materialia, 58 (2010) p.3613-23.

[0105] [4] DK Patel & SR Kalidindi, Correlation of spherical nanoindentation stress-strain curves to simple compression stress-strain curves for elastic-plastic isotropic materials using finite element models, Acta Materialia, 112 (2016) p.295-302.

[0106] [5] J Dean & TW Clyne, Extraction of Plasticity Parameters from a Single Test using a Spherical Indenter and FEM Modelling, Mechanics of Materials, 105 (2017) p.112-22.

[0107] [6] JE Campbell, RP Thompson, J Dean & TW Clyne, Experimental and Computational Issues for Automated Extraction of Plasticity Parameters from Spherical Indentation, Mechanics of Materials, 124 (2018) p.118-31.

[0108] [7] JE Campbell, RP Thompson, J Dean & TW Clyne, Comparison between stress-strain plots obtained from indentation plastometry, based on residual indent profiles, and from uniaxial testing, Acta Materialia, 168 (2019) p.87-99.

[0109] [8] M Burley, JE Campbell, R Reiff-Musgrove, J Dean & TW Clyne, The Effect of Residual Stresses on Stress-Strain Curves Obtained via Profilometry-Based Inverse Finite Element Method Indentation Plastometry, Adv. Eng. Mats., 23 (2021 ) p.2001478.

[0110] [9] YT Tang, JE Campbell, M Burley, J Dean, RC Reed & TW Clyne, Use of Profilometry-based Indentation Plastometry to obtain Stress-Strain Curves from Small Superalloy Components made by Additive Manufacturing, Materialia, 15 (2021 ) p.101017.

[0111]

[0010] JE Campbell, H Zhang, M Burley, M Gee, AT Fry, J Dean & TW Clyne, A Critical Appraisal of the Instrumented Indentation Technique (IIT) and Profilometry-based Inverse FEM Indentation Plastometry (PIP) for Obtaining Stress-Strain Curves, Adv. Eng. Mats., 23 (2021 ) p.2001496.

[0011] TW Clyne, JE Campbell, M Burley & J Dean, Profilometry-based Inverse FEM Indentation Plastometry (PIP), Adv. Eng. Mats., (2021 ) p.21004037.

[0112]

[0012] Kang et al, Metals 2018, 8, 354; doi:10.3390 / met8050354

[0113]

[0013] Nayyar et al, "COMPARISON BETWEEN YIELD STRENGTH RESULTS OBTAINED FROM METHODS USING BOTH FLATTENED AND NON-FLATTENED SPECIMENS", Proceedings of the 2020 13th International Pipeline Conference, IPC2020, September 28-30, 2020

[0014] Rashid et al, "STANDARDIZATION OF FLATTENING PROCEDURE OF TRANSVERSE TO

[0114] PIPE AXIS STRAP TENSILE SAMPLES", Proceedings of the 2018 12th International Pipeline Conference, IPC2018, September 24-28, 2018, Calgary, Alberta, Canada

Claims

CLAIMS1 . A method of performing profilometry-based indentation plastometry, including: a measuring step of scanning a surface of a sample, the surface having an indentation formed therein, using a profilometer to obtain scanned data representing the shape of the scanned surface, a curvature correction step of correcting the scanned data by applying a transform function to obtain corrected data in which a curvature of the scanned surface represented in the scanned data is reduced in a first surface direction, and a determining step of determining a material characteristic of the sample using the corrected data.

2. The method according to claim 1 , wherein the transform function is a function derived by calculating a function of curvature in the first surface direction and converting the function of curvature to a linear form, optionally wherein the function of curvature defines a circle, an ellipse, or a quadratic curve.

3. The method according to claim 2, wherein the function of curvature is calculated by fitting a best- fit curve to the scanned data in the first surface direction.

4. The method according to claim 2, including an additional measuring step of scanning the surface of the sample to obtain additional scanned data representing the shape of the scanned surface, wherein the function of curvature is calculated by fitting a best-fit curve to the additional scanned data in the first surface direction.

5. The method according to any one of the preceding claims, wherein the scanned data comprises an array of points associated with a set of coordinates corresponding to the shape of the scanned surface.

6. The method according to claim 5, wherein the curvature correction step includes: applying the transform function to each point of the array of points to obtain an updated array of points associated with a corrected set of coordinates.

7. The method according to claims 5 or 6, wherein the curvature correction step includes: selecting a sub-set of points from the array of points; and calculating a best-fit curve based on the coordinates associated with the sub-set of points.

8. The method according to claim 7, wherein the sub-set of points is selected from one or more edge regions of the scanned data representing the shape of the scanned surface.

9. The method according to any one of the preceding claims, wherein the curvature correction step is repeated for a second surface direction perpendicular to the first surface direction to obtain correcteddata in which the curvature of the scanned surface represented in the scanned data is also reduced in the second surface direction.

10. The method according to any one of the preceding claims, wherein the sample comprises a substantially cylindrical body and the first surface direction is a circumferential direction or an axial direction of the substantially cylindrical body.11 . The method according to any one of the preceding claims, wherein the indentation is formed using an indenter having a contact surface by applying a load to press the contact surface of the indenter into the surface of the sample.

12. An apparatus for performing profilometry-based indentation plastometry, the apparatus including: a profilometer for scanning a surface of a sample to obtain scanned data representing the shape of the scanned surface; and a computer system programmed to: execute a curvature correction process of correcting the scanned data by applying a transform function to obtain corrected data in which a curvature of the scanned surface represented in the scanned data is reduced in a first surface direction, and determine a material characteristic of the sample using the corrected data.

13. A computer program comprising code which, when the code is executed on a computer, causes the computer to execute a curvature correction process of correcting scanned data obtained from a profilometer for scanning a surface of a sample to obtain scanned data representing the shape of the scanned surface and input to the computer by applying a transform function to obtain corrected data in which a curvature of the scanned surface represented in the scanned data is reduced in a first surface direction.

14. A computer readable medium storing the computer program according to claim 13.

15. A computer programmed to execute the computer program according to claim 13.

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