DEBRUYNE DIMITRI (BE)
DENYS KRISTOF (BE)
US5905204A | 1999-05-18 | |||
US20120287248A1 | 2012-11-15 |
Claims 1. A test specimen (1) comprising a first material, the specimen comprising a gauge region (2) having first and second end regions (3, 4) spaced apart in a first direction (y), wherein the gauge region (2) comprises a plurality of test regions (171, 172, 173, 174, 175) comprising the first material spaced apart along the first direction (y), wherein the gauge region (2) further comprises at least two recesses (181, 182, 183, 184. 185. 191. 192. 193. 194. 195), each test region (171, 172, 173, 174, 175) being defined by at least one corresponding recess (181, 182, 183, 184, 185, 191, 192, 193, 194, 195) in the gauge section, wherein the gauge region (2) has first and second opposite faces (5, 6) extending along the first direction (y), wherein one of the at least two recesses (181, 182, 183, 184, 185) is disposed in the first face (5) and the other of the at least two recesses (191, 192, 193, 194, 195) is disposed in the second face (6), wherein the at least two recesses (181, 182, 183, 184, 185, 191, 192, 193, 194, 195) have a cross-section in a plane substantially parallel to the first and second faces (5, 6), wherein the cross-section is substantially circular and have the same diameter (D). 2. A specimen according to claim 1, wherein the cross-section is disk shaped, the surface (197) in the recess being substantially flat. 3. A specimen according to any of the previous claims, wherein the plurality of test regions (171, 172, 173, 174, 175) comprises a first test region (171) defined by a first corresponding recess (181) in a first face (5) of the gauge region (2). 4. A specimen according to claim 3, wherein the plurality of test regions (171, 172, 173, 174, 175) comprises a second test region (175) defined by a second corresponding recess (195) in a second face (6) of the gauge region (2) which is opposite the first face (5) of the gauge region (2). 5. A specimen according to any preceding claim, wherein the plurality of test regions (171, 172, 173, 174, 175) comprises a third test region (172) defined by a first corresponding pair of recesses (182, 192) in the gauge region (2), the first pair of recesses comprising a third recess (182) in the first face (5) of the gauge region (2) and a fourth recess (192) in the second face (6) of the gauge region (2), wherein the third recess (182) is opposite the fourth recess (192). 6. A specimen according to claim 5, wherein each recess has a cross-section in a plane substantially parallel to the first and second faces, wherein the cross-section is substantially circular. 7. A specimen according to any preceding claim, wherein each of the plurality of test regions (171, 172, 173, 174, 175) comprising the first material has a thickness (t) measured in a direction substantially perpendicular to the first and second faces (5, 6), wherein the thickness of each of the plurality of test regions (171, 172, 173, 174, 175) is substantially the same. 8. A specimen according to any preceding claim, wherein each recess (181, 182, 183, 184, 185, 19) has a cross-section in a plane substantially parallel to the first and second faces (5, 6), wherein each recess (181, 182, 183, 184, 185, 19) has an extent in a direction substantially perpendicular to the first and second faces (5, 6), and wherein the cross-section of each recess (181, 182, 183, 184, 185, 191, 192, 193, 194. 195) is substantially constant over the extent of each recess (181, 182, 183, 184, 185, 191, 192, 193, 194, 195). 9. A specimen according to any preceding claim, wherein each of the plurality of test regions (171, 172, 173, 174. 175) has an extent in a second direction (z), the second direction being substantially perpendicular to the first and second faces (5, 6), wherein the extent of each of the plurality of test regions (171, 172, 173. 174. 175) does not coincide substantially with the extent of any other of the plurality of test regions. 10. A specimen according to claim 9, wherein the sum of the extent of the plurality of test regions (171, 172, 173, 174, 175) is substantially equal to a thickness of the gauge region in the second direction (z) in a region which does not include a test region. 11. A specimen according to any preceding claim, further comprising a first shoulder section (7) adjacent to the first end region (3) of the gauge region (2), the first shoulder section (7) having a first shoulder section width (ws), and a second shoulder section (8) adjacent to the second end region (4) of the gauge region (2), the second shoulder section (8) having a second shoulder section width (ws), wherein the gauge region (2) has a gauge region width (wg), and wherein the first shoulder section width (ws) and the second shoulder section width (ws) are each greater than the gauge region width (wg). 12. A method of manufacturing a specimen according to any preceding claim comprising: providing a material sample comprising a gauge region; and forming the plurality of recesses in the gauge region of the material sample. 13. A method of performing a tensile strength test comprising: providing (S1601) a specimen according to any one of claims 1 to 10; - applying (S1602) a stress to at least the gauge region of the specimen; - performing (S1603) a digital image correlation measurement on at least one of the plurality of test regions; and - determining (S1604) at least one material property of at least one of the plurality of test regions in dependence upon the digital image correlation measurement. 14. The method of claim 13, further comprising: - calculating (S1302) a first strain of a test region using a numerical model; - calculating (S1303) a value of a cost function in dependence upon the first strain and a second strain of a test region determined in dependence upon the digital image correlation measurement; and - updating (S1305b) one or more parameters of the numerical model in dependence upon the value of the cost function. 15. The method of claim 14, further comprising, if the value of the cost function is below a predetermined value, outputting (S1305a) one or more parameters of the numerical model. 16. The method of any one of claims 13 to 15, wherein providing the tensile test specimen comprises a specimen preparation step, wherein the specimen preparation step comprises: providing a material sample comprising a gauge region; and forming the plurality of recesses in the gauge region of the material sample. 17. Use of a specimen according to any one of claims 1 to 11 in digital image correlation measurements and/or setups. |
Field of the Invention
The present invention relates to a test specimen, and more specifically it relates to a tensile test specimen.
Background
During a steelmaking process, steel can undergo a series of heating and cooling steps. In a cooling step, an outer surface of the steel can solidify faster than an inner section, which can result in an inhomogeneous microstructure and chemical composition throughout the thickness of the steel. This can result in an anisotropy, or variation in mechanical properties of the steel along different directions. The inhomogeneity can also result in a variation in strain hardening behavior throughout the thickness of the steel.
Reliable measurement of the yield stress is required in order to conform with industry standards (for example, for use of the steel in pipelines, conformity to "ASTM A20 / A20M Standard Specification for General Requirements for Steel Plates for Pressure Vessels" may be required). Reliable measurement of the yield stress can also be beneficial in optimizing a design of a product which incorporates the high strength steel (for example, optimizing a quantity of the steel used).
Such a variation in mechanical properties along the thickness of the steel cannot be measured using a conventional through-thickness tensile test (Z-test) which averages the strain hardening behavior over the thickness direction, or will only measure over the weakest region within the thickness.
One method of measuring a variation in mechanical properties through the thickness is to perform hardness tests along the thickness direction, from which a yield strength can be approximated. However, hardness measurements include a substantial variation on each indentation whereby measuring the through-thickness inhomogeneity becomes inaccurate. Furthermore, only the yield strength can be obtained, hence no strain hardening behavior can be measured.
Another procedure involves slicing a dog-bone sample over the thickness into multiple material layers or slices. A tensile test can be performed on each slice and the strain hardening behavior through the thickness can be determined by aggregating the results of the tensile tests. The slicing can be achieved using a wire-cut electrical discharge machining (EDM) process. Such a process can cause heating in a part of the sample, resulting in a heat affected zone, and this can cause a mechanical property of one or more material layers to be changed. In addition, a part of the sample may be removed during the EDM process which can result again in inaccurately measured parameters. Also, due to the slicing process, the residual stresses of the specimen can be partially eliminated. As a result of these effects, the tensile test measurements on the slices may not be representative of the material properties of the unsliced sample. Instead of slicing a specimen over the thickness direction, round bar specimens can be machined throughout the thickness of the specimen along the thickness direction, parallel to the rolling plane. By performing tensile tests on these round bars, the strain hardening behaviour through the thickness can be obtained. This procedure, however, is experimentally expensive and cannot measure the strain hardening of the surfaces layers since it is removed during machining.
Thus it is desired to provide an improved sample and method for tensile testing. Summary
It is an object of embodiments of the present invention to provide test specimens for tensile testing.
It is another object of embodiments of the present invention to provide efficiently measurable and easy to produce test specimens.
The above objectives are accomplished by a method and device according to the present invention.
According to a first aspect of the present invention, there is provided a tensile test specimen. The tensile test specimen comprises a first material. The tensile test specimen comprises a gauge region having first and second end regions spaced apart in a first direction, wherein the gauge region comprises a plurality of test regions comprising the first material spaced apart along the first direction. The gauge region comprises at least two recesses. Each test region is defined by at least one corresponding recess in the gauge section.
The gauge region has first and second opposite faces extending along the first direction. At least one of the at least two recesses is disposed in the first face and at least the other of the at least two recesses is disposed in the second face. The at least two recesses have a circular cross-section in a plane substantially parallel to the first and second faces. They also have the same diameter.
In some embodiments, the cross-section is disk shaped and the surface in the recess is substantially flat.
In some embodiments the test regions are equidistant test regions. In further specific embodiments the each test region has comparable dimensions of test surfaces.
The plurality of test regions may comprise a first test region defined by a first corresponding recess in a first face of the gauge region. The plurality of test regions may comprise a second test region defined by a second corresponding recess in a second face of the gauge region which is opposite the first face of the gauge region. The plurality of test regions may comprise a third test region defined by a first corresponding pair of recesses in the gauge region, the first pair of recesses comprising a third recess in the first face of the gauge region and a fourth recess in the second face of the gauge region, wherein the third recess is opposite the fourth recess. Each of the plurality of test regions comprising the first material may have a thickness measured in a direction substantially perpendicular to the first and second faces, wherein the thickness of each of the plurality of test regions is substantially the same.
Each recess may have a cross-section in a plane substantially parallel to the first and second faces, wherein the cross-section is substantially circular.
Each recess may have a cross-section in a plane substantially parallel to the first and second faces, wherein each recess has an extent in a direction substantially perpendicular to the first and second faces, and wherein the cross-section of each recess is substantially constant over the extent of each recess.
Each of the plurality of test regions may have an extent in a second direction, the second direction being substantially perpendicular to the first and second faces, wherein the extent of each of the plurality of test regions does not coincide substantially with the extent of any other of the plurality of test regions. The sum of the extent of the plurality of test regions may be substantially equal to a thickness of the gauge region in the second direction in a region which does not include a test region.
The specimen may further comprise a first shoulder section adjacent to the first end region of the gauge region, the first shoulder section having a first shoulder section width, and a second shoulder section adjacent to the second end region of the gauge region, the second shoulder section having a second shoulder section width, wherein the gauge region has a gauge region width, and wherein the first shoulder section width and the second shoulder section width are each greater than the gauge region width.
According to a second aspect of the present invention there is provided a method of manufacturing a specimen according to the first aspect, the method comprising providing a material sample comprising a gauge region; and forming the plurality of recesses in the gauge region of the material sample. In preferred embodiments providing a plurality of recesses is performed in preferably a non-heated manner without excess removal of gauge region material along the thickness (besides the recesses), for example by a milling process. It is an advantage of embodiments of the present invention the gauge region material is minimally affected by the heat input and no excess material is removed besides the provided recesses, in contrast to the slicing method. Heat input and excess material removal during slicing can affect the actual strain hardening behaviour. Consequently, the material properties obtained by performing measurements on test specimens according to embodiments of the present invention are more accurate than e.g. the known dog bone samples which are affected by the slicing effects. According to a third aspect of the present invention there is provided a method of performing a tensile strength test, the method comprising: providing a specimen according to the first aspect; applying a stress to at least the gauge region of the specimen; performing a digital image correlation measurement on at least one of the plurality of test regions; and determining at least one material property of at least one of the plurality of test regions in dependence upon the digital image correlation measurement.
The method may further comprise: calculating a first strain of a test region using a numerical model; calculating a value of a cost function in dependence upon the first strain and a second strain of a test region determined in dependence upon the digital image correlation measurement; and updating one or more parameters of the numerical model in dependence upon the value of the cost function.
The method may further comprise, if the value of the cost function is below a predetermined value, outputting one or more parameters of the numerical model.
Providing the tensile test specimen may comprise a specimen preparation step, wherein the specimen preparation step comprises: providing a material sample comprising a gauge region; and forming the plurality of recesses in the gauge region of the material sample.
According to a fourth aspect of the present invention there is provided use of a specimen according to the first aspect in digital image correlation measurements and/or setups.
Particular and preferred aspects of the invention are set out in the accompanying independent and dependent claims. Features from the dependent claims may be combined with features of the independent claims and with features of other dependent claims as appropriate and not merely as explicitly set out in the claims. These and other aspects of the invention will be apparent from and elucidated with reference to the embodiment(s) described hereinafter.
Brief Description of the Drawings
Certain embodiments of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which: Figure 1 is a schematic perspective view of a tensile test specimen according to embodiments of the present invention;
Figure 2a is a plan view of a tensile test specimen according to embodiments of the present invention, the plan view being directed towards the first face of the gauge region;
Figure 2b is a plan view of a tensile test specimen according to embodiments of the present invention, the plan view being directed towards the second face of the gauge region;
Figure 3 is a cross-sectional view of a tensile test specimen according to embodiments of the present invention, the cross-sectional view being in an x-z plane which intersects test regions of the tensile test specimen and taken along line A-A' of Figure 2a;
Figure 4 is a cross-sectional view as in Figure 3 with further parameters indicated;
Figure 5a is a perspective view of a dog-bone specimen known in the art;
Figure 5b is a perspective view of a series of slices of a dog-bone specimen known in the art;
Figure 5c illustrates strain application to a series of slices of a dog-bone specimen known in the art;
Figure 6 is a plot of stress as a function of equivalent plastic strain for dog-bone specimen slices as illustrated in Figure 5c;
Figure 7 is a plot of Vickers hardness as a function of through thickness of dog-bone specimen known in the art;
Figure 8 is a plot of the accuracy e SWi f t of the identified strain hardening behaviour for each layer of a test specimen according to embodiments of the present invention as a function of recess diameter of the test regions;
Figure 9a is a plan view of a tensile test specimen according to embodiments of the present invention indicating various parameters of the specimen;
Figure 9b is a cross-section view of the tensile test specimen of Figure 9a taken along line B-B' of Figure 9a; Figure 10 is a plot of the reference strain hardening behavior of layers of a tensile test specimen according to embodiments of the present invention;
Figure 11 is a schematic layout of a digital image correlation experiment which can be used to measure a tensile test specimen according to embodiments of the present invention;
Figure 12 is a flowchart of a finite element model updating process;
Figure 13 is a plot of an initial Swift model, Swift models for five material layers with parameters obtained by a FEMU process, and experimentally measured strain hardening behavior for each layer;
Figure 14a is a plot of experimentally measured x direction strain component e** for load step 5 out of 7;
Figure 14b is a plot of e** calculated by a finite element model updating (FEMU) process for a load equal to that applied in load step 5 out of 7;
Figure 14c is a plot of the discrepancy between the experimental measured and FEMU-determined strain component e cc ;
Figure 15 is a flow chart of a method of performing a tensile stress test. The drawings are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes. Any reference signs in the claims shall not be construed as limiting the scope.
In the different drawings, the same reference signs refer to the same or analogous elements.
Detailed Description of Certain Embodiments
The present invention will be described with respect to particular embodiments and with reference to certain drawings but the invention is not limited thereto but only by the claims. The drawings described are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes. The dimensions and the relative dimensions do not correspond to actual reductions to practice of the invention.
Furthermore, the terms first, second and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a sequence, either temporally, spatially, in ranking or in any other manner. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other sequences than described or illustrated herein.
Moreover, the terms top, under and the like in the description and the claims are used for descriptive purposes and not necessarily for describing relative positions. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other orientations than described or illustrated herein.
It is to be noticed that the term "comprising", used in the claims, should not be interpreted as being restricted to the means listed thereafter; it does not exclude other elements or steps. It is thus to be interpreted as specifying the presence of the stated features, integers, steps or components as referred to, but does not preclude the presence or addition of one or more other features, integers, steps or components, or groups thereof. Thus, the scope of the expression "a device comprising means A and B" should not be limited to devices consisting only of components A and B. It means that with respect to the present invention, the only relevant components of the device are A and B.
Reference throughout this specification to "one embodiment" or "an embodiment" means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases "in one embodiment" or "in an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment, but may. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.
Similarly it should be appreciated that in the description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects. This method of disclosure, however, is not to be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of this invention.
Furthermore, while some embodiments described herein include some but not other features included in other embodiments, combinations of features of different embodiments are meant to be within the scope of the invention, and form different embodiments, as would be understood by those in the art. For example, in the following claims, any of the claimed embodiments can be used in any combination.
In the description provided herein, numerous specific details are set forth. Flowever, it is understood that embodiments of the invention may be practiced without these specific details. In other instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.
Referring to Figures 1, 2a, 2b, and 3, a tensile test specimen (or "specimen") 1 according to embodiments of the present invention includes a gauge region 2 comprising a first material. In preferred embodiments the entire gauge region is made of one material, e.g. first material, whereby the material exhibits a property variation (e.g. strain variation) through its thickness z. The gauge region 2 comprises a first end region 3 and a second end region 4. The first end region 3 and the second end region 4 are spaced apart in a first direction y. The gauge region 2 comprises a first face 5 and a second face 6 opposite the first face 5. The first face 5 and the second face 6 each extend along the first direction y between the first end region 3 and the second end region 4. The first face 5 and the second face 6 are substantially planar in a plane which includes the first direction y and a second direction x which is perpendicular to the first direction y. The first face 5 and the second face 6 are spaced apart in a third direction z which is perpendicular to the first direction y and the second direction x.
The specimen 1 in embodiments of the present invention comprises a first shoulder section 7 and a second shoulder section 8 which are spaced apart in the third direction. The first shoulder section 7 is preferably adjacent to the first end region 3 of the gauge region 2. The second shoulder section 8 is adjacent to the second end region 4 of the gauge region 2. The gauge region 2 has a width w g in the x direction and the first and second shoulder sections 7, 8 each have a width w s in the x direction which is preferably greater than the gauge region width w g .
The gauge region 2 has a length L g in the y direction and the specimen 1 has a length L s in the y direction.
The specimen 1 according to embodiments of the present invention comprises first and second connecting regions 9, 10 respectively. The first connecting region 9 is disposed between the first end region 3 and the first shoulder section 7. The second connecting region 10 is disposed between the second end region 4 and the second shoulder section 8.
The width of the first connecting region 9 at an end of the first connecting region 9 which is preferably adjacent to the first end region 3 is substantially equal to the width of the first end region 3. The width of the first connecting region 9 at an end of the first connecting region 9 which is adjacent to the first shoulder region 7 is preferably substantially equal to the width of the first shoulder region 7. The first connecting region 9 has a width which varies along the y direction between these two width values. For example, in preferred embodiments, the first connecting region 9 has an edge face running between the first end region 3 and the first shoulder region 7 which is a curved face having a radius of curvature. In some embodiments, the first connecting region 9 has a width which increases monotonically, that is, the first connecting region has an edge face running between the first end region 3 and the first shoulder region 7 which is a planar face.
In embodiments the width of the second connecting region 10 at an end of the second connecting region 10 which is adjacent to the second end region 4 is preferably substantially equal to the width of the second end region 4. The width of the second connecting region 10 at an end of the second connecting region 10 which is adjacent to the second shoulder region 8 is preferably substantially equal to the width of the second shoulder region 8. The second connecting region 10 has a width which varies along the y direction between these two width values. For example, in preferred embodiments, the second connecting region 10 has an edge face running between the second end region 4 and the second shoulder region 8 which is a curved face having a radius of curvature. In some embodiments, the second connecting region 10 has a width which increases monotonically, that is, the second connecting region has an edge face running between the second end region 4 and the second shoulder region 8 which is a planar face.
In embodiments of the present invention the gauge region comprises at least 2 test regions spaced apart in a first direction y. In preferred embodiments, the test regions closest to the first and second end regions 3, 4 are each defined by only one recess, one of which is provided on the first face 5 and the other on the second face 6. In embodiments of two or more test regions, the remaining test regions may be provided in an ordered manner between the test regions provided closest to the first and second end region. These remaining test regions are each defined by two recesses provided at the same position but on opposites side of the faces 5, 6 of the gauge region. The recesses (and their depths) are provided such that the thickness of each test region t = thickness of the gauge region (T)/( sum of test regions) is representative of a layer of the test specimen, resulting in that when each test region has been evaluated an indication can be provided of the change of the strain properties of the material as a function of the thickness direction. The test regions are preferably provided in a step-wise or ordered way, that is, the depth of recesses in a particular face of the test region increases (or decreases) monotonically from one end region to the opposite end region.
Depending on the sample material, the production method available and/or the overall thickness of the test specimen the number of test regions can be chosen.
A relatively large number of test regions can allow to probe the through thickness more finely than a relatively small number of test regions. The number of test regions is preferably at least 4. The number of test regions may preferably be more than 4 and less than 12, however in some embodiments the number of test regions may be greater than 12.
In alternative embodiments it is possible to provide the test regions and their representative thickness in a non- ordered way and thus non-consecutively following each other, however this may create moments in the specimen by the large jumps which will affect the overall deformation as it will induce bending next to tension much more than if they are put in an ordered manner according to preferred embodiments of the invention.
In a specific embodiment, the gauge region may comprise first, second, third, fourth, and fifth test regions 171, 172, 173, 174, 175 respectively, which are spaced apart in the first direction. Each test region 171, 172, 173, 174, 175 comprises a thickness t of first material remaining in the third direction z and is defined by a first corresponding recess 181, 182, 183, 184, 185 in the first face 5 and additionally or alternatively by a second corresponding recess 191, 192, 193, 194, 195 in the second face 6 of the gauge region 2. The recesses are preferably generally circular in cross-section, for a cross-section taken in the x-y plane. However, the recesses may have any suitable shape in cross-section, for example an oval shape, a square shape, a rectangular shape, any regular or non-regular polygonal shape, a non-polygonal shape. In embodiments, the walls of the recesses are preferably substantially perpendicular to the test region 171, 172, 173, 174, 175 surface, however in alternative embodiments the walls may be inclined with respect to the test region 171, 172, 173, 174, 175 surface.
For example, referring to Figure 3, the first test region 171 is defined by a first test region first corresponding recess 181 in the first face 5. The second test region 172 is defined by a second test region first corresponding recess 182 in the first face 5 and by a second test region second corresponding recess 192 in the second face 6. The second test region first corresponding recess 182 in the first face 5 is opposite the second test region second corresponding recess 192 in the second face 6, that is, the first corresponding recess 182 and the second corresponding recess 192 are spaced apart in the z direction and are not substantially spaced apart in the x direction or in the y direction. The third test region 173 is defined by a third test region first corresponding recess 183 in the first face 5 and by a third test region second corresponding recess 193 in the second face 6. The third test region first corresponding recess 183 in the first face 5 is opposite the third test region second corresponding recess 193 in the second face 6. The fourth test region 174 is defined by a fourth test region first corresponding recess 184 in the first face 5 and by a fourth test region second corresponding recess 194 in the second face 6. The fourth test region first corresponding recess 184 in the first face 5 is opposite the fourth test region second corresponding recess 194 in the second face 6. The fifth test region 175 is defined by a fifth test region first corresponding recess 195 in the second face 6. In Figure 3, the surface 197 in the recess is also shown.
The test region thickness t is measured in the z direction. The test region thickness t is equal to one fifth of a thickness T of the gauge region 2 in a region which does not include any test region 171, 172, 173, 174, 175. That is, the sum of the thicknesses t of each of the test regions 171, 172, 173, 174, 175 is equal to the thickness T of the gauge region in a region which does not include any test region 171, 172, 173, 174, 175. The thickness T of the gauge region may be measured, for example, in the first end region 3 or the second end region 4, or in a region A shown in Figure 4 which is between two test regions.
Referring to Figure 4, the first test region first corresponding recess 8i has a depth d 81 measured from the first face 5 to the first test region 171 in the z direction.
The second test region first corresponding recess 182 has a depth d 82 measured from the first face 5 to the second test region 172 in the z direction. The depth d 82 is less than the depth d 81 . The second test region second corresponding recess 192 has a depth d 92 measured from the second face 6 to the second test region 172 in the z direction.
The third test region first corresponding recess 183 has a depth d 83 measured from the first face 5 to the third test region 173 in the z direction. The depth d 83 is less than the depth d 82 . The third test region second corresponding recess 193 has a depth d 93 measured from the second face 6 to the third test region 173 in the z direction. The depth d 93 is equal to the depth d 83 and is greater than the depth d 92 .
The fourth test region first corresponding recess 184 has a depth d 84 measured from the first face 5 to the fourth test region 174 in the z direction. The depth d 84 is less than the depth d 83 . The fourth test region second corresponding recess 194 has a depth d 94 measured from the second face 6 to the fourth test region 174 in the z direction. The depth d 94 is greater than the depth d 94 .
The fifth test region first corresponding recess 195 has a depth d 95 measured from the second face 6 to the fifth test region 175 in the z direction. The depth d 95 is equal to the depth d 81 .
Each test region extends, in the z direction, over a portion of the thickness T of the gauge region 2. The portion is different for each test region, that is, the extent in the z direction of each test region does not overlap substantially with the extent of any other test region in the z direction. That is, the sum of the extents of the test regions serves to span the thickness of the gauge region. In preferred embodiments the cross-section of the gauge region of a test specimen according to embodiments of the present invention exhibits point symmetry with respect to its central point, the middle of the gauge region.
Thus, the present invention allows to provide a single specimen having a plurality of test regions which collectively span the thickness of the specimen, which allows to perform a tensile test measurement for more than one slice without requiring the specimen to be sliced into separate samples.
Experimental examples using test samples known in the art and test specimen according to embodiments of the present invention.
To have a benchmark for the inhomogeneous strain hardening behaviour through the thickness of a 10 mm thick high yield structural steel (e.g. S690QL grade), a dog bone sample 20 known in the art and thus not containing recesses was tested. Referring to Figure 5a, the dog bone sample 20 has first and second ends 21, 22 respectively spaced apart in the y direction. The dog bone sample 20 includes a sample gauge region 23 between the first end 21 and the second end 22. The dog bone sample 20 has a thickness in the z direction and the sample gauge region 23 extends in the x and y directions. The dog bone sample 20 was sliced along its length into 5 layers LI, L2, L3, L4, L5 (Figure 5b) over the thickness by an EDM process. Each dog bone sample slice had a resulting thickness in the z direction of approximately 1.8 mm (which is less than the expected 2mm).
Next, a tensile test was performed on each dog bone layer (as illustrated in Figure 5c, wherein arrows All, A21, A31, A41, A51 illustrate stress applied to corresponding layers LI, L2, L3, L4, L5 respectively in a first direction along the z axis and arrows A12, A22, A32, A42, A52 illustrate stress applied to corresponding layers LI, L2, L3, L4, L5 respectively in a second direction along the z axis which is opposite the first direction) using a Zwick Z250 tensile bench with a load capacity of 250 kN. An A80 extensometer with an initial gage length of 80 mm was used to measure the elongation.
The results of the tensile tests are shown in Figure 6 where the true stress s is plotted as a function of equivalent plastic strain e eq pi . The numbering of the slices which represent the material layers is the same as that in Figure 5b where 1 and 5 each represent an outside material layer (layers LI and L5). Additionally, the yield stress of each material layer is shown in the first row of table I:
Table I: yield stresses c p0.2 (MPa) of sample or specimen layers
A substantial difference between the yield stresses of outer layers LI and L5 with respect to the yield stresses of the inner layers is clear. Further, it is seen that the strain hardening behaviour is not symmetrical with respect to the mid-thickness region, as the initial yield stress of layer LI is substantially lower than that of layer L5.
Slicing a specimen into layers using EDM and subsequently, performing a tensile test is a time consuming task. Moreover, part of the material is removed during slicing (1.8 mm thickness instead of 2mm) while the material layers are potentially affected by the heat input. Both of these affect the actual strain hardening behaviour. Consequently, the material properties obtained by performing measurements on slices resulting from slicing of a dog bone sample may be unreliable due to the slicing effects.
Using a second dog bone sample not containing recesses known in the art, the second dog bone sample remaining unsliced, the initial yield stresses through the thickness were obtained via microhardness measurements along the thickness direction. From a Vickers hardness test, the yield stress can be estimated according to equation 1:
s 0 = — -— 0.1" (equation 1) where HV is the Vickers hardness and n is the strain hardening exponent (approximately 0.05 for the S690QL steel grade). The Vickers microhardness tests were performed on a Zwick Indetec ZHV with a load of 9.8 N and a magnification of 400:1. The sample was polished so as to provide an even surface in order to accurately measure the micro indentations. 38 indentations were performed on a straight line, starting from layer LI up to L5. The layers are labelled in the same manner as for the sliced dog bone sample, whilst understanding that the second dog bone sample is unsliced. The distance between the centres of two adjacent indentations was 250 pm, which is slightly larger than the minimum three times the mean diagonal length of the indentation specified by the standard ISO 6507-1 Metallic materials - Vickers hardness test, 2005. Three repetitions of Vickers hardness measurements (HV) were performed and the results are shown in Figure 7. A substantial variation of the measured values between test repetitions can be observed. It can be seen, however, that the outer region near layer 1 has a substantial lower HV value than those of the inner regions and the outer region near layer 5, which indicates that a substantial lower yield stress could be present at one side of the dog bone sample 20. In second row of Table II, the estimation of the yield stresses for each slice is given by using equation 1 while averaging the hardness measurement results over each slice. It can be seen that a lower yield stress is measured at both the outside layers. However, substantial larger true stress values at a plastic strain of 0.2% (s r o. 2 ) are estimated than the o p0.2 values obtained from measurements of slices of the dog bone specimen.
It can be concluded that, although measuring initial yield strength with a Vickers microhardness test may in some circumstances provide a small indication of yield stress variation through the thickness of a sample, it is not an accurate method.
As seen from the above results, the S690QL grade exhibits different strain hardening behaviours through the thickness of the sample. As a result, the thickness surface of a dog bone sample 20, as illustrated by area B in Figure 5a, could exhibit a difference in strain fields over the thickness region B during a tensile test. The thickness surface B of a dog bone sample 20 is a surface in the y-z plane which extends along the thickness direction and is perpendicular to a plane in which the slices are made. Strain is applied in the longitudinal (y) direction. A possible variation in strain fields was measured using a stereo-digital image correlation (stereo-DIC) measurement over the thickness surface. A strain field over the thickness surface measured using DIC, wherein the sample gauge section 23 is plastically deforming, was studied. No difference in strain values was observed due to the different material properties. Furthermore, no variation in strain fields along the transversal (z) direction was observed. To validate this measurement, a tensile test on a dog bone sample was simulated using a finite element (FE) model with the 5 different strain hardening behaviours of Figure 6.
No variation in longitudinal strain fields through the thickness was observed, neither along the transverse direction, which is in agreement with the DIC measurement.
When studying the e eq pi values over the thickness surface of the FE model, a clear difference between the layers (into which the dog bone sample 20 is sliced) could be observed due to the different strain hardening behaviours. However, the e eq pi component cannot be measured separately because only the combination of the plastic and elastic strain components can be measured using DIC. It can be seen that measuring over the thickness surface with DIC does not provide enough sensitivity to characterize the through-thickness inhomogeneity of a material sample.
Embodiments of the present invention provide an improved specimen and method which can overcome one or more limitations of existing specimens and methods.
A first test specimen according to embodiments of the present invention was modelled using a finite element (FE) model. Referring to Figures 9a and 9b, the first test specimen had the following parameters (which are provided by means of example only and are not meant to be limiting): the gauge region comprises 5 test regions; the recesses are substantially circular in cross-section in the x-y plane and each recess has a diameter D of 40mm as measured in the x-y plane; the width w g of the gauge region as measured in the x direction is 60 mm; the length L g of the gauge region in the y direction is 160 mm; the length L s of the specimen in the y direction is 400 mm; the width w s of each shoulder region as measured in the x direction is 65 mm; the connecting region edges are arc shaped with radius of curvature R of 81.25 mm; the thickness t of each test region as measured in the z direction is 2 mm; the thickness T of the gauge region as measured in the z direction is 10 mm and the specimen has uniform thickness of 10 mm in regions which do not include a test region. In particular, the thickness of the shoulder regions and of the connecting regions is 10 mm. The shortest distance s between the centres of two adjacent recesses in the y direction is 30 mm.
To verify the identification procedure and to optimise the dimensions of the test specimen according to embodiments of the present invention, a numerical concept study was performed using specimen parameters of the first test specimen.
For the virtual experiment, an FE model of the test specimen was modelled with 5 different material layers (numbered in the same order as in Fig. 5b). Each material layer has a thickness equal to the thickness t of a test region. Each layer has a reference strain hardening behaviour which is plotted as the solid lines in Fig. 10. The 5 reference strain hardening models are Swift models, because the pre-necking region of the S690QL grade could adequately be followed by a Swift strain hardening model. As a consequence, 15 parameters need to be identified simultaneously; 5 through-thickness layers, each containing a Swift model with 3 parameters. The Swift hardening law can be expressed as
(equation 2) wherein K is the deformation resistance, e 0 is the initial deformation, n is the hardening exponent, c eq is the equivalent stress, and z p f q is the equivalent plastic strain.
Subsequently, a finite element model updating (FEMU) process was employed to characterise the 15 parameters. Because the Levenberg-Marquardt algorithm is not able to find the minimum of the objective function with 15 parameters, an Adaptive Nelder-Mead Simplex method was used.
During the FEMU process, the discrepancy between surface strain fields in each test region 7 (these surface strain fields being obtained from a virtual experiment (or a DIC measurement during a physical experiment)) and the current surface strain fields in the FE simulation are minimised. Because the FE simulation is displacement driven, a general cost function C(p) was minimized, wherein the general cost function is decomposed into two separate cost functions:
C7(p) = C(p)i + £7{p) 2
(equation 3) wherein the first cost function C(p) i is formed by the numerical (num) and experimental (exp) strain components e cc , £ yy and e zz normalized by their root mean square (RMS) of the region of interest:
(equation 4) and the second cost function C(p) 2 consists of the experimentally measured and numerically computed tensile force normalized by the experimental value:
The subscripts "exp" represent the experimental response in case of an actual test or the reference response in case of the numerical concept study. e cc is the normal strain component in the -direction, e yy is the normal strain component in the y-direction, and e zz is the normal strain component in the z-direction. e xy is the shear strain component in the x-y plane.
To obtain the most accurate parameters, there is preferably a good balance between the DIC sensitivity with respect to the material parameters and the dimensions of the specimen. The material parameter identification is achieved by a local optimization procedure which calculates sensitivities of the parameters. The geometry of the specimen can influence the sensitivity of a parameter. The FEMU process was repeated for recess diameters of 10 mm, 20 mm, and 30 mm with the remaining dimensions unchanged, to investigate any difference in accuracy of the modelling. The accuracy e SWi f t of the identified strain hardening behaviour for each layer is expressed by:
(equation 5)
wherein: k is a number of points in the stress-strain curve described by equation 2; o y / ef is the reference equivalent stress used in the virtual experiment; and o y,i ID is the identified equivalent stress. This is plotted in Figure 8 as a function of recess diameter D. It can be inferred that the specimen with a dimension D of 20 mm could reproduce the 5 through-thickness strain hardening behaviours with the highest accuracy e SWi f t and consequently, is the preferred geometry for this 10 mm thick S690QL grade. The FEMU process can be repeated whilst varying other parameters than the recess diameters in order to determine parameters with the highest accuracy, such as the thickness t of a test region, the separation s of the centres of adjacent test regions, the shape of a test region (which may be other than circular, for example elliptical, square, rectangular, an irregular shape).
Experiment to characterise the through-thickness inhomogeneity
The FEMU simulations show that a specimen according to embodiments of the present invention can accurately characterise the through-thickness strain hardening behaviour.
A second test specimen was prepared having the geometry of the first test specimen except that the recess diameter was 20 mm. The specimen was machined out of S690QL grade steel using a milling process. Alternative machining processes for the specimen are possible, for example electric discharge machining. Subsequently a quasi-static tensile test was performed using an MTS 1000 kN tensile bench equipped with hydraulic wedge grips. A stereo-DIC setup was used to acquire test region surface displacement fields and consequently, the test region surface strain fields. The DIC settings were as follows:
Table II: specification of DIC parameters for stereo-DIC measurement
Figure 11 is a schematic representation of the DIC setup used to measure a test specimen according to embodiments of the present invention. The second test specimen 30 is held in wedge grips 31 at each end of the specimen. A lamp 32 is directed at the first face 33 of the specimen 30. The specimen 30 includes five test regions 7 as described hereinbefore. First and second cameras 34, 35 respectively are directed at the first face 33 of the specimen 30 in a stereo configuration. First and second cameras 34, 35 are in communication with a control computer 36 configured to provide signals to the first and second cameras and to receive signals and/or data from the first and second cameras.
A FEMU process was performed to simultaneously identify 5 independent Swift strain hardening models (since the second test specimen 30 comprises 5 test regions). Each model corresponds to a material layer in the specimen, wherein each layer includes exactly one of the test regions. In embodiments wherein a test specimen comprises a different number of test regions, the number of independent Swift strain hardening models will be equal to the number of test regions. The Swift parameters obtained from a tensile test on a dog bone sample (not including test regions according to embodiments of the present invention) were used as initial parameters for the five material layers modelled.
Referring to Figure 12, a flowchart of an FEMU process is shown. The FEMU takes as input a set of initial parameters, for example Swift law parameters (the initial parameters may be for example obtained from a tensile test on a dog bone sample not including test regions) and boundary conditions (for example, relating to clamping of the specimen in the tensile test apparatus) which are dependent on the particular experiment for which the FEMU process is performing the modelling (step S1301). Strain fields are calculated using a Swift model for each material layer in the specimen using the finite element model and the boundary conditions and parameters (step S1302). A global cost function is evaluated in dependence upon the calculated strain field for each layer and the experimentally measured strain field for the test region corresponding to each layer (step 1303).
The cost function may be, for example: (equation 6) wherein m is the number of load steps and n,the number of data points in the DIC measurement taken at a load step /. A load step is the point at which the DIC image is taken and is characterized by the load applied to the sample. Thus the FEMU model uses the results for all load steps simultaneously at each cost function evaluation step.
The value of the cost function is compared with a predetermined threshold value (step S1304). If the cost function value is less than the threshold value, the parameters of the Swift model are output (step S1305a). If the cost function value is greater than the threshold value, one or more parameters of the Swift model for one or more of the layers is modified (step S1305b) and the process returns to step S1302. The predetermined threshold value may depend on the particular properties and parameters of the specimen.
The difference between the cost function at the present step and the cost function of the preceding step (the preceding step having one or more parameters different to parameters at the current step) may be determined and compared with a threshold value and the next step to be followed may depend on this comparison. For example, if the relative variation of the cost function over successive steps is less than 1%, step S1305a is then followed (output of parameters). If the relative variation of the cost function over successive steps is greater than 1%, step S1305b is followed (modification of parameters and return to step S1302).
Referring to Figure 13, the initial Swift model is shown by the solid black line. The 5 Swift models for the 5 layers, with Swift model parameters as identified by the FEMU process, are shown by the plotted open shapes as indicated for each layer. The dashed lines show experimentally measured strain hardening behaviour as obtained by strain measurements on dog bone sample slices which do not include test regions (Figure 5c). . The Swift model for each layer as identified by the FEMU process should coincide with the experimentally measured values (open shapes) for each layer and a qualitative agreement can be observed.
Referring again to Table I, the yield stresses are set out for each material layer (third row). Where a layer or material is referred to in relation to a specimen according to embodiments of the present invention, it is meant the layer which includes a corresponding test region for which strain fields were measured experimentally, as described hereinbefore in relation to Figure 9a, 9b. For example, referring to Figure 3, the corresponding material layer for first test region 171 is a layer which has thickness t in the z direction and includes the second face 4, that is, an outer layer of the specimen.
It is clear from Table I that for layer LI, the FEMU process for the specimen according to embodiments of the present invention results in a substantially lower yield stress compared to the inner material layers, which is in agreement with the results obtained from the sliced dog bone sample. Similarly, for layer L5, a lower yield stress is identified, which is in agreement with the slicing procedure. Hence, it can be inferred that each of the outside layers exhibits a lower yield stress as compared to those of the inner material layers.
Referring to Figure 14a, the experimentally measured strain in the x direction e cc is shown for load step 5 out of 7. The FEMU calculated e » , is shown in Figure 14b for a load equal to that applied in experimental load step 5 out of 7. The discrepancy between the exp4erimental e « of Figure 14a and the FEMU calculated e « of Figure 14b is shown in Figure 14c. It is seen that the experimental and FEMU strain fields are in good agreement with each other. Furthermore, a different strain level is present at each material layer due to variation in strain hardening behaviours between different layers. A dissimilarity between the strain hardening behavior of a sample which is sliced into discrete slices and the strain hardening behavior of a test specimen according to embodiments of the present invention, which may be determined using an inverse characterisation method as described herein, may arise for one or more reasons. First, the EDM process by which the dog bone sample is sliced may cause a heat affected zone to be formed in a slice. The process can also remove a part of the thickness of the characterised material layer and can remove residual stresses. Second, the Swift model used in the FEMU process allows a good following of the strain hardening behaviour of the outside material layers, while a linear function may allow an improved approximation of the inner material layers.
A global optimisation algorithm, for example a simulated annealing algorithm, could be used in the FEMU process and could improve the characterised strain hardening models, however, this may require a larger number of iterations.
Embodiments of the present invention also provide a method of manufacturing a tensile test specimen. The method comprises a step of providing a material sample comprising a gauge region and a step of forming the plurality of recesses in the gauge region of the material sample.
Referring to Figure 15, a flowchart of a method of performing a tensile strength test is shown. The method comprises providing a tensile test specimen according to embodiments of the present invention (step S1601). A stress is applied to at least the gauge region of the specimen (step S1602). A digital image correlation measurement is performed on at least one of the plurality of test regions (step S1603). At least one material property of at least one of the plurality of test regions is determined in dependence upon the digital image correlation measurement (step S1604).
Providing the tensile test specimen (step S1601) may comprise providing a material sample comprising a gauge region and forming a plurality of recesses in the gauge region of the material sample so as to provide a tensile test specimen according to embodiments of the present invention.
Determining at least one material property (step S1604) may comprise calculating a first strain of a test region using a numerical model; calculating a value of a cost function in dependence upon the first strain and a second strain of a test region determined in dependence upon the digital image correlation measurement; and updating one or more parameters of the numerical model in dependence upon the value of the cost function, as described hereinbefore.
Determining at least one material property (step 1604) may comprise, if the value of the cost function is below a predetermined value, outputting one or more parameters of the numerical model.
Modifications
It will be appreciated that many modifications may be made to the embodiments hereinbefore described.
In some embodiments, the shoulder regions may have a different thickness to that of the gauge region. The shoulder regions may be generally cylindrical in shape.
Embodiments of the present invention are not limited to a specimen comprising S690QL and may include any specimen comprising a material which exhibits strain hardening which varies through its thickness. For example, the specimen may comprise a pure metal or metal alloy, a plastics material, a composite, a foam, a rubber etc.. Although the stereo-DIC experimental setup is described in relation to cameras and lamp directed at one face of the specimen, the present invention is not limited to this specific embodiment. The cameras and lamp may be directed at an opposite face of the specimen which includes test regions. The stereo-DIC setup may comprise an additional set of cameras and lamp such that measurements can be made of strain fields on each face of the specimen simultaneously.
In some embodiments, the cross-section of one, more or all of the recesses is disk shaped. In some embodiments, the surface in the one, more or all of the recesses may be substantially flat, e.g. flat. The height variation on the surface may e.g. be less than 50 micrometer, e.g. may have an upper limit between 50pm and 25pm, e.g. may be even smaller than 25pm. Such flatness may be measured using a coordinate measuring machine, allowing to measure the flatness of the surface with an accuracy of up to a few micrometer. The surface advantageously is as flat as possible. It is to be noted that a random distribution of the height variation results in less effects on the tensile strength measurements achievable with the test specimen, compared to for example a pronounced error in one location.
The present invention is not limited to embodiments comprising five test regions, that is, embodiments wherein a material property of five material layers of the specimen can be measured. For example, a specimen according to embodiments of the present invention may comprise first and second test regions, wherein each test region has a thickness equal to one half of the thickness of the gauge region in a region which does not include a test region. A specimen may comprise first, second, and third test regions, wherein each test region has a thickness equal to one third of the thickness of the gauge region in a region which does not include a test region. In general, a specimen according to embodiments of the present invention may comprise N test regions, wherein each test region has a thickness equal to 1/N times the thickness of the gauge region in a region which does not include a test region. Each test region preferably has the same thickness so as to obtain substantially the same load distribution across the regions, otherwise one test region may deform much more than the other test regions and the required stress/strain would not be obtained in these other regions. It will be understood that the depths of corresponding recesses will be such as to provide test regions having the required thicknesses and locations within the thickness of the gauge region.