A method and a system for determining at least one mechanical property of a sample

Abstract

The present invention relates to a method for determining at least one mechanical property of sample (2), the method comprising the steps of providing the sample (2), wherein the sample (2) comprises a dimension in a main direction (20); mounting the sample (2) at a mounting end (4) of the sample (2), wherein a free end (3) of the sample (2) is freely movable in a direction perpendicular to the main direction (20); shaking the mounted end of the sample (2) at an excitation frequency to excite an oscillatory bending of the sample (2) about a centre line (21) perpendicular to the main direction (20); determining a bending radius (R) of the sample (2) at a predetermined deflection or a determined deflection of the sample (2); calculating a bending stress using the bending radius (R); and calculating the at least one mechanical property of the sample (2) using the bending stress and a number of oscillations of the sample (2) until failure of the sample (2) or the bending stress at a plurality of excitation frequencies or the bending stress at a plurality of excitation frequencies and a description of a geometry of the sample (2).

Description

[0001] A method and a system for determining at least one mechanical property of a sample

[0002] TECHNICAL FIELD

[0003] The present disclosure relates to a method and a system for determining at least one mechanical property of a sample.

[0004] BACKGROUND

[0005] Measuring of a mechanical property of a sample like bending fatigue strength, damping or elastic constant typically requires a complex and costly equipment for testing and measuring.

[0006] SUMMARY

[0007] It is an aspect of the present disclosure to provide a method and a system for determining at least one mechanical property of a sample which are simplified compared to the prior art, thus reducing both costs and effort.

[0008] The above aspect is solved by a method according to independent claim 1 of the present application. The method according to the present disclosure comprises the steps of: providing the sample, wherein the sample comprises a dimension in a main direction; mounting the sample at a mounting end of the sample, wherein a free end of the sample is freely movable in a direction perpendicular to the main direction; shaking the mounted end of the sample at an excitation frequency to excite an oscillatory bending of the sample about a centre line perpendicular to the main direction; determining a bending radius of the sample at a predetermined deflection or a determined deflection of the sample; calculating a bending stress using the bending radius; and calculating the at least one mechanical property of the sample using the bending stress and a number of oscillations of the sample until failure of the sample or the bending stress at a plurality of excitation frequencies or the bending stress at a plurality of excitation frequencies and a description of a geometry of the sample.

[0009] It is the basic concept of the method according to the present disclosure to force the sample to an oscillatory motion of its free end relative to the mounting end and to determine the bending radius of the sample at a predetermined deflection or a determined deflection of the sample. The bending radius is a direct measure for the bending stress applied to the sample. Determining the bending radius of the sample from a measurement of the sample is a fast and robust calculation with high accuracy. The respect mechanical property of the sample can then be calculated on basis of some assumptions. The predetermined deflection or the determined deflection is non-zero, i.e., a sample is in a bent state during an oscillation at the point in time when the sample is measured in order to determine the bending radius. It is important once the minimum bending radius, i.e. maximum bending of the sample is determined at a plurality of subsequent oscillations of the sample, that the bending radius is determined for an identical deflection of the sample each time.

[0010] According to embodiments, the predetermined deflection or the determined deflection may be tuned either before the method or during the performance of the method.

[0011] The bending stress, Obending, of the bent and thus curved sample can be derived from a thickness t of the sample, the bending radius R and the Young’s modulus E of the material according to the following equation:

[0012] According to embodiments, the thickness of the sample is measured using a micrometer screw. Young’s modulus is for example provided by a datasheet of sample’s material and the radius is measured.

[0013] According to embodiments, the surface of the sample is planar or cylindrical.

[0014] According to embodiments of the present disclosure, the sample may have a shape of a strip, a rod or a plate.

[0015] According to embodiments, the sample is a strip, wherein a dimension of the sample in the main direction is larger than a dimension of the sample in each of the two transverse directions, wherein the transverse directions are perpendicular to each other and are both perpendicular to the main direction.

[0016] According to embodiments, a material of the sample is selected from a group consisting of plastic, metal, paper and wood or a combination thereof.

[0017] According to embodiments, the step of determining the bending radius comprises a measurement of the bending radius or a measurement of a parameter indicative for the bending radius. According to embodiments, the step of determining the bending radius comprises: measuring a profile of a surface of the sample along a line with the sample at the predetermined deflection or the determined deflection, wherein the line is parallel to the main direction or wherein the line and the main direction form an angle smaller than 90°; and calculating the bending radius from the profile.

[0018] According to embodiments, a profile of the surface of the sample is measured using a profilometer. In an embodiment, the profilometer is a contactless profilometer, e.g., a laser profilometer. A contactless profilometer measures the profile of the surface of the sample without the need to mechanically interact with the surface. Profilometers measuring the profile of the surface of the sample with a high repetition rate and are commercially available. Typically, profilometers, in particular laser profilometers, are used to measure a surface’s profile in order to quantify the roughness of a sample. However, a profilometer can also be used for determining the microscopic shape, i.e., the bending radius, of the surface according to the present disclosure.

[0019] The main direction can be described to connect the mounted end and the free end of the sample. Thus, the sample mounted at its mounting end will experience a bending about an axis being non-parallel to the main direction. Consequently, the line of the profile measurement must be different from a direction perpendicular to the main direction.

[0020] According to embodiments, the length of the line will depend on the sample and the laser profilometer. For example, a length of the line may be in a range from 3 mm to 10 mm, such as in a range from 4 mm to 8 mm.

[0021] According to embodiments, the profile of the surface of the sample along the line is measured as a distance of the surface of the sample from a reference line. The reference line is parallel to the plane surface of the sample and is in a non-deflected zero position. This distance is the parameter to be measured by the sensor. The distance is indicative for or a direct measure for the bending radius.

[0022] According to embodiments, after measuring the profile of the surface of the sample, the profile is described in Cartesian coordinates enabling an analysis of the bending radius of the surface by calculations ruled by basic geometrical considerations. According to embodiments of the present disclosure, the mechanical property of the sample is a bending fatigue strength of the sample, wherein the bending fatigue strength is calculated from the bending stress and the number of oscillations of the sample until failure of the sample.

[0023] According to embodiments, the mechanical property of the sample is a damping factor of the sample, wherein the damping factor is calculated from the bending stress at a plurality of excitation frequencies.

[0024] According to embodiments, the mechanical property of the sample is a resonance frequency of the sample, wherein the resonance frequency is calculated from the bending stress at a plurality of excitation frequencies and a geometry of the sample.

[0025] In order to calculate the bending stress, O bending, Young’s modulus, E, is required. In an embodiment Young’s modulus, E, is derived from a table or textbook. In a further embodiment, Young’s modulus, E, of the sample is determined using a method similar to a method according to the present invention, wherein the method to determine Young’s modulus, E, comprises the steps of: providing the sample, wherein the sample comprises a dimension in a main direction; mounting the sample at a mounting end of the sample, wherein a free end of the sample is freely movable in a direction perpendicular to the main direction; shaking the mounted end of the sample at an excitation frequency to excite an oscillatory bending of the sample about a centre line perpendicular to the main direction; measuring an amplitude of the sample at a fixed point on the sample for a plurality of excitation frequencies; determining the resonance frequency of the sample from the measured amplitude over the excitation frequencies; and calculating Young’s modulus using the determined resonance frequency and a geometry of the sample. At the sample’s resonance frequency, the amplitude of the oscillating sample will show a maximum.

[0026] According to embodiments, the step of measuring the amplitude of the oscillating sample includes the steps: measuring the maximum deflection of a single point on the line of the profile of the surface of the sample for each step of the excitation frequency.

[0027] Youngs modulus, E, can be expressed as wherein co is the resonance frequency determined by the measurement of the resonance curve, k is a parameter corresponding to a characteristic vibration mode, I is the second moment of area of the sample ( / = - — - ) for a sample with a rectangular crosssection, wherein width is the width of the sample perpendicular to the main direction) and is the mass density of the material of the sample and Q is the cross section area.

[0028] According to embodiments, the deflection is measured versus the excitation frequency starting 10 Hz or 20 Hz below the expected resonance frequency and stepping the excitation frequency in a step size which may be 0.1 Hz up to an excitation frequency 10 Hz or 20 Hz above the resonance frequency. However, the step size may be larger or smaller than mentioned herein.

[0029] According to embodiments, the mechanical property is the sample’s G-modulus or Poisson’s ratio.

[0030] In an embodiment, wherein the measured mechanical property of the sample is the damping factor, the resonance frequency of the sample or Young’s modulus, the plurality of excitation frequencies includes the mechanical resonance movement of the sample.

[0031] Due to the clamping of the sample at one end and an oscillatory motion of the free end, the resonance frequency referred to is a resonance frequency of an oscillatory motion of the sample bending the sample about one or a plurality of axes perpendicular to the main direction.

[0032] In an embodiment, wherein the excitation frequency is not varied when determining the mechanical property, the excitation frequency is equal to a mechanical resonance frequency of the sample. Driving the oscillatory bending of the sample with this resonance frequency leads to the largest possible bending and thus the largest bending stress of the sample.

[0033] In an embodiment, wherein the sample is excited with the resonance frequency, the bending radius is determined at the maximum deflection of the sample. The maximum deflection then is the predetermined deflection or the determined deflection. The maximum deflection corresponds to the maximum amplitude of the oscillation. Care must be taken to ensure that the predetermined deflection or the determined deflection at which the bending radius of the sample is always determined at the same side relative to the non-bent zero position of the sample.

[0034] In an embodiment, wherein the mechanical property of the sample is the bending fatigue strength of the sample, the steps of determining a bending radius of the sample at a predetermined deflection or the determined deflection of the sample, and calculating a bending stress using the bending radius; are carried out a plurality of times and at least an amplitude or the excitation frequency of the shaking is controlled to minimize a difference between the bending stress and a predetermined desired bending stress.

[0035] In an embodiment, the at least one mechanical property is determined using a statistical evaluation of a plurality of essentially identical samples.

[0036] In an embodiment, the bending fatigue strength of the sample and optionally the relevant statistical parameters (e.g., standard deviation, 95% or 99% fatigue strength) are determined and calculated by a staircase evaluation or a Wohler curve evaluation of a plurality of measurements carried for a plurality of samples. A typical number of samples required ranges from 10 to 30.

[0037] According to embodiments, the plurality of samples is a plurality of essentially identical or identical samples. An essentially identical sample requires that the geometry of the plurality of samples is essentially identical. In an embodiment, the material of the plurality of samples is essentially identical. With respect to the geometry essentially identical means identical within the typical tolerances of manufacturing a mechanical sample. With respect to the material an essentially identical material is a material comprising the same chemical composition but might vary with respect to the microstructure of the plurality of samples, e.g., different precipitation or inclusions or surface defects.

[0038] Insofar as in the foregoing as well as the following description of embodiments and in the claims, reference is made to either the method for measuring at least one mechanical property of the sample or the system for measuring at least one mechanical property of the sample, the features described are applicable for both the method and the system.

[0039] At least one of the above aspects is also solved by a system according to independent claim 11 of the present disclosure. A system for measuring at least one mechanical property of the sample according to the present disclosure comprises a sample mount configured to hold the sample at a single mounting end of the sample; a shaker configured to cause an oscillation of the sample mount at an excitation frequency; a sensor configured to measure a parameter indicative for a bending radius of the sample at a predetermined deflection of the sample or at a determined deflection of the sample; and a control unit. The control unit is connected to the shaker and to the sensor to receive the parameter from the sensor. The control unit is further configured to control the excitation frequency of the shaker. Furthermore, the control unit is configured to determine a bending radius from the parameter, to calculate a bending stress using the bending radius and to calculate the at least one mechanical property of the sample using the bending stress and a number of oscillations of the sample until failure of the sample, or the bending stress at a plurality of excitation frequencies, or the bending stress at a plurality of excitation frequencies and a description of a geometry of the sample.

[0040] The foregoing as well as the following detailed description of the embodiment will be understood when read in conjunction with the appended drawings. It should be understood that the embodiments depicted are not limited to the precise arrangements and instrumentalities shown. In the figures equal elements are denoted by identical reference numbers.

[0041] BRIEF DESCRIPTION OF THE FIGURES

[0042] Figure 1 is a schematic representation of a system for measuring a mechanical property of a sample;

[0043] Figure 2 is a coordinate system in which a representation of a profile of the surface of the sample measured with the system of figure 1 and the values derived from the profile are shown.

[0044] DETAILED DESCRIPTION

[0045] Figure 1 schematically illustrates a system 1 set up for measuring a mechanical property of a sample 2. In the example described the sample 2 is a metal strip whose bending fatigue strength as a mechanical property in the sense of the present application shall be determined.

[0046] The sample 2 has a free end 3 and a mounting end 4. The mounting end 4 is clamped at a clamping means 5 as the sample mount of an electromechanical shaker 6. Once the clamping means 5 is periodically moved up and down by the shaker 6, the sample 2 starts an oscillatory motion. During this oscillatory motion the free end 3 is deflected upwardly and downwardly relative to the mounting end 4 of the sample 2. The geometry of the sample 2, once not deflected, has a major extension in a main direction 20. The oscillatory motion of the free end 3 occurs in a direction perpendicular to the main direction 20. Due to the oscillation, the sample 2 bends about a centre line 21 being perpendicular to the main direction 20.

[0047] During the periodical oscillation of the free end 3, a profile 7 of a surface 8 of the sample 2 is measured using a laser profilometer 9 as a sensor of the system 1. The laser profilometer 9 measures the profile 7 as a distance of a plurality of spots on a line 10 on the surface 8 from a reference plane 11. Once the sample 2 is not excited by the shaker 6, the reference plane 11 is parallel to the planar surface 8 of the sample 2.

[0048] A control unit 12 is connected to the profilometer 9 and to a driver 13 of the shaker 6. The control unit 12 records the profiles 7 measured by the profilometer 9. Furthermore, the control unit 12 controls the driver 13 and thus the oscillating motion of the shaker 6.

[0049] In the example described, the control unit 12 controls the driver such that the sample 2 is excited at a resonance frequency. The resonance frequency is characterized by a maximum amplitude of the oscillating motion of the free end 3 of the sample 2 and thus a maximum deflection of the free end 3. The deflection is directly observable in the profiles 7 recorded by the control unit 12. A control of the oscillation such that excitation of the sample 2 occurs at the resonance frequency leads to a maximum bending stress of the sample 2.

[0050] In order to determine the bending fatigue strength, the sample 2 is oscillated until it fails. The number of oscillations of the sample till failure of the sample 2 is counted and recorded together with the bending stress of the sample 2 during oscillation.

[0051] A number of 15 essentially identical samples 2 are measured in three groups. For the first group five samples are measured exciting an oscillation of these samples at a first bending stress, for example at 1200 MPa, for the second group five samples are measured exciting an oscillation of these samples at a second bending stress, for example at 1300 MPa, and for the third group five samples are measured exciting an oscillation of these samples at a third bending stress, for example at 1400 MPa. The first, second and third bending stresses differ from each other, wherein the amplitude of the excitation is varied from the first group to the third group, corresponding to the variation of the bending stress. After measurement of all three groups of samples 2, a Wohler curve is plotted as the bending stress over the (log) number of oscillations to failure.

[0052] A key to the method carried out by the system 1 is how the bending stress, abending, is derived from the profile 7. This part of the method is now described with reference to figure 2.

[0053] It is the underlying assumption that the curved profile 7 of the bent sample 2 belongs to a circle 14 with a radius R. This radius R is the radius of curvature or bending radius of the sample 2. Since the profile 7 is an arc on this circle 14 with a radius R, one can determine R from the chord line 15 and sagitta 16 of the profile 7:

[0054] The first and last x, y coordinates of the profile 7 are taken as the starting point 17 and end point 18 of the chord line 15.

[0055] Based on these two points, one determines the slope m and the y-intercept b of the chord line 15 connecting these two points 17, 18, as well as the midpoint 19 coordinates along this line y = mx + b

[0056] Ay y2- i m = — = -

[0057] Ax x2— %i b = y-L — (m • = X2+ XI .

[0058] ■ mid 2 ’ Tmid

[0059] The length L of the chord line 15 is determined between the starting point 17 and end point 18:

[0060] The sagitta’s 16 length s is determined by finding the shortest distance between the midpoint 19 and the profile 7. The algorithm takes the (x,y) coordinates of the midpoint 19, then iterates through all (x,y) coordinates of the profile 7 and takes the one which gives the shortest length. This line might somewhat differ from the line perpendicular to the chord, however, the deviation is within the order of a few micrometers which is below 1 % of the length of the sagitta 16. (Amid i) T Vmid Ti)

[0061] Based on the formula below the radius R is calculated from the length s of the sagitta 16 and the half-length of the chord line 15

[0062] In order to have some indication about how well the profile fits on the circle, whose radius R was determined before, the following steps are carried out to fit the circle on the profile. Based on the slope m, y-intercept b and midpoint 19, coordinates xmid, ymid were determined for the chord line 15, a perpendicular line is fitted on the chord, which perpendicular line inter sects the midpoint 19

[0063] Y' = m • x + b'

[0064] 1 m' = - m

[0065] Based on the origin of the circle, the whole circle 14 belonging to the arc can be drawn. The circle 14 is plotted as individual (x,y) point pairs using the parametric plot formulas for a circle with an origin at (Xo, Yo)

[0066] Since it is known that the profile 7 is located at the lower half of the circle 14, and the exact X- coordinates, of the profile 7 are also know, the corresponding Y-coordinates yarcof the circle 14 based on these X-coordinates x (e.g., between -4 mm and 4 mm) can be calculated

[0067] Now, the Y-coordinates of the fitted circle 7 are known for each given X-coordinate. The Y- coordinates of the fitted circle and of the profile are compared. The values should be within a few tens of micrometers.

[0068] The difference between the fitted circle and the captured profile can be used to determine the quality of the fitting.

[0069] The bending stress of the curved cantilever can be derived from the thickness t of the material, the radius of the curvature R and the Young’s modulus of the material E according to the following equation:

[0070] E - t bending n The thickness of the material can be measured with a micrometer screw, the Young’s modulus is provided by the material’s datasheet and the radius is measured using the test system.

[0071] For the purposes of the original disclosure, it is pointed out that all features as they become apparent to a person skilled in the art from the present description, the drawings and the claims, even if they have been specifically described only in connection with certain further features, can be combined both individually and in any desired combinations with other of the features or groups of features disclosed herein, unless this has been expressly excluded or technical circumstances render such combinations impossible or pointless. A comprehensive, explicit description of all conceivable combinations of features is omitted here only for the sake of brevity and readability of the description.

[0072] While the invention has been illustrated and described in detail in the drawings and the foregoing description, this illustration and description are merely exemplary and are not intended to limit the scope of protection as defined by the claims. The invention is not limited to the embodiments disclosed.

[0073] Variations of the disclosed embodiments will be apparent to those skilled in the art from the drawings, description and appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "one" or "a" does not exclude a plurality. The mere fact that certain features are claimed in different claims does not exclude their combination. Reference signs in the claims are not intended to limit the scope of protection.

[0074] REFERENCE NUMERALS

[0075] 1 System

[0076] 2 Sample

[0077] 3 free end of the sample

[0078] 4 mounting end

[0079] 5 clamping means

[0080] 6 Shaker

[0081] 7 Profile

[0082] 8 surface of the sample 2

[0083] 9 Profilometer

[0084] 10 Line

[0085] 11 reference plane

[0086] 12 control unit

[0087] 13 Driver

[0088] 14 Circle

[0089] 15 chord line

[0090] 16 Sagitta

[0091] 17 starting point

[0092] 18 end point

[0093] 19 Midpoint

[0094] 20 main direction

[0095] 21 centre line

Claims

CLAIMS1. A method for determining at least one mechanical property of a sample (2), the method comprising the steps of providing the sample (2), wherein the sample (2) comprises a dimension in a main direction (20); mounting the sample (2) at a mounting end (4) of the sample (2), wherein a free end (3) of the sample (2) is freely movable in a direction perpendicular to the main direction (20); shaking the mounted end of the sample (2) at an excitation frequency to excite an oscillatory bending of the sample (2) about a centre line (21) perpendicular to the main direction (20); determining a bending radius (R) of the sample (2) at a predetermined deflection or a determined deflection of the sample (2); calculating a bending stress using the bending radius (R); and calculating the at least one mechanical property of the sample (2) using the bending stress and a number of oscillations of the sample (2) until failure of the sample (2) or the bending stress at a plurality of excitation frequencies or the bending stress at a plurality of excitation frequencies and a description of a geometry of the sample (2).

2. The method according to the previous claim, wherein the step of determining the bending radius (R) comprises measuring a profile of a surface of the sample (2) along a line with the sample at the predetermined deflection or the determined deflection, wherein the line is parallel to the main direction or wherein the line and the main direction form an angle smaller than 90 degrees; and calculating the bending radius (R) from the profile.

3. The method according to any one of the previous claims, wherein the mechanical property of the sample (2) is a bending fatigue strength of the sample (2), wherein the bending fatigue strength is calculated from the bending stress and the number of oscillations of the sample (2) until failure of the sample (2).

4. The method according to any one of the previous claims, wherein the mechanical property of the sample (2) is a damping factor of the sample (2), wherein the damping factor is calculated from the bending stress at a plurality of excitation frequencies.

5. The method according to any one of the previous claims, wherein the mechanical property of the sample (2) is a resonance frequency of the sample (2), wherein the resonance frequency is calculated from the bending stress at a plurality of excitation frequencies and a geometry of the sample (2).

6. The method according to any one of the previous claims, wherein in addition to the mechanical property of the sample, Young’s modulus of the sample is determined by the steps: measuring an amplitude of the sample at a fixed point on the sample for a plurality of excitation frequencies; determining the resonance frequency of the sample from the measured amplitude over the excitation frequencies; and calculating Young’s modulus using the determined resonance frequency and a geometry of the sample.

7. The method according to any one of claims 4 to 6, wherein the plurality of excitation frequencies includes a mechanical resonance frequency of the sample (2).

8. The method according to any one of claims 1 to 3, wherein the excitation frequency is equal to a mechanical resonance frequency of the sample (2).

9. The method according to any one of claims 1 to 3, wherein the steps of determining a bending radius (R) of the sample (2) at a predetermined deflection or a determined deflection of the sample; and calculating a bending stress using the bending radius (R); are carried out a plurality of times and at least an amplitude or the excitation frequency of the shaking is controlled to minimize a difference of the bending stress and a predetermined desired bending stress.

10. The method according to any one of the previous claims, wherein the at least one mechanical property is determined using a statistical evaluation of a plurality of essentially identical samples.

11. A system (1) for measuring at least one mechanical property of a sample, the system comprisinga sample mount (5) configured to hold the sample (2) at a single mounting end (4) of the sample (2); a shaker (6) configured to cause an oscillation of the sample mount (5) at an excitation frequency; a sensor configured to measure a parameter indicative for a bending radius (R) of the sample (2) at a predetermined deflection or a determined deflection of the sample; and a control unit (12), wherein the control unit (12) is connected to the shaker (6), wherein the control unit (12) is configured to control the excitation frequency of the shaker (6), wherein the control unit (12) is connected to the sensor (9) to receive the parameter from the sensor, and wherein the control unit is configured to determine a bending radius (R) from the parameter, to calculate a bending stress using the bending radius (R) and to calculate the at least one mechanical property of the sample (2) using the bending stress and a number of oscillations of the sample (2) until failure of the sample (2) or the bending stress at a plurality of excitation frequencies or the bending stress at a plurality of excitation frequencies and a description of a geometry of the sample (2).

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