WO2015094007A1 - Method for determining mechanical properties of a material - Google Patents

Method for determining mechanical properties of a material Download PDF

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Publication number
WO2015094007A1
WO2015094007A1 PCT/RU2013/001132 RU2013001132W WO2015094007A1 WO 2015094007 A1 WO2015094007 A1 WO 2015094007A1 RU 2013001132 W RU2013001132 W RU 2013001132W WO 2015094007 A1 WO2015094007 A1 WO 2015094007A1
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Prior art keywords
tool
standoff
mechanical properties
contact
vibration
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Ceased
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PCT/RU2013/001132
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French (fr)
Inventor
Yamid Pico
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Schlumberger Canada Ltd
Services Petroliers Schlumberger SA
Schlumberger Technology BV
Schlumberger Holdings Ltd
Prad Research and Development Ltd
Original Assignee
Schlumberger Canada Ltd
Services Petroliers Schlumberger SA
Schlumberger Technology BV
Schlumberger Holdings Ltd
Prad Research and Development Ltd
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Filing date
Publication date
Application filed by Schlumberger Canada Ltd, Services Petroliers Schlumberger SA, Schlumberger Technology BV, Schlumberger Holdings Ltd, Prad Research and Development Ltd filed Critical Schlumberger Canada Ltd
Priority to PCT/RU2013/001132 priority Critical patent/WO2015094007A1/en
Priority to RU2016124146A priority patent/RU2626067C1/en
Priority to US15/105,960 priority patent/US9897522B2/en
Publication of WO2015094007A1 publication Critical patent/WO2015094007A1/en
Anticipated expiration legal-status Critical
Ceased legal-status Critical Current

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/40—Investigating hardness or rebound hardness
    • G01N3/405—Investigating hardness or rebound hardness by determining the vibration frequency of a sensing element in contact with the specimen
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H1/00—Measuring characteristics of vibrations in solids by using direct conduction to the detector
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/04—Analysing solids
    • G01N29/045—Analysing solids by imparting shocks to the workpiece and detecting the vibrations or the acoustic waves caused by the shocks
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/04—Analysing solids
    • G01N29/11—Analysing solids by measuring attenuation of acoustic waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/40—Investigating hardness or rebound hardness
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/40—Investigating hardness or rebound hardness
    • G01N3/42—Investigating hardness or rebound hardness by performing impressions under a steady load by indentors, e.g. sphere, pyramid
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0001—Type of application of the stress
    • G01N2203/0005—Repeated or cyclic
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/02—Indexing codes associated with the analysed material
    • G01N2291/028—Material parameters
    • G01N2291/02827—Elastic parameters, strength or force
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/10—Number of transducers
    • G01N2291/101—Number of transducers one transducer

Definitions

  • This invention relates to methods for determination of mechanical properties of materials, namely Young modulus and Poisson ratio, and can be used, for example, for studying a formation surrounding a borehole, a ground floor or any surface for which material properties are to be measured.
  • the proposed method provides for easy and fast determination of mechanical properties of materials which requires only information on dynamic properties of a tool being used and can be done in situ.
  • the method for determining mechanical properties of a material comprises disposing a tool having at least one vibration sensor and at least one standoff in a contact with a material. Then the at least one standoff of the tool is pushed into the material and vibration is excited by at least one vibration source. At least one coupling frequency of the tool is measured by the at least one vibration sensor and a contact stiffness of the at least one standoff is determined based on the determined coupling frequency. The mechanical properties of the material are determined based on the determined contact stiffness of the at least one standoff and on dynamic properties of the at least one standoff.
  • the vibration source can be disposed inside or outside the tool.
  • the material can be a formation surrounding a borehole.
  • the tool can be clamped to the material.
  • the mechanical properties of the material and of the at least one standoff are Poisson ratio and Young modulus of the material and of the at least one standoff.
  • Figure 1(a) shows an example of a tool with three standoffs
  • Fig.2 shows a dynamic diagram for the tool showed in Fig. l
  • Fig. 3 shows two variants of possible shapes of the standoffs.
  • Fig. 1 it is shown an example of a tool according to the proposed invention.
  • the tool has standoffs (contact points) 1 and holes 2 for vibration sensors.
  • the vibration sensors can be geophones or accelerometers that can measure direction of vibration.
  • At least one vibration source also can be disposed inside the tool.
  • the vibration source can be a shaker type or any vibration device capable of generate controlled vibration in a defined wave band. All those vibration sensors and vibration sources can be located in different positions in the tool and with different orientation. This is with the purpose of having the possibility of excitation of different vibration modes. It is especially important for addressing anisotropy materials and for quality control of measurements.
  • At least one standoff of the tool is pushed into the material and vibration is excited by the vibration source. Vibration can be excited by any external or internal vibration source.
  • At least one coupling frequency (a frequency at which the tool starts to vibrate due to the contact (coupling)) of the tool is measured by the at least one vibration sensor disposed inside the tool. The coupling frequencies are measured by examining a spectrum of the acquired readings of the vibration sensors.
  • a clamping force and a mass and moment of inertia of the tool are known, a shape and mechanical properties of the standoffs are also known.
  • a combination of dynamic equations and equations for contact can be solved to find the unknowns - Young modulus and Poisson ratio of the material where the tool is located (and if necessary clamped).
  • the configuration can be freely chosen and can be used two or more standoffs for quality control. Knowing two first coupling frequencies of a particular configuration of the tool allows to calculate the Young modulus and Poisson coefficient of the material where the tool is located. Even with only the first coupling frequency registered for any configuration, it is possible to have a good approximation of the Young modulus regarding a good initial estimation of Poisson ratio.
  • anisotropic material the larger the number of the frequencies, the more is the number of material properties that can be determined.
  • Equations of motion give the relationship to calculate coupling frequencies (Lagrange equation of the system) for the tool.
  • k is a contact stiffness and A is a projected contact area.
  • ⁇ , E are Poisson ratio and Young modulus of the material to be tested respectively
  • ⁇ ', ⁇ ' are Poisson ratio and Young modulus of the standoffs.
  • the definition of the contact area A depends on a shape of the standoff. It is calculated using Hertz contact theory.
  • R is a radius of a round standoff
  • h is a height of penetration of the standoff into the material.
  • the obtained value of the contact stiffness can be introduced in the formulas of the frequencies (1):
  • the described procedure is general, for any shape or mechanical design of the tool and any shape and material of the standoffs.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Biochemistry (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Chemical & Material Sciences (AREA)
  • Analytical Chemistry (AREA)
  • Health & Medical Sciences (AREA)
  • General Health & Medical Sciences (AREA)
  • Immunology (AREA)
  • Pathology (AREA)
  • Acoustics & Sound (AREA)
  • Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
  • Investigating Or Analyzing Materials By The Use Of Ultrasonic Waves (AREA)

Abstract

A tool having at least one vibration sensor and at least one standoff is disposed in a contact with a material and the at least one standoff of the tool is pushed into the material. Vibration is excited by the at least one vibration source and at least one coupling frequency of the tool is measured by the at least one vibration sensor. Based on the determined coupling frequency determining a contact stiffness of the at least one standoff and the mechanical properties of the material are determined taking into account mechanical properties of the at least one standoff.

Description

METHOD FOR DETERMINING MECHANICAL PROPERTIES OF A
MATERIAL
FIELD OF THE INVENTION
This invention relates to methods for determination of mechanical properties of materials, namely Young modulus and Poisson ratio, and can be used, for example, for studying a formation surrounding a borehole, a ground floor or any surface for which material properties are to be measured.
BACKGROUND OF THE INVENTION
Many none destructive methods for determining mechanical properties of materials are known, such as wave propagation methods and micro/nano indentation methods (see, for example, General relationship between contact stiffness, contact depth, and mechanical properties for indentation in linear visco elastic solids using axisymetric indenters of arbitrary profile, Yang-Tse Chenga, Che-Min Cheng. 2005, APPLIED PHYSICS LETTERS 87, 1 11914, or An analysis of nanoindentation in linearly elastic solids. B. Poon a, D. Rittel b, G. Ravichandran. s.l. : International Journal of Solids and Structures 45, 2008, pp. 6018-6033). The known method provides for measuring hardness based on loading and unloading of specimens and can be accomplished only in laboratories.
The proposed method provides for easy and fast determination of mechanical properties of materials which requires only information on dynamic properties of a tool being used and can be done in situ. SUMMARY OF THE INVENTION
The method for determining mechanical properties of a material comprises disposing a tool having at least one vibration sensor and at least one standoff in a contact with a material. Then the at least one standoff of the tool is pushed into the material and vibration is excited by at least one vibration source. At least one coupling frequency of the tool is measured by the at least one vibration sensor and a contact stiffness of the at least one standoff is determined based on the determined coupling frequency. The mechanical properties of the material are determined based on the determined contact stiffness of the at least one standoff and on dynamic properties of the at least one standoff.
The vibration source can be disposed inside or outside the tool.
The material can be a formation surrounding a borehole.
The tool can be clamped to the material.
The mechanical properties of the material and of the at least one standoff are Poisson ratio and Young modulus of the material and of the at least one standoff.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention is explained by drawings where Figure 1(a) shows an example of a tool with three standoffs, Fig.2 shows a dynamic diagram for the tool showed in Fig. l, Fig. 3 shows two variants of possible shapes of the standoffs.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
On Fig. 1 it is shown an example of a tool according to the proposed invention. The tool has standoffs (contact points) 1 and holes 2 for vibration sensors. The vibration sensors can be geophones or accelerometers that can measure direction of vibration. At least one vibration source also can be disposed inside the tool. The vibration source can be a shaker type or any vibration device capable of generate controlled vibration in a defined wave band. All those vibration sensors and vibration sources can be located in different positions in the tool and with different orientation. This is with the purpose of having the possibility of excitation of different vibration modes. It is especially important for addressing anisotropy materials and for quality control of measurements.
Then the at least one standoff of the tool is pushed into the material and vibration is excited by the vibration source. Vibration can be excited by any external or internal vibration source. At least one coupling frequency (a frequency at which the tool starts to vibrate due to the contact (coupling)) of the tool is measured by the at least one vibration sensor disposed inside the tool. The coupling frequencies are measured by examining a spectrum of the acquired readings of the vibration sensors.
A clamping force and a mass and moment of inertia of the tool are known, a shape and mechanical properties of the standoffs are also known. A combination of dynamic equations and equations for contact can be solved to find the unknowns - Young modulus and Poisson ratio of the material where the tool is located (and if necessary clamped). For the case of an isotropy material, the configuration can be freely chosen and can be used two or more standoffs for quality control. Knowing two first coupling frequencies of a particular configuration of the tool allows to calculate the Young modulus and Poisson coefficient of the material where the tool is located. Even with only the first coupling frequency registered for any configuration, it is possible to have a good approximation of the Young modulus regarding a good initial estimation of Poisson ratio. For the case of anisotropic material the larger the number of the frequencies, the more is the number of material properties that can be determined.
Below it is described a procedure for obtaining the equations for the case of using a tool with three standoffs shown on Fig. l .
Equations of motion give the relationship to calculate coupling frequencies (Lagrange equation of the system) for the tool. We obtain:
"cou
"cou
"coups
Figure imgf000005_0001
where Qcoupi; Ω00„ρ2; Ωοοιιρ3 are the coupling frequencies of the tool, ki, k2, k3 -contact stiffness of three standoffs. Based on specific design it is possible to achieve very similar values of the contact stiffness so we can assume them equal: k]= k2=k3. Parameters d, c and a are distances from a center of mass to the location of the standoffs (see Fig.2); m is a mass of the tool, and I2, I3 are moments of inertia of the tool body/package respect to an axis of rotation. Making several measurements of the frequencies, a more robust value of the frequencies can be obtained.
Below, based on contact theory several relationships for the contact stiffness are derived, the main relationshi is
Figure imgf000005_0002
where k is a contact stiffness and A is a projected contact area.
Er is a reduced stiffness modulus that is defined as 1 = (l - u) (Ι - ')
Er E E '
Here, υ, E are Poisson ratio and Young modulus of the material to be tested respectively, υ', Ε' are Poisson ratio and Young modulus of the standoffs.
The definition of the contact area A depends on a shape of the standoff. It is calculated using Hertz contact theory.
Bellow there are examples of calculation for two shapes of the standoffs (Fig.3a and 3b).
Semi spherical stand off
Using Hertz contact theory, is possible to relate a clamping force of the tool to the contact area. For a shape as indicated in the Fig.3a, an area of contact will be
A2 = . R. h
where R is a radius of a round standoff, h is a height of penetration of the standoff into the material. A force is related to the reduced modulus and area of contact by
Figure imgf000006_0001
From this the following relationship is obtained
Figure imgf000006_0002
Using this the relationship for the stiffness contact for the round standoff (with υ, E) pushed with a force F into a sam le (with υ', Ε') is obtained
Figure imgf000006_0003
The obtained value of the contact stiffness can be introduced in the formulas of the frequencies (1 ):
Figure imgf000007_0001
k2 - d 2 + k3 - d 2
Ω
Figure imgf000007_0002
with
Figure imgf000007_0003
Er is found and then Young modulus and Poisson ratio of the tested material are determined.
Conical stand offs (Spikes)
As for the previous case Hertz contact theory is used to relate a clamping force to a contact area. For a shape as indicated in Fig.3b, the area of contact will be
π
h . tan (^ - 0)
A2 =
7Γ
Where Θ is an angle defining a sharpness of the standoffs, h - a depth of penetration into the material. The force is related to the reduced modulus and area of contact by
Figure imgf000007_0004
From this the relationship is obtained
Figure imgf000008_0001
Using this the relationship for the stiffness contact for a conical standoff (with υ, E) pushed with a force F into a casing (with υ', Ε') is obtained
Figure imgf000008_0002
The obtained value of the contact stiffness can be introduced in the formulas of the frequencies (1):
a | 2 £, + 2 k2 + 2 k3
Ω COUp I
Figure imgf000008_0003
with ■ F■ tan -
Figure imgf000008_0004
Then it is solved for Er and then Young modulus and Poisson ratio of the tested material are determined.
The described procedure is general, for any shape or mechanical design of the tool and any shape and material of the standoffs.

Claims

Claims
1. A method for determining mechanical properties of a material comprising:
- disposing a tool having at least one vibration sensor and at least one standoff in a contact with a material,
- pushing the at least one standoff of the tool into the material,
- exciting vibration by the at least one vibration source,
- measuring at least one coupling frequency of the tool by the at least one vibration sensor,
- determining a contact stiffness of the at least one standoff based on the determined coupling frequency and
determining the mechanical properties of the material based on the determined contact stiffness of the at least one standoff and on mechanical properties of the at least one standoff.
2. The method of claim 1 wherein the at least one vibration source is disposed inside the tool.
3. The method of claim 1 wherein the at least one vibration source is disposed outside the tool.
4. The method of claim 1 wherein the mechanical properties of the material and of the at least one standoff are Poisson ratio and Young modulus of the material and of the at least one standoff.
5. The method of claim 1 wherein material is a formation surrounding a borehole.
6. The method of claim 1 wherein the tool is clamped to the material.
PCT/RU2013/001132 2013-12-18 2013-12-18 Method for determining mechanical properties of a material Ceased WO2015094007A1 (en)

Priority Applications (3)

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PCT/RU2013/001132 WO2015094007A1 (en) 2013-12-18 2013-12-18 Method for determining mechanical properties of a material
RU2016124146A RU2626067C1 (en) 2013-12-18 2013-12-18 Method of determining mechanical properties of material
US15/105,960 US9897522B2 (en) 2013-12-18 2013-12-18 Method for determining mechanical properties of a material

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Cited By (1)

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Publication number Priority date Publication date Assignee Title
GB2537365A (en) * 2015-04-13 2016-10-19 Fuchs Anton Method and device for efficient determination of the vibro-acoustic properties of sound insulation materials

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SU1597687A1 (en) * 1988-02-17 1990-10-07 Каунасский Политехнический Институт Им.Антанаса Снечкуса Device for measuring hardness
JPH02264843A (en) * 1989-04-05 1990-10-29 Toshiba Corp Hardness measuring apparatus
DE4306243A1 (en) * 1993-02-27 1993-09-23 Uwe Paetzold Hardness test method - using ultrasonic contact, with hard body on vibrated rod, and measuring with body in and not in contact with test material
RU2108561C1 (en) * 1996-11-18 1998-04-10 Закрытое акционерное общество "НТЕ" Gear measuring mechanical characteristics of materials
JP2004361251A (en) * 2003-06-05 2004-12-24 Axiom Co Ltd Instrument for measuring hardness using ultrasonic vibration

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Patent Citations (5)

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Publication number Priority date Publication date Assignee Title
SU1597687A1 (en) * 1988-02-17 1990-10-07 Каунасский Политехнический Институт Им.Антанаса Снечкуса Device for measuring hardness
JPH02264843A (en) * 1989-04-05 1990-10-29 Toshiba Corp Hardness measuring apparatus
DE4306243A1 (en) * 1993-02-27 1993-09-23 Uwe Paetzold Hardness test method - using ultrasonic contact, with hard body on vibrated rod, and measuring with body in and not in contact with test material
RU2108561C1 (en) * 1996-11-18 1998-04-10 Закрытое акционерное общество "НТЕ" Gear measuring mechanical characteristics of materials
JP2004361251A (en) * 2003-06-05 2004-12-24 Axiom Co Ltd Instrument for measuring hardness using ultrasonic vibration

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB2537365A (en) * 2015-04-13 2016-10-19 Fuchs Anton Method and device for efficient determination of the vibro-acoustic properties of sound insulation materials
GB2537365B (en) * 2015-04-13 2018-04-25 Kompetenzzentrum Das Virtuelle Fahrzeug Method and device for efficient determination of the vibro-acoustic properties of sound insulation materials

Also Published As

Publication number Publication date
US9897522B2 (en) 2018-02-20
RU2626067C1 (en) 2017-07-21
US20170030814A1 (en) 2017-02-02

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