CN111060414B - Method for measuring and calculating toughness, strength and elasticity of organic material - Google Patents

Method for measuring and calculating toughness, strength and elasticity of organic material Download PDF

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CN111060414B
CN111060414B CN201911400928.8A CN201911400928A CN111060414B CN 111060414 B CN111060414 B CN 111060414B CN 201911400928 A CN201911400928 A CN 201911400928A CN 111060414 B CN111060414 B CN 111060414B
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unloading
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钟高余
韦志毅
叶飞
钱柏帆
闫伟青
田益明
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Fudan University
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    • G—PHYSICS
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    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
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    • G01N3/42—Investigating hardness or rebound hardness by performing impressions under a steady load by indentors, e.g. sphere, pyramid
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    • 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
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Abstract

The invention belongs to the technical field of material characteristic measurement, and particularly relates to a method for measuring and calculating the toughness, strength and elasticity of an organic material. The method comprises the following steps: carrying out single loading-unloading test on the organic material by using a nano indenter, wherein the load and the strain used in the test must be in a proper range to obtain a single loading curve of the organic material; carrying out optimized data fitting on the unloading curve by using a nano indentation unloading curve fitting formula, and calculating to obtain three fitting parameters; and substituting the three parameters into a calculation formula of toughness, strength and elasticity parameters to obtain mechanical characteristic parameters of the material, such as toughness, strength, elasticity and the like. The method is suitable for testing the mechanical parameters of loose organic materials, in particular to the mechanical parameters of materials with van der Waals force (molecular force) interaction. The method and the tool for testing the mechanical properties of the materials can be established, and are convenient to use, accurate in measurement and wide in application range.

Description

Method for measuring and calculating toughness, strength and elasticity of organic material
Technical Field
The invention belongs to the technical field of material characteristic measurement, and particularly relates to a method for measuring and calculating the toughness, strength and elasticity (or elasticity) of a material.
Background
With the application of organic electronics, organic light emitting diodes, organic solar cells, printed circuits, wearable devices and intelligent robots are developing, and the mechanical properties of organic thin film materials are receiving more and more attention. Currently, a nanomechanical test system (or nanoindenter tester) is an advanced tool for testing mechanical properties of materials. However, most researchers still understand the loading-unloading curve obtained by nanoindentation test only about macroscopic mechanical properties, while the intrinsic physical principle is still mostly vague, and we believe that the loading-unloading curve reflects the relationship between the distance of two adjacent molecules in an organic thin film and the applied force, and the relationship between the intermolecular distance and the intermolecular force can be described by the Ronnerd-Jones (Lennard-Jones) potential. Therefore, the present invention uses the lenard-jones potential theory to derive and fit the unloading curve and obtains five important mechanical performance parameters from the parameters of the unloading curve. These mechanical properties of a material include young's modulus, which represents stiffness, bonding force, which represents strength, bonding energy, which represents toughness, and distance, which represents elasticity or elasticity, from an equilibrium position to a position with maximum tensile stress. By the method, more convenient and practical tools can be developed to test various mechanical properties of the material, and the method has a good application prospect.
Disclosure of Invention
The invention aims to provide a novel measuring and calculating method for testing the strength, toughness and elasticity of a material.
The invention provides a measuring and calculating method of material strength, toughness and elasticity, which can reflect the mechanical properties of materials, eliminate interference factors and facilitate comparison of the mechanical properties of different materials, and the method comprises the following specific steps:
(1) carrying out a single loading-unloading test on the material bonded by Van der Waals force, such as most organic materials, by using a nanoindenter to obtain a single nanoindentation load curve of the material;
(2) applying a Ronneder-Jones potential theory describing the relationship between intermolecular force and intermolecular distance to deduce and obtain a functional relationship between the load and the pressing depth in the unloading curve, and performing optimal fitting of computer software operation on the load curve by using the function to obtain optimal fitting parameters;
(3) and (3) deducing relational expressions for representing the strength, toughness and elasticity of the material according to a Ronal-Jones potential theory, substituting the optimal fitting parameters obtained in the steps into the relational expressions, and calculating to obtain mechanical property parameters reflecting the strength, toughness and elasticity of the material.
In step (2), the formula for fitting the unloading curve is derived according to the Ronneard-Jones potential and is as follows:
Figure BDA0002347429040000021
wherein F is unloadingLoad in the curve, h is the depth of penetration in the unloading curve, hmThe indentation depth when the stress is zero, and epsilon is a parameter to be fitted: value of lowest point of intermolecular interaction potential energy, rmFor the parameters to be fitted: the thickness of the film actually participating in the deformation is at equilibrium.
In the step (3), in the unloading curve, a formula for characterizing the toughness of the material is as follows:
Figure BDA0002347429040000022
in the formula, VbIs the binding energy per unit area of the material, and epsilon is a parameter obtained by fitting an unloading curve, represents the lowest point of a potential energy curve, and reflects the absolute value of the attraction potential between molecules. D is the diameter of the flat indenter used for the nanoindentation test. And substituting the parameters obtained by the unloading curve fitting into the formula to obtain the numerical value of the toughness parameter of the material.
In the step (3), in the unloading curve, a formula for representing the strength of the material is as follows:
Figure BDA0002347429040000023
in the formula, FbThe maximum tensile stress between the material molecules is reflected as the unit area bonding force of the material. Epsilon is a parameter obtained by fitting an unloading curve, represents the lowest point of a potential energy curve between molecules, and reflects the absolute value of the attraction potential between molecules. D is the diameter of the flat indenter used for the nanoindentation test. r ismThe parameters obtained for the unloading curve fitting represent the total thickness of all the organic materials participating in deformation during the measurement process in the equilibrium state after unloading. And substituting the parameters obtained by the unloading curve fitting into the formula to obtain the numerical values of the material strength parameters.
In the step (3), in the unloading curve, a formula for representing the material stretching performance is as follows:
Lb＝0.109rm
in the formula, LbIs a materialThe displacement required to pass from equilibrium condition to maximum tensile stress. r ismThe parameters obtained for the unloading curve fitting represent the total thickness of all the organic materials participating in deformation during the measurement process in the equilibrium state after unloading. And substituting the parameters obtained by the unloading curve fitting into the formula to obtain the numerical value of the material elasticity parameter.
The invention has the advantages that: the novel method for measuring and calculating the mechanical property parameters of the strength, the toughness and the elasticity of the material is more convenient to test and calculate, can reflect the mechanical properties of the material, eliminates a plurality of interference factors, is more suitable for comparing the mechanical properties of different materials, and has great significance for developing a measuring method and a measuring tool for the mechanical properties of the material. The method is suitable for testing the mechanical parameters of loose organic materials, in particular to the mechanical parameters of materials with van der Waals force (molecular force) interaction. The standardized testing method and the standardized testing tool for the mechanics of materials, which are convenient to use, accurate in measurement and wide in application range, can be established.
Drawings
Fig. 1 is a schematic view of a nanoindentation apparatus and a measured load-unload curve. The upper part of the graph is the load curve obtained by the actual nanoindentation test. It can be seen that the force applied to the material increases with increasing penetration depth, including three processes, loading, holding and unloading. The unloading curve generally reflects substantially the inherent mechanical properties of the material itself. The lower left part of the figure shows a schematic view of a flat press head pressing into the surface of the material (pressure to the right), and the middle part shows the pressed-in material film. The depth of penetration is h. The penetration depth at zero load after unloading (indicating the molecules are in equilibrium) is hm. It is assumed that the N molecular layers participate in the deformation while the fixed substrate does not. The total distance between the molecules is Nr, with an initial value of Nr0Can be assumed as rm. Actual distance between molecules is Nr＝rm-(h-hm)。
FIG. 2 is a load curve for a progressive multiple test of a Polymethylmethacrylate (PMMA) film measured using a nanoindenter from which a suitable load pressure range can be found; the inset shows the depth of penetration (black, i.e. upper curve) and the force (blue, i.e. lower curve) as a function of time, and it can be seen whether there is creep or plastic deformation of the material.
FIG. 3 is a load-unload curve of a PMMA film measured in a single test at a maximum stress of 1.2 mN; the inset shows the load curve under a large stress (maximum 10 mN). The thicker red curve is the unloading curve obtained by automatic optimization fitting of computer software.
Detailed Description
Example 1
The following description will be made by taking a polymethyl methacrylate (PMMA) organic film as an example and referring to the drawings.
Fig. 1 is a schematic diagram of a nanoindentation apparatus and a load-unload curve measured by a nanoindenter, which may help to understand the physical significance of the load curve and fitting parameters.
FIG. 2 is a load curve for a progressive number of tests of PMMA film measured using a nanoindenter from which a suitable loading pressure range can be found; the inset shows the variation of the penetration depth (black) and force (blue) over time, and it can be seen whether there is creep or plastic deformation of the material.
FIG. 3 shows the load curve measured at a low pressure (maximum 1.2 mN). The red bold line is the load curve obtained by fitting, the inset is the load curve measured under a larger pressure, and the inset shows that the stiffness is higher under the influence of a rigid substrate under a larger pressure (1.5-10 mN), but the insert does not show plastic deformation under a smaller pressure (less than 1.5 mN). The fitted curve and the experimental curve are seen to have a high degree of overlap. The equation used to fit the unloading curve is:
Figure BDA0002347429040000031
by setting the fitting equation, after optimized automatic fitting is performed by data processing software, the following three parameters are obtained:
(1)
Figure BDA0002347429040000032
(2)hm＝31.645nm；
(3)rm＝690nm。
the three parameters are respectively substituted into a formula for representing the toughness, strength and elasticity of the material to obtain:
(1) toughness parameters of PMMA: binding energy per unit area: vb＝95.454mJ/m2；
(2) PMMA strength parameters: unit area binding force: fb＝1.4885MPa；
(3) PMMA elasticity (elasticity) parameters: displacement through which a material is drawn from an equilibrium state to have a maximum tensile stress: l isb＝75.21nm。
We compared four mechanical parameters (toughness, strength, stiffness and elasticity) of six common organic thin film materials, as shown in the table below. The six materials are: polyethylene (PE), polypropylene (PP), polymethyl methacrylate (PMMA), Polytetrafluoroethylene (PTFE), Polyethylene terephthalate (PET), Polyimide (PI).
Four mechanical parameters of six organic materials obtained by nano indentation unloading curve fitting
Parametric material PET PI PMMA PP PE PTFE
Vb(mJ/m2) 15828.03 1496.82 95.454 11.46 0.6975 0.2252
Fb(MPa) 10.6369 3.344 1.4885 0.5605 0.5223 0.072
E0(MPa) 11.2 11.8 906.5 42.8 608 36.1
Lb(nm) 43600 13080 75.21 599.5 39.24 92.65
Note that the Poisson ratio "v" is set to 0 here and the indenter diameter is 20 microns.
The above examples illustrate the feasibility and advancement of the present invention. In addition, the examples are only for explaining the present invention, and are not intended to limit the present invention.

Claims (1)

1. A method for measuring and calculating strength, toughness and elasticity of a material is characterized by comprising the following specific steps:
(1) carrying out single loading-unloading test on the material combined by the Van der Waals force by using a nano-indenter to obtain a single nano-indentation load curve of the material;
(2) applying a Ronneder-Jones potential theory describing the relationship between intermolecular force and intermolecular distance to deduce and obtain a functional relationship between the load and the pressing depth in the unloading curve, and performing optimal fitting of computer software operation on the load curve by using the function to obtain optimal fitting parameters;
(3) deriving relational expressions representing the strength, toughness and elasticity of the material according to a Ronald-Jones potential theory, substituting the optimal fitting parameters obtained in the steps into the relational expressions, and calculating to obtain mechanical property parameters reflecting the strength, toughness and elasticity of the material;
the formula derived from the lenard-jones potential for fitting the unloading curve is:
Figure FDA0003472160110000011
where F is the load in the unloading curve, h is the penetration depth in the unloading curve, hmThe indentation depth when the stress is zero, and epsilon is a parameter to be fitted: value of lowest point of intermolecular interaction potential energy, rmFor the parameters to be fitted: the thickness of the film actually participating in deformation in a balanced state; wherein:
in the unloading curve, a formula for representing the toughness of the material is as follows:
Figure FDA0003472160110000012
in the formula, VbIs the unit area binding energy of the material, and epsilon is a parameter obtained by fitting an unloading curve, represents the lowest point of a potential energy curve and reflects the absolute value of the attraction potential between molecules; d is the diameter of a flat pressure head used for the nano indentation test; substituting the parameters obtained by the unloading curve fitting into the formula to obtain the numerical value of the toughness parameter of the material;
in the unloading curve, the formula for characterizing the strength of the material is as follows:
Figure FDA0003472160110000013
in the formula, FbThe unit area binding force of the material is shown, and epsilon is a parameter obtained by fitting an unloading curve, represents the lowest point of a potential energy curve between molecules and reflects the absolute value of attraction potential between the molecules; d is the diameter of a flat pressure head used for the nano indentation test; r ismParameters obtained by fitting the unloading curve represent the total thickness of all the organic materials participating in deformation in the measurement process in the equilibrium state after unloading; substituting the parameters obtained by the unloading curve fitting into the formula to obtain the numerical values of the material strength parameters;
in the unloading curve, a formula for representing the material stretching performance is as follows:
Lb＝0.109rm
in the formula, LbThe displacement which the material needs to pass when the material is stretched from the equilibrium state to the maximum tensile stress; r ismParameters obtained by fitting the unloading curve represent the total thickness of all the organic materials participating in deformation in the measurement process in the equilibrium state after unloading; and substituting the parameters obtained by the unloading curve fitting into the formula to obtain the numerical value of the material elasticity parameter.
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2003012566A (en) * 2001-07-02 2003-01-15 Ricoh Co Ltd Molecular simulation method
CN101806690A (en) * 2010-05-04 2010-08-18 中国地质大学（北京） Method for testing physical performances of film and film-substrate interface based on nanometer indentation continuous stiffness curve
CN102455263A (en) * 2010-10-27 2012-05-16 中国科学院金属研究所 Method for obtaining mechanical property of metal material based on load-depth curve
CN103530438A (en) * 2012-07-05 2014-01-22 住友橡胶工业株式会社 Method for simulating polymer material
CN108507892A (en) * 2018-03-19 2018-09-07 复旦大学 A kind of organic film Young's modulus standardization measuring method

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2003012566A (en) * 2001-07-02 2003-01-15 Ricoh Co Ltd Molecular simulation method
CN101806690A (en) * 2010-05-04 2010-08-18 中国地质大学（北京） Method for testing physical performances of film and film-substrate interface based on nanometer indentation continuous stiffness curve
CN102455263A (en) * 2010-10-27 2012-05-16 中国科学院金属研究所 Method for obtaining mechanical property of metal material based on load-depth curve
CN103530438A (en) * 2012-07-05 2014-01-22 住友橡胶工业株式会社 Method for simulating polymer material
CN108507892A (en) * 2018-03-19 2018-09-07 复旦大学 A kind of organic film Young's modulus standardization measuring method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
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