CN113866088B - Method for simultaneously predicting interface strength and interface toughness of film-substrate system - Google Patents

Method for simultaneously predicting interface strength and interface toughness of film-substrate system Download PDF

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CN113866088B
CN113866088B CN202111068667.1A CN202111068667A CN113866088B CN 113866088 B CN113866088 B CN 113866088B CN 202111068667 A CN202111068667 A CN 202111068667A CN 113866088 B CN113866088 B CN 113866088B
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strength
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CN113866088A (en
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彭志龙
尹涵彬
姚寅
张博
陈少华
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Beijing Institute of Technology BIT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N19/00—Investigating materials by mechanical methods
    • G01N19/04—Measuring adhesive force between materials, e.g. of sealing tape, of coating
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Abstract

The invention discloses a method for simultaneously predicting the interface strength and the interface toughness of a film-substrate system, which comprises the following steps: step one: establishing a relationship between interfacial stress and interfacial separation displacement between the film and the substrate; step two: establishing the relationship between the maximum tearing force of the film and the interface strength and the interface toughness by using a tearing experiment of the film at 90 degrees according to the relationship between the interface stress and the interface separation displacement in the first step; step three: and (3) according to the relationship between the maximum tearing force of the film and the interface strength and the interface toughness in the second step and the tearing force value of the film reaching a steady state stage under the 90-degree tearing angle of the film, the tearing force value is equal to the interface toughness, and the interface strength and the interface toughness are obtained.

Description

Method for simultaneously predicting interface strength and interface toughness of film-substrate system
Technical Field
The invention relates to the technical field of surface and interface mechanics, in particular to a method for simultaneously predicting the interface strength and the interface toughness of a film-substrate system.
Background
Film-substrate systems are widely visible in practical engineering and modern industry, such as microelectronics, smart skins in rail transit, advanced functional coatings, etc. The interfacial mechanical properties of the film-substrate system often affect the service performance of the overall structure, device or equipment. Even in nature, membrane/base models are often used to reveal the adhesive crawling mechanisms of living beings such as geckos. Two basic physical quantities characterizing interfacial mechanical properties are interfacial strength and interfacial toughness. Therefore, how to effectively predict the interfacial strength and interfacial toughness of a film-substrate system has been a general scientific concern in the industry and scientific community.
There are various experimental methods for measuring mechanical properties of a film-substrate structure interface, and a tear-off method (peel-test) is a widely adopted method because of simplicity and easiness in operation. In theory, the Kendall model is a classical model that characterizes film tear performance. The Kendall model establishes a quantitative relationship between the tear force applied by the film during the steady state tear phase and the angle of tear, tensile strain energy of the film, and interfacial toughness (adhesion energy). In particular, when the film is torn at 90 degrees, the tear force is about equal in value to the interfacial toughness. Thus, the Kendall model provides a method of directly measuring interface toughness. However, the Kendall model does not relate to information of interface strength. Therefore, the effective method for simultaneously and quantitatively predicting the interface strength and the interface toughness has important scientific significance and practical application value.
Disclosure of Invention
In view of the above, the present invention provides a method for simultaneously predicting the interfacial strength and the interfacial toughness of a film-substrate system, which can simultaneously and quantitatively predict the interfacial strength and the interfacial toughness of the film-substrate system.
The technical scheme of the invention is as follows: a method for simultaneously predicting film-substrate system interface strength and interface toughness, comprising the steps of:
step one: establishing a relationship between interfacial stress and interfacial separation displacement between the film and the substrate;
step two: establishing the relationship between the maximum tearing force of the film and the interface strength and the interface toughness by using a tearing experiment of the film at 90 degrees according to the relationship between the interface stress and the interface separation displacement in the first step;
step three: and (3) according to the relationship between the maximum tearing force of the film and the interface strength and the interface toughness in the second step and the tearing force value of the film reaching a steady state stage under the 90-degree tearing angle of the film, the tearing force value is equal to the interface toughness, and the interface strength and the interface toughness are obtained.
Preferably, in the first step, the relationship between the interface stress and the interface separation displacement is: t=f (δ);
wherein T is the interface stress, and delta is the interface separation displacement.
Preferably, for a normal stress model, the relationship between interface stress and interface separation displacement is:
wherein,indicating interface strength, ++>Indicating the maximum separation displacement of the interface.
Preferably, for the linear elastic model, the relationship between the interface stress and the interface separation displacement is:
wherein,indicating interface strength, ++>Indicating the maximum separation displacement of the interface.
Preferably, for bilinear models, the relationship of interface stress to interface separation displacement is:
wherein,indicating interface strength, ++>Representing the maximum separation displacement of the interface delta 1 Indicating the interfacial separation displacement when the interfacial stress reaches the interfacial strength.
Preferably, for a linear-normal stress model, the relationship of interface stress to interface separation displacement is:
wherein,indicating interface strength, ++>Representing the maximum separation displacement of the interface delta 1 Indicating the interfacial separation displacement when the interfacial stress reaches the interfacial strength.
Preferably, for the stress trapezoid distribution model, the relationship between the interface stress and the interface separation displacement is:
wherein,indicating interface strength, ++>Representing the maximum separation displacement of the interface delta 1 Represents the interfacial separation displacement, delta when the interfacial stress reaches the interfacial strength 2 Is the interfacial separation displacement at which interfacial stress begins to soften.
Preferably, in the second step, the thin film deformation is approximately regarded as a small deformation, and the thin film is regarded as a beam model; introducing a rectangular coordinate system (x, y), wherein the origin of coordinates is arranged at the action point of the tearing force F; the control equation for the film deformation from the pure bending theory of the beam is:
wherein,y is the bending deformation of the film at position x, T is the interfacial stress, E is the Young's modulus of the film, I=h 3 The moment of inertia of the film, h is the film thickness, and EI is the bending stiffness of the film;
the relation between the interface stress and the interface separation displacement in the first step is brought into a control equation of the film deformation, and the bending deformation y of the film is obtained;
by passing throughMaximum tear force of the film is obtained>
Wherein,representing the maximum separation displacement of the interface, beta being a coefficient related to the shape factor alpha of the cohesion model only, +.>Represents interfacial strength, G c Is denoted by interface toughness->Delta is the interfacial separation displacement.
Preferably, in the third step, the interfacial strength and the interfacial toughness are:
wherein F is steady Is the tearing force in the steady state stage, F max And F steady Obtained through a film tearing experiment.
Preferably, the form factorWherein delta 1 Indicating the interfacial fraction when the interfacial stress reaches the interfacial strengthDisplacement, delta 2 Is the interfacial separation displacement at which interfacial stress begins to soften.
The beneficial effects are that:
according to the method disclosed by the invention, three stages of the tear force and tear displacement curve of the film in the 90-degree tear test are utilized: in the initial tear stage, the tear force gradually increases with the increase of the tear displacement, and when the tear force increases to a maximum value, the tear force gradually transitions (transition stage) to the steady-state tear stage (the tear force in the steady-state stage is numerically equal to the interface toughness); when the film reaches a steady state tearing stage, the tearing force is kept unchanged; the initial debonding stage of the film often controls the interfacial failure, and the maximum tear force that occurs during the initial debonding stage is often related to the interfacial strength; therefore, the interface strength and the interface toughness of the film-substrate system can be predicted simultaneously and quantitatively, the defect that the interface toughness can only be obtained in the current film tear test is effectively overcome, and a theoretical basis is provided for the optimal design of the film-substrate system interface.
Drawings
FIG. 1 shows a cohesive constitutive model, (a) a normal stress model, (b) a linear elastic model, (c) a linear-normal stress model, (d) a bilinear model, and (e) a stress trapezoid distribution model in the prior art.
FIG. 2 is a schematic view of the initiation of tear-off of a film according to the present invention.
FIG. 3 shows maximum tear force F max And (3) with(a) the interfacial stress satisfies a bilinear distribution (α=0); (b) the interfacial stress satisfies a trapezoidal distribution (α=0.5).
Fig. 4 is a graph showing the variation of β and α.
Detailed Description
The invention will now be described in detail by way of example with reference to the accompanying drawings.
The embodiment provides a method for simultaneously predicting the interface strength and the interface toughness of a film-substrate system, which can simultaneously and quantitatively predict the interface strength and the interface toughness of the film-substrate system.
The method comprises the following steps:
step one: establishing a characterization relation of interface interaction between the film and the substrate;
interface interactions are typically characterized by a cohesive model that characterizes the relationship of interface stress to interface separation displacement; as shown in fig. 1, the currently common cohesion model includes: a normal stress model, a linear elastic model, a bilinear model, a stress trapezoid distribution model and the like;
for each cohesive model, the relationship of interfacial stress to interfacial separation displacement is as follows:
1. for a constant stress model, the relationship of interface stress to interface separation displacement can be expressed as:
wherein T is the interface stress, delta is the interface separation displacement,indicating interface strength, ++>Representing the maximum separation displacement of the interface;
2. for the linear elastic model, the relationship of interface stress to interface separation displacement can be expressed as:
3. for bilinear models, the relationship of interface stress to interface separation displacement can be expressed as:
wherein delta 1 Representing the interface separation displacement when the interface stress reaches the interface strength;
4. for a linear-normal stress model, the relationship of interface stress to interface separation displacement can be expressed as:
5. for a stress trapezoidal distribution model, the relationship of interface stress and interface separation displacement can be expressed as:
wherein delta 2 Interfacial separation displacement when interfacial stress begins to soften;
for different cohesive force models, a shape factor may be definedWhen α=1, the interfacial stress is in a normal stress distribution form (as shown in fig. 1 (a)); when α=0, the interfacial stress is in the form of linear elasticity or bilinear distribution (as shown in fig. 1 (b) and (d)); when 0 is<α<1, the interfacial stress is in a trapezoid distribution form (as shown in fig. 1 (c) and (e));
step two: solving the maximum tearing force of the film;
when the end part of the film is subjected to the action of the tearing force in the vertical direction (90-degree tearing), the interface between the film and the substrate is gradually opened along with the increase of the tearing force, and the displacement (deflection) of the film in the vertical direction is equal to the opening displacement of the interface; it is known that in the interfacial cohesion region, the film deformation can be regarded approximately as small deformation, and the film can be regarded as a beam model; for convenience of analysis, as shown in fig. 2, a rectangular coordinate system (x, y) is introduced, and the origin of coordinates is set at the rightmost end of the film, namely, the application point of the tearing force F; the control equation for the film deformation obtained from the pure bending theory of the beam is:
where y is the deflection of the film at position x, E is the young's modulus of the film, i=h 3 The moment of inertia of the film (h is the film thickness), and EI represents the bending stiffness of the film;
optionally, characterizing interface interaction by an interface cohesive force model, and bringing interface stress distribution (namely, a relation between interface stress and interface separation displacement) in the first step into the control equation of the film deformation, so as to obtain the bending deformation (namely, y) of the film; it is known that when the interfacial separation displacement at the point of application of the tear force at the end of the film reaches the interfacial maximum separation displacement, the tear force reaches a maximum, i.e. byMaximum tear force F of the film can be obtained max ；
Through calculation, for different cohesive force models, the maximum tearing force of the film meets the unified expression relation:
wherein β is a coefficient related to only the shape factor α of the cohesive force model, and for any α, the corresponding β value, G, can be found by looking up a graph c Is the interface toughness, and can be expressed as
Step three: calculating the steady-state tearing force of the film;
from the classical Kendall model, when the film reached a steady state at a 90 degree tear angle, the tear force value of the film was equal to the interfacial toughness, and therefore,
F steady ＝G c ；
step four: acquiring interface strength and interface toughness;
the maximum tearing force of the film in the second step and the steady tearing force of the film in the third step can simultaneously obtain the following expressions:
wherein F is max And F steady Can be directly obtained through a film tearing experiment.
In this example, the Young's modulus E of the film and the film thickness h can be measured by experiments.
In this embodiment, in order to further verify the correctness of the unified expression relationship satisfied by the maximum film tearing force calculated in the second step, the film tearing process is simulated by using the commercial software ABAQUS, and the simulation is performed for the cohesive force model to satisfy bilinear and trapezoidal distributions, so that the young modulus E and the interface strength of the film are foundAnd interface toughness G c How to take the value, the maximum tearing force F of the film max Always with->In direct proportion (as shown in fig. 3), the relationship between the coefficient β and the form factor α is as shown in fig. 4, and it is known that the corresponding β value can be obtained for any α value.
In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (7)

1. A method for simultaneously predicting the interfacial strength and interfacial toughness of a film-substrate system, comprising the steps of:
step one: establishing a relationship between interfacial stress and interfacial separation displacement between the film and the substrate;
step two: establishing the relationship between the maximum tearing force of the film and the interface strength and the interface toughness by using a tearing experiment of the film at 90 degrees according to the relationship between the interface stress and the interface separation displacement in the first step;
step three: according to the relationship between the maximum tearing force of the film and the interface strength and the interface toughness in the second step and the tearing force value of the film reaching a steady state stage under the 90-degree tearing angle, the film is equal to the interface toughness in value, and the interface strength and the interface toughness are obtained at the same time;
in the second step, the thin film deformation is approximately regarded as small deformation, and the thin film is regarded as a beam model; introducing a rectangular coordinate system (x, y), and setting a coordinate origin at the tear-off forceAn action point; the control equation for the film deformation from the pure bending theory of the beam is:
；
wherein,for the film in position->Bending deformation of the part->For interface stress +.>Young's modulus of film, +.>For the moment of inertia of the film,/->For the film thickness>Representing the bending stiffness of the film;
the relation between the interface stress and the interface separation displacement in the first step is brought into a control equation of the film deformation to obtain the bending deformation of the film；
By passing throughObtaining maximum tearing force of the film>；
Wherein,representing the maximum separation displacement of the interface +.>Shape factor for model of cohesion only +.>Related coefficients,/->Indicating interface strength, ++>Is denoted by interface toughness->，/>Separating and displacing for the interface;
in the third step, the interface strength and the interface toughness are as follows:
；
wherein,for the tear-off force in the steady state phase +.>And->The film is obtained through a film tearing experiment;
the form factorWherein->Represents the interfacial separation displacement when the interfacial stress reaches the interfacial strength,interfacial separation displacement when interfacial stress begins to soften;
when (when)When the interface stress is in a normal stress distribution form; when->When the interface stress is in a linear elasticity or bilinear distribution form; when->When the interface stress is in a trapezoid distribution form.
2. The method for simultaneously predicting the interfacial strength and the interfacial toughness of a thin film-substrate system according to claim 1, wherein in the first step, the relationship between the interfacial stress and the interfacial separation displacement is:；
wherein,for interface stress +.>For interfacial separation displacement.
3. The method of simultaneous predicting film-substrate system interface strength and interface toughness of claim 2, wherein for a constant stress model, the relationship of interface stress to interface separation displacement is:
wherein,indicating interface strength, ++>Indicating the maximum separation displacement of the interface.
4. The method of simultaneously predicting film-substrate system interface strength and interface toughness of claim 2, wherein for the linear elastic model, the relationship of interface stress to interface separation displacement is:
wherein,indicating interface strength, ++>Indicating the maximum separation displacement of the interface.
5. The method of simultaneously predicting film-substrate system interface strength and interface toughness of claim 2, wherein for a bilinear model, the relationship of interface stress to interface separation displacement is:
wherein,indicating interface strength, ++>Representing the maximum separation displacement of the interface +.>Indicating the interfacial separation displacement when the interfacial stress reaches the interfacial strength.
6. The method of simultaneously predicting film-substrate system interface strength and interface toughness of claim 2, wherein for the linear-normal stress model, the relationship of interface stress to interface separation displacement is:
wherein,indicating interface strength, ++>Representing the maximum separation displacement of the interface +.>Indicating interface shouldInterface separation displacement when the force reaches the interface strength.
7. The method of simultaneously predicting film-substrate system interface strength and interface toughness of claim 2, wherein for a stress trapezoidal distribution model, the relationship of interface stress to interface separation displacement is:
wherein,indicating interface strength, ++>Representing the maximum separation displacement of the interface +.>Indicating the interfacial separation displacement when the interfacial stress reaches the interfacial strength, < >>Is the interfacial separation displacement at which interfacial stress begins to soften.
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