CN111859663B - Design method of anti-icing and deicing coating on large-area coating surface - Google Patents
Design method of anti-icing and deicing coating on large-area coating surface Download PDFInfo
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Abstract
The invention relates to a design method of an anti-icing and deicing coating on the surface of a large-area coating. The invention belongs to the technical field of coating deicing and anti-icing, and a force accumulation model is constructed according to the damage of an interface between an ice layer and a coating; analyzing the damage process of the ice layer according to the constructed force accumulation model, and determining the damage mode of the ice layer; determining the interface toughness; determining a critical length of an interface between the ice layer and the coating based on the determined ice layer failure mode and the interface toughness. The invention is based on the excellent anti-icing and deicing performances of the super-hydrophobic surface, uses the low-interface toughness coating to reduce the critical length of the coating, enables the deicing force to reach the maximum in a smaller icing area, enables the deicing force to be far lower than that of the conventional low-interface strength coating in large-area use, solves the problems of difficult large-area deicing and high cost, and plays a guiding role in the design of the conventional anti-icing and deicing coating.
Description
Technical Field
The invention relates to the technical field of coating deicing and anti-icing, in particular to a design method of an anti-deicing coating on the surface of a large-area coating.
Background
The ice accretion brings a series of safety, efficiency and economic problems to large-area surfaces (surfaces with the length of a plane surface exceeding 50m and even 100 m) such as airplane wings, wind driven generator blades, solar cell panels, ship hulls and the like. Superhydrophobic surfaces are considered to be one of the ideal strategies in the field of ice control because of their excellent hydrophobicity. At present, research on the application of super-hydrophobic surfaces in the field of ice prevention has made certain progress, and mainly focuses on accelerating resilience of supercooled water droplets, delaying freezing of supercooled water droplets, and reducing solid-liquid ice adhesion. However, there is less research into the direction of deicing for large area surfaces. The existing deicing principle of mature anti-icing coatings is to reduce the interface damage shear strength of ice and the coating surface to enable the ice layer on the surface to be easily removed, and all coatings are low interface strength coatings, but the interface shear strength belongs to the intrinsic property of materials, and the value of the interface shear strength is a fixed value, so the ice adhesion force of the ice layer is in direct proportion to the size of an icing area, the larger the icing area is, the larger the ice adhesion force is, the larger the required deicing force is, and the more difficult the deicing is. The method includes the steps that a cohesive force model is built to simulate a shearing failure mode of an ice layer, the fact that the failure of the ice layer can be divided into two modes, namely a strength control mode and a toughness control mode, the failure of the ice layer is caused by the length of an interface between the ice layer and a coating, the length of the interface when the two failure modes are equivalent is a critical length, the length of the interface is the strength control mode when the length of the interface is lower than the critical length, the size of the ice adhesion force of the ice layer is determined by the size of the interface strength, at the moment, the ice adhesion force is in direct proportion to the area and is increased along with the increase of the area, and the minimum deicing force for removing the ice layer is increased along with the increase of the area; when the interface length is higher than the critical length, the toughness control mode is adopted, the ice adhesion force of the ice layer is determined by the toughness of the interface, the ice adhesion force reaches the maximum value at the moment and cannot be increased continuously, so the minimum deicing force for removing the ice layer cannot be increased, and the interface strength of the ice layer can be reduced along with the increase of the area. The design uses a low-surface-toughness material, so that the size requirement of deicing force required by a large-area surface is greatly reduced, and the design has strong guiding significance on the preparation of a large-area deicing coating.
Disclosure of Invention
The invention provides a design method of an anti-icing and deicing coating on the surface of a large-area coating, aiming at solving the problems of high ice adhesion and difficult deicing of the existing large-area surface, and the invention provides the following technical scheme:
a method for designing an anti-icing coating on the surface of a large-area coating comprises the following steps:
step 1: constructing a cohesion model according to the damage of the interface between the ice layer and the coating;
step 2: analyzing the damage process of the ice layer according to the constructed cohesion model, and determining the damage mode of the ice layer;
and step 3: carrying out an icing experiment on the surface of the coating, measuring the magnitude of deicing force under the same icing condition, the same ice layer thickness and different interface lengths, and determining the toughness of the interface according to the deicing force;
and 4, step 4: determining a critical length of an interface between the ice layer and the coating based on the determined ice layer failure mode and the interface toughness.
Preferably, the step 1 specifically comprises:
when the ice layer and the coating are in shear type damage, constructing a cohesion model, setting the elastic modulus of the ice layer to be E, the thickness to be h and the length to be L, applying an external force F to one end when the ice layer partially slides, wherein the external force F is an average unit width force, and the shear stress of an interface between the ice and the rigid substrate is tau (x);
when the crack between the ice layer and the coating is damaged, a Dugdale model is constructed, and the shear stress before the interface damage is generated is a constant value
I.e. the maximum shear strength, the shear stress is transferred through the cohesive layer until the crack length between the ice layer and the coating reaches the critical length LCThe displacement u reaches the critical displacement ucThereafter, rapid crack propagation occurs, which causes the interface between the ice and the coating to break.
Preferably, the step 2 specifically comprises:
when a cohesion model is adopted, neglecting the stress concentration phenomenon, adopting a finite element method, taking out a section infinitesimal in an ice layer, determining a unit force balance equation of the infinitesimal in the x direction, and expressing the balance equation by the following formula:
obtaining the relation between the area compressive stress sigma (x) and the area displacement u (x) relative to the substrate according to the constitutive equation of ice, and expressing the relation between sigma (x) and sigma (x) by the following formula:
determining a self-control differential equation of u (x) according to the relation between sigma (x) and a unit force balance equation of the infinitesimal in the x direction, and expressing the differential equation by the following formula:
finding a constraint condition, determining a general solution of a self-control differential equation of u (x), applying an external force F to the position where x is 0, obtaining a stress boundary condition where x is 0, and expressing the boundary condition by the following formula:
σ(0)＝F/h
determining a displacement boundary condition at x-0 from the stress boundary condition at x-0 and the relationship of σ (x) to σ (x), the displacement boundary condition being represented by:
u′(0)＝-F/Eh
when L isCWhen the displacement is less than L, the generated slippage is partial slippage, the displacement at the critical part of the slippage area and the non-slippage area is 0, and x is obtained as LCThe displacement boundary condition (x) is represented by the following equation (x ═ L)CDisplacement boundary conditions of (1):
u(LC)＝0
substituting the displacement boundary condition at x ═ 0 and x ═ L into the general solution of the displacementCDetermining the relative displacement u (x) between the ice layer and the coating;
according to the gamma and u in different cohesion modelscObtaining u from the relationship ofcBy the equation of the overall stress balance and the equation of u (0) ═ u when the interface breaksCObtaining the maximum external force F under different interface lengthsmax；
When the Dugdale model is adopted, a simple model of the slip between the ice and the coating is established according to the Dugdale model, and the toughness is expressed by the following formula;
will be provided with
Substituting the displacement u (x) into a self-control differential equation to solve a general solution of the displacement u (x), wherein the general solution is expressed by the following formula:
the special solution for the displacement u (x) is represented by:
when the length of the interface L is larger than LCWhen the interface is partially slipped, the interface is damaged into a toughness control mode, and the maximum critical displacement is generated before the failure of the interface
In this case, u (0) is equal to uCDetermining the maximum external force FmaxThe self-large external force F is represented by the following formulamax：
When L < LCWhen the shear strength is not equal to the maximum shear strength, the interface is completely slipped, the interface is destroyed to be in an intensity control mode, and the maximum shear strength in the model is obtained
Is a constant, and the maximum external force is solved according to the analysis of the integral stress balance:
according to a linear cohesive relationship, in τ (x)(x) form, shear stress is linearly related to displacement in direct proportion, where k is shear stiffness, and when interfacial failure reaches critical displacement u (x) at displacement u (x)cWhen the shear stress reaches the maximum shear strength
The interfacial toughness is represented by the following formula:
according to Γ and
represents a cohesive relationship and shear stiffness by the formula:
the general solution of the displacement u (x) is obtained by substituting τ (x) into ku (x) into the autoregulation differential equation of the displacement u (x), and is expressed by the following equation:
u(x)＝Aeωx+Be-ωx
determining a special solution of the solution displacement u (x), the special solution being represented by:
when the crack starts to propagate, u (0) is uCDetermining the maximum external force FmaxThe maximum external force F is represented by the following formulamax：
By taking
And
the result of an asymptote of the very short and very long interfacial connection length is obtained:
when in use
When the temperature of the water is higher than the set temperature,
when in use
When the temperature of the water is higher than the set temperature,
preferably, the damage mode of the ice layer is divided into a strength control mode and a toughness control mode, the damage mode of the ice layer is determined according to the length of an interface between the ice layer and the coating, and the ice layer is in the strength control mode when the length of the interface is minimum; and when the interface length is maximum, the mode is in a toughness control mode.
Preferably, the step 3 specifically comprises: performing an icing test on the surface of the coating, measuring the deicing force under the same icing condition, the same ice layer thickness and different interface lengths, increasing the minimum deicing force along with the increase of the interface length, gradually smoothing the increase of the minimum deicing force to the maximum, and calculating the deicing force F of unit width according to the maximum value of the minimum deicing forceiceMeasured by the test of FiceSubstituting F to obtain an interfaceToughness, the interfacial toughness is represented by the formula:
the analysis is carried out by a cohesion model, the coating is taken as an intermediate phase between the ice layer and the substrate, the coating is expressed in a linear elastic form, and the maximum shearing strength of the interface failure between the ice layer and the coating is
Determining a shear displacement at the break of the coating, said displacement being represented by the formula:
wherein G is the shear modulus, γ, of the coatingcIs a shear stress of
Shear strain when, t is the coating thickness;
and measuring the shear modulus of the coating material through a tensile shear test to obtain the interfacial toughness of the coating.
Preferably, the step 4 specifically includes: when the length of the interface is the shortest,
the destruction of the interface is controlled by the interface strength; when the length of the interface is at its longest,
the interface toughness controls the damage of the interface, the two damage modes are equivalent to each other, and the critical length L of the two damage modes is obtainedCThe critical length is represented by the following formula:
evaluating the deicing capacity of the coating under different interface lengths according to a cohesion model by obtaining the interface strength and the interface toughness of the coating;
the interface toughness of the coating is the minimum, the critical length is the shortest, in the process that the icing area is gradually increased, the area of the ice layer exceeds the critical length of the coating with low interface toughness, the minimum deicing force reaches the maximum value at the moment, the increase of the minimum deicing force is not continued along with the increase of the area of the ice layer, and the deicing force in large-area use is lower than that of the conventional coating with low interface strength.
The invention has the following beneficial effects:
the designed large-area deicing method is based on the excellent deicing performance of the super-hydrophobic surface, the critical length of the coating is reduced by using the low-interface toughness coating, the deicing force can be maximized in a small icing area, the minimum deicing force required by the coating in large-area use is far lower than that of a conventional low-interface strength coating, the problems of difficulty in large-area deicing and high cost are solved, and the design of the conventional deicing prevention coating is guided.
The invention adopts two cohesion models, analyzes and discusses the process of ice layer damage, and determines that the damage of the ice layer is divided into two processes: when the length of the crack caused by the external force applied in the shearing direction of the ice layer is less than the critical length, the ice layer is in an interface strength control mode; and when the crack length reaches the critical length, the method is in an interface toughness control mode. Because the ice layers on different surfaces have different areas and the critical lengths of the ice layers change along with the toughness of the surfaces, whether the ice layers can enter an interface toughness control mode or not can be judged according to the size relation between the interface length of the ice layers and the critical lengths of the ice layers, a damage mode of the ice layers with smaller interface lengths and without the interface toughness control mode is called a strength control mode, and a damage mode of the ice layers with larger interface lengths and without the interface toughness control mode is called a toughness control mode.
The large-area ice prevention and removal has potential significance in the ice prevention field. The minimum deicing force in the shearing direction is generally considered to determine the difficulty degree of deicing, the minimum deicing force is related to the icing area, the larger the icing area is, the larger the required minimum deicing force is, and therefore, the problem of how to reduce the minimum deicing force of the large-area ice layer is solved. Typically, the minimum de-icing force required is reduced by selecting a low interfacial strength material to reduce the interfacial shear strength between ice and the coating, however, when a low interfacial toughness material is used to make the anti-icing coating, the interfacial shear strength of such material is typically higher than that of conventional low interfacial shear strength anti-icing coatings when the area is smaller; however, when the area is large enough, the deicing force of the low-interface toughness coating reaches the maximum value and cannot be increased continuously, and the interface destruction shear strength of the coating is reduced along with the increase of the area. Therefore, when facing large-area deicing, the minimum deicing force and the interface failure shear strength of the low-interface toughness coating are far lower than those of the conventional low-interface failure shear strength coating, and the deicing performance is more excellent.
Drawings
FIG. 1 is a schematic diagram of a cohesion model;
FIG. 2 is a diagram of the Dugdale model and the linear cohesive model;
FIG. 3 is a graph of the maximum load interface length of the Dugdale model versus the linear cohesion model.
Detailed Description
The present invention will be described in detail with reference to specific examples.
The first embodiment is as follows:
the invention provides a design method of an anti-icing and deicing coating on the surface of a large-area coating, which comprises the following steps:
a method for designing an anti-icing coating on the surface of a large-area coating comprises the following steps:
step 1: constructing a force accumulation model according to the damage of the interface between the ice layer and the coating;
the step 1 specifically comprises the following steps:
when the ice layer and the coating are in shear type damage, constructing a cohesion model, setting the elastic modulus of the ice layer as E, the thickness as h and the length as L, applying an external force F to one end when the ice layer is partially slipped, wherein the external force F is an average unit width force, and the shear stress of an interface between the ice and the rigid substrate is tau (x);
when the crack between the ice layer and the coating is damaged, a Dugdale model is constructed, and the shear stress before the interface damage is generated is a constant value
I.e. the maximum shear strength, the shear stress is transferred through the cohesive layer until the crack length between the ice layer and the coating reaches the critical length LCThe displacement u reaches the critical displacement ucThereafter, rapid crack propagation occurs, which causes the interface between the ice and the coating to break.
Step 2: analyzing the damage process of the ice layer according to the constructed force accumulation model, and determining the damage mode of the ice layer;
the step 2 specifically comprises the following steps:
when a cohesion model is adopted, neglecting the stress concentration phenomenon, adopting a finite element method, taking out a section infinitesimal in an ice layer, determining a unit force balance equation of the infinitesimal in the x direction, and expressing the balance equation by the following formula:
obtaining the relation between the area compressive stress sigma (x) and the area displacement u (x) relative to the substrate according to the constitutive equation of ice, and expressing the relation between sigma (x) and sigma (x) by the following formula:
determining a self-control differential equation of u (x) according to the relation between sigma (x) and a unit force balance equation of the infinitesimal in the x direction, and expressing the differential equation by the following formula:
finding a constraint condition, determining a general solution of a self-control differential equation of u (x), applying an external force F to the position where x is 0, obtaining a stress boundary condition where x is 0, and expressing the boundary condition by the following formula:
σ(0)＝F/h
determining a displacement boundary condition at x-0 from the stress boundary condition at x-0 and the relationship of σ (x) to σ (x), the displacement boundary condition being represented by:
u′(0)＝-F/Eh
when L isCWhen the displacement is less than L, the generated slippage is partial slippage, the displacement at the critical part of the slippage area and the non-slippage area is 0, and x is obtained as LCThe displacement boundary condition (x) is represented by the following equation (x ═ L)CDisplacement boundary conditions of (1):
u(LC)＝0
substituting the displacement boundary condition at x ═ 0 and x ═ L into the general solution of the displacementCDetermining the relative displacement u (x) between the ice layer and the coating;
according to the gamma and u in different cohesion modelscObtaining u from the relationship ofcBy the equation of the overall stress balance and the equation of u (0) ═ u when the interface breaksCObtaining the maximum external force F under the conditions of different interface lengthsmax；
When the Dugdale model is adopted, a simple model of the slip between the ice and the coating is established according to the Dugdale model, and the toughness is expressed by the following formula;
will be provided with
Substituting the displacement u (x) into a self-control differential equation to solve a general solution of the displacement u (x), wherein the general solution is expressed by the following formula:
the special solution for the displacement u (x) is represented by:
when the length of the interface L is larger than LCWhen the interface is partially slipped, the interface is damaged into a toughness control mode, and the maximum critical displacement is generated before the failure of the interface
When u (0) is equal to uCDetermining the maximum external force FmaxThe self-large external force F is represented by the following formulamax：
When L < LCWhen the shear strength is not equal to the maximum shear strength, the interface is completely slipped, the interface is destroyed to be in an intensity control mode, and the maximum shear strength in the model is obtained
Is a constant, and the maximum external force is solved according to the analysis of the integral stress balance:
shear stress is linearly related to displacement in the form of τ (x) ═ ku (x) according to a linear cohesive relationship, where k is shear stiffness, when interfacial failure reaches a critical displacement u (x) at displacement u (x)cWhen the shear stress reaches the maximum shear strength
The interfacial toughness is represented by the following formula:
according to Γ and
represents a cohesive relationship and shear stiffness by the formula:
the general solution of the displacement u (x) is obtained by substituting τ (x) into ku (x) into the autoregulation differential equation of the displacement u (x), and is expressed by the following equation:
u(x)＝Aeωx+Be-ωx
determining a special solution of the solution displacement u (x), the special solution being represented by:
when the crack starts to propagate, u (0) ═ uCDetermining the maximum external force FmaxThe maximum external force F is represented by the following formulamax：
By taking
And
to obtain an extremely short and an extremely long interfacial connection lengthAsymptotic results of degree:
when in use
When the temperature of the water is higher than the set temperature,
when in use
When the temperature of the water is higher than the set temperature,
the damage mode of the ice layer is divided into a strength control mode and a toughness control mode, the damage mode of the ice layer is determined according to the length of an interface between the ice layer and the coating, the ice layer is in the strength control mode when the length of the interface is minimum, and the interface strength is used as a reference parameter of the difficulty degree of the damage of the ice layer; and when the interface length is maximum, the method is in a toughness control mode, and the interface toughness is used as a reference parameter of the damage difficulty degree of the ice layer.
And step 3: carrying out an icing experiment on the surface of the coating, measuring the magnitude of deicing force under the same icing condition, the same ice layer thickness and different interface lengths, and determining the toughness of the interface according to the deicing force;
the step 3 specifically comprises the following steps: the icing test is carried out on the surface of the coating, the minimum deicing force required under the same icing condition, the same ice layer thickness and different interface lengths is measured, the minimum deicing force can be increased along with the increase of the interface length, when the interface length is increased to a certain length, the increase of the minimum deicing force can gradually and smoothly reach the maximum value, and the deicing force F of unit width is calculated according to the maximum valueiceMeasured by the test of FiceSubstituting F to obtain interfacial toughness by the following formulaRepresents the interfacial toughness:
the analysis is carried out by a cohesion model, the coating is taken as an intermediate phase between the ice layer and the substrate, the coating is expressed in a linear elastic form, and the maximum shearing strength of the interface failure between the ice layer and the coating is
Determining a shear displacement at the break of the coating, said displacement being represented by the formula:
wherein G is the shear modulus of the coating, γcIs a shear stress of
Shear strain when, t is the coating thickness;
and measuring the shear modulus of the coating material through a tensile shear test to obtain the interfacial toughness of the coating.
And 4, step 4: determining a critical length of an interface between the ice layer and the coating based on the determined ice layer failure mode and the interface toughness.
The step 4 specifically comprises the following steps: when the length of the interface is the shortest,
controlling the damage of the interface according to the interface strength; when the length of the interface is at its longest,
the destruction of the interface is controlled by the toughness of the interface, so that the external forces of the two destruction modes are equalSolving the critical length L of two failure modesCThe critical length is represented by the following formula:
evaluating the deicing capacity of the coating under different interface lengths according to a cohesion model by obtaining the interface strength and the interface toughness of the coating;
the interface toughness of the coating is the minimum, the critical length is the shortest, in the process that the icing area is gradually increased, the area of the ice layer exceeds the critical length of the coating with low interface toughness, at the moment, the minimum deicing force reaches the maximum value and is not continuously increased along with the increase of the area of the ice layer, and the minimum deicing force in large-area use is far lower than that of the conventional coating with low interface strength.
The second embodiment is as follows:
the present embodiment will be described with reference to fig. 1, and the specific steps of the cohesion model in which the interface between the ice layer and the coating layer is damaged by shear are as follows:
step A, constructing a cohesion model, setting the elastic modulus of an ice layer as E, the thickness as h, the length as L, partial slippage of the ice layer, and the interface length of a slippage area as LCAn external force F, which is an average unit width force, is applied to one end (x ═ 0). The shear stress at the interface between the ice and the rigid substrate is τ (x).
Step B, neglecting the stress concentration phenomenon, taking out a section infinitesimal in the ice layer by using a finite element method, and listing the unit force balance equation of the point in the x direction:
step C, obtaining the relation between the area compressive stress sigma (x) and the displacement u (x) of the area relative to the substrate by the constitutive equation of the ice:
step D, substituting the formula (3-2) into the formula (3-1) to obtain a self-control differential equation of u (x):
and E, searching constraint conditions for solving the general solution of the equation. Since the external force F is applied at x-0, the stress boundary condition at x-0 is obtained:
σ(0)＝F/h (4)
by substituting formula (4) for formula (2), we can solve the displacement boundary condition where x is 0:
u′(0)＝-F/Eh (5)
discussion slip zone Length LCL, the slippage generated at the moment is partial slippage, the displacement at the critical part of the slippage area and the non-slippage area is 0, and x is obtained as LCDisplacement boundary conditions of (1):
u(LC)＝0 (6)
and F, substituting two displacement boundary condition expressions (5) and (6) in the general solution of the displacement to solve the expression of the relative displacement u (x) between the ice layer and the coating.
G, according to gamma and u in different cohesion modelscObtaining u from the relationship ofcBy the equation of the overall stress balance and the equation of u (0) ═ u when the interface breaksCObtaining the maximum external force F under different interface lengthsmax。
The third concrete implementation mode: in the present embodiment, the calculation process is the same as the first embodiment by substituting the Dugdale model and the linear cohesion model for calculation and analysis in the second step, and comparing the two solutions.
Step a1, Dugdale model: assuming that the shear stress before the occurrence of the interface failure is constant
I.e. maximum shear strengthShear stress is transmitted through the cohesive layer until the crack length between the ice layer and the coating reaches the critical length LCThe displacement u reaches the critical displacement ucThereafter, rapid crack propagation occurs, which causes the interface between the ice and the coating to break. A simple model of the slip between ice and coating can be established according to the Dugdale model, where toughness:
will be provided with
Substituting the displacement u (x) into the autocontrol differential equation (3) to solve the general solution of the displacement u (x):
substituting the displacement boundary condition equations (5) and (6) into the equation (7) to obtain a special solution of the displacement u (x):
when the length of the interface L is larger than LCWhen the interface is partially slipped, the interface is damaged into a toughness control mode, and the maximum critical displacement before the interface failure is generated is deduced from the formula (7)
When u (0) is equal to uCThe maximum external force F is solved by substituting formula (9)max：
When L < LCWhen the shear strength is too high, the interface is completely slipped and the interface is destroyed to be in the strength control mode because of the maximum shear strength in the model
The external force is a constant, and the maximum external force can be solved according to the analysis of the whole stress balance:
step a2, linear cohesion relationship, in the form of τ (x) ═ ku (x), i.e., shear stress is linearly related to displacement in direct proportion, where k is shear stiffness. It is also assumed that the interface failure reaches the critical displacement u (x)cWhen the value of the shear stress reaches the maximum shear strength
And the interface toughness can be calculated as:
is represented by gamma and
expressed as a cohesive relationship, the shear stiffness can be obtained:
similarly, the general solution of the displacement u (x) is solved by substituting τ (x) into ku (x) into the autoregulation differential equation (3) of the displacement u (x):
u(x)＝Aeωx+Be-ωx (13)
wherein:
substituting the displacement boundary condition equations (5) and (6) into the equation (13) to obtain a special solution of the displacement u (x):
when the crack starts to propagate, u (0) ═ uCBy substituting the formulas (11) and (12) into the formula (15), the maximum external force F is solvedmax：
By taking
And
the result of an asymptote of the very short and very long interfacial connection length is obtained:
when in use
When, equation (16) becomes:
by substituting the value of ω in equation (14) into equation (18), the maximum external force can be obtained:
when in use
When, equation (16) becomes:
step B, comparing the two cohesion models, the length of the interface can be foundWhen the interface length is shorter and longer, the expression of the maximum external force is the same, when the interface length is shorter,
the destruction of the interface is controlled by the interface strength; when the length of the interface is relatively long,
the interface toughness controls the damage of the interface, so that the external forces of the two damage modes are equal to obtain the critical length L of the two damage modesC：
Therefore, to find LCThe interfacial toughness Γ of the coating material needs to be calculated.
The fourth concrete implementation mode: the method for calculating the toughness of the coating interface is realized according to the following steps:
step A1, performing an icing test on the coating surface, measuring the minimum deicing force required under the same icing condition, the same ice layer thickness and different interface lengths, wherein the deicing force can be increased along with the increase of the interface length, when the interface length is increased to a certain length, the increase of the deicing force can be gradually gentle and gradual and reaches the maximum, and calculating the deicing force F of unit width according to the maximum valueiceCombining formula (19), F determined by the testiceSubstituting F to obtain the interface toughness:
step A2, analysis by cohesion model, with the coating as the interphase between the ice layer and the substrate, assuming the coating is in linear elastic form and the maximum shear strength of the interfacial failure between the ice layer and the coating is
The shear displacement at the coating break is then:
wherein G is the shear modulus, γ, of the coatingcIs a shear stress of
The shear strain in time, t being the coating thickness, can be solved to approximate the interfacial toughness:
the shear modulus of the coating material was measured by a tensile shear test according to GBT7124-2008, and the coating interfacial toughness was calculated according to equation (23).
The definition table is shown in table 1 below:
TABLE 1 physical definition Table
The above is only a preferred embodiment of the method for designing the anti-icing and deicing coating on the surface of the large-area coating, and the protection scope of the method for designing the anti-icing and deicing coating on the surface of the large-area coating is not limited to the above-mentioned examples, and all technical solutions belonging to the idea belong to the protection scope of the present invention. It should be noted that modifications and variations which do not depart from the gist of the invention will be those skilled in the art to which the invention pertains and which are intended to be within the scope of the invention.
Claims (2)
1. A design method of an anti-icing and deicing coating on the surface of a large-area coating is characterized by comprising the following steps: the method comprises the following steps:
step 1: constructing an internal focusing force model according to the damage of the interface between the ice layer and the coating;
the step 1 specifically comprises the following steps:
when the ice layer and the coating are in shear type damage, constructing a cohesion model, setting the elastic modulus of the ice layer as E, the thickness as h and the length as L, applying an external force F to one end when the ice layer is partially slipped, wherein the external force F is an average unit width force, and the shear stress of an interface between the ice and the rigid substrate is tau (x);
when the crack between the ice layer and the coating is damaged, a Dugdale model is constructed, and the shear stress before the interface damage is generated is a constant value
I.e. the maximum shear strength, the shear stress is transferred through the cohesive layer until the crack length between the ice layer and the coating reaches the critical length LCThe displacement u reaches the critical displacement ucThen, the crack rapidly expands, so that the interface between the ice and the coating is damaged;
step 2: analyzing the damage process of the ice layer according to the built internal focusing force model, and determining the damage mode of the ice layer;
the step 2 specifically comprises the following steps:
when a cohesion model is adopted, neglecting the stress concentration phenomenon, adopting a finite element method, taking out a section infinitesimal in an ice layer, determining a unit force balance equation of the infinitesimal in the x direction, and expressing the balance equation by the following formula:
obtaining the relation between the area compressive stress sigma (x) and the area displacement u (x) relative to the substrate according to the constitutive equation of ice, and expressing the relation between u (x) and sigma (x) by the following formula:
determining a self-control differential equation of u (x) according to the relation between u (x) and sigma (x) and a unit force balance equation of the infinitesimal in the x direction, and expressing the differential equation by the following formula:
finding a constraint condition, determining a general solution of a self-control differential equation of u (x), applying an external force F to the position where x is 0, obtaining a stress boundary condition where x is 0, and expressing the stress boundary condition by the following formula:
σ(0)＝F/h
determining a displacement boundary condition at x-0 from the stress boundary condition at x-0 and the relationship of u (x) to σ (x), the displacement boundary condition being represented by:
u′(0)＝-F/Eh
when L isCWhen the displacement is less than L, the generated slippage is partial slippage, the displacement at the critical part of the slippage area and the non-slippage area is 0, and x is obtained as LCThe displacement boundary condition (x) is represented by the following equation (x ═ L)CDisplacement boundary conditions of (1):
u(LC)＝0
substituting the displacement boundary condition at x ═ 0 and x ═ L into the general solution of the displacementCDetermining the relative displacement u (x) between the ice layer and the coating;
according to the gamma and u in different cohesion modelscObtaining u from the relationship ofcBy the equation of the overall stress balance and the equation of u (0) ═ u when the interface breaksCObtaining the maximum external force F under different interface lengthsmax；
When the Dugdale model is adopted, a simple model of the slip between the ice and the coating is established according to the Dugdale model, and the toughness is expressed by the following formula;
will be provided with
Substituting the displacement u (x) into a self-control differential equation to solve a general solution of the displacement u (x), wherein the general solution is expressed by the following formula:
the special solution for the displacement u (x) is represented by:
when the length of the interface L is larger than LCWhen the interface is partially slipped, the interface is damaged into a toughness control mode, and the maximum critical displacement is generated before the failure of the interface
When u (0) is equal to uCDetermining the maximum external force FmaxThe maximum external force F is represented by the following formulamax：
When L < LCWhen the shear strength is not equal to the maximum shear strength, the interface is completely slipped, the interface is destroyed to be in an intensity control mode, and the maximum shear strength in the model is obtained
Is a constant, and the maximum external force is solved according to the analysis of the integral stress balance:
shear stress is linearly related to displacement in the form of τ (x) ═ ku (x) according to a linear cohesive relationship, where k is shear stiffness, when interfacial failure reaches a critical displacement u (x) at displacement u (x)cWhen the shear stress reaches the maximum shear strength
The interfacial toughness is represented by the following formula:
according to Γ and
represents a cohesive relationship and shear stiffness by the formula:
substituting τ (x) ═ ku (x) into the autoregulation differential equation for the displacement u (x), and solving the general solution for the displacement u (x), which is expressed by the following equation:
u(x)＝Aeωx+Be-ωx
determining a special solution of the solution displacement u (x), the special solution being represented by:
when the crack starts to propagate, u (0) ═ uCDetermining the maximum external force FmaxThe maximum external force F is represented by the following formulamax：
By taking
And
the result of an asymptote of the very short and very long interfacial connection length is obtained:
when in use
When the temperature of the water is higher than the set temperature,
when in use
When the temperature of the water is higher than the set temperature,
and step 3: carrying out an icing experiment on the surface of the coating, measuring the magnitude of deicing force under the same icing condition, the same ice layer thickness and different interface lengths, and determining the toughness of the interface according to the deicing force;
the step 3 specifically comprises the following steps: performing an icing test on the surface of the coating, measuring the deicing force under the same icing condition, the same ice layer thickness and different interface lengths, wherein the deicing force can be increased along with the increase of the interface length when the interface length is increasedWhen the ice removing force is increased to a certain length, the ice removing force is gradually and smoothly increased to the maximum, and the ice removing force F of unit width is calculated according to the maximum ice removing forceiceMeasured by the test of FiceSubstituting F gives the interfacial toughness, which is represented by the following formula:
the analysis is carried out by a cohesion model, the coating is taken as an intermediate phase between the ice layer and the substrate, the coating is expressed in a linear elastic form, and the maximum shearing strength of the interface failure between the ice layer and the coating is
Determining a shear displacement at the break of the coating, said shear displacement being represented by the formula:
wherein G is the shear modulus, γ, of the coatingcIs a shear stress of
Shear strain when, t is the coating thickness;
measuring the shear modulus of the coating material through a tensile shear test to obtain the toughness of the coating interface;
and 4, step 4: determining the critical length of the interface between the ice layer and the coating according to the determined ice layer damage mode and the interface toughness;
the step 4 specifically comprises the following steps: when the length of the interface is the shortest,
controlling the damage of the interface according to the interface strength; when the length of the interface is at its longest,
the interface toughness controls the damage of the interface, so that the external forces of the two damage modes are equal to obtain the critical length L of the two damage modesCThe critical length is represented by the following formula:
evaluating the deicing capacity of the coating under different interface lengths according to a cohesion model by obtaining the interface strength and the interface toughness of the coating;
the interface toughness of the coating is the minimum, the critical length is the shortest, in the process that the icing area is gradually increased, the area of the ice layer exceeds the critical length of the coating with low interface toughness, at the moment, the deicing force reaches the maximum value and is not continuously increased along with the increase of the area of the ice layer, and the deicing force in large-area use is far lower than that of the conventional coating with low interface strength.
2. The method of claim 1, wherein the step of designing the anti-icing and anti-icing coating on the surface of the large area coating comprises: the damage mode of the ice layer is divided into a strength control mode and a toughness control mode, the damage mode of the ice layer is determined according to the length of an interface between the ice layer and the coating, and the ice layer is in the strength control mode when the length of the interface is minimum; and when the interface length is maximum, the mode is in a toughness control mode.
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