CN110222363B - Characterization and application of three-dimensional creep characteristic of orthotropic material - Google Patents

Characterization and application of three-dimensional creep characteristic of orthotropic material Download PDF

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CN110222363B
CN110222363B CN201910345257.3A CN201910345257A CN110222363B CN 110222363 B CN110222363 B CN 110222363B CN 201910345257 A CN201910345257 A CN 201910345257A CN 110222363 B CN110222363 B CN 110222363B
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李列列
管俊峰
姚贤华
何双华
朱学超
高勇伟
高新亮
徐宁
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North China University of Water Resources and Electric Power
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Abstract

The invention discloses characterization and application of three-dimensional creep characteristics of an orthotropic material, and aims to solve the technical problem that the creep mechanical characteristics of the orthotropic material are difficult to be comprehensively reflected by the conventional creep model. The method for representing the three-dimensional creep characteristic of the orthotropic material provides a method for representing the three-dimensional creep characteristic of the orthotropic material in a three-dimensional spacexoyIs the creep constitutive equation of the plane of the bedding plane. The invention establishes the orthotropic material three-dimensional creep model which can reflect the orthotropic material in the true sense for the first time, can realize the purpose of adopting a set of creep parameters and simultaneously showing the creep characteristics of the orthotropic material in different bedding directions, and has wide application range.

Description

Characterization and application of three-dimensional creep characteristic of orthotropic material
Technical Field
The invention relates to the technical field of material stress strain, in particular to characterization and application of three-dimensional creep characteristics of an orthotropic material.
Background
Materials in nature can be divided into isotropic materials and anisotropic materials. Where transverse isotropy and orthogonal anisotropy are two classifications of anisotropy. Creep deformation has become one of the important factors affecting the life and overhaul of these orthotropic materials, such as stratified rock mass, orthotropic materials such as concrete, wood, rock mass in tunnel anchorage areas, turbine blades of aircraft engines, oriented crystalline material (ZD 17G), and the composite materials that are widely used at present.
Creep deformation of orthotropic materials includes elastic deformation as well as viscoelastic deformation over time. Due to the orthotropic properties of the material, both the elastic deformation as well as the viscoelastic deformation during creep of the material exhibit anisotropic characteristics.
Most of the existing creep constitutive models for the orthotropic materials are based on some experimental phenomena, creep parameters in different directions are simply identified into different mutually independent values by constructing one-dimensional creep constitutive models, and the orthotropic three-dimensional creep constitutive models are not established in the true sense, so that the creep mechanical properties of the orthotropic materials are difficult to be fully reflected by the existing creep models.
Therefore, for orthotropic materials, a three-dimensional creep constitutive model suitable for describing orthotropic materials is urgently needed to be developed and researched so as to more truly represent or reflect the nature of the orthotropic material creep deformation, and further provide more accurate decision or design basis for the construction of concrete engineering, machinery, industry and the like.
Disclosure of Invention
The invention aims to provide representation and application of three-dimensional creep characteristics of an orthotropic material, so as to solve the technical problem that the creep mechanical characteristics of the orthotropic material are difficult to be comprehensively reflected by the conventional creep model.
In order to solve the technical problems, the technical scheme is as follows:
design derivationA method for characterizing the three-dimensional creep characteristics of orthotropic material, i.e. the three-dimensional creep model of orthotropic material, in three-dimensional spaceoxyzIs a three-dimensional space coordinate system (as shown in figure 1), and the creep constitutive equation is as follows:
Figure 495373DEST_PATH_IMAGE001
-formula(s); />
Figure DEST_PATH_IMAGE002
-formula (t);
Figure 474830DEST_PATH_IMAGE003
-formula (u);
Figure DEST_PATH_IMAGE004
-formula (v);
Figure 254567DEST_PATH_IMAGE005
-formula (w);
Figure DEST_PATH_IMAGE006
-formula (x);
in the formula (I), the compound is shown in the specification,εorth xis composed ofxThe direction of the positive strain is changed,εorth yis composed ofyThe direction of the positive strain is changed,εorth zis composed ofzA positive strain in direction;γorth yzis composed ofoyzThe shear strain of the plane is changed,γorth xyis composed ofoxyPlanar shear strain;σ x is composed ofxThe direction of the positive stress is normal and the stress,σ y is composed ofyThe direction of the positive stress is normal and the stress,σ z is composed ofzA directional normal stress;τ xy is composed ofoxyPlanar shear stress;μ zy 、μ zx 、μ xy are respectively asozyA plane surface,ozxA plane surface,oxyA planar poisson's ratio;Ex M、ηx M、Ex k、ηx kand correspondingny 1、ny 2、ny 3、ny 4、nz 1、nz 2、nz 3、nz 4AndηB kis an independent tension-compression creep parameter;tis time.
The characterization model is applied to the design, analysis, simulation or prediction of the stability or deformation of the orthotropic material in the mechanical or civil engineering field.
Preferably, the orthotropic material is any one of concrete, wood, rock mass of a tunnel anchoring zone, turbine blades of an aircraft engine, a directional crystallization material and a composite material.
Compared with the prior art, the invention has the beneficial technical effects that:
the invention establishes a three-dimensional creep constitutive model capable of reflecting the characteristics of the orthotropic material for the first time, can accurately represent and describe the three-dimensional creep characteristics of the orthotropic material, lays a theoretical foundation for research and analysis, and has important significance for the development of industries such as machinery, civil engineering and the like.
Such as: the turbine blade of the aircraft engine is an orthotropic material, the creep deformation and the creep rupture life of the turbine blade are one of important factors influencing the overhaul period of the engine and the service life of the turbine blade, and the service life of the turbine blade can be predicted according to the characterization method of the invention; the composite material widely applied at present mostly shows the property of orthotropic, and always shows a certain creep deformation due to the influence of a matrix, while the creep deformation of the composite material usually shows after several months and years, and can possibly generate large deformation which is not allowed in engineering, and the deformation can be predicted according to the characterization method of the invention; the rock mass of the tunnel anchoring area can be regarded as a cylindrical orthogonal anisotropy equivalent anchoring body, and the long-term stability of the rock mass of the anchoring area can be analyzed by adopting the characterization method of the invention; the wood is used as a natural high polymer material and is also a typical orthotropic material, the creep deformation of the wood is an important influence factor influencing the quality of engineering components, wood products and the structural design safety, and the creep deformation rule of the wood can be simulated and predicted by adopting the characterization method of the invention.
In a word, the characterization method of the three-dimensional creep characteristic of the orthotropic material provides scientific basis for the research of the creep law of the orthotropic material, and has important guiding significance for related design and analysis.
Drawings
FIG. 1 is a schematic diagram of a coordinate system;
FIG. 2 is a schematic view of a creep model;
fig. 3 is a schematic diagram of a coordinate system of a transverse isotropic material.
Detailed Description
The following examples are intended to illustrate the present invention in detail and should not be construed as limiting the scope of the present invention in any way.
The materials referred to in the following examples are all commercially available conventional materials unless otherwise specified; the steps or test methods involved, if not otherwise specified, are conventional; the named parameters, if not otherwise stated, are conventional terms of art.
The first embodiment is as follows: construction of three-dimensional creep constitutive equation of orthotropic material
1. It was found that the creep characteristics of orthotropic materials have the following characteristics:
(1) The loading initial stage has instantaneous elastic deformation, and the model contains an elastic element;
(2) As time increases, the creep rate gradually decreases and gradually approaches a constant, so the model should have viscous elements;
(3) At low stress levels, the strain value of the creep curve remains unchanged after reaching a certain limit value, so that the model should comprise a parallel connection of an elastic element and a viscous element;
the model of the creep element that can be obtained to describe orthotropic materials is shown in FIG. 2:
2. the model of the element of fig. 2 was subjected to mechanical analysis.
(1) The elastic elements and the viscous elements in the Maxwell body are connected in series, and have the following relations:
Figure 462826DEST_PATH_IMAGE007
-formula (a); />
Figure DEST_PATH_IMAGE008
-formula (b);
in the formula, D is an operator, and D = D/dt.
(2) The elastic element and the viscous element in the Kelvin body are connected in parallel, and have the following relationship:
Figure 339515DEST_PATH_IMAGE009
-formula (c);
Figure DEST_PATH_IMAGE010
-formula (d);
in the formulae (a) to (d),E M ，E K elastic parameters of a Maxwell body and a Kelvin body are respectively set;η M ，η K the viscosity parameters of Maxwell and Kelvin bodies, respectively.
The one-dimensional creep model in fig. 2 is formed by connecting Maxwell body and Kelvin body in series, and can be obtained as follows:
Figure 161978DEST_PATH_IMAGE011
-formula (e);
substituting the formulas (b) and (d) into the formula (e) to obtain:
Figure DEST_PATH_IMAGE012
-formula (f);
measuring creep compliance:
Figure 242060DEST_PATH_IMAGE013
then equation (f) can be written as:
Figure DEST_PATH_IMAGE014
-formula (g);
by integrating operator D in equation (f), the final one-dimensional creep constitutive equation can be obtained:
Figure 503277DEST_PATH_IMAGE015
-formula (h);
3. orthotropic material creep constitutive equation
According to a creep constitutive equation established under a one-dimensional condition, the creep constitutive equation is popularized to a three-dimensional stress state through a normal Poisson ratio method.
The specific method comprises the following steps: the Poisson's ratio during object creep is assumed to not change with time and stress, and is equal to the Poisson's ratio in the elastic phase,μ(σ,t)=μis a constant real constant. Based on this assumption the creep equation is generalized from one-dimensional to three-dimensional states.
The stress-strain relationship of the orthotropic material in a three-dimensional stress space is as follows:
Figure DEST_PATH_IMAGE016
-formula (i);
in the formula: {ε orth Is an elastic strain matrix, a great apertureσ orth Is a three-dimensional stress matrix, a great faceH orth Is a compliance matrix, which can be expressed as:
Figure 985205DEST_PATH_IMAGE017
Figure DEST_PATH_IMAGE018
in the formula:E x 、E y 、E z the elastic moduli of the x-axis, the y-axis and the z-axis respectively,μ yz 、μ xz 、μ xy respectively the Poisson ratios of an oyz plane, an oxz plane and an oxy plane,G yz 、G xz 、G xy shear modulus in the oyz plane, oxz plane, and oxy plane, respectively.
In order to calculate the three-dimensional creep constitutive equation of orthorhombic anisotropic body under the condition of constant Poisson ratio, according to the research of Shexin Ring (reference: shexin Ring. Relationship of elastic modulus and shear modulus of paper material), a retaining pocketH orth Three shear moduli ofG xy 、G xz 、G yz Has the following approximate relationship:
Figure 40886DEST_PATH_IMAGE019
-formula (j);
Figure DEST_PATH_IMAGE020
-formula (k);
Figure 602405DEST_PATH_IMAGE021
-formula (l);
considering the symmetry of orthotropic material parameters, there are:
Figure DEST_PATH_IMAGE022
-formula (m);
substituting formula (m) into formula (k) yields:
Figure 339417DEST_PATH_IMAGE023
-formula (n);
when the orthotropic degeneracy is transverse isotropy, the oxy plane is assumed to be a transverse isotropy bedding plane, the z axis is perpendicular to the xoy plane, and the x, y and z axes accord with the right-hand rotation method.
Is provided withE x =E y =E h ，E z =E v ，μ zx =μ zy =μ hv ，μ xy =μ hh Then, the formula (j) and the formula (n) can be changed to:
Figure DEST_PATH_IMAGE024
-formula (o);
Figure 925119DEST_PATH_IMAGE025
-formula (p);
the formula (o) is a function relation of elastic parameters of orthotropic body, and the formula (p) is an approximate function relation of elastic parameters proposed by Saint-Venant.
Order ton y = E y /E x ，n z = E z /E x The compliance matrix of the formula (i)H orth } can be written as:
Figure DEST_PATH_IMAGE026
-formula (q);
Figure 168013DEST_PATH_IMAGE027
the three-dimensional creep equation for orthotropic anisotropy can be derived:
Figure DEST_PATH_IMAGE028
-formula (r).
4. Orthotropic creep equation development
For orthotropic materials, the elastic modulus and Poisson's ratio in three directions under the elastic state are mutually independent and conform to the corresponding material elastic parameter conversion relation, and the viscoelastic parameter conversion relation in the creep process is assumed to be the same as the elastic stage. According to the assumption of the constant Poisson ratio, the Poisson ratio in the creep process is equal to the Poisson ratio in the elastic stage and is kept unchanged, and the difference of creep mechanical behaviors in different directions is considered, so that the x direction in the orthotropic three-dimensional creep model hasEx M、ηx M、Ex k、ηx kAnd correspondingny 1、ny 2、ny 3、ny 4、nz 1、nz 2、nz 3、nz 4And total 12 independent tension-compression creep parameters.
It should be noted that in the creep equation, only the tensile and compressive creep parameters in the x direction, the creep parameters in the y and z directions and the creep parameters in the xy plane, the yz plane and the zx plane are all calculated by the creep parameters in the x direction through the compliance matrix of the formula (q), and the difference of the creep mechanical properties of the orthogonal anisotropic material in the three directions of the x axis, the y axis and the z axis is considered, and the formula (r) is developed according to the orthogonal anisotropic viscoelasticity parameters, so that:
Figure 409638DEST_PATH_IMAGE001
-formula(s);
Figure 747079DEST_PATH_IMAGE002
-formula (t);
Figure 390550DEST_PATH_IMAGE003
-formula (u);
Figure 538766DEST_PATH_IMAGE004
-formula (v);
Figure 267687DEST_PATH_IMAGE005
-formula (w); />
Figure 346502DEST_PATH_IMAGE006
-formula (x).
Example two: relation with transverse isotropic material creep constitutive equation
When the creep mechanical properties of the orthogonal anisotropy in two directions, such as the x-axis and the y-axis, are the same, the orthogonal anisotropy material degenerates into a transverse isotropic material, assuming that the xoy plane is a transverse isotropic plane and the z-axis is perpendicular to the xoy plane, as shown in fig. 3, the x, y and z axes conform to the right-hand rotation rule, and there areE x =E y =E h ，μ zx =μ zy =μ hv ，μ xy =μ hh . Since the creep mechanical properties of the x-axis and the y-axis are the same, the method hasny 1=1(iThe expressions(s) to (x) can be written as the following equations (I) to (VI) which characterize the three-dimensional creep model of the transverse isotropic rock mass (see the description in the patent application document of the inventor with the application number of 2019103378772), that is, the orthotropic material can be changed into the creep constitutive of the transverse isotropic material after being degraded, so that the correctness of the three-dimensional creep constitutive equation of the orthotropic material in the first embodiment of the invention can be further verified.
Figure 906796DEST_PATH_IMAGE029
-formula (I);
Figure DEST_PATH_IMAGE030
-formula (II);
Figure 678443DEST_PATH_IMAGE031
-formula (III);
Figure DEST_PATH_IMAGE032
-formula (IV); />
Figure 442131DEST_PATH_IMAGE033
-formula (V);
Figure DEST_PATH_IMAGE034
-formula (VI).
While the present invention has been described in detail with reference to the drawings and the embodiments, those skilled in the art will appreciate that various changes and modifications can be made to the specific parameters in the above embodiments without departing from the spirit of the present invention, and it is intended to cover various embodiments within the scope of the present invention, and detailed descriptions thereof will be omitted.

Claims (1)

1. An application of a creep constitutive equation in the design, analysis, simulation or prediction of the stability or deformation of an orthotropic material in the mechanical or civil engineering field is disclosed, wherein an oxyz is taken as a three-dimensional space coordinate system, and the following creep constitutive equation is adopted to characterize the three-dimensional creep property of the orthotropic material:
Figure FDA0004037618920000011
Figure FDA0004037618920000012
Figure FDA0004037618920000013
Figure FDA0004037618920000014
Figure FDA0004037618920000015
Figure FDA0004037618920000021
/>
in the above-mentioned formulas, the first and second groups,
Figure FDA0004037618920000022
positively strained in the x-direction>
Figure FDA0004037618920000023
Positively strained in the y-direction>
Figure FDA0004037618920000024
Is positive z-direction strain; />
Figure FDA0004037618920000025
Is the shear strain in the oyz plane>
Figure FDA0004037618920000026
Shear strain for the oxy plane; sigma x Is positive stress in the x direction, σ y Positive stress in the y direction, σ z Positive stress in the z direction; tau is xy Shear stress of the oxy plane; mu.s zy 、μ zx 、μ xy Poisson's ratio of ozy plane, ozx plane and oxy plane respectively;
Figure FDA0004037618920000027
and corresponding +>
Figure FDA0004037618920000028
Figure FDA0004037618920000029
And &>
Figure FDA00040376189200000210
Is an independent tension-compression creep parameter; t is time;
the orthotropic material is any one of concrete, wood, rock mass of a tunnel anchoring area, turbine blades of an aircraft engine, a directional crystallization material and a composite material.
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CN107228798A (en) * 2017-06-23 2017-10-03 中国矿业大学 A kind of method for describing coated fabric membrane material anisotropy creep behaviour
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CN104179176A (en) * 2014-08-08 2014-12-03 山东科技大学 Anchor wire prestress loss and rock-soil body creep coupling based computing method for side slope creep values
CN107228798A (en) * 2017-06-23 2017-10-03 中国矿业大学 A kind of method for describing coated fabric membrane material anisotropy creep behaviour
CN108931448A (en) * 2018-05-07 2018-12-04 华南理工大学 A kind of prediction technique of high chrome Material Thermodynamics response and spleen tissue extracts damage
CN109187199A (en) * 2018-09-18 2019-01-11 中国石油大学(华东) The viscoelasticity theory analysis method of anchored rock mass creep properties under uniaxial compression

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