CN110222363A - The characterization and application of orthotropic material three-dimensional creep properties - Google Patents
The characterization and application of orthotropic material three-dimensional creep properties Download PDFInfo
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Abstract
The invention discloses the characterizations and application of a kind of orthotropic material three-dimensional creep properties, it is intended to solve existing creep model and be difficult to the technical issues of reflecting the Creep Mechanics characteristic of orthotropic material comprehensively.The method that the present invention characterizes orthotropic material three-dimensional creep properties provides in three-dimensional space, ifxoyCreep Equation where bed plane when plane.The present invention establishes the orthotropic material three-dimensional creep model that can truly reflect orthotropic material for the first time, the purpose for showing orthotropic material difference stratification direction creeping characteristic simultaneously using a set of creep parameters can be achieved, have wide range of applications.
Description
Technical field
The present invention relates to material stress strain gauge technique fields, and in particular to a kind of orthotropic material three-dimensional creep is special
The characterization and application of property.
Background technique
Material in nature can be divided into isotropic material and anisotropic material.Wherein transverse isotropy and orthogonal
Anisotropy is two classification in anisotropy.Tranversely isotropic material such as beded rock mass, orthotropic material is such as
Concrete, timber, the rock mass of tunnel anchorage zone, aero-turbine leaf, crystallizing materials (ZD17G) and wide at present
The composite material of general use, the deformation of creep have become an important factor for influencing these orthotropic material service life and overhaul
One of.
The deformation of creep of orthotropic material include flexible deformation and over time and occur viscoelasticity
Deformation.Due to the orthotropy of material properties, flexible deformation and the viscoelasticity deformation of material creep process are shown
Anisotropic feature.
The existing creep constitutive model for orthotropic material is mostly to pass through building according to some experimental phenomenas
The creep parameters of different directions are simply recognized as different mutually independent values by one-dimensional creep constitutive model, and are not set up true
Orthotropy three-dimensional creep constitutive model in positive meaning, thus existing creep model be difficult to reflect comprehensively it is orthogonal respectively to
The Creep Mechanics characteristic of unlike material.
Therefore, for orthotropic material, it would be highly desirable to which developmental research goes out to be suitable for that orthotropy can be described
The three-dimensional creep constitutive model of material, to more can truly characterize or reflect the orthotropic material deformation of creep
Essence, and then more accurately decision or design considerations are provided for construction such as concrete works, machinery, industry.
Summary of the invention
The technical problem to be solved in the present invention is to provide a kind of characterization of orthotropic material three-dimensional creep properties and
Using the technology for being difficult to the Creep Mechanics characteristic of reflection orthotropic material comprehensively to solve existing creep model is asked
Topic.
In order to solve the above technical problems, it is specific the technical solution adopted is as follows:
Design derives a kind of method for characterizing orthotropic material three-dimensional creep properties, i.e. orthotropic material is three-dimensional
Creep model, in three-dimensional space, ifoxyzFor three-dimensional coordinate system (as shown in Figure 1), Creep Equation are as follows:
--- formula (s)；
--- formula (t)；
--- formula (u)；
--- formula (v)；
--- formula (w)；
--- formula (x)；
In formula,εorth xForxDirection normal strain,εorth yForyDirection normal strain,εorth zForzDirection normal strain；γ orth yzForoyzThe shearing strain of plane,γorth xyForoxyThe shearing strain of plane；σ x ForxDirection direct stress,σ y ForyDirection
Direct stress,σ z ForzDirection direct stress；τ xy ForoxyThe shear stress of plane；μ zy 、μ zx 、μ xy RespectivelyozyPlane,ozxPlane,oxy
The Poisson's ratio of plane；Ex M、ηx M、Ex k、ηx kAnd it is correspondingny 1、ny 2、ny 3、ny 4、nz 1、nz 2、nz 3、nz 4WithηB kIt is independent tension and compression creep parameters；tFor the time.
Above-mentioned characterization model mechanical or civil engineering field orthotropic material stability or the design and analysis of deformation,
Application in simulation or prediction.
Preferably, the orthotropic material is concrete, timber, the rock mass of tunnel anchorage zone, aero-engine
Any one of turbine leaf, crystallizing materials, composite material.
Compared with prior art, the beneficial technical effect of the present invention lies in:
The present invention establishes the three-dimensional creep constitutive model for reflecting orthotropic material characteristic truly for the first time,
Can accurate characterization the three-dimensional creep properties of orthotropic material are described, established theoretical basis to research and analyse, to it is mechanical,
The development of the industries such as civil engineering has important meaning.
Such as: aero engine turbine blades are a kind of orthotropic material, the deformation of creep and life-span of creep rupture
To influence the engine overhaul phase and one of an important factor for leaf longevity, can characterizing method according to the present invention predict its service life；
The composite material being widely used at present, multilist reveal orthotropic property, due to the influence of its matrix, always show one
The fixed deformation of creep, and the deformation of creep of composite material, usually in some months, several Nian Houcai can be showed, it is possible to create engineering
On the large deformation that does not allow, can characterizing method according to the present invention predict its deformation；The rock mass of tunnel anchorage zone can be considered cylinder
The equivalent anchoring body of type orthotropy can be used characterizing method of the invention and divide the long-time stability of anchorage zone rock mass
Analysis；Timber is as a kind of natural polymers material and a kind of typical orthotropic material, the deformation of creep
It is to influence engineering component quality, the important factor in order of woodwork and structure design safety, characterization side of the invention can be used
The deformation of creep rule of method simulation and prediction timber.
In short, the characterizing method of orthotropic material three-dimensional creep properties of the invention, is orthotropy material
The research of material Creep Rule provides scientific basis, has important directive significance to relevant design and analysis.
Detailed description of the invention
Fig. 1 is coordinate system schematic diagram；
Fig. 2 is creep model schematic diagram；
Fig. 3 is tranversely isotropic material coordinate system schematic diagram.
Specific embodiment
Illustrate a specific embodiment of the invention with reference to the accompanying drawings and examples, but following embodiment is used only in detail
It describes the bright present invention in detail, does not limit the scope of the invention in any way.
Related material is commercially available conventional material unless otherwise instructed in the examples below；It is related to be related to
The step of or test method be unless otherwise instructed conventional method；Related name parameter is unless otherwise instructed
This field general term.
Embodiment one: the building of the three-dimensional Creep Equation of orthotropic material
1. the study found that the creep properties of orthotropic material have the feature that
(1) load initial stage has Instantaneous elastic deformation, should contain in model and have elastic component；
(2) as time increases, creep rate gradually decreases, and gradually approximation levels off to some constant, therefore should have in model
Toughness element；
(3) under low stress level, after creep curve reaches some limiting value, strain value is remained unchanged, therefore is answered in model
It is in parallel with adhesive elements comprising elastic element；
The creep component models that can must describe orthotropic material are as shown in Figure 2:
2. pair Fig. 2 component models carry out mechanical analysis.
(1) Maxwell body elastic element is connected with adhesive elements, has following relationship:
--- formula (a)；
--- formula (b)；
In formula, D is operator, D=d/dt.
(2) Kelvin body elastic element is in parallel with adhesive elements, has following relationship:
--- formula (c)；
--- formula (d)；
In formula (a)~formula (d),E M ,E K The respectively elastic parameter of Maxwell body and Kelvin body；η M ,η K Respectively Maxwell
The sticky parameter of body and Kelvin body.
One-dimensional creep model in Fig. 2 is connected in series by Maxwell body and Kelvin body, can be obtained:
--- formula (e)；
Formula (b), (d) are substituted into formula (e), obtained:
--- formula (f)；
Count creep compliance:
, then formula (f) is writeable are as follows:
--- formula (g)；
By integrating to the operator D in formula (f), final one-dimensional Creep Equation can be obtained:
--- formula (h)；
3. orthotropic material Creep Equation
According to the Creep Equation established under one-dimensional condition, three-dimensional stress constraint is generalized to by constant Poisson's ratio method.
Method particularly includes: Poisson's ratio is assumed in object creep process not at any time and stress changes, and is equal to elastic stage
Poisson's ratio,μ(σ,t)=μFor constant real constant.Creep Equation is generalized to three-dimensional state from one-dimensional state based on this hypothesis.
Stress-strain relation of the orthotropic material in three-dimensional stress space are as follows:
--- formula (i)；
In formula:ε orth Be elastic strain matrix, {σ orth Be triaxiality matrix, {H orth It is flexibility matrix, it can indicate respectively
Are as follows:
In formula:E x 、E y 、E z , be respectively x-axis, y-axis, z-axis elasticity modulus,μ yz 、μ xz 、μ xy Respectively oyz plane, oxz plane,
The Poisson's ratio of oxy plane,G yz 、G xz 、G xy The respectively modulus of shearing of oyz plane, oxz plane, oxy plane.
To inquire into three-dimensional Creep Equation of orthotropic solid under the conditions of constant Poisson's ratio, according to grinding for Xie Yihuan
Study carefully (bibliography: the relationship of Xie Yihuan paper material elasticity modulus and modulus of shearing),H orth In three modulus of shearingG xy 、G xz 、G yz With following approximation relation:
--- formula (j)；
--- formula (k)；
--- formula (l)；
The symmetry for considering orthotropic material parameter, has:
--- formula (m)；
Formula (m) is substituted into formula (k), can be obtained:
--- formula (n)；
When Orthotropy sexual involution is transverse isotropy, it is assumed that oxy plane is transverse isotropy bed plane, and z-axis is hung down
Directly in xoy plane, x, y, z axis meets right hand corkscrew rule.
IfE x =E y =E h ,E z =E v ,μ zx =μ zy =μ hv ,μ xy =μ hh , then formula (j), formula (n) can be changed respectively are as follows:
--- formula (o)；
--- formula (p)；
Formula (o) is orthotropic solid elastic parameter functional relation, and formula (p) is the elasticity ginseng that Saint-Venant is proposed
Number approximate function formula.
It enablesn y = E y /E x ,n z = E z /E x , then formula (i) flexibility matrixH orth Writeable are as follows:
--- formula (q)；
Orthotropic three-dimensional Creep Equation can be obtained:
--- formula (r).
4. orthotropy Creep Equation is unfolded
For orthotropic material, the elasticity modulus in three directions and Poisson's ratio are independent from each other under elastic stage,
And meet corresponding elastic properties of materials parameter conversion relationship, it is assumed that viscoelasticity parameter conversion relationship and elastic stage phase in creep process
Together.According to constant Poisson's ratio it is assumed that the Poisson's ratio in creep process is equal to the Poisson's ratio of elastic stage and remains unchanged, consider different
The otherness of direction Creep Mechanics behavior, then there is the direction x in orthotropy three-dimensional creep modelEx M、ηx M、Ex k、ηx kAnd it is correspondingny 1、ny 2、ny 3、ny 4、nz 1、nz 2、nz 3、nz 4, totally 12 independent tension and compression creep parameters.
It should be noted that only the tension and compression creep parameters in the direction x, the direction y, z and x/y plane, yz are flat in Creep Equation
Face, zx plane creep parameters calculated by the creep parameters in the direction x by the flexibility matrix of formula (q), consider Orthotropy
Property material x-axis, y-axis, the otherness of three direction Creep Mechanics characteristics of z-axis, formula (r) is pressed into above-mentioned orthotropy viscoelasticity
Parametric evolving can obtain:
--- formula (s)；
--- formula (t)；
--- formula (u)；
--- formula (v)；
--- formula (w)；
--- formula (x).
Embodiment two: the relationship with tranversely isotropic material Creep Equation
When orthotropy both direction, such as when x-axis is identical with y-axis Creep Mechanics characteristic, then orthotropic material
Degenerating is tranversely isotropic material, it is assumed that xoy plane is transverse isotropy face, and z-axis is perpendicular to xoy plane, such as Fig. 3 institute
Show, x, y, z axis meets right hand corkscrew rule, hasE x =E y =E h ,μ zx =μ zy =μ hv ,μ xy =μ hh .Since x-axis and y-axis Creep Mechanics are special
Property is identical, then hasny1=1(i=1,2,3,4), x, the tension and compression creep parameters of y-axis are equal, and formula (s)~formula (x) can be written as following table
Equation formula (I)~formula (VI) of transverse isotropic rockmass three-dimensional creep model is levied (in detail referring to another application number of the present inventor
For the record in 2019103378772 application for a patent for invention file), i.e. orthotropic material can become by degeneration
For this structure of the creep of tranversely isotropic material, so as to further verify orthotropic material in the embodiment of the present invention one
Three-dimensional Creep Equation correctness.
--- formula (I)；
--- formula (II)；
--- formula (III)；
--- formula (IV)；
--- formula (V)；
--- formula (VI).
The present invention is described in detail above in conjunction with drawings and examples, still, those of skill in the art
Member is it is understood that without departing from the purpose of the present invention, can also carry out each design parameter in above-described embodiment
Change, forms multiple specific embodiments, is common variation range of the invention, is no longer described in detail one by one herein.
Claims (3)
1. a kind of characterizing method of orthotropic material three-dimensional creep properties, ifoxyzFor three-dimensional coordinate system, use
Following Creep Equation is characterized:
--- formula (s)；
--- formula (t)；
--- formula (u)；
--- formula (v)；
--- formula (w)；
--- formula (x)；
It is above it is various in,εorth xForxDirection normal strain,εorth yForyDirection normal strain,εorth zForzIt just answers in direction
Become；γorth yzForoyzThe shearing strain of plane,γorth xyForoxyThe shearing strain of plane；σ x ForxDirection direct stress,σ y Fory
Direction direct stress,σ z ForzDirection direct stress；τ xy ForoxyThe shear stress of plane；μ zy 、μ zx 、μ xy RespectivelyozyPlane,ozxIt is flat
Face,oxyThe Poisson's ratio of plane；Ex M、ηx M、Ex k、ηx kAnd it is correspondingny 1、ny 2、ny 3、ny 4、nz 1、nz 2、nz 3、nz 4WithηBkIt is independent tension and compression creep parameters；tFor the time.
2. the Creep Equation established in claim 1 in mechanical or civil engineering field orthotropic material stability or
Application in the design and analysis of deformation, simulation or prediction.
3. application according to claim 2, which is characterized in that the orthotropic material is concrete, timber, tunnel
Any one of the rock mass of road anchorage zone, aero-turbine leaf, crystallizing materials, composite material.
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| US20180365356A1 (en) * | 2016-11-09 | 2018-12-20 | China University Of Petroleum (East China) | Design method for creep-fatigue strength of plate-fin heat exchanger |
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