CN104330300B - Superhigh temperature ceramic material heat-damage stiffness of coupling indirect measurement method - Google Patents

Abstract

The invention discloses superhigh temperature ceramic material hot injury's stiffness of coupling indirect measurement method, elastic modelling quantity under experimental data that the method varies with temperature according to the superhigh temperature ceramic material elastic modelling quantity that records and reference temperature, set up material hot injury stiffness of coupling and the mathematical expression model of elastic modelling quantity under different temperatures, calculate the material hot injury's stiffness of coupling at a temperature of corresponding with superhigh temperature ceramic material elastic modelling quantity.The solution have the advantages that: achieve the reliable prediction of material hot injury stiffness of coupling at each temperature.

Description

Superhigh temperature ceramic material heat-damage stiffness of coupling indirect measurement method

Technical field

The present invention relates to the intensity indirect measurement method of a kind of superhigh temperature ceramic material.

Background technology

Superhigh temperature ceramics (Ultra High Temperature Ceramics is called for short UHTCs) refers to more than more than 2000 DEG C Remaining to the most heat-resisting advanced ceramic as usual used under the conditions of having oxygen etc., this superhigh temperature ceramic material reaches 1600 DEG C in temperature Time still there is preferable non-oxidizability, it is mainly used in the thermal protection system of the aircraft such as hypersonic missile, space shuttle System is such as the hot junction of nose of wing, end cap and electromotor.

Elevated temperature strength described in present patent application refers to the temperature strength of materials in the range of 1200 DEG C 3200 DEG C.As The superhigh temperature ceramic material of hypersonic aircraft thermally protective materials, its elevated temperature strength is to weigh the important ginseng of reliability of material Number.The elevated temperature strength improving superhigh temperature ceramic material is exactly the target that industry is pursued all the time, this nature and elevated temperature strength Measurement be associated.At present, the research about elevated temperature strength lays particular emphasis on experimentation, and the temperature of experiment test also ratio is relatively low, Not reaching far away the test condition of elevated temperature strength, low-temperature test cannot obtain the data of elevated temperature strength.

At present, the difficulty of elevated temperature strength test is very big, and experimental expenses is expensive, does not has unified method of testing and standard, surveys Examination value dispersibility is big.Intensity experiment belongs to a series of destructive test, needs a series of test specimen, to ceramic material by Relatively big in there is initial imperfection and process variations, the strength of materials (σ corresponding at temperature T will be caused_th(T) experimental result) Inaccurate；In contrast, elastic modelling quantity (E (T)) corresponding at temperature T only need to use same test specimen to carry out testing, The once data of experiment just available a series of elastic modulus Es (T), it is to avoid the experimental result brought because of test specimen difference is not Accurately.

Ceramic three-point bending test at high temperature is used for elevated temperature strength (σ_th(T) prediction), due to superhigh temperature ceramic material Along with its tension and compression anisotropy of rising of temperature gradually strengthens, need to be modified 3 curved strength calculation formula eliminating The anisotropic impact of its tension and compression, but, the most how 3 curved strength calculation formula are made and reasonably repairing Difficult problem the most unsolved.

The high temperature fracture intensity of the superhigh temperature ceramic material with micro-crack is referred to as heat-damage stiffness of coupling, because superhigh temperature ceramics The elevated temperature strength prediction of material belongs at present the most unsolved technical barrier, thus superhigh temperature ceramic material hot-damage couples The prediction of intensity is the technical barrier in this area equally.

Summary of the invention

The technical problem to be solved is just to provide between a kind of superhigh temperature ceramic material heat-damage stiffness of coupling Connecing measuring method, it can predict material heat-damage stiffness of coupling at each temperature.

The technical problem to be solved is realized by such technical scheme, according to the superhigh temperature pottery recorded Elastic modelling quantity under experimental data that ceramic material elastic modelling quantity varies with temperature and reference temperature, sets up material heat under different temperatures -damage stiffness of coupling and the mathematical expression model of elastic modelling quantity, calculate the temperature corresponding with superhigh temperature ceramic material elastic modelling quantity Under material heat-damage stiffness of coupling；Set up material heat-damage stiffness of coupling and the mathematical expression of elastic modelling quantity under different temperatures The step of model includes:

The first step, set up the mathematical expression model of intensity and elastic modelling quantity under the different temperatures of material initial damage state and be

${\mathrm{\σ}}_{th}\left(T\right)={\[\frac{{\left({\mathrm{\σ}}_{th}^0\right)}^2}{E_0}E\left(T\right)\[1-\frac{1}{{\∫}_0^{T_m}{C}_p\left(T\right)dT+{\mathrm{\ΔH}}_M}{\∫}_0^T{C}_p\left(T\right)dT\]\]}^{1/2}$

In formula, σ_th(T) being the strength of materials corresponding at temperature T, E (T) is elastic modelling quantity corresponding at temperature T,For The strength of materials at reference temperature 0 DEG C, E₀For the elasticity modulus of materials at reference temperature 0 DEG C, C_p(T) it is at temperature T Corresponding level pressure thermal capacitance, Δ H_MFor heat of fusion, T_mFusing point for material；

Second step, the mathematical expression model setting up intensity relevant to material damage under reference temperature are

${\mathrm{\σ}}_0^f={\[\frac{E_0{G}_0^f}{2(1-{\mathrm{\ν}}^2)l}{\[1+\frac{16(1-{\mathrm{\ν}}^2){\mathrm{Nl}}^3}{3}\]}^{-1}\]}^{1/2}$

In formula,For Critical fracture intensity,For energy to failure, E₀For elasticity during material flawless under reference temperature Modulus, ν is Poisson's ratio, and l is half length of crackle, and N is the crackle number in unit volume；

3rd step, set up superhigh temperature ceramic material heat-damage stiffness of coupling mathematical expression model be

${\mathrm{\σ}}_{th}(T,l)={\[\frac{K_{IC}^{2}E(T,N,l)}{2E_0(1-{\mathrm{\ν}}^2){\left(\frac{3V}{4\mathrm{\π}\mathrm{\α}}\right)}^{1/3}}\[1-\frac{1}{{\∫}_0^{T_m}{C}_p\left(T\right)dT+{\mathrm{\ΔH}}_M}{\∫}_0^T{C}_p\left(T\right)dT\]\]}^{1/2}$

In formula, σ_th(T l) is heat-damage stiffness of coupling, K_ICStraining fracture toughness for material plane, (T, N l) are E Elastic modelling quantity during corresponding at temperature T existence crackle, E₀For elastic modelling quantity during material flawless under reference temperature, ν For Poisson's ratio, V is single lesion volume, and α is lesion shape coefficient, C_p(T) it is level pressure thermal capacitance corresponding at temperature T, ΔH_MFor heat of fusion, T_mFusing point for material.

Owing to establishing material heat-damage stiffness of coupling and the mathematical expression model of elastic modelling quantity under different temperatures, and this mathematics Formula model does not has any fitting parameter；In mathematical expression model, the experimental data that elasticity modulus of materials varies with temperature is easy Obtaining from experiment, the elastic modelling quantity under reference temperature can be readily obtained by experiment, and thermal capacitance, Poisson's ratio, heat of fusion etc. can To find from Materials Handbook easily, the material heat-damage stiffness of coupling thus calculating prediction avoids elevated temperature strength in fact The difficulty that test strip is come, it is achieved that carry out the prediction of material heat-damage stiffness of coupling under existence conditions with mathematical expression model, Mathematical expression model discloses the Physical Mechanism affecting material heat-damage stiffness of coupling.

The solution have the advantages that: achieve the reliable prediction of material heat-damage stiffness of coupling at each temperature.

Accompanying drawing explanation

The accompanying drawing of the present invention is described as follows:

Fig. 1 is the curve chart that the elastic modulus E (T) of TiC ceramic material varies with temperature；

Fig. 2 is elevated temperature strength σ of TiC ceramic material prediction_th(T) curve chart varied with temperature；

Fig. 3 is (the Δ σ under different temperatures T_th/ Δ l) is with Δ l variation relation curve；

Fig. 4 is (the Δ σ under different temperatures T_th/ Δ E) with Δ E variation relation curve.

Detailed description of the invention

Insight of the invention is that the difficult point measuring superhigh temperature ceramic material heat-rupture test simplifies, from easily obtaining Parameter such as elasticity modulus of materials, level pressure thermal capacitance, Poisson's ratio, heat of fusion etc. set out, set up superhigh temperature ceramic material heat- Damage stiffness of coupling mathematical expression model.

The invention will be further described with embodiment below in conjunction with the accompanying drawings:

Present method invention is: the experimental data varied with temperature according to the superhigh temperature ceramic material elastic modelling quantity recorded and ginseng Elastic modelling quantity at a temperature of examining, sets up material heat-damage stiffness of coupling and the mathematical expression model of elastic modelling quantity under different temperatures, Calculate the material heat-damage stiffness of coupling at a temperature of corresponding with superhigh temperature ceramic material elastic modelling quantity.

Set up material heat-damage stiffness of coupling under different temperatures as follows with the step of the mathematical expression model of elastic modelling quantity:

The first step, set up the mathematical expression model of intensity and elastic modelling quantity under the different temperatures of material initial damage state

The basic imagination that this mathematical expression model is set up is: 1., to a kind of certain material, it is believed that it exists an energy storage limit, One changeless Energy maximum value of correspondence when i.e. material occurs to destroy, this maximum can characterize by strain energy, also Can characterize with heat energy.2., say to the execution of material, it is believed that between heat energy and strain energy that material stores There is a kind of quantitative equivalent relation.

The energy storage ultimate value being obtained unit volume material by above imagination is

$W_{TOTAL}=K\left(W_T\right(T)+{\mathrm{\ΔH}}_M)+W_{{\mathrm{\σ}}_{th}}\left(T\right)---\left(1\right)$

In formula (1), W_TOTALFor the energy storage ultimate value of unit volume material, T is Current Temperatures, W_T(T) it is corresponding heat energy,For strain energy corresponding during material damage, K is the energy conversion factor between heat energy and strain energy；ΔH_MIt is molten Heat-transformation.

Assume ceramic material when loading, stress and strain meets linear elasticity relation, then ceramic material is corresponding when destroying should Change can be into

$W_{{\mathrm{\σ}}_{th}}\left(T\right)=\frac{{\left({\mathrm{\σ}}_{th}\right(T\left)\right)}^2}{2E\left(T\right)}---\left(2\right)$

In formula (2), σ_th(T) being the temperature dependency intensity of initial damage state, E (T) is springform corresponding at a temperature of T Amount.

With 0 DEG C as reference temperature, corresponding heat energy is represented by:

$W_T\left(T\right)={\∫}_0^T{C}_p\left(T\right)dT---\left(3\right)$

In formula (3), C_p(T) it is level pressure thermal capacitance corresponding at a temperature of T.

From formula (3):

W_T(0)=0 (4)

T_mFor the fusing point of material, due to σ in formula (2)_th(T_m)=0, so

$W_{{\mathrm{\σ}}_{th}}\left(T_m\right)=0---\left(5\right)$

As T=0, Δ H_M=0, by the available following relational expression of formula (4), (5) and (1):

$W_{TOTAL}=W_{{\mathrm{\σ}}_{th}}{|}_{T=0}=K\left(W_T\right(T)+{\mathrm{\ΔH}}_M){|}_{T=T_m}---\left(6\right)$

Can be obtained by formula (6):

$K=\frac{W_{{\mathrm{\σ}}_{th}}{|}_{T=0}}{\left(W_T\right(T)+{\mathrm{\ΔH}}_M){|}_{T=T_m}}=\frac{{\left({\mathrm{\σ}}_{th}^0\right)}^2}{2E_0}/\left({\∫}_0^{T_m}{C}_p\right(T)dT+{\mathrm{\ΔH}}_M)---\left(7\right)$

In formula (7),E₀It is respectively the strength of materials at reference temperature 0 DEG C and elastic modelling quantity.

To ceramic material, owing to its tensile property relatively compression performance is poor, study its hot strength more important.Consider uniaxial tension feelings Shape:

$\begin{array}{c}{W}_{TOTAL}=K\left(W_T\left(T\right)+{\mathrm{\ΔH}}_M\right)+W_{{\mathrm{\σ}}_{th}}\left(T\right)\\ =K\left({\∫}_0^T{C}_p\left(T\right)dT+{\mathrm{\ΔH}}_M\right)+\frac{{\left({\mathrm{\σ}}_{th}\left(T\right)\right)}^2}{2E\left(T\right)}\end{array}---\left(8\right)$

If known K, C_p(T), E (T), Δ H_Mσ can be sought by formula (8)_th(T):

${\mathrm{\σ}}_{th}\left(T\right)={\[2E\left(T\right)\[W_{TOTAL}-K{\∫}_0^T{C}_p\left(T\right)dT-{\mathrm{K\ΔH}}_M\]\]}^{1/2}---\left(9\right)$

As T < T_mTime: Δ H_M=0, so

${\mathrm{\&sigma;}}_{th}\left(T\right)={\&lsqb;2E\left(T\right)\&lsqb;W_{TOTAL}-K{\&Integral;}_0^T{C}_p\left(T\right)dT\&rsqb;\&rsqb;}^{1/2}---\left(10\right)$

The leading portion equation of wushu (6) and (7) substitute into formula (10) and can obtain:

${\mathrm{\&sigma;}}_{th}\left(T\right)={\&lsqb;\frac{{\left({\mathrm{\&sigma;}}_{th}^0\right)}^2}{E_0}E\left(T\right)\&lsqb;1-\frac{1}{{\&Integral;}_0^{T_m}{C}_p\left(T\right)dT+{\mathrm{\&Delta;H}}_M}{\&Integral;}_0^T{C}_p\left(T\right)dT\&rsqb;\&rsqb;}^{1/2}---\left(11\right)$

In formula (11), σ_th(T) being the strength of materials corresponding at temperature T, E (T) is elastic modelling quantity corresponding at temperature T, For the strength of materials at reference temperature 0 DEG C, E₀For the elasticity modulus of materials at reference temperature 0 DEG C, C_p(T) it is temperature T The level pressure thermal capacitance of lower correspondence, Δ H_MFor heat of fusion, T_mFusing point for material.

Second step, set up the mathematical expression model of intensity relevant to material damage under reference temperature

According to the record of teaching material " fracture theory basis " (Fan Tianyou, Science Press, Beijing, 2003), for flat Flat-shaped crackle, Critical fracture intensityFollowing relation is there is with l:

${\mathrm{\&sigma;}}_0^f={\&lsqb;\frac{E_{l0}{G}_0^f}{2(1-{\mathrm{\&nu;}}^2)l}\&rsqb;}^{1/2}---\left(12\right)$

In formula (12), E_l0、ν、It is respectively the elastic modelling quantity of material original state, Poisson's ratio and fracture under reference temperature Can, l is half length of crackle.

When material damage build-up effect is obvious, it is considered to the material damage accumulation impact on elastic modelling quantity, if in material Crackle is uniformly distributed, then microcrack parameter l and elasticity modulus of materials E_l0Relational expression be:

$E_{l0}=E_0{\&lsqb;1+\frac{16(1-{\mathrm{\&nu;}}^2){\mathrm{Nl}}^3}{3}\&rsqb;}^{-1}---\left(13\right)$

In formula (13), E₀For elastic modelling quantity during material flawless, N is the crackle number in unit volume, i.e. crack density. Micro-crack does not has big impact to Poisson's ratio ν of material.

Owing to high temperature is the cumulative process of a widely distributed microstructure damage and unwise to single crack size Sense, therefore for considering the damage accumulation impact on intensity, utilizes the fracture strength expression formula that formula (12), (13) can be revised:

${\mathrm{\&sigma;}}_0^f={\&lsqb;\frac{E_0{G}_0^f}{2(1-{\mathrm{\&nu;}}^2)l}{\&lsqb;1+\frac{16(1-{\mathrm{\&nu;}}^2){\mathrm{Nl}}^3}{3}\&rsqb;}^{-1}\&rsqb;}^{1/2}---\left(14\right)$

In formula (14),For Critical fracture intensity,For energy to failure, E₀For elastic modelling quantity during material flawless, ν For Poisson's ratio, l is half length of crackle, and N is the crackle number in unit volume.

3rd step, set up superhigh temperature ceramic material heat-damage stiffness of coupling mathematical expression model

Along with the rising of temperature, the high temperature of fragile material is the accumulation of a widely distributed microstructure damage Journey, insensitive to single crack size, high-temperature damage crackle tends to elliposoidal.

As T < T_mTime high temperature fracture intensity expression formula be:

$\begin{array}{c}{\mathrm{\&sigma;}}_{th}\left(T,l\right)={\mathrm{\&sigma;}}_{th}\left(T\right){\mathrm{\&sigma;}}_0^f/{\mathrm{\&sigma;}}_{th}^0\\ ={\&lsqb;\frac{G_0^{f}E\left(T\right)}{2\left(1-{\mathrm{\&nu;}}^2\right)l}\&lsqb;1-\frac{1}{{\&Integral;}_0^{T_m}{C}_p\left(T\right)dT+{\mathrm{\&Delta;H}}_M}{\&Integral;}_0^T{C}_p\left(T\right)dT\&rsqb;{\&lsqb;1+\frac{16\left(1-{\mathrm{\&nu;}}^2\right){\mathrm{Nl}}^3}{3}\&rsqb;}^{-1}\&rsqb;}^{1/2}\end{array}---\left(15\right)$

(15) formula is simplified further:

The elastic modelling quantity recorded by experiment is clearly temperature and the coefficient result of material damage, therefore, experiment records Elastic modelling quantity can be designated as E (T, N, l):

$E(T,N,l)=E\left(T\right){\&lsqb;1+\frac{16(1-{\mathrm{\&nu;}}^2){\mathrm{Nl}}^3}{3}\&rsqb;}^{-1}---\left(16\right)$

Deformed by (16) formula:

$E\left(T\right)=E(T,N,l)\&lsqb;1+\frac{16(1-{\mathrm{\&nu;}}^2){\mathrm{Nl}}^3}{3}\&rsqb;---\left(17\right)$

Wushu (17) substitutes into formula (15) and can obtain, T < T_mTime high temperature fracture intensity expression formula:

${\mathrm{\&sigma;}}_{th}(T,l)={\&lsqb;\frac{G_0^{f}E\left(T,N,l\right)}{2(1-{\mathrm{\&nu;}}^2)l}\&lsqb;1-\frac{1}{{\&Integral;}_0^{T_m}{C}_p\left(T\right)dT+{\mathrm{\&Delta;H}}_M}{\&Integral;}_0^T{C}_p\left(T\right)dT\&rsqb;\&rsqb;}^{1/2}---\left(18\right)$

For plane stress situation:

$G_0^f=\frac{K_{IC}^2}{E_0}---\left(19\right)$

In formula (19), K_ICIt is that material plane strains fracture toughness.Research shows, along with the elevated insult crackle of temperature Tending to elliposoidal, l tends to the radius of ball, then

${\mathrm{\&sigma;}}_{th}(T,l)={\&lsqb;\frac{K_{IC}^{2}E(T,N,l)}{2E_0(1-{\mathrm{\&nu;}}^2){\left(\frac{3V}{4\mathrm{\&pi;}\mathrm{\&alpha;}}\right)}^{1/3}}\&lsqb;1-\frac{1}{{\&Integral;}_0^{T_m}{C}_p\left(T\right)dT+{\mathrm{\&Delta;H}}_M}{\&Integral;}_0^T{C}_p\left(T\right)dT\&rsqb;\&rsqb;}^{1/2}---\left(20\right)$

In formula (20), σ_th(T l) is heat-damage stiffness of coupling, K_ICStraining fracture toughness for material plane, (T, N l) are E Elastic modelling quantity during corresponding at temperature T existence crackle, E₀For elastic modelling quantity during material flawless under reference temperature, ν For Poisson's ratio, C_p(T) it is level pressure thermal capacitance corresponding at temperature T, Δ H_MFor heat of fusion, T_mFor the fusing point of material, V is Single lesion volume, single lesion volume refers to the volume of a damage in test specimen, and α is lesion shape coefficient, in order to Describe the change of crack shape, half long l and the lesion shape factor alpha of crackle can be obtained by laboratory observation, by l and α Can determine major axis and the minor axis length of elliposoidal crackle, thus calculate single elliposoidal lesion volume V.

Embodiment

Below with the superhigh temperature ceramic material heat-damage stiffness of coupling mathematical expression model of formula (20), make pottery with titanium carbide (TiC) As a example by porcelain, implement this material heat-damage stiffness of coupling and be predicted, and the Sensitivity Analysis to intensity relevant parameter.

1, the springform under the experimental data that varies with temperature of elastic modelling quantity of test superhigh temperature ceramic material and reference temperature Amount

The experiment test that elastic modelling quantity varies with temperature uses Chinese patent literature CN 102944466 A disclosed for surpassing Mechanics Performance Testing apparatus and method under high-temperature oxidation environment, are installed to TiC ceramic test piece test on device, close The fire door of high temperature furnace, is heated to different predetermined temperatures, insulation, loads, record load and the experiment number of test specimen elongation According to, by data analysis obtain TiC ceramic material the data that vary with temperature of elastic modulus E (T), depict it Change curve as it is shown in figure 1, in FIG, due to the shortage of elastic modulus E (T) high temperature experimental data, according to existing Elastic modelling quantity is extrapolated by experimental data, in order to next step utilize mathematical expression model prediction TiC ceramic material heat- Damage stiffness of coupling.

Titanium carbide (TiC) ceramic material is shown in Table 1 to the material parameter that heat-damage stiffness of coupling is relevant.

The material parameter of table 1 TiC

Material parameter	Parameter value
		E0(GPa)	444
ν	0.195
		KIC(MPa·m1/2)	3.82
Tm(℃)	3016.85
		ΔHM(cal/mol)	17000
Cp(T)(cal/mol)	11.94+0.23×10-3T-3.53×105T-2+0.45×10-6T2

In upper table, E₀Obtained by experiment, ν, K_IC、T_m、ΔH_M、C_p(T) by consulting handbook, document obtains.

2, by the mathematical expression model of formula (20), the material at a temperature of corresponding with superhigh temperature ceramic material elastic modelling quantity is calculated Material heat-damage stiffness of coupling

The data varied with temperature by the elastic modulus E (T) of Fig. 1, according to the mathematical expression model of formula (20), calculate Material heat-damage stiffness of coupling, obtains the material heat-damage stiffness of coupling σ of prediction_th(T, curve chart l) varied with temperature, As in figure 2 it is shown, Fig. 2, Fig. 3 and Fig. 4 use σ_thRepresent material heat-damage stiffness of coupling σ_th(T,l).Can from Fig. 2 Go out: predictive value coincide preferably with experiment value.So the prediction that this method is to superhigh temperature ceramic material heat-damage stiffness of coupling It is reliable.

Heat-damage stiffness of coupling to the sensitivity of crack size as it is shown on figure 3, Δ σ in figure_thFor intensity increment, Δ l is for splitting The long increment of stricture of vagina half.In Fig. 3, curve a, b, c, d, e, f be respectively T=24 DEG C, T=903 DEG C, T=1502 DEG C, T=2102 DEG C, T=2902 DEG C, the Δ σ of T=3017 DEG C_thThe relation that/Δ l changes with Δ l.

From figure 3, it can be seen that along with the rising of temperature, material heat-damage stiffness of coupling σ_thSensitivity to crack size More and more lower；The sensitivity change with l increase and decrease amplitude, ao l is can be seen that by the variation tendency of curve corresponding to lower temperature Trend, l increasing degree is the least more notable；Reduction amplitude is the biggest more notable.And temperature higher time, material heat-damage coupling Intensity σ_thRelatively low to the sensitivity of crackle size increase Δ l and change is little.

Heat-damage stiffness of coupling to the sensitivity of elastic modelling quantity as shown in Figure 4, Δ σ in figure_thFor intensity increment, Δ E is bullet Property modulus increment.In Fig. 4, curve g, h, i, j, k, l be respectively T=24 DEG C, T=903 DEG C, T=1502 DEG C, T=2102 DEG C, T=2902 DEG C, the Δ σ of T=3017 DEG C_thThe relation that/Δ E changes with Δ E.

From fig. 4, it can be seen that along with the rising of temperature, material heat-damage stiffness of coupling σ_thSensitivity to elastic modelling quantity Increasingly stronger, i.e. improve elastic modelling quantity during high temperature to material heat-damage stiffness of coupling σ_thImprove effect obvious；From higher temperatures The variation tendency of the curve that degree is corresponding is it can be seen that along with the increase of elastic modelling quantity amplification Δ E, material heat-damage coupling is strong Degree σ_thIts sensitivity is gradually lowered；And temperature relatively low time, material heat-damage stiffness of coupling σ_thElastic modelling quantity is increased The sensitivity of width Δ E is relatively low and change is little.

Compared with prior art, the invention have the advantage that

(1) C is passed through_p(T) temperature is separated with defective effect, and C_p(T) can obtain from Materials Handbook easily；

(2) energy to failure G_fVariation with temperature trend is more complicated, and experiment is difficult to obtain, and this mathematical expression model only uses reference At a temperature of energy to failure, avoid the dependence to its temperature dependency；

(3) mathematical expression model preferably discloses the Physical Mechanism controlling elevated temperature strength；

(4) it is applicable to whole temperature history；

(5) can convert to various situations easily, when the accumulation not considering temperature impact, not considering damage and the change of shape Florence Griffith strength model it is during change.

Claims (1)

1. superhigh temperature ceramic material heat-damage stiffness of coupling indirect measurement method, according to the superhigh temperature ceramic material springform recorded Measure the elastic modelling quantity under the experimental data and reference temperature varied with temperature, set up material heat-damage coupling under different temperatures Intensity and the mathematical expression model of elastic modelling quantity, calculate the material heat at a temperature of corresponding with superhigh temperature ceramic material elastic modelling quantity -damage stiffness of coupling；It is characterized in that, set up material heat-damage stiffness of coupling and the mathematical expression of elastic modelling quantity under different temperatures The step of model includes:

The first step, set up the mathematical expression model of intensity and elastic modelling quantity under the different temperatures of material initial damage state and be

${\mathrm{\&sigma;}}_{th}\left(T\right)={\&lsqb;\frac{{\left({\mathrm{\&sigma;}}_{th}^0\right)}^2}{E_0}E\left(T\right)\&lsqb;1-\frac{1}{{\&Integral;}_0^{T_m}{C}_p\left(T\right)dT+{\mathrm{\&Delta;H}}_M}{\&Integral;}_0^T{C}_p\left(T\right)dT\&rsqb;\&rsqb;}^{1/2}$

In formula, σ_th(T) being the strength of materials corresponding at temperature T, E (T) is elastic modelling quantity corresponding at temperature T,For The strength of materials at reference temperature 0 DEG C, E₀For the elasticity modulus of materials at reference temperature 0 DEG C, C_p(T) it is at temperature T Corresponding level pressure thermal capacitance, Δ H_MFor heat of fusion, T_mFusing point for material；

Second step, the mathematical expression model setting up intensity relevant to material damage under reference temperature are

${\mathrm{\&sigma;}}_0^f={\&lsqb;\frac{E_0{G}_0^f}{2(1-{\mathrm{\&nu;}}^2)l}{\&lsqb;1+\frac{16(1-{\mathrm{\&nu;}}^2){\mathrm{Nl}}^3}{3}\&rsqb;}^{-1}\&rsqb;}^{1/2}$

In formula,For Critical fracture intensity,For energy to failure, E₀For elasticity during material flawless under reference temperature Modulus, ν is Poisson's ratio, and l is half length of crackle, and N is the crackle number in unit volume；

3rd step, set up superhigh temperature ceramic material heat-damage stiffness of coupling mathematical expression model be

${\mathrm{\&sigma;}}_{th}(T,l)={\&lsqb;\frac{K_{IC}^{2}E(T,N,l)}{2E_0(1-{\mathrm{\&nu;}}^2){\left(\frac{3V}{4\mathrm{\&pi;}\mathrm{\&alpha;}}\right)}^{1/3}}\&lsqb;1-\frac{1}{{\&Integral;}_0^{T_m}{C}_p\left(T\right)dT+{\mathrm{\&Delta;H}}_M}{\&Integral;}_0^T{C}_p\left(T\right)dT\&rsqb;\&rsqb;}^{1/2}$

In formula, σ_th(T l) is heat-damage stiffness of coupling, K_ICStraining fracture toughness for material plane, (T, N l) are E Elastic modelling quantity during corresponding at temperature T existence crackle, E₀For elastic modelling quantity during material flawless under reference temperature, ν For Poisson's ratio, V is single lesion volume, and α is lesion shape coefficient, C_p(T) it is level pressure thermal capacitance corresponding at temperature T, ΔH_MFor heat of fusion, T_mFusing point for material.