CN102589995B - Method for forecasting uniaxial constitutive relation of material according to press hardness - Google Patents

Abstract

The invention discloses a method for forecasting the uniaxial constitutive relation of material according to press hardness, comprising the following steps: in a press hardness detecting system consisting of a press head loading unit, a deformation detecting unit and a data processing unit, the press head loading unit presses material to be detected by press heads with different appearances, and the deformation detecting unit detects the corresponding deformation of the material to be detected and inputs into the data processing unit to obtain the constitutive parameters E, sigma y and n of forecasting material, so that the portable measurement of the uniaxial constitutive relation of the material and the serviced structural part can be realized by the simple method for forecasting the uniaxial constitutive relation of the material according to the press hardness.

Description

A kind of method of penetration hardness prediction material single shaft constitutive relation

Technical field:

The present invention relates to the metal material Performance Detection, especially in the field of detecting of using as a servant construction material single shaft constitutive relation.

Background technology:

Uniaxial stress-strain curve (being constitutive relation) is as the most basic material mechanical performance, plays an important role for design and the military service of engineering component.The common way of obtaining material single shaft constitutive relation is to take starting material processing or carry out tension test behind the engineering component intercepting standard tensile sample in the laboratory.Yet the military service engineering component for through damaged, problem such as aging does not allow therefrom to intercept standard sample, thereby makes that traditional stretching test method can't be used for measuring in the single shaft constitutive relation of labour member.On the other hand, for welded structure, the material single shaft constitutive relation in weld seam, heat-affected zone, mother metal district has larger difference usually, and traditional stretching test method also is not easy to realize the Study on dispersity of welding material constitutive relation and weld assembly is stressed and the explication de texte of distortion.At above-mentioned situation, still there is not the portable detection technique of the harmless or little damage that can be used for the prediction of material single shaft constitutive relation at present.

The penetration hardness test is that the certain load of a kind of usefulness is pressed into measured material with the pressure head of stipulating, compares the method for measured material soft or hard with the size of material surface local plastic deformation.Hardness number is characterized by the ratio of maximum test force with the corresponding area of indentation.Because pressure head, load and the difference of load duration, penetration hardness mainly comprises several types such as Brinell hardness, Rockwell's hardness, Vickers hardness.Traditional penetration hardness test is simple, comprise that instrumentation products such as Brinell tester, Rockwell hardometer, Vickers, microhardness testers, multi-usage sclerometer and handhold portable sclerometer continue to bring out, but this series products only can be used for the measurement of material hardness.In fact, the indentation test process has contained the abundant information of measured material bullet, plastic yield behavior, by this traditional experiment method is carried out technological innovation, maybe can realize little damage of material single shaft constitutive relation, portable measurement.Oliver and Pharr, Oliver W C, Pharr G M.An improved technique for determining hardness and elastic modulus using load and displacement sensing indention experiments[J] .Journal of Materials Research, 1992,7:1564-1583. test the ram load P-compression distance h curve that add in uninstall process by continuous recording at penetration hardness based on the Elastic Contact theory, proposed classical elasticity modulus of materials and be pressed into measuring method.The typical loading of pressing in P-degree of depth h curve that Fig. 1 obtains for the penetration hardness test.This technical scheme through type (1) is found the solution the elastic modulus E of material.

$\left\{\begin{array}{c}{E}_r=\frac{\sqrt{\mathrm{\π}}}{2\mathrm{\β}}\frac{S}{\sqrt{A_c}}\\ \frac{1}{E_r}=\frac{1-v^2}{E}+\frac{1-v_{\mathrm{ind}}^2}{E_{\mathrm{ind}}}\\ A_c=f\left(h_c\right)\\ h_c=h_m-\mathrm{\μ}\frac{P_m}{S}\end{array}\right.---\left(1\right)$

Wherein, β, μ are the constant relevant with indenter shape, and S is the Elastic Contact rigidity among Fig. 1, and v is the Poisson ratio of sample, E _IndAnd v _IndBe respectively elastic modulus and the Poisson ratio of pressure head, A _cBe the projected area of pressure head and the sample contact region of maximum load correspondence, by contact degree of depth h _cContact with it.

For the material that satisfies Hollomon power law hardening Plastic, its stretching trus stress σ and true strain ε satisfy formula (2):

$\left\{\begin{array}{cc}\mathrm{\σ}=\mathrm{E\ϵ}& \mathrm{\σ}\≤{\mathrm{\σ}}_y\\ \mathrm{\σ}={{\mathrm{\σ}}_y}^{(1-n)}{E}^n{\mathrm{\ϵ}}_p^n& \mathrm{\σ}>{\mathrm{\σ}}_y\end{array}\right.---\left(2\right)$

In the formula, E is elastic modulus, σ _yBe the reference yield stress, n is the hardening Plastic index.

Be pressed into situation for the circular cone pressure head, think that it (is P=Ch that its load p-degree of depth h loading curve meets secondary power law feature ²), by seeking loading coefficient C with characterizing stress σ _rSingle corresponding relation, thereby two pressure head method Bucaille J L have been proposed, Stauss S, Fellder E, Michler J.Determination of plastic properties of metals by instrumented indentation using different sharp indenters.Acta Materialia, 2003,51:1663-1678. material constitutive parameter σ _y, finding the solution by formula (3) of n undertaken.

$\left\{\begin{array}{c}\frac{C}{{\mathrm{\σ}}_r}=c_1\·{\left(\ln \frac{E_r}{{\mathrm{\σ}}_r}\right)}^3+c_2\·{\left(\ln \frac{E_r}{{\mathrm{\σ}}_r}\right)}^2+c_3\·\ln \frac{E_r}{{\mathrm{\σ}}_r}+c_4\\ {\mathrm{\σ}}_r={\mathrm{\σ}}_y\·{(1+\frac{E}{{\mathrm{\σ}}_y}\·{\mathrm{\ϵ}}_r)}^n\end{array}\right.---\left(3\right)$

Be pressed into situation for spherical indenter, attempt the load p in the indentation test and compression distance h with the stress in the uniaxial tensile test, strain facies correspondence, thereby directly from load-compression distance curve, try to achieve plasticity parameter σ _y

In the prior art scheme, asking for of elastic modulus needs by complete load p-degree of depth h unloading segment calibration curve information, and particularly the precision of Elastic Contact rigidity is difficult to effective assurance.Two pressure head methods for circular cone is pressed into characterize stress σ _rDetermine not only need by a large amount of numerical analyses, on the other hand, load p-degree of depth h load test curve is not in strict conformity with secondary power law feature, thus the dispersiveness that causes loading coefficient C is bigger.Be pressed into situation for sphere, it is big and precision of prediction is lower to seek the direct corresponding relation difficulty of the same drawing stress of loading of pressing in P, degree of depth h, strain, only can obtain the elastic mould value of material, the single shaft constitutive relation of unpredictable material.

Summary of the invention

Deficiency in view of the existing program of above statement, the object of the present invention is to provide a kind of method of penetration hardness prediction material single shaft constitutive relation, make it the method prediction material single shaft constitutive relation by traditional penetration hardness, Hardness Prediction meets the material single shaft constitutive relation of power law sclerosis feature, is convenient to use at portable instrument.

To achieve these goals, technical solution of the present invention is:

A kind of method of penetration hardness prediction material single shaft constitutive relation, have the pressure head loading unit, be out of shape in the penetration hardness detection system that detects unit and data processing unit formation, the pressure head loading unit adopts different profile pressure heads to be pressed into measured material, and distortion detects unit (data acquisition unit) and detects measured material and be out of shape accordingly and be input to data processing unit to obtain constitutive parameter E, the σ of prediction material _y, n, and calculate to obtain the single shaft constitutive relation by following formula:

$\left\{\begin{array}{cc}\mathrm{\σ}=\mathrm{E\ϵ}& \mathrm{\σ}\≤{\mathrm{\σ}}_y\\ \mathrm{\σ}={{\mathrm{\σ}}_y}^{(1-n)}{E}^n{\mathrm{\ϵ}}_p^n& \mathrm{\σ}>{\mathrm{\σ}}_y\end{array}\right.,$

E is elastic modulus, σ _yBe the reference yield stress, n is the hardening Plastic index,

In the formula:

σ is the stretching trus stress, and ε is true strain; And:

1), when described pressure head loading unit adopts spherical indenter, the spherical indenter that described different profile pressure heads are two different-diameters, described data processing unit is according to gained spherical indenter penetration hardness H _{S_D/F}Try to achieve material constitutive parameter E, σ by following formula _y, n:

$\left\{\begin{array}{c}\left\{\begin{array}{c}\frac{E}{H_{S\_D/F}}=k_{1\_D/F}{\left(\frac{E}{{\mathrm{\σ}}_y}\right)}^{k_{2\_D/F}}\\ k_{1\_D/F}={\mathrm{\α}}_{11\_D/F}n+{\mathrm{\α}}_{12\_D/F}\\ k_{2\_D/F}={\mathrm{\α}}_{21\_D/F}{n}^2+{\mathrm{\α}}_{22\_D/F}n+{\mathrm{\α}}_{23\_D/F}\end{array}\right.\\ \frac{E}{H_{S\_D/F}}=k_{3\_D/F}{\left(\frac{W_t}{W_e}\right)}^2+k_{4\_D/F}\left(\frac{W_t}{W_e}\right)+k_{5\_D/F}\end{array}\right.$

In the formula: W _t/ W _eFor being pressed into total work W in the loading of pressing in P-degree of depth h curve continuously in the spherical indenter penetration hardness test _tWith elastic unloading merit W _eRatio, k _{1_D/F}, k _{2_D/F}, k _{3_D/F}, k _{4_D/F}, k _{5_D/F}, α _{11_D/F}, α _{12_D/F}, α _{21_D/F}, α _{22_D/F}, α _{23_D/F}Be the undetermined parameter corresponding to different-diameter spherical indenter different tests power.

2), when described pressure head loading unit adopts the circular cone pressure head, the circular cone pressure head that described different profile pressure heads are two different cone angle, described data processing unit is according to gained circular cone pressure head penetration hardness H _{C_ θ}Try to achieve material constitutive parameter E, σ by following formula _y, n:

$\left\{\begin{array}{c}\left\{\begin{array}{c}\frac{E}{H_{C\_\mathrm{\θ}}}=k_{1\_\mathrm{\θ}}{\left(\frac{E}{{\mathrm{\σ}}_y}\right)}^{k_{2\_\mathrm{\θ}}}\\ k_{1\_\mathrm{\θ}}={\mathrm{\β}}_{11\_\mathrm{\θ}}n+{\mathrm{\β}}_{12\_\mathrm{\θ}}\\ k_{2\_\mathrm{\θ}}={\mathrm{\β}}_{21\_\mathrm{\θ}}n+{\mathrm{\β}}_{22\_\mathrm{\θ}}\end{array}\right.\\ \frac{E}{H_{C\_\mathrm{\θ}}}=k_{3\_\mathrm{\θ}}\left(\frac{W_t}{W_e}\right)+k_{4\_\mathrm{\θ}}\end{array}\right.$

In the formula: θ represents the awl half-angle of circular cone pressure head, W _t/ W _eFor being pressed into total work W in the loading of pressing in P-degree of depth h curve continuously in the circular cone pressure head penetration hardness test _tWith elastic unloading merit W _eRatio, k _{1_ θ}, k _{2_ θ}, k _{3_ θ}, k _{4_ θ}, β _{11_ θ}, β _{12_ θ}, β _{21_ θ}, β _{22_ θ}Be the undetermined parameter corresponding to difference awl half-angle conical indenter.

Description of drawings:

Fig. 1 is typical loading of pressing in P-degree of depth h curve map.

Fig. 2 is the synoptic diagram of implementation of the present invention.

Fig. 3 is the loading of pressing in-depth curve figure of embodiment of the invention T225NG titanium alloy sample.

Fig. 4 is this structure of embodiment of the invention T225NG titanium alloy single shaft curve prediction result schematic diagram.

Embodiment

The invention will be further described below in conjunction with accompanying drawing.

The present invention is based on finite element numerical simulation and dimensional analysis method and proposed respectively technical know-how system based on spherical indenter, circular cone pressure head penetration hardness prediction material single shaft constitutive relation.

A) spherical indenter penetration hardness prediction material single shaft constitutive relation

Finite element numerical simulation and dimensional analysis result show spherical indenter penetration hardness H _{S_D/F}With material constitutive parameter E, σ _y, n satisfies following relation:

$\left\{\begin{array}{c}\left\{\begin{array}{c}\frac{E}{H_{S\_D/F}}=k_{1\_D/F}{\left(\frac{E}{{\mathrm{\σ}}_y}\right)}^{k_{2\_D/F}}\\ k_{1\_D/F}={\mathrm{\α}}_{11\_D/F}n+{\mathrm{\α}}_{12\_D/F}\\ k_{2\_D/F}={\mathrm{\α}}_{21\_D/F}{n}^2+{\mathrm{\α}}_{22\_D/F}n+{\mathrm{\α}}_{23\_D/F}\end{array}\right.\\ \frac{E}{H_{S\_D/F}}=k_{3\_D/F}{\left(\frac{W_t}{W_e}\right)}^2+k_{4\_D/F}\left(\frac{W_t}{W_e}\right)+k_{5\_D/F}\end{array}\right.---\left(4\right)$

Because the spherical indenter penetration hardness is relevant with test power with the pressure head diameter, so D represents different pressure head diameters and test power with F in the formula (4), correspondingly, parameter

Be the spherical indenter penetration hardness value of different scales.W _t/ W _eFor being pressed into total work W in the loading of pressing in P-degree of depth h curve continuously in the spherical indenter penetration hardness test _tWith elastic unloading merit W _eRatio.Parameter corresponding to different-diameter spherical indenter different tests power in the formula (4) sees Table 1.

Table 1: the parameter value in the formula (4)

In technical solution of the present invention, the spherical indenter penetration hardness of two kinds of different scales of employing just can be doped constitutive parameter E, the σ of measured material or member by formula (4) _y, n, and then determine its single shaft constitutive relation by formula (2).

B) circular cone pressure head penetration hardness prediction material single shaft constitutive relation

Finite element numerical simulation and dimensional analysis result show circular cone pressure head penetration hardness H _{C_ θ}With material constitutive parameter E, σ _y, n satisfies following relation:

$\left\{\begin{array}{c}\left\{\begin{array}{c}\frac{E}{H_{C\_\mathrm{\θ}}}=k_{1\_\mathrm{\θ}}{\left(\frac{E}{{\mathrm{\σ}}_y}\right)}^{k_{2\_\mathrm{\θ}}}\\ k_{1\_\mathrm{\θ}}={\mathrm{\β}}_{11\_\mathrm{\θ}}n+{\mathrm{\β}}_{12\_\mathrm{\θ}}\\ k_{2\_\mathrm{\θ}}={\mathrm{\β}}_{21\_\mathrm{\θ}}n+{\mathrm{\β}}_{22\_\mathrm{\θ}}\end{array}\right.\\ \frac{E}{H_{C\_\mathrm{\θ}}}=k_{3\_\mathrm{\θ}}\left(\frac{W_t}{W_e}\right)+k_{4\_\mathrm{\θ}}\end{array}\right.---\left(5\right)$

Because the circular cone pressure head has the self similarity feature, thus the be not put to the test influence of power size of circular cone pressure head penetration hardness, only the angle with the circular cone pressure head is relevant, so the middle θ of formula (5) represents the awl half-angle of circular cone pressure head, correspondingly, parameter

Be the circular cone pressure head penetration hardness value under the awl half-angle θ.W _t/ W _eFor being pressed into total work W in the loading of pressing in P-degree of depth h curve continuously in the circular cone pressure head penetration hardness test _tWith elastic unloading merit W _eRatio.Parameter corresponding to difference awl half-angle circular cone pressure head in the formula (5) sees Table 2.

Table 2: the parameter value in the formula (5)

Awl half-angle θ	β 11_θ	β 12_θ	β 21_θ	β 22_θ	k 3_θ	k 4_θ
							60°	0.9299	0.6560	-0.7514	0.8730	3.0877	4.1088
70.3°	2.9748	0.1690	-0.713	0.8448	5.2813	4.7288

In technical solution of the present invention, the circular cone pressure head penetration hardness of two kinds of different angles of employing just can be doped constitutive parameter E, the σ of measured material or member by formula (5) _y, n, and then determine its single shaft constitutive relation by formula (2).

Embodiment

Adopting the awl half-angle respectively is that the circular cone pressure head of 60 ° and 70.3 ° carries out penetration hardness to same T225NG titanium alloy sample and tests and ask for its this structure of single shaft curve.Fig. 3 is the loading of pressing in-depth curve of the T225NG titanium alloy sample that obtained by 60 ° and 70.3 ° of conical indenter indentation tests respectively.Flow chart of data processing is: at first by taking out maximum load P in loading of pressing in-depth curve _MaxAnd corresponding maximum compression distance h _Max, and try to achieve Elastic Contact rigidity S by the unloading segment curve, calculate the degree of depth that contacts of pressure head and sample then

Thereby the conical indenter penetration hardness corresponding to different cone angle is

The hardness H corresponding to two conical indenters that will obtain afterwards _{C_ θ}Substitution formula (5) is tried to achieve constitutive parameter E, σ _y, n, determined the single shaft constitutive relation of T225NG titanium alloy sample at last by formula (2).Fig. 4 is the comparison with this structure curve that is obtained by traditional tension test of this structure of T225NG titanium alloy single shaft curve of technical solution of the present invention prediction.

Claims (3)

1. the method for penetration hardness prediction material single shaft constitutive relation, have the pressure head loading unit, be out of shape in the penetration hardness detection system that detects unit and data processing unit formation, the pressure head loading unit adopts different profile pressure heads to be pressed into measured material, and distortion detects the unit and detects measured material and be out of shape accordingly and be input to data processing unit to obtain constitutive parameter E, the σ of prediction material _y, n, and calculate to obtain the single shaft constitutive relation by following formula:

$\left\{\begin{array}{cc}\mathrm{\σ}=\mathrm{E\ϵ}& \mathrm{\σ}\≤{\mathrm{\σ}}_y\\ \mathrm{\σ}={{\mathrm{\σ}}_y}^{(1-n)}{E}^n{\mathrm{\ϵ}}_p^n& \mathrm{\σ}>{\mathrm{\σ}}_y\end{array}\right.,$

E is elastic modulus, σ _yBe the reference yield stress, n is the hardening Plastic index,

In the formula:

σ is the stretching trus stress, and ε is true strain; And:

1), when described pressure head loading unit adopts spherical indenter, the spherical indenter that described different profile pressure heads are two different-diameters, described data processing unit is according to gained spherical indenter penetration hardness H _{S_D/F}Try to achieve material constitutive parameter E, σ by following formula _y, n:

$\left\{\begin{array}{c}\left\{\begin{array}{c}\frac{E}{H_{S\_D/F}}=k_{1\_D/F}{\left(\frac{E}{{\mathrm{\σ}}_y}\right)}^{k_{2\_D/F}}\\ k_{1\_D/F}={\mathrm{\α}}_{11\_D/F}n+{\mathrm{\α}}_{12\_D/F}\\ k_{2\_D/F}={\mathrm{\α}}_{21\_D/F}{n}^2+{\mathrm{\α}}_{22\_D/F}n+{\mathrm{\α}}_{23\_D/F}\end{array}\right.\\ \frac{E}{H_{S\_D/F}}=k_{3\_D/F}{\left(\frac{W_t}{W_e}\right)}^2+k_{4\_D/F}\left(\frac{W_t}{W_e}\right)+k_{5\_D/F}\end{array}\right.$

In the formula: W _t/ W _eFor being pressed into total work W in the loading of pressing in P-degree of depth h curve continuously in the spherical indenter penetration hardness test _tWith elastic unloading merit W _eRatio, k _{1_D/F}, k _{2_D/F}, k _{3_D/F}, k _{4_D/F}, k _{5_D/F}, α _{11_D/F}, α _{12_D/F}, α _{21_D/F}, α _{22_D/F}, α _{23_D/F}Be the undetermined parameter corresponding to different-diameter spherical indenter different tests power;

2), when described pressure head loading unit adopts the circular cone pressure head, the circular cone pressure head that described different profile pressure heads are two different cone angle, described data processing unit is according to gained circular cone pressure head penetration hardness H _{C_ θ}Try to achieve material constitutive parameter E, σ by following formula _y, n:

$\left\{\begin{array}{c}\left\{\begin{array}{c}\frac{E}{H_{C\_\mathrm{\θ}}}=k_{1\_\mathrm{\θ}}{\left(\frac{E}{{\mathrm{\σ}}_y}\right)}^{k_{2\_\mathrm{\θ}}}\\ k_{1\_\mathrm{\θ}}={\mathrm{\β}}_{11\_\mathrm{\θ}}n+{\mathrm{\β}}_{12\_\mathrm{\θ}}\\ k_{2\_\mathrm{\θ}}={\mathrm{\β}}_{21\_\mathrm{\θ}}n+{\mathrm{\β}}_{22\_\mathrm{\θ}}\end{array}\right.\\ \frac{E}{H_{C\_\mathrm{\θ}}}=k_{3\_\mathrm{\θ}}\left(\frac{W_t}{\mathrm{We}}\right)+k_{4\_\mathrm{\θ}}\end{array}\right.$

In the formula: θ represents the awl half-angle of circular cone pressure head, W _t/ W _eFor being pressed into total work W in the loading of pressing in P-degree of depth h curve continuously in the circular cone pressure head penetration hardness test _tWith elastic unloading merit W _eRatio, k _{1_ θ}, k _{2_ θ}, k _{3_ θ}, k _{4_ θ}, β _{11_ θ}, β _{12_ θ}, β _{21_ θ}, β _{22_ θ}Be the undetermined parameter corresponding to difference awl half-angle conical indenter.

2. the method for a kind of penetration hardness prediction material single shaft constitutive relation according to claim 1 is characterized in that the diameter of the spherical indenter of two different-diameters is respectively 2.5mm and 5mm when adopting spherical indenter.

3. the method for a kind of penetration hardness prediction material single shaft constitutive relation according to claim 1 is characterized in that the awl half-angle of the circular cone pressure head of two different cone angle is respectively 60 ° and 70.3 ° when adopting the circular cone pressure head.

Images