CN104165814B - Vickers indentation based material elastoplasticity instrumented indentation test method - Google Patents

Abstract

The invention discloses an instrumented indentation test method for elastic-plastic parameters of metal materials based on Vickers indentation. The method uses a Vickers indenter to instrumentally indent the metal material to obtain a load-displacement curve and Vickers indentation to determine the strain hardening of the metal material. Index n, elastic modulus E, conditional yield strength σ _0.2 and strength limit σ _b . Compared with the instrumented indentation test method using two or more pyramidal indenters with different cone vertex angles, this method only uses a single Vickers indenter to perform instrumented indentation tests on metal materials and supplemented by Vickers indentation geometric parameters The test can determine the strain hardening exponent n, elastic modulus E, conditional yield strength σ _0.2 and strength limit σ _b of the metal material, avoiding the need to separately design and process non-standard pyramids with different cone apex angles than the standard cone indenter before the test The problem of the indenter, as well as the need to replace the indenter during the test and the resulting problem of recalibration of the instrument compliance, improves the test efficiency.

Description

Instrumented indentation test method for elastic-plastic parameters of materials based on Vickers indentation

technical field

The invention belongs to the field of testing mechanical properties of materials. Specifically, it relates to a method for testing strain hardening exponent, elastic modulus, conditional yield strength σ _0.2 and strength limit σ _b of metal materials by using an instrumented indenter and a Vickers indenter.

Background technique

The instrumented indentation test technology obtains the indentation load-displacement curve by synchronously measuring the indentation load acting on the diamond indenter and the indentation depth of the diamond indenter into the surface of the tested material in real time. The dimensionless functional relationship between the mechanical property parameters of the measured material can identify many mechanical property parameters of the measured material.

The instrumented indentation test of the elastic modulus of materials mainly includes the "Oliver-Pharr method" or "slope method" proposed by W.C.Oliver and G.M.Pharr and the "Ma Dejun method" or "pure energy method" proposed by Ma Dejun. The theoretical basis of the "slope method" is the theory of small deformation elasticity. Since the plastic behavior and large geometric deformation of the measured material under the action of the indenter are not considered, the "slope method" is applied to the measured material with a low strain hardening index. The test results seriously deviate from the true value of elastic modulus. The "pure energy method" takes into account the nonlinearity of material, geometry and contact boundary conditions, so the test accuracy of its elastic modulus is higher than that of the "slope method". Nevertheless, the "pure energy method" still has a certain theoretical test error, which is due to the unknown strain hardening exponent of the tested material, so trying to identify the strain hardening exponent of the tested material is the key to improving the elastic modulus of the material. The only valid way to achieve precision.

The instrumented indentation test of material strain hardening index and yield strength currently has a single ball indenter indentation method based on a spherical indenter and a multiple cone indenter indentation method based on different cone apex angles. The difficulty encountered in the indentation method is that the geometrical machining accuracy of spherical indenters with a radius of several or tens of microns is difficult to meet the test requirements. Therefore, the instrumented indentation test method based on the strain hardening exponent and yield strength of materials based on spherical indenters It is difficult to make a difference in practical application or engineering. The application of multiple cone indenter indentation method does not have the problem of indenter manufacturing, but the test process requires the replacement of pyramidal indenters with different cone apex angles, and the flexibility of the instrument needs to be re-calibrated. It is difficult and time-consuming, so it is less efficient to use the multi-cone indenter indentation method for testing.

Aiming at the problems existing in the instrumented indentation test of elastic-plastic parameters of metal materials at present, the present invention proposes an instrument based on Vickers indentation for metal material strain hardening exponent, modulus of elasticity, conditional yield strength σ _0.2 and strength limit σ _b Press-in test method.

Contents of the invention

The object of the present invention is to provide a kind of metal material elastoplastic parameter instrumentation indentation test method based on Vickers indentation, utilize this method to determine the elastoplastic parameter of metal material including strain hardening exponent, modulus of elasticity, conditional yield strength σ _0.2 and the strength limit σ _b . Compared with the instrumented indentation test method using two or more pyramidal indenters with different cone vertex angles, this method only uses a single Vickers indenter to perform instrumented indentation tests on metal materials and supplemented by Vickers indentation geometric parameters The test can determine the strain hardening exponent n, elastic modulus E, conditional yield strength σ _0.2 and strength limit σ _b of the metal material, avoiding the need to separately design and process non-standard pyramids with different cone apex angles than the standard cone indenter before the test The problem of the indenter, as well as the need to replace the indenter during the test and the resulting problem of recalibration of the instrument compliance, improves the test efficiency.

In order to achieve the above object, the present invention adopts the following technical solutions:

An instrumented indentation test method for elastoplastic parameters of metal materials based on Vickers indentation. The method uses a single Vickers indenter to indent the metal material with the load-displacement curve and indentation to determine the strain hardening index and elastic modulus of the metal material. yield strength σ _0.2 and strength limit σ _b ; firstly, the ratio of the median distance to the nominal median distance of the Vickers indentation and the instrumented indentation specific work were used to determine the strain hardening exponent of the metal material; secondly, the instrumented indentation Determine the elastic modulus of the metal material by using the specific work of indentation, the nominal hardness of instrumented indentation, and the strain hardening index obtained from the test; finally, the elastic modulus and strain hardening index of the metal material are determined by using the specific work of indentation, the nominal hardness of instrumented indentation, and the measured strain hardening index Determine the conditional yield strength σ _0.2 and strength limit σ _b of metallic materials. Specifically include the following steps:

1) Use an instrumented indenter and a diamond Vickers indenter to implement an instrumented indentation test with a maximum indentation load of P _m on the material to be tested to obtain an indentation load-displacement curve, and use this curve to determine the diamond Vickers indentation. The maximum indentation depth h _m of the head, the nominal hardness H _n =P _m /A(h _m ), where A(h _m ) is the cross-sectional area of the diamond Vickers indenter corresponding to the maximum indentation depth, when the diamond is not considered When the Vickers indenter tip is blunted When considering the passivation of the tip of the diamond Vickers indenter, A(h _m ) should be determined by the area function A(h) of the diamond Vickers indenter, that is

2) Calculate the indentation loading work W _t and unloading work W _e by integrating the loading curve and unloading curve in the load-displacement curve relationship respectively, and calculate the indentation specific work W _e /W _t on this basis;

3) Measure the distances from the center of the Vickers indentation to the boundaries of the four indentations: d ₁ , d ₂ , d ₃ and d ₄ , and determine the middle distance d=(d ₁ +d ₂ +d ₃ +d ₄ )/4 and its ratio d/d _n to the nominal median distance d _n =h _m tan68°;

4) According to the relationship between instrumented indentation specific work W _e /W _t and d/d _n under four different hardening indices (n ₁ =0, n ₂ =0.15, n ₃ =0.30, n ₄ =0.45) (the values of polynomial coefficients a _ij (i=1,...,4; j=0,1,2) are listed in Table 1) determine respectively when i gets 1,2,3,4 corresponding (d/d _n ) the value of _i , and then determine n′ according to the Lagrangian interpolation formula:

${\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\underset{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{\overset{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; \}</span>$

Further determine the strain hardening exponent n of the tested material according to the non-negative principle:

n=max{n',0}

Table 1. Values of polynomial coefficients a _ij (i=1,...,4; j=0,1,2)

5) According to the relationship between the instrumented indentation specific work W _e /W _t and the ratio H _n /E _c under four different hardening exponents n _i (i=1, 2, 3, 4) (the value of polynomial coefficient b _ij (i=1, ..., 4; j=0, ..., 6) is listed in table 2) determine respectively when i gets 1,2,3,4 corresponding (H _n /E _c ) _i value, and then use the Lagrange interpolation formula to determine H _n /E _c :

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; i</span>}}\underset{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{\overset{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$

Further determine the combined elastic modulus E _c of the tested material and the diamond Vickers indenter according to the instrumented indentation nominal hardness H _n and the ratio H _n /E _c :

E _c ＝H _n /(H _n /E _c )

And the elastic modulus E of the tested material:

$\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1.32</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ]</span>$

Among them, the elastic modulus E _i of the diamond Vickers indenter = 1141GPa, Poisson's ratio v _i = 0.07, and the Poisson's ratio v of the tested material can be determined according to the material manual;

Table 2. Values of polynomial coefficients b _ij (i=1,...,4;.j=0,...,6)

6) According to 4 different hardening exponents n _i (i=1, 2, 3, 4) and 3 different ratios of the tested material to the plane strain modulus of elasticity of the diamond indenter η _j (j=1, 2, 3) (η ₁ = 0.0671, η ₂ = 0.1917, η ₃ = 0.3834) The ratio relationship between the instrumented indentation specific work W _e /W _t and the yield strength to the nominal hardness (the value of polynomial coefficient c _ijk (i=1,...,4; j=1,2,3; k=0,...,6) is listed in table 3) determine respectively that i gets 1,2, 3, 4, j take the corresponding (σ _y /H _n ) _ij (i=1,...,4; j=1, 2, 3) value when 1, 2, 3, and then according to and η _j (j=1, 2, 3) are determined by the Lagrangian interpolation formula σ _y /H _n :

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \{</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; ij</span>}}\underset{\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; \}</span>\underset{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{\overset{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$

Further determine the yield strength σ _y of the tested material according to the instrumented indentation nominal hardness H _n and the ratio σ _y /H _n :

σ _y =H _n (σ _y /H _n )

And determine the conditional yield strength σ _0.2 of the tested material by the relational formula σ _0.2 =σ _y ^1-n [σ _0.2 +0.002E] ⁿ ;

Table 3. Values of polynomial coefficients c _ijk (i=1,...,4; j=1,2,3; k=0,...,6)

7) Calculate ε _y = σ _y /E, and use the relation Determine ε _b , and finally determine the strength limit σ _b of the tested material:

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; v\&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; ></span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\end{array}\right.$

Wherein, in step 5), if the Poisson's ratio of the tested material cannot be determined by the material manual, the value is 0.3.

Compared with the instrumented indentation test method using two or more pyramidal indenters with different cone apex angles, the present invention only uses a single Vickers indenter to implement instrumented indentation tests on metal materials, supplemented by Vickers indentation geometric parameters The test can determine the strain hardening exponent n, elastic modulus E, conditional yield strength σ _0.2 and strength limit σ _b of the metal material, avoiding the need to separately design and process non-standard pyramids with different cone apex angles than the standard cone indenter before the test The problem of the indenter, as well as the need to replace the indenter during the test and the resulting problem of recalibration of the instrument compliance, improves the test efficiency.

Description of drawings:

Figure 1a is a schematic diagram of the Vickers indentation in the case of bulging;

Figure 1b is a schematic diagram of the Vickers indentation under subsidence;

Fig. 2 is a schematic diagram of Vickers indenter;

Figure 3 is a schematic diagram of instrumented press-in loading and unloading curves and loading and unloading work;

Fig. 4a is corresponding to n=0, and _n takes _0.0671 , _0.1917 and 0.3834 three numerical values respectively _Hn /Er-We/Wt relationship diagram;

Fig. 4b is the _Hn /Er-We/Wt relationship diagram corresponding to _n =0.15, and _n takes _0.0671 , 0.1917 and 0.3834 three numerical values respectively;

Fig. 4c is corresponding to n=0.30, and _n takes _0.0671 , _0.1917 and 0.3834 three numerical values respectively _Hn /Er-We/Wt relationship diagram;

Fig. 4d is corresponding to n=0.45, and n takes 0.0671, 0.1917 and 0.3834 three numerical values respectively H _n /E _r -W _e /W _t relationship diagram;

Fig. 5 a is corresponding to n=0, and n takes _0.0671 , _0.1917 and 0.3834 three numerical values respectively _Hn / _Ec -We/Wt relationship diagram;

Fig. 5b is the _Hn / _Ec -We/Wt relationship diagram corresponding to _n =0.15, and n takes three values of _0.0671 , 0.1917 and 0.3834 respectively;

Fig. 5c is corresponding to n=0.30, and n takes _0.0671 , _0.1917 and 0.3834 three numerical values respectively _Hn / _Ec -We/Wt relation diagram;

Fig. 5d is corresponding to n=0.45, and η takes _0.0671 , _0.1917 and 0.3834 three numerical values respectively _Hn / _Ec -We/Wt relationship diagram;

Fig. 6 is the H _n /E _c -W _e /W _t relationship diagram when n represented by formula (16) is 0, 0.15, 0.30 and 0.45 respectively;

Fig. 7 is the d/d _n- W _e /W _t relationship diagram corresponding to different n and η;

Fig. 8a is corresponding to η=0.0671, and n respectively takes 0, 0.15, 0.30 and 0.45 four values σ _y /H _n -W _e /W _t relationship diagram;

Fig. 8b is corresponding to η=0.1917, and n respectively takes 0, 0.15, 0.30 and 0.45 four numerical values σ _y /H _n -W _e /W _t relationship diagram;

Fig. 8c is corresponding to η=0.3834, and n respectively takes 0, 0.15, 0.30 and 0.45 four numerical values σ _y /H _n -W _e /W _t relation diagram;

Fig. 9 is the instrumented indentation load-displacement curve of 6061 aluminum alloy;

Figure 10 is the instrumented indentation load-displacement curve of S45C carbon steel;

Figure 11 is the instrumented indentation load-displacement curve of SS316 stainless steel;

Figure 12 is the instrumented indentation load-displacement curve of brass;

Figure 13 is a comparison of the true stress-strain relationship of 6061 aluminum alloy obtained by instrumented indentation test and standard uniaxial tensile test;

Figure 14 is a comparison of the true stress-strain relationship of S45C carbon steel obtained by instrumented indentation test and standard uniaxial tensile test;

Figure 15 is a comparison of the true stress-strain relationship of SS316 stainless steel obtained by instrumented indentation test and standard uniaxial tensile test;

Figure 16 is a comparison of the true stress-strain relationship of brass obtained by instrumented indentation testing and standard uniaxial tensile testing, respectively.

detailed description

The method of the present invention will be described in detail below in conjunction with the accompanying drawings, but these embodiments are for illustrative purposes only, and are not intended to limit the scope of the present invention. This application proposes an instrumented indentation test method for elastoplastic parameters of metal materials based on Vickers indentation. The method uses a single Vickers indenter to indent the metal material to obtain the load-displacement curve and indentation to determine the strain hardening of the metal material. exponent, elastic modulus, conditional yield strength σ _0.2 and strength limit σ _b ; firstly, use the ratio of the Vickers indentation mid-edge to the nominal mid-edge and the instrumented indentation specific work to determine the strain hardening exponent of the metal material; secondly, Determine the elastic modulus of the metal material by using the instrumented indentation specific work, the instrumented indentation nominal hardness and the strain hardening index obtained from the test; finally, use the instrumented indentation specific work, the instrumented indentation nominal hardness and the measured elastic modulus and the strain hardening exponent determine the conditional yield strength σ _0.2 and the strength limit σ _b of metallic materials. Specifically include the following steps:

1) Use an instrumented indenter and a diamond Vickers indenter to implement an instrumented indentation test with a maximum indentation load of P _m on the material to be tested to obtain an indentation load-displacement curve, and use this curve to determine the diamond Vickers indentation. The maximum indentation depth h _m of the head, the nominal hardness H _n =P _m /A(h _m ), where A(h _m ) is the cross-sectional area of the diamond Vickers indenter corresponding to the maximum indentation depth, when the diamond is not considered When the Vickers indenter tip is blunted When considering the passivation of the tip of the diamond Vickers indenter, A(h _m ) should be determined by the area function A(h) of the diamond Vickers indenter, that is

2) Calculate the indentation loading work W _t and unloading work W _e by integrating the loading curve and unloading curve in the load-displacement curve relationship respectively, and calculate the indentation specific work W _e /W _t on this basis;

3) Measure the distances from the center of the Vickers indentation to the boundaries of the four indentations: d ₁ , d ₂ , d ₃ and d ₄ , and determine the middle distance d=(d ₁ +d ₂ +d ₃ +d ₄ )/4 and its ratio d/d _n to the nominal median distance d _n =h _m tan68°;

4) According to the relationship between instrumented indentation specific work W _e /W _t and d/d _n under four different hardening indices (n ₁ =0, n ₂ =0.15, n ₃ =0.30, n ₄ =0.45) (the values of polynomial coefficients a _ij (i=1,...,4; j=0,1,2) are listed in Table 1) determine respectively when i gets 1,2,3,4 corresponding (d/d _n ) the value of _i , and then determine n′ according to the Lagrangian interpolation formula:

${\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\underset{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{\overset{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; \}</span>$

Further determine the strain hardening exponent n of the tested material according to the non-negative principle:

n=max{n',0}

Table 1. Values of polynomial coefficients a _ij (i=1,...,4; j=0,1,2)

5) According to the relationship between the instrumented indentation specific work W _e /W _t and the ratio H _n /E _c under four different hardening exponents n _i (i=1, 2, 3, 4) (the value of polynomial coefficient b _ij (i=1, ..., 4; j=0, ..., 6) is listed in table 2) determine respectively when i gets 1,2,3,4 corresponding (H _n /E _c ) _i value, and then use the Lagrange interpolation formula to determine H _n /E _c :

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; i</span>}}\underset{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{\overset{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$

Further determine the combined elastic modulus E _c of the tested material and the diamond Vickers indenter according to the instrumented indentation nominal hardness H _n and the ratio H _n /E _c :

E _c ＝H _n /(H _n /E _c )

And the elastic modulus E of the tested material:

$\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1.32</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ]</span>$

Among them, the elastic modulus E _i of the diamond Vickers indenter = 1141GPa, Poisson's ratio v _i = 0.07, and the Poisson's ratio v of the tested material can be determined according to the material manual;

Table 2. Values of polynomial coefficients b _ij (i=1,...,4; j=0,...,6)

6) According to 4 different hardening exponents n _i (i=1, 2, 3, 4) and 3 different ratios of the tested material to the plane strain modulus of elasticity of the diamond indenter η _j (j=1, 2, 3) (η ₁ = 0.0671, η ₂ = 0.1917, η ₃ = 0.3834) The ratio relationship between the instrumented indentation specific work W _e /W _t and the yield strength to the nominal hardness (the value of polynomial coefficient c _ijk (i=1,...,4; j=1,2,3; k=0,...,6) is listed in table 3) determine respectively that i gets 1,2, 3, 4, j take the corresponding (σ _y /H _n ) _ij (i=1,...,4; j=1, 2, 3) value when 1, 2, 3, and then according to and η _j (j=1, 2, 3) are determined by the Lagrangian interpolation formula σ _y /H _n :

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \{</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; ij</span>}}\underset{\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; \}</span>\underset{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{\overset{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$

Further determine the yield strength σ _y of the tested material according to the instrumented indentation nominal hardness H _n and the ratio σ _y /H _n :

σ _y =H _n (σ _y /H _n )

And determine the conditional yield strength σ _0.2 of the tested material by the relational formula σ _0.2 =σ _y ^1-n [σ _0.2 +0.002E] ⁿ ;

Table 3. Values of polynomial coefficients c _ijk (i=1,...,4; j=1,2,3; k=0,...,6)

7) Calculate ε _y = σ _y /E, and use the relation Determine ε _b , and finally determine the strength limit σ _b of the tested material:

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; v\&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; ></span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\end{array}\right.$

The formation process of the present invention will be described in detail below. The schematic diagram of the Vickers indentation is shown in Figure 1a and Figure 1b. The margin d in the Vickers indentation is defined as the average of the distances d ₁ , d ₂ , d ₃ and d ₄ from the center of the Vickers indentation to the boundaries of the four indentations. That is, d=(d ₁ +d ₂ +d ₃ +d ₄ )/4. The schematic diagram of the diamond Vickers indenter is shown in Figure 2. According to the maximum indentation depth h _m , the middle distance of the Vickers nominal indentation is defined d _n =h _m tan68°. The schematic diagram of the instrumented indentation load-displacement curve is shown in Figure 3. The vertical axis represents the indentation load P, and the horizontal axis represents the indentation depth h. The loading curve is 1, the unloading curve is 2, and the loading work W _t area is 3. The _unloading work area is 4. The maximum indentation load set by instrumented indentation is P _m , and the corresponding maximum indentation depth is h _m . Use A(h _m ) to represent the cross-sectional area of the diamond Vickers indenter at the position of the maximum indentation depth h _m , then the nominal hardness H _n is defined as the maximum indentation load P _m and the cross-sectional area of the diamond Vickers indenter The ratio of the area A(h _m ), that is, H _n =P _m /A(h _m ). Further define instrumented indentation loading work W _t and unloading work W _e to be the work done by the diamond Vickers indenter in the loading stage and unloading stage when implementing instrumented indentation, and their values are respectively equal to the loading curve and unloading curve and instrumentation The area enclosed by the abscissa of the indentation load-displacement curve. Instrumented indentation specific work W _e /W _t is the ratio of unloading work W _e to loading work W _t .

The diamond Vickers indenter is regarded as an elastic body, and its elastic modulus and Poisson's ratio are represented by E _i and vi _i respectively; the measured material is regarded as an elastoplastic body, and its uniaxial true stress-strain relationship is expressed by linear elasticity and Hollomon power The hardening function is composed, and its elastic modulus and Poisson's ratio are represented by E and v, respectively, and the yield strength and strain hardening exponent are represented by _σy and n, respectively. Based on the above settings and ignoring the friction between the diamond Vickers indenter and the tested material, the instrumented indentation nominal hardness H _n , the instrumented indentation specific energy W _e /W _t and the distance between the center edge and the nominal center edge of the Vickers indentation The ratio of distance d/d _n can be expressed as the yield strength σ _y , strain hardening exponent n, elastic modulus E, Poisson’s ratio v of the tested material and the elastic modulus E _i , Poisson’s ratio v of the diamond Vickers indenter _i and the function of the maximum pressing depth h _m :

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; W</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

where E/(1-v ² ) and are the plane strain elastic moduli of the tested material and the diamond Vickers indenter, respectively. Using the reduced modulus of elasticity and the ratio of the plane strain modulus of elasticity The plane strain elastic modulus of the tested material and the diamond Vickers indenter can be expressed as:

E/(1-v ² )=(η+1)E _r (4)

${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Then, equations (1), (2) and (3) can be rewritten as:

H _n =Γ _H2 (σ _y , n, E _r , η, h _m ) (6)

W _e /W _t =Γ _W2 (σ _y , n, E _r , η, h _m ) (7)

d/d _n =Γ _D2 (σ _y , n, E _r , η, h _m ) (8)

Applying the dimension ∏ theorem, equations (6), (7) and (8) can be simplified as:

H _n /E _r =Γ _H3 (σ _y /E _r , n, η) (9)

W _e /W _t =Γ _W3 (σ _y /E _r , n, η) (10)

d/d _n =Γ _D3 (σ _y /E _r , n, η) (11)

From formula (10) can get:

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; W</span>}\mathrm{<span\; class="notranslate">\; 3</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

Substitute formula (12) into formula (9) and formula (11) to get:

H _n /E _r =Γ _H4 (W _e /W _t , n, η) (13)

d/d _n =Γ _D4 (W _e /W _t , n, η) (14)

From formula (12) and formula (13) can get:

σ _y /H _n =Γ ₅ (W _e /W _t , n, η) (15)

The explicit solutions of formula (13), formula (14) and formula (15) can be obtained by finite element numerical simulation. In the simulation, the elastic modulus of the diamond Vickers indenter is E _i =1141GPa, and the Poisson's ratio is v _i =0.07. The elastic modulus E of the tested material is set to 70GPa, 200GPa and 400GPa respectively; the yield strength σ _y ranges from 0.7 to 160000MPa; the strain hardening exponent n takes 0, 0.15, 0.3 and 0.45; Poisson The ratio v takes a fixed value of 0.3. The ratio η of the plane strain elastic modulus of the tested material to the diamond Vickers indenter is 0.0671, 0.1917 and 0.3834 respectively; the contact friction coefficient between the tested material and the diamond Vickers indenter is zero.

Accompanying drawing 4a, accompanying drawing 4b, accompanying drawing 4c and accompanying drawing 4d are the _Hn / _Er -We/ _Wt relationship diagram corresponding to different _n and η, as can be seen from the figure, for the determined strain hardening exponent n , η has a certain influence on the H _n /E _r -W _e /W _t relationship, which indicates that the reduced elastic modulus E _r cannot accurately reflect the comprehensive elastic effect between the tested material and the diamond Vickers indenter. For this, define the joint modulus of elasticity ${\mathrm{E.}}_c=1/[(1-v^2)/\mathrm{E.}+1.32(1-v_i^2)/{\mathrm{E.}}_i],$ And replace the reduced modulus of elasticity E _r to obtain the relationship of H _n /E _c -W _e /W _t , the results are shown in accompanying drawing 5a, accompanying drawing 5b, accompanying drawing 5c and accompanying drawing 5d, can see from the figure It is shown that for a determined strain hardening exponent _n , the _Hn / _Ec -We/ _Wt relation is hardly affected by η. Therefore, polynomial functions can be used to perform curve fitting on the H _n /E _c -W _e /W _t relationship under four different values of the strain hardening exponent n, and the results are expressed as:

${<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

Among them, i=1,...,4 correspond to 4 different values of strain hardening exponent n: 0, 0.15, 0.3, 0.45; the value of coefficient b _ij (j=0,...,6) see Table 2. The relationship of H _n /E _c -W _e /W _t when n represented by formula (16) is 0, 0.15, 0.30 and 0.45 is shown in Fig. 6 .

Table 2. Values of coefficient b _ij (i=1,...,4; j=0,...,6)

Accompanying drawing 7 is the d/d _n- W _e /W _t relationship diagram corresponding to different n and η, as can be seen from the figure, for the determined strain hardening exponent n, η is to d/d _n- W _e /W _t The relationship effect can be ignored. Therefore, the polynomial function can be used to perform curve fitting on the d/d _n -W _e /W _t relationship under four different values of the strain hardening exponent n, and the result is expressed as:

${<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

Among them, i=1,...,4 correspond to four different values of strain hardening exponent n: 0, 0.15, 0.3, 0.45; the values of coefficient a _ij (j=0, 1, 2) are shown in Table 1 .

Table 1. Values of coefficient a _ij (i=1,...,4; j=0,1,2)

Accompanying drawing 8a, accompanying drawing 8b and accompanying drawing 8c are σ _y /H _n -W _e /W _t relationship diagram corresponding to different n and η. The polynomial function is used to fit the relationship of σ _y /H _n -W _e /W _t , and the result can be expressed as:

${<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; ijk</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

Wherein, i=1,..., the value of 4 corresponding n is 0,0.15,0.3,0.45; The value of j=1,2,3 corresponding n is 0.0671,0.1917,0.3834; Coefficient c _ijk (k= 0,...,6) see Table 3 for the values.

Table 3. Values of coefficient c _ijk (i=1,...,4; j=1,2,3; k=0,...,6)

application example

6061 aluminum alloy, S45C carbon steel, SS316 stainless steel and brass were selected for instrumented indentation experiments. According to the experimental procedure proposed by the inventor, the high-precision instrumented indenter developed by the inventor and has been authorized by the national invention patent [Ma Dejun, Song Zhongkang, Guo Junhong, Chen Wei. A high-precision indenter and diamond indenter indenter Calculation method of sample depth. Patent No.: ZL201110118464.9] and diamond Vickers indenter were used to repeat 5 times of instrumented indentation experiments on different areas of 6061 aluminum alloy, S45C carbon steel, SS316 stainless steel and brass. Figure 9, Figure 10, Figure 11 and Figure 12 are the instrumented indentation load-displacement curves of 6061 aluminum alloy, S45C carbon steel, SS316 stainless steel and brass, respectively. The optical microscope can be used to observe the distance between the Vickers indentation of 6061 aluminum alloy, S45C carbon steel, SS316 stainless steel and brass.

According to the instrumented indentation load-displacement curve and the Vickers indentation, the instrumented indentation nominal hardness H _n , the instrumented indentation specific energy W _e /W _t , and the margin and nominal value of the Vickers indentation can be determined respectively. The ratio d/d _n of the middle edge distance, the results are shown in Table 4. On this basis, the method proposed by the inventor can be used to determine the strain hardening exponent n, elastic modulus E, conditional yield strength σ _0.2 and strength limit of the tested material σ _b . In order to compare with the results of the standard uniaxial tensile test, the same materials used in the instrumented indentation test were made of 6061 aluminum alloy, S45C carbon steel, SS316 stainless steel and brass to make standard uniaxial tensile test specimens, and respectively Implement 2 standard uniaxial tensile tests, and use the average value of the 2 tests as the test result of the material uniaxial tensile test, then the modulus of elasticity, strain hardening exponent, The conditional yield strength and strength limit are E _uniaxial = 71GPa, n _uniaxial = 0.052, σ _{0.2 uniaxial} = 299.37MPa and σ _{b uniaxial} = 366.25MPa; the elasticity of S45C carbon steel measured by standard uniaxial tensile test Modulus, strain hardening exponent, conditional yield strength and strength limit are E _uniaxial = 201GPa, n _uniaxial = 0.176, σ _{0.2 uniaxial} = 431.08MPa and σ _{b uniaxial} = 612.84MPa; by standard uniaxial tensile test The measured elastic modulus, strain hardening index, conditional yield strength and strength limit of SS316 stainless steel are E _uniaxial = 184GPa, n _uniaxial = 0.134, σ _{0.2 uniaxial} = 610.11MPa and σ _{b uniaxial} = 827.51MPa; The elastic modulus, strain hardening index, conditional yield strength and strength limit of brass measured by the standard uniaxial tensile test are E _uniaxial = 83GPa, n _uniaxial = 0.125, σ _{0.2 uniaxial} = 346.67MPa and σ _b uniaxial _Shaft = 421.23 MPa. Comparison of instrumented indentation test results with uniaxial tensile test results for elastic modulus, strain hardening exponent, conditional yield strength, and strength limit of 6061 aluminum alloy, S45C carbon steel, SS316 stainless steel, and brass allows determination of instrumented The test error of the press-in test result: E _Err = (EE _uniaxial ) / E _uniaxial , Δn = nn _uniaxial , σ _0.2Err = (σ _0.2 -σ _{0.2 uniaxial} ) / σ _{0.2 uniaxial} and σ _bErr = ( σ _b -σ _{b uniaxial} )/σ _{b uniaxial} , the results are shown in Table 4. It can be seen from the table that the relative test errors of elastic modulus of 6061 aluminum alloy, S45C carbon steel, SS316 stainless steel and brass are 4.40%, 1.73%, -0.34% and 11%, respectively, and the absolute test errors of strain hardening exponent are respectively are 0.008, 0.001, 0.013 and -0.010, the relative test errors of the conditional yield strength σ _0.2 are 10.04%, -5.37%, 8.65% and 1.26% respectively, and the relative test errors of the strength limit σ _b are -2.61% and 9.45% respectively , 11.95% and 5.05%. Further, the true stress-strain relationship can be plotted based on the average values of strain hardening exponent n, elastic modulus E and conditional yield strength σ _0.2 of 6061 aluminum alloy, S45C carbon steel, SS316 stainless steel and brass measured by instrumented indentation experiments , the comparison of this relationship with the true stress-strain relationship measured by the standard uniaxial tensile test is shown in Figure 13, Figure 14, Figure 15 and Figure 16, and in Figure 13, Figure 14, Figure 15 and Figure 16 , the horizontal axis is the true strain ε, the vertical axis is the true stress σ, the dashed line is the result of the instrumented indentation test, the thick solid line is the uniaxial tensile test 1, and the thin solid line is the uniaxial tensile test 2. It can be seen from the figure that the two have good consistency. A review of the above experimental results shows that the Vickers indentation-based instrumented indentation test method for elastic-plastic parameters of metal materials proposed by the inventor is feasible and very effective.

Table 4. Instrumented indentation test results and test errors of elastic-plastic parameters of 6061 aluminum alloy, S45C carbon steel, SS316 stainless steel and brass

Although the specific embodiments of the present invention have been described and illustrated in detail above, it should be pointed out that we can make various equivalent changes and modifications to the above-mentioned embodiments according to the concept of the present invention, and the functional effects produced by it are still the same. Anything beyond the spirit covered by the specification and drawings shall be within the protection scope of the present invention.

Claims (2)

1. a kind of material elastic-plastic mechanical parameter instrumentation press-in method of testing based on vickers impression, the method utilizes vickers Pressure head instrumentation press-in metal material gained load-displacement curves and vickers impression determine that the strain hardening of metal material refers to Number n, elastic modelling quantity e, offset yield strength σ_0.2And strength degree σ_b, specifically include following steps:

1) utilizing instrumentation press fit instrument and diamond vickers pressure head that measured material is implemented with a certain maximum loading of pressing in is p_m's Instrumentation press-in test, obtains loading of pressing in-displacement curve, determines diamond vickers pressure head using this curve simultaneously Big compression distance h_m, nominal hardness h_n=p_m/a(h_m), wherein, a (h_m) it is diamond vickers during corresponding maximum compression distance Pressure head cross-sectional area, when not considering the passivation of diamond vickers indenter tipAnd consider diamond During the passivation of vickers indenter tip, then a (h_m) should be determined by area function a (h) of diamond vickers pressure head, that is,

2) pass through to integrate the loading curve in load-displacement curves relation and unloading curve calculating press-in loading work(w respectively_t, unloading Work(w_e, and calculate press-in ratio work(w on this basis_e/w_t；

3) distance on vickers impression center to four impression borders: d is measured respectively by microscope₁、d₂、d₃And d₄, and determine Middle back gauge d=(d₁+d₂+d₃+d₄)/4 and its with back gauge d in name_n=d_mTan68 ° of ratio d/d_n；

4) according to 4 different hardenability value n₁=0, n₂=0.15, n₃=0.30, n₄Instrumentation press-in ratio work(w under=0.45_e/ w_tWith d/d_nRelationWherein, i value is respectively 1,2,3,4 and corresponds to 4 different hardening Index, multinomial coefficient a_ij(i=1 ..., 4；J=0,1,2) value is:

Determine that i takes corresponding (d/d when 1,2,3,4 respectively_n)_iValue, then determines n ' according to Lagrange's interpolation formula:

Determine strain hardening exponent n of tested material further according to non-negative principle:

N=max { n ', 0 }

5) according to 4 different hardenability value n_iInstrumentation press-in ratio work(w under (i=1,2,3,4)_e/w_tWith ratio h_n/e_cRelationWherein, e_cCombine elastic modelling quantity for tested material and diamond vickers pressure head, Multinomial coefficient b_ij(i=1 ..., 4；J=0 ..., 6) value be:

Determine that i takes corresponding (h when 1,2,3,4 respectively_n/e_c)_iValue, then determines h using Lagrange's interpolation formula_n/e_c:

Further nominal hardness h is pressed into according to instrumentation_nAnd ratio h_n/e_cDetermine tested material and diamond vickers pressure head Joint elastic modelling quantity e_c:

e_c=h_n/(h_n/e_c)

And the elastic modelling quantity e of tested material:

Wherein, the elastic modelling quantity e of diamond vickers pressure head_i=1141gpa, Poisson's ratio v_i=0.07, the pool of tested material Pine can determine according to Materials Handbook than v；

6) according to 4 different hardenability value n_iThe tested material of (i=1,2,3,4) and 3 differences and diamond penetrator plane strain The ratio η of elastic modelling quantity_j(j=1,2,3) (η₁=0.0671, η₂=0.1917, η₃=0.3834) the instrumentation press-in ratio work(w under_e/ w_tWith yield strength with nominal hardness ratio relationWherein, multinomial coefficient c_ijk(i= 1 ..., 4；J=1,2,3；K=0 ..., 6) value be:

Determine respectively i take 1,2,3,4, j take corresponding (σ when 1,2,3_y/h_n)_ij(i=1 ..., 4；J=1,2,3) value, Ran Hougen According toAnd η_j(j=1,2,3) value determines σ by Lagrange's interpolation formula_y/h_n:

Further nominal hardness h is pressed into according to instrumentation_nAnd ratio σ_y/h_nDetermine yield strength σ of tested material_y:

σ_y=h_n(σ_y/h_n)

And by relational expressionDetermine offset yield strength σ of tested material_0.2；

7) calculate ε_y=σ_y/ e, and by relational expressionDetermine ε_b, finally determine the strong of tested material Degree limit σ_b:

.

2. a kind of material elastic-plastic mechanical parameter instrumentation based on vickers impression is pressed into method of testing as claimed in claim 1, Wherein, step 5) in, if the Poisson's ratio of measured material can not be determined by Materials Handbook, value is 0.3.