CN104165814A - Vickers indentation based material elastoplasticity instrumented indentation test method - Google Patents

Abstract

The invention discloses a Vickers indentation based material elastoplasticity instrumented indentation test method. The method utilizes a Vickers indenter to carry out instrumented indentation on a metal material to obtain a load-displacement curve and utilizes the Vickers indentation to determine the following parameters of a metal material: strain hardening exponent (n), elastic modulus (E), offset yield strength (sigma 0.2), and strength limit (sigma b). Compared to an instrumented indentation test method using two or more pyramid intender with different cone apex angles, the provided method only uses a single Vickers indenter to carry out an instrumented indentation test on a metal material and is capable of determining the strain hardening exponent (n), elastic modulus (E), offset yield strength (sigma 0.2), and strength limit (sigma b) of the metal material by carrying out Vickers indentation geometrical parameter tests. Avoided are the problems that non-standard pyramid indenters, whose cone apex angles are different from those of the standard pyramid intenders, need to be individually designed and processed; intenders need to be changed in the testing process, and the instrument flexibility needs to be readjusted after exchanging the intenders, so the test efficiency is improved.

Description

Material elastic-plastic mechanical parameter instrumentation based on Vickers impression is pressed into method of testing

Technical field

The invention belongs to material mechanical performance field tests.Being specifically related to one utilizes instrumentation press fit instrument and Vickers pressure head to test metal material strain hardening exponent, elastic modulus, offset yield strength σ _0.2and strength degree σ _bmethod.

Background technology

Instrumentation is pressed into measuring technology and acts on by real-time synchronization measurement the compression distance that loading of pressing on diamond penetrator and diamond penetrator be pressed into measured material surface and obtain loading of pressing in-displacement curve, be pressed into the dimensionless functional relation between response and measured material mechanical property parameters according to instrumentation, can identify many mechanical property parameters of measured material.

The instrumentation of elasticity modulus of materials is pressed into test and mainly contains " the Oliver-Pharr method " or " gradient method " of W.C.Oliver and G.M.Pharr proposition and " horse German army method " or " the pure ENERGY METHOD " that horse German army proposes.The theoretical foundation of " gradient method " is small deformation theory of elasticity, owing to not considering the plastic behavior of measured material under pressure head effect and how much large deformation, make " gradient method " in the time being applied to the measured material of low strain hardening exponent, test result substantial deviation elastic modulus true value." pure ENERGY METHOD " considered the non-linear of material, geometry and contact boundary condition, and the measuring accuracy of its elastic modulus is therefore higher than " gradient method ".However, still there is certain theoretical test error in " pure ENERGY METHOD ", this error comes from strain hardening exponent the unknown of measured material, and the strain hardening exponent of therefore managing to identify tested material is to improve elasticity modulus of materials instrumentation and be pressed into unique effective way of measuring accuracy.

The instrumentation of material strain hardenability value and yield strength is pressed into test and has at present the single ball pressure head plunging based on spherical indenter and the multiple cone pressure head plunging based on cone bearings of various cone top angle, wherein apply difficulty that single ball pressure head plunging runs into and be that to manufacture radius be several or its how much machining precisioies of spherical indenter of tens microns are difficult to meet test request, therefore, the instrumentation of the material strain hardenability value based on spherical indenter and yield strength is pressed into method of testing and is having little scope for one's talents aspect practical application or through engineering approaches.Apply the problem that multiple cone pressure head plunging do not exist pressure head manufacture view, but test process need to be changed the pyramid pressure head at cone bearings of various cone top angle, need instrument flexibility again to demarcate simultaneously, and both difficulties consuming time of Accurate Calibration instrument flexibility, therefore to test its efficiency lower for the many cones of application pressure head plunging.

Be pressed into for metal current material elastic-plastic mechanical parameter instrumentation the problem existing in test, the present invention proposes a kind of metal material strain hardening exponent, elastic modulus, offset yield strength σ based on Vickers impression _0.2and strength degree σ _binstrumentation be pressed into method of testing.

Summary of the invention

The object of this invention is to provide a kind of metal material elastic-plastic mechanical parameter instrumentation based on Vickers impression and be pressed into method of testing, utilize the method can determine that the elastic-plastic mechanical parameter of metal material comprises strain hardening exponent, elastic modulus, offset yield strength σ _0.2and strength degree σ _b.Compared with being pressed into method of testing with the pyramid pressure head instrumentation that uses two or more cone bearings of various cone top angles, the method is only used single Vickers pressure head to be pressed into test and be aided with Vickers impression geometric parameter to metal material enforcement instrumentation and tests strain hardening exponent n, elastic modulus E, the offset yield strength σ that can determine metal material _0.2and strength degree σ _bavoid needing before test design processing to be separately different from the non-standard pyramid pressure head problem of standard icicle pressure head cone apex angle, and in test process, need the problem that need to again demarcate instrument flexibility of changing pressure head and causing thus, improve testing efficiency.

To achieve these goals, the present invention adopts following technical scheme:

Metal material elastic-plastic mechanical parameter instrumentation based on Vickers impression is pressed into a method of testing, and the method utilizes single Vickers pressure head instrumentation to be pressed into metal material gained load-displacement curves and impression to determine strain hardening exponent, elastic modulus, the offset yield strength σ of metal material _0.2and strength degree σ _b; First, utilize in Vickers impression ratio and the instrumentation of back gauge in back gauge and name to be pressed into the strain hardening exponent of determining metal material than merit; Secondly, utilize instrumentation to be pressed into than merit, instrumentation and be pressed into nominal hardness and test gained strain hardening exponent the elastic modulus of determining metal material; Finally, utilize instrumentation to be pressed into the offset yield strength σ that is pressed into nominal hardness and test gained elastic modulus and strain hardening exponent and determines metal material than merit, instrumentation _0.2with strength degree σ _b.Specifically comprise the following steps:

1) utilizing instrumentation press fit instrument and adamas Vickers pressure head to implement a certain maximum loading of pressing in to measured material is P _minstrumentation be pressed into test, obtain loading of pressing in-displacement curve, utilize this curve to determine the maximum compression distance h of adamas Vickers pressure head simultaneously _m, nominal hardness H _n=P _m/ A (h _m), wherein, A (h _m) adamas Vickers pressure head cross-sectional area while being corresponding maximum compression distance, in the time not considering the crest truncation of adamas Vickers pressure head and while considering the crest truncation of adamas Vickers pressure head, A (h _m) should be determined by the area function A (h) of adamas Vickers pressure head,

2) calculate to be pressed into by the loading curve in integration load-displacement curves relation respectively and unloading curve and load merit W _t, unloading merit W _e, and calculate and be pressed into than merit W on this basis _e/ W _t;

3) measure respectively the distance on an impression border, Vickers impression center to four by microscope: d ₁, d ₂, d ₃and d ₄, and back gauge d=(d in determining ₁+ d ₂+ d ₃+ d ₄)/4 and with name in back gauge d _n=h _mthe ratio d/d of tan68 ° _n;

4) according to 4 different hardenability value (n ₁=0, n ₂=0.15, n ₃=0.30, n ₄=0.45) instrumentation under is pressed into than merit W _e/ W _twith d/d _nrelation (multinomial coefficient a _ij(i=1 ..., 4; J=0,1,2) value is listed in table 1) determine that respectively i gets the corresponding (d/d of 1,2,3,4 o'clock _n) _ivalue, then determine n ' according to Lagrange's interpolation formula:

$n^{\′}=\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{n}_i\underset{\underset{k\≠i}{k=1}}{\overset{4}{\mathrm{\Π}}}\left\{\right[(d/d_n)-{(d/d_n)}_k]/[{(d/d_n)}_i-{(d/d_n)}_k\left]\right\}$

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

n＝max{n′，0}

Table 1. multinomial coefficient a _ij(i=1 ..., 4; J=0,1,2) value

5) according to 4 different hardenability value n _iinstrumentation under (i=1,2,3,4) is pressed into than merit W _e/ W _twith ratio H _n/ E _crelation (multinomial coefficient b _ij(i=1 ..., 4; J=0 ..., 6) value list in table 2) respectively determine i get the corresponding (H of 1,2,3,4 o'clock _n/ E _c) _ivalue, then utilizes Lagrange's interpolation formula to determine H _n/ E _c:

$H_n/E_c=\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{(H_n/E_c)}_i\underset{\underset{k\≠i}{k=1}}{\overset{4}{\mathrm{\Π}}}[(n-n_k)/(n_i-n_k)]$

Further be pressed into nominal hardness H according to instrumentation _nand ratio H _n/ E _cdetermine the elastic modulus E of combining of tested material and adamas Vickers pressure head _c:

E _c＝H _n/(H _n/E _c)

And the elastic modulus E of tested material:

$E=(1-v^2)/[1/E_c-1.32(1-v_i^2)/E_i]$

Wherein, the elastic modulus E of adamas Vickers pressure head _i=1141GPa, Poisson ratio v _i=0.07, the Poisson ratio v of tested material can determine according to material handbook;

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

6) according to 4 different hardenability value n _ithe ratio η of (i=1,2,3,4) and 3 tested materials of difference and diamond penetrator plane-strain elastic modulus _j(j=1,2,3) (η ₁=0.0671, η ₂=0.1917, η ₃=0.3834) instrumentation under is pressed into than merit W _e/ W _twith the ratio relation of yield strength with nominal hardness (multinomial coefficient c _ijk(i=1 ..., 4; J=1,2,3; K=0 ..., 6) value list in table 3) respectively determine i get 1,2,3,4, j gets the corresponding (σ of 1,2,3 o'clock _y/ H _n) _ij(i=1 ..., 4; J=1,2,3) value, then basis and η _j(j=1,2,3) value is determined σ by Lagrange's interpolation formula _y/ H _n:

${\mathrm{\σ}}_y/H_n=\underset{i=1}{\overset{4}{\mathrm{\Σ}}}\left\{\underset{j=1}{\overset{3}{\mathrm{\Σ}}}{({\mathrm{\σ}}_y/H_n)}_{\mathrm{ij}}\underset{\underset{m\≠j}{m=1}}{\overset{3}{\mathrm{\Π}}}\right[(\mathrm{\η}-{\mathrm{\η}}_m)/({\mathrm{\η}}_j-{\mathrm{\η}}_m)\left]\right\}\underset{\underset{k\≠i}{k=1}}{\overset{4}{\mathrm{\Π}}}[(n-n_k)/(n_j-n_k)]$

Further be pressed into nominal hardness H according to instrumentation _nand ratio σ _y/ H _ndetermine the yield strength σ of tested material _y:

σ _y＝H _n(σ _y/H _n)

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

Table 3. multinomial coefficient c _ijk(i=1 ..., 4; J=1,2,3; K=0 ..., 6) value

7) calculate ε _y=σ _y/ E, and by relational expression determine ε _b, the finally strength degree σ of definite tested material _b:

${\mathrm{\σ}}_b=\left\{\begin{array}{cc}{\mathrm{\σ}}_y/\exp \left({2\mathrm{v\ϵ}}_y\right),& {\mathrm{\ϵ}}_b\≤{\mathrm{\ϵ}}_y\\ {\mathrm{\σ}}_y{({\mathrm{\ϵ}}_b/{\mathrm{\ϵ}}_y)}^n/\exp [{\mathrm{\ϵ}}_b+(2v-1){\mathrm{\ϵ}}_y^{1-n}{\mathrm{\ϵ}}_b^n],& {\mathrm{\ϵ}}_b>{\mathrm{\ϵ}}_y\end{array}\right.$

Wherein, step 5) in, if the Poisson ratio of measured material can not be determined by material handbook, value is 0.3.

Compared with being pressed into method of testing with the pyramid pressure head instrumentation that uses two or more cone bearings of various cone top angles, the present invention only uses single Vickers pressure head to be pressed into test and be aided with Vickers impression geometric parameter to metal material enforcement instrumentation and tests strain hardening exponent n, elastic modulus E, the offset yield strength σ that can determine metal material _0.2and strength degree σ _bavoid needing before test design processing to be separately different from the non-standard pyramid pressure head problem of standard icicle pressure head cone apex angle, and in test process, need the problem that need to again demarcate instrument flexibility of changing pressure head and causing thus, improve testing efficiency.

Brief description of the drawings:

Fig. 1 a is the Vickers impression schematic diagram in the protruding situation of drum;

Fig. 1 b is the Vickers impression schematic diagram in depression situation;

Fig. 2 is Vickers pressure head schematic diagram;

Fig. 3 is that instrumentation is pressed into Load-unload curve and Load-unload merit schematic diagram;

Fig. 4 a is corresponding n=0, and η gets respectively the H of 0.0671,0.1917 and 0.3834 3 numerical value _n/ E _r-W _e/ W _tgraph of a relation;

Fig. 4 b is corresponding n=0.15, and η gets respectively the H of 0.0671,0.1917 and 0.3834 3 numerical value _n/ E _r-W _e/ W _tgraph of a relation;

Fig. 4 c is corresponding n=0.30, and η gets respectively the H of 0.0671,0.1917 and 0.3834 3 numerical value _n/ E _r-W _e/ W _tgraph of a relation;

Fig. 4 d is corresponding n=0.45, and η gets respectively the H of 0.0671,0.1917 and 0.3834 3 numerical value _n/ E _r-W _e/ W _tgraph of a relation;

Fig. 5 a is corresponding n=0, and η gets respectively the H of 0.0671,0.1917 and 0.3834 3 numerical value _n/ E _c-W _e/ W _tgraph of a relation;

Fig. 5 b is corresponding n=0.15, and η gets respectively the H of 0.0671,0.1917 and 0.3834 3 numerical value _n/ E _c-W _e/ W _tgraph of a relation;

Fig. 5 c is corresponding n=0.30, and η gets respectively the H of 0.0671,0.1917 and 0.3834 3 numerical value _n/ E _c-W _e/ W _tgraph of a relation;

Fig. 5 d is corresponding n=0.45, and η gets respectively the H of 0.0671,0.1917 and 0.3834 3 numerical value _n/ E _c-W _e/ W _tgraph of a relation;

Fig. 6 is that the n of formula (16) representative gets respectively 0,0.15,0.30 and the H of 0.45 o'clock _n/ E _c-W _e/ W _tgraph of a relation;

Fig. 7 is the d/d of corresponding different n and η _n-W _e/ W _tgraph of a relation;

Fig. 8 a is corresponding η=0.0671, and n gets respectively the σ of 0,0.15,0.30 and 0.45 four numerical value _y/ H _n-W _e/ W _tgraph of a relation;

Fig. 8 b is corresponding η=0.1917, and n gets respectively the σ of 0,0.15,0.30 and 0.45 four numerical value _y/ H _n-W _e/ W _tgraph of a relation;

Fig. 8 c is corresponding η=0.3834, and n gets respectively the σ of 0,0.15,0.30 and 0.45 four numerical value _y/ H _n-W _e/ W _tgraph of a relation;

Fig. 9 is the instrumentation loading of pressing in-displacement curve of 6061 aluminium alloys;

Figure 10 is the instrumentation loading of pressing in-displacement curve of S45C carbon steel;

Figure 11 is the stainless instrumentation loading of pressing in-displacement curve of SS316;

Figure 12 is the instrumentation loading of pressing in-displacement curve of brass;

Figure 13 adopts respectively instrumentation to be pressed into the comparison of the true strain-stress relation of test and standard uniaxial tensile test gained 6061 aluminium alloys;

Figure 14 adopts respectively instrumentation to be pressed into the comparison of the true strain-stress relation of test and standard uniaxial tensile test gained S45C carbon steel;

Figure 15 adopts respectively instrumentation to be pressed into the comparison of test and the stainless true strain-stress relation of standard uniaxial tensile test gained SS316;

Figure 16 adopts respectively instrumentation to be pressed into the comparison of the true strain-stress relation of test and standard uniaxial tensile test gained brass.

Embodiment

Below in conjunction with the drawings method of the present invention is elaborated, but these embodiment are only illustrative objects, are not intended to scope of the present invention to carry out any restriction.The application has proposed a kind of metal material elastic-plastic mechanical parameter instrumentation based on Vickers impression and has been pressed into method of testing, and the method utilizes single Vickers pressure head instrumentation to be pressed into metal material gained load-displacement curves and impression to determine strain hardening exponent, elastic modulus, the offset yield strength σ of metal material _0.2and strength degree σ _b; First, utilize in Vickers impression ratio and the instrumentation of back gauge in back gauge and name to be pressed into the strain hardening exponent of determining metal material than merit; Secondly, utilize instrumentation to be pressed into than merit, instrumentation and be pressed into nominal hardness and test gained strain hardening exponent the elastic modulus of determining metal material; Finally, utilize instrumentation to be pressed into the offset yield strength σ that is pressed into nominal hardness and test gained elastic modulus and strain hardening exponent and determines metal material than merit, instrumentation _0.2with strength degree σ _b.Specifically comprise the following steps:

1) utilizing instrumentation press fit instrument and adamas Vickers pressure head to implement a certain maximum loading of pressing in to measured material is P _minstrumentation be pressed into test, obtain loading of pressing in-displacement curve, utilize this curve to determine the maximum compression distance h of adamas Vickers pressure head simultaneously _m, nominal hardness H _n=P _m/ A (h _m), wherein, A (h _m) adamas Vickers pressure head cross-sectional area while being corresponding maximum compression distance, in the time not considering the crest truncation of adamas Vickers pressure head and while considering the crest truncation of adamas Vickers pressure head, A (h _m) should be determined by the area function A (h) of adamas Vickers pressure head,

2) calculate to be pressed into by the loading curve in integration load-displacement curves relation respectively and unloading curve and load merit W _t, unloading merit W _e, and calculate and be pressed into than merit W on this basis _e/ W _t;

3) measure respectively the distance on an impression border, Vickers impression center to four by microscope: d ₁, d ₂, d ₃and d ₄, and back gauge d=(d in determining ₁+ d ₂+ d ₃+ d ₄)/4 and with name in back gauge d _n=h _mthe ratio d/d of tan68 ° _n;

4) according to 4 different hardenability value (n ₁=0, n ₂=0.15, n ₃=0.30, n ₄=0.45) instrumentation under is pressed into than merit W _e/ W _twith d/d _nrelation (multinomial coefficient a _ij(i=1 ..., 4; J=0,1,2) value is listed in table 1) determine that respectively i gets the corresponding (d/d of 1,2,3,4 o'clock _n) _ivalue, then determine n ' according to Lagrange's interpolation formula:

$n^{\′}=\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{n}_i\underset{\underset{k\≠i}{k=1}}{\overset{4}{\mathrm{\Π}}}\left\{\right[(d/d_n)-{(d/d_n)}_k]/[{(d/d_n)}_i-{(d/d_n)}_k\left]\right\}$

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

n＝max{n′，0}

Table 1. multinomial coefficient a _ij(i=1 ..., 4; J=0,1,2) value

5) according to 4 different hardenability value n _iinstrumentation under (i=1,2,3,4) is pressed into than merit W _e/ W _twith ratio H _n/ E _crelation (multinomial coefficient b _ij(i=1 ..., 4; J=0 ..., 6) value list in table 2) respectively determine i get the corresponding (H of 1,2,3,4 o'clock _n/ E _c) _ivalue, then utilizes Lagrange's interpolation formula to determine H _n/ E _c:

$H_n/E_c=\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{(H_n/E_c)}_i\underset{\underset{k\≠i}{k=1}}{\overset{4}{\mathrm{\Π}}}[(n-n_k)/(n_i-n_k)]$

Further be pressed into nominal hardness H according to instrumentation _nand ratio H _n/ E _cdetermine the elastic modulus E of combining of tested material and adamas Vickers pressure head _c:

E _c＝H _n/(H _n/E _c)

And the elastic modulus E of tested material:

$E=(1-v^2)/[1/E_c-1.32(1-v_i^2)/E_i]$

Wherein, the elastic modulus E of adamas Vickers pressure head _i=1141GPa, Poisson ratio v _i=0.07, the Poisson ratio v of tested material can determine according to material handbook;

Table 2. multinomial coefficient b _ij(i=1 ..., 4; J=0 ..., 6) value

6) according to 4 different hardenability value n _ithe ratio η of (i=1,2,3,4) and 3 tested materials of difference and diamond penetrator plane-strain elastic modulus _j(j=1,2,3) (η ₁=0.0671, η ₂=0.1917, η ₃=0.3834) instrumentation under is pressed into than merit W _e/ W _twith the ratio relation of yield strength with nominal hardness (multinomial coefficient c _ijk(i=1 ..., 4; J=1,2,3; K=0 ..., 6) value list in table 3) respectively determine i get 1,2,3,4, j gets the corresponding (σ of 1,2,3 o'clock _y/ H _n) _ij(i=1 ..., 4; J=1,2,3) value, then basis and η _j(j=1,2,3) value is determined σ by Lagrange's interpolation formula _y/ H _n:

${\mathrm{\σ}}_y/H_n=\underset{i=1}{\overset{4}{\mathrm{\Σ}}}\left\{\underset{j=1}{\overset{3}{\mathrm{\Σ}}}{({\mathrm{\σ}}_y/H_n)}_{\mathrm{ij}}\underset{\underset{m\≠j}{m=1}}{\overset{3}{\mathrm{\Π}}}\right[(\mathrm{\η}-{\mathrm{\η}}_m)/({\mathrm{\η}}_j-{\mathrm{\η}}_m)\left]\right\}\underset{\underset{k\≠i}{k=1}}{\overset{4}{\mathrm{\Π}}}[(n-n_k)/(n_j-n_k)]$

Further be pressed into nominal hardness H according to instrumentation _nand ratio σ _y/ H _ndetermine the yield strength σ of tested material _y:

σ _y＝H _n(σ _y/H _n)

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

Table 3. multinomial coefficient c _ijk(i=1 ..., 4; J=1,2,3; K=0 ..., 6) value

7) calculate ε _y=σ _y/ E, and by relational expression determine ε _b, the finally strength degree σ of definite tested material _b:

${\mathrm{\σ}}_b=\left\{\begin{array}{cc}{\mathrm{\σ}}_y/\exp \left({2\mathrm{v\ϵ}}_y\right),& {\mathrm{\ϵ}}_b\≤{\mathrm{\ϵ}}_y\\ {\mathrm{\σ}}_y{({\mathrm{\ϵ}}_b/{\mathrm{\ϵ}}_y)}^n/\exp [{\mathrm{\ϵ}}_b+(2v-1){\mathrm{\ϵ}}_y^{1-n}{\mathrm{\ϵ}}_b^n],& {\mathrm{\ϵ}}_b>{\mathrm{\ϵ}}_y\end{array}\right.$

Below describe forming process of the present invention in detail.Vickers impression schematic diagram is as shown in accompanying drawing 1a and accompanying drawing 1b, and in definition Vickers impression, back gauge d is Vickers impression center to a four impression frontier distance d ₁, d ₂, d ₃and d ₄mean value, i.e. d=(d ₁+ d ₂+ d ₃+ d ₄)/4.Adamas Vickers pressure head schematic diagram as shown in Figure 2, according to maximum compression distance h _mback gauge d in definition Vickers name impression _n=h _mtan68 °.As shown in Figure 3, the longitudinal axis represents loading of pressing in P to instrumentation loading of pressing in-displacement curve schematic diagram, and transverse axis represents compression distance h, and loading curve is 1, and unloading curve is 2, loads merit W _tregion is 3, unloading merit W _eregion is 4.It is P that instrumentation is pressed into the maximum loading of pressing in setting _m, the maximum compression distance of answering is in contrast h _m.With A (h _m) represent that adamas Vickers pressure head is at maximum compression distance h _mthe adamas Vickers pressure head cross-sectional area of position, nominal hardness H _nbe defined as maximum loading of pressing in P _mwith adamas Vickers pressure head cross-sectional area A (h _m) ratio, i.e. H _n=P _m/ A (h _m).Further definition instrumentation is pressed into and loads merit W _twith unloading merit W _ebe respectively and implement instrumentation adamas Vickers pressure head is in load phase and unloading phase institute work while being pressed into, its value equals respectively loading curve and unloading curve and instrumentation loading of pressing in-displacement curve area that horizontal ordinate encloses.Instrumentation is pressed into than merit W _e/ W _tfor unloading merit W _ewith loading merit W _tratio.

Adamas Vickers pressure head is considered as to elastic body, and its elastic modulus and Poisson ratio are used respectively E _iand v _irepresent; Measured material is considered as elasticoplastic body, and its single shaft true strain-stress relation is made up of linear elasticity and Hollomon power hardening function, and its elastic modulus and Poisson ratio represent with E and v respectively simultaneously, and yield strength and strain hardening exponent are used respectively σ _yrepresent with n.Based on above-mentioned setting and ignore the friction of adamas Vickers pressure head and tested storeroom, instrumentation is pressed into nominal hardness H _n, instrumentation is pressed into than merit W _e/ W _tand the ratio d/d of back gauge in back gauge and name in Vickers impression _ncan be expressed as the yield strength σ of measured material _y, strain hardening exponent n, elastic modulus E, Poisson ratio v and adamas Vickers pressure head elastic modulus E _i, Poisson ratio v _iand maximum compression distance h _mfunction:

$H_n={\mathrm{\Γ}}_{H1}({\mathrm{\σ}}_y,n,E/(1-v^2),E_i/(1-v_i^2),h_m)---\left(1\right)$

$W_e/W_t={\mathrm{\Γ}}_{W1}({\mathrm{\σ}}_y,n,E/(1-v^2),E_i/(1-v_i^2),h_m)---\left(2\right)$

$d/d_n={\mathrm{\Γ}}_{D1}({\mathrm{\σ}}_y,n,E/(1-v^2),E_i/(1-v_i^2),h_m)---\left(3\right)$

Wherein E/ (1-v ²) and be respectively the plane-strain elastic modulus of measured material and adamas Vickers pressure head.Elastic modulus is amounted in utilization and the ratio of plane-strain elastic modulus the plane-strain elastic modulus of measured material and adamas Vickers pressure head can be expressed as:

E/(1-v ²)＝(η+1)E _r (4)

$E_i/(1-v_i^2)=\left[(\mathrm{\η}+1)E_r\right]/\mathrm{\η}---\left(5\right)$

So formula (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)

Application dimension ∏ theorem, formula (6), (7) and (8) can be reduced to:

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)

Can be obtained by formula (10):

${\mathrm{\σ}}_y/E_r={\mathrm{\Γ}}_{W3}^{-1}(W_e/W_t,n,\mathrm{\η})---\left(12\right)$

Formula (12) substitution formula (9) and formula (11) are obtained:

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)

Can be obtained by formula (12) and formula (13):

σ _y/H _n＝Γ ₅(W _e/W _t，n，η) (15)

Can obtain the explicit solution of formula (13), formula (14) and formula (15) by finite element numerical simulation.In simulation, the Elastic Modulus Values of adamas Vickers pressure head is E _i=1141GPa, Poisson ratio value is v _i=0.07.The value of measured material elastic modulus E is made as respectively 70GPa, 200GPa and 400GPa; Yield strength σ _yspan be 0.7～160000MPa; The value of strain hardening exponent n is 0,0.15,0.3 and 0.45; Poisson ratio v gets fixed value 0.3.Measured material is respectively 0.0671,0.1917 and 0.3834 with the ratio η of the plane-strain elastic modulus of adamas Vickers pressure head; Coefficient of contact friction value between measured material and adamas Vickers pressure head is zero.

Accompanying drawing 4a, accompanying drawing 4b, accompanying drawing 4c and accompanying drawing 4d are the H of corresponding different n and η _n/ E _r-W _e/ W _tgraph of a relation, as can be seen from the figure, for definite strain hardening exponent n, η is to H _n/ E _r-W _e/ W _trelation has a certain impact, and this shows to amount to elastic modulus E _rcan not accurately reflect the comprehensive elastic effect between measured material and adamas Vickers pressure head.For this reason, definition associating elastic modulus $E_c=1/[(1-v^2)/E+1.32(1-v_i^2)/E_i],$ And substituted and amounted to elastic modulus E _rcan obtain H _n/ E _c-W _e/ W _trelation, result as shown in accompanying drawing 5a, accompanying drawing 5b, accompanying drawing 5c and accompanying drawing 5d, as can be seen from the figure, for definite strain hardening exponent n, H _n/ E _c-W _e/ W _trelation is subject to the impact of η hardly.So, can utilize polynomial function to the H under 4 of strain hardening exponent n different value condition _n/ E _c-W _e/ W _trelation carries out curve fitting, and result is expressed as:

${(H_n/E_c)}_i=\underset{j=0}{\overset{6}{\mathrm{\Σ}}}{b}_{\mathrm{ij}}{(W_e/W_t)}^j---\left(16\right)$

Wherein, i=1 ..., 4 different values of the corresponding strain hardening exponent n of 4 difference: 0,0.15,0.3,0.45; Coefficient b _ij(j=0 ..., 6) value in table 2.The n of formula (16) representative gets respectively 0,0.15,0.30 and the H of 0.45 o'clock _n/ E _c-W _e/ W _trelation as shown in Figure 6.

Table 2. coefficient b _ij(i=1 ..., 4; J=0 ..., 6) value

Accompanying drawing 7 is the d/d of corresponding different n and η _n-W _e/ W _tgraph of a relation, as can be seen from the figure, for definite strain hardening exponent n, η is to d/d _n-W _e/ W _tthe impact of relation can be ignored.Therefore, can utilize polynomial function to the d/d under 4 of strain hardening exponent n different value condition _n-W _e/ W _trelation carries out curve fitting, and result is expressed as:

${(d/d_n)}_i=\underset{j=0}{\overset{2}{\mathrm{\Σ}}}{a}_{\mathrm{ij}}{(W_e/W_t)}^j---\left(17\right)$

Wherein, i=1 ..., 4 different values of the corresponding strain hardening exponent n of 4 difference: 0,0.15,0.3,0.45; Coefficient a _ijthe value of (j=0,1,2) is in table 1.

Table 1. coefficient a _ij(i=1 ..., 4; J=0,1,2) value

Accompanying drawing 8a, accompanying drawing 8b and accompanying drawing 8c are the σ of corresponding different n and η _y/ H _n-W _e/ W _tgraph of a relation.Utilize polynomial function to σ _y/ H _n-W _e/ W _trelation is carried out matching, and result can be expressed as:

${({\mathrm{\σ}}_y/H_n)}_{\mathrm{ij}}=\underset{k=0}{\overset{6}{\mathrm{\Σ}}}{c}_{\mathrm{ijk}}{(W_e/W_t)}^k---\left(18\right)$

Wherein, i=1 ..., the value of 4 corresponding n is 0,0.15,0.3,0.45; J=1, the value of 2,3 corresponding η is 0.0671,0.1917,0.3834; Coefficient c _ijk(k=0 ..., 6) value in table 3.

Table 3. coefficient c _ijk(i=1 ..., 4; J=1,2,3; K=0 ..., 6) value

Application Example

Select 6061 aluminium alloys, S45C carbon steel, SS316 stainless steel and brass to carry out instrumentation and be pressed into experiment.According to experimental procedure that inventor carries, high precision instrument press fit instrument [the horse German army of national inventing patent mandate is developed and has obtained in application voluntarily, Song Zhongkang, Guo Junhong, Chen Wei. the computing method of a kind of high precision press fit instrument and the diamond penetrator pressing in sample degree of depth. the patent No.: ZL201110118464.9] and adamas Vickers pressure head 6061 aluminium alloys, S45C carbon steel, SS316 stainless steel and brass zones of different repeated to 5 instrumentations be pressed into experiment.Fig. 9, Figure 10, Figure 11 and Figure 12 are respectively the instrumentation loading of pressing in-displacement curve of 6061 aluminium alloys, S45C carbon steel, SS316 stainless steel and brass.Applied optics microscope can be observed respectively back gauge in the Vickers impression of 6061 aluminium alloys, S45C carbon steel, SS316 stainless steel and brass.

According to instrumentation loading of pressing in-displacement curve and Vickers impression, can determine respectively that the instrumentation of measured material is pressed into nominal hardness H _n, instrumentation is pressed into than merit W _e/ W _tand the ratio d/d of back gauge in back gauge and name in Vickers impression _n, result is as table 4, just application invention people institute extracting method can be determined strain hardening exponent n, elastic modulus E, the offset yield strength σ of tested material on this basis _0.2and strength degree σ _b.In order to compare with standard uniaxial tensile test result, the same material that instrumentation is pressed into experiment 6061 aluminium alloys used, S45C carbon steel, SS316 stainless steel and brass is made respectively standard uniaxial tension sample, and it is implemented respectively to standard uniaxial tensile test 2 times, using the mean value of 2 tests as the test result of material uniaxial tensile test, elastic modulus, strain hardening exponent, offset yield strength and the strength degree of 6061 aluminium alloys of being measured by standard uniaxial tensile test are respectively E _{single shaft}=71GPa, n _{single shaft}=0.052, σ _{0.2 single shaft}=299.37MPa and σ _{b single shaft}=366.25MPa; Elastic modulus, strain hardening exponent, offset yield strength and the strength degree of the S45C carbon steel of being measured by standard uniaxial tensile test are respectively E _{single shaft}=201GPa, n _{single shaft}=0.176, σ _{0.2 single shaft}=431.08MPa and σ _{b single shaft}=612.84MPa; The stainless elastic modulus of SS316, strain hardening exponent, offset yield strength and the strength degree measured by standard uniaxial tensile test are respectively E _{single shaft}=184GPa, n _{single shaft}=0.134, σ _{0.2 single shaft}=610.11MPa and σ _{b single shaft}=827.51MPa; Elastic modulus, strain hardening exponent, offset yield strength and the strength degree of the brass of being measured by standard uniaxial tensile test are respectively E _{single shaft}=83GPa, n _{single shaft}=0.125, σ _{0.2 single shaft}=346.67MPa and σ _{b single shaft}=421.23MPa.The instrumentation of elastic modulus, strain hardening exponent, offset yield strength and the strength degree of 6061 aluminium alloys, S45C carbon steel, SS316 stainless steel and brass is pressed into test result and uniaxial tensile test result compares, can determines that instrumentation is pressed into the test error of test result: E _err=(E-E _{single shaft})/E _{single shaft}, Δ n=n-n _{single shaft}, σ _0.2Err=(σ _0.2-σ _{0.2 single shaft})/σ _{0.2 single shaft}and σ _bErr=(σ _b-σ _{b single shaft})/σ _{b single shaft}, the results are shown in Table 4.As can be seen from the table, the relative test error of elastic modulus of 6061 aluminium alloys, S45C carbon steel, SS316 stainless steel and brass is respectively 4.40%, 1.73% ,-0.34% and 11%, the absolute test error of strain hardening exponent is respectively 0.008,0.001,0.013 and-0.010, offset yield strength σ _0.2relative test error be respectively 10.04% ,-5.37%, 8.65% and 1.26%, strength degree σ _brelative test error be respectively-2.61%, 9.45%, 11.95% and 5.05%.Further be pressed into according to instrumentation the strain hardening exponent n, elastic modulus E and the offset yield strength σ that test 6061 aluminium alloys, S45C carbon steel, SS316 stainless steel and the brass that record _0.2mean value can draw its true strain-stress relation, the comparison of the true strain-stress relation that this relation and standard uniaxial tensile test record is as shown in accompanying drawing 13, Figure 14, Figure 15 and Figure 16, in accompanying drawing 13, Figure 14, Figure 15 and Figure 16, transverse axis is logarithmic strain ε, the longitudinal axis is true stress σ, dotted line is that instrumentation is pressed into test result, and heavy line is uniaxial tensile test one, and fine line is uniaxial tensile test two.As can be seen from the figure both have good consistance.Make a general survey of above experimental result and show, it is feasible and very effective that the metal material elastic-plastic mechanical parameter instrumentation of inventor's carry based on Vickers impression is pressed into method of testing.

Table 4.6061 aluminium alloy, S45C carbon steel, SS316 stainless steel and brass elastic-plastic mechanical parameter instrumentation are pressed into test result and test error

Although above the specific embodiment of the present invention has been given to describe in detail and explanation; but what should indicate is; we can carry out various equivalences to above-mentioned embodiment according to conception of the present invention and change and amendment; when its function producing does not exceed spiritual that instructions and accompanying drawing contain yet, all should be within protection scope of the present invention.

Claims (2)

1. the material elastic-plastic mechanical parameter instrumentation based on Vickers impression is pressed into a method of testing, and the method utilizes Vickers pressure head instrumentation to be pressed into metal material gained load-displacement curves and Vickers impression to determine strain hardening exponent n, elastic modulus E, the offset yield strength σ of metal material _0.2and strength degree σ _b, specifically comprise the following steps:

1) utilizing instrumentation press fit instrument and adamas Vickers pressure head to implement a certain maximum loading of pressing in to measured material is P _minstrumentation be pressed into test, obtain loading of pressing in-displacement curve, utilize this curve to determine the maximum compression distance h of adamas Vickers pressure head simultaneously _m, nominal hardness H _n=P _m/ A (h _m), wherein, A (h _m) adamas Vickers pressure head cross-sectional area while being corresponding maximum compression distance, in the time not considering the crest truncation of adamas Vickers pressure head and while considering the crest truncation of adamas Vickers pressure head, A (h _m) should be determined by the area function A (h) of adamas Vickers pressure head,

2) calculate to be pressed into by the loading curve in integration load-displacement curves relation respectively and unloading curve and load merit W _t, unloading merit W _e, and calculate and be pressed into than merit W on this basis _e/ W _t;

3) measure respectively the distance on an impression border, Vickers impression center to four by microscope: d ₁, d ₂, d ₃and d ₄, and back gauge d=(d in determining ₁+ d ₂+ d ₃+ d ₄)/4 and with name in back gauge d _n=h _mthe ratio d/d of tan68 ° _n;

4) according to 4 different hardenability value (n ₁=0, n ₂=0.15, n ₃=0.30, n ₄=0.45) instrumentation under is pressed into than merit W _e/ W _twith d/d _nrelation wherein, i value is respectively 1,2,3,4 (corresponding to 4 different hardenability values), multinomial coefficient a _ij(i=1 ..., 4; J=0,1,2) value is:

Determine that respectively i gets the corresponding (d/d of 1,2,3,4 o'clock _n) _ivalue, then determine n ' according to Lagrange's interpolation formula:

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

n＝max{n′，0}

5) according to 4 different hardenability value n _iinstrumentation under (i=1,2,3,4) is pressed into than merit W _e/ W _twith ratio H _n/ E _crelation wherein, E _cfor tested material and the elastic modulus of combining of adamas Vickers pressure head, multinomial coefficient b _ij(i=1 ..., 4; J=0 ..., 6) value be:

Determine that respectively i gets the corresponding (H of 1,2,3,4 o'clock _n/ E _c) _ivalue, then utilizes Lagrange's interpolation formula to determine H _n/ E _c:

Further be pressed into nominal hardness H according to instrumentation _nand ratio H _n/ E _cdetermine the elastic modulus E of combining of tested material and adamas Vickers pressure head _c:

E _c＝H _n/(H _n/E _c)

And the elastic modulus E of tested material:

Wherein, the elastic modulus E of adamas Vickers pressure head _i=1141GPa, Poisson ratio v _i=0.07, the Poisson ratio v of tested material can determine according to material handbook;

6) according to 4 different hardenability value n _ithe ratio η of (i=1,2,3,4) and 3 tested materials of difference and diamond penetrator plane-strain elastic modulus _j(j=1,2,3) (η ₁=0.0671, η ₂=0.1917, η ₃=0.3834) instrumentation under is pressed into than merit W _e/ W _twith the ratio relation of yield strength with nominal hardness wherein, multinomial coefficient c _ijk(i=1 ..., 4; J=1,2,3; K=0 ..., 6) value be:

Determine that respectively i gets 1,2,3,4, j gets the corresponding (σ of 1,2,3 o'clock _y/ H _n) _ij(i=1 ..., 4; J=1,2,3) value, then basis and η _j(j=1,2,3) value is determined σ by Lagrange's interpolation formula _y/ H _n:

Further be pressed into nominal hardness H according to instrumentation _nand ratio σ _y/ H _ndetermine the yield strength σ of tested material _y:

σ _y＝H _n(σ _y/H _n)

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

7) calculate ε _y=σ _y/ E, and by relational expression determine ε _b, the finally strength degree σ of definite tested material _b:

。

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