CN104165814B - 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.Specifically related to one kind utilizes instrumentation press fit instrument and vickers Pressure head test metal material strain hardening exponent, elastic modelling quantity, offset yield strength σ_0.2And strength degree σ_bMethod.

Background technology

Instrumentation press-in measuring technology acts on loading of pressing in and Buddha's warrior attendant on diamond penetrator by real-time synchronization measurement The compression distance that stone pressure head is pressed into measured material surface obtains loading of pressing in-displacement curve, is pressed into response and quilt according to instrumentation Survey the dimensionless functional relation between material mechanical parameters, many mechanical property parameters of recognizable measured material.

The instrumentation press-in test of elasticity modulus of materials mainly has the " oliver- that w.c.oliver and g.m.pharr proposes " horse German army method " or " pure ENERGY METHOD " that pharr method " or " gradient method " and horse German army propose.The reason of " gradient method " It is small deformation elastic theory by basis, due to not considering plastic behavior under pressure head effect for the measured material and geometrical large distortion, So that " gradient method " is when being applied to the measured material of low strain dynamic hardenability value, test result substantial deviation elastic modelling quantity is true Value." pure ENERGY METHOD " considers the non-linear of material, geometry and contact boundary condition, and the measuring accuracy of its elastic modelling quantity is therefore It is higher than " gradient method ".Even so, " pure ENERGY METHOD " still has certain theoretical test error, this error comes from tested The strain hardening exponent of material is unknown, therefore manages to identify that the strain hardening exponent of tested material is to improve elasticity modulus of materials Instrumentation is pressed into unique effective way of measuring accuracy.

The instrumentation press-in test of material strain hardenability value and yield strength presently, there are single based on spherical indenter Ball pressure head plunging and the multiple cone pressure head plunging based on cone bearings of various cone top angle, wherein apply single ball pressure head plunging to run into Difficulty is that manufacture radius is several or tens microns its geometry machining accuracy of spherical indenter is difficult to meet test request, therefore, Material strain hardenability value based on spherical indenter is pressed into method of testing in practical application or engineering with the instrumentation of yield strength Change aspect is had little scope for one's talents.There is not pressure head manufacture view in application multiple cone pressure head plunging, but test process needs more Change the pyramid pressure head at cone bearings of various cone top angle, simultaneously need to re-scaling to machine compliance, and Accurate Calibration machine compliance both consumed When again difficult, therefore apply bore pressure head plunging carry out testing it less efficient.

For problem present in the press-in test of metal current material elastic-plastic mechanical parameter instrumentation, the present invention proposes one kind Metal material strain hardening exponent based on vickers impression, elastic modelling quantity, offset yield strength σ_0.2And strength degree σ_b's Instrumentation is pressed into method of testing.

Content of the invention

It is an object of the invention to provide a kind of metal material elastic-plastic mechanical parameter instrumentation press-in based on vickers impression is surveyed Method for testing, using the elastic-plastic mechanical parameter that the method can determine metal material include strain hardening exponent, elastic modelling quantity, condition bend Take intensity σ_0.2And strength degree σ_b.With the pyramid pressure head instrumentation press-in test using two or more cone bearings of various cone top angles Method is compared, and the method is only implemented instrumentation press-in using single vickers pressure head and tested and be aided with vickers to metal material The test of impression geometric parameter can determine that strain hardening exponent n of metal material, elastic modelling quantity e, offset yield strength σ_0.2And it is strong Degree limit σ_b, it is to avoid need individually designed processing before test different from the non-standard pyramid pressure head of standard icicle pressure head cone-apex angle Replaceable pressure head and the problem needing machine compliance is re-scaled thus leading to is needed in problem, and test process, Improve testing efficiency.

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

A kind of metal material elastic-plastic mechanical parameter instrumentation press-in method of testing based on vickers impression, the method utilizes Single vickers pressure head instrumentation is pressed into metal material gained load-displacement curves and impression determines metal material should be hardening Change index, elastic modelling quantity, offset yield strength σ_0.2And strength degree σ_b；First, using back gauge in vickers impression and name The ratio of middle back gauge and instrumentation are pressed into the strain hardening exponent determining metal material than work(；Secondly, using instrumentation press-in than work(, Instrumentation is pressed into nominal hardness and test gained strain hardening exponent determines the elastic modelling quantity of metal material；Finally, using instrument Change the bar that press-in determines metal material than work(, instrumentation press-in nominal hardness and test gained elastic modelling quantity and strain hardening exponent Part yield strength σ_0.2With strength degree σ_b.Specifically include following steps:

1) using instrumentation press fit instrument and diamond vickers pressure head, measured material being implemented with a certain maximum loading of pressing in is p_mInstrumentation press-in test, obtain loading of pressing in-displacement curve, determine diamond vickers pressure head using this curve simultaneously Maximum compression distance h_m, nominal hardness h_n=p_m/a(h_m), wherein, a (h_m) it is diamond during corresponding maximum compression distance Vickers pressure head cross-sectional area, when not considering the passivation of diamond vickers indenter tipAnd consider gold During the passivation of hard rock 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(respectively w_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 back gauge d=(d in determining₁+d₂+d₃+d₄)/4 and its with back gauge d in name_n=h_mTan68 ° of ratio d/d_n；

4) according to 4 different hardenability value (n₁=0, n₂=0.15, n₃=0.30, n₄=0.45) the instrumentation press-in under Ratio work(w_e/w_tWith d/d_nRelation(multinomial coefficient a_ij(i=1 ..., 4；J=0,1,2) Value be listed in table 1) respectively determine i take corresponding (d/d when 1,2,3,4_n)_iValue, then determines according to Lagrange's interpolation formula N ':

$n^{\′}=\underset{i=1}{\overset{4}{\mathrm{\σ}}}{n}_i\underset{\underset{k\&notequal;i}{k=1}}{\overset{4}{\mathrm{\π}}}\left\{\right[(d/d_n)-{(d/d_n)}_k]/[{(d/d_n)}_i-{(d/d_n)}_k\left]\right\}$

Determine strain hardening exponent n of tested material further 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 press-in ratio work(w under (i=1,2,3,4)_e/w_tWith ratio h_n/e_c's Relation(multinomial coefficient b_ij(i=1 ..., 4；J=0 ..., 6) value be listed in table 2) 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:

$h_n/e_c=\underset{i=1}{\overset{4}{\mathrm{\σ}}}{(h_n/e_c)}_i\underset{\underset{k\&notequal;i}{k=1}}{\overset{4}{\mathrm{\π}}}[(n-n_k)/(n_i-n_k)]$

Further nominal hardness h is pressed into according to instrumentation_nAnd ratio h_n/e_cDetermine tested material and diamond vickers The joint elastic modelling quantity e of pressure head_c:

e_c=h_n/(h_n/e_c)

And the elastic modelling quantity e of tested material:

$e=(1-v^2)/[1/e_c-1.32(1-v_i^2)/e_i]$

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

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

6) according to 4 different hardenability value n_iThe tested material of (i=1,2,3,4) and 3 differences and diamond penetrator are put down The ratio η of Changeable elastic modulus is answered in face_j(j=1,2,3) (η₁=0.0671, η₂=0.1917, η₃=0.3834) the instrumentation press-in under Ratio work(w_e/w_tWith yield strength with nominal hardness ratio relation(multinomial coefficient c_ijk(i =1 ..., 4；J=1,2,3；K=0 ..., 6) value be listed in table 3) determine respectively i take 1,2,3, phase when 4, j takes 1,2,3 Should (σ_y/h_n)_ij(i=1 ..., 4；J=1,2,3) value, then basisAnd η_j(j= 1,2,3) value determines σ by Lagrange's interpolation formula_y/h_n:

${\mathrm{\σ}}_y/h_n=\underset{i=1}{\overset{4}{\mathrm{\σ}}}\left\{\underset{j=1}{\overset{3}{\mathrm{\σ}}}{({\mathrm{\σ}}_y/h_n)}_{\mathrm{ij}}\underset{\underset{m\&notequal;j}{m=1}}{\overset{3}{\mathrm{\π}}}\right[(\mathrm{\η}-{\mathrm{\η}}_m)/({\mathrm{\η}}_j-{\mathrm{\η}}_m)\left]\right\}\underset{\underset{k\&notequal;i}{k=1}}{\overset{4}{\mathrm{\π}}}[(n-n_k)/(n_j-n_k)]$

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 expression σ_0.2=σ_y ^1-n[σ_0.2+0.002e]ⁿDetermine 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 expressionDetermine ε_b, finally determine tested material Strength degree σ_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's ratio of measured material can not be determined by Materials Handbook, value is 0.3.

Compared with the pyramid pressure head instrumentation press-in method of testing using two or more cone bearings of various cone top angles, this Bright only using single vickers pressure head, metal material enforcement instrumentation press-in is tested and is aided with vickers impression geometric parameter Test can determine that strain hardening exponent n of metal material, elastic modelling quantity e, offset yield strength σ_0.2And strength degree σ_b, keep away Need individually designed processing before having exempted to test different from the non-standard pyramid pressure head problem of standard icicle pressure head cone-apex angle, and survey Need replaceable pressure head and the problem needing machine compliance is re-scaled thus leading to during examination, improve test effect Rate.

Brief description:

Fig. 1 a be drum convex in the case of vickers impression schematic diagram；

Fig. 1 b is the vickers impression schematic diagram in the case of depression；

Fig. 2 is vickers pressure head schematic diagram；

Fig. 3 is instrumentation press-in Load-unload curve and Load-unload work(schematic diagram；

Fig. 4 a is corresponding n=0, and η takes the h of 0.0671,0.1917 and 0.3834 3 numerical value respectively_n/e_r-w_e/w_tRelation Figure；

Fig. 4 b is corresponding n=0.15, and η takes the h of 0.0671,0.1917 and 0.3834 3 numerical value respectively_n/e_r-w_e/w_tClose System's figure；

Fig. 4 c is corresponding n=0.30, and η takes the h of 0.0671,0.1917 and 0.3834 3 numerical value respectively_n/e_r-w_e/w_tClose System's figure；

Fig. 4 d is corresponding n=0.45, and η takes the h of 0.0671,0.1917 and 0.3834 3 numerical value respectively_n/e_r-w_e/w_tClose System's figure；

Fig. 5 a is corresponding n=0, and η takes the h of 0.0671,0.1917 and 0.3834 3 numerical value respectively_n/e_c-w_e/w_tRelation Figure；

Fig. 5 b is corresponding n=0.15, and η takes the h of 0.0671,0.1917 and 0.3834 3 numerical value respectively_n/e_c-w_e/w_tClose System's figure；

Fig. 5 c is corresponding n=0.30, and η takes the h of 0.0671,0.1917 and 0.3834 3 numerical value respectively_n/e_c-w_e/w_tClose System's figure；

Fig. 5 d is corresponding n=0.45, and η takes the h of 0.0671,0.1917 and 0.3834 3 numerical value respectively_n/e_c-w_e/w_tClose System's figure；

Fig. 6 is that the n representated by formula (16) takes h when 0,0.15,0.30 and 0.45 respectively_n/e_c-w_e/w_tGraph of a relation；

Fig. 7 is the d/d of corresponding difference n and η_n-w_e/w_tGraph of a relation；

Fig. 8 a is corresponding η=0.0671, and n takes the σ of 0,0.15,0.30 and 0.45 4 numerical value respectively_y/h_n-w_e/w_tRelation Figure；

Fig. 8 b is corresponding η=0.1917, and n takes the σ of 0,0.15,0.30 and 0.45 4 numerical value respectively_y/h_n-w_e/w_tRelation Figure；

Fig. 8 c is corresponding η=0.3834, and n takes the σ of 0,0.15,0.30 and 0.45 4 numerical value respectively_y/h_n-w_e/w_tRelation Figure；

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 ss316 stainless instrumentation loading of pressing in-displacement curve；

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

Figure 13 is to be respectively adopted instrumentation press-in test to answer with the true of standard uniaxial tensile test gained 6061 aluminium alloy The comparison of power-strain stress relation；

Figure 14 be respectively adopted instrumentation press-in test and standard uniaxial tensile test gained s45c carbon steel true stress- The comparison of strain stress relation；

Figure 15 is to be respectively adopted instrumentation press-in test and standard uniaxial tensile test gained ss316 is stainless truly should The comparison of power-strain stress relation；

Figure 16 is the true strain-stress being respectively adopted instrumentation press-in test and standard uniaxial tensile test gained pyrite The comparison of relation.

Specific embodiment

Below by way of combining accompanying drawing, the method for the present invention is described in detail, but these embodiments are only the mesh illustrating It is no intended to any restriction is carried out to the scope of the present invention.Present applicant proposes a kind of metal material based on vickers impression Material elastic-plastic mechanical parameter instrumentation press-in method of testing, the method utilizes single vickers pressure head instrumentation to be pressed into metal material institute Load-displacement curves and impression determine the strain hardening exponent of metal material, elastic modelling quantity, offset yield strength σ_0.2And it is strong Degree limit σ_b；First, it is pressed into and determines metal material than work(with the ratio of back gauge in name and instrumentation using back gauge in vickers impression The strain hardening exponent of material；Secondly, using instrumentation press-in than work(, instrumentation press-in nominal hardness and test gained strain hardening Index determines the elastic modelling quantity of metal material；Finally, using instrumentation press-in than work(, instrumentation press-in nominal hardness and test institute Obtain elastic modelling quantity and strain hardening exponent determines offset yield strength σ of metal material_0.2With strength degree σ_b.Specifically include with Lower step:

1) using instrumentation press fit instrument and diamond vickers pressure head, measured material being implemented with a certain maximum loading of pressing in is p_mInstrumentation press-in test, obtain loading of pressing in-displacement curve, determine diamond vickers pressure head using this curve simultaneously Maximum compression distance h_m, nominal hardness h_n=p_m/a(h_m), wherein, a (h_m) it is diamond during corresponding maximum compression distance Vickers pressure head cross-sectional area, when not considering the passivation of diamond vickers indenter tipAnd consider gold During the passivation of hard rock vickers indenter tip, then a (h_m) should be determined by area function a (h) of diamond vickers pressure head, I.e.

2) pass through to integrate the loading curve in load-displacement curves relation and unloading curve calculating press-in loading work(respectively w_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 back gauge d=(d in determining₁+d₂+d₃+d₄)/4 and its with back gauge d in name_n=h_mTan68 ° of ratio d/d_n；

4) according to 4 different hardenability value (n₁=0, n₂=0.15, n₃=0.30, n₄=0.45) the instrumentation press-in under Ratio work(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 i takes corresponding (d/d when 1,2,3,4 respectively_n)_iValue, then determines according to Lagrange's interpolation formula N ':

$n^{\′}=\underset{i=1}{\overset{4}{\mathrm{\σ}}}{n}_i\underset{\underset{k\&notequal;i}{k=1}}{\overset{4}{\mathrm{\π}}}\left\{\right[(d/d_n)-{(d/d_n)}_k]/[{(d/d_n)}_i-{(d/d_n)}_k\left]\right\}$

Determine strain hardening exponent n of tested material further 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 press-in ratio work(w under (i=1,2,3,4)_e/w_tWith ratio h_n/e_c's Relation(multinomial coefficient b_ij(i=1 ..., 4；J=0 ..., 6) value be listed in table 2) 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:

$h_n/e_c=\underset{i=1}{\overset{4}{\mathrm{\σ}}}{(h_n/e_c)}_i\underset{\underset{k\&notequal;i}{k=1}}{\overset{4}{\mathrm{\π}}}[(n-n_k)/(n_i-n_k)]$

Further nominal hardness h is pressed into according to instrumentation_nAnd ratio h_n/e_cDetermine tested material and diamond vickers The joint elastic modelling quantity e of pressure head_c:

e_c=h_n/(h_n/e_c)

And the elastic modelling quantity e of tested material:

$e=(1-v^2)/[1/e_c-1.32(1-v_i^2)/e_i]$

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

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

6) according to 4 different hardenability value n_iThe tested material of (i=1,2,3,4) and 3 differences and diamond penetrator are put down The ratio η of Changeable elastic modulus is answered in face_j(j=1,2,3) (η₁=0.0671, η₂=0.1917, η₃=0.3834) the instrumentation press-in under Ratio work(w_e/w_tWith yield strength with nominal hardness ratio relation(multinomial coefficient c_ijk(i =1 ..., 4；J=1,2,3；K=0 ..., 6) value be listed in table 3) determine respectively i take 1,2,3, phase when 4, j takes 1,2,3 Should (σ_y/h_n)_ij(i=1 ..., 4；J=1,2,3) value, then basisAnd η_j(j= 1,2,3) value determines σ by Lagrange's interpolation formula_y/h_n:

${\mathrm{\σ}}_y/h_n=\underset{i=1}{\overset{4}{\mathrm{\σ}}}\left\{\underset{j=1}{\overset{3}{\mathrm{\σ}}}{({\mathrm{\σ}}_y/h_n)}_{\mathrm{ij}}\underset{\underset{m\&notequal;j}{m=1}}{\overset{3}{\mathrm{\π}}}\right[(\mathrm{\η}-{\mathrm{\η}}_m)/({\mathrm{\η}}_j-{\mathrm{\η}}_m)\left]\right\}\underset{\underset{k\&notequal;i}{k=1}}{\overset{4}{\mathrm{\π}}}[(n-n_k)/(n_j-n_k)]$

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 expression σ_0.2=σ_y ^1-n[σ_0.2+0.002e]ⁿDetermine 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 expressionDetermine ε_b, finally determine tested material Strength degree σ_b:

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

The forming process of the present invention described further below.Vickers impression schematic diagram is as shown in accompanying drawing 1a and accompanying drawing 1b, fixed In adopted vickers impression, back gauge d is vickers impression center to four impression frontier distance d₁、d₂、d₃And d₄Meansigma methodss, that is, D=(d₁+d₂+d₃+d₄)/4.Diamond vickers pressure head schematic diagram as shown in Figure 2, according to maximum compression distance h_mDefinition Back gauge d in vickers name impression_n=h_mtan68°.Instrumentation loading of pressing in-displacement curve schematic diagram as shown in Figure 3, is indulged Axle represents loading of pressing in p, and transverse axis represents compression distance h, and loading curve is 1, and unloading curve is 2, loads work(w_tRegion is 3, unloads Carry work(w_eRegion is 4.The set maximum loading of pressing in of instrumentation press-in is p_m, corresponding maximum compression distance is h_m. With a (h_m) represent diamond vickers pressure head in maximum compression distance h_mDiamond vickers pressure head cross-sectional area at position, Then nominal hardness h_nIt is defined as maximum loading of pressing in p_mWith diamond vickers pressure head cross-sectional area a (h_m) ratio, i.e. h_n= p_m/a(h_m).Define instrumentation press-in further and load work(w_tWith unloading work(w_eIt is respectively diamond when implementing instrumentation press-in Vickers pressure head is respectively equal to loading curve and unloading curve and instrument in load phase and unloading phase work done, its value Change the enclosed area of loading of pressing in-displacement curve abscissa.Instrumentation is pressed into ratio work(w_e/w_tFor unloading work(w_eWith loading work(w_tRatio Value.

Diamond vickers pressure head is considered as elastomer, its elastic modelling quantity and Poisson's ratio use e respectively_iAnd v_iRepresent；Tested 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, simultaneously Its elastic modelling quantity and Poisson's ratio are represented with e and v respectively, and yield strength and strain hardening exponent use σ respectively_yRepresent with n.Based on upper State the friction setting and ignoring diamond vickers pressure head and tested storeroom, then instrumentation press-in nominal hardness h_n, instrument Change press-in ratio work(w_e/w_tAnd in vickers impression back gauge with name in back gauge ratio d/d_nMeasured material can be expressed as Yield strength σ_y, strain hardening exponent n, the elastic modelling quantity e of elastic modelling quantity e, Poisson's ratio v and diamond vickers pressure head_i, pool Pine compares 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-v²) andIt is respectively the plane strain bullet of measured material and diamond vickers pressure head Property modulus.Using equivalent elastic modelling quantityAnd the ratio of plane-strain elastic modulusThe plane-strain elastic modulus of measured material and diamond vickers pressure head can be divided It is not expressed as:

e/(1-v²)=(η+1) e_r(4)

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

Then, 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) and (9)

w_e/w_t=γ_w3(σ_y/e_r, n, η) and (10)

d/d_n=γ_d3(σ_y/e_r, n, η) and (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) is substituted into formula (9) and formula (11) obtains:

h_n/e_r=γ_h4(w_e/w_t, n, η) and (13)

d/d_n=γ_d4(w_e/w_t, n, η) and (14)

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

σ_y/h_n=γ₅(w_e/w_t, n, η) and (15)

The explicit solution of formula (13), formula (14) and formula (15) can be obtained by finite element numerical simulation.Diamond in simulation The Elastic Modulus Values of vickers pressure head are e_i=1141gpa, Poisson's ratio value is v_i=0.07.Measured material elastic modelling quantity e Value be set to 70gpa, 200gpa and 400gpa；Yield strength σ_ySpan be 0.7～160000mpa；Strain The value of hardenability value n is 0,0.15,0.3 and 0.45；Poisson's ratio v takes fixed value 0.3.Measured material and diamond vickers The ratio η of the plane-strain elastic modulus of pressure head is respectively 0.0671,0.1917 and 0.3834；Measured material and diamond Coefficient of contact friction value between vickers pressure head is zero.

Accompanying drawing 4a, accompanying drawing 4b, accompanying drawing 4c and accompanying drawing 4d are the h of corresponding difference n and η_n/e_r-w_e/w_tGraph of a relation, can from figure To find out, for strain hardening exponent n determining, η is to h_n/e_r-w_e/w_tRelation has a certain impact, and this shows equivalent elasticity Modulus e_rThe comprehensive buoyancy effect between measured material and diamond vickers pressure head can not be accurately reflected.For this reason, definition joint Elastic modelling quantity $e_c=1/[(1-v^2)/e+1.32(1-v_i^2)/e_i],$ And substituted equivalent elastic modelling quantity e_rH can be obtained_n/e_c- w_e/w_tRelation, result as shown in accompanying drawing 5a, accompanying drawing 5b, accompanying drawing 5c and accompanying drawing 5d, it can be seen that for the strain determining Hardenability value n, h_n/e_c-w_e/w_tRelation is hardly affected by η.Thus it is possible to using polynomial function to strain hardening exponent H under the different value condition of 4 of n_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 corresponds to 4 of strain hardening exponent n different values respectively: 0,0.15,0.3,0.45；System Number b_ijThe value of (j=0 ..., 6) is shown in Table 2.N representated by formula (16) takes h when 0,0.15,0.30 and 0.45 respectively_n/e_c- w_e/w_tRelation is 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 difference n and η_n-w_e/w_tGraph of a relation, it can be seen that should be hardening for determine Change index n, η is to d/d_n-w_e/w_tThe impact of relation can be ignored.Therefore, it can using polynomial function to strain hardening exponent n 4 different value condition under d/d_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 corresponds to 4 of strain hardening exponent n different values respectively: 0,0.15,0.3,0.45；System Number a_ijThe value of (j=0,1,2) is shown 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 difference n and η_y/h_n-w_e/w_tGraph of a relation.Using polynomial function To σ_y/h_n-w_e/w_tRelation is fitted, and result is represented by:

${({\mathrm{\σ}}_y/h_n)}_{\mathrm{ij}}=\underset{k=0}{\overset{6}{\mathrm{\σ}}}{c}_{\mathrm{ijk}}{(w_e/w_t)}^k---\left(18\right)$

Wherein, the value of the corresponding n of i=1 ..., 4 is 0,0.15,0.3,0.45；J=1, the values of 2,3 corresponding η are 0.0671,0.1917,0.3834；Coefficient c_ijkThe value of (k=0 ..., 6) is shown in Table 3.

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

Application Example

6061 aluminium alloys, s45c carbon steel, ss316 rustless steel and pyrite is selected to carry out instrumentation micro-indentation test.According to invention The carried experimental procedure of people, application is voluntarily developed and has been obtained the high precision instrument press fit instrument [Ma De of national inventing patent mandate Army, Song Zhongkang, Guo Junhong, Chen Wei. the computational methods of a kind of high accuracy press fit instrument and diamond penetrator pressing in sample depth. patent Number: zl201110118464.9] and diamond vickers pressure head to 6061 aluminium alloys, s45c carbon steel, ss316 rustless steel and Huang Copper zones of different repeats 5 instrumentation micro-indentation test.Fig. 9, Figure 10, Figure 11 and Figure 12 are respectively 6061 aluminium alloys, s45c Instrumentation loading of pressing in-the displacement curve of carbon steel, ss316 rustless steel and pyrite.Application Optics microscope can observe 6061 respectively Back gauge in aluminium alloy, the vickers impression of s45c carbon steel, ss316 rustless steel and pyrite.

According to instrumentation loading of pressing in-displacement curve and vickers impression, the instrumentation of measured material can be determined respectively Press-in nominal hardness h_n, instrumentation press-in ratio work(w_e/w_tAnd in vickers impression back gauge with name in back gauge ratio d/d_n, knot Really as table 4, application invention people institute extracting method just can determine that strain hardening exponent n of tested material, springform on this basis Amount e, offset yield strength σ_0.2And strength degree σ_b.In order to be compared with standard uniaxial tensile test result, by instrumentation Used by micro-indentation test, the identical material of 6061 aluminium alloys, s45c carbon steel, ss316 rustless steel and pyrite is respectively prepared standard single shaft and draws Stretch sample, and it is implemented respectively with 2 standard uniaxial tensile tests, tried as material uniaxial tension using the meansigma methodss of 2 tests The test result tested, then the elastic modelling quantity of 6061 aluminium alloys being measured by standard uniaxial tensile test, strain hardening exponent, condition Yield strength and strength degree 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；The elastic modelling quantity of s45c carbon steel that measured by standard uniaxial tensile test, strain hardening exponent, offset yield are strong Degree and strength degree 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；By The stainless elastic modelling quantity of ss316, strain hardening exponent, offset yield strength and intensity pole that standard uniaxial tensile test measures Limit is respectively e_{Single shaft}=184gpa, n_{Single shaft}=0.134, σ_{0.2 single shaft}=610.11mpa and σ_{B single shaft}=827.51mpa；Drawn by standard single shaft The elastic modelling quantity of pyrite, strain hardening exponent, offset yield strength and the strength degree of stretching test mensure 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.By 6061 aluminium alloys, s45c carbon steel, The instrumentation press-in of the elastic modelling quantity of ss316 rustless steel and pyrite, strain hardening exponent, offset yield strength and strength degree is surveyed Test result and uniaxial tensile test result are compared it may be determined 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 elastic modelling quantity of 6061 aluminium alloys, s45c carbon steel, ss316 rustless steel and pyrite is relative to test error Respectively 4.40%, 1.73%, -0.34% and 11%, the absolute test error respectively 0.008 of strain hardening exponent, 0.001st, 0.013 and -0.010, offset yield strength σ_0.2Relative test error be respectively 10.04%, -5.37%, 8.65% With 1.26%, strength degree σ_bRelative test error be respectively -2.61%, 9.45%, 11.95% and 5.05%.Further 6061 aluminium alloys that recorded according to instrumentation micro-indentation test, strain hardening exponent n of s45c carbon steel, ss316 rustless steel and pyrite, Elastic modelling quantity e and offset yield strength σ_0.2Meansigma methodss can draw its true strain-stress relation, this relation and standard list The comparison of the true strain-stress relation that axle tension test records as shown in accompanying drawing 13, Figure 14, Figure 15 and Figure 16, accompanying drawing 13, In Figure 14, Figure 15 and Figure 16, transverse axis is logarithmic strain ε, and the longitudinal axis is true stress σ, and dotted line is pressed into test result for instrumentation, slightly Solid line is uniaxial tensile test one, and fine line is uniaxial tensile test two.As can be seen from the figure have preferably consistent both Property.Make a general survey of above test result indicate that, inventor is put forward the metal material elastic-plastic mechanical parameter instrumentation pressure based on vickers impression Input testing method is feasible and very effective.

Table 4.6061 aluminium alloy, s45c carbon steel, ss316 rustless steel and pyrite elastic-plastic mechanical parameter instrumentation press-in test result With test error

Although above the specific embodiment of the present invention being given with detailed description and illustrating, it should be noted that We can carry out various equivalent changes according to the conception of the present invention and change to above-mentioned embodiment, and function produced by it is made With still without departing from description and accompanying drawing covered spiritual when, all should be within 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.