CN104101551A - Material Vickers hardness determining method based on instrumented indentation of Berkovich and nominal hardness hardness - Google Patents
Material Vickers hardness determining method based on instrumented indentation of Berkovich and nominal hardness hardness Download PDFInfo
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- CN104101551A CN104101551A CN201410349037.5A CN201410349037A CN104101551A CN 104101551 A CN104101551 A CN 104101551A CN 201410349037 A CN201410349037 A CN 201410349037A CN 104101551 A CN104101551 A CN 104101551A
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Abstract
The invention discloses a material Vickers hardness determining method based on instrumented indentation of Berkovich and nominal hardness hardness. According to the method, instrumented indentation specific work and nominal hardness of a tested material are determined by a load-displacement curve obtained by instrumented indentation of a Berkovich indenter into the material, and then the Vickers hardness of the tested material is further determined by means of an established function relationship. According to the value of the method, the problem that the Berkovich indenter is widely used in conventional instrumented indentation test while the Vickers hardness of the tested material cannot be obtained is solved.
Description
Technical field
The invention belongs to material mechanical performance field tests.Be specifically related to a kind of Berkovich of utilization pressure head instrumentation loading of pressing in-displacement curve and determine the method for measured material Vickers hardness.
Background technology
The Vickers hardness of material is generally measured by Vickers, its ultimate principle be utilize adamas Vickers pressure head to material surface implement a certain maximum loading of pressing in be P
vmbe pressed into test, keep unloading after maximum loading of pressing in 15-30 second, then measure Vickers impression catercorner length d by microscope, finally determine the Vickers hardness of material: H by formula
v (indentation method)=2sin68 ° of P
vm/ d
2.In above-mentioned measuring process, impression catercorner length definite is basis, and Vickers impression drift angle whether clear be the key that affect measurement of impression catercorner length.In the time that test load is little or material surface has roughness problem, often exists and cause measuring impression catercorner length difficulty or inaccurate problem because Vickers impression drift angle is unintelligible.For this problem, people succeeded in developing and can measure adamas Vickers or Berkovich pressure head simultaneously and be pressed into loading of pressing in and the compression distance (or claiming to be pressed into displacement) in materials process in the early 1990s in last century, and the method for testing that material hardness is new proposed accordingly, such hardness is referred to as instrumentation penetration hardness, and this quasi-instrument is referred to as instrumentation press fit instrument.The testing feature of instrumentation penetration hardness is not need to measure impression catercorner length.But, use instrumentation penetration hardness also to have an outstanding problem, it and traditional Vickers hardness be related to problem.For addressing this problem, the present invention's application dimension theorem and PLASTIC FINITE ELEMENT ANALYSIS numerical analysis method have been set up a kind of method of determining material Vickers hardness than merit and nominal hardness that is pressed into based on Berkovich pressure head instrumentation, the method is utilized Berkovich pressure head instrumentation to be pressed into material gained load-displacement curves to determine that the instrumentation of measured material is pressed into than merit and nominal hardness, then utilizes the funtcional relationship of setting up further to determine the Vickers hardness of measured material.The value of the method is that it has solved instrumentation in the past and has been pressed into the problem that is widely used Berkovich pressure head and can not obtain tested material Vickers hardness of testing.
Summary of the invention
The object of this invention is to provide a kind of method that the Berkovich of utilization pressure head and instrumentation thereof are pressed into test material gained load-displacement curves and determine material Vickers hardness.The value of the method is that it has solved instrumentation in the past and has been pressed into the problem that is widely used Berkovich pressure head and can not obtain tested material Vickers hardness of testing.
To achieve these goals, the present invention adopts following technical scheme:
A kind of method that is pressed into nominal hardness and determines material Vickers hardness based on instrumentation Berkovich, the method is utilized Berkovich pressure head instrumentation to be pressed into material gained load-displacement curves to determine that the instrumentation of measured material is pressed into than merit and nominal hardness, then utilize the funtcional relationship of setting up further to determine the Vickers hardness of measured material, specifically comprise the following steps:
1) utilizing instrumentation press fit instrument and adamas Berkovich 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 Berkovich pressure head simultaneously
mwith nominal hardness H
n=P
m/ A (h
m), wherein, A (h
m) pressure head cross-sectional area while being corresponding maximum compression distance, in the time not considering pressure head crest truncation
and while considering pressure head crest truncation, A (h
m) should be determined by the area function A (h) of 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) according to Vickers hardness H
vbe pressed into than merit W with instrumentation
e/ W
tand nominal hardness H
nrelation finally determine the Vickers hardness H of measured material
v:
H
v＝H
nf(W
e/W
t)
＝H
n[0.7229+2.9354(W
e/W
t)-16.0845(W
e/W
t)
2+59.6427(W
e/W
t)
3
-116.6338(W
e/W
t)
4+114.3549(W
e/W
t)
5-44.2678(W
e/W
t)
6]
The value of the method is that it has solved instrumentation in the past and has been pressed into the problem that is widely used Berkovich pressure head and can not obtain tested material Vickers hardness of testing.
Brief description of the drawings:
Fig. 1 is that instrumentation Berkovich is pressed into Load-unload curve and Load-unload merit schematic diagram;
Fig. 2 is the H under the different n of finite element numerical analysis gained and η
v/ H
nwith W
e/ W
trelation;
Fig. 3 is the Vickers hardness theoretical error (H definite based on instrumentation Berkovich method of press-fitting
v-Eq. (7)-H
v-FEM)/H
v-FEMwith W
e/ W
trelation.
Fig. 4 a is the instrumentation Berkovich loading of pressing in-displacement curve of S45C medium carbon steel sample.
Fig. 4 b is the instrumentation Berkovich loading of pressing in-displacement curve of SS304 stainless steel sample.
Fig. 4 c is the instrumentation Berkovich loading of pressing in-displacement curve of SS316 stainless steel sample.
Fig. 4 d is the instrumentation Berkovich loading of pressing in-displacement curve of 6061A1 alloy sample.
Fig. 4 e is the instrumentation Berkovich loading of pressing in-displacement curve of brass sample.
Fig. 5 a is silicon nitride (Si
3n
4) the instrumentation Berkovich loading of pressing in-displacement curve of sample.
Fig. 5 b is zirconia (ZrO
2) the instrumentation Berkovich loading of pressing in-displacement curve of sample.
Fig. 5 c is the instrumentation Berkovich loading of pressing in-displacement curve of Zirconia reinforced alumina (ZTA) sample.
Fig. 5 d is aluminium oxide (Al
2o
3) the instrumentation Berkovich loading of pressing in-displacement curve of sample.
Fig. 5 e is the instrumentation Berkovich loading of pressing in-displacement curve of molten silicon (Silica) sample.
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 method that is pressed into nominal hardness and determines material Vickers hardness based on instrumentation Berkovich, the method is utilized Berkovich pressure head instrumentation to be pressed into material gained load-displacement curves to determine that the instrumentation of measured material is pressed into than merit and nominal hardness, then utilize the funtcional relationship of setting up further to determine the Vickers hardness of measured material, specifically comprise the following steps:
1) utilizing instrumentation press fit instrument and adamas Berkovich 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 Berkovich pressure head simultaneously
mwith nominal hardness H
n=P
m/ A (h
m), wherein, A (h
m) pressure head cross-sectional area while being corresponding maximum compression distance, in the time not considering the crest truncation of adamas Berkovich pressure head
and while considering the crest truncation of adamas Berkovich pressure head, A (h
m) should be determined by the area function A (h) of 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) according to Vickers hardness H
vbe pressed into than merit W with instrumentation
e/ W
tand nominal hardness H
nrelation finally determine the Vickers hardness H of measured material
v:
H
v＝H
nf(W
e/w
t)
＝H
n[0.7229+2.9354(W
e/W
t)-16.0845(W
e/E
t)
2+59.6427(W
e/W
t)
3
-116.6338(W
e/W
t)
4+114.3549(W
e/W
t)
5-44.2678(W
e/W
t)
6]
Below describe forming process of the present invention in detail.As shown in Figure 1, wherein, ordinate represents loading of pressing in P to instrumentation Berkovich loading of pressing in-displacement curve schematic diagram, and horizontal ordinate 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 a certain 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 Berkovich pressure head is at the adamas Berkovich of maximum compression distance position pressure head cross-sectional area, nominal hardness H
nbe defined as maximum loading of pressing in P
mwith adamas Berkovich 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 Berkovich 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.
Set up instrumentation Berkovich for application finite element numerical methods analyst and be pressed into nominal hardness H
nwith material Vickers hardness H
vbetween funtcional relationship, adamas Berkovich pressure head and adamas Vickers pressure head are considered as elastic body by we, its elastic modulus is E
i=1141GPa, and Poisson ratio is v
i=0.07; Measured material is considered as elasticoplastic body, and the value of its elastic modulus E is respectively 70GPa, 200GPa and 400GPa, and Poisson ratio v is constant 0.3, corresponding
value is respectively 0.0671,0.1917 and 0.3834, and its single shaft true strain-stress relation is made up of linear elasticity and Hollomon power hardening function, and the value of material strain hardenability value n is respectively 0,0.15,0.3 and 0.45, yield strength σ
yvalue ensure than merit W
e/ W
twithin the scope of 0.01-0.85, adamas Berkovich pressure head and adamas Vickers pressure head are 0.15 with the friction factor value of being pressed storeroom, and the maximum compression distance of adamas Berkovich pressure head instrumentation is h
m, maximum loading of pressing in is P
m, H
n=P
m/ A (h
m).Be further h by corresponding Vickers pressure head maximum compression distance
mtime maximum loading of pressing in be made as P
vmusing the maximum length that in Vickers impression diagonal, contact stress is non-zero region as the contact length that loads moment Vickers impression diagonal, corresponding two-end-point is the two relative summits that load moment Vickers impression, after unloading, distance between this relative summit is the catercorner length D of Vickers impression, now, H
v=2sin68 ° of P
vm/ D
2.Based on above-mentioned setting, than hardness H
v/ H
nand than merit W
e/ W
tcan be expressed as minor function:
Obtained by (2) formula:
(3) formula substitution (1) formula is obtained:
Application dimension Π theorem is considered the ratio of plane-strain elastic modulus simultaneously
(4) formula can be rewritten as:
H
v/H
n＝f
H2(W
e/W
t，n，η) (5)
Utilize finite element numerical computing method can obtain the explicit solution of (5) formula, Fig. 2 shows the H under the different n of finite element numerical analysis gained and η
v/ H
nwith W
e/ W
trelation, can be represented as by this relation of curve:
H
v/H
n＝f(W
e/W
t)
＝0.7229+2.9354(W
e/W
t)-16.0845(W
e/W
t)
2+59.6427(W
e/W
t)
3 (6)
-116.6338(W
e/W
t)
4+114.3549(W
e/W
t)
5-44.2678(W
e/W
t)
6
Further, H
vcan be represented as:
H
v＝H
nf(W
e/W
t)
＝H
n[0.7229+2.9354(W
e/W
t)-16.0845(W
e/W
t)
2+59.6427(W
e/W
t)
3 (7)
-116.6338(W
e/W
t)
4+114.3549(W
e/W
t)
5-44.2678(W
e/W
t)
6]
Fig. 3 calculates Vickers hardness H based on instrumentation method of press-fitting that is based on formula (7)
vtheoretical error (H
v-Eq. (7)-H
v-FEM)/H
v-FEMwith W
e/ W
tbetween relation, wherein, H
v-Eq. (7)for the Vickers hardness based on formula (7) is calculated result, H
v-FEMfor based on finite element numerical analysis gained Vickers hardness; As can be seen from the figure, error is with than merit W
e/ W
tincrease and reduce, when than merit W
e/ W
tincrease at 0.3 o'clock, error (H by 0.01
v-Eq. (7)-H
v-FEM)/H
v-FEMby ± 10.5% being decreased to ± 2.7%, and when than merit 0.4≤W
e/ W
t≤ 0.8 o'clock, error | (H
v-Eq. (7)-H
v-FEM)/H
v-FEM|≤2.4%.
Application Example
The tested metal material sample that experiment is selected is S45C medium carbon steel, SS304 stainless steel, SS316 stainless steel, 6061A1 alloy and brass; Stupalith sample is silicon nitride (Si
3n
4), zirconia (ZrO
2), Zirconia reinforced alumina (ZTA), aluminium oxide (Al
2o
3) and molten silicon (Silica).Application obtains high precision instrument press fit instrument [horse German army, Song Zhongkang, Guo Junhong, the Chen Wei: the computing method of a kind of high precision press fit instrument and the diamond penetrator pressing in sample degree of depth of national inventing patent mandate in advance.The patent No.: ZL201110118464.9] and adamas Berkovich pressure head above-mentioned 5 kinds of metal materials and 5 kinds of stupaliths carried out respectively to instrumentation be pressed into experiment, wherein, to 5 kinds of metal materials and 3 kinds of stupalith Si
3n
4, ZrO
2and the maximum loading of pressing in that ZTA selects is 50N, and for Al
2o
3the maximum loading of pressing in that stupalith is selected is 25N, and for Silica, the maximum loading of pressing in of selecting is 0.25N.For ensureing the accuracy of test result, every kind of material experiment repeats 10 times, Fig. 4 a, Fig. 4 b, Fig. 4 c, Fig. 4 d, Fig. 4 e are respectively instrumentation Berkovich loading of pressing in-displacement empirical curve of above-mentioned 5 kinds of metal materials, and Fig. 5 a, Fig. 5 b, Fig. 5 c, Fig. 5 d, Fig. 5 e are respectively instrumentation Berkovich loading of pressing in-displacement empirical curve of above-mentioned 5 kinds of stupaliths.Utilize this curve first to determine that the instrumentation of measured material is pressed into than merit W
e/ W
twith nominal hardness H
n, then according to the further Vickers hardness of definite measured material of formula (7)
H
v-Eq.(7)＝H
n[0.7229+2.9354(W
e/W
t)-16.0845(W
e/W
t)
2+59.6427(W
e/W
t)
3
-116.6338(W
e/W
t)
4+114.3549(W
e/W
t)
5-44.2678(W
e/W
t)
6]
In addition, above-mentioned 10 kinds of materials are carried out to Vickers and be pressed into test, and utilize its Vickers impression catercorner length of optical microscope measuring d, and determine its Vickers hardness: H according to definition
v-indentation method=2sin68 ° of P
m/ d
2, above-mentioned experimental result is together with Vickers hardness H
v-Eq. (7)with H
v-indentation methodbetween relative error (H
v-Eq. (7)-H
v-indentation method)/H
v-indentation methodall list in table 1.
5 kinds of metals that table 1 is determined based on the inventive method and average and the error thereof of 5 kinds of stupalith Vickers hardnesses
As can be seen from Table 1, based on the definite material Vickers hardness of the inventive method except the test error (11.356%) of molten silicon (Silica) is slightly large, the test error of all the other metals and stupalith Vickers hardness all in ± 7.8% scope, thereby verified the validity of institute of the present invention construction method.
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 (1)
1. one kind is pressed into nominal hardness and determines the method for material Vickers hardness based on instrumentation Berkovich, the method is utilized Berkovich pressure head instrumentation to be pressed into material gained load-displacement curves to determine that the instrumentation of measured material is pressed into than merit and nominal hardness, then utilize the funtcional relationship of setting up further to determine the Vickers hardness of measured material, specifically comprise the following steps:
1) utilizing instrumentation press fit instrument and adamas Berkovich 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 Berkovich pressure head simultaneously
mwith nominal hardness H
n=P
m/ A (h
m), wherein, A (h
m) pressure head cross-sectional area while being corresponding maximum compression distance, in the time not considering pressure head crest truncation
and while considering pressure head crest truncation, A (h
m) should be determined by the area function A (h) of 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) according to Vickers hardness H
vbe pressed into than merit W with instrumentation
e/ W
tand nominal hardness H
nrelation finally determine the Vickers hardness H of measured material
v:
H
v＝H
nf(W
e/W
t)
＝H
n[0.7229+2.9354(W
e/W
t)-16.0845(W
e/W
t)
2+59.6427(W
e/W
t)
3
-116.6338(W
e/W
t)
4+114.3549(W
e/W
t)
5-44.2678(W
e/W
t)
6]
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|---|---|---|---|
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106769570A (en) * | 2016-11-22 | 2017-05-31 | 银邦金属复合材料股份有限公司 | A kind of detection method of composite constituent element layer hardness |
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2014
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| Title |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106769570A (en) * | 2016-11-22 | 2017-05-31 | 银邦金属复合材料股份有限公司 | A kind of detection method of composite constituent element layer hardness |
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Application publication date: 20141015 |