CN104122154B - Method for testing ceramic material fracture toughness by means of instrumented Vickers indentation - Google Patents

Abstract

The invention discloses a method for testing ceramic material fracture toughness by means of instrumented Vickers indentation. According to the method, the fracture toughness KIC of a ceramic material is determined by virtue of a load-displacement curve and the length of a crack in indentation diagonal direction of an indented material, wherein the load-displacement curve is obtained by means of indenting the ceramic material by a Vickers indenter in an instrumented way. Compared with a conventional indented method, the method disclosed by the invention has the advantages that (1) a KIC formula is built based on elastic-plastic finite element analysis and satisfies the requirement on the equivalent fracture toughness of a crack tip, so that the precision is higher compared with that of the conventional indented method; (2) without distinguishing the cracking forms of cracks, the built KIC formula is applicable to not only semi-coin middle cracks but also Palmqvist radial cracks; (3) the method is applicable to relatively extensive ceramic materials and the relatively extensive test range; (4) the elasticity modulus and the fracture toughness of the ceramic materials can be tested simultaneously, and the problem that the elasticity modulus of the ceramic material needs to be tested in advance by adopting other technical means in the conventional indented method is avoided, so that the test is rapid, convenient and efficient.

Description

Ceramic materials fracture toughness instrumentation vickers 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 Impression diagonal crack initiation length testing ceramic materials fracture toughness k_icMethod.

Background technology

At present, the method for test ceramic materials fracture toughness mainly has face crack bending method (scf), chevron-shaped cut beam method (cnb), monolateral pre- CRACKED BEAM method (sepb), Single edge notch beam (senb) and conventional indentation method (im).In view of application The factors such as convenience, efficiency, requirement to sample yardstick, im has a clear superiority compared with scf, cnb, sepb, senb, thus obtains Extensively apply.Even so, fracture toughness k that conventional indentation method is relied on_icComputing formula system is based on semi analytic semiempirical side Method is set up, and therefore there is many impact conventional indentation method of testing measuring accuracies and application aspect: 1) the method will The crack initiation face of vickers impression diagonal is assumed to be preferably semicircle crack initiation face geometry, its crackle Most advanced and sophisticated geometry is unsatisfactory for the required grade k of real crack cracking_icValue basic demand；2) k being set up based on semi analytic semi-empirical method_ic Demarcating of its coefficient of computing formula is based on limited ceramic material experimental data, leads to k_icThe ceramic material scope that formula is suitable for Less；3) conventional indentation method needs to distinguish the crack initiation form of vickers impression diagonal: half coin middle crack (half penny shaped crack or median crack (hpc)) or Pasteur's radial cracking (palmqvist crack Or radial crack (rc)), and it is directed to semi analytic semiempirical k that two kinds of crack initiation forms are set up_icComputing formula is in application There is transition region k in aspect_icValue is discontinuous and is difficult even to judge the problem of transition region crack initiation form；4) tradition pressure Trace method there is a problem of in advance ceramic material elastic modelling quantity need to being tested by other technological means；5) conventional indentation side Method there is a problem of leading to because vickers impression drift angle is unintelligible measure impression catercorner length difficulty.

For above-mentioned situation, present invention application dimension theorem and PLASTIC FINITE ELEMENT ANALYSIS numerical analysis method establish one kind newly Based on vickers pressure head ceramic materials fracture toughness instrumentation press-in recognition methods.Compared with conventional indentation method, the party Method has the advantage that (1) k_icThe foundation of formula come from PLASTIC FINITE ELEMENT ANALYSIS numerical analysis meet simultaneously crack tip fracture tough Property equivalent requirement, thus compared with the semi analytic semiempirical formula of conventional indentation method, there is higher precision；(2) need not measure Vickers impression catercorner length, it is to avoid what conventional indentation method existed leads to because vickers impression drift angle is unintelligible to measure The difficult problem of impression catercorner length；(3) k setting up_icFormula is not only suitable for half coin middle crack (half penny Shaped crack or median crack) it is also applied for Pasteur's radial cracking (palmqvist crack or radial Crack), it is to avoid what conventional indentation method existed not only needs but also the problem of the above-mentioned difference crack initiation form that is not easily distinguishable；(4) Applicable ceramic material and test scope are wide, can cover instrumentation press-in than work(numerical value from all potteries of 0.3 to 0.71 scope The ratio of material and vickers impression diagonal crack initiation length and nominal impression catercorner length is from 1.05 to 6 scopes All test case；(5) test to ceramic material elastic modelling quantity and fracture toughness can be completed, it is to avoid conventional indentation simultaneously The problem that in advance ceramic material elastic modelling quantity need to be tested by other technological means that method exists, thus test is just Prompt, efficient.

Content of the invention

It is an object of the invention to provide a kind of ceramic materials fracture toughness instrumentation vickers is pressed into method of testing.With biography System creasing method is compared, and the inventive method is capable of higher measuring accuracy, need not distinguish crack initiation form, applicable pottery Ceramic material and test scope are wider, can complete to ceramic material elastic modelling quantity and fracture toughness simultaneously test, it is to avoid tradition What creasing method existed need to be by the problem that other technological means are tested to ceramic material elastic modelling quantity in advance so that test Convenient, efficient.

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

A kind of ceramic materials fracture toughness instrumentation vickers is pressed into method of testing, and the method utilizes vickers pressure head instrument Deviceization is pressed into ceramic material gained load-displacement curves and is determined pottery by pressure material impression diagonal crack initiation length Fracture toughness k of material_ic, 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, the nominal long a=3.5h of impression diagonal half_mAnd nominal hardness

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) measure the long c of 4 crack initiations half of vickers impression diagonal respectively by light microscope₁、c₂、c₃With c₄, simultaneously by its average c=(c₁+c₂+c₃+c₄)/4 are long as the crack initiation half of this instrumentation press-in test, and calculate ratio Value c/a, adjusts p further_mSize make ratio c/a and ratio work(w_e/w_tMeet relation: 1.05≤c/a≤1.5 and

0.71≥w_e/w_t≥(w_e/w_t)₀=0.591-0.194 (c/a) or 1.5 ＜ c/a≤6 and

0.71≥w_e/w_t≥0.3；

4) the nominal hardness h being determined according to instrumentation press-in test_nAnd ratio work(w_e/w_tDetermine the Young's modulus of measured material That is, elastic modelling quantity e=(1-0.2²)/{[0.007625(w_e/w_t)⁶

-0.005516(w_e/w_t)⁵-0.048401(w_e/w_t)⁴+0.110937(w_e/w_t)³-0.157669(w_e/w_t)²+ 0.170204(w_e/w_t)]/h_n-1.32(1-0.07²)/1141 }, determine measured material and diamond vickers pressure head simultaneously The ratio of plane-strain elastic modulus

η=[e/ (1-0.2²)]/[1141/(1-0.07²)], wherein, the dimension of e is " gpa " (Ji Pa)；

5) calculate fracture toughness k of tested ceramic material_ic:

k_ic=(10^-6p_m/c^1.5)[1+f_c(c/a)η]f_w(w_e/w_t),

Wherein, f_c(c/a)=0.0068 (c/a)²- 0.1118 (c/a)+0.8295,

f_w(w_e/w_t)=0.0757 (w_e/w_t)²-0.1956(w_e/w_t)+0.1285, k_icDimension be(million Handkerchief rice^1/2)、p_mDimension be " n " (newton), c and a dimension be " m " (rice).

Compared with conventional indentation method, the invention has the advantages that

(1)k_icThe foundation of formula comes from the equivalence that PLASTIC FINITE ELEMENT ANALYSIS numerical analysis meets crack tip fracture toughness simultaneously Require, thus compared with the semi analytic semiempirical formula of conventional indentation method, there is higher precision；

(2) need not measure vickers impression catercorner length, it is to avoid conventional indentation method exist because of vickers pressure Trace drift angle is unintelligible to be led to measure the difficult problem of impression catercorner length；

(3) k setting up_icFormula is not only suitable for half coin middle crack (half penny shaped crack or Median crack) it is also applied for Pasteur's radial cracking (palmqvist crack or radial crack), it is to avoid tradition What creasing method existed not only needs but also the problem of the above-mentioned difference crack initiation form that is not easily distinguishable；

(4) ceramic material being suitable for and test scope are wide, can cover instrumentation press-in than work(numerical value from 0.3 to 0.71 scope All ceramic materials and vickers impression diagonal crack initiation length and nominal impression catercorner length ratio from All test case of 1.05 to 6 scopes；

(5) test to ceramic material elastic modelling quantity and fracture toughness can be completed, it is to avoid conventional indentation method is deposited simultaneously The problem that in advance ceramic material elastic modelling quantity need to be tested by other technological means, thus test convenient, efficient.

Brief description:

Fig. 1 is instrumentation press-in Load-unload curve and Load-unload work(schematic diagram；

Fig. 2 is based on grade k_icThe impression diagonal crack initiation geometric representation that value determines；

Fig. 3 is that finite element numerical analysis gained meets relation: 1.05≤c/a≤1.5 and 0.71 >=w_e/w_t≥(w_e/w_t)₀= 0.591-0.194 (c/a) or 1.5 ＜ c/a≤6 and 0.71 >=w_e/w_tK in the case of >=0.3 different c/a and η_ic/{(10^{- 6}p_m/c^1.5)[1+f_c(c/a) η] } and w_e/w_tRelation；

Fig. 4 is the k that the present invention is set up_icTheoretical error (the k of computing formula_ic-eq.(10)-k_ic-fem)/k_ic-femWith than work( w_e/w_tGraph of a relation；

Fig. 5 a is based on conventional indentation method calculating k under different η during c/a=1.05_icTheoretical error (k_{ic-traditional}- k_ic-fem)/k_ic-femWith ratio work(w_e/w_tGraph of a relation；

Fig. 5 b is based on conventional indentation method calculating k under different η during c/a=1.25_icTheoretical error (k_{ic-traditional}- k_ic-fem)/k_ic-femWith ratio work(w_e/w_tGraph of a relation；

Fig. 5 c is based on conventional indentation method calculating k under different η during c/a=1.5_icTheoretical error (k_{ic-traditional}- k_ic-fem)/k_ic-femWith ratio work(w_e/w_tGraph of a relation；

Fig. 5 d is based on conventional indentation method calculating k under different η during c/a=2.25_icTheoretical error (k_{ic-traditional}- k_ic-fem)/k_ic-femWith ratio work(w_e/w_tGraph of a relation；

Fig. 5 e is based on conventional indentation method calculating k under different η during c/a=3_icTheoretical error (k_{ic-traditional}- k_ic-fem)/k_ic-femWith ratio work(w_e/w_tGraph of a relation；

Fig. 5 f is based on conventional indentation method calculating k under different η during c/a=4.5_icTheoretical error (k_{ic-traditional}- k_ic-fem)/k_ic-femWith ratio work(w_e/w_tGraph of a relation；

Fig. 5 g is based on conventional indentation method calculating k under different η during c/a=6_icTheoretical error (k_{ic-traditional}- k_ic-fem)/k_ic-femWith ratio work(w_e/w_tGraph of a relation；

Fig. 6 a is silicon nitride sample (si₃n₄) instrumentation loading of pressing in-displacement curve；

Fig. 6 b is zirconium oxide sample (zro₂) instrumentation loading of pressing in-displacement curve；

Fig. 6 c is the instrumentation loading of pressing in-displacement curve of Zirconia reinforced alumina sample (zta)；

Fig. 6 d is alumina sample (al₂o₃) instrumentation loading of pressing in-displacement curve；

Fig. 6 e is the instrumentation loading of pressing in-displacement curve of molten silicon sample (fused silica)；

Fig. 7 is the long schematic diagram of 4 crack initiations half of vickers impression diagonal.

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 ceramic materials fracture toughness instrumentation vickers is pressed into method of testing, the method utilizes Vickers pressure head instrumentation is pressed into ceramic material gained load-displacement curves and is opened by pressure material impression diagonal crackle Split fracture toughness k that length determines ceramic material_ic, 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, the nominal long a=3.5h of impression diagonal half_mAnd nominal hardness

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) measure the long c of 4 crack initiations half of vickers impression diagonal respectively by light microscope₁、c₂、c₃With c₄, simultaneously by its average c=(c₁+c₂+c₃+c₄)/4 are long as the crack initiation half of this instrumentation press-in test, and calculate ratio Value c/a, adjusts p further_mSize make ratio c/a and ratio work(w_e/w_tMeet relation: 1.05≤c/a≤1.5 and

0.71≥w_e/w_t≥(w_e/w_t)₀=0.591-0.194 (c/a) or 1.5 ＜ c/a≤6 and

0.71≥w_e/w_t≥0.3；

4) the nominal hardness h being determined according to instrumentation press-in test_nAnd ratio work(w_e/w_tDetermine the Young's modulus of measured material That is, elastic modelling quantity e=(1-0.2²)/{[0.007625(w_e/w_t)⁶-0.005516(w_e/w_t)⁵-0.048401(w_e/w_t)⁴+ 0.110937(w_e/w_t)³-0.157669(w_e/w_t)²+0.170204(w_e/w_t)]/h_n-1.32(1-0.07²)/1141 }, really simultaneously Determine the ratio of measured material and the plane-strain elastic modulus of diamond vickers pressure head

η=[e/ (1-0.2²)]/[1141/(1-0.07²)], wherein, the dimension of e is " gpa " (Ji Pa)；

5) calculate fracture toughness k of tested ceramic material_ic:

k_ic=(10^-6p_m/c^1.5)[1+f_c(c/a)η]f_w(w_e/w_t),

Wherein, f_c(c/a)=0.0068 (c/a)²- 0.1118 (c/a)+0.8295,

f_w(w_e/w_t)=0.0757 (w_e/w_t)²-0.1956(w_e/w_t)+0.1285,

k_icDimension be(MPa rice^1/2)、p_mDimension be " n " (newton), c and a dimension be " m " (rice).

The forming process of the present invention described further below.Instrumentation loading of pressing in-displacement curve schematic diagram such as accompanying drawing 1 institute Show, the longitudinal axis represents loading of pressing in p, transverse axis represents compression distance h, loading curve is 1, unloading curve is 2, loads work(w_tRegion is 3, unload work(w_eRegion is 4.Wherein, the set a certain 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 at maximum compression distance position for the diamond vickers pressure head Head cross-sectional area, 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 and implement instrumentation press-in When diamond vickers pressure head in load phase and unloading phase work done, its value is respectively equal to loading curve and unloading is bent Line and instrumentation loading of pressing in-enclosed area of displacement curve abscissa.Instrumentation is pressed into ratio work(w_e/w_tFor unloading work(w_eWith loading Work(w_tRatio.According to h_nAnd w_e/w_tSimultaneously utilize inventor propose " testing Young modulus of material through instrumented micron indentation Method " (horse German army, " material mechanical performance instrumentation be pressed into test philosophy ", National Defense Industry Press, 2010) can determine by The Young's modulus of material of measuring and monitoring the growth of standing timber that is, elastic modelling quantity e=(1-0.2²)/{[0.007625(w_e/w_t)⁶

-0.005516(w_e/w_t)⁵-0.048401(w_e/w_t)⁴+0.110937(w_e/w_t)³-0.157669(w_e/w_t)²+ 0.170204(w_e/w_t)]/h_n-1.32(1-0.07²)/1141 }, can determine that measured material is pressed with diamond vickers simultaneously The ratio η=[e/ (1-0.2 of the plane-strain elastic modulus of head²)]/[1141/(1-0.07²)] (dimension of e is " gpa ").

Set up fracture toughness k for application finite element numerical method_icWith instrumentation press-in parameter, tested ceramic material parameter with And the functional relation between vickers impression diagonal crack initiation length, diamond vickers pressure head is considered as bullet by us Gonosome, its elastic modelling quantity and Poisson's ratio are respectively e_i=1141gpa and v_i=0.07；Measured material is considered as elasticoplastic body, its elasticity Modulus is respectively e and v=0.2 with Poisson's ratio, and its single shaft true strain-stress relation is by linear elasticity and hollomon power hardening letter Array becomes, and yield strength and strain hardening exponent use σ respectively_yRepresent with n, between diamond vickers pressure head and measured material Coefficient of friction takes definite value 0.15, and instrumentation maximum compression distance is h_m, load is p_m, vickers impression diagonal crackle opens Split half a length of c, a length of a=3.5h of nominal impression diagonal half_m.Based on above-mentioned it is assumed that then fracture toughness k_icCan be expressed as Minor function:

k_ic=f_k1(σ_y, n, e/ (1-v²), e_i/(1-v_i ²), c, a) (1)

Discounting for crackle, ratio work(w is pressed into instrumentation_e/w_tImpact, then w_e/w_tCan be expressed as:

w_e/w_t=f_w1(σ_y, n, e/ (1-v²), e_i/(1-v_i ²)) (2)

Obtained by (2) formula:

${\mathrm{\σ}}_y=f_{w1}^{-1}(w_e/w_t,n,e/(1-v^2),e_i/(1-{v_i}^2))---\left(3\right)$

(3) formula substitution (1) formula is obtained:

k_ic=f_k2(w_e/w_t, n, e/ (1-v²), e_i/(1-v_i ²), c, a) (4)

Application dimension ∏ theorem considers the ratio of plane-strain elastic modulus simultaneously $\mathrm{\η}=[e/(1-v^2)]/[e_i/(1-v_i^2)],$ Then (4) formula can be rewritten as:

k_ic/{[e/(1-v²)]c^0.5}=f_k3(w_e/w_t, n, η, c/a) and (5)

Similarly, instrumentation maximum loading of pressing in p_mCan be represented as following functional relation:

p_m=f_p1(w_e/w_t, n, e/ (1-v²), e_i/(1-v_i ²), a) (6)

Apply dimension ∏ theorem, then (6) formula can be rewritten as:

p_m/{[e/(1-v²)]a²}=f_p2(w_e/w_t, n, η) and (7)

(5) formula and (7) formula are divided by:

k_ic/(p_m/c^1.5)=(c/a)²f_k3(w_e/w_t, n, η, c/a) and=f_k4(w_e/w_t, n, η, c/a) and (8)

The explicit solution of (8) formula can be obtained using finite element numerical computational methods, wherein, realize the k such as crack tip_icValue will The basic step asked is: first, it is assumed that the crack initiation face geometry of vickers impression diagonal is half elliptic, And equidistantly take 5-7 node as reference mode on the elliptic curve of cracking face, calculate its k respectively_icValue；Secondly, according to each ginseng Examine node k_icThe size of value is adjusted to its position, and the reference mode after SPL is smoothly connected adjustment is formed newly Crack initiation face geometry；Finally calculate the reference mode k after adjustment_icValue, and repeat said process up to each reference node The k of point_icValue difference is less than ± 5%, and that finally realizes crack tip waits k_icValue requires.Fig. 2 is based on grade k_icThe pressure that value determines Trace diagonal crack initiation geometric representation, in figure curve " 1 ", " 2 ", " 3 " respectively typical three kinds of crack initiations are several What shape.

In finite element numerical calculating process, the elastic modelling quantity e of ceramic material respectively value be 70gpa, 200gpa, 400gpa and 600gpa, Poisson's ratio v=0.2, correspondingly η respectively equal to 0.0635,0.1817,0.3634 and 0.5451, hardening Index n takes 0, yield strength σ_yValue meet following requirement: when 1.05≤c/a≤1.5,0.71 >=w_e/w_t≥(w_e/w_t)₀ =0.591-0.194 (c/a), and when 1.5 ＜ c/a≤6,0.71 >=w_e/w_t>=0.3, ratio c/a take 1.05 respectively, 1.25, 1.5th, 2.25,3,4.5 and 6.Work as k_icDimension be、p_mDimension be " n ", the dimension of c and a be " m ", and f_c (c/a)=0.0068 (c/a)²During -0.1118 (c/a)+0.8295, Fig. 3 show finite element numerical analysis gained difference c/a and K in the case of η_ic/{(10^-6p_m/c^1.5)[1+f_c(c/a) η] } it is pressed into ratio work(w with instrumentation_e/w_tBetween numerical relation it is clear that it Approximately meet functional relation, and can determine that this functional relation is by the method for curve matching:

k_ic/{(10^-6p_m/c^1.5)[1+f_c(c/a)η]} (9)

=f_w(w_e/w_t)=0.0757 (w_e/w_t)²-0.1956(w_e/w_t)+0.1285 conversion (9) formula, you can derive and utilize The computing formula that its fracture toughness tested by vickers pressure head instrumentation press-in ceramic material is:

k_ic=(10^-6p_m/c^1.5)[1+f_c(c/a)η]f_w(w_e/w_t) (10) wherein, f_c(c/a)=0.0068 (c/a)²- 0.1118 (c/a)+0.8295,

f_w(w_e/w_t)=0.0757 (w_e/w_t)²-0.1956(w_e/w_t)+0.1285, k_icDimension be(million Handkerchief rice^1/2)、p_mDimension be " n " (newton), c and a dimension be " m " (rice), Fig. 4 be based on formula (10) calculate k_icReason By error (k_ic-eq.(10)-k_ic-fem)/k_ic-femWith ratio work(w_e/w_tGraph of a relation, wherein, k_ic-eq.(10)It is based on formula (10) Fracture toughness result of calculation, k_ic-femIt is the fracture toughness result of calculation based on finite element numerical analysis；It can be seen that When than work(in 0.3≤w_e/w_tDuring≤0.5 scope, error | (k_ic-eq.(10)-k_ic-fem)/k_ic-fem|≤7%, and as 0.5 ＜ w_e/w_t During≤0.71 scope, error | (k_ic-eq.(10)-k_ic-fem)/k_ic-fem|≤10%.

Simultaneously can be to the long a ' of ceramic material vickers impression diagonal half and Vickers by finite element method HardnessIt is simulated, and then the k to conventional indentation method_icComputing formula is analyzed, wherein, Anstis formula, Japanese national industrial standard jisr1607, lawn formula, evans formula and niihara formula are respectively such as Under:

k_ic-anstis=0.0154 (e/h_v)^0.5p_mc^-1.5, (c/a ' >=2) (anstis formula)

k_ic-jisr=0.018 (e/h_v)^0.5p_mc^-1.5, (c/a ' >=2.5) (jisr formula)

k_ic-lawn=0.0134 (e/h_v)^0.5p_mc^-1.5, (1.5≤c/a '≤7) (lawn formula)

k_ic-evans=0.16h_v(a′)²c^-1.5, (2≤c/a '≤6) (evans formula)

k_ic-niihara=0.0181e^0.4h_v ^0.6a′(c-a′)^-0.5, (1.25≤c/a '≤3.5) (niihara formula)

k_ic-niihara=0.0667e^0.4h_v ^0.6(a′)²c^-1.5, (c/a ' >=2.5) (niihara formula)

If using k_{ic-traditional}Represent and gained fracture toughness result is calculated based on above-mentioned formula, then conventional indentation method calculates k_icTheoretical error be (k_{ic-traditional}-k_ic-fem)/k_ic-fem, Fig. 5 a, Fig. 5 b, Fig. 5 c, Fig. 5 d, Fig. 5 e, Fig. 5 f, Fig. 5 g divide Do not show under different c/a and η based on conventional indentation method calculate k_icTheoretical error (k_{ic-traditional}-k_ic-fem)/k_ic-fem With ratio work(w_e/w_tRelation, it can be seen that when than work(in 0.3≤w_e/w_tWhen in the range of≤0.4, error keeps substantially Constant, and work as than work(in 0.4 ＜ w_e/w_tWhen in the range of≤0.71, then error increases rapid increase with than work(, thus and conventional indentation Method is compared, and the fracture toughness computing formula that the present invention sets up substantially has accuracy benefits.

Application Example

The tested ceramic material that experiment is selected is silicon nitride sample (si₃n₄), zirconium oxide sample (zro₂), Zirconium oxide plasticizing Alumina sample (zta), alumina sample (al₂o₃) and molten silicon sample (fused silica).Application obtains country in advance Invention patent mandate high precision instrument press fit instrument [horse German army, Song Zhongkang, Guo Junhong, Chen Wei. a kind of high accuracy press fit instrument and The computational methods of diamond penetrator pressing in sample depth. the patent No.: zl201110118464.9] and diamond vickers pressure head Instrumentation micro-indentation test is carried out to above-mentioned 5 kinds of ceramic materials, wherein, to si₃n₄、zro₂, zta and al₂o₃Material, selection is Big loading of pressing in is 100n, and for silica, the maximum loading of pressing in of selection is 2n.For ensureing the accurate of test result Property, every kind of material experiment repeats 10 times, and Fig. 6 a, Fig. 6 b, Fig. 6 c, Fig. 6 d, Fig. 6 e are respectively the instrument of above-mentioned 5 kinds of ceramic materials Device loading of pressing in-shift assays curve.

Using light microscope, vickers impression diagonal is measured respectively to the sample having been carried out instrumentation press-in test The long c of 4 crack initiations half on direction₁、c₂、c₃And c₄, as shown in fig. 7, simultaneously by its average c=(c₁+c₂+c₃+c₄)/4 conduct The crack initiation half of this instrumentation press-in test is long, is put forward test fracture toughness k according to inventor further_icMethod calculate The fracture toughness of above-mentioned material, result is listed in table 1.

15 kinds of ceramic materials fracture toughness test result averages of table

The test result of the inventive method and the comparison of conventional indentation method and Single edge notch beam (senb) test result It is listed in table 2.

Table 2 test result of the present invention and the comparison (unit: mpa m of conventional indentation method and senb method test result^{1 /2})

From table 2 it can be seen that in addition to silica, fracture toughness test value k of remaining 4 kinds of ceramic material_ic-eq.(10)With k_ic-anstisAll be closer to, its reason can from Fig. 5 c, Fig. 5 d, Fig. 5 e (k_{ic-traditional}-k_ic-fem)/k_ic-femWith ratio work(w_e/ w_tRelation be explained, when than work(, and c/a is in 2-3 scope, , the computational accuracy highest of now anstis formula, therefore k are described_ic-anstisWith k_ic-eq.(10)Value is closest；And for Silica material, due to its ratio work(w_e/w_t=0.69, then (k equally from Fig. 5 a_{ic-traditional}-k_ic-fem)/k_ic-femWith than work( w_e/w_tRelation can be seen that the fracture toughness result of calculation of now all conventional indentation methods all relatively limited unit numerical analysis knots Fruit exceeds about 40%～140%, thus leads to the fracture toughness result of calculation (k of all conventional indentation methods_ic-anstis、 k_ic-lawn、k_ic-jisr1607、k_ic-evansAnd k_ic-niihara) compared with k_ic-eq.(10)Value is high by about 40%～140%.According to S.m.wiederhorn (fracture surface energy of glass.j.am ceram.soc.1969,52:99- 105), fracture toughness k of silica material_icValue is about 0.798 mpa m^1/2, test result with institute of the present invention construction method k_ic-eq.(10)=0.77mpa m^1/2Extremely close, thus demonstrating the validity of institute of the present invention construction method.

Additionally, except silica material (not carrying out senb test), the senb experiment of remaining 4 kinds of ceramic materials fracture toughness Result is pressed into test result and the fracture toughness test result based on conventional indentation method apparently higher than instrumentation, and its reason is During preparation senb sample, no matter manually how narrow the sample otch of cutting is, and the most advanced and sophisticated radius of curvature of its otch is all the time than nature The radius of curvature of crack tip is big, thus leading to test result bigger than normal.

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 specification and accompanying drawing covered spiritual when, all should be within protection scope of the present invention.

Claims (1)

1. a kind of ceramic materials fracture toughness instrumentation vickers is pressed into method of testing, and the method utilizes vickers pressure head instrument Change press-in ceramic material gained load-displacement curves and ceramic material is determined by pressure material impression diagonal crack initiation length Fracture toughness k of material_ic, 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, the nominal long a=3.5h of impression diagonal half_mAnd nominal hardness

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) measure the long c of 4 crack initiations half of vickers impression diagonal respectively by light microscope₁、c₂、c₃And c₄, with When by its average c=(c₁+c₂+c₃+c₄)/4 are long as the crack initiation half of this instrumentation press-in test, and ratio calculated c/ A, adjusts p further_mSize make ratio c/a and ratio work(w_e/w_tMeet relation: 1.05≤c/a≤1.5 and

0.71≥w_e/w_t≥(w_e/w_t)₀=0.591-0.194 (c/a) or 1.5 ＜ c/a≤6 and

0.71≥w_e/w_t≥0.3；

4) the nominal hardness h being determined according to instrumentation press-in test_nAnd ratio work(w_e/w_tDetermine measured material Young's modulus that is, Elastic modelling quantity e=(1-0.2²)/{[0.007625(w_e/w_t)⁶-0.005516(w_e/w_t)⁵-0.048401(w_e/w_t)⁴+ 0.110937(w_e/w_t)³-0.157669(w_e/w_t)²+0.170204(w_e/w_t)]/h_n-1.32(1-0.07²)/1141 }, really simultaneously Determine the ratio η=[e/ (1-0.2 of measured material and the plane-strain elastic modulus of diamond vickers pressure head²)]/[1141/(1- 0.07²)], wherein, the dimension of e is " gpa " (Ji Pa)；

5) calculate fracture toughness k of tested ceramic material_ic:

k_ic=(10^-6p_m/c^1.5)[1+f_c(c/a)η]f_w(w_e/w_t),

Wherein, f_c(c/a)=0.0068 (c/a)²- 0.1118 (c/a)+0.8295,

f_w(w_e/w_t)=0.0757 (w_e/w_t)²-0.1956(w_e/w_t)+0.1285,

k_icDimension be(MPa rice^1/2)、p_mDimension be " n " (newton), c and a dimension be " m " (rice).