CN105510162A - Nanoindentation testing method for elastic moduli of austenite phase and martensite phase of shape memory alloy - Google Patents

Abstract

The invention provides a nanoindentation testing method for the elastic moduli of an austenite phase and a martensite phase of a shape memory alloy. The method comprises the following steps: multiple nanoindentation experiments at different depths; data processing by using the Oliver-Pharr method on the basis of experimental results; and regression analysis via empirical formulas obtained by using the Hertz contact theory and parameter analysis so as to obtain the elastic moduli of the austenite phase and the martensite phase. The testing method is simple in principles and easy in steps and can rapidly obtain the elastic moduli of the austenite phase and the martensite phase by implementing the nanoindentation experiments at different depths and using the calculation formulas put forward; and formulas used in the process of calculation are based on theories, experimental results are highly reliable, the process of a data processing algorithm is intelligible, and the data processing algorithm can be easily programmed.

Description

A kind of nano-indenter test method of marmem austenite and martensitic phase elastic modulus

Technical field

The invention belongs to nano-indenter test new method, for measuring the elastic modulus of marmem austenite and martensite two-phase.

Background technology

Marmem is a kind of intellectual material, and wherein Ni-Ti-based shape memory alloy is the most superior class of super-elasticity and shape-memory properties.This material has been widely used in micro electronmechanical, medical, aviation and automobile and other industries.The superelastic properties of marmem is derived from the transformation between the austenite phase of cubic lattice structure and the martensitic phase of oblique cubic lattice structure: alloy is adding in loading, stress once response exceedes austenite and starts stress to martensite transfor mation, and namely austenite starts to become martensite mutually; During unloading, first martensitic elastic unloading occurs, change beginning stress lower than martensite to austenite once stress, martensite transforms back into initial austenite phase gradually.Found by literature survey, the elastic modulus difference of austenite and martensitic phase is comparatively large, and they are two important mechanics parameters of the mechanical behavior of accurate description marmem alloy, and under macro-scale, can pass through dullness-unloading test matching obtains; But under micro-nano-scale, the measurement of marmem austenite and martensitic phase elastic modulus does not also have ripe method at present.

Using Nanoindentation is a kind of a kind of method of testing that quick, conveniently can must obtain the consistency and elasticity modulus of small dimensional material sample.In recent years, Using Nanoindentation is widely used in the Mechanics Performance Testing of metal material, intellectual material and biomaterial etc. under micro-nano-scale.Adopt Oliver-Pharr method to analyze load-displacement curves, be easy to obtain elasticity modulus of materials and hardness, have and be convenient to realization, fast and accurately advantage.Traditional nano impress method is mainly used in the mechanical property measuring monophase materials, for this phase-change material of marmem, if directly adopt Oliver-Pharr method to obtain elastic modulus, it will be the mixing elastic modulus of austenite and martensite two-phase, cannot as effective mechanics parameter.

Summary of the invention

In view of the limitation in the Mechanics Performance Testing of Oliver-Pharr method under phase-change material miniature scale, the object of the invention is to propose a kind of new nano-indenter test method, for determining the elastic modulus of marmem austenite and martensite two-phase.

A mark test method for marmem austenite and martensite elastic modulus, comprises following five steps:

Step 1, carry out once the little degree of depth spherical indentation experiment, require h _m/ R≤0.001, calculates austenite elastic modulus E by formula one _a;

$E_a=\frac{3P_m(1-v_a^2)}{4h_m\sqrt{{\mathrm{Rh}}_m}}$ (formula one)

Wherein, P _mfor the maximum load value in indentation test; h _mit is maximum depth of cup; v _a=0.33 is the Poisson ratio of austenite phase; R is spherical indenter radius;

Step 2, carry out the repeatedly indentation test of different depth, require that depth capacity place material has entered the martensitic traoformation stage, basis for estimation is that the load-displacement curves of response presents the hysteretic loop do not closed, as shown in Figure 2;

Austenite elastic modulus E in step 3, the experimental data utilizing many experiments in step 2 and step 1 _a, positive phase transformation can be obtained by formula two and start stress austenite elasticity degree of depth h can be drawn finally by formula three ₀;

${\mathrm{\σ}}_a^s=E_a{\left(\frac{P_0}{17.92E_a{R}^2}\right)}^{\frac{1}{3}}$ (formula two)

$h_0=5.31R{\left(\frac{{\mathrm{\σ}}_a^s}{E_a}\right)}^2$ (formula three)

Wherein, P ₀it is elastic ultimate load; h ₀it is the critical depth of cup starting to occur martensitic traoformation; that positive phase transformation starts stress.

Step 4, utilize the experimental data of many experiments in step 2, calculate Indentation Modulus E by Oliver-Pharr method _op: first by the unloading rigidity S of the fitting formula assumed (specified) load-displacement curve shown in formula four, calculate contact degree of depth h by formula five _c, substitute into formula six and calculate reduction modulus E _r, by S and E _rsubstitute into formula seven and calculate Indentation Modulus E _op;

S=Bm (h _m-h' _f) ^m-1(formula four)

$h_c=h_m-\frac{0.75P_m}{S}$ (formula five)

$E_r=\frac{S}{2\sqrt{2{\mathrm{Rh}}_c-h_c^2}}$ (formula six)

$E_{op}=\frac{1-v_s^2}{\frac{1}{E_r}-\frac{1-v_i^2}{E_i}}$ (formula seven)

Wherein, h' _f, B and m is fitting parameter, E _i=1170GPa and v _i=0.07 elastic modulus and the Poisson ratio being respectively diamond spherical pressure head, v _s=0.33 is the Poisson ratio of test sample book marmem.

Step 5, E by step 4 _op, h in step 4 ₀can make with between graph of a relation, then carry out regretional analysis by formula eight and can obtain martensite elastic modulus E _mwith parameter γ;

$\frac{E_a}{E_{op}}=e^{-\mathrm{\γ}(h_m-h_0)/R)}+\frac{E_a}{E_m}\left(1-e^{-\mathrm{\γ}(h_m-h_0)/R)}\right)$ (formula eight)

Wherein, γ is the parameter depending on material properties.

(experiment number is associated with required curve precision to present invention employs repeatedly indentation test, fitting precision and experiment number positive correlation), different maximum depths of cup is set and obtains load p-displacement h curve, still the method that Oliver-Pharr method calculates Indentation Modulus is remained, by follow-up theoretical analysis and data analysis, isolate austenite and martensite elastic modulus.The theoretical formula adopted is based on classical Hertzian contact theory, and the accuracy of the austenite of acquisition and martensitic phase elastic modulus is high and with a high credibility.

Accompanying drawing illustrates:

Fig. 1 nano-indenter test method flow diagram of the present invention;

Fig. 2 marmem austenite of the present invention and the definition of martensite elastic modulus

Fig. 3 the present invention time nano impress loading-depth curve;

Nano impress loading-depth curve under the different depth of cup of Fig. 4 the present invention;

Fig. 5 dimensionless Indentation Modulus-degree of depth regression analysis curve of the present invention.

Embodiment

Below by accompanying drawing and embodiment, the present invention is further elaborated.

Fig. 1 shows the nanoindentation method flow of a kind of marmem austenite and martensite elastic modulus, austenite elastic modulus E _awith martensite elastic modulus E _mfig. 2 is shown in definition on stress σ-strain stress curve.

It is pointed out that the nano-indentation experiment related in the present invention all adopts spherical indenter.

Embodiment is described below:

Step 1, carry out once little degree of depth indentation test, require h _m/ R≤0.001, calculates austenite elastic modulus E by formula one _a;

$P_m=\frac{4E_a{h}_m\sqrt{{\mathrm{Rh}}_m}}{3(1-v_a^2)}$ (formula one)

Wherein, P _mfor the maximum load value in nano-indentation experiment, h _mit is maximum depth of cup; v _a=0.33 is the Poisson ratio of austenite phase; R is spherical indenter radius; H is depth of cup angle value; E _ait is austenite elastic modulus; When depth of cup is limited in h _m/ R≤0.001, not yet there is martensitic traoformation in material, is in the austenite linear elastic deformation stage, and application Hertzian contact theory solves linear elasticity contact problems, through Simulation, through the E that formula one is tried to achieve _amaximum error is no more than 1.99%;

Step 2, carry out the repeatedly indentation test of different depth, require that depth capacity place material has entered the martensitic traoformation stage, the indentation load P-degree of depth h curve of acquisition as shown in Figure 3.Three phases can be divided into: elastic unloading mixed phase, reverse transformation and austenite elastic unloading stage according to unloading curve.When loading curve and unloading curve do not overlap, show that alloy there occurs the positive phase transformation of martensite and reverse transformation, the Indentation Modulus obtained by unloading curve initial segment is austenite and martensitic mixing modulus, otherwise Indentation Modulus is austenitic elastic modulus.

Austenite elastic modulus E in step 3, the experimental data utilizing step 2 and step 1 _a, positive transformation stress can be obtained by formula two austenite elasticity degree of depth h can be drawn finally by formula three ₀;

${\mathrm{\σ}}_a^s=E_a{\left(\frac{P_0}{17.92E_a{R}^2}\right)}^{\frac{1}{3}}$ (formula two)

$h_0=5.31R{\left(\frac{{\mathrm{\σ}}_a^s}{E_a}\right)}^2$ (formula three)

Wherein, P ₀it is elastic ultimate load; h ₀it is the critical depth of cup starting to undergo phase transition; that positive phase transformation starts stress; Due to the load p-degree of depth h line smoothing of nano-indentation experiment, the loading-depth curve being drawn elasticity loading curve and experiment acquisition by formula one is contrasted, and obtain the bifurcation of two curves, the load that bifurcation is corresponding is P ₀value, substituting into formula two can obtain the last critical depth of cup h that martensitic traoformation occurs by formula three obtains again ₀;

Formula two and formula three all can be obtained by Hertzian contact theory, and are adopted by pertinent literature;

Step 4, the nano-indentation experiment data extraction load p-degree of depth h curve utilized in step 2, as shown in Figure 3, calculate Indentation Modulus E by Oliver-Pharr method _op: first by the unloading rigidity S of the fitting formula assumed (specified) load-displacement curve shown in formula four, calculate contact degree of depth h by formula five _c, substitute into formula six and calculate reduction modulus E _r, by S and E _rsubstitute into formula seven and calculate Indentation Modulus E _op;

S=Bm (h _m-h' _f) ^m-1(formula four)

$h_c=h_m-\frac{0.75P_m}{S}$ (formula five)

$E_r=\frac{S}{2\sqrt{2{\mathrm{Rh}}_c-h_c^2}}$ (formula six)

$E_{op}=\frac{1-v_s^2}{\frac{1}{E_r}-\frac{1-v_i^2}{E_i}}$ (formula seven)

Wherein, h' _f, B and m is fitting parameter, E _i=1170GPa and v _i=0.07 elastic modulus and the Poisson ratio being respectively diamond spherical pressure head, v _s=0.33 is the Poisson ratio of test sample book marmem.

Step 5, implement the nano indentation test of different depth of cup, obtain the indentation load P-depth of cup h curve under different depth of cup, as shown in Figure 4.By the h that step 3 obtains ₀with the E that step 4 obtains _opdraw out dimensionless with between graph of a relation, as shown in Figure 5.Utilize formula eight to carry out nonlinear regression analysis and can obtain martensite elastic modulus E _m;

$\frac{E_a}{E_{op}}=e^{-\mathrm{\γ}(h_m-h_0)/R)}+\frac{E_a}{E_m}\left(1-e^{-\mathrm{\γ}(h_m-h_0)/R)}\right)$ (formula eight)

Wherein, E _opit is the Indentation Modulus that Oliver-Pharr method is obtained; h _mit is maximum depth of cup; γ is the fitting parameter depending on material properties; The austenite elastic modulus E predicted by formula one _a=99.52GPa, desired value E _a=100GPa, error is 0.48%, the martensite elastic modulus E predicted by formula eight _m=66.19GPa, desired value E _m=70GPa, error is 5.44%, at engineering tolerance interval and so on.

The functional relation of austenite elastic modulus, martensite elastic modulus and Indentation Modulus that formula eight is set up, summed up by a large amount of numerical simulations and Parameter analysis to obtain, the constitutive model adopted in its Numerical Experiment has demonstrated its rationality, so formula correctly can reflect the relation between three.

Claims (3)

1. a nano-indenter test method for marmem austenite and martensitic phase elastic modulus, is characterized in that, comprise the following steps:

Step 1, carry out the little degree of depth indentation test of an elastic response, calculate austenite elastic modulus E by formula one _a;

$E_a=\frac{3P_m(1-v_a^2)}{4h_m\sqrt{{\mathrm{Rh}}_m}}$ (formula one)

Wherein, h _mit is maximum depth of cup; P _mfor the maximum load value in indentation test; v _ait is the Poisson ratio of austenite phase; R is spherical indenter radius;

Step 2, carry out repeatedly the indentation test of different depth, require that depth capacity place material has entered the martensitic traoformation stage, basis for estimation is that the load-displacement curves of response presents closed hysteretic loop;

Austenite elastic modulus E in step 3, the experimental data utilizing many experiments in step 2 and step 1 _a, positive transformation stress can be obtained by formula two austenite elastic impression degree of depth h can be drawn finally by formula three ₀;

${\mathrm{\σ}}_a^s=E_a{\left(\frac{P_0}{17.92E_a{R}^2}\right)}^{\frac{1}{3}}$ (formula two)

$h_0=5.31R{\left(\frac{{\mathrm{\σ}}_a^s}{E_a}\right)}^2$ (formula three)

Wherein, P ₀it is elastic ultimate load; h ₀start the critical depth of cup of austenite to martensite transfor mation occurs;

Step 4, utilize the experimental data of many experiments in step 2, calculate Indentation Modulus E by Oliver-Pharr method _op: first by the unloading rigidity S of the fitting formula assumed (specified) load-displacement curve shown in formula four, calculate contact degree of depth h by formula five _c, substitute into formula six and calculate reduction modulus E _r, by S and E _rsubstitute into formula seven and calculate Indentation Modulus E _op;

S=Bm (h _m-h' _f) ^m-1(formula four)

$h_c=h_m-\frac{0.75P_m}{S}$ (formula five)

$E_r=\frac{S}{2\sqrt{2{\mathrm{Rh}}_c-h_c^2}}$ (formula six)

$E_{op}=\frac{1-v_s^2}{\frac{1}{E_r}-\frac{1-v_i^2}{E_i}}$ (formula seven)

Wherein, h' _f, B and m is fitting parameter, E _i=1170GPa and v _i=0.07 elastic modulus and the Poisson ratio being respectively diamond spherical pressure head, v _s=0.33 is the Poisson ratio of test sample book marmem;

Step 5, under different depth of cup, calculate Indentation Modulus E by step 4 _opwith critical depth of cup h ₀, then draw out dimensionless with between graph of a relation, utilize formula eight to carry out nonlinear regression analysis and can draw martensite elastic modulus E _m;

$\frac{E_a}{E_{op}}=e^{-\mathrm{\γ}(h_m-h_0)/R)}+\frac{E_a}{E_m}(1-e^{-\mathrm{\γ}(h_m-h_0)/R)})$ (formula eight)

Wherein, E _opit is the Indentation Modulus that Oliver-Pharr method is obtained; h _mit is maximum depth of cup; γ is the fitting parameter depending on material properties.

2. method of testing as claimed in claim 1, is characterized in that, in described step 1, requires that indentation test meets the demands h _m/ R≤0.001, wherein h _mit is maximum depth of cup; R is spherical indenter radius.

3. method of testing as claimed in claim 1, it is characterized in that, described in step 2, repeatedly the indentation test of different depth is to obtain load p-displacement h curve, and experiment number is associated with required curve precision.