CN102221544B - Method for measuring propagation velocity of electric creeping waves at ferroelectric ceramic crack tip - Google Patents

Abstract

The invention discloses a method for measuring the propagation velocity of electric creeping waves at the ferroelectric ceramic crack tip. The method comprises the following steps: firstly, cutting a ferroelectric material into a test piece with a length* width* thickness specification of h* s * t; cutting into s/2 cracks at the middle part of the test piece; after the tempering processing, coating an electrode respectively on a top thickness plane and a bottom thickness plane of the test piece; placing the test piece under a polarization optical instrument; painting marks at positions in front of, above and behind the crack tip position; switching on direct current voltage and timing; recording the optical image of the whole test piece once every 30 seconds until more then1500 seconds when an optical color stripe image on the test piece is stable and a polarized light color image is expanded to positions above and below the crack tip of the test piece and the front boundary of the crack tip of the test piece; and finally, respectively calculating three time numerical values of the electric creeping waves which are spread from the crack tip to the three marks in front of, above and behind the crack tip position, and further obtaining the wave velocity of the electric creeping waves.

Description

Ferroelectric ceramics crack tip electricity creep velocity of wave propagation measuring method

Technical field

The present invention relates to adopt polarized-light technique to measure ferroelectric ceramics crack tip electricity creeping wave along splitting the velocity of propagation that point points to all directions.

Background technology

Ferroelectric ceramics is widely used in electronics industry, instrument and meter industry, for example, and sensor, actuator or the like.Ferroelectric material is hard brittle material often, and the appearance of crackle is difficult to avoid in its manufacture process and in the industrial use.And ferroelectric ceramic material often receives the effect of highfield when using, and the most advanced and sophisticated Process Zone of crackle will be non-linear.Famous electric fatigue crack propagation problem is exactly one of reason that causes ferroelectric material destruction.Because the concentration effect of crack tip electric field intensity; Even when external electric field has only coercive electric field part; Internal field just surpasses coercive electric field intensity in the Process Zone, and electricdomain colony wherein polarizes, and distributing from original sensing at random becomes colony's sensing external electric field direction.But the velocity of propagation of external electric field is the light velocity, but crack tip is because the electricdomain rotational speed that electric creep causes is extremely slow.It is very important measuring this electric creep wave propagation velocity, because the size and dimension that it is directly arranging crack tip Process Zone electricity yield region concerns over time, and then directly influences the stability of crackle under electric load.

The discovery of electricdomain rotation phenomenon is nearly 30 years thing, and the discovery of electric creep is nearly 10 years thing.Its expression formula is:

${\stackrel{\&CenterDot;}{P}}_3^r={\stackrel{\&CenterDot;}{P}}_0{({\mathrm{<figure-callout\; id="3"\; label="E"\; filenames="HDA0000050479450000011.png"\; state="\{\{state\}\}">E</figure-callout>}}_3/E_c)}^m---\left(1\right)$

Here

Be local polarisation speed,

Be the polarization rate constant, E ₃Be local electric field intensity, E _cBe the coercive electric field of ferroelectric material, m is the power exponent of ferroelectric material electricity creep.

Forefathers have made some experimental studies [Liu QD, Huber JE (2006) Creep in ferroelectrics due to unipolar electrical loading.J Europ Ceram Soc, Vol.29, pp.2799-2806 to the electric creep of ferroelectric material; Liu QD; Fleck NA; Huber JE Chu DP (2009) Birefringencemeasurements of creep near an electrode tip in transparent PLZT.J Europ CeramSoc; Vol.29; Pp2289-2296], proved that formula (1) sets up, and PLZT (lead lanthanum zirconate titanate) ferroelectric material has been obtained the concrete numerical value of the power exponent m of the electric creep of polarization rate constant

.

And what parallel therewith is that creep causes near the research of the dislocation emission (dislocation emission) the crack tip to twentieth century foreign scholar's eighties to the toughness material mechanicalness.Ferroelectric material crack tip under pure electric load should have corresponding physical phenomenon, the rotation emission problem (domain switching emission) of the crack tip field electricdomain that this invention that Here it is is pointed out.

It is pointed out that the rotation problem that all relate to the ferroelectric material electricdomain and the domestic and foreign literature of electric creep, have following weak point:

1, they only relate to the basic Physical Mechanism of electricdomain rotation, do not recognize that this crucial phenomenon of crack tip electricdomain emission is a fluctuation problem, does not more relate to the speed (velocityofthe emission) of electricdomain emission, i.e. the speed of fluctuation certainly.

2, forefathers cause destruction to the ferroelectric ceramic material electricity; Perhaps the electricdomain rotation problem and the polarization problem in crack tip district recognized in the theory of crack problem and experimental study; But; They to nearly most advanced and sophisticated inelastic region confirm do not consider time dependent rule, certainly do not consider more that electricdomain is from splitting the influence of point emission to the inelastic region.

3, especially; Former study does not recognize that the speed of this electricdomain emission is very slow; Magnitude is little meter per second (we find 400 seconds just moved 0.5mm); And other people do not know: although this fluctuation is very slow, finally still can propagate into almost whole zone (except that the regional area at crack tip rear).We find, the plane domain of a 10mm * 5mm, and electricdomain was launched back 1500 seconds, and the electricdomain emission makes almost whole test specimen by disturbance.To the high all electric fatigue problems (for example, more than the frequency 1HZ) of crackle of ferroelectric ceramics, the electricdomain of the nearly sharp Process Zone of crackle has little time counter-rotating at all like this, and the effect of electricdomain shielding is obvious inadequately; And to extremely low frequency (for example 0.1HZ), the electricdomain in the Process Zone has sufficient time reversal, consumed energy, and shielding effect is just obviously.

Summary of the invention

Because ferroelectric ceramic material crack tip electricity creep velocity of wave propagation will influence the crack Propagation of crackle under the low-frequency alternating electric field in the ferroelectric material greatly; And reflecting the temporal correlation of the non-linear process district size and dimension of ferroelectric material crack tip; And growth rate in time, Changing Pattern; The measuring method that the purpose of this invention is to provide a kind of ferroelectric ceramic material crack tip electricity creep wave propagation and speed thereof; Through to the polarization process of ferroelectric ceramics crack tip Process Zone with calculate with the relevant measurement of time; Can calculate polarization speed rule indirectly; This has important practical value for the industry member ferroelectric ceramics at electric fatigue crack expansion characteristic and residual life, simultaneously to improving and improve ferroelectric material quality, polarization speed, improves and confirms that perhaps its electricity causes brokenly bosom toughness and range of application is of practical significance.

For reaching above purpose, the present invention takes following technical scheme to be achieved:

A kind of ferroelectric ceramics crack tip electricity creep velocity of wave propagation measuring method is characterized in that, comprises the steps:

(1) the polarization constant of known transparent iron electric material

Coercive electric field E _c, the power exponent m of electric creep is with the test specimen of ferroelectric material cut growth * wide * thick=h * s * t; Cut out crackle at the test specimen middle part; Crack length is the half the of specimen width, i.e. s/2 is after temper; Be coated with top electrode on test specimen top thickness plane and bottom thickness plane again, it is coercive electric field E that preparation connection DC voltage makes the average electric field strength E of test specimen _c1/2;

(2) this test specimen is placed under the polarization optics instrument; The A place, the place ahead of splitting sharp position, split sharp position above B place, the C place, rear of splitting sharp position smear mark; A, B, C three places are l to the distance of splitting point, connect DC voltage, start the clock; Can observe the optical color stripe pattern and changing along with the time, near the crack tip to diffusion at a distance;

(3) every optical imagery that write down whole test specimen at a distance from 30 seconds once; Up to more than 1500 seconds; Till the optics color fringe image stabilization, this moment, the polarized light coloured image expanded to upper and lower border of test specimen and right margin, i.e. the top of crack tip, below and border, the place ahead on the test specimen;

(4) through calculate obtain respectively electric creeping wave from crack tip propagate into the top A that splits sharp position, the B place, the place ahead of splitting sharp position, three time numerical value of three marks in C place, rear that split sharp position; Like this, the creep velocity of wave is exactly to be exactly the velocity of wave of creeping wave on this direction apart from l divided by one in above-mentioned three time numerical value.

In the such scheme, the h * s * t=10mm * 5mm * 0.2mm of test specimen described in the step (1); Can be chosen as 0.5～1mm according to the sample dimensions size apart from l described in the step (2).

Compared with prior art, the present invention is that not recognize also that forefathers the ferroelectric material crack tip has under the situation of electricdomain emission phenomenon (Domain Switching Emission from a crack tip) disclosed.Forefathers only find and have studied in great detail dislocation emission phenomenon (the Dislocation emission from cracks of the metal material crack tip under the no electromechanical Coupling; Anderson P.M.and Rice, J.R., 1986; Dislocation emission from cracks in crystals along crystal interfaces; ScriptaMetallurgica, Vol.20, pp.1467-1472).And this invention is to be directed against the mechanical-electric coupling material before not polarizing, the crack tip electricdomain rotation emission phenomenon that under pure electric load, takes place, and observe the image of launching and measured emission rate.This invention is significant to the crackle stability assessment of ferroelectric material under low all electric fatigue situation.

Description of drawings

Below in conjunction with accompanying drawing and embodiment the present invention is done further detailed description.

Fig. 1 is the ferroelectric treadmill test synoptic diagram that has crackle.Among the figure: the PLZT ferroelectric material is transparent, and crackle 3 and cracked zone 2 are arranged on its upper surface 1; Polarized light 4 is propagated from bottom to top, is microscope 6 and computer processor unit 5 above, and the electrode of extra electric field is in the test specimen both sides.

Fig. 2 be the optical parametric sin δ that measures over time.

Fig. 3 is the principal strain difference ε under optical parametric sin δ and the material electricity load ₃₃-ε ₁₁Between approximate linear.

The photo of the slow propagation (evolution in time) of the electricdomain rotation wave that Fig. 4 observes for the present invention.

The electricdomain rotation wave velocity of propagation of 3 points that Fig. 5 observes for the present invention (A is 0.5mm in crack tip the place ahead, and B is 0.5mm above the tip, and C is at most advanced and sophisticated rear 0.5mm) is measured.

Embodiment

A kind of measuring method of ferroelectric material crack tip electricity creeping wave (electricdomain rotation wave) velocity of propagation comprises the steps:

(1) known is the polarization constant of transparent ferroelectric material (like PLZT series polycrystalline ferroelectric ceramics) before polarization

Coercive electric field E _c, the power exponent m of electric creep is with the test specimen of ferroelectric material cut growth * wide * thick=h * s * t=10mm * 5mm * 0.2mm; Cut out crackle at the test specimen middle part with diamond tool; Crack length is the half the of specimen width, and promptly 5mm is coated with top electrode on test specimen top thickness plane and bottom thickness plane again; The electric field intensity that preparation connection DC voltage adds test specimen is 1/2 of coercive electric field, and promptly DC voltage v equals 0.5E divided by test specimen length h _c, as shown in Figure 1.Certainly, the size of test specimen can be selected according to researcher's needs, also can be from 0E to electric field intensity _cTo 0.5E _cNeeds according to the researcher are selected, and external electric field is strong more, and caused electricdomain rotation transmitted wave speed is just fast more.

(2) the ferroelectric test specimen with 10mm * 5mm * 0.2mm is placed under the optical microscope; The utilization polarizing light irradiation penetrates test specimen below test specimen, and the microscope above making can receive optical imagery; Connect direct supply 1000V, make the intensity of extra electric field reach 0.5E _c, as shown in Figure 1.In the present embodiment, mark is smeared at (A point), the 0.5mm place, top (B point) of splitting sharp position, the 0.5mm place, rear (C point) of splitting sharp position at the 0.5mm place, the place ahead of splitting sharp position, connects DC voltage, starts the clock.A, B, the position of three designated recorder points of C or apart from also can the regulating apart from l of crack tip, for example, the 0.5mm distance can be adjusted into 1mm by the basic sample dimensions of experimenter.

(3) extra electric field gets started timing after connecting; And the electricdomain rotation emission situation (coloured image) of observation ferroelectric material crack tip is whenever taken the photograph a photochrome at a distance from 30 second beats; Up to more than 1500 seconds; Till the optics color fringe image stabilization, this moment, the polarized light coloured image expanded to upper and lower border of test specimen and right margin, i.e. the top of crack tip, below and border, the place ahead on the test specimen; But the border polarized light coloured image at crack tip rear can't expand to.As shown in Figure 5, can observe the optical color stripe pattern and change along with the time, near the crack tip to diffusion at a distance.

(4) because the electric creep properties of ferroelectric material:

${\stackrel{\&CenterDot;}{P}}_3^r={\stackrel{\&CenterDot;}{P}}_0{({\mathrm{<figure-callout\; id="3"\; label="E"\; filenames="HDA0000050479450000011.png"\; state="\{\{state\}\}">E</figure-callout>}}_3/E_c)}^m---\left(1\right)$

Here

E ₃, E _cBe respectively residual polarization speed, polarization speed, electric field intensity, tender stupid electric field intensity.Thus, apply electric load after, all electrical quantities, mechanical quantities on each point in the test specimen of this sheet band crackle, for example, displacement, strain, stress, electric field, electric displacement, amount of polarization or the like are all changing in time.Like this, the polarized light image that receives of microscope is also changing in time.

Because optical parametric sin δ and strain have linear relationship and electric displacement to have quadratic function relation and electric field intensity linear relationship to be arranged, obtain these physical quantitys and change of time curve respectively through simple mathematical calculating; The electricity creeping wave is from crack tip propagates into the top 0.5mm (B point) that splits sharp position, the 0.5mm place, the place ahead (A point) of splitting sharp position, the rear 0.5mm (C point) that splits sharp position locates three marks three time numerical value; Like this; The creep velocity of wave is exactly that 0.5mm (promptly emits from crack tip and arrives A divided by one in above-mentioned three time numerical value respectively; B; The time that C) be exactly the velocity of wave (promptly emit and arrive A, B, the average velocity of wave that C at 3) of creeping wave on this direction at 3 from crack tip.

In the step (4), said simple mathematical is calculated, and can be calculated mechanical quantity and electrical quantities by the optical quantities that optical instrument measures, and computing formula is (ASTM-D4093-95) as follows:

Notice that (x3), the direction of propagation of light wave is x to three reference directions that mark among Fig. 1 for x1, x2 ₂, the electric field loading direction is x ₃Two refraction coefficient (n are arranged respectively in the normal plane of light wave propagation direction ₁, n ₃), represent that respectively light wave is at (x ₁, x ₃) velocity of propagation (n on the direction _i=c ₀/ c _i, c ₀Be light velocity of propagation in a vacuum); For initially without hyperpolarization or through for the homogeneous material of temper, n ₁=n ₂=n ₃=n ₀And at x ₃The electric field of direction loads and will cause at x ₁, x ₃Light wave velocity variations on the direction is different (Δ n=n ₁-n ₃≠ 0), this just causes (x ₂, x ₃) plane and (x ₁, x ₃) the relative differences δ (relativephase difference) or the relative delay Γ (relative retardation) on plane:

$\mathrm{\&delta;}=\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\mathrm{\&Delta;n}\&CenterDot;t,---\left(2\right)$

Γ＝Δn·t， (3)

Here λ is the wavelength of light wave, and t is the thickness of material.

Unite States Standard (USS) (ASTM D4093-95 is arranged; 2001; Standard Test Method for PhotoelasticMeasurements of Birefringence and Residual Strains in Transparent or TranslucentPlastic materials.American Society for Testing and Materials); Through the rotation test specimen, can find the maximum value of offset light, then intensity of polarization light is:

$I=I_0{\sin }^2\frac{\mathrm{\&delta;}}{2},---\left(4\right)$

Here I ₀Be the light intensity that penetrates when not having birefringence, I is the light intensity of measuring when birefringence is arranged.

To monochromatic light, by formula (4), differing δ is the thickness t that is proportional to test specimen.For thicker test specimen or stronger birefringence material, δ maybe be greater than π.At this moment, the measurement of light intensity is difficult to tell and differs δ or 2 π-δ.This effect can prove with the test specimen on quartzy limit.Differ δ along with the variation of thickness is linear, test observation to the position of blackstreak on, differ δ=2m π, m is extra exponent number here, the ferroelectric material test specimen generally is to show high order (δ＞π).Use polarized-light technique (the rotating polarizertechnique) can avoid this difficulty.

Because symmetry, Fig. 1 has only shown 1/4th test specimens, and intensity of polarization light is:

Here

is angle excursion.Use modern polarized light instrument such as Oxonian Metripol ^TMOr the Oosight of Cambridge University ^TMThe polarized light instrument can be measured the I on the whole test specimen simultaneously ₀, | sin δ | with

Obtain like this | sin δ | image.Through following approximate formula:

n≈n ₀+a ₁E (6)

And make external electric field E＜＜E _c, following formula is exactly that a good approximate formula (is generally got 0.5E _c＜E＜E _c),

δ/δ ₀∝(E ₃/E _c) ²， (7)

By document (Geday MA, 2001, Birefringence imaging, PhD thesis, OxfordUniversity England) can know, polarized light tensor sum photoelastic tensor has following relation:

${\left(\frac{1}{{\mathrm{\&Delta;n}}^2}\right)}_{\mathrm{ij}}=p_{\mathrm{ijkl}}{\mathrm{\&epsiv;}}_{\mathrm{kl}}+g_{\mathrm{ijmn}}{P}_m{P}_n,---\left(8\right)$

Here ε _KlBe strain tensor, P is the material polarization that external electric field causes, and (p _Ijkl, g _Ijmn) be light-elasticity coefficient (elasto-optical coefficients) and secondary electricity-spectrum number (quadratic electro-opticalcoefficients).Refraction is from n ₀Variation (Δ n) will depend on

$\mathrm{\&Delta;n}=r^p{\left(P_3^r\right)}^2,---\left(9\right)$

Here r ^pElectricity-the optical coefficient of residual polarization, we obtain for the PLZT8/65/35 material: r ^p=0.28m ⁴C ^-2(Liu QD, Huber JE (2006) Creep in ferroelectrics due to unipolarelectrical loading.J Europ Ceram Soc 29,2799-2806; Liu QD, Fleck NA, HuberJE Chu DP (2009) Birefringence measurements of creep near an electrode tip intransparent PLZT.J Europ Ceram Soc 29,2289-2296).

Measured anaclasis and strain-dependent.By formula (7); We can obtain poor (the ASTM D4093-95 of two principal strains in the test specimen plane; 2001, Standard Test Method for PhotoelasticMeasurements of Birefringence and Residual Strains in Transparent or TranslucentPlastic materials.American Society for Testing and Materials):

δ/δ ₀∝(ε ₂-ε ₁)， (10)

Here ε ₁Be that strain along slow-axis direction (is n ₁Direction), ε ₂Be that strain along quick shaft direction (is n ₂Direction).

Equally, use formula (2), (9), (10) can obtain following approximate formula:

δ∝Δn∝P ²∝ε (11)

The Metripol of Oxford University that is to use shown in Figure 2 ^TMPLZT 8/65/35 ferroelectric ceramic material of polarized light apparatus measures is at electric field E=0.725E _cUnder loading | sin δ | time dependent curve.| sin δ | numerical value shaken back and forth severally, show above-mentioned reached for birefringent multistage time (δ～π).| sin δ | each peak value corresponding a δ value, promptly for the N order, the pi/2 of δ=(2N-1).First peak value 1.0 is corresponding to first order, and the order peak value that gets off successively decreases.This be since in polarization process the transparency of test specimen descend and to cause.But periodic feature is still very obvious, so the strain that we can use foil gauge record 1,3 direction simultaneously over time, thereby obtains δ and (ε ₃₃-ε ₁₁) relation curve (as shown in Figure 3).From Fig. 3, can find out δ and (ε ₃₃-ε ₁₁) be linear relationship, the slope of the straight line among the figure can be confirmed.Thus, the δ numerical value that each point obtains in test on the test specimen can be converted into ε ₃₃-ε ₁₁Numerical value, same, | sin δ | also and ε ₃₃-ε ₁₁Follow variation.After electric field applies, if on point | sin δ | in a period of time, do not change, explain that then the ripple of electricdomain rotation still is undisturbed this point, otherwise, if on this aspect | sin δ | unexpected variation, explain that ripple arrives.Use this relation can to ferroelectric material contain crackle, cavity and be mingled with etc. heterogeneous characteristics whole audience δ or | sin δ | optical measurement turn to the principal strain difference field or the overstrain field measurement of the two-dimentional whole audience, and then can be converted into about the relevant information of electricdomain motion and electricdomain emission and measure.

Shown in Figure 4 is the electricdomain rotation emission situation that the present invention obtains, and redness wherein (dark color) zone is corresponding | sin δ | and the=1st, the homogeneous strain field of not disturbed by crackle.5 figure among Fig. 4 show that the electricdomain rotation emits from crack tip, after 1500 seconds, expand to almost whole zone (having only crackle very fraction zone behind not by disturbance).It is thus clear that the velocity of wave of this special ripple (wave due to the domainswitching emission from the crack tip) is very slowly.Fig. 5 has shown the special some A of three on the test specimen, B, C (respectively crack tip the place ahead, above, the rear, all apart from 0.5 millimeter of crack tip) go up the situation that this ripple reaches.Can see, before 400 seconds, on 3 | sin δ | (be proportional to principal strain difference ε ₃₃-ε ₁₁) obvious difference is arranged, strain differential is the highest on the B point, and the A point takes second place, and the C point is minimum., before 400 seconds, on each point | sin δ | (it is poor to be proportional to principal strain) is approximate constant.In case surpass 400 seconds, on each point | sin δ | the electricdomain rotation wave institute disturbance that (it is poor to be proportional to principal strain) emitted from crack tip significantly.Because every all is 0.5 millimeter apart from the tip, and the disturbance time all is 400 seconds, the average velocity of wave of visible this electricdomain rotation wave is 0.5mm/400s=1.25 μ m/s, and velocity of wave itself is isotropic, is identical along three direction velocities of wave promptly.

Claims (3)

1. a ferroelectric ceramics crack tip electricity creep velocity of wave propagation measuring method is characterized in that, comprises the steps:

(1) the polarization constant of known transparent iron electric material

, coercive electric field E _c, the power exponent m of electric creep is with the test specimen of ferroelectric material cut growth * wide * thick=h * s * t; Cut out crackle at the test specimen middle part; Crack length is the half the of specimen width, i.e. s/2 is after temper; Be coated with top electrode on test specimen top thickness plane and bottom thickness plane again, it is coercive electric field E that preparation connection DC voltage makes the average electric field strength E of test specimen _c1/2;

(2) this test specimen is placed under the optical microscope, the utilization polarizing light irradiation penetrates test specimen below test specimen; Microscope above making can receive optical imagery, the A place, the place ahead of splitting sharp position, split sharp position above B place, the C place, rear of splitting sharp position smear mark, A, B, C three places are l to splitting sharp distance; Connect DC voltage; Start the clock, can observe the optical color stripe pattern and changing along with the time, near the crack tip to diffusion at a distance;

(3) every optical imagery that write down whole test specimen at a distance from 30 seconds once; Up to more than 1500 seconds; Till the optics color fringe image stabilization, this moment, the polarized light coloured image expanded to upper and lower border of test specimen and right margin, i.e. the top of crack tip, below and border, the place ahead on the test specimen;

(4) through calculate obtain respectively electric creeping wave from crack tip propagate into the place ahead A that splits sharp position, the B place, top of splitting sharp position, three time numerical value of three marks in C place, rear that split sharp position; Like this, be exactly the velocity of wave of creeping wave on this direction apart from l divided by one in above-mentioned three time numerical value.

2. ferroelectric ceramics crack tip electricity creep velocity of wave propagation measuring method as claimed in claim 1 is characterized in that the h * s * t=10mm * 5mm * 0.2mm of test specimen described in the step (1).

3. ferroelectric ceramics crack tip as claimed in claim 1 electricity creep velocity of wave propagation measuring method is characterized in that, is 0.5～1mm apart from l described in the step (2).

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