CN106092785A - The method using asymmetric crackle test fatigue crack growth rate - Google Patents

Abstract

The present invention relates to investigating fatigue crack expansion technology, the method being specifically related to use asymmetric crackle test fatigue crack growth rate.Comprising: process along the asymmetric breach of X-axis at test specimen active section；Asymmetric gap test piece will be contained be clamped on fatigue machine and carry out fatigue crack propagation test；Measure asymmetric crackle left and right split point extension information；The left and right point that splits is estimated fatigue crack growth rate respectively, calculates the left and right stress intensity factor range splitting point of asymmetric crackle under the conditions of clamping border；Ask for fatigue crack growth rate parameter C of material respectively_A、n_AAnd C_B、n_B.Which solve M (T) test specimen and data invalid problem after asymmetric crackle occurs；Left and right crack tip stress intensity factor range is different, and fatigue crack growth rate is the most different, and compared with M (T) test specimen symmetry crackle, data volume increases, and effective information increases；Can the positions and dimensions of the asymmetric breach of reasonable disposition, it is achieved gamut fatigue crack growth rate is tested.

Description

The method using asymmetric crackle test fatigue crack growth rate

Technical field

The present invention relates to investigating fatigue crack expansion technology, split in particular to using asymmetric crackle test fatigue The method of stricture of vagina spreading rate.

Background technology

Fatigue/Fracture under repeated load effect is the topmost failure mode of Flight Vehicle Structure, in order to ensure structure Safety and economy, the modern commonly used durability of advanced aircraft structure/damage tolerance thought is used to carry out structure design.Press This design philosophy requirement, at structured design phase, Analysis of Fatigue Crack Growth to be carried out and damage tolerance test to determine structure Maintenance interval, and the fatigue crack growth rate of material is by the fundamental performance parameter of Analysis of Fatigue Crack Growth.To this end, from The 1950's, carry out substantial amounts of fatigue of materials crack propagation rate measurement method research both at home and abroad, defined tired Labor crack growth rate testing standard method, such as U.S. ASTM E647 series, Europe BS ISO 12108 series, China GB/T 6398 series, in above-mentioned standard, it is stipulated that sample type, fatigue crack length measuring method and data processing method.

Fatigue crack growth rate testing standard gives 3 kinds of typical test specimens: standard compact tension specimen C (T) sample, mark True centric stretching M (T) sample, standard SEN three-point bending SE (B) sample.Wherein, C (T) sample and SE (B) sample can not Fatigue crack growth rate test under negative stress ratio (R < 0).And M (T) sample can be used for the fatigue under positive and negative stress ratio Crack growth rate is tested, applied widely, has obtained commonly used.

Fatigue crack length measuring method mainly has: ocular estimate, potentiometry and flexibility method.Ocular estimate generally uses digital aobvious Surface of test piece is amplified by micro mirror, by digital data transmission to computer, demonstrates the image of surface of test piece, pass through in display window The crack tip that mobile microscope makes image show overlaps with default graticule, reads microscopical position on grating digital readout, It is the coordinate of crack tip.Ocular estimate is simple to operate, directly perceived, and precision is high, the highest to equipment requirements.Potentiometry can record and wear Crack length, need not manual operation, but potentiometry certainty of measurement is easily by external interference, to line-hit in process of the test thoroughly Obvious especially, and need to demarcate before testing, calibration process is complicated, and result is unreliable；Need after off-test to split Stricture of vagina leading edge Curvature modification.Flexibility method goes for different measurement environment and test material, but flexibility method exists asks as follows Topic: the requirement to testing machine is higher；Needing before experiment to carry out elastic modelling quantity demarcation, calibration process is more complicated, and calibration result is not Uniquely, relevant with load and crack length；Need after off-test to carry out crack front Curvature modification.It addition, potentiometry and soft There is even more serious problem in degree method: to C (T) test specimen and SEB (T) test specimen, once cracks can spread is not along plane of symmetry direction, then electricity Position method and flexibility method lost efficacy；To M (T) test specimen, by standard-required, once cracks can spread is asymmetric, then method of testing lost efficacy.With electricity Position method is compared with flexibility method, the measurement result of ocular estimate more true and accurate, to C (T), SEB (T) test specimen, if using range estimation Method, even if cracks can spread deflection, also can carry out the Treatment Analysis of data, but try the M (T) that current laboratory is widely used Part, when cracks can spread is asymmetric, according to standards such as ASTM, the cracks can spread data now recorded only as invalid data at Reason.Test finds, even traditional widely used metal material, uses M (T) test specimen to carry out fatigue crack growth rate survey During examination, also can crack the asymmetric phenomenon of extension.And along with the appearance of various new materials, such as metal laminate, 3D beats , more and more there is the phenomenon of the asymmetric extension of fatigue crack in print metal material, monocrystal material, metal-base composites, as By standard-required, fruit thinks that result is invalid, certainly will cause the waste of substantial amounts of man power and material.

Summary of the invention

It is an object of the invention to provide a kind of method using asymmetric crackle test fatigue crack growth rate, not only The problem that can solve cannot effectively utilize M (T) test specimen asymmetric cracks can spread data in existing testing standard；And, left and right Crack tip stress intensity factor range is different, and fatigue crack growth rate is the most different, compared with M (T) test specimen symmetry crackle, asymmetric Crackle valid data amount increases by 1 times, and effective information substantially increases, and can save test specimen and manpower, financial resources；Also by reasonable disposition The positions and dimensions of asymmetric breach, it is achieved the test of gamut fatigue crack growth rate.

The present invention relates to a kind of method using asymmetric crackle test fatigue crack growth rate, comprising:

Use equal thickness vertical bar shaped test specimen, process the asymmetric breach along X-axis at test specimen active section；

By the specimen holder with asymmetric breach on the chuck of fatigue machine, breach to upper grip, lower chuck Apart from identical；Make loading direction be perpendicular to breach surface, then apply constant-amplitude fatigue loading, carry out fatigue crack propagation test；

Measuring the information of asymmetric cracks can spread, and record fatigue load effect times N, described information includes: test specimen is at X Axial half-breadth W, length L of test specimen active section, the coordinate a of right crack tip A_A, the coordinate a of left crack tip B_B；

UtilizeWherein, A is that crackle half is long, a=(a_A-a_B)/2,

m^(A,B)(a_A,a_B,x) For right crack tip, the weight function of left crack tip, being used for asking for clamping the asymmetric crackle right side under the conditions of border, to split point stress strong Degree factor K_AWith left crack tip stress intensity factor K_B；

Point is split on the calculating right side, sharp stress intensity factor range Δ K is split on a left side_A、ΔK_B, computing formula is Δ K_A=K_A(1-R)、 ΔK_B=K_B(1-R), wherein, R is stress ratio；

Estimate respectively the asymmetric crackle right side split point, a left side split point fatigue crack growth rate (da/dN)_A、(da/dN)_B；

According to described Δ K_A, described (da/dN)_A, described Δ K_B, described (da/dN)_BAsk for the fatigue crack of material respectively Spreading rate parameter C_A、n_AAnd C_B、n_B。

In certain embodiments, being preferably, described test specimen is equal thickness plate；Deviation test specimen center, asymmetric breach center Line；The processing mode of described asymmetric breach is line cutting.

In certain embodiments, it is preferably, in described fatigue crack growth rate is tested, uses ocular estimate to measure fatigue Crack size；Described method also includes: periodically smear coloring liquid at crack tip.

In certain embodiments, being preferably, the information of the asymmetric cracks can spread of described measurement includes:

Observe the crackle amplified by digit microscope；

Mobile described digit microscope, makes the tip of the crackle of described amplification overlap with default graticule；

The test frequency of described fatigue machine is reduced, grating digital readout chi reads right crack tip A, left Crack Tip The coordinate a of end B_A、a_B。

In certain embodiments, it is preferably, asks for clamping the asymmetric crackle right crack tip stress intensity factor under the conditions of border K_A, left crack tip stress intensity factor K_BIncluding:

According to the clamping feature of boundary condition and test specimen itself about the feature of Y-axis Stiffness elasticity coupling, set up asymmetric splitting The equivalent model that stricture of vagina stress intensity factor solves；

Stress strength factor K under the conditions of strain energy according to cracks in body, additional bending moment, and free Uniform Tension_σ ^(A,B)、 Stress strength factor K under simple bending load_M ^(A,B), obtain K based on described equivalent model_A、K_B。

In certain embodiments, being preferably, described equivalent model is:

Clamping boundary condition is equivalent to the common effect of free Uniform Tension σ and simple bending load M, and makes test specimen end Corner in portion's X-Y plane is equal to 0；

K^(A,B)=K_σ ^(A,B)+K_M ^(A,B)。

In certain embodiments, it is preferably, the stress strength factor K under the conditions of described free Uniform Tension_σ ^(A,B)Ask for Mode is:

Wherein,

σ (x) is flawless body Y-direction stress distribution of imagination crack surface under free Uniform Tension stress σ, and σ=P/S, P are Load, S is the cross-sectional area of test specimen；σ (x)=σ, x are integration coordinate.

In certain embodiments, it is preferably, stress strength factor K under described simple bending load effect_M ^(A,B)Ask for mode For:

Wherein,

σ_MX () is flawless body Y-direction stress distribution of imagination crack surface under the simple bending load M effect of far field；Assuming that test specimen Thickness is unit thickness,M is simple bending load.

In certain embodiments, it is preferably, described (da/dN)_A, described (da/dN)_BPredictor method be:

Wherein, a_A,i、a_B,iExpression i & lt interpretation obtains respectively right crack tip A, a left side are split The coordinate of stricture of vagina tip B, N_i、N_i+1The load cycle number of record when representing i & lt and i+1 time interpretation crackle respectively；

Or

Wherein,

Subscript n is equal in 7 matchings 3, equal to 2 in 5 matchings；Coefficient b₀、b₁、b₂It is with at interval [a_i-n,a_i+n] press between crack length observation and match value The regression parameter that determines of the minimum principle of sum of square of deviations；Match valueCorrespond to load cycle number N_iMatching crackle long Degree；Parameter C₁And C₂For converting input data.

In certain embodiments, it is preferably, described fatigue of materials crack growth rate parameter C_A、n_AAnd C_B、n_BThe side of asking for Method includes:

Determine the given applied stress equation than lower fatigue crack growth rate:

ByData carry out linear fit, determine material Fatigue crack growth rate parameter C of material_A、n_AAnd C_B、n_B。

A kind of method using asymmetric crackle test fatigue crack growth rate that the embodiment of the present invention provides, with existing Technology is compared, it is contemplated that in loading procedure, and the two ends of test specimen are not freely, but are clamped in testing machine by fixture block and press from both sides up and down On head, fixture block can retrain the rotation in the displacement of test piece end X-direction and X-Y plane, and test specimen itself is about Y-axis rigidity not Symmetry, therefore set up the equivalent model that stress intensity factor solves, splitting point with the crackle right side asymmetric under the conditions of asking for gripper edge circle should Force intensity factor K_A, left crack tip stress intensity factor K_B, be calculated respectively the right side split point, a left side split point fatigue crack growth rate (da/dN)_A、(da/dN)_B, and stress intensity factor range right under the conditions of clamping border, that point is split on a left side, then use Paris formula Describe fatigue crack growth rate, obtained fatigue crack growth rate parameter C of material by data matching_A、n_AAnd C_B、n_B。

Test specimen containing asymmetric breach is carried out fatigue crack growth rate test, uses grating digital readout chi to read and split point Position, it is adaptable to the measurement of asymmetric cracks can spread information.

Accompanying drawing explanation

Fig. 1 is the step of the method using asymmetric crackle test fatigue crack growth rate in one embodiment of the invention Schematic diagram；

Fig. 2 is the schematic diagram of the test specimen in one embodiment of the invention containing asymmetric crackle；

Fig. 3 is surface of test piece crackle interpretation interface of the present invention schematic diagram；

Fig. 4 is equivalent model schematic diagram.

Detailed description of the invention

Combine accompanying drawing below by specific embodiment the present invention is described in further detail.

In view of there is no the method using asymmetric crackle to carry out fatigue crack growth rate test, the present invention provides A kind of method using asymmetric crackle test fatigue crack growth rate.

The method includes:

Use equal thickness vertical bar shaped test specimen, process the asymmetric breach along X-axis at test specimen active section；

By the specimen holder with asymmetric breach on the upper lower chuck of fatigue machine, breach to upper grip, lower folder The distance of head is identical, makes loading direction be perpendicular to breach surface, i.e. loading direction and is parallel to Y-axis, and then applying stress ratio is R's Constant-amplitude fatigue loading, carries out fatigue crack propagation test；

Measure the information of asymmetric cracks can spread, and record fatigue load effect times N；Described information includes: test specimen is at X Axial half-breadth W, length L of test specimen active section, the coordinate a of right crack tip A_A, the coordinate a of left crack tip B_B；

UtilizeIts In, a is that crackle half is long, a=(a_A-a_B)/2,

m^(A,B)(a_A,a_B,x) For crack tip weight function right, left, it is used for asking for clamping asymmetric crackle right crack tip stress intensity factor K under the conditions of border_A, left Crack tip stress intensity factor K_B；

Calculate stress intensity factor range Δ K right, that point is split on a left side_A、ΔK_B, computing formula is Δ K_A=K_A(1-R)、ΔK_B= K_B(1-R), wherein, R is stress ratio；

Estimate respectively the asymmetric crackle right side split point, a left side split point fatigue crack growth rate (da/dN)_A、(da/dN)_B,

According to described Δ K_A, described (da/dN)_A, described Δ K_B, described (da/dN)_BAsk for the fatigue crack of material respectively Spreading rate parameter C_A、n_AAnd C_B、n_B。

Test specimen containing asymmetric breach is carried out fatigue crack growth rate test, uses grating digital readout chi to read and split point Position, it is adaptable to the measurement of asymmetric cracks can spread information.In view of in loading procedure, the two ends of test specimen are not freely, But it being clamped on testing machine on lower chuck by fixture block, fixture block can retrain in displacement and the X-Y plane of test piece end X-direction Rotate, and test specimen itself is about Y-axis Stiffness elasticity coupling, therefore set up the equivalent model that stress intensity factor solves, to ask for folder Hold asymmetric crackle right crack tip stress intensity factor K under boundary condition_A, left crack tip stress intensity factor K_B, estimate the right side respectively and split Point, a left side split the fatigue crack growth rate (da/dN) of point_A、(da/dN)_B, and under the conditions of calculating clamping border, answering of point is split on the right side, a left side Force intensity factor range, is then described fatigue crack growth rate with Paris formula, is obtained the fatigue of material by data matching Crack growth rate parameter C_A、n_AAnd C_B、n_B。

Next technology is described in detail:

A kind of method using asymmetric crackle test fatigue crack growth rate, as it is shown in figure 1, comprise the steps:

Step 101, manufactures the test specimen containing asymmetric breach；

Use equal thickness plate processing test specimen, use line cutting mode, lack along the asymmetric of X-axis in the processing of test specimen active section Mouthful, as shown in Figure 2.

Step 102, carries out the fatigue crack growth rate test of asymmetric crackle

It is fixed to test specimen on fatigue machine carry out fatigue crack growth rate test, in the present embodiment, employing Fatigue machine is MTS 880 electo hydraulic servocontrolled fatigue testing machine, and dynamic load error is less than 2%, and static load error is less than 1%, meets GB/ The standard-required of T16825 and JJG556.

Fatigue crack propagation test is carried out under atmosphere at room temperature environment, and test specimen is clamped directly at the upper lower chuck of testing machine On, use axially loaded mode, sinusoidal wave, test frequency f=5～30 hertz.

In investigating fatigue crack expansion, measure crack size according to pre-determined reading time interval, and record load and follow Ring number of times.Using interpreting system to carry out crackle direct-reading, this interpreting system is by electric displacement platform controller, OISC033 step motor control Device, grating digital readout chi, digit microscope etc. form, the crackle on digit microscope alignment test specimen, and digit microscope is with computer even Connecing, transmit the crack image amplified to computer, the display window of computer demonstrates the crack image of amplification.Wherein motor Drive digit microscope moves, and by mobile microscope, makes the crack tip of display overlap with default graticule, then crack tip Position by grating digital readout chi read.Wherein as in figure 2 it is shown, need the size of record to include: test specimen half-breadth W, test specimen work Length L of section；The coordinate a of crack tip A, B right, left_A、a_B(initial point overlaps with test specimen centrage, test specimen centrage and Y-axis weight Close).Record fatigue load effect times N simultaneously.

Should be noted that following 2 points:

First point, in order to determine crack tip more accurately, uses frequency reducing method, i.e. splits in interpretation during interpretation crackle During stricture of vagina, test frequency is reduced to f=1Hz.

Second point, in order to reduce owing to crack closure causes crack tip to judge the unclear error brought, as shown in Figure 3 Face crack interpretation interface, process of the test uses non-corrosive coloring liquid periodically spread upon crack tip.

Step 103, asks for clamping asymmetric crackle right crack tip stress intensity factor K under the conditions of border_A, a left side split point stress strong Degree factor K_B；

The removable following steps that are divided into of this step:

Step 103-1, before asking for, the feature of development test machine clamping boundary condition:

1) piece lengths is limited, is not at infinity to load；

2) load mode is not the free uniform loads in two ends.Test specimen is to be clamped on testing machine on lower chuck by fixture block , upper lower chuck is respectively arranged with two fixture blocks, applies longitudinal Tensile or Compressive Loading by fixture block with the static friction of specimen holder end.Fixture block can be about Rotation in the displacement of the bundle X-direction containing asymmetric crackle test piece end and X-Y plane.

3) due to the constraint of frame, fixture can only be axially movable.

Due to the existence of asymmetric crackle, cracks in body, about Y-axis Stiffness elasticity coupling, is stretched under the conditions of clamping border During load effect, rigid cartridge constraint is equivalent to be applied with extra moment of flexure, thus sets up the equivalence that stress intensity factor solves Model.This equivalent model is:

Clamping boundary condition is equivalent to free Uniform Tension and simple bending load acts on jointly so that the corner of test piece end Equal to 0, as shown in Figure 4, displacement=0 of end X-direction, corner=0 in the X-Y plane of end, the displacement one of end Y-direction Causing, σ=P/S, P are the load applied, and S is the cross-sectional area of test specimen；

According to the principle of stacking of line elastomer, the expression formula of the stress intensity factor of point is split on right a, left side:It is free Uniform Tension condition bottom right, the stress intensity factor of left crack tip,It is simple bending load effect bottom right, the stress intensity factor of left crack tip.

Step 103-2, asks for the stress intensity factor under the conditions of free Uniform Tension

Weight-function method is used to provide asymmetric crackle approximate solution of stress intensity factor under the conditions of free Uniform Tension, Crack tip stress intensity factor right, leftExpression formula be:

$K_{\mathrm{\&sigma;}}^{(A,B)}={\&Integral;}_{\underset{surface}{crack}}\mathrm{\&sigma;}\left(x\right)m^{(A,B)}(a_A,a_B,x)dx---\left(3\right)$

In formula, σ (x) is the flawless body Y-direction stress distribution of imagination crack surface, σ=P/S, P under Uniform Tension stress σ For load, S is the cross-sectional area of test specimen；σ (x)=σ, a_A、a_BCoordinate (initial point and test specimen center for crack tip A, B right, left Line overlaps), x is integration coordinate, m^(A,B)(a_A,a_B, x) it being the weight function of crack tip right, left, its expression formula is:

$m^{A,B}(x,a_A,a_B)=\frac{1}{\sqrt{\mathrm{\&pi;}a}{f}_0^{A,B}}\left[\begin{array}{c}({\mathrm{\&beta;}}_1^{A,B}\frac{r_A}{W}+{\mathrm{\&beta;}}_2^{A,B}\frac{r_B}{W}){\left(\frac{r_{B,A}}{r_{A,B}}\right)}^{1/2}\\ +({\mathrm{\&beta;}}_3^{A,B}+{\mathrm{\&beta;}}_4^{A,B}\frac{r_A}{W}+{\mathrm{\&beta;}}_5^{A,B}\frac{r_B}{W}){\left(\frac{r_A}{W}\frac{r_B}{W}\right)}^{1/2}\\ +{\mathrm{\&beta;}}_6^{A,B}{\left(\frac{r_A}{W}\frac{r_B}{W}\right)}^{3/2}\end{array}\right]---\left(4\right)$

In formula,Modifying factor for stress intensity factor of crack asymmetric under the conditions of free Uniform Tension；

r_A=a_A-x, r_B=x-a_B, W is half plate width, coefficientTable Reach formula as follows:

${\mathrm{\&beta;}}_1^A=\frac{f_0^B}{2\mathrm{\&alpha;}}$

${\mathrm{\&beta;}}_2^A=\frac{f_0^A}{2\mathrm{\&alpha;}}$

${\mathrm{\&beta;}}_3^A=\frac{f_0^B}{\mathrm{\&alpha;}}$

${\mathrm{\&beta;}}_4^A=\frac{1}{2\mathrm{\&alpha;}}\&lsqb;\frac{\&part;f_0^B}{\&part;\mathrm{\&alpha;}}+\frac{\&part;f_0^B}{\&part;\mathrm{\&epsiv;}}\&rsqb;-\frac{f_0^B}{2{\mathrm{\&alpha;}}^2}$

${\mathrm{\&beta;}}_5^A=\frac{1}{2\mathrm{\&alpha;}}\&lsqb;\frac{\&part;f_0^A}{\&part;\mathrm{\&alpha;}}+\frac{\&part;f_0^A}{\&part;\mathrm{\&epsiv;}}\&rsqb;-\frac{f_0^A}{2{\mathrm{\&alpha;}}^2}+\frac{3}{2}\frac{C}{{\mathrm{\&alpha;}}^2}$

${\mathrm{\&beta;}}_6^A=\frac{1}{2{\mathrm{\&alpha;}}^2}\&lsqb;\frac{\&part;C}{\&part;\mathrm{\&alpha;}}+\frac{\&part;C}{\&part;\mathrm{\&epsiv;}}-\frac{2C}{\mathrm{\&alpha;}}\&rsqb;$

${\mathrm{\&beta;}}_1^B=\frac{f_0^B}{2\mathrm{\&alpha;}}$

${\mathrm{\&beta;}}_2^B=\frac{f_0^A}{2\mathrm{\&alpha;}}$

${\mathrm{\&beta;}}_3^B=\frac{f_0^A}{\mathrm{\&alpha;}}$

${\mathrm{\&beta;}}_4^B=\frac{1}{2\mathrm{\&alpha;}}\&lsqb;\frac{\&part;f_0^B}{\&part;\mathrm{\&alpha;}}-\frac{\&part;f_0^B}{\&part;\mathrm{\&epsiv;}}\&rsqb;-\frac{f_0^B}{2{\mathrm{\&alpha;}}^2}+\frac{3}{2}\frac{C}{{\mathrm{\&alpha;}}^2}$

${\mathrm{\&beta;}}_5^B=\frac{1}{2\mathrm{\&alpha;}}\&lsqb;\frac{\&part;f_0^A}{\&part;\mathrm{\&alpha;}}-\frac{\&part;f_0^A}{\&part;\mathrm{\&epsiv;}}\&rsqb;-\frac{f_0^A}{2{\mathrm{\&alpha;}}^2}$

${\mathrm{\&beta;}}_6^B=\frac{1}{2{\mathrm{\&alpha;}}^2}\&lsqb;\frac{\&part;C}{\&part;\mathrm{\&alpha;}}-\frac{\&part;C}{\&part;\mathrm{\&epsiv;}}-\frac{2C}{\mathrm{\&alpha;}}\&rsqb;$

Wherein, a=(a_A-a_B)/2, e=(a_A+a_B)/2, α=a/W, ε=e/W, λ=a/ (W-e).When eccentric distance e > 0 time,

$C=\frac{8}{3}\&lsqb;\mathrm{\&Phi;}-\frac{1}{2}(f_0^A+f_0^B)\&rsqb;$

$f_0^A=1+\underset{i=2}{\overset{19}{\&Sigma;}}{C}_i\left(\mathrm{\&epsiv;}\right){\mathrm{\&lambda;}}^i$

$f_0^B=1+\underset{i=2}{\overset{19}{\&Sigma;}}{C}_i\left(\mathrm{\&epsiv;}\right){(-\mathrm{\&lambda;})}^i$

$\frac{\&part;f_0^A}{\&part;\mathrm{\&alpha;}}=\frac{1}{\mathrm{\&alpha;}}\underset{i=2}{\overset{19}{\&Sigma;}}{C}_i\left(\mathrm{\&epsiv;}\right){\mathrm{i\&lambda;}}^i$

$\frac{\&part;f_0^A}{\&part;\mathrm{\&epsiv;}}=\underset{i=2}{\overset{19}{\&Sigma;}}{\mathrm{\&lambda;}}^i\&lsqb;\frac{\&part;C_i\left(\mathrm{\&epsiv;}\right)}{\&part;\mathrm{\&epsiv;}}+\frac{\mathrm{\&lambda;}}{\mathrm{\&alpha;}}{\mathrm{iC}}_i\left(\mathrm{\&epsiv;}\right)\&rsqb;$

$\frac{\&part;f_0^B}{\&part;\mathrm{\&alpha;}}=\frac{1}{\mathrm{\&alpha;}}\underset{i=2}{\overset{19}{\&Sigma;}}{C}_i\left(\mathrm{\&epsiv;}\right)i{(-\mathrm{\&lambda;})}^i$

$\frac{\&part;f_0^B}{\&part;\mathrm{\&epsiv;}}=\underset{i=2}{\overset{19}{\&Sigma;}}{(-\mathrm{\&lambda;})}^i\&lsqb;\frac{\&part;C_i\left(\mathrm{\&epsiv;}\right)}{\&part;\mathrm{\&epsiv;}}+\frac{\mathrm{\&lambda;}}{\mathrm{\&alpha;}}{\mathrm{iC}}_i\left(\mathrm{\&epsiv;}\right)\&rsqb;$

$C_i\left(\mathrm{\&epsiv;}\right)=\underset{j=0}{\overset{10}{\&Sigma;}}{\mathrm{\&gamma;}}_{ij}{\mathrm{\&epsiv;}}^j$

$\frac{\&part;C}{\&part;\mathrm{\&alpha;}}=\frac{8}{3}\&lsqb;\frac{\&part;\mathrm{\&Phi;}}{\&part;\mathrm{\&alpha;}}-\frac{1}{2}(\frac{\&part;f_0^A}{\&part;\mathrm{\&alpha;}}+\frac{\&part;f_0^B}{\&part;\mathrm{\&alpha;}})\&rsqb;$

$\frac{\&part;C}{\&part;\mathrm{\&epsiv;}}=\frac{8}{3}\&lsqb;\frac{\&part;\mathrm{\&Phi;}}{\&part;\mathrm{\&epsiv;}}-\frac{1}{2}(\frac{\&part;f_0^A}{\&part;\mathrm{\&epsiv;}}+\frac{\&part;f_0^B}{\&part;\mathrm{\&epsiv;}})\&rsqb;$

$\frac{\&part;\mathrm{\&Phi;}}{\&part;\mathrm{\&alpha;}}=\frac{1}{\mathrm{\&alpha;}}\&lsqb;{\left(f_0^A\right)}^2+{\left(f_0^B\right)}^2-2\mathrm{\&Phi;}\&rsqb;$

$\frac{\&part;\mathrm{\&Phi;}}{\&part;\mathrm{\&epsiv;}}=\frac{2}{\mathrm{\&alpha;}}\mathrm{\&Omega;}$

$\mathrm{\&Phi;}=1+2\underset{i=2}{\overset{19}{\&Sigma;}}{C}_i\&lsqb;1+{(-1)}^i\&rsqb;\frac{{\mathrm{\&lambda;}}^i}{i+2}+\underset{i=2}{\overset{19}{\&Sigma;}}\underset{j=2}{\overset{19}{\&Sigma;}}{C}_i{C}_j\frac{{\mathrm{\&lambda;}}^{i+j}}{i+j+2}\&lsqb;1+{(-1)}^{i+j}\&rsqb;$

$\mathrm{\&Omega;}=\underset{i=2}{\overset{19}{\&Sigma;}}(1-\mathrm{\&epsiv;})\&lsqb;1+{(-1)}^i\&rsqb;\frac{{\mathrm{\&lambda;}}^{i+1}}{i+2}\&lsqb;\frac{\&part;C_i}{\&part;\mathrm{\&epsiv;}}+\frac{i}{1-\mathrm{\&epsiv;}}{C}_i\&rsqb;+\underset{i=2}{\overset{19}{\&Sigma;}}\underset{j=2}{\overset{19}{\&Sigma;}}(1-\mathrm{\&epsiv;})\&lsqb;1+{(-1)}^{i+j}\&rsqb;\frac{{\mathrm{\&lambda;}}^{i+j+1}}{i+j+2}{C}_j\&lsqb;\frac{\&part;C_i}{\&part;\mathrm{\&epsiv;}}+\frac{i}{1-\mathrm{\&epsiv;}}{C}_i\&rsqb;$

Expression formulaCoefficient gamma_ijValue be shown in Table 1.

Table 1 coefficient gamma_ijValue

Step 103-3, asks for the stress intensity factor of asymmetric crackle under simple bending load effect

Stress intensity factor under simple bending load effect, its form is as follows:

$K_M^{(A,B)}={\&Integral;}_{\underset{surface}{crack}}{\mathrm{\&sigma;}}_M\left(x\right)m^{(A,B)}(a_A,a_B,x)dx---\left(5\right)$

In formula: σ_MX () is flawless body Y-direction stress distribution of imagination crack surface under simple bending load M effect, it is assumed that test specimen Thickness is unit thickness, σ_MX the expression formula of () is:

${\mathrm{\&sigma;}}_M\left(x\right)=\frac{3M}{2W^2}\frac{x}{W}---\left(6\right)$

Thus can under the effect of simple bending load M, asymmetric crackle two split point stress intensity factor:

$K_M^{(A,B)}={\&Integral;}_{\underset{surface}{crack}}\frac{3M}{2W^2}\frac{x}{W}{m}^{(A,B)}(a_A,a_B,x)dx---\left(7\right)$

Step 103-4, the stress intensity factor of asymmetric crackle based on equivalent model solves

(1) additional bending moment solves

1) strain energy of cracks in body

From energy principle, cracks in body strain energy V under free Uniform Tension and simple bending load act on jointly comprises Two parts, a part be crack surface surface can U, another part is flawless body being answered by during with cracks in body same load Becoming can V₀, i.e.

V=U+V₀ (8)

Assuming that specimen thickness is unit thickness, the expression formula of crack surface surface energy is

$U={\&Integral;}_0^{a}G\left(x\right)dx---\left(9\right)$

In formula, a is that crackle half is long, and G (x) is energy release rate, and its expression formula is

$G\left(x\right)=\frac{{\left(K_{\mathrm{\&sigma;}}\right(x)+K_M(x\left)\right)}^2}{E}---\left(10\right)$

In formula, E is the elastic modelling quantity waiting slab.

For line elastomer, V₀Expression formula as follows:

$V_0=\frac{1}{2E}\underset{\&Sigma;}{\&Integral;}{(\mathrm{\&sigma;}+{\mathrm{\&sigma;}}_M)}^{2}dV---\left(11\right)$

In formula, Σ is integral domain, is taken as entire plate；σ is the Y-direction direct stress that free Uniform Tension causes；σ_MIt it is simple bending The Y-direction direct stress that load causes, i.e. flawless body is the Y-direction stress distribution of imagination crack surface under simple bending load M effect.

Formula (11) can be written as

$V_0=\frac{1}{2E}{\&Integral;}_{\&Sigma;}{\mathrm{\&sigma;}}^{2}dV+\frac{1}{2E}{\&Integral;}_{\&Sigma;}{{\mathrm{\&sigma;}}_M}^{2}dV--\left(12\right)$

If the bending stiffness of rectangular slab is k, then V₀Expression formula can be written as form:

$V_0=\frac{1}{2E}{\&Integral;}_{\&Sigma;}{\mathrm{\&sigma;}}^{2}dV+\frac{M^2}{2k}---\left(13\right)$

In formula, k is bending stiffness, it is assumed that specimen thickness is unit thickness,I is the inertia in cross section Square.

Such that it is able to obtain the strain energy of cracks in body:

$V={\&Integral;}_0^a\frac{{\left(K_{\mathrm{\&sigma;}}\right(x)+K_M(x\left)\right)}^2}{E}dx+\frac{1}{2E}{\&Integral;}_{\&Sigma;}{\mathrm{\&sigma;}}^{2}dV+\frac{M^2}{2k}---\left(14\right)$

2) additional bending moment calculates

Test machine clamping boundary condition to the constraint of test specimen corner it is believed that apply an additional bending moment to test specimen so that it is Corner is 0.By cassette theorem, the corner of test piece endAnd end corner is limited, i.e. θ=0.Thus have

$\frac{\&part;V}{\&part;M}=0---\left(15\right)$

I.e.

$2{\&Integral;}_0^a\frac{\left(K_{\mathrm{\&sigma;}}\right(x)+K_M(x\left)\right)}{E}\frac{\&part;K_M\left(x\right)}{\&part;M}dx+\frac{3ML}{2{\mathrm{EW}}^3}=0---\left(16\right)$

ByCan obtain

$M=-\frac{{\&Integral;}_0^a{\&Integral;}_{\underset{surface}{crack}}{m}^{(A,B)}(a_A,a_B,x)dx\&CenterDot;\left({\&Integral;}_{\underset{surface}{crack}}{\mathrm{xm}}^{(A,B)}\right(a_A,a_B,x\left)dx\right)dx}{{\&Integral;}_0^a{\&Integral;}_{\underset{surface}{crack}}{\mathrm{xm}}^{(A,B)}(a_A,a_B,x)dx\&CenterDot;\left({\&Integral;}_{\underset{surface}{crack}}\frac{3}{2W^2}\frac{x}{W}{m}^{(A,B)}\right(a_A,a_B,x\left)dx\right)dx+\frac{L}{2}}\mathrm{\&sigma;}---\left(17\right)$

(2) stress intensity factor under the conditions of clamping border

Formula (17) is substituted into formula (7), and then based on equivalent model, byCan obtain

$K^{(A,B)}\left(a\right)=\left({\&Integral;}_{\underset{surface}{crack}}{m}^{(A,B)}\right(a_A,a_B,x)dx+{\&Integral;}_{\underset{surface}{crack}}\frac{3\mathrm{\&phi;}}{2W^2}\frac{x}{W}{m}^{(A,B)}(a_A,a_B,x\left)dx\right)\mathrm{\&sigma;}---\left(18\right)$

In formula,

$\mathrm{\&phi;}=-\frac{{\&Integral;}_0^a{\&Integral;}_{\underset{surface}{crack}}{m}^{(A,B)}(a_A,a_B,x)dx\&CenterDot;\left({\&Integral;}_{\underset{surface}{crack}}{\mathrm{xm}}^{(A,B)}\right(a_A,a_B,x\left)dx\right)dx}{{\&Integral;}_0^a{\&Integral;}_{\underset{surface}{crack}}{\mathrm{xm}}^{(A,B)}(a_A,a_B,x)dx\&CenterDot;\left({\&Integral;}_{\underset{surface}{crack}}\frac{3}{2W^2}\frac{x}{W}{m}^{(A,B)}\right(a_A,a_B,x\left)dx\right)dx+\frac{L}{2}}---\left(19\right)$

Thus can calculate the stress strength factor K that under clamping border, asymmetric crackle is right, point is split on a left side_A、K_B。

Step 104, processes the asymmetric cracks can spread information measured, asks for the fatigue crack growth rate of material Parameter.

This step is removable is divided into following content:

Step 104-1, da/dN estimates

For asymmetric crackle, owing to left and right crack tip stress intensity factor range is different, fatigue crack growth rate Can, tackle (a of left crack tip_B, N) and the and (a of right crack tip_A, N) process respectively.Estimate crack Propagation speed Rate, generally uses secant method or incremental polynomials method.

(1) secant method

For calculating the secant method of crack growth rate, da/dN is generally expressed as follows:

$\begin{array}{c}{\left(\frac{da}{dN}\right)}_A=\frac{\left|a_{A,i+1}-a_{A,i}\right|}{M_{i+1}-N_i}\\ {\left(\frac{da}{dN}\right)}_B=\frac{\left|a_{B,i+1}-a_{B,i}\right|}{M_{i+1}-N_i}\end{array}---\left(20\right)$

In formula, subscript A, B represent that point is split on the right side of asymmetric crackle and point is split on a left side respectively；(a_A,i, N_i)、(a_B,i, N_i) difference table Show that (coordinate of crack tip, the load cycle number) of point is split on the right side that i & lt interpretation obtains, a left side.

(2) incremental polynomials method

Incremental polynomials is to arbitrary test data point i and the most each n point, altogether 2n+1 consecutive numbers strong point, uses such as Lower quadratic polynomial is fitted, derivation.N value of counting desirable 2,3,4, typically takes 3.

$\widehat{a_i}=b_0+b_1\left(\frac{N_i-C_1}{C_2}\right)+b_2{\left(\frac{N_i-C_1}{C_2}\right)}^2---\left(21\right)$

In formula (21),a_i-n≤a≤a_i+n.Coefficient b₀、b₁、b₂It is At interval [a_i-n,a_i+n] press method of least square (even if the sum of square of deviations between crack length observation and match value is minimum) really Fixed regression parameter.Match valueCorrespond to load cycle number N_iMatching crack length.Parameter C₁And C₂It is defeated for converting Enter data, with the difficulty avoided when determining regression parameter in numerical computations.At N_iThe crack growth rate at place is asked by formula (21) Lead and obtain:

${\left(\frac{da}{dN}\right)}_{\widehat{a_i}}=\frac{b_1}{C_2}+\frac{2b_2(N_i-C_1)}{C_2^2}---\left(22\right)$

Utilize corresponding to N_iMatching crack lengthCalculate the Δ K value corresponding with da/dN value.

The fatigue crack growth rate curve slickness that incremental polynomials obtains is more preferable, the dispersibility of the crack growth rate be given Be given less than secant method, but the dispersibility of crack growth rate that incremental polynomials is given may be less than real crackle The dispersion of spreading rate.

Step 104-2, the determination of fatigue crack growth rate parameter

Given applied stress generally uses Paris formula than the expression for fatigue crack propagateion under R, describes two and splits point extension The Paris formula of speed is

$\begin{array}{c}{\left(\frac{da}{dN}\right)}_A=C_A{\left({\mathrm{\&Delta;K}}_A\right)}^{n_A}\\ {\left(\frac{da}{dN}\right)}_B=C_B{\left({\mathrm{\&Delta;K}}_B\right)}^{n_B}\end{array}---\left(23\right)$

In formula, Δ K_A=K_A(1-R)、ΔK_B=K_B(1-R) represent that the stress intensity factor range of point, R are split in right a, left side respectively For stress ratio.

Take the logarithm and be converted in both sides

$\begin{array}{c}\ln {\left(\frac{da}{dN}\right)}_A=1g{C}_A+n_A\&CenterDot;{\mathrm{lg\&Delta;K}}_A\\ \ln {\left(\frac{da}{dN}\right)}_B=1g{C}_B+n_B\&CenterDot;{\mathrm{lg\&Delta;K}}_B\end{array}---\left(24\right)$

ByData carry out linear fit, estimate material Fatigue crack growth rate parameter C of material_A、n_A、C_B、n_B。

The method, compared with existing fatigue crack growth rate standard method of test, possesses following advantage:

(1) problem " when the extension of M (T) specimen crack is asymmetric, data invalid " in working standard is solved；By existing mark Standard thinks that invalid transformation of data is valid data, saves human and material resources, financial resources；

(2) asymmetric crackle is utilized to carry out fatigue crack growth rate test, due to the left and right stress intensity factor splitting point Range is different, and fatigue crack growth rate is the most different, split with symmetrical crackle middle left and right point only as one split point compared with, no Symmetrical crackle is left and right to be split point and can split point as two and separately process, it is thus achieved that cracks can spread data volume increase by 1 times, effectively believe Breath substantially increases；

(3) different due to left and right fatigue crack growth rate, the left and right point that splits of asymmetric crackle can split point as two Process, such that it is able to by proof stress level, the positions and dimensions of the asymmetric breach of reasonable Arrangement, it is achieved in relatively short period of time Inside carry out FR fatigue crack growth rate test, test period and workload can be effectively saved.

The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, for the skill of this area For art personnel, the present invention can have various modifications and variations.All within the spirit and principles in the present invention, that is made any repaiies Change, equivalent, improvement etc., should be included within the scope of the present invention.

Claims (10)

1. the method using asymmetric crackle test fatigue crack growth rate, it is characterised in that:

Use equal thickness vertical bar shaped test specimen, process the asymmetric breach along X-axis at test specimen active section；

By the specimen holder with asymmetric breach on the chuck of fatigue machine, breach to upper grip, the distance of lower chuck Identical；Make loading direction be perpendicular to breach surface, then apply constant-amplitude fatigue loading, carry out fatigue crack propagation test；

Measuring the information of asymmetric cracks can spread, and record fatigue load effect times N, described information includes: test specimen is in X-axis side To half-breadth W, length L of test specimen active section, the coordinate a of right crack tip A_A, the coordinate a of left crack tip B_B；

UtilizeWherein, a is Crackle half is long, a=(a_A-a_B)/2,

m^(A,B)(a_A,a_B, it is x) right Crack tip, the weight function of left crack tip, be used for asking for clamping under the conditions of border the right crack tip stress intensity of asymmetric crackle because of Sub-K_AWith left crack tip stress intensity factor K_B；

Point is split on the calculating right side, sharp stress intensity factor range Δ K is split on a left side_A、ΔK_B, computing formula is Δ K_A=K_A(1-R)、ΔK_B= K_B(1-R), wherein, R is stress ratio；

Estimate respectively the asymmetric crackle right side split point, a left side split point fatigue crack growth rate (da/dN)_A、(da/dN)_B；

According to described Δ K_A, described (da/dN)_A, described Δ K_B, described (da/dN)_BAsk for the crack Propagation speed of material respectively Rate parameter C_A、n_AAnd C_B、n_B。

2. the method using asymmetric crackle test fatigue crack growth rate as claimed in claim 1, it is characterised in that institute Stating test specimen is equal thickness plate；Asymmetric breach center deviation test specimen centrage；The processing mode of described asymmetric breach is that line is cut Cut.

3. the method using asymmetric crackle test fatigue crack growth rate as claimed in claim 1, it is characterised in that In the test of described fatigue crack growth rate, ocular estimate is used to measure fatigue crack size；Described method also includes: periodically splitting Coloring liquid is smeared at stricture of vagina tip.

4. the method using asymmetric crackle test fatigue crack growth rate as claimed in claim 1, it is characterised in that institute State and measure the information of asymmetric cracks can spread and include:

Observe the crackle amplified by digit microscope；

Mobile described digit microscope, makes the tip of the crackle of described amplification overlap with default graticule；

The test frequency of described fatigue machine is reduced, grating digital readout chi reads right crack tip A, left crack tip B Coordinate a_A、a_B。

5. the method using asymmetric crackle test fatigue crack growth rate as claimed in claim 1, it is characterised in that ask Take asymmetric crackle right crack tip stress intensity factor K under the conditions of clamping border_A, left crack tip stress intensity factor K_BIncluding:

According to the clamping feature of boundary condition and test specimen itself about the feature of Y-axis Stiffness elasticity coupling, set up asymmetric crackle and answer The equivalent model that the force intensity factor solves；

Stress strength factor K under the conditions of strain energy according to cracks in body, additional bending moment, and free Uniform Tension_σ ^(A,B), simple bending Stress strength factor K under load_M ^(A,B), obtain K based on described equivalent model_A、K_B。

6. the method using asymmetric crackle test fatigue crack growth rate as claimed in claim 5, it is characterised in that institute Stating equivalent model is:

Clamping boundary condition is equivalent to the common effect of free Uniform Tension σ and simple bending load M, and makes test piece end X- Corner in Y plane is equal to 0；

K^(A,B)=K_σ ^(A,B)+K_M ^(A,B)。

7. the method using asymmetric crackle test fatigue crack growth rate as claimed in claim 5, it is characterised in that institute State the stress strength factor K under the conditions of free Uniform Tension_σ ^(A,B)Mode of asking for be:

Wherein,

σ (x) is flawless body Y-direction stress distribution of imagination crack surface under free Uniform Tension stress σ, and σ=P/S, P are for carrying Lotus, S is the cross-sectional area of test specimen；σ (x)=σ, x are integration coordinate.

8. the method using asymmetric crackle test fatigue crack growth rate as claimed in claim 5, it is characterised in that institute State the stress strength factor K under simple bending load effect_M ^(A,B)Mode of asking for be:

Wherein,

σ_MX () is flawless body Y-direction stress distribution of imagination crack surface under the simple bending load M effect of far field；Assuming that specimen thickness is Unit thickness,M is simple bending load.

9. the method using asymmetric crackle test fatigue crack growth rate as described in any one of claim 1-8, it is special Levy and be, described (da/dN)_A, described (da/dN)_BPredictor method be:

Wherein, a_A,i、a_B,iThe right crack tip A that expression i & lt interpretation obtains respectively, left Crack Tip The coordinate of end B, N_i、N_i+1The load cycle number of record when representing i & lt and i+1 time interpretation crackle respectively；

Or

Wherein,

a_i-n≤a≤a_i+n, subscript n is equal to 3 in 7 matchings, 5 Equal to 2 in some matching；Coefficient b₀、b₁、b₂It is with at interval [a_i-n,a_i+n] press between crack length observation and match value inclined The regression parameter that the difference minimum principle of quadratic sum determines；Match valueCorrespond to load cycle number N_iMatching crack length；Ginseng Number C₁And C₂For converting input data.

10. the method using asymmetric crackle test fatigue crack growth rate as claimed in claim 1, it is characterised in that Described fatigue of materials crack growth rate parameter C_A、n_AAnd C_B、n_BAcquiring method include:

Determine the given applied stress equation than lower fatigue crack growth rate:

ByData carry out linear fit, determine material Fatigue crack growth rate parameter C_A、n_AAnd C_B、n_B。