CN102519783B - Nondestructive measurement method for M-integral of multi-defective material - Google Patents

Abstract

The invention discloses a nondestructive measurement method for the M-integral of a multi-defective material. The method comprises: by means of digit speckle correlated technologies, utilizing optical measurement equipment ARAMIS 4M(GOM mbh) to measure the displacement field on the surface of a test piece; conducting smoothing treatment on the displacement field by a mean filter, and using cubic spline fitting to obtain gradients of the displacement field along two coordinate axes; through a constitutive equation of the material, calculating the stress field on the material surface as well as the strain energy density distribution; and carrying out substitution on a definition expression of the M-integral, choosing any defect-containing closed path, as well as calculating the M-integral through numerical integration. Applicable to various defects and defect clusters, the method of the invention can be used for assessing various forms of material damage and structural integrity in the fields of aerospace, aviation, and machinery, etc.

Description

The non-destructive measuring method of many defective materials M integration

Technical field

The present invention relates to a kind of mechanical parameter---the non-destructive measuring method of M integration.

Technical background

In the research of many defective materials damage mechanics, around the M integration of defect, characterized the energy release rate of this defect self-similar propagation.As a kind of material fracture toughness parameter, can be widely used in aerospace vehicle and a large amount of Structural Design.Its definition expression formula is as follows:

W=σ wherein _ijε _ij/ 2, σ _kj, ε _ij, u _kand n _ibe respectively material strain energy density, stress, strain, displacement and around the outer normal vector of the closed path of integration C of defect; U wherein _{k, i}for displacement is to relevant coordinate x _ipartial differential.Be similar to J integration, M integration is also a kind of Path-independent Integrals, and its value does not rely on path and chooses.Through the research of decades, M integration as one can exosyndrome material in the mechanical parameter of various microdefects and evolution thereof, in material damage and structural intergrity assessment, play an important role.

Experiment measuring M integrated value, needs to measure the mechanical quantities such as stress field, strain field and strain energy distribution along path of integration.For the experimental measurement method research of M integration parameter, be almost also blank at present both at home and abroad.King and Herrmann[King, R.B.and Herrmann, G. (1981) Nondestructive Evaluation of the J and M-integrals, ASME Journal of Applied Mechanics, 48,83-87] for two kinds of simple simple check lines (monolateral crackle and centre burst), a kind of method of nondestructive measurement M integration has been proposed.The method is brought the analytic solution of Crack Field under the load of even far field into M integral expression, by simplifying, obtains the simplification expression formula of M integration under this crackle form, and then by measurement means such as foil gauge and displacement transducers, obtains M integrated value.Its method has obvious weak point: (1) the method can only, for special damage type, exist the simple check line of analytic solution.And defect in material is conventionally very complicated, both comprised simple check line, also comprise multiple cracks or the crackle group of multi-form distribution, also may relate to simultaneously other damage types as hole, be mingled with etc.For these, be conventionally difficult to find the defective form of analytic solution, it is very difficult that follow-up simplification and derivation will become.(2) theoretic defect, the method is to be based upon on the basis of a series of simplification.Therefore, in theory, the parameter that it is derived is not a strict exact solution.(3) the method is utilized strain and the displacement of traditional foil gauge and displacement sensor test specimen, and need to choose special path of integration and calculate M integration, and its measurement means is limited by test specimen and measures the restriction of bad border, is difficult to wide popularization and application.

In addition, along with the development of Experimental Mechanics and relevant computer graphics disposal technology, Digital Speckle Correlation Method is grown up and is applied to gradually in the deformation measurement of material and structure.Applied Digital speckle correlation technique is measured the displacement field of many defective materials, the most important feature of its method is exactly to adopt digitized recording mode to make full use of the processing power of computing machine, there is in-site measurement, real-time visual demonstration and high-precision feature, thereby improved the efficiency of deformation test.It mainly utilizes image correlation method analysis to be subject to the specimen surface Digital Image Data (the speckle point of the stochastic distribution of body surface is recorded in digital picture) under load, utilizes the gray-scale value pattern of digital picture to carry out Accurate Measurement distortion (displacement).Have light path simple, to measurement environment require low, to light source requirements low (laser, common natural white light or general lighting all can), the feature such as can formulate arbitrarily to measurement range.

Summary of the invention

The present invention is directed to the existing problem of conventional art, pass through Digital Speckle Correlation Method, provide a kind of by directly measuring material surface displacement field, and then obtain material surface strain field and stress field, and by the definition expression formula of M integration, choose any closed path and carry out numerical integration, and then try to achieve the method for M integrated value, there is the features such as high, the applicable defect object of accuracy of measurement is wide in range, measurement calculating is easy, load can load arbitrarily.

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

A non-destructive measuring method for many defective materials M integration, is characterized in that, comprises the steps:

(1) the Complex Situation microdefect group who exists for two-dimentional member damages test specimen, in order to increase the intensity contrast value of digital speckle, first test specimen surface spraying is become to the speckle state of stochastic distribution, it is 25 ° that ARAMIS two camera lens angles are set, and with MTS equipment, test specimen is loaded.

(2) by the test specimen surface state of one group of angled black and white shot record loading procedure, utilize three-dimensional digital image related software calculate each comparison film displacement field u under corresponding deformation state _xand u _y.

(3) use mean filter means to process containing noisy displacement field, to obtain smoothed data; Displacement field after smoothing processing is carried out to matching with cubic spline curve on two change in coordinate axis direction, asks its gradient, obtain displacement field along the derivative of two coordinate directions:

with

according to the geometric equation of material:

${\mathrm{\ϵ}}_{\mathrm{xx}}=\frac{\∂u_x}{\∂x};$ ${\mathrm{\ϵ}}_{\mathrm{yy}}=\frac{\∂u_y}{\∂y};$ ${\mathrm{\ϵ}}_{\mathrm{xy}}=\frac{1}{2}(\frac{\∂u_x}{\∂y}+\frac{\∂u_y}{\∂x});$

Can calculate the strain field of trying to achieve test specimen surface.Under plane stress problem, the constitutive equation of linear elastic materials is:

$\left[\begin{array}{c}{\mathrm{\σ}}_{\mathrm{xx}}\\ {\mathrm{\σ}}_{\mathrm{yy}}\\ {\mathrm{\σ}}_{\mathrm{xy}}\end{array}\right]=\frac{E}{1-{\mathrm{\υ}}^2}\left[\begin{array}{ccc}1& \mathrm{\ν}& 0\\ v& 1& 0\\ 0& 0& \frac{1-\mathrm{\ν}}{2}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ϵ}}_{\mathrm{xx}}\\ {\mathrm{\ϵ}}_{\mathrm{yy}}\\ 2{\mathrm{\ϵ}}_{\mathrm{xy}}\end{array}\right]---\left(2\right)$

Wherein E is elasticity modulus of materials, and ν is Poisson ratio;

By the strain stress obtaining above _xx, ε _yy, ε _xy, utilize this stress-strain relation, try to achieve the stress state on test specimen surface, and then the strain energy density distribution w=σ on test specimen surface _xxε _xx/ 2+ σ _yyε _yy/ 2+ σ _xyε _xyalso can obtain.

(4) by digital speckle technology and mean filter smoothing algorithm, try to achieve displacement field u _xand u _y; Cubic Spline Fitting is tried to achieve the partial derivative of displacement

with

geometric equation is tried to achieve strain field ε _xx, ε _yy, ε _xy; Constitutive equation is tried to achieve stress field σ _xx, σ _yy, σ _xy; All integration items in M Definitions On Integration formula (1) obtain, choose any path of integration around defect, on substitution path stress, strain and strain energy density state a little, by numerical integration interpolation algorithm, M integrated value can be tried to achieve.

The present invention is applicable to various defect and defect cluster within the scope of hard brittle material and metal material linear elasticity, system utilizes Digital Speckle Correlation Method to carry out the nondestructive measurement of M integration both at home and abroad first, is also to announce first the M integration non-destructive measuring method of many defective materials both at home and abroad.Compare with the people's such as King method, not only applicable object is wide in range, and does not need different defective form derivation computing formula, does not also need to choose special path of integration, does not more need to be limited by the various restrictions of traditional foil gauge.The measurement means that the present invention announces directly comes from the definition expression formula of M integration, and the value accuracy measuring is higher, can be used for assessing the various forms of material damages in field and the structural intergrities such as space flight, aviation, machinery.

Accompanying drawing explanation

Below in conjunction with the drawings and the specific embodiments, the present invention is described in further detail.

Fig. 1 is the schematic diagram of ARAMIS 4M measurement mechanism used and sample in the inventive method.

Fig. 2 sample defect and path of integration schematic diagram.

Fig. 3 is embodiment of the present invention center single hole defect sample dimensions and path of integration schematic diagram.

Fig. 4 is that test specimen displacement field of the present invention distributes.Wherein (a) figure is the original displacement of x direction; (b) figure is x direction displacement result after smoothing filter is processed; (c) figure is the original displacement of y direction; (d) figure is y direction displacement result after smoothing filter is processed.

Fig. 5 is that test specimen strain field of the present invention and displacement partial derivative distribute: (a) figure is x direction normal strain; (b) figure is y direction normal strain; (c) figure is the derivative of x direction displacement to y; (d) figure is the derivative of y direction displacement to x.

Embodiment

As shown in Figure 1 and Figure 2, a kind of non-destructive measuring method of many defective materials M integration, comprises the steps:

(1) the complicated microdefect group who exists for two-dimentional member damages test specimen, in order to increase the intensity contrast value of digital speckle, first test specimen surface spraying is become to the speckle state of stochastic distribution, ARAMIS 4M (the three-dimensional optical deformation measuring system of producing for German GOM company is set, this system is utilized the distortion on digital picture related algorithm calculation testing piece surface) two camera lens angles are 25 °, with MTS-880 (mechanical test and the simulation system of producing for American MTS company) equipment, test specimen loaded.

(2) by the test specimen surface state of one group of angled black and white shot record loading procedure, utilize three-dimensional digital image related software calculate each comparison film displacement field u under corresponding deformation state _xand u _y.

(3) use mean filter means to process containing noisy displacement field, to obtain smoothed data; Displacement field after smoothing processing is carried out to matching with cubic spline curve on two change in coordinate axis direction, asks its gradient, obtain displacement field along the derivative of two coordinate directions:

with

according to the geometric equation of material:

${\mathrm{\ϵ}}_{\mathrm{xx}}=\frac{\∂u_x}{\∂x};$ ${\mathrm{\ϵ}}_{\mathrm{yy}}=\frac{\∂u_y}{\∂y};$ ${\mathrm{\ϵ}}_{\mathrm{xy}}=\frac{1}{2}(\frac{\∂u_x}{\∂y}+\frac{\∂u_y}{\∂x});$

Can calculate the strain field of trying to achieve test specimen surface.Under plane stress problem, the constitutive equation of linear elastic materials is:

$\left[\begin{array}{c}{\mathrm{\σ}}_{\mathrm{xx}}\\ {\mathrm{\σ}}_{\mathrm{yy}}\\ {\mathrm{\σ}}_{\mathrm{xy}}\end{array}\right]=\frac{E}{1-{\mathrm{\υ}}^2}\left[\begin{array}{ccc}1& \mathrm{\ν}& 0\\ v& 1& 0\\ 0& 0& \frac{1-\mathrm{\ν}}{2}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ϵ}}_{\mathrm{xx}}\\ {\mathrm{\ϵ}}_{\mathrm{yy}}\\ 2{\mathrm{\ϵ}}_{\mathrm{xy}}\end{array}\right]---\left(2\right)$

Wherein E is elasticity modulus of materials, and ν is Poisson ratio;

By the strain stress obtaining above _xx, ε _yy, ε _xy, utilize this stress-strain relation, try to achieve the stress state on test specimen surface, and then the strain energy density distribution w=σ on test specimen surface _xxε _xx/ 2+ σ _yyε _yy/ 2+ σ _xyε _xyalso can obtain.

(4) choose any path of integration around defect, on substitution path stress, strain and strain energy density state a little, by numerical integration interpolation algorithm, M integrated value can be tried to achieve.

Below in conjunction with material center single hole defect example, the experiment measuring of M integration is described further:

1. the material for test in example is LY12 duralumin, hard alumin ium alloy, and its elastic modulus is 68.5Gpa, and Poisson ratio is 0.33; Scantling 80 * 60 * 3mm, there is a circular hole defect that diameter is 5mm in test specimen central authorities; Utilize MTS-880 testing machine to the loading that stretches of test specimen two ends, load is fixed as 29037N, is roughly equal to 167.5MPa, loads schematic diagram and M path of integration and selects as shown in Figure 3.

2. optical measuring apparatus is installed as shown in Figure 1.The 3D-DIC measuring system ARAMIS 4M that selects GOM company to produce, its parameter arranges as shown in table 1, and the displacement measurement precision under this measurement volumes is about 0.001mm.

3. the displacement field under the test specimen stress state being calculated by ARAMIS is shown in Fig. 4 (a, c); Adopt 5 * 5 mean filter smoothing algorithms to process data, obtain the displacement field after level and smooth, shown in Fig. 4 (b, d).

4. utilize cubic spline function, the displacement data of smoothly crossing is asked to directional derivative, obtain x direction normal strain as shown in Fig. 5 (a); Shown in y direction normal strain Fig. 5 (b); The displacement of x direction is to shown in derivative Fig. 5 (c) of y; The displacement of y direction is to shown in derivative Fig. 5 (d) of x.

5. utilize material constitutive equation (2), the components of stress on calculation testing piece surface, and then obtain strain energy density distribution.

6. the displacement of step 3-5 being asked, strain, stress and strain energy density substitution M integral expression (1), choose different path of integration, by numerical integration method, calculates M integrated value; Table 2 has provided the experimental result value of M integration under different paths, and compares with result of finite element; Can find out, this experimental technique records M integration and presents expectedly path independence characteristic, and its measurement result and result of finite element are coincide, and error is less than 0.1.

Table 1.ARAMIS 4M experimental facilities parameter

Experiment measuring M integration and finite element result under the different path of integration of table 2.

Note: wherein different s and h value represent different path of integration, as shown in Figure 3.

Claims (1)

1. a non-destructive measuring method for the M of defective material more than integration, is characterized in that, comprises the following steps:

(1) test specimen of the complex form microdefect group damage existing for two-dimentional member, first becomes test specimen surface spraying the speckle state of stochastic distribution, and it is 25 ° that ARAMIS two camera lens angles are set, and with MTS equipment, test specimen is loaded;

(2) by becoming the test specimen surface state of the ARAMIS shot record loading procedure of 25 ° of angles, utilize 3-dimensional digital speckle related software calculate each comparison film deformation displacement field u under corresponding loading _xand u _y;

(3) use mean filter means to process containing noisy displacement field, to obtain smoothed data; Displacement field after smoothing processing is carried out to matching with cubic spline curve on two change in coordinate axis direction, asks its gradient, and then obtain displacement field along the partial derivative of two coordinate directions:

with

according to the geometric equation of material:

${\mathrm{\ϵ}}_{\mathrm{xx}}=\frac{{\∂u}_x}{\∂x};{\mathrm{\ϵ}}_{\mathrm{yy}}=\frac{{\∂u}_y}{\∂y};{\mathrm{\ϵ}}_{\mathrm{xy}}=\frac{1}{2}(\frac{{\∂u}_x}{\∂y}+\frac{{\∂u}_y}{\∂x});$

The strain field ε on test specimen surface is tried to achieve in calculating _xx, ε _yy, ε _xy; By the constitutive equation of linear elastic materials:

$\left[\begin{array}{c}{\mathrm{\σ}}_{\mathrm{xx}}\\ {\mathrm{\σ}}_{\mathrm{yy}}\\ {\mathrm{\σ}}_{\mathrm{xy}}\end{array}\right]=\frac{E}{1-v^2}\left[\begin{array}{ccc}1& v& 0\\ v& 1& 0\\ 0& 0& \frac{1-v}{2}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ϵ}}_{\mathrm{xx}}\\ {\mathrm{\ϵ}}_{\mathrm{yy}}\\ {2\mathrm{\ϵ}}_{\mathrm{xy}}\end{array}\right]$

Wherein E is elasticity modulus of materials, and ν is Poisson ratio, obtains the stress state σ on test specimen surface _xx, σ _yy, σ _xy; And then the strain energy density distribution w=σ on acquisition test specimen surface _xxε _xx/ 2+ σ _yyε _yy/ 2+ σ _xyε _xy;

(4) choose any closed path of integration around defect, by path stress, displacement gradient, strain and strain energy density state substitution M Definitions On Integration expression formula a little, by numerical integration interpolation algorithm, calculate M integrated value.

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