CN104390860A - Determination method for failure parameters of materials with complex defects - Google Patents

Abstract

The invention discloses a determination method for failure parameters of materials with complex defects. The determination method comprises the following steps: firstly, preparing material test pieces, then carrying out polishing treatment on the surfaces of the test pieces, and spraying reflection-eliminating paint with two color differences to the surface of each test piece till the surface of each test piece is in a speckle state; then carrying out tensile loading on the two ends of each test piece by utilizing a mechanical testing machine till the test piece is completely broken; then carrying out image recording on the loading process by using 3D-DIC optical measuring equipment, thereby obtaining displacement-field distribution of the whole-process loading of each test piece; selecting a closed integration path enclosing all the defects, and obtaining a value of M integration by utilizing a definition formula of the M integration; and finally, calculating the failure parameters of samples, wherein Pi is equal to ME/(Sigma<2>A<D>), the failure rule of the complex defects of the materials is defined as that Pi is more than or equal to Pi<C>, and when the calculated Pi parameter reaches to the critical value Pi<C>, the defects start to be unstable and extend.

Description

Containing the assay method of complicated defective material failure parameter

Technical field

The present invention relates to a kind of method describing the ultimate failure state of complicated defective material.

Background technology

For the material containing complicated defect, on the one hand, the calculating of the crack tip controling parameter such as the energy release rate in fracturing mechanics, stress intensity factor and J integration criterion, need macroscopic cracking length, the shape that clearly can survey, and for the complicated defect cluster of material, be then difficult to obtain clear and definite lead crack pattern.And along with the development of modern project material, strong heterogeneous material such as such as porous metal foam material, nano-porous film material, ferroelectric polycrystalline material etc. is widely used.These material internals often comprise complicated defect, and interference shielding effect between each defect is also very complicated, makes the inherent vice evolution mode under the effect of material outer load and evolution result be difficult to be predicted accurately and estimate.On the other hand, the expansion of single micro-crack is not sufficient to the ultimate failure causing material, the one-tenth embryo of inherent vice, breed, expand, merge into macroscopic cracking, until Crack Extension makes material generation unstable failure, material is ultimate failure, in order to describe the ultimate failure state of complicated defective material, we need to set up the failure criteria that describes complicated defective material ultimate failure.Under material configuration mechanical frame, if when research shows that path of integration is the closed curve comprising all microdefects, as the M integration of one of material configuration power key concept, its value depends on the fracture damage factor such as material behavior, plus load condition, concrete defect characteristic (as type, shape, density). obviously, allly damages relevant various factors to Materials Fracture and can be embodied to some extent by M integration.Therefore, the failure criteria of the complicated defect of a kind of effective description can be set up based on the M integral concept of material configuration mechanics.

Particular kind of relationship is there is based on M integration and external applied load, elastic modulus, damaged area.There is following failure parameter Π:

$\mathrm{\&Pi;}=\frac{\mathrm{ME}}{{\mathrm{\&sigma;}}^2{A}_D}---\left(1\right)$

In formula: A _drepresent the area of damage field; σ is external applied load; E is the elastic modulus of material matrix; Coefficient Π we be referred to as the damage parameter of complicated defective material, be called for short Π parameter, it can be understood to material failure driving force, and as the external parameter that is only determined by the physical dimension of material behavior, damage field area and test specimen.This parameter will have vital role in prediction is containing the failure behaviour of complicated defective material.

In formula (1), the definition expression formula of M integration is as follows:

In formula: w=σ _ijε _ij/ 2, σ _kj, ε i _j, u _kand n _ibe respectively material strain energy density, stress, strain, displacement and close the outer normal vector of path of integration C around defect; Wherein u _k,ifor displacement is to dependent coordinate x _ipartial differential.

Like this, the failure criteria describing the complicated defect of material finally can be expressed as:

Π≥Π _C(3)

Wherein, Π _cbe critical value during material ultimate failure, failure parameter Π represents the destructiveness of complicated defect system.

In addition, for the experiment measuring of material failure parameter, and the critical value Π of material _cexperimental calibration, not a set of effective method up to now.

Summary of the invention

The object of this invention is to provide a kind of experiment measuring containing complicated defective material failure parameter Π and critical value Π _cthe method of experimental calibration.The method has simply, and effectively, feasible feature, can be used as the reference of measuring complicated defective material component failure toughness.

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

Containing an assay method for complicated defective material failure parameter, it is characterized in that, comprise the steps:

(1) prepare the slightly wide strip test specimen in two ends totally 4, its thickness is 2mm, punches in the middle part of test specimen, and diameter is 2mm, 4mm, 5mm, 6mm respectively;

(2) surface of test piece carries out polishing, then each surface of test piece reflectorised paint that disappears of two kinds of aberration is sprayed into speckle state, is convenient to camera lens identification and computational analysis;

(3) mechanics machine is utilized to carry out tensile loads to each test specimen two ends, loading velocity is 0.1mm/s, until test specimen ruptures completely, use 3D-DIC optical measuring apparatus to carry out image record with the capture rate of 60/min to loading procedure, obtain the displacement field distribution that each test specimen whole process loads;

(4) along two change in coordinate axis direction, cubic spline interpolation is carried out to displacement field, and obtains the displacement gradient component of displacement field along two coordinate directions thus: with

(5) by the constitutive equation of linear elasticity, via three components of strain:

${\mathrm{\&epsiv;}}_{\mathrm{xx}}={\&PartialD;u}_x/\&PartialD;x;{\mathrm{\&epsiv;}}_{\mathrm{yy}}=\&PartialD;u_y/\&PartialD;y;{\mathrm{\&epsiv;}}_{\mathrm{xy}}=\frac{1}{2}({\&PartialD;u}_x/\&PartialD;y+{\&PartialD;u}_y/\&PartialD;x)$

Obtain the distribution of each test specimen Stress Field Distribution and strain energy density field, choose the closed path of integration surrounding arbitrarily all defect, utilize the definition of M integration to obtain M principal value of integral:

(6) more all test specimens are got distance heart 3cm place, hole and make a line perpendicular to loading direction, the stress on this line is approximate thinks far field external applied load stress; Get the value of its mean stress as far field external applied load stress σ, the damaged area A of sample _dreplacement is similar to the area of hole;

(7) sample failure parameter is calculated: Π=ME/ (σ ²a _d), wherein M is step (5) gained, σ, A _dfor step (6) gained, E is elasticity modulus of materials;

(8) failure criteria of the complicated defect of material is defined as: Π>=Π _c, utilize the Π parameter that step (7) calculates, when it reaches critical value Π _ctime, represent defect and start unstable propagation.

In such scheme, the displacement field described in step (3) is by the smoothing process of mean filter, the displacement field comparatively pressing close to true field.

Advantage of the present invention is:

By preparation containing the tensile test specimen under different pore size circular hole defect, unilateral stretching is carried out to this test specimen, utilize Π critical parameter value Π during Digital Speckle Correlation Method test measuring method measurement defect test specimen generation unstable failure _c, achieve this critical parameter value Π _cexperimental calibration.The method have accuracy of measurement higher, be suitable for defect object wide in range, measure the features such as easy, load can load arbitrarily.

The present invention is applicable to the material failure predicting and evaluating containing various defect and defect cluster, can be used for solving traditional damage mechanics and fracturing mechanics is insurmountable destroys problem containing complicated defect, is applicable to damage and the Failure Assessment of construction material and structure.

Accompanying drawing explanation

Fig. 1 is Specimen Shape schematic diagram used in the inventive method.

Fig. 2 is the surface picture of test specimen being carried out to speckle process.

Fig. 3 is that test specimen ruptures the black-and-white photograph of forward and backward state.Wherein: (a) figure is before test specimen fracture; B () figure is after test specimen fracture.

Specific implementation method

Below in conjunction with a poly (methyl methacrylate) plate containing circular hole defect example, the inventive method is described in further details:

(1) test specimen in example as shown in Figure 1, with test specimen geometric center for punching in the center of circle.Wherein the thickness of test specimen is 2mm, and hole diameter is respectively 2mm, 4mm, 5mm, 6mm, has done altogether 4 (Fig. 3).Pmma material elastic modulus is 3.0GPa, and linear elasticity Poisson ratio is 0.35.

(2) polishing is carried out on material test specimen surface, then each surface of test piece reflectorised paint that disappears of two kinds of aberration large (as black-and-white two color) is sprayed out the speckle state with high-contrast, fine grained, one-tenth stochastic distribution, be convenient to identification and the computational analysis of camera lens, its test specimen speckle pattern as shown in Figure 2.

(3) MTS-880 testing machine (MTS-880 is mechanical test and the simulation system of the production of American MTS company) is utilized to carry out tensile loads to each test specimen two ends, in view of the distortion of material for test is less, in order to observe convenient, have employed slower loading velocity, carry out with the speed of 0.1mm/s, until test specimen ruptures completely.The 3D-DIC optical measuring apparatus ARAMIS-4M that loading procedure uses GOM company to produce carries out image record with 60/min, so as to obtaining the displacement field distribution under the omnidistance stress state of each test specimen, before and after test specimen destruction as shown in Figure 3.

(4) displacement field owing to obtaining in step (3) contains noise, by mean filter to the smoothing process of displacement field, comparatively pressed close to the displacement field of true field, again along two change in coordinate axis direction, cubic spline interpolation is carried out to displacement field, and obtains the displacement gradient component of displacement field along two coordinate directions thus: with

(5) at normal temperatures, organic glass is typical hard brittle material, and in the situation of component without obviously distortion generation fracture, be referred to as brittle fracture, during fracture there is not plastic yield in material, and by the constitutive equation of linear elasticity, we can via three components of strain:

${\mathrm{\&epsiv;}}_{\mathrm{xx}}={\&PartialD;u}_x/\&PartialD;x;{\mathrm{\&epsiv;}}_{\mathrm{yy}}=\&PartialD;u_y/\&PartialD;y;{\mathrm{\&epsiv;}}_{\mathrm{xy}}=\frac{1}{2}({\&PartialD;u}_x/\&PartialD;y+{\&PartialD;u}_y/\&PartialD;x)$

Obtain the distribution of each test specimen stress field and the distribution of strain energy density field.Choose the closed path of integration surrounding arbitrarily all defect, utilize the definition of M integration can obtain M principal value of integral:

(6) more all test specimens are got distance heart 3cm place, hole and make a line perpendicular to loading direction, the stress on this line can be similar to thinks far field external applied load stress; Get the value of its mean stress as far field external applied load stress σ.In addition, the damaged area A of material _dreplacement can be similar to the area of hole.

(7) Calculating material failure parameter: Π=ME/ (σ ²a _d), wherein M is step (5) gained, σ, A _dfor step (6) gained; E is elasticity modulus of materials;

(8) failure criteria of the complicated defect of material is defined as: Π>=Π _c, utilize the Π parameter that step (6) calculates, when it reaches critical value Π _ctime, represent defect and start unstable propagation.

Under table 1 provides different pore size circular hole defect, borderline failure load value, M integration critical value, failure parameter Π value when construction instability destroys.Result can find, the critical M integrated value that lost efficacy is very strong to the dependence of material configuration, critical value based on the failure parameter Π of M integration proposition then has nothing to do with defect configuration, in all test specimens, the Π value of material damage critical moment is close to constant value (± 5% error), that is, Π is material build-in attribute, independent of defect type.Concerning this material of organic glass, regardless of its defect configuration, at the critical moment occurring to lose efficacy, failure parameter Π value is about 3.2.

Under table 1 different pore size circular hole defect, critical Π value when construction instability destroys

Claims (2)

1., containing an assay method for complicated defective material failure parameter, it is characterized in that, comprise the steps:

(1) prepare the slightly wide strip test specimen in two ends totally 4, its thickness is 2mm, punches in the middle part of test specimen, and diameter is 2mm, 4mm, 5mm, 6mm respectively;

(2) surface of test piece carries out polishing, then each surface of test piece reflectorised paint that disappears of two kinds of aberration is sprayed into speckle state, is convenient to camera lens identification and computational analysis;

(3) mechanics machine is utilized to carry out tensile loads to each test specimen two ends, loading velocity is 0.1mm/s, until test specimen ruptures completely, use 3D-DIC optical measuring apparatus to carry out image record with the capture rate of 60/min to loading procedure, obtain the displacement field distribution that each test specimen whole process loads;

(4) along two change in coordinate axis direction, cubic spline interpolation is carried out to displacement field, and obtains the displacement gradient component of displacement field along two coordinate directions thus: with

(5) by the constitutive equation of linear elasticity, via three components of strain:

${\mathrm{\&epsiv;}}_{\mathrm{xx}}=\&PartialD;u_x/\&PartialD;x;{\mathrm{\&epsiv;}}_{\mathrm{yy}}=\&PartialD;u_y/\&PartialD;y;{\mathrm{\&epsiv;}}_{\mathrm{xy}}=\frac{1}{2}(\&PartialD;u_x/\&PartialD;y+\&PartialD;u_y/\&PartialD;x)$

Obtain the distribution of each test specimen Stress Field Distribution and strain energy density field, choose the closed path of integration surrounding arbitrarily all defect, utilize the definition of M integration to obtain M principal value of integral:

(6) more all test specimens are got distance heart 3cm place, hole and make a line perpendicular to loading direction, the stress on this line is approximate thinks far field external applied load stress; Get the value of its mean stress as far field external applied load stress σ, the damaged area A of sample _dreplacement is similar to the area of hole;

(7) sample failure parameter is calculated: Π=ME/ (σ ²a _d), wherein M is step (5) gained, σ, A _dfor step (6) gained, E is elasticity modulus of materials;

(8) failure criteria of the complicated defect of material is defined as: Π>=Π _c, utilize the Π parameter that step (7) calculates, when it reaches critical value Π _ctime, represent defect and start unstable propagation.

2. the assay method containing complicated defective material failure parameter as claimed in claim 1, it is characterized in that, the displacement field described in step (3) is by the smoothing process of mean filter, the displacement field comparatively pressing close to true field.