CN109520817B - Real-time measuring method for crack tip expansion length in composite material fracture process - Google Patents

Real-time measuring method for crack tip expansion length in composite material fracture process Download PDF

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CN109520817B
CN109520817B CN201811366089.8A CN201811366089A CN109520817B CN 109520817 B CN109520817 B CN 109520817B CN 201811366089 A CN201811366089 A CN 201811366089A CN 109520817 B CN109520817 B CN 109520817B
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齐乐华
晁许江
谢稳伟
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Northwestern Polytechnical University
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Abstract

The invention relates to a real-time measuring method for the crack tip expansion length in the composite material fracture process. In particular to a method for directly determining the crack propagation length in real time by using load-displacement data of experimental tests on the basis of the equivalent flexibility of a double-cantilever beam containing cracks. The invention provides a method for directly obtaining the crack propagation length in the fracture test process of the composite material without the assistance of additional optical digital image equipment, thereby greatly reducing the test cost. On the basis of load-displacement test data, the method establishes a relation between the crack propagation length and load-displacement data in the test process by calculating the equivalent flexibility of a DCB beam containing cracks, so as to realize real-time and quantitative monitoring of the crack propagation length; the invention considers the deflection contribution of the cantilever beam generated by bending and shearing deformation in the DCB beam test, and improves the calculation precision of the final fracture toughness.

Description

Real-time measuring method for crack tip expansion length in composite material fracture process
Technical Field
The invention belongs to the field of composite materials, and relates to a real-time measuring method for crack tip expansion length in a Double Cantilever Beam (DCB) test composite material fracture process. In particular to a method for directly determining the crack propagation length in real time by using load-displacement data of experimental tests on the basis of the equivalent flexibility of a double-cantilever beam containing cracks.
Background
Fiber reinforced composites have been widely used in aerospace and automotive electronics due to their high specific strength and modulus. However, due to the limited load carrying capacity of the matrix portion in the composite, interlayer debond cracking becomes one of the main failure modes of composite laminates. Particularly at the free boundaries of the composite structure and where the initial defects are created by the removal process. Therefore, fracture toughness, which is an important parameter for measuring the debonding crack resistance of the composite material, has important significance in the application process of the composite material. The accurate definition of the parameters not only can provide important reference for structural design, but also can provide basis for the research of fracture damage behaviors of the fiber reinforced composite material.
At present, the DCB method is often used to test the type I fracture toughness of composite materials, and in order to obtain fracture toughness parameters, in addition to the load during crack propagation and the displacement at the point of application of the load, the propagation length of the crack tip needs to be measured according to the ASTM (American Society of Testing materials) D5528 experimental test standard. In the experiment, the shape of the crack tip region of the composite material is complex, and the real position of the crack tip is difficult to determine by adopting a naked eye observation mode, so that large errors are generated in measurement of the crack propagation length and calculation of the fracture toughness of the material.
The documents Arrese A, Boyano A, Gracia J D, et al. A novel procedure to a derivative of the chemical law in DCB tests [ J ]. compositions Science & Technology,2017,152:76-84, mention the method of experimentally adding auxiliary optical digital image-related devices such as (DIC or Linear Voltage Differential Transformer (LVDT)) to obtain crack propagation length. Although the relative propagation length of cracks in the DCB test can be achieved with additional optics and the like, these optics are typically very expensive, greatly increasing the cost of the experiment.
In patent No. 201410805431.5, the inventor designs a clamp to enlarge the crack tip position of the DCB sample to improve the observability of the crack tip propagation length. However, the design and manufacture of these non-standard clamps increase the research cost, and for the fiber reinforced composite material, the crack tip has irregular shape, so the observation difficulty still exists by adopting the method.
Disclosure of Invention
The technical problem to be solved is as follows: the method aims to solve the problem that the crack tip propagation length is difficult to determine in real time in the process of testing the fracture toughness of the composite material by adopting a DCB method in the prior art. The invention provides a method for directly obtaining the crack propagation length in the fracture test process of a composite material without the assistance of additional optical digital image equipment. On the basis of load-displacement test data, the method establishes a relation between the crack propagation length and load-displacement data in the test process by calculating the equivalent flexibility of a DCB beam containing cracks, so as to realize real-time and quantitative monitoring of the crack propagation length; the method can be applied to fiber reinforced composite materials, and can also provide important supplement for determining the crack propagation length in the fracture test process of other composite materials such as biological composite materials, aggregate structural materials and the like.
The technical scheme of the invention is as follows: a real-time measuring method for the crack tip expansion length in the composite material fracture process is characterized by comprising the following specific steps:
the method comprises the following steps: preparing a DCB beam standard sample for the I-type composite material fracture test, clamping the DCB beam standard sample in a mechanical test instrument for testing, and recording the load P and displacement data of a chuck at each stage;
step two: different stress distribution conditions of different positions before and after the crack tip on the DCB beam standard sample are different, and the size parameter x of different stress distribution sections is calculated by using the geometric dimension and the material elasticity parameter of the DCB beam standard sample1，x2And x3The calculation formula is expressed as follows;
Figure BDA0001868595990000021
wherein E is3The transverse Young modulus of a DCB beam standard sample; i is the rotational inertia of the DCB beam standard sample; w is the width of the DCB beam standard sample, and h is the thickness of the DCB beams on two sides of the crack; a is the crack length; ebIs the flexural modulus, G, of the DCB Beam Material13＝G12Is the shear modulus of the DCB standard sample material;
γ1＝x1+2x2，
Figure BDA0001868595990000031
size parameter x according to the aforementioned stress distribution1，x2And x3Defining a characteristic parameter beta of the DCB beami＝1,2,3,4The expression is as follows:
Figure BDA0001868595990000032
the displacement of the end part of the free section of the DCB beam standard sample is the comprehensive effect of different stress distribution sections, and according to the expression form of the deflection and the corner of the cantilever beam, the deflection and the corner generated by the free end in front of the crack tip are expressed as follows:
Figure BDA0001868595990000033
step three: according to the stress distribution and the deformation distribution of the DCB beam standard sample, calculating the displacement of the crack free end of the DCB beam standard sample in the load direction according to the following formula:
Figure BDA0001868595990000034
wherein U is the strain energy of the DCB beam standard sample in the loading process, PjThe load along the j direction, M is the bending moment borne by the DCB beam standard sample, Q is the shearing force borne by the DCB beam standard sample, and A is the cross-sectional area of the DCB beam standard sample;
applying a unit load in the vertical direction to the end of the free section of the standard sample of the DCB beam, deducing and obtaining the bending moment and the shearing force of the standard sample of the DCB beam at different stress distribution sections, and calculating and obtaining the displacement generated by the loading point at the end of the free section of the standard sample of the DCB beam according to the following formula:
Figure BDA0001868595990000035
step four: according to the displacement expression of the loading point at the end part of the DCB beam standard sample free section obtained in the third step, the equivalent crack length is included
Figure BDA0001868595990000041
The overall compliance of the DCB beam of (a) is expressed as:
Figure BDA0001868595990000042
therefore, the load point real-time load-displacement data P-obtained through experimental tests is substituted into a formula (6), the equivalent crack length is the only unknown quantity at the moment, the extended equivalent crack length is obtained through solving the formula, and the extended length of the crack tip is further obtained.
Advantageous effects
The invention has the beneficial effects that:
(1) and the deflection contribution of the cantilever beam generated by bending and shearing deformation in the DCB beam test is considered, so that the calculation precision of the final fracture toughness is improved.
(2) According to the load-displacement curve data of the DCB beam test result, the crack tip expansion length of each stage in the fracture process is quantitatively determined in real time.
(3) Compared with the prior art, the method can accurately obtain the crack tip expansion length in the fracture toughness test process without additional optical digital image equipment, thereby greatly reducing the test cost.
Drawings
FIG. 1 is a schematic view of a DCB beam test;
FIG. 2 is a graph of load-displacement curves obtained using a one-way T300/977-2DCB experimental test;
FIG. 3 is a force analysis diagram of a single-sided (lower half of crack) DCB beam;
FIG. 4 is a crack propagation length curve corresponding to different displacement states of a loading point calculated by the method of the present invention.
Detailed Description
The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
Referring to the attached figures 1-4, the method for obtaining the crack propagation length in the DCB beam standard sample testing process comprises the following steps:
the method comprises the following steps: the samples required for the DCB test were prepared according to the type I composite fracture test standard, where the material selected was a DCB sample prepared from 20 layers of unidirectional T300/977-2. Mechanical parameter E thereof1＝150GPa，E2＝E3＝11GPa，G12＝G23＝6GPa，Eb96GPa (elastic properties of the material are from the document Moris A B D, Marques A T, et al model-I interlaminar fraction of carbon/epoxy cross-mixes [ J].Composites Science&Technology,2002,62(5): 679-; the geometry of the test specimen was: h 2mm, w 20mm, a 55mm, and L150 mm. And testing the prepared sample on a universal testing machine, and recording load-displacement (P-) curve data of a test result.
Step two: and (4) calculating size parameters of different stress distribution sections of the DCB beam according to the stress distribution condition on the cantilever beam on one side in the DCB sample and the material parameters and the geometric size of the sample mentioned in the step one.
Figure BDA0001868595990000051
Wherein E is3The transverse Young modulus of a DCB beam standard sample; i is the rotational inertia of the DCB beam standard sample; w is the width of the DCB beam standard sample, and h is the thickness of the DCB beams on two sides of the crack; a is the crack length; ebIs the flexural modulus, G, of the DCB Beam Material13＝G12Is the shear modulus of the DCB standard sample material;
γ1＝x1+2x2，
Figure BDA0001868595990000052
the numerical values obtained by calculation are respectively: x is the number of1＝9.983，x2＝0.3393，x31.78; the numerical value of the stress distribution size parameter is substituted into the following formula to define the characteristic parameter beta of the DCB beami＝1,2,3,4:
Figure BDA0001868595990000061
The numerical values obtained by calculation are respectively: β 1 ═ 14.2,. beta.2 ═ 0.1185,. beta.3 ═ 22.1, and. beta.4 ═ 0.63. The deflection and corner of the DCB beam due to bending and shear deformation in the free-section portion before the crack tip are thus expressed as:
Figure BDA0001868595990000062
step three: according to the stress distribution and the deformation distribution of the DCB beam, the deflection deformation generated by bending and shearing deformation in the test is considered. The displacement of the end load point of the DCB beam in the load direction is represented as:
Figure BDA0001868595990000063
and (3) substituting the parameters obtained by calculation in the step (II) into a formula (4) to obtain a displacement expression form of the DCB beam loading point corresponding to the load change in the test process:
Figure BDA0001868595990000064
step four: according to the displacement expression of the end DCB beam loading point obtained in the third step, the equivalent crack length is
Figure BDA0001868595990000065
The overall compliance of the DCB beam of (a) is expressed as a function of:
Figure BDA0001868595990000066
in the above formula, only the crack length
Figure BDA0001868595990000067
Is unknown, and therefore, the load-displacement data P-obtained at different test stages in the experiment is substituted into equation (6). And solving the function to obtain the crack propagation length of the DCB sample at different loading stages.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention.

Claims (1)

1. A real-time measuring method for the crack tip expansion length in the composite material fracture process is characterized by comprising the following specific steps:
the method comprises the following steps: preparing a DCB beam standard sample for the I-type composite material fracture test, clamping the DCB beam standard sample in a mechanical test instrument for testing, and recording the load P and displacement data of a chuck at each stage;
step two: different stress distribution conditions of different positions before and after the crack tip on the DCB beam standard sample are different, and the size parameter x of different stress distribution sections is calculated by using the geometric dimension and the material elasticity parameter of the DCB beam standard sample1，x2And x3The calculation formula is expressed as follows;
Figure FDA0001868595980000011
wherein E is3The transverse Young modulus of a DCB beam standard sample; i is the rotational inertia of the DCB beam standard sample; w is the width of the DCB beam standard sample, and h is the thickness of the DCB beams on two sides of the crack; a is the crack length; ebIs the flexural modulus, G, of the DCB Beam Material13＝G12Is the shear modulus of the DCB standard sample material;
Figure FDA0001868595980000012
size parameter x according to the aforementioned stress distribution1，x2And x3Defining a characteristic parameter beta of the DCB beami＝1,2,3,4The expression is as follows:
Figure FDA0001868595980000013
the displacement of the end part of the free section of the DCB beam standard sample is the comprehensive effect of different stress distribution sections, and according to the expression form of the deflection and the corner of the cantilever beam, the deflection and the corner generated by the free end in front of the crack tip are expressed as follows:
Figure FDA0001868595980000021
step three: according to the stress distribution and the deformation distribution of the DCB beam standard sample, calculating the displacement of the crack free end of the DCB beam standard sample in the load direction according to the following formula:
Figure FDA0001868595980000022
wherein U is the strain energy of the DCB beam standard sample in the loading process, PjThe load along the j direction, M is the bending moment borne by the DCB beam standard sample, Q is the shearing force borne by the DCB beam standard sample, and A is the cross-sectional area of the DCB beam standard sample;
applying a unit load in the vertical direction to the end of the free section of the standard sample of the DCB beam, deducing and obtaining the bending moment and the shearing force of the standard sample of the DCB beam at different stress distribution sections, and calculating and obtaining the displacement generated by the loading point at the end of the free section of the standard sample of the DCB beam according to the following formula:
Figure FDA0001868595980000023
step four: according to the displacement expression of the loading point at the end part of the DCB beam standard sample free section obtained in the third step, the equivalent crack length is included
Figure FDA0001868595980000024
Of the DCB beamThe degree is expressed as:
Figure FDA0001868595980000025
therefore, the load point real-time load-displacement data P-obtained through experimental tests is substituted into a formula (6), the equivalent crack length is the only unknown quantity at the moment, the extended equivalent crack length is obtained through solving the formula, and the extended length of the crack tip is further obtained.
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