Improved test for characterizing the toughness of Mode II interfaces and associated test specimen

Abstract

Improved test for characterizing interface toughness in mode II and associated test specimen. The specimen (10) has an initial notch (40) extending across the entire width of the specimen (10) parallel to its plane P. The specimen comprises three parts following each other longitudinally in a contiguous manner, namely a thin part (11) of thickness H0, a thick part (13) of thickness H2, with H2 > H0, and an intermediate transition part (12) of variable thickness H1, located between the thin part (11) and the thick part (13).The initial notch (40) is capable of propagating into the intermediate portion (12) and possibly into the thick portion (13) parallel to plane P when the specimen (10) is subjected to a three-point bending test, with a first support (21) located under the thin portion (11), a second support (22) located under the thick portion (13), and a load (30) applied to the thick portion (13) between the first support (21) and the second support (22). Figure to be published with the abbreviation: Figure 6.

Description

Title of the invention: Improved test for characterizing the toughness of Mode II interfaces and associated test specimen. TECHNICAL FIELD OF THE INVENTION

[0001] The invention relates to a new test for characterizing the critical energy release rate during mode II crack propagation at the interface, this test being based on the bending of a notched specimen. TECHNOLOGICAL BACKGROUND OF THE INVENTION

[0002] The toughness of a material is its ability to resist crack propagation. There are three types of crack propagation modes, which are illustrated in [Fig. 1]. The invention relates to the second crack propagation mode, designated as Mode II, also known as plane shear mode. It should be noted that in the case of crack propagation between two substrates, i.e., at an interface, this is called delamination. To experimentally determine the toughness of a material or an interface, a pre-notched specimen of said material, also called a notched bar, is used. This specimen is broken by subjecting it to bending in order to estimate its resistance to the propagation of this defect. A specimen is usually rectangular in shape.

[0003] ASTM D7905 / D7905M-14 describes a test for characterizing the propagation of a crack at an interface in mode IL. The objective of such a test is to characterize the critical energy release rate during mode II crack propagation at the interface, as a function of its length. This is also referred to as the interfacial fracture energy. This test is also known as the ENF test (End-Notched Flexure test). As illustrated in [Fig. 2], the ENF test consists of a three-point bending load on a notched specimen 10', where said specimen 10' is placed on two simple supports 20' and subjected to a load 30' applied from above at the midpoint of the specimen 10'.

[0004] The energy required to grow the crack 40' by one unit area dS corresponds to the proportion of energy GdS that would be released elastically by the specimen if it actually propagated. G is called the energy release rate and can be estimated by the following formula:

[0005] [Math.l] _ P2.dC U ~ 2B da

[0006] With: • a is the length of the crack (assuming a straight front) • B the width of the test specimen • C the complacency or flexibility of the system • P the load seen by the system

[0007] A crack can propagate stably or unstably. For a crack to propagate stably, the load must constantly increase to allow the crack to propagate. In this case, the energy release rate decreases with the crack length at a fixed load. Conversely, unstable propagation corresponds to an increase in the energy release rate with the crack length at a constant load. In other words, the crack can propagate "spontaneously" without an increase in the load.

[0008] In the case of ENF, the propagation of the crack 40' is generally unstable, particularly when the length of the pre-notch is less than approximately 0.7 times the distance between the position of the first support 20' and the point of application of the load 30'. Indeed, in the case of ENF, it is possible to propagate the crack 40' stably to a maximum length of 0.3 times the aforementioned distance, but with a friction effect near the point of application of the load 30'.

[0009] The compliance C, or flexibility of the system, is given by: C(a) = U / P, where U corresponds to the imposed displacement. When propagation is unstable, the compliance and the crack length cannot be measured during the test. Indeed, the stability range, that is, the interval of crack length for which propagation is stable, is severely limited, at best 15% of the length between the two supports 20', or 30% of the distance between the position of the first support 20' and the point of application of the load 30. The experimental compliance is therefore estimated for different lengths of the initial crack (15 mm, 25 mm, and 35 mm) by loading the specimen without allowing the crack to propagate. To do this, the specimen is successively displaced between the supports as illustrated in [Fig. 3].

[0010] In order to evaluate the evolution of the critical value of the energy release rate as a function of the crack length, it is highly desirable to obtain stable crack propagation.

[0011] Other tests are also known for characterizing the propagation of a crack at a Mode II interface, but these are not standardized. These include the ONF (Over-Notched Flexure test) shown in [Fig. 4] and the 4ENF (4-point bending End-Notched Flexure test) shown in [Fig. 5], which provide stable crack propagation under bending loads at three and four points, respectively. However, these tests are sensitive to friction effects between the crack lips 41' of the crack 40', because the tip 42' of the initial crack 40' is positioned near or after the point of application of the load 30', which again leads to an overestimation of the critical value of the critical energy release rate.

[0012] Thus, to accurately measure the critical value of the critical energy release rate, there is a need for a test to characterize the propagation of a crack at an interface in mode II, which improves the stability of crack propagation while limiting the friction phenomenon between the crack lips. Summary of the invention

[0013] The invention offers a solution to the problems mentioned above by providing a test specimen having a thickness transition located between a first support point located on the side of the initial notch and the point of application of the load, and by shifting the point of application of the load, usually in a central position, towards a second support point located on the opposite side to the first support point and away from the initial notch.

[0014] One aspect of the invention relates to a test specimen intended to characterize the energy release rate during mode II crack propagation, said specimen extending longitudinally along the X-X' axis in a plane P and having an initial notch extending over the entire width of the specimen along the X-X' axis parallel to the plane P, the specimen comprising three parts following each other longitudinally in a contiguous manner, namely: • a thin part having a constant thickness H0 and a non-zero length L0, • a thick part having a constant thickness H2 and a non-zero length L2, with H2 > H0, and • an intermediate transition section of thickness having a thickness H1 that varies longitudinally along the X-X' axis and a non-zero length L1, this intermediate section being located between the thin section and the thick section, where H1 = H0 at the level of the thin section and H1 = H2 at the level of the thick section; and where • the initial notch is located at least in the thin part and is able to propagate into the intermediate part and possibly into the thick part along the X-X' axis parallel to the plane P when the specimen is subjected to three-point bending.

[0015] For a given displacement, stable propagation corresponds to a positive second derivative of the stiffness (inverse of the flexibility) as a function of the crack length. Thus, increasing the thickness of the specimen along the crack propagation path compensates for the decrease in stiffness with increasing crack length, so that this decrease in stiffness occurs less and less rapidly as the crack length increases. The increase in The thickness advantageously increases the region over which the crack propagates stably, as shown in the graph in [Fig. 8]. Increasing the specimen thickness along the crack propagation path also moves this stability region further away from the point of load application, thus limiting the effects of friction.

[0016] In addition to the characteristics mentioned in the preceding paragraph, the test specimen according to one aspect of the invention may have one or more additional characteristics from among the following, considered individually or according to all technically possible combinations: • the variation of the thickness H1 of the intermediate part along the X-X' axis, from thickness HO to thickness H2, is linear; • the initial notch extends along the entire length of the thin part, in particular to avoid instability from the start of the test and to maximize the propagation length; • the initial notch extends partially into the intermediate part, which does not reduce the advantages provided by the invention with regard to stability and friction, but simply decreases the possible propagation length; • the initial notch divides the thin part into two lips, each having the same thickness hO; • 2 x hO < H2 < 5 x hO, preferably H2 = 4 x hO; • L1 > L2; • The test specimen is formed of two identical layers of material bonded together, where the initial notch extends parallel to plane P at the interface between the two layers of material; and • the two layers of identical material each have the same thickness h2 in the thick part, with H2 = 2 x h2.

[0017] Another aspect of the invention relates to a test method for characterizing the energy release rate during mode II crack propagation at the interface, this test method being based on the three-point bending of a notched specimen and where the notched specimen is a test specimen as described above.

[0018] According to one aspect of the invention, the test specimen is positioned horizontally, placed on two simple supports and subjected to a load applied to the top of the specimen, where: • a first simple support is located under the thin part, • a second simple support is located under the thick part, • the load is applied to the thick part, in a longitudinal position along the X-X' axis located between the longitudinal position of the first support and the longitudinal position of the second support.

[0019] Offsetting the point of application of the load and shifting it towards the second support point advantageously amplifies the two benefits mentioned previously, namely increasing the stability range and limiting the effects of friction. The crack front is located upstream of the point of application of the load (and no longer downstream as in the 4ENF or ONF test), which further limits the effect of friction between the crack lips. It is necessary to experimentally measure the compliance as a function of the crack length in order to estimate G using equation [Math 1]. However, since the propagation is stable, this is done during the test. It is therefore no longer necessary to change the position of the specimen.

[0020] The invention and its various applications will be better understood upon reading the following description and examining the accompanying figures. BRIEF DESCRIPTION OF THE FIGURES

[0021] The figures are presented for illustrative purposes only and are in no way limiting of the invention.

[0022] [Fig.1] illustrates the three types of cracking.

[0023] [Fig.2] illustrates the ENF test of ASTM D7905 / D7905M-14.

[0024] [Fig.3] illustrates the experimental measurement of compliance for three different initial crack lengths for the ENF test.

[0025] [Fig.4] illustrates the ONF test.

[0026] [Fig.5] illustrates the 4ENF test.

[0027] [Fig.6] illustrates the test according to the invention.

[0028] [Fig.7] illustrates the test specimen according to the invention.

[0029] [Fig.8] is a graph illustrating the stability domain of crack propagation for the ENF test and for the test according to the invention.

[0030] On [Fig.2] to [Fig.6] the specimen is seen in profile and the surface of crack propagation is represented by dotted lines. DETAILED DESCRIPTION

[0031] Unless otherwise specified, the same element appearing on different figures has a unique reference.

[0032] By convention, in the present application, the thickness of a part or piece means the height of said part or piece along an axis orthogonal to the plane P in which the specimen 10 extends, and the length of a part or piece means the distance along the axis X-X' along which said part or piece extends in the plane P, where the axis X-X' is the axis along which the specimen 10 extends longitudinally.

[0033] Similarly, in a conventional manner, three-point bending refers to a conventional mechanical test where a specimen 10 is placed on two simple supports 20 and subjected to a load 30 applied to the top of the specimen 10 with simple contact. As a reminder, simple support or simple contact refers to a point support or contact represented by a sphere-plane connection.

[0034] The test specimen 10 according to the invention is intended to be used for a test aimed at characterizing the rate of energy release during the mode II propagation of a crack at the interface.

[0035] This test specimen 10 extends longitudinally along the X-X' axis in a plane P.

[0036] The test specimen 10 according to the invention is formed of three successive parts along the X-X' axis, namely a first part 11, a second part 13 having a thickness greater than the first part 11, and an intermediate part 12, forming the junction between the first part 11 and the second part 13 in order to achieve a thickness transition. For the sake of simplicity, the first part 11 is hereinafter referred to as the "thin part 11" and the second part 13 is referred to as the "thick part 13".

[0037] As shown in [Fig. 7], the thin section 11 has a constant thickness H0 and a non-zero length L0, the thick section 13 has a constant thickness H2 and a non-zero length L2, with H2 > H0, and the intermediate section 12 has a non-zero thickness H1 that varies longitudinally along the X-X' axis and also a non-zero length L1. Preferably, the length L1 of the intermediate section 12 is greater than the length L2 of the thick section 13. Similarly, the length L2 of the thick section 13 is preferably greater than the length L0 of the thin section 11.

[0038] According to a preferred embodiment of the invention, L0 represents 15 to 20% of the length L of the specimen 10, L1 represents 45 to 55% of the length L, and L2 represents 30 to 40% of the length L. A specimen 10, for example, has a length L of 150 to 250 mm and a width of 15 to 30 mm. Of course, the specimen 10 can have many other combinations of dimensions.

[0039] Since the intermediate portion 12 is located between the thin portion 11 and the thick portion 13, it has a thickness H1 = H0 at its junction with the thin portion 11 and a thickness H1 = H2 at its junction with the thick portion 13. The thickness H1 of the intermediate portion 12 increases from H1 = H0 to H1 = H2 along the X-X' axis. This increase in the thickness H1 of the intermediate portion 12 along the X-X' axis is designed so that the thickness transition allows for stable propagation, regardless of its shape. It is not necessarily linear.

[0040] According to a preferred embodiment of the invention, the thickness HO represents 2 to 5% of the length L of the specimen 10 and the thickness H2 represents 5 to 10% of the length L. For example, H0 can be between 8 and 10 mm, while H2 can be between 15 and 20 mm. Of course, the specimen 10 can have many other combinations of dimensions.

[0041] Conventionally, the specimen 10 has an initial notch 40 extending across its entire width parallel to plane P. This initial notch 40 continues along the X-X' axis into the thin section 11, with an opening portion 43 located at the free end of the thin section 11 (on the left in the figures). Opposite its opening portion 43 along the X-X' axis, the initial notch 40 terminates with an end designated as the tip 42 of the crack.

[0042] According to a preferred embodiment of the invention, the initial notch 40 is provided along the entire length LO of the thin part 11, without extending into the intermediate part 12. Thus, the tip 42 of the crack is preferably located at the junction between the thin part 11 and the intermediate part 12.

[0043] The initial notch 40 is intended to propagate into the intermediate part 12 and possibly into the thick part 13 along the axis X-X' parallel to the plane P when the specimen 10 is subjected to three-point bending.

[0044] The initial notch 40 divides the thin portion 11 into two lips 41, each preferably having the same thickness h0. Thus, the thickness H2 is preferably between twice and five times that of H0, and more preferably approximately four times that of h0. For example, h0 can be between 4 and 5 mm.

[0045] The test method according to the invention for characterizing the energy release rate during Mode II crack propagation 40 is suitable for all types of test specimens 10 used where the two substrates thereof are identical in geometry and in the materials of their constituents, the two substrates being symmetrical with respect to the characterized interface. The initial notch 40 extends parallel to the plane P at the interface, this interface and the crack propagation surface 50 being substantially coincident. The two layers of material preferably each have the same thickness h2 in the thicker portion 13, with H2 = 2 x h2.

[0046] The test method according to the invention is based on the three-point bending of a test specimen 10 according to the invention.

[0047] As shown in [Fig. 6], in this test method, the test specimen 10 is positioned horizontally, resting on two simple supports 20, 21, 22 and subjected to a load 30 applied to the top of the specimen 10. The first simple support 21 is located under the thin part 11, at a distance DI from the free end of the thin part 11 (left in [Fig. 6]), while the second simple support 22 is located under the thick section 13, at a distance D2 from the free end of the thick section 13 (right in [Fig. 6]). The distances DI and D2 are, for example, slight overlengths that ensure that the specimen 10 remains securely in place on its supports 20, 21, 22 during the test. The distances DI and D2 are preferably equal, but they can be different.

[0048] The load 30 is applied from the top of the specimen 10 onto the thick portion 13, with simple contact at a point located at a distance D3 from the free end of the thick portion 13 (on the right in the figures). The load 30 is applied at a point located between the longitudinal position of the first support 21 and the longitudinal position of the second support 22. The distance D3 is, for example, such that the ratio D3 / L is between 0.2 and 0.3.

[0049] Thus, the test method according to the invention differs principally from known tests, in particular from the ENF test of ASTM D7905 / D7905M-14 and the ONF and 4ENF tests, in that the specimen 10 has a thickness transition, with increasing thickness along the propagation surface 50 of the initial notch 40, and in that the point of application of the load 30 is not central but offset in the direction of the second support 22.

[0050] According to the invention, the initial notch 40 is located at least in the thin part 11. Depending on the extent of the stability domain, the initial notch 40 can also extend partially into the intermediate part 12.

[0051] During a test according to the invention, the initial notch 40 propagates at least partially into the intermediate part 12. Depending on the material(s) from which the specimen 10 is made, the initial notch 40 may also, but not necessarily, according to the test, propagate at least partially into the thick part 13. This propagation takes place along the propagation surface 50, along the axis X-X' and in a plane parallel to the plane P.

[0052] To demonstrate the advantages of the test method according to the invention, [Fig. 8] is a graph illustrating the stability range of crack propagation for the ENF test (bold, dashed curve) and for the test according to the invention (bold, solid curve). The stability range refers to a crack length interval for which propagation is stable. The stability range is characterized by the fact that, for the application of a given load (here, the load is applied with imposed displacement), the energy release rate is lower if the crack length is greater. In the example provided, which allowed the graphs to be generated (with a specimen having a length of 200 mm), the solution of the invention makes it possible to obtain a DS1NV stability range of 100 mm compared to a DSENF stability range of 30 mm for the reference test. [Fig. 8], these stability domains are represented by hatching. On this graph, the endpoint located to the right of each curve corresponds to the position of application of the load.

[0053] It should be noted that [Fig. 8] is an example of the stability range that exists for the dimensions of a given specimen, and illustrates the potential of the proposed test. This range may be slightly larger or smaller if the dimensions of the specimen change.

[0054] It can be seen that the solution of the invention makes it possible both to keep the stability domain away from the point of application of the load and to limit the effects of friction, unlike the reference test where the propagation is unstable.

[0055] Although described through a number of examples, variants and embodiments, the test specimen according to the invention and the test method according to the invention using this test specimen include various variants, modifications and improvements which will be obvious to a person skilled in the art, it being understood that these variants, modifications and improvements are part of the scope of the invention.

Claims

Demands

1. A test method for characterizing the energy release rate during Mode II crack propagation at the interface, this test method being based on the three-point bending of a test specimen (10) extending longitudinally along the X-X' axis in a plane P and having an initial notch (40) extending across the entire width of the specimen (10) along the X-X' axis parallel to the plane P, characterized in that the specimen (10) comprises three longitudinally contiguous parts, namely: - a thin part (11) having a constant thickness H0 and a non-zero length L0, - a thick part (13) having a constant thickness H2 and a non-zero length L2, with H2 > H0, and - an intermediate transition part (12) of thickness having a thickness H1 that varies longitudinally along the axis X-X' and a non-zero length L1,this intermediate part (12) being located between the thin part (11) and the thick part (13), where H1 = H0 at the level of the thin part (11) and H1 = H2 at the level of the thick part (13); and in that - the initial notch (40) of the test specimen (10) subjected to three-point bending is located at least in the thin part (11) and is capable of propagating into the intermediate part (12) and possibly into the thick part (13) along the axis X-X' parallel to the plane P when the specimen (10) is subjected to three-point bending.

2. Test method according to claim 1, characterized in that the initial notch (40) of the test specimen (10) subjected to three-point bending extends over the entire length of the thin part (H).

3. Test method according to claim 2, characterized in that the initial notch (40) of the test specimen (10) subjected to three-point bending extends over the entire length of the thin part (11) and continues partially into the intermediate part (12).

4. A test method according to any one of the preceding claims, characterized in that the initial notch (40) of the test specimen (10) subjected to three-point bending divides the thin part (11) in two lips (41) each having the same thickness h0.

5. Test method according to the preceding claim, characterized in that the test specimen (10) subjected to three-point bending is such that 2 x hO < H2 < 5 x hO, preferably H2 = 4 x hO.

6. Test method according to any one of the preceding claims, characterized in that the test specimen (10) subjected to three-point bending is such that L1 > L2.

7. Test method according to any one of the preceding claims, characterized in that the test specimen (10) subjected to three-point bending is formed of two layers of identical materials assembled together, where the initial notch (40) extends parallel to the plane P at the interface located between the two layers of materials.

8. Test method according to the preceding claim, characterized in that the two layers of identical material of the test specimen (10) subjected to three-point bending each have the same thickness h2 in the thick part, with H2 = 2 x h2.

9. Test method according to any one of the preceding claims, wherein the specimen (10) is positioned horizontally, placed on two simple supports (20, 21, 22) and subjected to a load applied on the top of the specimen (10), and characterized in that: - a first simple support (21) is located under the thin part (H), - a second simple support (22) is located under the thick part (13), - the load (30) is applied on the thick part (13), in a longitudinal position along the axis X-X' located between the longitudinal position of the first support (21) and the longitudinal position of the second support (22).

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