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 the characterization of the toughness of interfaces in mode II 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 propagation of a crack 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 mode, which are illustrated in [Fig.l]. The invention focuses on 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, therefore at an interface, we speak of 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, which is broken by subjecting it to bending in order to estimate its resistance to the propagation of this defect. A specimen usually has the shape of a rectangular parallelepiped.

[0003] The ASTM D7905 / D7905M-14 standard describes a test for characterizing the propagation of a crack at an interface in mode II. The objective of such a test is to characterize the critical energy release rate during the propagation in mode II of a crack at the interface, as a function of its length. This is also referred to as 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 loading on a notched 10' specimen, where said 10' specimen is placed on two simple 20' supports and subjected to a 30' load applied from above in the middle of the 10' specimen.

[0004] The energy required to make the crack 40' grow by one unit area dS corresponds to the portion of energy GdS that would be elastically released 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] p = / J 7C 2 B to a

[0006] With: • the length of the crack (with a front assumed to be rectilinear) • B the width of the test piece • C the complacency or flexibility of the system • P the load seen by the system

[0007] A crack can propagate in a stable or unstable manner. For a crack to propagate in a stable manner, the load must always increase to allow the crack to propagate. In this case, the value of the energy release rate decreases with the length of the crack at a fixed load. Conversely, unstable propagation corresponds to an increase in the value of the energy release rate with the length of the crack 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, in particular 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 make the crack 40' propagate stably at most by a length of 0.3 times the aforementioned distance, but with a friction effect close to 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 the propagation is unstable, the compliance and the length of the crack cannot be measured during the test. Indeed, the stability domain, that is to say the interval of length of the crack for which the propagation is stable, is strongly 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 stressing the specimen without causing the crack to propagate. To do this, the specimen is successively moved 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 length of the crack, it is strongly desired to obtain stable propagation of the crack.

[0011] Other tests are also known for characterizing the propagation of a crack in an interface in mode II, but these are not the subject of a standard. Thus, the ONF test (from the English Over-Notched Flexure test) illustrated in [Fig. 4] and the 4ENF test (from the English 4-point bending End-Notched Flexure test) illustrated in [Fig. 5] are known, which make it possible to obtain stable propagation of the crack for bending loads at three and four points respectively. These tests are however sensitive to friction effects between the lips 41' of the crack 40', because the tip 42' of the initial crack 40' is positioned close to 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 measure the critical value of the critical energy release rate accurately, there is a need for a test making it possible to characterize the propagation of a crack of an interface in mode II, which makes it possible to improve the stability of a propagation of a crack while limiting the phenomenon of friction between the lips of the crack. 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 side opposite the first support point and distant from the initial notch.

[0014] One aspect of the invention relates to a test specimen for characterizing the energy release rate during mode II propagation of a crack, said specimen extending longitudinally along the axis X-X' in a plane P and having an initial notch extending over the entire width of the specimen along the axis X-X' parallel to the plane P, the specimen comprising three parts succeeding one another 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 thickness transition part having a thickness H1 which varies longitudinally along the X-X' axis and a non-zero length L1, this intermediate part being located between the thin part and the thick part, where H1 = H0 at the level of the thin part and H1 = H2 at the level of the thick part; and where • the initial notch is located at least in the thin part and is capable of propagating in the intermediate part and possibly in the thick part along the X-X' axis parallel to the plane P when the test piece is subjected to three-point bending.

[0015] With imposed 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 makes it possible to compensate for the decrease in stiffness with increasing crack length, so that this decrease in stiffness occurs less and less quickly with increasing crack length. Increasing the thickness advantageously allows to increase the domain for which the crack propagates in a stable manner as shown in the graph of [Fig.8]. Increasing the thickness of the specimen along the crack propagation path also allows to move this stability domain away from the point of application of the load and therefore to limit the effects of friction.

[0016] In addition to the characteristics which have just been mentioned in the preceding paragraph, the test piece 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 the thickness HO to the thickness H2, is linear; • the initial notch extends over the entire length of the thin part, in particular in order 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 reduces 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 piece is formed from two layers of identical materials assembled together, where the initial notch extends parallel to plane P at the interface between the two layers of materials; and • the two layers of identical materials 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 propagation of a crack at the interface, this test method being based on 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 piece is positioned horizontally, placed on two simple supports and subjected to a load applied to the top of the test piece, 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] The off-centering of the load application point and its shift toward the second support point advantageously amplify the two advantages mentioned above, namely the increase in the stability domain and the limitation of the effects of friction. The crack front is well located upstream of the load application point (and no longer downstream as for the 4ENF or ONF test), which makes it possible to further limit the effect of friction between the lips of the crack. It is necessary to experimentally measure the compliance as a function of the crack length to be able to estimate G by the relationship [Math 1]. On the other hand, since the propagation is stable, this is achieved during the test. It is then 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 information purposes only and in no way limit the invention.

[0022] [Fig.l] 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 complacency 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] In [Fig.2] to [Fig.6] the test piece is seen in profile and the crack propagation surface is represented by dotted lines. DETAILED DESCRIPTION

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

[0032] By convention, in the present application, by thickness of a part or a piece, we mean the height of said part or piece along an axis orthogonal to the plane P in which the test piece 10 extends, and by length of a part or a piece, we mean 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 test piece 10 extends longitudinally.

[0033] Similarly, conventionally, by three-point bending, we mean a test classical mechanics where a test piece 10 is placed on two simple supports 20 and subjected to a load 30 applied to the top of the test piece 10 with a simple contact. As a reminder, by simple support or simple contact, we mean a support or a point 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 energy release rate during mode II propagation of a crack at the interface.

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

[0036] The test piece 10 according to the invention is formed of three successive parts along the axis X-X', 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 reasons of simplification of reading, the first part 11 is hereinafter referred to as "thin part 11" and the second part 13 is referred to as "thick part 13".

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

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

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

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

[0041] Conventionally, the test piece 10 has an initial notch 40 extending over the entire width of the test piece 10 parallel to the plane P. This initial notch 40 extends along the axis X-X' in the thin part 11, with an emerging part 43 located at the free end of the thin part 11 (on the left in the figures). Opposite its emerging part 43 along the axis X-X', the initial notch 40 ends 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 in the intermediate part 12 and possibly in the thick part 13 along the axis X-X' parallel to the plane P when the test piece 10 is subjected to three-point bending.

[0044] The initial notch 40 divides the thin part 11 into two lips 41 each preferably having the same thickness h0. Thus, the thickness H2 is preferably between double and quintuple of H0, more preferably substantially quadruple 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 propagation of a crack 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 the 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 propagation surface 50 of the crack being substantially coincident. The two layers of materials preferably each have the same thickness h2 in the thick part 13, with H2 = 2 x h2.

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

[0047] As shown in [Fig.6], in this test method, the test piece 10 is positioned horizontally, placed on two simple supports 20, 21, 22 and subjected to a load 30 applied to the top of the test piece 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 (on the left in [Fig.6]), while the second simple support 22 is located under the thick part 13, at a distance D2 from the free end of the thick part 13 (on the right in [Fig.6]). The distances DI and D2 are for example slight excess lengths which ensure that the test piece 10 remains 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 above the test piece 10 to the thick part 13, with a simple contact at a point located at a distance D3 from the free end of the thick part 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 mainly from known tests, in particular from the ENF test of the ASTM D7905 / D7905M-14 standard and from the ONF and 4ENF tests, in that the test piece 10 has a thickness transition, with an 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 in the intermediate part 12. Depending on the material(s) from which the test piece 10 is made, the initial notch 40 may also, but not necessarily, depending on the test, propagate at least partially in 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] In order to demonstrate the advantages of the test method according to the invention, [Fig. 8] is a graph illustrating the stability domain of crack propagation for the ENF test (bold dotted curve) and for the test according to the invention (bold solid curve). The stability domain refers to an interval of crack length for which propagation is stable. The stability domain is characterized by the fact that, for the application of a given load (here the loading is carried out at imposed displacement), the energy release rate is lower if the crack length is greater. In the proposed example which made it possible to produce the graphs (with a test piece having a length of 200 mm), the solution of the invention makes it possible to obtain a stability domain DSinv of 100 mm against a stability domain DSenf of 30 mm for the reference test. In [Fig.8], these stability domains are represented by hatching. On this graph, the end located to the right of each curve corresponds to the position of application of the load.

[0053] Note that [Fig.8] is an example of the stability domain that exists for the dimensions of a given specimen, and serves to illustrate the potential of the proposed test. This domain 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 certain number of examples, variants and embodiments, the test piece according to the invention and the test method according to the invention using this test piece include various variants, modifications and improvements which will be obvious to those skilled in the art, it being understood that these variants, modifications and improvements are part of the scope of the invention.

Claims

Claims

1. Test specimen (10) for characterizing the energy release rate during mode II propagation of a crack, said specimen (10) extending longitudinally along the axis X-X' in a plane P and having an initial notch (40) extending over the entire width of the specimen (10) along the axis X-X' parallel to the plane P, characterized in that the specimen (10) comprises three parts succeeding each other longitudinally in a contiguous manner, 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 thickness transition part (12) having a thickness H1 varying 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 (ll) and Hl = H2 at the level of the thick part (13); and in that - the initial notch (40) is located at least in the thin part (11) and is capable of propagating in the intermediate part (12) and possibly in the thick part (13) along the axis X-X' parallel to the plane P when the test piece (10) is subjected to three-point bending.,

2. Test tube (10) according to claim 1, characterized in that the initial notch (40) extends over the entire length of the thin part (11).

3. Test piece (10) according to claim 2, characterized in that the initial notch (40) extends over the entire length of the thin part (11) and extends partially into the intermediate part (12).

4. Test piece (10) according to any one of the preceding claims, characterized in that the initial notch (40) divides the thin part (11) into two lips (41) each having the same thickness h0.

5. Test tube (10) according to the preceding claim, characterized in that 2 x hO < H2 < 5 x hO, preferably H2 = 4 x hO.

6. Test tube (10) according to any one of the preceding claims, characterized in that L1 > L2.

7. Test piece (10) according to any one of the preceding claims, characterized in that it is formed from two layers of identical materials assembled together, where the initial notch (40) extends parallel to the plane P at the level of the interface located between the two layers of materials.

8. Test tube (10) according to the preceding claim, characterized in that the two layers of identical materials each have the same thickness h2 in the thick part, with H2 = 2 x h2.

9. Test method for characterizing the energy release rate during mode II propagation of a crack at the interface, this test method being based on three-point bending of a notched specimen and characterized in that the notched specimen is a specimen (10) according to any one of the preceding claims.

10. Method according to the preceding claim, where the test piece (10) is positioned horizontally, placed on two simple supports (20, 21, 22) and subjected to a load applied to the top of the test piece (10), and characterized in that: - a first simple support (21) is located under the thin part (11), - a second simple support (22) is located under the thick part (13), - the load (30) is applied to 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).

Images