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Influence of the interface ply orientation on the fatigue behaviour of bonded joints in composite materials
International Journal of Fatigue 32 (2010) 82–93
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Influence of the interface ply orientation on the fatigue behaviour of bonded joints in composite materials Giovanni Meneghetti a, Marino Quaresimin b,*, Mauro Ricotta a a b
Department of Mechanical Engineering – University of Padova, Via Venezia 1, 35131 Padova, Italy Department of Management and Engineering – University of Padova, Stradella S. Nicola 3 – 36100 Vicenza, Italy
a r t i c l e
i n f o
Article history: Available online 15 February 2009 Keywords: Composite bonded joints Interface orientation Crack initiation Crack propagation Life prediction
a b s t r a c t The paper deals with the study of the fatigue behaviour of bonded joints in composite materials. The influence of the orientation of the composite layer at the adhesive–adherend interface is investigated on single lap joints prepared by carbon fabric/epoxy laminates bonded together with a two-part epoxy adhesive. Different laminate lay-ups ([45/02]s and [452/0]s), overlap lengths (20 and 40 mm) and corner geometry of bonded area (square edge and fillet, respectively) were investigated under tension–tension fatigue. Particular attention was devoted to the analysis of the fatigue damage evolution to identify initiation and subsequent growth of cracks. A previous model developed by the authors, for the prediction of the fatigue life of bonded joints as the sum of an initiation and propagation phase, was successfully applied to summarise the new data. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction The modification of the lay-up near the overlap area of a bonded joint allows a further and helpful variable to the design process of these structural connections in composite materials. The resulting changes in the overall behaviour of the joint can involve global, and independent, variation of tensile and bending stiffness [1,2] as well as local modification of the elastic properties of the facing materials. As a further consequence, the global stress distributions and those near the singular locations at the end of the bonded overlap [3,4] can be significantly altered, thus influencing the static and fatigue properties of the joint. Very few investigations are available in the literature on this subject and the findings about the influence of ply orientation at the adhesive/adherend interface on static and fatigue strength are not always consistent. Matthews and Tester [1] investigated the static properties of CFRP single lap joints made of UD laminates manufactured with several combinations of 0°, 45° and 45° layers. Joint strength was found to increase with proportion of 0° plies, the greatest values being obtained for all 0° joint. The lay-up and the overlap length were both found to influence the failure mode, with the stiffer joint usually failing in the adhesive. Renton and Vinson [5] tested glass/epoxy single lap joints with all 0° or 45/0/45/0 UD laminate adherends. They found a limited effect of the interface ply orientation on the static strength of the * Corresponding author. E-mail address: [email protected] (M. Quaresimin). 0142-1123/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2009.02.008
joints. However they reported a reduction of about 20–40% in the high cycle fatigue strength of the angle-ply construction when compared to that with all the plies aligned. In terms of damage evolution under fatigue loading, they identified adhesive failure for all the 0° joints, while the 45/0/45/0 failed in the 45° ply adjacent to the adhesive. Ferreira et al. [6], investigated the behaviour of [0]7 and woven glass/polypropylene single lap joints of differ½45=45=0 s ent overlap length. An average decrease of about 30% in the fatigue joints when compared to shear strength was found for ½45=45=0 s those made with [0]7 lay-up. In the extensive literature re-analysis on the behaviour of bonded joints in composite under cyclic loading presented in Ref. [7], De Goeij et al. indicated a negligible influence of the interface ply orientation on static strength, while under fatigue loading all 0° joints behave better than those with 45° and 90° oriented ply at the interface. Johnson and Mall [8], analysed the fatigue behaviour of carbon/ epoxy cracked lap shear joints made with three different lay-ups, namely [0/±45/90]s/[0/±45/90]2s, [±45/0/90]2s/[±45/0/90]2s, [90/ ±45/0]2s/[90/±45/0]2s, and bonded with two different adhesives, a thermosetting paste and a modified epoxy adhesive. Three interface conditions were thus investigated: 0/0, 45/45 and 90/90. For the 0/0 interface joints, initiation and growth of a fatigue crack occurred in the adhesive region. In the case of 45 interface plies, cracks initiated in the adhesive layer, then grew in the adhesive or as intraply failure in the ±45 layer and, eventually, propagated as delamination at the 45/0 interface. For the 90 interface plies the fatigue damage initiated as transverse cracks and then
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0
ΔHo vs Ni
Ni
Life for crack initiation
Nf
SERR vs da/dN Life for crack propagation
Table 1 Properties of Scotch Weld 9323 B/A adhesive [11]. E (MPa)
G (MPa)
m
sr (MPa)
2870
1050
0.37
39.1
Fig. 1. Schematic of modelling of the two phases of the joint fatigue life [10].
propagated as a combination of intraply failure and delamination. The authors concluded that 0/0 and 45/45 interfaces exhibited similar threshold for crack initiation, measured in terms of total strain energy release rate. However, although included in the experimental scatter, the average values they calculated for the 45/45 interface joints were about 10% higher than those for the 0/0 interface joints. 45/45 interfaces were also found to be stronger than the 90/90. The brief discussion above seems to indicate the absence, in general, of significant benefits from changing the interface ply orientation. However, the results of Johnson and Mall put some lights on the possible role, as a strengthening mechanism, of the more complicated damage evolution when the orientation at the adhesive/adherend interface is different from 0/0. In this work the fatigue behaviour of carbon fabric/epoxy single lap bonded joints is investigated with particular reference to the possible influence of stacking sequence and orientation of the layer at the adhesive–adherend interface. For this aim, the new results are compared with those of the previous research [9] on single lap joints made from [0]6 laminates of the same material. The influence of overlap length and corner geometry is also investigated together with the extensive assessment of the evolution of damage and crack patterns during fatigue life. Eventually, the new results are successfully summarised and described by a life prediction model recently presented by the authors [10]. The model is based on the actual mechanics of the fatigue damage evolution and describes the joint lifetime as the sequence of a crack nucleation phase followed by a propagation phase at the adherend/adhesive interface. As schematically shown in Fig. 1, the nucleation phase is described by using a generalised Stress Intensity Factor (SIF) approach, which rationalises the fatigue life to crack initiation. The life spent in the propagation phase can be obtained by the integration of a Paris-like power law relating the Strain Energy Release Rate (SERR) to the rate of crack growth.
well as the laminate and adhesive layer thickness, 1.65 mm and 0.15 mm, respectively. Two laminate lay-ups ([45/02]s and [452/0]s), two overlap lengths (20 and 40 mm) and two geometry corners (square edge and spew fillet) were investigated in the test programme. The manufacturing of the bonded panels was done according to the procedure reported in [9]. Only joints produced from laminates with peel-ply were tested. All the joints were cut from the bonded panels and tested at room temperature on a servo-hydraulic MTS 858 Mini Bionix II machine equipped with a 15 kN load cells. The static behaviour of the joints was investigated by means of tensile tests under displacement control with a crosshead speed equal to 2 mm/min. The fatigue tests were carried out under load control, with a sinusoidal wave, nominal load ratio R = 0.05 and a test frequency variable in the range of 10–15 Hz depending on the applied stress level. To investigate damage evolution during fatigue loading and to assess the fraction of life spent for crack nucleation and propagation, the joints were subjected to repeated blocks of fatigue loading at constant amplitude, up to the failure of the joint. At the end of each block, the damage patterns were observed and measured on the polished edges of the joints, by using a Leica Metallux 3 optical microscope equipped with a Leica camera DC 100 providing a geometrical accuracy of 0.05 mm. 3. Static test results The results of static tensile tests of the joints are summarised in Tables 2 and 3 and plotted in Fig. 3. Tensile strength data of the original laminates are included for comparison. Since the failure never involved the adhesive layer, results are presented in terms of nominal tensile stress on the adherends, simply calculated by dividing the applied tensile load by the transversal section of one adherend. Non-uniform stress distribution and stress singularity at the end of the overlap were not considered.
2. Materials, joint geometry and test procedures Tensile static and fatigue tests were carried out on single lap bonded joints, with the overall geometry shown in Fig. 2. The joints were manufactured from autoclave-moulded laminates (Seal TexipregÒ CC206, T300 twill 2 2 carbon fibre fabric/ET442 toughened epoxy matrix) and bonded with the two-part epoxy adhesive 9323 B/A by 3 M [11], the properties of which are given in Table 1. Joint width (24 mm) and overall length (260 mm) were kept constant as
Y
1.65
X
20
260
Y
Corner geometry
Overlap (mm)
rUTS (MPa)
c.o.v. (%)
Failure modea
Square edge
20 40
388 495
2.4 14.9
LF Mixed
Spew fillet
20 40
459 434
0.3 21.8
LF Mixed
a LF: laminate failure at the end of bonded area (see Fig. 4); mixed: laminate failure and damage of the bonded layer; (tensile strength of [45/02]s laminates 500 MPa c.o.v. 12%).
F
w = 20, 40
24
Table 2 Tensile strength of [45/02]s joints.
SE
Table 3 Tensile strength of [452/0]s joints. Corner geometry
Overlap (mm)
rUTS (MPa)
c.o.v. (%)
Failure modea
Square edge
20 40
324 336
4.1 5.8
LFF LFF
Spew fillet
20 40
333 319
1.6 3.6
LFF LFF
X
Lay-up: [45/02]s; [452/0]s Fig. 2. Geometry of the single lap bonded joint (w = 20 and 40 mm). SE = square edge joint; F = fillet joint.
a LFF: laminate failure far from the end of the overlap (see Fig. 5); (tensile strength of [452/0]s laminates 350 MPa c.o.v. 4%).
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600 200
400
σmax [MPa]
Tensile strength [MPa]
500
300 200
[45/02]s square edge SE F[45/02]s fillet
100
SE [452[452/0]s /0]s square edge F[45 [452/0]s 2/0]s fillet
100
40
1E3
[0]6 w=40 mm, from ref. [9] [45/02]s w=40 mm [452/0]s w=40 mm [0]6 w=20 mm, from ref. [9] [45/02]s w=20 mm [452/0]s w=20 mm
1E4
0 20
1E5 Cycles to failure
1E6
1E7
40 Overlap length [mm]
Fig. 6. Influence of the overlap length on the fatigue strength of square edge joints (fatigue curves plotted are for [0]6 joints).
Fig. 3. Tensile test results for [45/02]s and [452/0]s joints (error bar = one standard deviation).
Failure of [45/02]s joints was characterised by different modes, as described in Table 2 and shown in Fig. 4: laminate failure at the end of the bonded area for 20 mm overlap joints (see Fig. 4) and mixed failure for those with 40 mm overlap. In the latter case, irrespective of corner geometry, joints exhibited significant and simultaneous damage both in the bonded layer and in the laminate far from the overlap end. This is the reason for the large scatter obtained and also of the unexpected (and unrealistic) decrease in the average strength for 40 mm spew fillet joints.
For the [452/0]s joints, tensile strength turned out to be independent from overlap length and corner geometry; this is justified by the fact that joints failed always in the laminates, far from the end of the overlap, as shown in Fig. 5. In this case the scatter of experimental data is clearly reduced and the strength of the joints is comparable with that of the original laminates. 4. Fatigue behaviour Figs. 6 and 7 show the fatigue data for square and spew fillet joints, respectively, in terms of maximum tensile stress on the
Fig. 4. Examples of static failure at the end of the bonded area for [45/02]s joints.
Fig. 5. Static failure in the adherends, outside the bonded area for [452/0]s joints.
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w=40 mm 200
σmax [MPa]
σmax [MPa]
200
100
40
1E3
[0]6 w=40 mm, from ref. [9] [45/02]s w=40 mm [452/0]s w=40 mm [0]6 w=20 mm, from ref. [9] [45/02]s w=20 mm [452/0]s w=20 mm 1E4
1E5 Cycles to failure
40
1E6
1E7
Fig. 7. Influence of the overlap length on the fatigue strength of spew fillet joints (fatigue curves plotted are for [0]6 joints).
adherends. Data previously obtained on [0]6 joints, taken from Ref. [9], are included for comparison. It can be observed that the presence of the 45° interface provides a slight improvement in the fatigue behaviour with respect to the 0° interface joints, only for the square edge corner geometry (Fig. 6). It is also seen that the fatigue strength is enhanced by increasing the overlap length, whatever the adopted stacking sequence. Moreover, by grouping the available results of the same overlap length, Figs. 8 and 9 show that the spew fillet geometry significantly extends the fatigue life with respect to the square edge geometry. A life extension factor of about one order of magnitude for the same applied load level can be observed for joints with 20 mm overlap. For the 40 mm overlap length joints, Fig. 9 shows a life extension factor of about three. It can be concluded that the changes in the fatigue strength due to the changes in stacking sequence and interface ply orientation are less significant that those introduced by modifying the corner geometry or increasing the overlap length. It is interesting to note that the ratio of the fatigue strengths for the same lay-up but different overlap lengths (20 or 40 mm) is in general different from two (see Figs. 6 and 7 and Table 4), then the effect of the overlap length on the fatigue behaviour of the joints cannot be rationalised by means of the mean shear stress calculated referring to the overlap area. As previously said, a different stress parameter based on the stress field intensity close to the
w=20 mm
σmax [MPa]
200
100
40
1E3
[0]6 fillet, from ref. [9] [45/02]s fillet [452/0]s fillet [0]6 square edge, from ref. [9] [45/02]s square edge [452/0]s square edge 1E4
1E5 Cycles to failure
100
1E6
1E7
Fig. 8. Influence of corner geometry on the fatigue strength of joints with 20 mm overlap length.
1E3
[0]6 fillet, from ref. [9] [45/02]s fillet [452/0]s fillet [0]6 square edge, from ref. [9] [45/02]s square edge [452/0]s square edge 1E4
1E5 Cycles to failure
1E6
1E7
Fig. 9. Influence of corner geometry on the fatigue strength of joints with 40 mm overlap length.
crack initiation point (namely the H0 parameter) should be used. Anyway such a parameter hardly correlates the total fatigue life since fatigue cracks were observed to spend only a fraction of the total fatigue life in the small zone were stresses are governed by H0. As briefly discussed in the introduction and suggested in the previous papers [9,10], the following choices were made: the total fatigue life was thought of as divided into life spent to nucleate a crack and life spent to propagate the crack up to final joint failure; the problem of a scientific definition of ‘crack initiation phase’ was not attacked, while a separation between crack initiation phase and crack propagation phase was based on the observation of a so-called (small) ‘technical crack’ having a fixed size related to the resolution of the inspection device adopted in the laboratory tests. That said, in the following paragraph a description of the fatigue damage evolution observed during the tests is reported, since the design approach proposed for bonded joints under cyclic loading is connected to our experimental findings. With the aim to supply the complete scenario of fatigue test results to the reader, Table 4 summarises the results of the statistical analysis of the available data, by assuming log-normal distribution of the number of cycles to failure. In the table the reference stress values at 2 106 cycles for a probability of survival of 50% and 90%, the value of the inverse slope k of S–N curves and the scatter index Tr (Tr = rMax,10%/rMax,90%) are listed. Eventually, as a general comment about the structural ‘‘efficiency” of this type of joint, it can be worth noting that the introduction of a bonded connection in a structural component could be not too harmful in terms of static strength, while leading to significant reductions in its load bearing capability under cyclic loading. This reduction can be quantified by calculating the ratio between the fatigue strength at two million cycles of the joints and the static strength of the plain laminate. The values of this ratio range from 0.10, in the case of [45/02]s square edge joints w = 20 mm, up to 0.31, in the case of [452/0]s fillet joints (w = 40 mm). Lower values, from 0.09 to 0.17, were reported in [9] for [0]6 joints. These values have to be compared with those one could expect for the plain laminates the joints are made of, ranging from 0.5 to 0.75 in the case of tension–tension fatigue loading [12]. In overall analysis of the results discussed in the work it should be kept in mind that the joints tested here were manufactured by
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Table 4 Results of the statistical analysis for the different series of fatigue data (fatigue strength values at 2 106 cycles). Lay-up
Corner geometry
Overlap (mm)
rVAX, 50% (MPa)
rVAX, 90% (MPa)
k
Tr
No. of data
[45/02]s
Square edge
20 40 20 40
51.3 101.5 89.8 125.5
46.5 – 73.9 110.1
5.47 8.38 8.07 9.08
1.215 – 1.479 1.300
4 2 4 4
20 40 20 40
52.8 94.2 79.4 107.0
42.2 82.8 71.3 97.5
4.77 6.15 7.31 5.62
1.646 1.295 1.240 1.204
5 4 6 5
Fillet [452/0]s
Square edge Fillet
bonding laminates made from fabric reinforced plies. Hence the conclusions provided are limited to this class of materials, while the behaviour of the joints made from UD ply-laminates could be different. 5. Fatigue damage evolution Let us now consider separately the fatigue damage evolution observed in spew fillet joints and square edge joints. Fig. 10a shows a typical crack path, as observed in the edge view of spew fillet joints. Independently on the applied load level, cracks were observed to initiate very near the toe of the bonded joint, close to the central position along the specimen width. In very few cases cracks were observed to initiate at the upper corner point between the adhesive and the laminate free surface (see Fig. 10b). An example of crack nucleation at the free surface of the adhesive fillet is presented in Fig. 11: in this case the adhesive whitening could be easily observed by eye. The number of cycle to initiate a crack in the fillet, detectable by visual inspection, which corresponds to the true crack nucleation was defined as Nit. After nucleation, the crack propagates along the specimen width toward the joint edges and then along the specimen longitudinal axis at the interface between adhesive and adherends as shown in Fig. 10a and b. Cracks emanating from the four corners of the joints, indicated as A, B, C and D in Fig. 12, were usually observed. According to what already done in the previous research [9], when one of these cracks reached the conventional length of 0.3 mm, measured on the laminate edge, that was identified as the ‘‘technical” crack initiation and the correspondent number of cycle as ‘number of cycle to crack initiation’ Ni. The life spent to propagate a crack up to final fatigue failure (Nf) was then calculated as the difference between the total life and the life to ‘‘technical” crack initiation and identified as number of cycles to crack propagation, Np. During the propagation phase, very complicated crack paths were usually observed. In par-
Fig. 12. Definition of ‘‘technical” crack for the evaluation of ‘‘technical” number of cycle to crack initiation, Ni, for square edge and fillet joints.
Fig. 10. Crack nucleation sites and crack paths in spew fillet joints.
ticular, cracks deviated from the interface adhesive-adherend path to become intralaminar and/or interlaminar before turning again along the main interface path, as widely described in Ref. [13]. The apparent inconsistency of considering as life to crack initiation Ni and not Nit can be clarified by considering that the propagation from the nucleation site in centre of the joint to its edges (in terms of number of cycles from Nit to Ni) occurs in a region fully controlled by the local stress field and by H0. Therefore, considering the crack initiation phase to be completed only after the crack has propagated in the joint width direction is consistent with both experimental observations and local stress analysis. As a further support of the choice made, the definition of a ‘‘technical crack” is the only possibility of identifying initiation in the square edge joints, where the observation of true crack nucleation via adhesive whitening, even if present, is impossible from a practical point of view due to the reduced thickness of the adhesive layer (0.15 mm). In this conditions, only a ‘‘technical” crack
Fig. 11. Crack initiation identified by adhesive whitening in a fillet joint.
Crack initiation D C A B
0.3
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initiation can be defined in correspondence of the number of cycles at which a crack of 0.3 mm is observed near one of the four corner of the joint. Then Fig. 12 holds true again in order to define the ‘‘technical” crack initiation stage.
Damage patterns during propagation were similar to those observed for fillet joints. Fig. 13 shows a typical example of initiation and crack propagation path at the adhesive–adherend interface, while Fig. 14 shows
Fig. 13. Interface crack initiation and propagation path in a square edge joint (lay-up [45/02]s; rmax = 65 MPa, w = 20 mm, Nf = 588,737 cycles).
Fig. 14. Crack initiation and intralaminar/interlaminar crack path in a square edge joint (lay-up [45/02]s; w = 20 mm, rmax = 95 MPa, Nf = 78,209 cycles).
Table 5 Results of block loading fatigue tests for [45/02]s joints. Corner geometry
Overlap (mm)
rmax (MPa)
Nit
Ni cycles
Nf cycles
Np cycles
Nit/Nf
Ni/Nf
Square edge
20 20 20 20 40 40 40
95 65 95 65 120 90 80
– – – – – – –
30,000 76,470 17,000 150,000 105,000 1,100,000 2,300,000
78,209 588,737 59,600 503,791 492,496 5,484,544 –
48,209 512,267 42,600 353,791 387,496 4,384,544 –
– – – – – – –
0.38 0.29 0.30 0.13 0.21 0.20 –
Fillet
20 20 20 20 40 40 40 40
126 126 100 100 180 180 125 125
83,000 47,000 310,000 300,000 2000 40,000 400,000 510,000
121,000 68,000 980,000 530,000 7000 55,000 1,610,000 1,085,000
182,091 93,220 1,163,120 609,618 63,735 90,237 2,819,191 1,533,993
61,091 25,220 183,120 79,618 56,735 35,237 1,209,191 448,993
0.46 0.50 0.27 0.49 0.031 0.44 0.14 0.33
0.67 0.73 0.84 0.87 0.11 0.61 0.57 0.71
Ni cycles
Table 6 Results of block loading fatigue tests for [452/0]s joints. Corner geometry
Overlap (mm)
rmax (MPa)
Nit
Square edge
20 20 20 20 20 40 40 40 40
95 95 65 65 65 145 145 120 120
– – – – – – – – –
Fillet
20 20 20 20 20 20 40 40 40 40 40
126 126 126 100 100 85 180 180 140 140 125
3000 15,000 2000 25,000 100,000 385,000 2000 250 100,000 50,000 30,000
Nf cycles
Np cycles
Nit/Nf
Ni/Nf
45,000 20,000 130,000 128,000 410,000 15,000 15,000 63,000 43,673
165,262 88,557 543,245 690,354 1,083,720 131,433 152,429 565,193 362,839
120,262 68,557 413,245 562,354 673,720 116,433 137,429 502,193 319,166
– – – – – – – – –
0.27 0.23 0.24 0.19 0.38 0.11 0.10 0.11 0.12
15,000 40,000 78,000 155,000 330,000 1,008,229 40,000 32,000 200,000 100,000 200,000
53,000 65,393 100,141 269,691 420,000 1,364,877 93,837 120,631 536,847 395,767 790,000
38,000 25,393 22,141 114,691 90,000 356,648 53,837 88,631 336,847 295,767 590,000
0.057 0.23 0.020 0.093 0.24 0.28 0.021 0.002 0.19 0.13 0.04
0.28 0.61 0.78 0.57 0.79 0.74 0.43 0.27 0.37 0.25 0.25
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Lay-up [452/0]s
200
w=20 mm
100
σmax [MPa]
σmax [MPa]
200
fillet square edge
40
1E3
1E7
Fig. 15a. Influence of corner geometry on crack initiation.
σmax [MPa]
w=20 mm
100
fillet square edge
1E3
1E4 1E5 1E6 Cycles for crack propagation, Np
1E7
Fig. 15b. Influence of corner geometry on crack propagation.
an example of fatigue damage evolution involving intralaminar/ interlaminar crack propagation paths. It is worth noting that for all bonded joints, either fillet or square edge, the crack length was measured by projecting the observed crack path onto the adhesive–adherend interface plane and the resulting projected length, including either interface crack and/ or delamination, was referred as ‘‘nominal” crack.
σmax [MPa]
100 Lay-up [452/0]s
1E3
1E3
1E4 1E5 1E6 Cycles for crack propagation, Np
1E7
Tables 5 and 6 summarise fatigue life as well as the relevant initiation and propagation fraction for the different tested joints. For the spew fillet joints two sets of data are also reported, namely Nit/ Nf and Ni/Nf ratios, being valid the previous definitions of Nit and Ni. For the square joints, only the Ni/Nf set of data is reported due to the impossibility, as discussed above, to detect the initiation, if any, at the central location of the joint. It is seen that for the same lay-up and over lap length, the fillet configuration significantly extends the normalised crack initiation phase with respect to the square edge configuration. The same conclusion can be drawn also from Fig. 15a, which is representative of the general behaviour of the joints: an extension of the crack initiation life for the same load level can be observed for fillet joints while, as expected, crack propagation life is almost the same independently on the corner configuration (Fig. 15b). Fig. 16a and b show the influence of overlap length on the initiation and propagation fatigue life, observed on [452/0]s square edge joints. Joints with 40 mm overlap experienced both a longer life to crack initiation and a longer propagation phase when compared, at the same stress level, with shorter overlap joint. This result is in agreement with the modelling approach discussed in the introduction. In fact, as discussed in more detail in the next paragraphs, shorter overlaps induce higher values of the generalised Stress Intensity Factor and therefore shorter life to crack initiation. At the same time the Strain Energy Release Rate for a cracked joint with 20 mm overlap is more than twice that of a joint with 40 mm overlap, by keeping constant both the crack length and the applied stress. This leads to a reduced propagation life for joints with shorter overlap. 6. Summary of initiation lives in terms of generalised stress intensity factor ‘H0’
200
40
w=40 mm w=20 mm
Fig. 16b. Influence of overlap length on crack propagation.
Lay-up [452/0]s
40
Lay-up [452/0]s 40
1E4 1E5 1E6 Cycles for crack initiation, Ni
200
100
w=40 mm w=20 mm
1E4 1E5 1E6 Cycles for crack initation, Ni Fig. 16a. Influence of overlap length on crack initiation.
1E7
As previously mentioned, neither the nominal stress acting on the adherend nor the average shear stress acting over the adhesive area are parameters suitable to rationalise the fatigue strength of the tested bonded joints. In order to summarise the fatigue strength of all the tested joints, a different stress parameter should be used, namely the intensity of the local stress field calculated close to the crack initiation point. Such a parameter has already been suggested in the past [14,15] and proved [10] to be able to rationalise the fatigue life to crack initiation of bonded joints having different overlap length. In the present paper the additional effect of the lay-up stacking sequence is considered. The theoretical basis for the stress analysis of bonded joints can be found elsewhere [3,4,14]. Here it is important to recall that being the radius
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at the toe of the bonded joints variable not only for different joints but even along the same bead, the corner configuration has been assumed to be geometrically singular both for fillet and for square edge joints. That is the root radius at the toe of the joint has been assumed to be equal to zero, according to the sketch reported by Fig. 17. The second reason why the local stresses are singular is due to the mismatch between the elastic properties of the adhesive and the adherend. The asymptotic stress field close to the singular point can be expressed by a stress expansion, in variable separable form, that describes analytically the entire stress distribution and can be conveniently truncated in many cases of practical interest [14]. The generalised stress intensity factor associated to the first term of such stress expansion, denoted by H0, depends on boundary conditions and joint configuration, the relevant singularity power associated is denoted by s and depends on both local geometry and elastic properties of the matching materials. As said above, H0, has been suggested as the controlling and unifying parameter for fatigue crack initiation. The reader is referred to Refs. [14,15] for a comprehensive treatment on this subject. In order to assess the generalised stress intensity factor H0, according to the previous research [4], linear elastic plain-strain numerical models were defined by using AnsysÒ 11.0 numerical code. Eight-node PLANE82 finite elements as available in Ansys element library were adopted. The in-plane elastic properties of the basic lamina (EX, EZ, GXZ, tXZ) were measured from suitable experimental test (for the frame of reference, see Fig. 2), the offaxis properties were calculated with the classical formulation of the theory of elasticity for orthotropic bodies and finally the outof-plane properties were estimated on the basis of morphological and micromechanical considerations. Table 7 lists the elastic properties of the basic lamina. Being the [45/02]s and [452/0]s laminates more compliant in bending than the [0]6 investigated in Ref. [4], one could argue that linear elastic analyses are not suitable or enough accurate anylonger for properly describing the singular stress fields and generalised stress intensity factor H0 near the critical locations in the joints. However, it should be also noted that the out-of-plane bending of the joints under tension is still negligible before crack starts to propagate and that the adoption of geometrical linear instead of non-linear analyses implies a significant saving in calculation time and, most of all, H0 values independent from the applied stress level. Therefore, it was decided to maintain the approach proposed in [4] and to investigate the stress field in the uncracked joints via linear elastic analyses. Fig. 17 shows the local frame of reference adopted in the analysis and an example of the singular stress distributions calculated along the adhesive–adherend interface. By analysing the stress– distance data obtained from the finite element analyses, the stress parameter H0 and the relevant exponent s (representative of the degree of singularity) can be calculated for each lay-up and overlap length. Being the numerical analyses linear, Table 8 summarises the results in terms of ratio between the local stress parameter H0 and the applied nominal stress r0. Table 8 clearly shows that H0/r0 increases as the overlap length decreases: these results explain the experimental fatigue behaviour, where the life to crack initiation increases while increasing the overlap length (see Fig. 16a). It is also worth noting that the stress singularity exponent s is not influenced by the lay-up sequences since the elastic material properties at the interface are
Table 8 Strength of singularity s and normalised values of generalised stress intensity factors H0. Square edge
Fillet
[45/02]s s = 0.432
[452/0]s s = 0.432
[45/02]s s = 0.226
[452/0]s s = 0.226
w (mm)
H0/r0 (mms)
H0/r0 (mms)
H0/r0 (mms)
H0/r0 (mms)
20 40
0.2374 0.2091
0.2585 0.2268
0.1900 0.1664
0.2076 0.1816
Data for [0]6 joints, from Ref. [4] s = 0.423 w (mm) H0/r0 (mms)
s = 0.199 H0/r0 (mms)
20 40
0.1683 0.1493
0.1713 0.1577
the same for both the lay-ups. Due to the different degree of singularity of the stress field pertinent to the two corner geometries, two sets of homogeneous data for square edge and fillet joints have to be defined. Figs. 18 and 19 show the available fatigue data in terms of range of variation of H0, DH0, for fillet and square edge joints, respectively. In order to appreciate the unifying capability of H0, the same data are also plotted in terms of nominal stresses. Both figures highlight that the scatter of the life to crack initiation is significantly reduced if the local rather than the nominal stress approach is adopted, as shown by the reduced values of the TH0 scatter index with respect to those of Tr. The scatter bands are defined in both cases for a survival probability of 10% and 90%, respectively, with a confidence level of 95%. In view of a comparison between the present fatigue data and those generated on [0]6 joints [9], Figs. 18 and 19 report also the previous H0-based fatigue curve with a survival probability of 50%. It is seen that a slight difference between the [0]6 and the present H0-fatigue curves exists, the higher difference of about 10% in strength being valid for square edge joint. However, it should be kept in mind that, in strict sense, the direct comparison of the H0-fatigue curves is not formally correct due to the difference in the degree of singularity of 0° and 45° degree interface (see again Table 8). Being this difference reasonably small, the comparison can be acceptable from an engineering standpoint. 7. Summary of crack growth data As explained before, fatigue crack growth was monitored at the four joint corners A, B, C and D (see Fig. 12) and the ‘‘nominal” crack length at each corner was measured from the projection on the adhesive–adherend interface of the observed crack path (including interface crack and/or delamination). To reduce the number of data to deal with and for an easier and more reliable modelling, (i) a linear crack front and (ii) a symmetrical crack propagation were assumed, according to what already suggested in [4,9]. As a consequence the mean value of the four ‘‘nominal” crack lengths was assumed as relevant in the subsequent crack growth calculations. Fig. 20 shows, as an example, the mean crack length versus the number of cycles as measured on some fillet joints; data previously obtained for [0]6 joints are included for comparison. Data in this form were then processed in order to calculate the crack growth
Table 7 Elastic properties of woven lamina used for FE analyses. EX (MPa)
EY (MPa)
EZ (MPa)
GXY (MPa)
GYZ (MPa)
GXZ (MPa)
mXY
mYZ
mXZ
58,050
6000
58,650
500
500
3300
0.27
0.27
0.06
90
G. Meneghetti et al. / International Journal of Fatigue 32 (2010) 82–93
σϑϑ σrϑ
y 0°
r
ϑ
Average nominal crack length [mm]
100
σrr
MATERIAL adhesive2
x
10
MATERIAL adherend1
σij/σnom
σrr-laminate
σrr-adhesive
1
σrθ
σθθ
Lay-up [45/02]s w=40 mm 0.1 1.E-03
[45 2/0] s; σL(100MPa) [452/0]s; max=100 MPa ] ; [45/0 σ 2 s L(100MPa) max=100 MPa [45/02]s; ; =113 MPa [0] σ 6 max [0]6
10
w=20 mm
5
0 0.0E+00
1.E-02
1.E-01
5.0E+05 Number of cycles
1.E+00
r/tadhesive
1.0E+06
Fig. 20. Crack length evolution for spew fillet joints.
Fig. 17. Local frame of reference and stress distributions at adhesive–adherend interface for [45/02]s fillet joint and overlap length 40 mm.
1.E-02 w=20 mm
1000
]
10
k=5.64
10
11.93 w=20 mm; [45/02]s w=40 mm; [45/02]s w=20 mm; [452/0]s
1.E-04
1.E-05 [45/(0)2]s; H (95MPa) [45 = 95 MPa 2/0] s; σmax [45/(0)2]s; L (65MPa) [45 2/0] s; σmax = 65 MPa [(45)2/0]s; H (95MPa) [45/0 2]s; σmax = 95 MPa [(45)2/0]s; L (65MPa) [45/0 2]s; σmax = 65 MPa
1.E-06
TH0 = 2.28
[0]6
1.E-07
w=40 mm; [452/0]s
1 1.E+04
da/dN [mm/cycle]
σmax [MPa]
100
0.43
Tσ = 3.02
100
1.E-03
ΔH0 [MPa mm
1000
0
1 1.E+07
1.E+05 1.E+06 Cycles for crack initiation
0.1
0.2
0.3
0.4
0.5
a/w Fig. 21. Trends of the crack growth rate for square edge joints.
Fig. 18. Comparison between S–N curve approach and local approach on fatigue crack initiation for [45/02]s and [452/0]s square edge bonded joints.
1000
1000
100
0.23
10
ΔH0 [MPa mm
σmax [MPa]
k=8.26
]
Tσ = 1.92
100 TΗ0 =1.51 16.27
10
[0]6
w=20 mm ; [45/02]s
Fig. 22. Deformed shape of a cracked joint and details of the FE model at the interface crack [4].
w=40 mm ; [45/02]s w=20 mm ; [452/0]s w=40 mm ; [452/0]s
1 1.E+03
1.E+04
1.E+05
1.E+06
1 1.E+07
Cycles for crack initiation Fig. 19. Comparison between S–N curve approach and local approach on fatigue crack initiation for [45/02]s and [452/0]s fillet bonded joints.
rates. In view of this, piece-wise second order polynomials were adopted to fit the data according to the suggestion of ASTM 64700 [16]. Results obtained for 20-mm-overlap square edge joints are shown in Fig. 21. For an easier comparison, the crack growth rate is plotted versus the average nominal crack length a normalised to the overlap length w. A clear influence of the applied stress
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G. Meneghetti et al. / International Journal of Fatigue 32 (2010) 82–93 Table 9 Paris curve data calculated for different probability of survival.
1200 GGtot,[452/0]s tot, [45 2/0]s GGtot,[45/02]s tot, [45/0 2]s GGtot,[0]6 tot, [0] 6 GG1,[452/0]s I, [45 2/0] s GG1 I, [45/0 2]s GG1,[0]6 I, [0] 6 GG2,[452/0]s II, [45 2/0] s GG2 II, [45/0 2]s GG2,[0]6 II, [0] 6
2
SERR component [J/m ]
1000
800
600
w= 20 mm σmax=100 MPa for [45 2/0] s σmax=100 MPa for [45/0 2]s σmax=110 MPa for [0] 6
DGeqv (J/m2)
DGtot (J/m2)
Data for [45/02]s and [452/0]s joints (analysed together) 50% P.S. D = 1.169 1011 n = 2.688 D = 4.058 1011 n = 2.688
D = 1.664 1011 n = 2.731
Data for [0]6 joints, from Ref. [10] 50% P.S. D = 2.421 1011 n = 2.723
D = 1.354 1011 n = 2.729
D = 9.658 1011 n = 2.723
D = 5.235 1011 n = 2.729
90% P.S.
400
D = 4.766 1012 n = 2.731
90% P.S.
200
1.E-02
0 0
0.1
0.2
0.3
0.4
[0]6
0.5
a/w
1.E-03
level can be recognised, i.e. higher fatigue stress results in faster crack propagation. For summarising the crack growth data in a Paris-like diagram, the Strain Energy Release Rate (SERR) was assumed to be the crack driving force. In order to estimate the SERR parameters for a given crack length, two-dimensional plain-strain finite element model were defined by using AnsysÒ software. For the sake of simplicity, cracks were always supposed to propagate symmetrically along the adhesive–adherend interface. Fig. 22 shows a schematic of the model adopted and details of the mesh close to the interface crack. Under tensile loading the out-of-plane bending of the uncracked joint can be neglected. Conversely, during the propagation phase the bending compliance of the specimen increases as the crack propagates. As a consequence, linear elastic models are not appropriate any longer to describe the stress distributions. Then geometrically non-linear analyses were performed when modelling the crack propagation phase. In order to calculate the SERR parameter the Virtual Crack Closure Technique (VCTT) was adopted [17–19]. Details on the application of such a technique are reported in Ref. [4]: here it is important to recall that the adopted mesh density was carefully calibrated to avoid the problems associated to the oscillating stress field near the interface crack tip. This required an element size on the order of 0.03 mm (see again Fig. 22). As an example of the results, Fig. 23 plots the SERR components as calculated from the non-linear finite element analyses valid for 20-mm-overlap joints. Mode I and Mode II components are reported, trends for [0]6 joints are again included for comparison. Having in hands rates of crack propagation and SERR trends it was possible to draw a Paris-like diagram, expressed in the form:
da ¼ D ðDGeqv Þn dN
ð1Þ
where DGeqv = (Geqv,max Geqv,min) is the range of equivalent SERR, as defined in [4], which represents one of the possibility to account for the combined presence of Mode I and Mode II loading (opening and sliding modes at the crack tip) and to the variation of the mode mixity during the fatigue life. The expression already proposed by the authors is reported in Eq. (2) for clarity.
Geqv ðaÞ ¼ GI ðaÞ þ
GII ðaÞ GII ðaÞ GI ðaÞ þ GII ðaÞ
ð2Þ
da/dN [mm/cycle]
Fig. 23. Trends of SERR components and influence of laminate lay-up.
1.E-04
10%
1.E-05 90% 50%
1.E-06
Serie1 [45/02]s Serie3 [452/0]s
1.E-07 10
100
1000
10000
ΔGeqv [J/m2] Fig. 24. Crack propagation scatter band for all the joints tested (crack growth rate vs. range of the equivalent SERR).
Results are summarised in Table 9 and in Fig. 24 where the relevant 10–90% scatter band is also plotted. As a comparison, the average curve previously found for [0]6 joints is also reported. It is seen that the lay-ups under investigation are characterised by a greater resistance to crack growth. A reason for that might be the much more complicated damage patterns observed in the specimens having a 45° interface tested in the present work with respect to those having a 0° interface tested previously. It is also worth noting from Table 9 that the D and n parameters characteristic of the crack propagation curve do not differ so much when the total SERR Gtot, defined as
Gtot ðaÞ ¼ GI ðaÞ þ GII ðaÞ
ð3Þ
rather than the equivalent SERR is considered in the analysis. 8. Life prediction A model has been recently presented by the authors [10] which describes the fatigue life of bonded joints in composite materials as the sum of the number of cycles needed to nucleate a fatigue crack Ni and the number of cycles Np required by this crack to propagate up to a critical length. Similarly, in the present paper the use of the proposed design curves for estimating the fatigue crack initiation life (see Figs. 18 and 19) and the crack propagation life (see Fig. 24), respectively, has been validated by comparing the experimental mean fatigue curves of the different test series with those estimated by adding
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G. Meneghetti et al. / International Journal of Fatigue 32 (2010) 82–93
Ni and Np. For a comprehensive description of the application procedure the reader is referred to Ref. [10]. In very brief, the assessment of the number of cycles to crack initiation is made from the
σmax [MPa]
σmax [MPa]
Overlap length: 20 mm Lay-up [45/02]s
200
Overlap length: 40 mm Lay-up [452/0]s
200
100
100
Experimental data Estimated life Nf (50% P.S.) 1E3 Experimental data Estimated life Ni (50% P.S.) 1E3
1E4
1E7
Fig. 25. Experimental 10–90% scatter band of the life to crack initiation for [45/02]s fillet joints (overlap 20 mm) compared with the model predictions.
Overlap length: 20 mm Lay-up [45/02]s
σmax [MPa]
100
Experimental data Estimated life Np (50% P.S.) 1E3
1E4 1E5 1E6 Cycles for crack propagation, Np
1E7
Fig. 26. Experimental 10–90% scatter band of the life to crack propagation for [45/ 02]s fillet joints (overlap 20 mm) compared with the model predictions.
Overlap length: 20 mm Lay-up [45/02]s
σmax [MPa]
200
100
Experimental data Estimated life Nf (50% P.S.) 1E3
1E4
1E5 1E6 Cycles to failure
1E7
Fig. 28. Experimental 10–90% scatter band of the fatigue data at failure for [452/0]s fillet joints (overlap 40 mm) compared with the model predictions.
1E5 1E6 Cycles for crack initiation, Ni
200
1E4
1E5 1E6 Cycles to failure
1E7
Fig. 27. Experimental 10–90% scatter band of the fatigue data at failure for [45/02]s fillet joints (overlap 20 mm) compared with the model predictions.
relevant DHo Ni scatter band (see Figs. 18 and 19) once the generalised stress intensity factor for the stress level of interest is evaluated. The number of cycle for crack propagation is obtained by integration of the crack propagation curve (Eq. (1), Table 9 and Fig. 24). The upper limit of the integration, that is the final crack length, is calculated by equating the equivalent SERR to the Mode I fracture toughness GIc (900 J/m2) of the adhesive, while the lower limit of integration corresponds to the ‘‘technical” crack (equal to 0.3 mm). The equivalent SERR as a function of the crack length ‘‘a” is obtained from non-linear finite element analyses (see, as an example, Fig. 23). The above procedure has been applied to all the available fatigue data by using the 50% survival probability curves for both crack initiation (see Figs. 18 and 19) and crack propagation (see Fig. 24). As representative comparisons, Figs. 25–27 show the predicted life to crack initiation, life for crack propagation, and total life, respectively, compared with the relevant 10–90% P.S. experimental scatter band for one of the series tested. A good agreement can be observed. For completeness, Fig. 28 shows the worst case obtained from this analysis. It can be noted that the prediction is, however, on the safe side and the predicted total life curve is still inside the 10–90% P.S. experimental scatter band. 9. Conclusions The fatigue behaviour of single lap bonded joints in composite materials with different stacking sequence and orientation of the ply at the adhesive–adherend interface was investigated. The main conclusions of the work can be summarised as follows: The presence of the 45° interface provides only a slight improvement in the overall fatigue strength when compared with previous data on [0]6 joints while resistance to crack propagation is significantly increased by the 45° interface. Joints made from [45/02]s and [452/0]s laminates behave similarly. The improvements in fatigue strength due to the changes in the interface ply orientation are, however, less effective than those introduced by changing the corner geometry or increasing the overlap length, which were seen to be much more influencing design parameters. A rather complicated damage scenario was identified during the analysis of damage evolution under fatigue loading: after nucleation near the adhesive toe, interface cracks and/or multiple intra/inter-laminar delamination paths were observed in most of the tested joints.
G. Meneghetti et al. / International Journal of Fatigue 32 (2010) 82–93
The fatigue life of the joints analysed in the present paper can be conveniently predicted as the sum of an initiation and a propagation phase. According to the prediction model, initiation data can be summarised in unique scatter bands (one valid for square edge joints and one valid for fillet joints) in terms of the generalised stress intensity factor while the propagation data are well described by a single crack propagation scatter band, whichever the corner geometry, relating the range of the equivalent strain energy release rate to the rate of crack growth.
References [1] Matthews FL, Tester TT. The influence of stacking sequence on the strength of bonded CFRP single lap joints. Int J Adhes Adhes 1985;5:13–8. [2] Boss JN, Ganesh VK, Lim CT. Modulus grading versus geometrical grading of composite adherends in single-lap bonded joints. Compos Struct 2003;62:113–21. [3] Barroso A, Mantic V, Paris F. General solution for anisotropic multimaterial corners. Int J Fract 2003;119:1–23. [4] Quaresimin M, Ricotta M. Stress intensity factors and strain energy release rates in single lap bonded joints in composite materials. Compos Sci Technol 2006;66:647–56. [5] Renton WJ, Vinson JR. Fatigue behavior of bonded joints in composite material structures. J Aircraft 1975;12(5):442–7. [6] Ferreira JAM, Reis PN, Costa JDM, Richardson MOW. Fatigue behaviour of composite adhesive lap joints. Compos Sci Technol 2002;62:1373–9.
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[7] De Goeij WC, Van Tooren MJL, Beukers A. Composite adhesive joints under cyclic loading. Mater Des 1999;20:213–21. [8] Johnson WS, Mall S. Influence of interface ply orientation on fatigue damage of adhesively bonded composite joints. J Compos Technol Res 1986;8:3–7. [9] Quaresimin M, Ricotta M. Fatigue behaviour and damage evolution of single lap bonded joints in composite material. Compos Sci Technol 2006;66:176–87. [10] Quaresimin M, Ricotta M. Life prediction of bonded joints in composite materials. Int J Fatigue 2006;28:1166–76. [11] 3M – Aerospace Technical Data Sheet Nb:13 (1998) – Scotch–Weld 9323 B/A. [12] Quaresimin M. Fatigue of woven composite laminates under tensile and compressive loading. In: Proceedings of ECCM10, 10th European conference on composite materials, June 3–7, Brugge, Belgium; 2002. [13] Lusiani M, Meneghetti G, Quaresimin M, Ricotta M. Damage evolution in composite bonded joints under fatigue loading. In: Proceedings of ECCM13, 13th European conference on composite materials, June 2–5, Stockholm, Sweden; 2008. [14] Lazzarin P, Quaresimin M, Ferro P. A two terms stress function approach to evaluate stress distributions in bonded joints of different geometry. J Strain Anal Eng Des 2002;37(5):385–98. [15] Lefebvre DR, Dillard DA. A stress singularity approach for the prediction of fatigue crack initiation in adhesive bonds. Part I: theory. J Adhesion 1999;70:119–38. [16] ASTM E 647-00. Standard test method for measurement of fatigue crack growth rates. American Society for Testing and Materials; 2000. [17] Rybicki EF, Kanninem MF. A finite element calculation of stress intensity factors by a modified crack closure integral. Eng Fract Mech 1977;9:931–8. [18] Raju IS. Calculation of strain energy release rates with higher order and singular finite elements. Eng Fract Mech 1987;28(3):251–74. [19] Krueger R, Minguet PJ, O_Brien TK. Implementation of interlaminar fracture mechanics in design: an overview. In: Proceedings of ICCM14, July 14–18, San Diego, USA; 2003.
Contents lists available at ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Influence of the interface ply orientation on the fatigue behaviour of bonded joints in composite materials Giovanni Meneghetti a, Marino Quaresimin b,*, Mauro Ricotta a a b
Department of Mechanical Engineering – University of Padova, Via Venezia 1, 35131 Padova, Italy Department of Management and Engineering – University of Padova, Stradella S. Nicola 3 – 36100 Vicenza, Italy
a r t i c l e
i n f o
Article history: Available online 15 February 2009 Keywords: Composite bonded joints Interface orientation Crack initiation Crack propagation Life prediction
a b s t r a c t The paper deals with the study of the fatigue behaviour of bonded joints in composite materials. The influence of the orientation of the composite layer at the adhesive–adherend interface is investigated on single lap joints prepared by carbon fabric/epoxy laminates bonded together with a two-part epoxy adhesive. Different laminate lay-ups ([45/02]s and [452/0]s), overlap lengths (20 and 40 mm) and corner geometry of bonded area (square edge and fillet, respectively) were investigated under tension–tension fatigue. Particular attention was devoted to the analysis of the fatigue damage evolution to identify initiation and subsequent growth of cracks. A previous model developed by the authors, for the prediction of the fatigue life of bonded joints as the sum of an initiation and propagation phase, was successfully applied to summarise the new data. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction The modification of the lay-up near the overlap area of a bonded joint allows a further and helpful variable to the design process of these structural connections in composite materials. The resulting changes in the overall behaviour of the joint can involve global, and independent, variation of tensile and bending stiffness [1,2] as well as local modification of the elastic properties of the facing materials. As a further consequence, the global stress distributions and those near the singular locations at the end of the bonded overlap [3,4] can be significantly altered, thus influencing the static and fatigue properties of the joint. Very few investigations are available in the literature on this subject and the findings about the influence of ply orientation at the adhesive/adherend interface on static and fatigue strength are not always consistent. Matthews and Tester [1] investigated the static properties of CFRP single lap joints made of UD laminates manufactured with several combinations of 0°, 45° and 45° layers. Joint strength was found to increase with proportion of 0° plies, the greatest values being obtained for all 0° joint. The lay-up and the overlap length were both found to influence the failure mode, with the stiffer joint usually failing in the adhesive. Renton and Vinson [5] tested glass/epoxy single lap joints with all 0° or 45/0/45/0 UD laminate adherends. They found a limited effect of the interface ply orientation on the static strength of the * Corresponding author. E-mail address: [email protected] (M. Quaresimin). 0142-1123/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2009.02.008
joints. However they reported a reduction of about 20–40% in the high cycle fatigue strength of the angle-ply construction when compared to that with all the plies aligned. In terms of damage evolution under fatigue loading, they identified adhesive failure for all the 0° joints, while the 45/0/45/0 failed in the 45° ply adjacent to the adhesive. Ferreira et al. [6], investigated the behaviour of [0]7 and woven glass/polypropylene single lap joints of differ½45=45=0 s ent overlap length. An average decrease of about 30% in the fatigue joints when compared to shear strength was found for ½45=45=0 s those made with [0]7 lay-up. In the extensive literature re-analysis on the behaviour of bonded joints in composite under cyclic loading presented in Ref. [7], De Goeij et al. indicated a negligible influence of the interface ply orientation on static strength, while under fatigue loading all 0° joints behave better than those with 45° and 90° oriented ply at the interface. Johnson and Mall [8], analysed the fatigue behaviour of carbon/ epoxy cracked lap shear joints made with three different lay-ups, namely [0/±45/90]s/[0/±45/90]2s, [±45/0/90]2s/[±45/0/90]2s, [90/ ±45/0]2s/[90/±45/0]2s, and bonded with two different adhesives, a thermosetting paste and a modified epoxy adhesive. Three interface conditions were thus investigated: 0/0, 45/45 and 90/90. For the 0/0 interface joints, initiation and growth of a fatigue crack occurred in the adhesive region. In the case of 45 interface plies, cracks initiated in the adhesive layer, then grew in the adhesive or as intraply failure in the ±45 layer and, eventually, propagated as delamination at the 45/0 interface. For the 90 interface plies the fatigue damage initiated as transverse cracks and then
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G. Meneghetti et al. / International Journal of Fatigue 32 (2010) 82–93
0
ΔHo vs Ni
Ni
Life for crack initiation
Nf
SERR vs da/dN Life for crack propagation
Table 1 Properties of Scotch Weld 9323 B/A adhesive [11]. E (MPa)
G (MPa)
m
sr (MPa)
2870
1050
0.37
39.1
Fig. 1. Schematic of modelling of the two phases of the joint fatigue life [10].
propagated as a combination of intraply failure and delamination. The authors concluded that 0/0 and 45/45 interfaces exhibited similar threshold for crack initiation, measured in terms of total strain energy release rate. However, although included in the experimental scatter, the average values they calculated for the 45/45 interface joints were about 10% higher than those for the 0/0 interface joints. 45/45 interfaces were also found to be stronger than the 90/90. The brief discussion above seems to indicate the absence, in general, of significant benefits from changing the interface ply orientation. However, the results of Johnson and Mall put some lights on the possible role, as a strengthening mechanism, of the more complicated damage evolution when the orientation at the adhesive/adherend interface is different from 0/0. In this work the fatigue behaviour of carbon fabric/epoxy single lap bonded joints is investigated with particular reference to the possible influence of stacking sequence and orientation of the layer at the adhesive–adherend interface. For this aim, the new results are compared with those of the previous research [9] on single lap joints made from [0]6 laminates of the same material. The influence of overlap length and corner geometry is also investigated together with the extensive assessment of the evolution of damage and crack patterns during fatigue life. Eventually, the new results are successfully summarised and described by a life prediction model recently presented by the authors [10]. The model is based on the actual mechanics of the fatigue damage evolution and describes the joint lifetime as the sequence of a crack nucleation phase followed by a propagation phase at the adherend/adhesive interface. As schematically shown in Fig. 1, the nucleation phase is described by using a generalised Stress Intensity Factor (SIF) approach, which rationalises the fatigue life to crack initiation. The life spent in the propagation phase can be obtained by the integration of a Paris-like power law relating the Strain Energy Release Rate (SERR) to the rate of crack growth.
well as the laminate and adhesive layer thickness, 1.65 mm and 0.15 mm, respectively. Two laminate lay-ups ([45/02]s and [452/0]s), two overlap lengths (20 and 40 mm) and two geometry corners (square edge and spew fillet) were investigated in the test programme. The manufacturing of the bonded panels was done according to the procedure reported in [9]. Only joints produced from laminates with peel-ply were tested. All the joints were cut from the bonded panels and tested at room temperature on a servo-hydraulic MTS 858 Mini Bionix II machine equipped with a 15 kN load cells. The static behaviour of the joints was investigated by means of tensile tests under displacement control with a crosshead speed equal to 2 mm/min. The fatigue tests were carried out under load control, with a sinusoidal wave, nominal load ratio R = 0.05 and a test frequency variable in the range of 10–15 Hz depending on the applied stress level. To investigate damage evolution during fatigue loading and to assess the fraction of life spent for crack nucleation and propagation, the joints were subjected to repeated blocks of fatigue loading at constant amplitude, up to the failure of the joint. At the end of each block, the damage patterns were observed and measured on the polished edges of the joints, by using a Leica Metallux 3 optical microscope equipped with a Leica camera DC 100 providing a geometrical accuracy of 0.05 mm. 3. Static test results The results of static tensile tests of the joints are summarised in Tables 2 and 3 and plotted in Fig. 3. Tensile strength data of the original laminates are included for comparison. Since the failure never involved the adhesive layer, results are presented in terms of nominal tensile stress on the adherends, simply calculated by dividing the applied tensile load by the transversal section of one adherend. Non-uniform stress distribution and stress singularity at the end of the overlap were not considered.
2. Materials, joint geometry and test procedures Tensile static and fatigue tests were carried out on single lap bonded joints, with the overall geometry shown in Fig. 2. The joints were manufactured from autoclave-moulded laminates (Seal TexipregÒ CC206, T300 twill 2 2 carbon fibre fabric/ET442 toughened epoxy matrix) and bonded with the two-part epoxy adhesive 9323 B/A by 3 M [11], the properties of which are given in Table 1. Joint width (24 mm) and overall length (260 mm) were kept constant as
Y
1.65
X
20
260
Y
Corner geometry
Overlap (mm)
rUTS (MPa)
c.o.v. (%)
Failure modea
Square edge
20 40
388 495
2.4 14.9
LF Mixed
Spew fillet
20 40
459 434
0.3 21.8
LF Mixed
a LF: laminate failure at the end of bonded area (see Fig. 4); mixed: laminate failure and damage of the bonded layer; (tensile strength of [45/02]s laminates 500 MPa c.o.v. 12%).
F
w = 20, 40
24
Table 2 Tensile strength of [45/02]s joints.
SE
Table 3 Tensile strength of [452/0]s joints. Corner geometry
Overlap (mm)
rUTS (MPa)
c.o.v. (%)
Failure modea
Square edge
20 40
324 336
4.1 5.8
LFF LFF
Spew fillet
20 40
333 319
1.6 3.6
LFF LFF
X
Lay-up: [45/02]s; [452/0]s Fig. 2. Geometry of the single lap bonded joint (w = 20 and 40 mm). SE = square edge joint; F = fillet joint.
a LFF: laminate failure far from the end of the overlap (see Fig. 5); (tensile strength of [452/0]s laminates 350 MPa c.o.v. 4%).
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600 200
400
σmax [MPa]
Tensile strength [MPa]
500
300 200
[45/02]s square edge SE F[45/02]s fillet
100
SE [452[452/0]s /0]s square edge F[45 [452/0]s 2/0]s fillet
100
40
1E3
[0]6 w=40 mm, from ref. [9] [45/02]s w=40 mm [452/0]s w=40 mm [0]6 w=20 mm, from ref. [9] [45/02]s w=20 mm [452/0]s w=20 mm
1E4
0 20
1E5 Cycles to failure
1E6
1E7
40 Overlap length [mm]
Fig. 6. Influence of the overlap length on the fatigue strength of square edge joints (fatigue curves plotted are for [0]6 joints).
Fig. 3. Tensile test results for [45/02]s and [452/0]s joints (error bar = one standard deviation).
Failure of [45/02]s joints was characterised by different modes, as described in Table 2 and shown in Fig. 4: laminate failure at the end of the bonded area for 20 mm overlap joints (see Fig. 4) and mixed failure for those with 40 mm overlap. In the latter case, irrespective of corner geometry, joints exhibited significant and simultaneous damage both in the bonded layer and in the laminate far from the overlap end. This is the reason for the large scatter obtained and also of the unexpected (and unrealistic) decrease in the average strength for 40 mm spew fillet joints.
For the [452/0]s joints, tensile strength turned out to be independent from overlap length and corner geometry; this is justified by the fact that joints failed always in the laminates, far from the end of the overlap, as shown in Fig. 5. In this case the scatter of experimental data is clearly reduced and the strength of the joints is comparable with that of the original laminates. 4. Fatigue behaviour Figs. 6 and 7 show the fatigue data for square and spew fillet joints, respectively, in terms of maximum tensile stress on the
Fig. 4. Examples of static failure at the end of the bonded area for [45/02]s joints.
Fig. 5. Static failure in the adherends, outside the bonded area for [452/0]s joints.
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w=40 mm 200
σmax [MPa]
σmax [MPa]
200
100
40
1E3
[0]6 w=40 mm, from ref. [9] [45/02]s w=40 mm [452/0]s w=40 mm [0]6 w=20 mm, from ref. [9] [45/02]s w=20 mm [452/0]s w=20 mm 1E4
1E5 Cycles to failure
40
1E6
1E7
Fig. 7. Influence of the overlap length on the fatigue strength of spew fillet joints (fatigue curves plotted are for [0]6 joints).
adherends. Data previously obtained on [0]6 joints, taken from Ref. [9], are included for comparison. It can be observed that the presence of the 45° interface provides a slight improvement in the fatigue behaviour with respect to the 0° interface joints, only for the square edge corner geometry (Fig. 6). It is also seen that the fatigue strength is enhanced by increasing the overlap length, whatever the adopted stacking sequence. Moreover, by grouping the available results of the same overlap length, Figs. 8 and 9 show that the spew fillet geometry significantly extends the fatigue life with respect to the square edge geometry. A life extension factor of about one order of magnitude for the same applied load level can be observed for joints with 20 mm overlap. For the 40 mm overlap length joints, Fig. 9 shows a life extension factor of about three. It can be concluded that the changes in the fatigue strength due to the changes in stacking sequence and interface ply orientation are less significant that those introduced by modifying the corner geometry or increasing the overlap length. It is interesting to note that the ratio of the fatigue strengths for the same lay-up but different overlap lengths (20 or 40 mm) is in general different from two (see Figs. 6 and 7 and Table 4), then the effect of the overlap length on the fatigue behaviour of the joints cannot be rationalised by means of the mean shear stress calculated referring to the overlap area. As previously said, a different stress parameter based on the stress field intensity close to the
w=20 mm
σmax [MPa]
200
100
40
1E3
[0]6 fillet, from ref. [9] [45/02]s fillet [452/0]s fillet [0]6 square edge, from ref. [9] [45/02]s square edge [452/0]s square edge 1E4
1E5 Cycles to failure
100
1E6
1E7
Fig. 8. Influence of corner geometry on the fatigue strength of joints with 20 mm overlap length.
1E3
[0]6 fillet, from ref. [9] [45/02]s fillet [452/0]s fillet [0]6 square edge, from ref. [9] [45/02]s square edge [452/0]s square edge 1E4
1E5 Cycles to failure
1E6
1E7
Fig. 9. Influence of corner geometry on the fatigue strength of joints with 40 mm overlap length.
crack initiation point (namely the H0 parameter) should be used. Anyway such a parameter hardly correlates the total fatigue life since fatigue cracks were observed to spend only a fraction of the total fatigue life in the small zone were stresses are governed by H0. As briefly discussed in the introduction and suggested in the previous papers [9,10], the following choices were made: the total fatigue life was thought of as divided into life spent to nucleate a crack and life spent to propagate the crack up to final joint failure; the problem of a scientific definition of ‘crack initiation phase’ was not attacked, while a separation between crack initiation phase and crack propagation phase was based on the observation of a so-called (small) ‘technical crack’ having a fixed size related to the resolution of the inspection device adopted in the laboratory tests. That said, in the following paragraph a description of the fatigue damage evolution observed during the tests is reported, since the design approach proposed for bonded joints under cyclic loading is connected to our experimental findings. With the aim to supply the complete scenario of fatigue test results to the reader, Table 4 summarises the results of the statistical analysis of the available data, by assuming log-normal distribution of the number of cycles to failure. In the table the reference stress values at 2 106 cycles for a probability of survival of 50% and 90%, the value of the inverse slope k of S–N curves and the scatter index Tr (Tr = rMax,10%/rMax,90%) are listed. Eventually, as a general comment about the structural ‘‘efficiency” of this type of joint, it can be worth noting that the introduction of a bonded connection in a structural component could be not too harmful in terms of static strength, while leading to significant reductions in its load bearing capability under cyclic loading. This reduction can be quantified by calculating the ratio between the fatigue strength at two million cycles of the joints and the static strength of the plain laminate. The values of this ratio range from 0.10, in the case of [45/02]s square edge joints w = 20 mm, up to 0.31, in the case of [452/0]s fillet joints (w = 40 mm). Lower values, from 0.09 to 0.17, were reported in [9] for [0]6 joints. These values have to be compared with those one could expect for the plain laminates the joints are made of, ranging from 0.5 to 0.75 in the case of tension–tension fatigue loading [12]. In overall analysis of the results discussed in the work it should be kept in mind that the joints tested here were manufactured by
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Table 4 Results of the statistical analysis for the different series of fatigue data (fatigue strength values at 2 106 cycles). Lay-up
Corner geometry
Overlap (mm)
rVAX, 50% (MPa)
rVAX, 90% (MPa)
k
Tr
No. of data
[45/02]s
Square edge
20 40 20 40
51.3 101.5 89.8 125.5
46.5 – 73.9 110.1
5.47 8.38 8.07 9.08
1.215 – 1.479 1.300
4 2 4 4
20 40 20 40
52.8 94.2 79.4 107.0
42.2 82.8 71.3 97.5
4.77 6.15 7.31 5.62
1.646 1.295 1.240 1.204
5 4 6 5
Fillet [452/0]s
Square edge Fillet
bonding laminates made from fabric reinforced plies. Hence the conclusions provided are limited to this class of materials, while the behaviour of the joints made from UD ply-laminates could be different. 5. Fatigue damage evolution Let us now consider separately the fatigue damage evolution observed in spew fillet joints and square edge joints. Fig. 10a shows a typical crack path, as observed in the edge view of spew fillet joints. Independently on the applied load level, cracks were observed to initiate very near the toe of the bonded joint, close to the central position along the specimen width. In very few cases cracks were observed to initiate at the upper corner point between the adhesive and the laminate free surface (see Fig. 10b). An example of crack nucleation at the free surface of the adhesive fillet is presented in Fig. 11: in this case the adhesive whitening could be easily observed by eye. The number of cycle to initiate a crack in the fillet, detectable by visual inspection, which corresponds to the true crack nucleation was defined as Nit. After nucleation, the crack propagates along the specimen width toward the joint edges and then along the specimen longitudinal axis at the interface between adhesive and adherends as shown in Fig. 10a and b. Cracks emanating from the four corners of the joints, indicated as A, B, C and D in Fig. 12, were usually observed. According to what already done in the previous research [9], when one of these cracks reached the conventional length of 0.3 mm, measured on the laminate edge, that was identified as the ‘‘technical” crack initiation and the correspondent number of cycle as ‘number of cycle to crack initiation’ Ni. The life spent to propagate a crack up to final fatigue failure (Nf) was then calculated as the difference between the total life and the life to ‘‘technical” crack initiation and identified as number of cycles to crack propagation, Np. During the propagation phase, very complicated crack paths were usually observed. In par-
Fig. 12. Definition of ‘‘technical” crack for the evaluation of ‘‘technical” number of cycle to crack initiation, Ni, for square edge and fillet joints.
Fig. 10. Crack nucleation sites and crack paths in spew fillet joints.
ticular, cracks deviated from the interface adhesive-adherend path to become intralaminar and/or interlaminar before turning again along the main interface path, as widely described in Ref. [13]. The apparent inconsistency of considering as life to crack initiation Ni and not Nit can be clarified by considering that the propagation from the nucleation site in centre of the joint to its edges (in terms of number of cycles from Nit to Ni) occurs in a region fully controlled by the local stress field and by H0. Therefore, considering the crack initiation phase to be completed only after the crack has propagated in the joint width direction is consistent with both experimental observations and local stress analysis. As a further support of the choice made, the definition of a ‘‘technical crack” is the only possibility of identifying initiation in the square edge joints, where the observation of true crack nucleation via adhesive whitening, even if present, is impossible from a practical point of view due to the reduced thickness of the adhesive layer (0.15 mm). In this conditions, only a ‘‘technical” crack
Fig. 11. Crack initiation identified by adhesive whitening in a fillet joint.
Crack initiation D C A B
0.3
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initiation can be defined in correspondence of the number of cycles at which a crack of 0.3 mm is observed near one of the four corner of the joint. Then Fig. 12 holds true again in order to define the ‘‘technical” crack initiation stage.
Damage patterns during propagation were similar to those observed for fillet joints. Fig. 13 shows a typical example of initiation and crack propagation path at the adhesive–adherend interface, while Fig. 14 shows
Fig. 13. Interface crack initiation and propagation path in a square edge joint (lay-up [45/02]s; rmax = 65 MPa, w = 20 mm, Nf = 588,737 cycles).
Fig. 14. Crack initiation and intralaminar/interlaminar crack path in a square edge joint (lay-up [45/02]s; w = 20 mm, rmax = 95 MPa, Nf = 78,209 cycles).
Table 5 Results of block loading fatigue tests for [45/02]s joints. Corner geometry
Overlap (mm)
rmax (MPa)
Nit
Ni cycles
Nf cycles
Np cycles
Nit/Nf
Ni/Nf
Square edge
20 20 20 20 40 40 40
95 65 95 65 120 90 80
– – – – – – –
30,000 76,470 17,000 150,000 105,000 1,100,000 2,300,000
78,209 588,737 59,600 503,791 492,496 5,484,544 –
48,209 512,267 42,600 353,791 387,496 4,384,544 –
– – – – – – –
0.38 0.29 0.30 0.13 0.21 0.20 –
Fillet
20 20 20 20 40 40 40 40
126 126 100 100 180 180 125 125
83,000 47,000 310,000 300,000 2000 40,000 400,000 510,000
121,000 68,000 980,000 530,000 7000 55,000 1,610,000 1,085,000
182,091 93,220 1,163,120 609,618 63,735 90,237 2,819,191 1,533,993
61,091 25,220 183,120 79,618 56,735 35,237 1,209,191 448,993
0.46 0.50 0.27 0.49 0.031 0.44 0.14 0.33
0.67 0.73 0.84 0.87 0.11 0.61 0.57 0.71
Ni cycles
Table 6 Results of block loading fatigue tests for [452/0]s joints. Corner geometry
Overlap (mm)
rmax (MPa)
Nit
Square edge
20 20 20 20 20 40 40 40 40
95 95 65 65 65 145 145 120 120
– – – – – – – – –
Fillet
20 20 20 20 20 20 40 40 40 40 40
126 126 126 100 100 85 180 180 140 140 125
3000 15,000 2000 25,000 100,000 385,000 2000 250 100,000 50,000 30,000
Nf cycles
Np cycles
Nit/Nf
Ni/Nf
45,000 20,000 130,000 128,000 410,000 15,000 15,000 63,000 43,673
165,262 88,557 543,245 690,354 1,083,720 131,433 152,429 565,193 362,839
120,262 68,557 413,245 562,354 673,720 116,433 137,429 502,193 319,166
– – – – – – – – –
0.27 0.23 0.24 0.19 0.38 0.11 0.10 0.11 0.12
15,000 40,000 78,000 155,000 330,000 1,008,229 40,000 32,000 200,000 100,000 200,000
53,000 65,393 100,141 269,691 420,000 1,364,877 93,837 120,631 536,847 395,767 790,000
38,000 25,393 22,141 114,691 90,000 356,648 53,837 88,631 336,847 295,767 590,000
0.057 0.23 0.020 0.093 0.24 0.28 0.021 0.002 0.19 0.13 0.04
0.28 0.61 0.78 0.57 0.79 0.74 0.43 0.27 0.37 0.25 0.25
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Lay-up [452/0]s
200
w=20 mm
100
σmax [MPa]
σmax [MPa]
200
fillet square edge
40
1E3
1E7
Fig. 15a. Influence of corner geometry on crack initiation.
σmax [MPa]
w=20 mm
100
fillet square edge
1E3
1E4 1E5 1E6 Cycles for crack propagation, Np
1E7
Fig. 15b. Influence of corner geometry on crack propagation.
an example of fatigue damage evolution involving intralaminar/ interlaminar crack propagation paths. It is worth noting that for all bonded joints, either fillet or square edge, the crack length was measured by projecting the observed crack path onto the adhesive–adherend interface plane and the resulting projected length, including either interface crack and/ or delamination, was referred as ‘‘nominal” crack.
σmax [MPa]
100 Lay-up [452/0]s
1E3
1E3
1E4 1E5 1E6 Cycles for crack propagation, Np
1E7
Tables 5 and 6 summarise fatigue life as well as the relevant initiation and propagation fraction for the different tested joints. For the spew fillet joints two sets of data are also reported, namely Nit/ Nf and Ni/Nf ratios, being valid the previous definitions of Nit and Ni. For the square joints, only the Ni/Nf set of data is reported due to the impossibility, as discussed above, to detect the initiation, if any, at the central location of the joint. It is seen that for the same lay-up and over lap length, the fillet configuration significantly extends the normalised crack initiation phase with respect to the square edge configuration. The same conclusion can be drawn also from Fig. 15a, which is representative of the general behaviour of the joints: an extension of the crack initiation life for the same load level can be observed for fillet joints while, as expected, crack propagation life is almost the same independently on the corner configuration (Fig. 15b). Fig. 16a and b show the influence of overlap length on the initiation and propagation fatigue life, observed on [452/0]s square edge joints. Joints with 40 mm overlap experienced both a longer life to crack initiation and a longer propagation phase when compared, at the same stress level, with shorter overlap joint. This result is in agreement with the modelling approach discussed in the introduction. In fact, as discussed in more detail in the next paragraphs, shorter overlaps induce higher values of the generalised Stress Intensity Factor and therefore shorter life to crack initiation. At the same time the Strain Energy Release Rate for a cracked joint with 20 mm overlap is more than twice that of a joint with 40 mm overlap, by keeping constant both the crack length and the applied stress. This leads to a reduced propagation life for joints with shorter overlap. 6. Summary of initiation lives in terms of generalised stress intensity factor ‘H0’
200
40
w=40 mm w=20 mm
Fig. 16b. Influence of overlap length on crack propagation.
Lay-up [452/0]s
40
Lay-up [452/0]s 40
1E4 1E5 1E6 Cycles for crack initiation, Ni
200
100
w=40 mm w=20 mm
1E4 1E5 1E6 Cycles for crack initation, Ni Fig. 16a. Influence of overlap length on crack initiation.
1E7
As previously mentioned, neither the nominal stress acting on the adherend nor the average shear stress acting over the adhesive area are parameters suitable to rationalise the fatigue strength of the tested bonded joints. In order to summarise the fatigue strength of all the tested joints, a different stress parameter should be used, namely the intensity of the local stress field calculated close to the crack initiation point. Such a parameter has already been suggested in the past [14,15] and proved [10] to be able to rationalise the fatigue life to crack initiation of bonded joints having different overlap length. In the present paper the additional effect of the lay-up stacking sequence is considered. The theoretical basis for the stress analysis of bonded joints can be found elsewhere [3,4,14]. Here it is important to recall that being the radius
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at the toe of the bonded joints variable not only for different joints but even along the same bead, the corner configuration has been assumed to be geometrically singular both for fillet and for square edge joints. That is the root radius at the toe of the joint has been assumed to be equal to zero, according to the sketch reported by Fig. 17. The second reason why the local stresses are singular is due to the mismatch between the elastic properties of the adhesive and the adherend. The asymptotic stress field close to the singular point can be expressed by a stress expansion, in variable separable form, that describes analytically the entire stress distribution and can be conveniently truncated in many cases of practical interest [14]. The generalised stress intensity factor associated to the first term of such stress expansion, denoted by H0, depends on boundary conditions and joint configuration, the relevant singularity power associated is denoted by s and depends on both local geometry and elastic properties of the matching materials. As said above, H0, has been suggested as the controlling and unifying parameter for fatigue crack initiation. The reader is referred to Refs. [14,15] for a comprehensive treatment on this subject. In order to assess the generalised stress intensity factor H0, according to the previous research [4], linear elastic plain-strain numerical models were defined by using AnsysÒ 11.0 numerical code. Eight-node PLANE82 finite elements as available in Ansys element library were adopted. The in-plane elastic properties of the basic lamina (EX, EZ, GXZ, tXZ) were measured from suitable experimental test (for the frame of reference, see Fig. 2), the offaxis properties were calculated with the classical formulation of the theory of elasticity for orthotropic bodies and finally the outof-plane properties were estimated on the basis of morphological and micromechanical considerations. Table 7 lists the elastic properties of the basic lamina. Being the [45/02]s and [452/0]s laminates more compliant in bending than the [0]6 investigated in Ref. [4], one could argue that linear elastic analyses are not suitable or enough accurate anylonger for properly describing the singular stress fields and generalised stress intensity factor H0 near the critical locations in the joints. However, it should be also noted that the out-of-plane bending of the joints under tension is still negligible before crack starts to propagate and that the adoption of geometrical linear instead of non-linear analyses implies a significant saving in calculation time and, most of all, H0 values independent from the applied stress level. Therefore, it was decided to maintain the approach proposed in [4] and to investigate the stress field in the uncracked joints via linear elastic analyses. Fig. 17 shows the local frame of reference adopted in the analysis and an example of the singular stress distributions calculated along the adhesive–adherend interface. By analysing the stress– distance data obtained from the finite element analyses, the stress parameter H0 and the relevant exponent s (representative of the degree of singularity) can be calculated for each lay-up and overlap length. Being the numerical analyses linear, Table 8 summarises the results in terms of ratio between the local stress parameter H0 and the applied nominal stress r0. Table 8 clearly shows that H0/r0 increases as the overlap length decreases: these results explain the experimental fatigue behaviour, where the life to crack initiation increases while increasing the overlap length (see Fig. 16a). It is also worth noting that the stress singularity exponent s is not influenced by the lay-up sequences since the elastic material properties at the interface are
Table 8 Strength of singularity s and normalised values of generalised stress intensity factors H0. Square edge
Fillet
[45/02]s s = 0.432
[452/0]s s = 0.432
[45/02]s s = 0.226
[452/0]s s = 0.226
w (mm)
H0/r0 (mms)
H0/r0 (mms)
H0/r0 (mms)
H0/r0 (mms)
20 40
0.2374 0.2091
0.2585 0.2268
0.1900 0.1664
0.2076 0.1816
Data for [0]6 joints, from Ref. [4] s = 0.423 w (mm) H0/r0 (mms)
s = 0.199 H0/r0 (mms)
20 40
0.1683 0.1493
0.1713 0.1577
the same for both the lay-ups. Due to the different degree of singularity of the stress field pertinent to the two corner geometries, two sets of homogeneous data for square edge and fillet joints have to be defined. Figs. 18 and 19 show the available fatigue data in terms of range of variation of H0, DH0, for fillet and square edge joints, respectively. In order to appreciate the unifying capability of H0, the same data are also plotted in terms of nominal stresses. Both figures highlight that the scatter of the life to crack initiation is significantly reduced if the local rather than the nominal stress approach is adopted, as shown by the reduced values of the TH0 scatter index with respect to those of Tr. The scatter bands are defined in both cases for a survival probability of 10% and 90%, respectively, with a confidence level of 95%. In view of a comparison between the present fatigue data and those generated on [0]6 joints [9], Figs. 18 and 19 report also the previous H0-based fatigue curve with a survival probability of 50%. It is seen that a slight difference between the [0]6 and the present H0-fatigue curves exists, the higher difference of about 10% in strength being valid for square edge joint. However, it should be kept in mind that, in strict sense, the direct comparison of the H0-fatigue curves is not formally correct due to the difference in the degree of singularity of 0° and 45° degree interface (see again Table 8). Being this difference reasonably small, the comparison can be acceptable from an engineering standpoint. 7. Summary of crack growth data As explained before, fatigue crack growth was monitored at the four joint corners A, B, C and D (see Fig. 12) and the ‘‘nominal” crack length at each corner was measured from the projection on the adhesive–adherend interface of the observed crack path (including interface crack and/or delamination). To reduce the number of data to deal with and for an easier and more reliable modelling, (i) a linear crack front and (ii) a symmetrical crack propagation were assumed, according to what already suggested in [4,9]. As a consequence the mean value of the four ‘‘nominal” crack lengths was assumed as relevant in the subsequent crack growth calculations. Fig. 20 shows, as an example, the mean crack length versus the number of cycles as measured on some fillet joints; data previously obtained for [0]6 joints are included for comparison. Data in this form were then processed in order to calculate the crack growth
Table 7 Elastic properties of woven lamina used for FE analyses. EX (MPa)
EY (MPa)
EZ (MPa)
GXY (MPa)
GYZ (MPa)
GXZ (MPa)
mXY
mYZ
mXZ
58,050
6000
58,650
500
500
3300
0.27
0.27
0.06
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G. Meneghetti et al. / International Journal of Fatigue 32 (2010) 82–93
σϑϑ σrϑ
y 0°
r
ϑ
Average nominal crack length [mm]
100
σrr
MATERIAL adhesive2
x
10
MATERIAL adherend1
σij/σnom
σrr-laminate
σrr-adhesive
1
σrθ
σθθ
Lay-up [45/02]s w=40 mm 0.1 1.E-03
[45 2/0] s; σL(100MPa) [452/0]s; max=100 MPa ] ; [45/0 σ 2 s L(100MPa) max=100 MPa [45/02]s; ; =113 MPa [0] σ 6 max [0]6
10
w=20 mm
5
0 0.0E+00
1.E-02
1.E-01
5.0E+05 Number of cycles
1.E+00
r/tadhesive
1.0E+06
Fig. 20. Crack length evolution for spew fillet joints.
Fig. 17. Local frame of reference and stress distributions at adhesive–adherend interface for [45/02]s fillet joint and overlap length 40 mm.
1.E-02 w=20 mm
1000
]
10
k=5.64
10
11.93 w=20 mm; [45/02]s w=40 mm; [45/02]s w=20 mm; [452/0]s
1.E-04
1.E-05 [45/(0)2]s; H (95MPa) [45 = 95 MPa 2/0] s; σmax [45/(0)2]s; L (65MPa) [45 2/0] s; σmax = 65 MPa [(45)2/0]s; H (95MPa) [45/0 2]s; σmax = 95 MPa [(45)2/0]s; L (65MPa) [45/0 2]s; σmax = 65 MPa
1.E-06
TH0 = 2.28
[0]6
1.E-07
w=40 mm; [452/0]s
1 1.E+04
da/dN [mm/cycle]
σmax [MPa]
100
0.43
Tσ = 3.02
100
1.E-03
ΔH0 [MPa mm
1000
0
1 1.E+07
1.E+05 1.E+06 Cycles for crack initiation
0.1
0.2
0.3
0.4
0.5
a/w Fig. 21. Trends of the crack growth rate for square edge joints.
Fig. 18. Comparison between S–N curve approach and local approach on fatigue crack initiation for [45/02]s and [452/0]s square edge bonded joints.
1000
1000
100
0.23
10
ΔH0 [MPa mm
σmax [MPa]
k=8.26
]
Tσ = 1.92
100 TΗ0 =1.51 16.27
10
[0]6
w=20 mm ; [45/02]s
Fig. 22. Deformed shape of a cracked joint and details of the FE model at the interface crack [4].
w=40 mm ; [45/02]s w=20 mm ; [452/0]s w=40 mm ; [452/0]s
1 1.E+03
1.E+04
1.E+05
1.E+06
1 1.E+07
Cycles for crack initiation Fig. 19. Comparison between S–N curve approach and local approach on fatigue crack initiation for [45/02]s and [452/0]s fillet bonded joints.
rates. In view of this, piece-wise second order polynomials were adopted to fit the data according to the suggestion of ASTM 64700 [16]. Results obtained for 20-mm-overlap square edge joints are shown in Fig. 21. For an easier comparison, the crack growth rate is plotted versus the average nominal crack length a normalised to the overlap length w. A clear influence of the applied stress
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G. Meneghetti et al. / International Journal of Fatigue 32 (2010) 82–93 Table 9 Paris curve data calculated for different probability of survival.
1200 GGtot,[452/0]s tot, [45 2/0]s GGtot,[45/02]s tot, [45/0 2]s GGtot,[0]6 tot, [0] 6 GG1,[452/0]s I, [45 2/0] s GG1 I, [45/0 2]s GG1,[0]6 I, [0] 6 GG2,[452/0]s II, [45 2/0] s GG2 II, [45/0 2]s GG2,[0]6 II, [0] 6
2
SERR component [J/m ]
1000
800
600
w= 20 mm σmax=100 MPa for [45 2/0] s σmax=100 MPa for [45/0 2]s σmax=110 MPa for [0] 6
DGeqv (J/m2)
DGtot (J/m2)
Data for [45/02]s and [452/0]s joints (analysed together) 50% P.S. D = 1.169 1011 n = 2.688 D = 4.058 1011 n = 2.688
D = 1.664 1011 n = 2.731
Data for [0]6 joints, from Ref. [10] 50% P.S. D = 2.421 1011 n = 2.723
D = 1.354 1011 n = 2.729
D = 9.658 1011 n = 2.723
D = 5.235 1011 n = 2.729
90% P.S.
400
D = 4.766 1012 n = 2.731
90% P.S.
200
1.E-02
0 0
0.1
0.2
0.3
0.4
[0]6
0.5
a/w
1.E-03
level can be recognised, i.e. higher fatigue stress results in faster crack propagation. For summarising the crack growth data in a Paris-like diagram, the Strain Energy Release Rate (SERR) was assumed to be the crack driving force. In order to estimate the SERR parameters for a given crack length, two-dimensional plain-strain finite element model were defined by using AnsysÒ software. For the sake of simplicity, cracks were always supposed to propagate symmetrically along the adhesive–adherend interface. Fig. 22 shows a schematic of the model adopted and details of the mesh close to the interface crack. Under tensile loading the out-of-plane bending of the uncracked joint can be neglected. Conversely, during the propagation phase the bending compliance of the specimen increases as the crack propagates. As a consequence, linear elastic models are not appropriate any longer to describe the stress distributions. Then geometrically non-linear analyses were performed when modelling the crack propagation phase. In order to calculate the SERR parameter the Virtual Crack Closure Technique (VCTT) was adopted [17–19]. Details on the application of such a technique are reported in Ref. [4]: here it is important to recall that the adopted mesh density was carefully calibrated to avoid the problems associated to the oscillating stress field near the interface crack tip. This required an element size on the order of 0.03 mm (see again Fig. 22). As an example of the results, Fig. 23 plots the SERR components as calculated from the non-linear finite element analyses valid for 20-mm-overlap joints. Mode I and Mode II components are reported, trends for [0]6 joints are again included for comparison. Having in hands rates of crack propagation and SERR trends it was possible to draw a Paris-like diagram, expressed in the form:
da ¼ D ðDGeqv Þn dN
ð1Þ
where DGeqv = (Geqv,max Geqv,min) is the range of equivalent SERR, as defined in [4], which represents one of the possibility to account for the combined presence of Mode I and Mode II loading (opening and sliding modes at the crack tip) and to the variation of the mode mixity during the fatigue life. The expression already proposed by the authors is reported in Eq. (2) for clarity.
Geqv ðaÞ ¼ GI ðaÞ þ
GII ðaÞ GII ðaÞ GI ðaÞ þ GII ðaÞ
ð2Þ
da/dN [mm/cycle]
Fig. 23. Trends of SERR components and influence of laminate lay-up.
1.E-04
10%
1.E-05 90% 50%
1.E-06
Serie1 [45/02]s Serie3 [452/0]s
1.E-07 10
100
1000
10000
ΔGeqv [J/m2] Fig. 24. Crack propagation scatter band for all the joints tested (crack growth rate vs. range of the equivalent SERR).
Results are summarised in Table 9 and in Fig. 24 where the relevant 10–90% scatter band is also plotted. As a comparison, the average curve previously found for [0]6 joints is also reported. It is seen that the lay-ups under investigation are characterised by a greater resistance to crack growth. A reason for that might be the much more complicated damage patterns observed in the specimens having a 45° interface tested in the present work with respect to those having a 0° interface tested previously. It is also worth noting from Table 9 that the D and n parameters characteristic of the crack propagation curve do not differ so much when the total SERR Gtot, defined as
Gtot ðaÞ ¼ GI ðaÞ þ GII ðaÞ
ð3Þ
rather than the equivalent SERR is considered in the analysis. 8. Life prediction A model has been recently presented by the authors [10] which describes the fatigue life of bonded joints in composite materials as the sum of the number of cycles needed to nucleate a fatigue crack Ni and the number of cycles Np required by this crack to propagate up to a critical length. Similarly, in the present paper the use of the proposed design curves for estimating the fatigue crack initiation life (see Figs. 18 and 19) and the crack propagation life (see Fig. 24), respectively, has been validated by comparing the experimental mean fatigue curves of the different test series with those estimated by adding
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G. Meneghetti et al. / International Journal of Fatigue 32 (2010) 82–93
Ni and Np. For a comprehensive description of the application procedure the reader is referred to Ref. [10]. In very brief, the assessment of the number of cycles to crack initiation is made from the
σmax [MPa]
σmax [MPa]
Overlap length: 20 mm Lay-up [45/02]s
200
Overlap length: 40 mm Lay-up [452/0]s
200
100
100
Experimental data Estimated life Nf (50% P.S.) 1E3 Experimental data Estimated life Ni (50% P.S.) 1E3
1E4
1E7
Fig. 25. Experimental 10–90% scatter band of the life to crack initiation for [45/02]s fillet joints (overlap 20 mm) compared with the model predictions.
Overlap length: 20 mm Lay-up [45/02]s
σmax [MPa]
100
Experimental data Estimated life Np (50% P.S.) 1E3
1E4 1E5 1E6 Cycles for crack propagation, Np
1E7
Fig. 26. Experimental 10–90% scatter band of the life to crack propagation for [45/ 02]s fillet joints (overlap 20 mm) compared with the model predictions.
Overlap length: 20 mm Lay-up [45/02]s
σmax [MPa]
200
100
Experimental data Estimated life Nf (50% P.S.) 1E3
1E4
1E5 1E6 Cycles to failure
1E7
Fig. 28. Experimental 10–90% scatter band of the fatigue data at failure for [452/0]s fillet joints (overlap 40 mm) compared with the model predictions.
1E5 1E6 Cycles for crack initiation, Ni
200
1E4
1E5 1E6 Cycles to failure
1E7
Fig. 27. Experimental 10–90% scatter band of the fatigue data at failure for [45/02]s fillet joints (overlap 20 mm) compared with the model predictions.
relevant DHo Ni scatter band (see Figs. 18 and 19) once the generalised stress intensity factor for the stress level of interest is evaluated. The number of cycle for crack propagation is obtained by integration of the crack propagation curve (Eq. (1), Table 9 and Fig. 24). The upper limit of the integration, that is the final crack length, is calculated by equating the equivalent SERR to the Mode I fracture toughness GIc (900 J/m2) of the adhesive, while the lower limit of integration corresponds to the ‘‘technical” crack (equal to 0.3 mm). The equivalent SERR as a function of the crack length ‘‘a” is obtained from non-linear finite element analyses (see, as an example, Fig. 23). The above procedure has been applied to all the available fatigue data by using the 50% survival probability curves for both crack initiation (see Figs. 18 and 19) and crack propagation (see Fig. 24). As representative comparisons, Figs. 25–27 show the predicted life to crack initiation, life for crack propagation, and total life, respectively, compared with the relevant 10–90% P.S. experimental scatter band for one of the series tested. A good agreement can be observed. For completeness, Fig. 28 shows the worst case obtained from this analysis. It can be noted that the prediction is, however, on the safe side and the predicted total life curve is still inside the 10–90% P.S. experimental scatter band. 9. Conclusions The fatigue behaviour of single lap bonded joints in composite materials with different stacking sequence and orientation of the ply at the adhesive–adherend interface was investigated. The main conclusions of the work can be summarised as follows: The presence of the 45° interface provides only a slight improvement in the overall fatigue strength when compared with previous data on [0]6 joints while resistance to crack propagation is significantly increased by the 45° interface. Joints made from [45/02]s and [452/0]s laminates behave similarly. The improvements in fatigue strength due to the changes in the interface ply orientation are, however, less effective than those introduced by changing the corner geometry or increasing the overlap length, which were seen to be much more influencing design parameters. A rather complicated damage scenario was identified during the analysis of damage evolution under fatigue loading: after nucleation near the adhesive toe, interface cracks and/or multiple intra/inter-laminar delamination paths were observed in most of the tested joints.
G. Meneghetti et al. / International Journal of Fatigue 32 (2010) 82–93
The fatigue life of the joints analysed in the present paper can be conveniently predicted as the sum of an initiation and a propagation phase. According to the prediction model, initiation data can be summarised in unique scatter bands (one valid for square edge joints and one valid for fillet joints) in terms of the generalised stress intensity factor while the propagation data are well described by a single crack propagation scatter band, whichever the corner geometry, relating the range of the equivalent strain energy release rate to the rate of crack growth.
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[7] De Goeij WC, Van Tooren MJL, Beukers A. Composite adhesive joints under cyclic loading. Mater Des 1999;20:213–21. [8] Johnson WS, Mall S. Influence of interface ply orientation on fatigue damage of adhesively bonded composite joints. J Compos Technol Res 1986;8:3–7. [9] Quaresimin M, Ricotta M. Fatigue behaviour and damage evolution of single lap bonded joints in composite material. Compos Sci Technol 2006;66:176–87. [10] Quaresimin M, Ricotta M. Life prediction of bonded joints in composite materials. Int J Fatigue 2006;28:1166–76. [11] 3M – Aerospace Technical Data Sheet Nb:13 (1998) – Scotch–Weld 9323 B/A. [12] Quaresimin M. Fatigue of woven composite laminates under tensile and compressive loading. In: Proceedings of ECCM10, 10th European conference on composite materials, June 3–7, Brugge, Belgium; 2002. [13] Lusiani M, Meneghetti G, Quaresimin M, Ricotta M. Damage evolution in composite bonded joints under fatigue loading. In: Proceedings of ECCM13, 13th European conference on composite materials, June 2–5, Stockholm, Sweden; 2008. [14] Lazzarin P, Quaresimin M, Ferro P. A two terms stress function approach to evaluate stress distributions in bonded joints of different geometry. J Strain Anal Eng Des 2002;37(5):385–98. [15] Lefebvre DR, Dillard DA. A stress singularity approach for the prediction of fatigue crack initiation in adhesive bonds. Part I: theory. J Adhesion 1999;70:119–38. [16] ASTM E 647-00. Standard test method for measurement of fatigue crack growth rates. American Society for Testing and Materials; 2000. [17] Rybicki EF, Kanninem MF. A finite element calculation of stress intensity factors by a modified crack closure integral. Eng Fract Mech 1977;9:931–8. [18] Raju IS. Calculation of strain energy release rates with higher order and singular finite elements. Eng Fract Mech 1987;28(3):251–74. [19] Krueger R, Minguet PJ, O_Brien TK. Implementation of interlaminar fracture mechanics in design: an overview. In: Proceedings of ICCM14, July 14–18, San Diego, USA; 2003.