The research investigated the effect of the repair of cracked aluminum plates by glass-epoxy composite patches on preventing fractures. This study was performed by subjecting 50 rectangular specimens of 80 mm wide, 150 mm long and 1 mm thickness each to uniaxial tensile test using the 600KN Santam testing machine at the laboratory of the Islamic Azad University of Hamedan, Iran (Figure1). Plates with central cracks with the length of 30 mm subjected to tensile loading at an extension speed of 0.2 mm per minute to the fracture point, were reinforced by one-sided composite patches shaped like an arrow in two opposite directions (Figure 2). To begin with, each plate was positioned vertically in the load cell between the lower and upper crossheads with gage length of 50 millimeters. In the subsequent steps, the Santam testing machine’s user software was customized with the desired shape, areas, lengths, widths, gage lengths, loading type and thickness of the cracked aluminum plates.
A through Q represented the letter designations on the aluminum specimens in accordance with the English alphabets. They were characterized by the following features. Alpha indicates half of the angle between two adjacent sides (both for the right and left). SL represents length of each adjacent side. In addition, L indicates the horizontal distance between the right and left edges of the arrow-shaped composite patch. Also, H represents the vertical height of the patch. Table 1 shows the measurements of the illustrated indicators for each category of the specimens.
Table 1: The measurements of each category of specimens
|
Specimen Category
|
Alpha Angle (degree)
|
Side Length (mm)
|
Horizontal Length L
(mm)
|
Vertical Length H
(mm)
|
|
A
|
50
|
30
|
60
|
40
|
|
B
|
30
|
20
|
55
|
13
|
|
C
|
53
|
25
|
50
|
40
|
|
D
|
53
|
25
|
45
|
45
|
|
E
|
61.35
|
30
|
45
|
55
|
|
F
|
36
|
23
|
55
|
27
|
|
G
|
40
|
10
|
26
|
13
|
|
H
|
30
|
13
|
40
|
13
|
|
I
|
20
|
20
|
55
|
13
|
|
J
|
40
|
20
|
45
|
25
|
|
K
|
35
|
23
|
55
|
26
|
|
L
|
52
|
35
|
65
|
55
|
|
M
|
40
|
20
|
45
|
25
|
|
N
|
36
|
23
|
55
|
27
|
|
O
|
49
|
18
|
55
|
27
|
|
P
|
20
|
15
|
50
|
10
|
|
Q
|
20
|
18
|
50
|
12
|
The security shield of the testing machine was closed properly before performing the tests for safety reasons. Tests were performed on several number of plates of each category to provide additional validation for the experimental results. As aluminum plates were tested, Force-Displacement linear graph was monitored and plotted by the user’s software of the testing machine. The obtained maximum fracture load and displacement extension for A to Q categories of experimentally tested plates with 0,90 t0 -45,45 orientations of glass fibers at failure were then reported as table 2 &3 show.
Table 2: The maximum fracture load and displacement extension for specimen category A to H
|
Cateogry
|
Specimen Number
|
Fibers Orientations
(degree)
|
Max Fracture Load
(Newton)
|
Max Displacement
Extension (mm)
|
|
A
|
1
|
0,90
|
14583
|
4.561
|
|
A
|
2
|
-45,45
|
11911
|
3.535
|
|
B
|
1
|
-45,45
|
11139
|
3.250
|
|
B
|
2
|
0,90
|
11492
|
3.343
|
|
C
|
1
|
0,90
|
12258
|
3.642
|
|
C
|
2
|
-45,45
|
12258
|
3.357
|
|
D
|
1
|
0,90
|
12405
|
3.663
|
|
D
|
2
|
-45,45
|
11904
|
3.520
|
|
D
|
3
|
-45,45
|
13067
|
3.673
|
|
D
|
4
|
-45,45
|
12302
|
3.379
|
|
D
|
5
|
-45,45
|
12272
|
3.288
|
|
E
|
1
|
0,90
|
12537
|
3.720
|
|
E
|
2
|
-45,45
|
12464
|
3.705
|
|
E
|
3
|
-45,45
|
11640
|
3.461
|
|
F
|
1
|
-45,45
|
11154
|
2.794
|
|
F
|
2
|
0,90
|
10668
|
3.165
|
|
F
|
3
|
-45,45
|
11213
|
3.346
|
|
F
|
4
|
0,90
|
11242
|
3.336
|
|
G
|
1
|
0,90
|
12096
|
3.618
|
|
G
|
2
|
-45,45
|
14406
|
4.203
|
|
G
|
3
|
-45,45
|
13185
|
3.909
|
|
G
|
4
|
0,90
|
9962
|
2.897
|
|
H
|
1
|
0,90
|
9741
|
2.882
|
|
H
|
2
|
0,90
|
9933
|
2.998
|
|
H
|
3
|
-45,45
|
11125
|
3.297
|
|
H
|
4
|
-45,45
|
15583
|
6.093
|
Table 3: The maximum fracture load and displacement extension for specimen category I to Q
|
Category
|
Specimen Number
|
Fibers Orientations
(degree)
|
Max Fracture Load
(Newton)
|
Max Displacement
Extension (mm)
|
|
I
|
1
|
0,90
|
10345
|
3.075
|
|
I
|
2
|
-45,45
|
11728
|
3.445
|
|
I
|
3
|
0,90
|
12155
|
3.637
|
|
I
|
4
|
-45,45
|
12155
|
4.756
|
|
J
|
1
|
0,90
|
11610
|
3.465
|
|
J
|
2
|
-45,45
|
12464
|
3.672
|
|
J
|
3
|
0,90
|
15936
|
4.741
|
|
K
|
1
|
0,90
|
10036
|
2.999
|
|
K
|
2
|
-45,45
|
11654
|
3.468
|
|
K
|
3
|
-45,45
|
9624
|
2.853
|
|
L
|
1
|
0,90
|
10153
|
3.043
|
|
L
|
2
|
-45,45
|
11345
|
3.395
|
|
M
|
1
|
-45,45
|
8182
|
2.472
|
|
M
|
2
|
0,90
|
8388
|
2.462
|
|
M
|
3
|
-45,45
|
13188
|
3.897
|
|
N
|
1
|
0,90
|
11581
|
4.510
|
|
N
|
2
|
-45,45
|
13405
|
3.997
|
|
N
|
3
|
0,90
|
11213
|
3.353
|
|
N
|
4
|
0,90
|
10786
|
3.188
|
|
O
|
1
|
-45,45
|
13479
|
3.951
|
|
O
|
2
|
0,90
|
14759
|
4.344
|
|
O
|
3
|
-45,45
|
11301
|
3.337
|
|
P
|
1
|
-45,45
|
10271
|
3.012
|
|
P
|
2
|
0,90
|
10536
|
3.102
|
|
Q
|
1
|
0,90
|
10271
|
3.026
|
|
Q
|
2
|
-45,45
|
9830
|
2.869
|
Numerical Simulation
1-Part Design
To design the different parts of the desired cracked aluminum plate repaired by glass-epoxy composite, ABAQUS software version 16.4 2021 release was employed for the finite element numerical simulation. For this aim, the 3D solid extrusion was used for the aluminum plate and the shell extrusion for the crack with the length of 30 mm. In addition, the optimum shape for the glass-epoxy composite patch was considered as specimen category J Number 3 in accordance with the real specimen performance under real experimental tensile loading test which used shell planar, was designed in part module of the employed software as shown in figures 3,4 &5.
2-Poperty
The Young’s Modulus and Poisson’s Ratio were used using the real characteristics of aluminum alloy 7075 taken from the literature as table 4.
Table 4: Material Properties of the aluminum alloy 7075
|
Layer Name
|
Young’s Modulus
|
Poisson’s Ratio
|
|
Aluminum Alooy7075
|
71.7 GPa
|
0.33
|
For engineering constants of the composite patch, the following data were used as table 5
Table 5: Material properties of the glass-epoxy composite patch
|
E1
|
E2
|
E3
|
Nu12
|
Nu13
|
Nu23
|
G12
|
G13
|
G23
|
|
40e9
|
10e9
|
10e9
|
0.30
|
0.30
|
0.40
|
3.8e9
|
3.8e9
|
3.4e9
|
Maximum principal stress and displacement at failure in which the crack can propagate for the plate and composite patch were considered 520 and 4.741 respectively. To set the plies order of glass fibers orientations, the composite layup feature was utilized. Next, two plies each with the thickness value of 0.5 mm and rotation angle of 0,90 were chosen. After that, axis 3 (Z) was selected as the local material orientation system for the normal of the patch (Figure6).
3-Assmebly
Prior to assembly, two surfaces with master and slave titles were created and assigned to the front and back surfaces of the plate and composite patch respectively to act as bond in interaction module. Next, the central crack was situated with 25 mm of distance from the edges of the plate. Then, the composite patch was placed on the crack 17.5 mm away of both right and left sides to repair the aluminum plate (Figures7&8).
4-Step
The general, static procedure type was selected and 1 second allocated as time period for the step. For the initial and minimum increment size ,0.2 and 0.002 were considered respectively.
5-Meshing
After making the parts dependent, the hex element shape with linear geometric order was selected for the plate. In addition, the structured technique by global seed size of 2 and 0.2 absolute value was employed to mesh the plate. It should be noted that, the C3D8R element type (an 8-node linear brick) was used for completing the meshing process (Figure9).
The composite patch was then partitioned into a rectangular in the center and two other triangular geometries in the right and left corners of the patch. The quad element shape with structured meshing technique and linear element type S4R (4-node doubly curved general-purpose shell) were allocated for meshing the rectangular geometry. Also, to mesh the triangular geometries, tri element shape with structured mesh technique and S3 element type (a 3-node triangular general-purpose shell) were employed (Figures10,11 &12).
6-Interaction
By using the shell-to-solid coupling feature and selecting all sides of the arrow-shaped composite patch, the bond between the front surface of the plate and back of the patch was created. To simulate the crack propagation, the XFEM method was performed and the tip for the central assembled crack with growth feature was determined (Figures13&14).
7-Loading
Two sets were created for the top and end of the plate through node selection. In the initial step, to determine the boundary conditions, the end-set was constrained as encastre and the top-set with only degree of moving freedom in Y direction was set. For the created step, the top-set was subjected to 4,7140 mm of displacement during tensile loading test (Figure15).
8-Job
By switching to the job module, the cracked aluminum plated repaired by single-sided glass-epoxy composite patch was submitted to be analyzed.
9-Visualization
In this module of the software, numerical results for the requested field output were visualized as in figure16.
The force-displacement linear graph for the specimen subjected to tensile loading was then plotted (Figure17).
The maximum fracture load for other categories of specimens were also obtained as in tables 6&7.
|
Table 6: The maximum fracture load for specimen category A to H
|
|
Category
|
Specimen Number
|
Maximum Fracture Load (Newton)
|
|
A
|
1
|
14620
|
|
A
|
2
|
11920
|
|
B
|
1
|
11329
|
|
B
|
2
|
11520
|
|
C
|
1
|
12280
|
|
C
|
2
|
12280
|
|
D
|
1
|
12410
|
|
D
|
2
|
11940
|
|
D
|
3
|
13130
|
|
D
|
4
|
12334
|
|
D
|
5
|
12280
|
|
E
|
1
|
12520
|
|
E
|
2
|
12460
|
|
E
|
3
|
11710
|
|
F
|
1
|
11180
|
|
F
|
2
|
10710
|
|
F
|
3
|
11280
|
|
F
|
4
|
11360
|
|
G
|
1
|
12260
|
|
G
|
2
|
14556
|
|
G
|
3
|
13210
|
|
G
|
4
|
9969
|
|
H
|
1
|
9809
|
|
H
|
2
|
10204
|
|
H
|
3
|
11240
|
|
H
|
4
|
15610
|
Table 7: The maximum fracture load for specimen category I to
|
Category
|
Specimen Number
|
Maximum Fracture Load (Newton)
|
|
I
|
1
|
10450
|
|
I
|
2
|
11729
|
|
I
|
3
|
12360
|
|
I
|
4
|
12190
|
|
J
|
1
|
11730
|
|
J
|
2
|
12469
|
|
J
|
3
|
16089
|
|
K
|
1
|
10121
|
|
K
|
2
|
11712
|
|
K
|
3
|
9630
|
|
L
|
1
|
10257
|
|
L
|
2
|
11440
|
|
M
|
1
|
8386
|
|
M
|
2
|
8339
|
|
M
|
3
|
13220
|
|
N
|
1
|
11600
|
|
N
|
2
|
13570
|
|
N
|
3
|
11330
|
|
N
|
4
|
10770
|
|
O
|
1
|
13480
|
|
O
|
2
|
14760
|
|
O
|
3
|
11380
|
|
P
|
1
|
10390
|
|
P
|
2
|
10580
|
|
Q
|
1
|
10340
|
|
Q
|
2
|
9840
|
To provide validated data, the results of the experimental tensile tests and were accurately compared with the results of numerical simulations for each specimen of categories as in tables 8&9.
Table 8: Error percentage for experimental and numerical results of specimen category A to H
|
Category
|
Specimen Number
|
Experimental Result
|
Numerical Result
|
Error Percentage
|
|
A
|
1
|
14583
|
14620
|
0.0026
|
|
A
|
2
|
11911
|
11920
|
0.0008
|
|
B
|
1
|
11139
|
11329
|
0.0168
|
|
B
|
2
|
11492
|
11520
|
0.0025
|
|
C
|
1
|
12258
|
12280
|
0.0018
|
|
C
|
2
|
12258
|
12280
|
0.0018
|
|
D
|
1
|
12405
|
12410
|
0.0005
|
|
D
|
2
|
11904
|
11940
|
0.0031
|
|
D
|
3
|
13067
|
13130
|
0.0048
|
|
D
|
4
|
12302
|
12334
|
0.0026
|
|
D
|
5
|
12272
|
12280
|
0.0007
|
|
E
|
1
|
12537
|
12520
|
0.0014
|
|
E
|
2
|
12464
|
12460
|
0.0004
|
|
E
|
3
|
11640
|
11710
|
0.0060
|
|
F
|
1
|
11154
|
11180
|
0.0024
|
|
F
|
2
|
10668
|
10710
|
0.0040
|
|
F
|
3
|
11213
|
11280
|
0.0060
|
|
F
|
4
|
11242
|
11360
|
0.0104
|
|
G
|
1
|
12096
|
12260
|
0.0134
|
|
G
|
2
|
14406
|
14556
|
0.0104
|
|
G
|
3
|
13185
|
13210
|
0.0019
|
|
G
|
4
|
9962
|
9969
|
0.0008
|
|
H
|
1
|
9741
|
9809
|
0.0070
|
|
H
|
2
|
9933
|
10204
|
0.0266
|
|
H
|
3
|
11125
|
11240
|
0.0103
|
|
H
|
4
|
15583
|
15610
|
0.0018
|
Table 9: Error percentage for experimental and numerical results pf specimen category I to Q
|
Category
|
Specimen Number
|
Experimental Result
|
Numerical Result
|
Error Percentage
|
|
I
|
1
|
10345
|
10450
|
0.0101
|
|
I
|
2
|
11728
|
11729
|
0.0001
|
|
I
|
3
|
12155
|
12360
|
0.0166
|
|
I
|
4
|
12155
|
12190
|
0.0029
|
|
J
|
1
|
11610
|
11730
|
0.0103
|
|
J
|
2
|
12464
|
12469
|
0.0005
|
|
J
|
3
|
15936
|
16089
|
0.0096
|
|
K
|
1
|
10036
|
10121
|
0.0084
|
|
K
|
2
|
11654
|
11712
|
0.0050
|
|
K
|
3
|
9624
|
9630
|
0.0007
|
|
L
|
1
|
10153
|
10257
|
0.0102
|
|
L
|
2
|
11345
|
11440
|
0.0084
|
|
M
|
1
|
8182
|
8386
|
0.0244
|
|
M
|
2
|
8388
|
8339
|
0.0059
|
|
M
|
3
|
13188
|
13220
|
0.0025
|
|
N
|
1
|
11581
|
11600
|
0.0017
|
|
N
|
2
|
13405
|
13570
|
0.0122
|
|
N
|
3
|
11213
|
11330
|
0.0104
|
|
N
|
4
|
10786
|
10770
|
0.0015
|
|
O
|
1
|
13479
|
13480
|
0.0001
|
|
O
|
2
|
14579
|
14760
|
0.0123
|
|
O
|
3
|
11301
|
11380
|
0.0070
|
|
P
|
1
|
10271
|
10390
|
0.0115
|
|
P
|
2
|
10536
|
10580
|
0.0015
|
|
Q
|
1
|
10271
|
10340
|
0.0067
|
|
Q
|
2
|
9830
|
9840
|
0.0019
|