5 Enabling Materials By Dimensionality: From 0D to 3D Carbon-Based. . .
167
the anisotropic response of these structures under uniaxial loading along different
directions, which results in a nonlinear, hyperelastic constitutive equation; (ii) the
significant depletion of the absolute mechanical response from parent to daughter
architectures, with a strong decrement in toughness, yield and ultimate strengths
(see also Table 5.3); and (iii) that the mechanical response is basically determined
by the reaction of triangular (tougher) or square (softer) shapes in the structures.
As a final remark, we point out that the picture so far described concerning the
absolute values slightly changes when we look at the specific properties reported
in the last two columns of Table 5.3. Indeed, the specific ultimate strength of our
novel 2D structures is comparable to graphene or even higher than the latter in
the case of the tilene parent. Nevertheless, the trend of the specific toughness,
which measures the ability of a material to absorb energy before fracture, is
overwhelmingly favourable to graphene with respect to the other structures.
Table 5.3 Fracture strain (first column), strength (second column), strength ×t (third column)
and toughness×t (fourth column) of the parent and daughter planar structures alongside the
specific strength and specific toughness (fifth and sixth columns). The conventional thickness of
the graphenic materials is considered to be t = 3.35 Å. In the table the following abbreviations
were used: p. = parent, d. = daughter
Fracture
Strength Toughness Specific
Specific
Loading strain
Strength ×t
×t
strength
toughness
direction (%)
(GPa)
(N/m)
(J m −2 )
(MNm kg −1 ) (MJ kg −1 )
Graphene
x
>35
112
37.5
>9.83
49.7
> 13.0
y
26–28
102
34.2
6.51
45.2
8.61
Graphene d. x
18–20
29.3
9.81
0.83
19.2
1.62
y
>30
67.7
22.6
>3.63
44.3
> 7.11
Tilene p.
x,y
24–26
99.6
33.4
5.55
49.7
8.27
45 ◦
32–34
79.1
26.5
5.68
39.5
8.47
Tilene
x,y
20–22
44.8
15.0
1.66
32.3
3.57
45 ◦
18–20
30.3
10.2
0.92
21.9
1.97
Flakene p. x
22–24
66.7
22.3
3.37
37.2
5.61
y
22–24
57.9
19.4
3.01
32.3
5.02
Flakene
x
12–14
23.6
7.92
0.49
18.7
1.16
y
14–16
25.8
8.63
0.63
20.4
1.49
Liskene
x,y
18–20
63.2
21.2
2.19
35.8
3.70
45 ◦
14–16
43.8
14.7
1.27
24.7
2.14
Liskene d. x,y
12–14
27.8
9.32
0.59
18.5
1.20
45 ◦
14–16
28.0
9.37
0.68
19.0
1.37
167
the anisotropic response of these structures under uniaxial loading along different
directions, which results in a nonlinear, hyperelastic constitutive equation; (ii) the
significant depletion of the absolute mechanical response from parent to daughter
architectures, with a strong decrement in toughness, yield and ultimate strengths
(see also Table 5.3); and (iii) that the mechanical response is basically determined
by the reaction of triangular (tougher) or square (softer) shapes in the structures.
As a final remark, we point out that the picture so far described concerning the
absolute values slightly changes when we look at the specific properties reported
in the last two columns of Table 5.3. Indeed, the specific ultimate strength of our
novel 2D structures is comparable to graphene or even higher than the latter in
the case of the tilene parent. Nevertheless, the trend of the specific toughness,
which measures the ability of a material to absorb energy before fracture, is
overwhelmingly favourable to graphene with respect to the other structures.
Table 5.3 Fracture strain (first column), strength (second column), strength ×t (third column)
and toughness×t (fourth column) of the parent and daughter planar structures alongside the
specific strength and specific toughness (fifth and sixth columns). The conventional thickness of
the graphenic materials is considered to be t = 3.35 Å. In the table the following abbreviations
were used: p. = parent, d. = daughter
Fracture
Strength Toughness Specific
Specific
Loading strain
Strength ×t
×t
strength
toughness
direction (%)
(GPa)
(N/m)
(J m −2 )
(MNm kg −1 ) (MJ kg −1 )
Graphene
x
>35
112
37.5
>9.83
49.7
> 13.0
y
26–28
102
34.2
6.51
45.2
8.61
Graphene d. x
18–20
29.3
9.81
0.83
19.2
1.62
y
>30
67.7
22.6
>3.63
44.3
> 7.11
Tilene p.
x,y
24–26
99.6
33.4
5.55
49.7
8.27
45 ◦
32–34
79.1
26.5
5.68
39.5
8.47
Tilene
x,y
20–22
44.8
15.0
1.66
32.3
3.57
45 ◦
18–20
30.3
10.2
0.92
21.9
1.97
Flakene p. x
22–24
66.7
22.3
3.37
37.2
5.61
y
22–24
57.9
19.4
3.01
32.3
5.02
Flakene
x
12–14
23.6
7.92
0.49
18.7
1.16
y
14–16
25.8
8.63
0.63
20.4
1.49
Liskene
x,y
18–20
63.2
21.2
2.19
35.8
3.70
45 ◦
14–16
43.8
14.7
1.27
24.7
2.14
Liskene d. x,y
12–14
27.8
9.32
0.59
18.5
1.20
45 ◦
14–16
28.0
9.37
0.68
19.0
1.37