48
2 Dynamic Compressive Mechanical Properties of UHPCC
2.4.6 Energy Absorption Capacity
The energy absorption capacity is always used to evaluate the dynamic mechanics
performance of a material and usually expressed as toughness, which can be determined by calculating the area under the stress–strain curves according to W =
σ dε,
where W denotes the toughness of a material, σ and ε are the stress and strain,
respectively.
Based on the dynamic stress–strain curves of UHPCC given in Fig. 2.11, Table 2.5
lists the corresponding dynamic toughness of UHPCC under various strain rates. W p
and W u represent the peak and ultimate dynamic toughness when the strain reaches
the peak and ultimate value, respectively. As shown in Fig. 2.11, the stress is at a
relative low level when the strain reaches 0.05. Thus, the ultimate strain is determined
as 0.05. “—” denotes that the dynamic toughness is not given since the stress–strain
curves are hysteretic and the peak stresses are not the actual failure stresses.
Figure 2.15 illustrates the comparison of the dynamic toughness of UHPCC with
varying steel fiber reinforcement at different strain rates. It indicates that, (i) both the
peak and ultimate dynamic toughness gradually increase with the increase of strain
rate; (ii) the steel fiber content and type almost have no effects on the peak dynamic
toughness of UHPCC; (iii) the ultimate dynamic toughness of UHPCC increases
with increasing the volumetric ratio of steel fibers, either with the micro-straight or
hooked steel fibers, and the influence of the former is more obvious. For example,
at the strain rate around 150 s
−1 , the ultimate dynamic toughness of UHPCC with
mixing 2.0% micro-straight steel fibers (33590 J/m
3 ) is 20.7% and 12.4% larger than
those of UHPCC with 1.0% micro-straight steel fibers (27820 J/m
3 ) and 2.0% hooked
steel fibers (29890 J/m
3 ), respectively. The reason may lie in that, the matrix will be
cracking firstly under the dynamic loadings and the steel fibers in the specimen resist
the formation and propagation of cracks. Increasing steel fiber content could make
more steel fibers to delay the crack propagation, which implies that more energy are
Table 2.5 Dynamic toughness of UHPCC
Test
No.
W p (J/m 3 ) W u (J/m 3 ) Test
No.
W p (J/m 3 ) W u (J/m 3 ) Test
No.
W p (J/m 3 ) W u (J/m 3 )
N-0-1 –
–
N-0-2 4810
14,040
N-0-3 5620
17,610
N-0-4 6990
24,230
N-0-5 8270
27,200
N-0-6 12,250
31,980
S-1-1 –
–
S-1-2 5440
14,430
S-1-3 6740
21,530
S-1-4 8220
27,820
S-1-5 9400
31,540
S-1-6 12,220
34,980
S-2-1 –
–
S-2-2 –
–
S-2-3 8730
24,170
S-2-4 7880
33,590
S-2-5 9320
36,070
S-2-6 12,930
40,360
H-1-1 –
–
H-1-2 4860
16,200
H-1-3 6170
20,700
H-1-4 7400
26,320
H-1-5 9570
30,040
H-1-6 12,980
34,100
H-2-1 –
–
H-2-2 5330
12,890
H-2-3 5540
20,940
H-2-4 7680
29,890
H-2-5 8880
35,930
H-2-6 12,860
37,890
2 Dynamic Compressive Mechanical Properties of UHPCC
2.4.6 Energy Absorption Capacity
The energy absorption capacity is always used to evaluate the dynamic mechanics
performance of a material and usually expressed as toughness, which can be determined by calculating the area under the stress–strain curves according to W =
σ dε,
where W denotes the toughness of a material, σ and ε are the stress and strain,
respectively.
Based on the dynamic stress–strain curves of UHPCC given in Fig. 2.11, Table 2.5
lists the corresponding dynamic toughness of UHPCC under various strain rates. W p
and W u represent the peak and ultimate dynamic toughness when the strain reaches
the peak and ultimate value, respectively. As shown in Fig. 2.11, the stress is at a
relative low level when the strain reaches 0.05. Thus, the ultimate strain is determined
as 0.05. “—” denotes that the dynamic toughness is not given since the stress–strain
curves are hysteretic and the peak stresses are not the actual failure stresses.
Figure 2.15 illustrates the comparison of the dynamic toughness of UHPCC with
varying steel fiber reinforcement at different strain rates. It indicates that, (i) both the
peak and ultimate dynamic toughness gradually increase with the increase of strain
rate; (ii) the steel fiber content and type almost have no effects on the peak dynamic
toughness of UHPCC; (iii) the ultimate dynamic toughness of UHPCC increases
with increasing the volumetric ratio of steel fibers, either with the micro-straight or
hooked steel fibers, and the influence of the former is more obvious. For example,
at the strain rate around 150 s
−1 , the ultimate dynamic toughness of UHPCC with
mixing 2.0% micro-straight steel fibers (33590 J/m
3 ) is 20.7% and 12.4% larger than
those of UHPCC with 1.0% micro-straight steel fibers (27820 J/m
3 ) and 2.0% hooked
steel fibers (29890 J/m
3 ), respectively. The reason may lie in that, the matrix will be
cracking firstly under the dynamic loadings and the steel fibers in the specimen resist
the formation and propagation of cracks. Increasing steel fiber content could make
more steel fibers to delay the crack propagation, which implies that more energy are
Table 2.5 Dynamic toughness of UHPCC
Test
No.
W p (J/m 3 ) W u (J/m 3 ) Test
No.
W p (J/m 3 ) W u (J/m 3 ) Test
No.
W p (J/m 3 ) W u (J/m 3 )
N-0-1 –
–
N-0-2 4810
14,040
N-0-3 5620
17,610
N-0-4 6990
24,230
N-0-5 8270
27,200
N-0-6 12,250
31,980
S-1-1 –
–
S-1-2 5440
14,430
S-1-3 6740
21,530
S-1-4 8220
27,820
S-1-5 9400
31,540
S-1-6 12,220
34,980
S-2-1 –
–
S-2-2 –
–
S-2-3 8730
24,170
S-2-4 7880
33,590
S-2-5 9320
36,070
S-2-6 12,930
40,360
H-1-1 –
–
H-1-2 4860
16,200
H-1-3 6170
20,700
H-1-4 7400
26,320
H-1-5 9570
30,040
H-1-6 12,980
34,100
H-2-1 –
–
H-2-2 5330
12,890
H-2-3 5540
20,940
H-2-4 7680
29,890
H-2-5 8880
35,930
H-2-6 12,860
37,890