Constituent Materials and Properties - Strengthening Design of Reinforced Concrete with FRP - page 68

periods exceeding 500,000 hours (about 57 years). These studies were conducted by
Yamaguchi et al. (1997) and Malvar (1998).
Fatigue is also a sudden failure at a cyclic relatively low stress range for an
extended period of time. For a stress ratio (minimum to maximum applied stress) of
0.1 using tension-tension sinusoidal low-cycle loading, the fatigue strength of CFRP
is 60%-70% of the static ultimate strength after 1 million cycles (ACI 440.2R-08).
Larson, Peterman, and Rasheed (2005) performed experiments on full-scale con-
crete beams prestressed with straight strands that were then strengthened with CFRP.
The failure mode observed was CFRP rupture for all beams tested under static and
fatigue loading. Furthermore, there was no reduction in the CFRP tensile strength at
static failure after 1 million cycles of fatigue at about 124 MPa (18 ksi) strand stress
range. However, the CFRP fatigue strength was about 79% of the static ultimate
strength after 3 million cycles of fatigue at about 248 MPa (36 ksi) strand stress
range (Rasheed, Larson, and Peterman 2006). On the other hand, GFRP undergoes
10% loss of static ultimate strength per decade of logarithmic life time (Mandell
1982). Odagiri, Matsumoto, and Nakai (1997) reported a tension-tension fatigue
strength of AFRP in the range of 54%-73% of the static ultimate strength after 2
million cycles of fatigue. Odagiri, Matsumoto, and Nakai (1997) suggested limiting
the maximum stress to 0.54-0.73 times the static tensile strength to avoid lifetime
fatigue failure. It is important to note that all these figures apply to unidirectional
composite with loading along the fiber direction.
Chapter Problems
Problem 3.1
Determine the laminate in-plane stiffness properties of AS-4 carbon/epoxy and
Kevlar 49/epoxy for 60% fiber volume fraction. Then compare your results with the
typical values given in the tables of the Delaware Encyclopedia of Composites . Use
imperial units. The Possion's ratio for epoxy = 0.37, for AS-4 carbon fiber = 0.17, and
for Kevlar 49 fiber = 0.32.
Problem 3.2
Determine the laminate in-plane stiffness properties of S-glass/epoxy for 60% fiber
volume fraction. Then compare your results with the typical values given in the
tables of the Delaware Encyclopedia of Composites . Use SI units. The Possion's
ratio for epoxy = 0.37 and for S-glass fiber = 0.22.
Problem 3.3
A test panel was fabricated using one ply only of carbon fiber/epoxy unidirectional
FRP system with the wet lay-up technique (Decker 2007). Based on the manufac-
turer's data sheet of this FRP system, the net fiber area is 0.0065 in. 2 /in. (0.165 mm 2 /
mm) width per ply. After the system has cured, five 2-in. (50.8 mm)-wide test cou-
pons are cut from the single-ply panel (CFRP-1 through CFRP-5). The test coupons
were tested in tension to rupture according to ASTM D3039. The following table
presents the results of the tension tests. Determine the average and the design tensile
properties based on the composite laminate and the net fiber area.