PSI - Issue 25

P. Santos et al. / Procedia Structural Integrity 25 (2020) 370–377 P. Santos../ Structural Integrity Procedia 00 (2019) 000–000

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laminates to various strain values. In this case strains correspondent to stresses of 21%, 50% and 75% of the maximum bending stress were considered. While the stress decreased around 8.1% after 180 min for 50 MPa, this value increases to 10.6% and 11.1% for 118 MPa and 177 MPa, respectively. It should be noted that for bending stresses higher than 50% of the maximum bending stress the stress relaxation is very similar regardless of the applied strain. Regarding the creep behaviour, Fig. 4 shows typical curves obtained from the experimental tests, where the displacement is the value obtained at any instant of the test (D) divided by its initial value (D 0 ). All curves present an instantaneous displacement, which is dependent of the stress level, followed by the primary and secondary creep stages that characterize the typical creep curves. For the current conditions, the third stage is expected to occur only for higher stress values or longer times. In detail, Fig.4a) shows that flax laminates present greater creep strains than the hybrids ones. For example, after 180 min, the creep strain increases about 23.1% for flax laminates, while this value is around 9.3% and 8.1% for 1xhybrid and 2xhybrid laminates (less than half for flax laminates), respectively. One more time, the hybridization degree is very important because, in this case, it decreases the creep displacements. In terms of sensitivity to higher bending stresses, Fig. 4b) shows an increasing of 3.3 and 5 times greater when the bending stresses of 118 MPa and 177 MPa are compared with 50 MPa.

1,15

1,25

1.13

1.12

1.24

Flax

D/D 0

1.11

D/D 0

1,20

1.23

177 MPa

1.22

1,10

1.12

1.11

1,15

118 MPa

1.10

1.09

1.08

1.08

1,10

1.07 1.08

1.07

1,05

1xhybrid

50 MPa

1.06

1,05

1.07

2xhybrid

1.06

1,00

1,00

0

50

100

150

200

0

50

100

150

200

Time [min]

Time [min]

b)

a)

Fig. 4. Creep curves for: a) different laminates, bending stress of 50 MPa; b) 2× hybrid laminates and different stress values.

To predict the viscoelastic response, several models are presented in bibliography. Regarding the stress relaxation behaviour, the Kohlrausch-Williams-Watts model (KWW) is widely used in several studies (Fancey 2005, Razavi Nouri 2012, Vaidyanathan et al. 2015, Reis et al.2019, Reis et al. 2019, Reis et al. 2019, Reis et al. 2020) where the relaxation function ∅ is given by: ∅ � � � � ��� � � � �� � � � � (2) where  (t) and  0 are, respectively, the stress at time t and at t = 0,  the fractional power exponent and  the KWW relaxation time. In terms of creep prediction, the Findley law (equation 3) is widely used to describe the creep behaviour of composite materials (Scott et al.1995, Xu et al. 2010, Bouafif et al. 2013, Georgiopoulos et al. 2015, Reis et al. 2020) inclusively for short-term creep tests (Gupta et al. 1980, Georgiopoulos et al. 2015, Almeida et al. 2018): � � � �� ��� � (3) where  (t) is the creep displacement at time t,  0 is the instantaneous elastic displacement, A is the amplitude of transient creep (time-dependent) and n is a constant independent of the stress and generally less than one.