PSI - Issue 50

Alexander Eremin et al. / Procedia Structural Integrity 50 (2023) 65–72 Alexander Eremin / Structural Integrity Procedia 00 (2019) 000 – 000

67 3

Due to the use of ±45° layup during tensile loading a scissor-like motion of fibers will occur, providing very high longitudinal strains up to fracture. Thus the standard sets a 5% limit of engineering shear strain as a criterion for a test stop. Engineering shear strain is calculated as:

(1)

12 i xi yi     

where ε xi and ε yi are longitudinal normal strain and lateral normal strain correspondingly. As a result maximum shear stress τ m , offset shear strength τ 0.2 , and shear modulus G are calculated. Maximum shear stress is calculated as:

(2)

(max) 2 P A





12(max)

where P max – maximum force at or below 5 % engineering shear strain, A – specimen cross-sectional area before test. In-plane shear modulus of elasticity G 12 was computed by a technique similar to the described above in the 2000 to 6000 με range of the engineering shear strain. 3.2. Tensile testing of orthotropic and quasi-isotropic layups The testing is governed by ASTM D 3039 «Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials». Specimens’ loading was conducted using servohydraulic testing machine BISS UTM 150. The AFRP and CFRP coupons were rectangular shaped with no reduced sections. ASTM proposes similar coupon sizes for orthotropic (OT) and quasi-isotropic (QI) layups. In doing so the AFRP coupons with an orthotropic [0 F ] 7S and quasi-isotropic [45 F /0 F ] 3S stacking sequences had the sizes of 215 х 25 х 2.4 mm 3 and 215 х 25 х 2.1 mm 3 correspondingly. CFRPs made of unidirectional carbon fiber tapes had stacking sequences of [0/90] 5S and [45/0/- 45/90] 2S and the sizes were 215 х 25 х 2.5 mm 3 and 215 х 25 х 2 mm 3 . All specimens were tabbed using glass fiber reinforced laminate with a thickness of 1.6 mm in order to prevent grip induced failure. Five coupons were tested for each FRP type and stacking sequence. The resulting gripped length was 115 mm and loading was performed at a rate of 1.2 mm/min. Processing of raw data involved calculation of ultimate tensile strength (UTS), failure strain, elastic modulus (by chord method) and Poisson ratio. Ultimate tensile strength corresponds to the stresses at maximum registered load and is calculated using the equation: where σ UTS – ultimate tensile strength, P max – maximum load registered by the load cell, A – cross-sectional area of untested coupon. The strain was measured using a software extensometer applied via digital image correlation method. The extensometer had a length of 65 mm corresponding to ASTM-specified one. It was placed in the center of the coupon symmetrically along both axes. Elastic modulus was determined using the chord method in the range from 1000 to 3000 µ ε . In contrast to ASTM the corresponding segment of the loading curve was linearly fit in order to filter the DIC data scatter while the D3039 standard utilizes a two-point linearization of the loading curve in the specified range. However, DIC data is often “noisy” and the errors utilizing the latter method are inherent. Chord modulus is calculated using the equation: max P A UTS   (3)

chord E

(4)

   

where Δσ – difference in applied tensile stress between the two strain points, Δε – difference between the two strain points (from 1000 to 3000 µε, where 1000 με = 0.001 absolute strain). Using the linear fitting technique the slope of the curve corresponds to the elastic modulus. Poisson ratio was determined using the who le ε xx and ε yy strain fields. The equation for calculation of Poisson ratio is: