PSI - Issue 37

Almudena Majano-Majano et al. / Procedia Structural Integrity 37 (2022) 492–499 Almudena Majano-Majano et al. / Structural Integrity Procedia 00 (2019) 000 – 000

495

4

two 3 mm diameter holes drilled 10 mm away from the end of the specimens. A conventional Instrom ® 1125 testing machine equipped with a load cell of 5 kN maximum capacity and 50 N/V gain was used. Specimens were loaded at 3 mm/min crosshead displacement control. The load ( P ) and the displacement of its point of application ( δ ) were recorded during each test. The crack tip opening displacement ( w ) was also registered using the optical metrology ARAMIS DIC-2D by GOM. This is a non contact system that applies the principles of digital image correlation (DIC) and makes it possible to measure the deformation field at the crack initiation zone. It is composed by a charge coupled device camera (8-bit Baumer Optronic FWX20 model) with a telecentric lens of 0.243±3% magnification, 29.3×22.1 mm 2 field of view and 11 mm field depth. A working distance of 103.5±3 mm was set, from which a conversion factor of 0.018 mm/pixel was obtained. To ensure proper granulometry contrast and isotropy at the magnification scale, a thin black and white speckle pattern was applied to the area of interest on the specimen surface using an airbrush IWATA, model CB-M. The images are divided into subsets, within which an independent displacement measurement is calculated by correlation for subsequent images. Image subsets of 15×15 pixels 2 size and 13×13 pixels 2 step were defined in a compromise between correlation and interpolation errors. The displacement resolution was in the range of 1-2×10 -2 pixel (0.18- 0.36 μm) . The crack tip opening displacements were then evaluated from a pair of imagen subsets located at the upper and lower part of the crack tip location. It was not necessary to measure the crack growth during the test since it would be difficult to identify the crack tip during propagation. It supports the application of the CBBM data reduction scheme to evaluate the R-curves. 2.3. Direct method for cohesive law estimation A direct method based on the experimental determination of the cohesive law is here applied. The cohesive law in mode I relates the traction ( σ I ) with the crack tip opening displacement ( w I ), and arises from the differentiation of the strain energy release rate ( G I ) with respect to w I in the form

( ) I

I I w dG dw =

I 

(1)

being

I w

( ) I w w  d I

= 

G

(2)

I

I

0

So this method requires an accurate measurement of G I evolution as a function of w I in the course of an experimental fracture test. The classical data reduction schemes for this purpose are based on the beam theory or compliance calibration method and require the crack length ( a ) monitoring during the test, which is difficult to be performed. To overcome this problem, the Compliance Based Beam method (CBBM) (de Moura et al. (2008a)) is here applied. It is based on the specimen compliance, Timoshenko beam theory and an equivalent crack length ( a eq ) concept, which avoids the experimental measurement of the crack growth and only depends on the data provided by the load displacement curve. From the formulation by Irwin and Kies (1954), the evolution of G I as a function of the crack length (i.e. the resistance curve to the material to the crack growth or R -curve) is

2 d 2 d P C B a

(3)

G

=

I

According to the Timoshenko beam theory and Castigliano theorem, and neglecting the adhesive thickness, the compliance C of a DCB specimen can be written as

3

8

12

a

a

C

=

+

(4)

3

5

BhG

L E Bh

LR