Experimental evaluation of cohesive laws components of mixed-mode I + II fracture characterization of cortical bone

Mixed-mode I + II fracture characterization of cortical bone tissue is addressed in this work. The mixed-mode bending test was used to impose different mode ratios. An equivalent crack length data reduction method was considered to obtain the strain energy release rate components. Crack opening and shear displacements were measured by means of digital image correlation. These quantities were then integrated to propose a direct evaluation of cohesive laws. The components of the cohesive laws for each mixed-mode loading were obtained by the uncoupled and Hogberg ¨ ’s methods. The later provided consistent evolution of strain energy release rate and peak stresses components in function of mode-ratio, revealing its appropriateness regarding the fracture characterization of cortical bone under mixed-mode I + II loading.The first and second author acknowledges the Portuguese Foundation for Science and Technology, under the project UIDB/04033/2020. The third and fifth authors acknowledge the ‘Laboratorio' Associado de Energia, Transportes e Aeronautica’ (LAETA) for the financial support by the project UID/EMS/50022/2019 and the financing of FCT/MCTES through national funds (PIDDAC) and UIDB/00667/2020 (UNIDEMI). The fourth author acknowledges the Portuguese Foundation for Science and Technology, under the project PTDC/EME-SIS/28225/2017

Determining mode I cohesive law of Pinus pinaster by coupling double cantilever beam test with digital image correlation

The direct identification of the cohesive law in pure mode I of Pinus pinaster is addressed. The approach couples the double cantilever beam (DCB) test with digital image correlation (DIC). Wooden beam specimens loaded in the radial-longitudinal (RL) fracture propagation system are used. The strain energy release rate in mode I (GI ) is uniquely determined from the load-displacement ( P ?? ) curve by means of the compliance-based beam method (CBBM). This method relies on the concept of equivalent elastic crack length ( eq a ) and therefore does not require the monitoring of crack propagation during test. The crack tip opening displacement in mode I ? ? I w is determined from the displacement field at the initial crack tip. The cohesive law in mode I I I (? ? w ) is then identified by numerical differentiation of the I I G ? w relationship. Moreover, the proposed procedure is validated by finite element analyses including cohesive zone modelling. It is concluded that the proposed data reduction scheme is adequate for assessing the cohesive law in pure mode I of P. pinaster

Equivalent crack based analyses of ENF and ELS tests

Equivalent crack based data reduction schemes have been recently proposed for mode II interlaminar fracture tests. These methods avoid the difficulties in monitoring crack propagation throughout the test, as the experimental compliance data is used to calculate the crack position. However, their accuracy has not been demonstrated. In this paper, application of equivalent crack approaches to End-Notched Flexure and End-Loaded Split tests was studied numerically. A cohesive zone damage model based on developed interface finite elements was used. Equivalent crack methods were found to be very accurate for both specimens, while classical beam theory based data reduction schemes underestimated fracture toughness.FCT - POCI/EME/57956/200

Evaluation of initiation criteria used in interlaminar fracture tests

The objective of this work was to evaluate the non-linearity (NL) and 5% offset or maximum load (5%-Max) criteria that are commonly used to define initiation in interlaminar fracture tests. This study is in the sequence of a previous paper where the mode I DCB and mode II ENF specimens were analysed. Finite element (FE) simulations of delamination growth were here performed for the mode II end-loaded split (ELS) and 4-point end-notched flexure (4ENF) tests. The results indicated that the formation of large process zones could affect significantly NL criteria. The maximum load point gave the most accurate toughness values, especially for the 4ENF specimen. Finally, present and previous results were compared to experimental data available in the literature

Assessment of initiation criteria used in interlaminar fracture tests of composites

Finite element (FE) simulations of delamination growth in mode I Double Cantilever Beam (DCB) and mode II End-Notched Flexure (ENF) specimens were conducted in order to evaluate the non-linearity (NL) and 5% offset or maximum load (5%-Max) criteria. The results showed a good performance of the 5%-Max criterion, while the NL criterion was inadequate for the ENF test. However, it was also found that large process zones in common ENF specimens may lead to significant toughness underestimations. In order to obtain accurate results it was necessary to increase the starter crack length and the support span

Influence of intralaminar cracking on the apparent interlaminar mode I fracture toughness of cross-ply laminates

One of the major difficulties in interlaminar fracture tests of multidirectional laminates is the high tendency for intralaminar cracking and the resulting wavy crack propagation. Experimental work showed that this occurred in double cantilever beam (DCB) tests of cross-ply laminates having a starter crack on a 0degrees/90degrees interface. Moreover, under steady-state propagation conditions, the apparent values of the critical strain energy release rate G(Ic) were two times higher than those of 0degrees/0degrees specimens. In this paper, a finite-element-based progressive damage model was used to simulate crack propagation in cross-ply specimens. The results showed that transverse cracking alone cannot be responsible for the above difference of G(Ic) values. Therefore, the higher propagation G(Ic) values for cross-plies must be attributed to the more extensive fibre bridging observed and to plastic deformations of the 90degrees interfacial ply.FCT - POCTI/EME/38731/2001, FEDER EU fun

Design and analysis of a new six-point edge crack torsion (6ECT) specimen for mode III interlaminar fracture characterisation

A new six-point edge crack torsion (6ECT) test is proposed for the measurement of the mode III interlaminar critical strain energy release rate GIIIC. In contrast with the common ECT test, which is limited to the evaluation of initiation GIIIC values, the 6ECT allows the measurement of a mode III R-curve. Actually, the existence of such effect has been suggested in various experimental studies. The suitability of the 6ECT carbon/epoxy specimens combined with an effective crack based data reduction scheme is validated by finite element analyses with the virtual crack closure technique and cohesive elements

Mode III interlaminar fracture of carbon/epoxy laminates using the Six-Point Edge Crack Torsion (6ECT)

The recently proposed Six-Point Edge Crack Torsion (6ECT) test was used to evaluate the mode III interlaminar fracture of carbon/epoxy laminates. Plate specimens with starter delaminations in 0/0, 0/90 and 0/45 interfaces were tested. Data reduction was performed with an effective crack scheme validated in a previous numerical study. The tests allowed the evaluation of fairly unambiguous initiation GIIIC values and of subsequent R-curves. Examinations of specimen cross-section showed considerable lengths of pure interlaminar propagation in specimens with starter delaminations in 0/90 and 0/45 interfaces. The latter specimens had the lowest initiation GIIIC values