PSI - Issue 18

Alexey N. Fedorenko et al. / Procedia Structural Integrity 18 (2019) 432–442 A.N. Fedorenko, B.N. Fedulov, E. V. Lomakin / Structural Integrity Procedia 00 (2019) 000–000

433

2

1. Introduction Selection of failure model for composite materials in engineering applications is problematic regardless of large number of works in this field. In general, failure criteria for composite laminates begin on typical lamina in-plane strength properties: tension/compression in longitudinal direction, tension/compression in transverse direction, shear strength. Interlaminar fracture toughness is commonly used for the prediction of interlaminar delamination, but Bouvet et al (2009) and Hallett et al (2008) use modelling techniques of intralaminar predefined cracks or intralaminar cracking in arbitrary direction. However, the use of simple models with introduction of the minimum available material constants always contradicts with experimentally observed nonlinear anisotropic behavior of composites. First, the entire failure envelope surface for combined stress conditions should be found. Many efforts were made on determination of physically reasonable failure envelope, e.g. Hashin (1980), Tsai and Wu (1971), Puck and Schürmann (1998), but anyway it requires very specific experiments or direct testing on biaxial or triaxial loading for validation, like ones provided by Soden et al (2002). Moreover, Dávila et al (2005), Pinho et al (2006), Camanho and Maimı´ (2007) report a requirement to use in situ lamina strength properties different from measured on standard tests and propose experimental methods of their determination, as in works Pinho et al (2006), Laffan et al (2010). Possible reasons of these differences are residual stress and manufacturing defects. A direct way for consideration of defects and residual stress is a modelling of full manufacturing process as propose Bondarchuk and Fedulov, (2019). After introduction of failure initiation criterion, next stage is a selection of damage evolution law. As well as for failure criterion, damage evolution should correlate with in situ lamina behavior, which is difficult for experimental determination. Failure model should be in consistency with nonlinear elastic model, since composites demonstrate nonlinear behavior in elastic range of applied stress. Nonlinear diagram for shear loading is one of the most studied effects, e.g. Sabik (2018), Paepegem et al (2006), Totry et al (2009), Makeev et al (2009), but a consideration of only nonlinear shear constitutive relation is insufficient for modelling. For example, works by Lomakin and Rabotnov (1978), Jones (1977), Sun et al (2009) are devoted to capture different moduli in tension and compression in elastic model. More general, experimental curves from off-axis loading considered by Hahn and Tsai (1973), Smith and Pascoe (1977), Chamis and Sinclar (1977) should be matched by simulation results. Discussing dynamical analysis, reports by Koerber et al (2010) and Hsiao et al (1998) found strain rate dependency to shear and transverse loading. For the efficient analysis, it is preferred to have a flexible approach based on utilization of commonly available properties from standard tests, but with possibility of extension to capture nonlinear effects. This paper presents a possible way to consider mentioned above effects inherent to composite materials with emphasis on engineering applications. 2. Problems under consideration In this paper, we consider possible approaches to problems inherent to composites as listed below:  Nonlinear anisotropic elasticity with susceptibility to stress state conditions  Nonlinear shear  Strain rate dependency 3. Failure initiation criterion and damage evolution Two material damage parameters are chosen as presented in Eq. (1) corresponding to fiber and matrix failure modes.   Failure initiation criterion Damage evolution

0

, fiber failure

0

initial value

1     

1 



(1)

0 matrix

, failure

1

initial value

2 

2 





For the parameters of Eq. (1) degraded elastic constants at damaged state 

 1 2 ,   are proposed to have form as