Verification of reinforcement isotropic solid model in conjunction with maximum shear stress criterion to anticipate mix
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O R I G I NA L PA P E R
Sadra Shahsavar · Mahdi Fakoor
· Filippo Berto
Verification of reinforcement isotropic solid model in conjunction with maximum shear stress criterion to anticipate mixed mode I/II fracture of composite materials
Received: 18 April 2020 / Revised: 7 August 2020 / Accepted: 27 August 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract In the present research, a new criterion based on maximum shear stress (MSS) theory is developed for fracture investigation of orthotropic materials under mixed mode I/II loading. The crack is assumed to be embedded both along and across the fibers in the isotropic matrix. Self-similar crack propagation is assumed based on experimental observations and the reinforcement isotropic solid (RIS) concept is utilized for theoretical derivation of the criterion. In this model, an istropic crack tip stress field is assumed and the effects of fibers are supposed as stress reduction factors. The superiority of employing MSS theory in conjunction with RIS model is proved by derivation of a direct MSS-based mixed mode fracture criterion with respect to the orthotropic crack tip stress field. Verification of the results is performed by comparison of the fracture limit curves with available experimental mixed mode fracture data.
List of symbols Ci j Ci j Cioff-axis j Cion-axis j ct , cn Ei j E L , E R , ET f i j (θ ), gi j (θ ) Gi j K I , K II K Ic , K IIc K Ikink , K IIkink L , R, T ni r V f , Vm x, y
Components of compliance matrix Components of compliance matrix in plane strain condition Off-axis components of compliance matrix On-axis components of compliance matrix Extensional and sliding compliance of a damaged body Young’s modulus Longitudinal, Radial and Tangential Young’s modulus for wood specimens Angular functions Shear modulus of composite material Mode I and mode II stress intensity factors Mode I and mode II fracture toughness Mode I and mode II stress intensity factors at the tip of the crack kink Longitudinal, Radial and Tangential orthotropy axes in wood specimen Reinforcement factor Distance from crack tip The volume fraction of fibers and the matrix in a composite Global coordinate system
S. Shahsavar · M. Fakoor (B) Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran E-mail: [email protected] F. Berto Norwegian University of Science and Technology, Trondheim, Norway
S. Shahsavar et al.
αi j βi (i = 1...6) θ λ νLR νLT νTR ξi (i = 1...3) ρi σiiso j σiortho j τ τcr ϕ χ ψ
Related to crack kink angle Damage coefficient in the theoretical criteria Arbitrary angle to show stress state in crack tip Dimensionless parameters Poisson’s ratio in RL direction Poisson’s ratio in TL direction Poisson’s ratio in RT direction Reinforcement factor Damage factor in fracture criteria Isotropic stress tensor Orthotropic stress tensor Shear stress Critical Shear stress Crack-Fiber angle Dimensionless parameters Airy stress function
Abbreviations ASER EMSS FEM MPS MSS MTS RIS RIS–MSS SED SER SIFs
Augmented strain energ
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