Mathematical Modelling of the Crack Propagation in Wood Materials

2008 ◽  
Vol 399 ◽  
pp. 177-182
Author(s):  
Eduard Marius Craciun ◽  
Tomasz Sadowski
Keyword(s):  
Mathematical Model ◽  
Crack Propagation ◽  
Critical Value ◽  
Mode I ◽  
Stress And Strain ◽  
Far Field ◽  
Mode I Crack ◽  
Wood Composite ◽  
Mechanical Problem ◽  
Strain Fields

In this paper we study the behaviour of a Mode I crack in a pre-stressed wood composite material. A mathematical model is associated to the mechanical problem. Starting from the boundary, constitutive and far field conditions we obtain the representation of the incremental displacement, stress and strain fields using two complex potentials. Using numerical analysis we determine the critical value, which causes crack propagation and the direction of crack propagation in a particular case of a Pine wood composite.

Mathematical Aspects Regarding Cracks Behaviour in Wood Composites

2014 ◽  
Vol 601 ◽  
pp. 108-111 ◽  
Author(s):  
Eduard Marius Craciun ◽  
Tomasz Sadowski ◽  
Liviu Marsavina ◽  
Adrian Rabaea
Keyword(s):  
Fracture Criterion ◽  
Propagation Direction ◽  
Stress And Strain ◽  
Wood Composite ◽  
Wood Composites ◽  
Mechanical Problem ◽  
Collinear Cracks ◽  
Strain Fields ◽  
Crack Tips ◽  
Plane Mode

In this paper we study the interaction of two unequal collinear cracks in a pre-stressed fiber reinforced wood composite material in anti-plane mode of fracture. A mathematical model is associated to the mechanical problem. Starting from the boundary, constitutive and far field conditions we obtain the representation of the incremental displacement, stress and strain fields using two complex potentials. Using Sih s generalized fracture criterion we determine the critical incremental shear stress which produce crack propagation and the crack tips propagation direction in a particular case of a Pine wood composite.

Mathematical Model of the Effective Properties of a Fiber Reinforced Composite with a Linearly Graded Transition Zone

2010 ◽  
Vol 38 (4) ◽  
pp. 286-307
Author(s):  
Carey F. Childers
Keyword(s):  
Mathematical Model ◽  
Transition Zone ◽  
Effective Properties ◽  
Local Stress ◽  
Stress And Strain ◽  
Fiber Reinforced ◽  
Strain Fields ◽  
Shear Moduli ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite

Abstract Tires are fabricated using single ply fiber reinforced composite materials, which consist of a set of aligned stiff fibers of steel material embedded in a softer matrix of rubber material. The main goal is to develop a mathematical model to determine the local stress and strain fields for this isotropic fiber and matrix separated by a linearly graded transition zone. This model will then yield expressions for the internal stress and strain fields surrounding a single fiber. The fields will be obtained when radial, axial, and shear loads are applied. The composite is then homogenized to determine its effective mechanical properties—elastic moduli, Poisson ratios, and shear moduli. The model allows for analysis of how composites interact in order to design composites which gain full advantage of their properties.

scholarly journals Mode I Crack Propagation Experimental Analysis of Adhesive Bonded Joints Comprising Glass Fibre Composite Material under Impact and Constant Amplitude Fatigue Loading

Materials ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 4380
Author(s):  
Alirio Andres Bautista Villamil ◽  
Juan Pablo Casas Rodriguez ◽  
Alicia Porras Holguin ◽  
Maribel Silva Barrera
Keyword(s):  
Crack Propagation ◽  
Structural Integrity ◽  
Crack Propagation Rate ◽  
Fatigue Loading ◽  
Propagation Rate ◽  
Operating Conditions ◽  
Impact Testing ◽  
Mode I ◽  
Mode I Crack ◽  
Constant Amplitude

The T-90 Calima is a low-wing monoplane aircraft. Its structure is mainly composed of different components of composite materials, which are mainly bonded by using adhesive joints of different thicknesses. The T-90 Calima is a trainer aircraft; thus, adverse operating conditions such as hard landings, which cause impact loads, may affect the structural integrity of aircrafts. As a result, in this study, the mode I crack propagation rate of a typical adhesive joint of the aircraft is estimated under impact and constant amplitude fatigue loading. To this end, effects of adhesive thickness on the mechanical performance of the joint under quasistatic loading conditions, impact and constant amplitude fatigue in double cantilever beam (DCB) specimens are experimentally investigated. Cyclic impact is induced using a drop-weight impact testing machine to obtain the crack propagation rate (da/dN) as a function of the maximum strain energy release rate (GImax) diagram; likewise, this diagram is also obtained under constant amplitude fatigue, and both diagrams are compared to determine the effect of each type of loading on the structural integrity of the joint. Results reveal that the crack propagation rate under impact fatigue is three orders of magnitude greater than that under constant amplitude fatigue.

Molecular dynamics study on atomic elastic stiffness at mode I crack along bi-metal interface

2021 ◽  
Vol 379 (2196) ◽  
pp. 20200124 ◽  
Author(s):  
K. Yashiro
Keyword(s):  
Molecular Dynamics ◽  
Surface Energy ◽  
Crack Propagation ◽  
Metal Structure ◽  
Elastic Stiffness ◽  
Mode I ◽  
Mode I Crack ◽  
Fracture Dynamics ◽  
The Difference ◽  
Deformation Modes

Propagation of mode I crack along bi-metal (001) interfaces of Fe/W, Fe/Ni, Fe/Co and Ti/Mg is simulated by molecular dynamics and discussed with the eigenvalue/vector of the atomic elastic stiffness, B i j a = Δ σ i a / Δ ε j , and surface energy. The crack does not propagate at the interface but in the adjacent phase of smaller surface energy, except in Fe/Ni. The 1st eigenvalue η a (1) , or the solution of B i j a Δ ε j = η a Δ ε i of each atom, clarifies the difference of ‘soft/hard’ of both phases at the onset of crack propagation. In the case of Fe/Ni, the η a (1) of Ni atoms remarkably decreases in the Fe/Ni bi-metal structure, even though Ni has higher η a (1) than Fe at no-load perfect lattices. Thus the rupture occurs in the Ni side even though the Ni has slightly higher (001) surface energy than Fe. Deformation modes at the crack propagation are also visualized by the eigenvector of η a (1)  < 0 unstable atoms. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

scholarly journals Discontinuous Dynamics of Mode-I Crack Propagation in Single Crystals

2018 ◽  
Vol 67 (2) ◽  
pp. 222-228
Author(s):  
Tomoaki NIIYAMA ◽  
Tomotsugu SHIMOKAWA ◽  
Taishi FUJIMOTO
Keyword(s):  
Crack Propagation ◽  
Single Crystals ◽  
Mode I ◽  
Mode I Crack

scholarly journals Mode I Crack Propagation under High Cyclic Loading in 316L Stainless Steel

2014 ◽  
Vol 3 ◽  
pp. 1197-1203 ◽  
Author(s):  
W. Zhang ◽  
S. Pommier ◽  
F. Curtit ◽  
G. Léopold ◽  
S. Courtin
Keyword(s):  
Stainless Steel ◽  
Cyclic Loading ◽  
Crack Propagation ◽  
316L Stainless Steel ◽  
Mode I ◽  
Mode I Crack
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