Viscoelastic Functionally Graded Materials Subjected to Antiplane Shear Fracture

2000 ◽  
Vol 68 (2) ◽  
pp. 284-293 ◽  
Author(s):  
G. H. Paulino ◽  
Z.-H. Jin
Keyword(s):  
Relaxation Time ◽  
Stress Intensity ◽  
Power Law ◽  
Functionally Graded Material ◽  
Relaxation Function ◽  
Functionally Graded ◽  
Antiplane Shear ◽  
Intensity Factors ◽  
Graded Material ◽  
Shear Relaxation

In this paper, a crack in a strip of a viscoelastic functionally graded material is studied under antiplane shear conditions. The shear relaxation function of the material is assumed as μ=μ0 expβy/hft, where h is a length scale and f(t) is a nondimensional function of time t having either the form ft=μ∞/μ0+1−μ∞/μ0exp−t/t0 for a linear standard solid, or ft=t0/tq for a power-law material model. We also consider the shear relaxation function μ=μ0 expβy/h[t0 expδy/h/t]q in which the relaxation time depends on the Cartesian coordinate y exponentially. Thus this latter model represents a power-law material with position-dependent relaxation time. In the above expressions, the parameters β, μ0,μ∞,t0; δ, q are material constants. An elastic crack problem is first solved and the correspondence principle (revisited) is used to obtain stress intensity factors for the viscoelastic functionally graded material. Formulas for stress intensity factors and crack displacement profiles are derived. Results for these quantities are discussed considering various material models and loading conditions.

Computation of dynamic stress intensity factors for cracks in three-dimensional functionally graded solids

2017 ◽  
Vol 233 (5) ◽  
pp. 862-873
Author(s):  
Safa Peyman ◽  
Rahmatollah Ghajar ◽  
Saeed Irani
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Material ◽  
Stress Intensity Factors ◽  
Material Properties ◽  
Dynamic Stress ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Interaction Integral ◽  
Graded Material

Dynamic stress intensity factors are important parameters in the dynamic fracture behavior of a cracked body. In this paper, an interaction integral method is utilized to compute the mixed-mode dynamic stress intensity factors of three-dimensional functionally graded material solids. Using a proper definition of actual and auxiliary fields, a new formulation and application of the interaction integral is proposed, which is independent of the derivatives of the material properties. ABAQUS finite element package is applied to analyze the functionally graded material cracked bodies. Accordingly, a user material subroutine is written for implementing the continuous variation of the material properties. Temperature was used as an additional variable to consider the variation of density. A research code is developed to compute the interaction integral. This code is then validated by solving some homogeneous and functionally graded material problems. Furthermore, the effect of the material properties on the dynamic stress intensity factors of FGM bodies with elliptical crack is investigated by taking the sigmoidal model into account. Several important fracture behavior of functionally graded material cracked bodies under dynamic loadings for different material property profiles are explored in detail.

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

2021 ◽  
pp. 146442072098817
Author(s):  
Md. Imran Ali ◽  
Mohammad Sikandar Azam
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Stiffness Matrix ◽  
Natural Vibration ◽  
Dynamic Stiffness ◽  
Functionally Graded ◽  
Neutral Surface ◽  
Functionally Graded Plate ◽  
Dynamic Stiffness Matrix ◽  
Graded Material

This paper presents the formulation of dynamic stiffness matrix for the natural vibration analysis of porous power-law functionally graded Levy-type plate. In the process of formulating the dynamic stiffness matrix, Kirchhoff-Love plate theory in tandem with the notion of neutral surface has been taken on board. The developed dynamic stiffness matrix, a transcendental function of frequency, has been solved through the Wittrick–Williams algorithm. Hamilton’s principle is used to obtain the equation of motion and associated natural boundary conditions of porous power-law functionally graded plate. The variation across the thickness of the functionally graded plate’s material properties follows the power-law function. During the fabrication process, the microvoids and pores develop in functionally graded material plates. Three types of porosity distributions are considered in this article: even, uneven, and logarithmic. The eigenvalues computed by the dynamic stiffness matrix using Wittrick–Williams algorithm for isotropic, power-law functionally graded, and porous power-law functionally graded plate are juxtaposed with previously referred results, and good agreement is found. The significance of various parameters of plate vis-à-vis aspect ratio ( L/b), boundary conditions, volume fraction index ( p), porosity parameter ( e), and porosity distribution on the eigenvalues of the porous power-law functionally graded plate is examined. The effect of material density ratio and Young’s modulus ratio on the natural vibration of porous power-law functionally graded plate is also explained in this article. The results also prove that the method provided in the present work is highly accurate and computationally efficient and could be confidently used as a reference for further study of porous functionally graded material plate.

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