On the dynamic energy release rate in functionally graded materials

2005 ◽  
Vol 131 (3) ◽  
pp. L31-L35 ◽  
Author(s):  
Shi Weichen
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Functionally Graded Materials ◽  
Release Rate ◽  
Functionally Graded ◽  
Graded Materials ◽  
Dynamic Energy Release Rate

Integral Representation of Energy Release Rate in Graded Materials

2006 ◽  
Vol 74 (5) ◽  
pp. 1046-1048 ◽  
Author(s):  
Z.-H. Jin ◽  
C. T. Sun
Keyword(s):  
Potential Energy ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Plastic Material ◽  
Contour Integral ◽  
Material System ◽  
Graded Materials ◽  
Elastic Plastic Material ◽  
Graded Interlayer

It is well known that, for homogeneous materials, the path-independent J contour integral is the (potential) energy release rate. For general nonhomogeneous, or graded materials, such a contour integral as the energy release rate does not exist. This work presents a rigorous derivation of the extended J integral for general graded materials from the potential energy variation with crack extension. Effects of crack shielding and amplification due to a graded interlayer in an elastic-plastic material system are discussed in terms of this integral.

The Dynamic Energy Release Rate for a Steadily Propagating Antiplane Shear Crack in a Linearly Viscoelastic Body

1987 ◽  
Vol 54 (3) ◽  
pp. 635-641 ◽  
Author(s):  
J. R. Walton
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Shear Crack ◽  
Viscoelastic Body ◽  
Antiplane Shear ◽  
Singular Stress ◽  
Crack Face ◽  
Standard Linear Solid ◽  
Dynamic Energy Release Rate

The steady-state propagation of a semi-infinite, antiplane shear crack is reconsidered for a general, infinite, homogeneous and isotropic linearly viscoelastic body. As with an earlier study, the inertial term in the equation of motion is retained and the shear modulus is only assumed to be positive, continuous, decreasing, and convex. A Barenblatt type failure zone is introduced in order to cancel the singular stress, and a numerically convenient expression for the dynamic Energy Release Rate (ERR) is derived for a rather general class of crack face loadings. The ERR is shown to have a complicated dependence on crack speed and material properties with significant qualitative differences between viscoelastic and elastic material. The results are illustrated with numerical calculations for both power-law material and a standard linear solid.

Analytical Study of Delamination in Multilayered Two-Dimensional Functionally Graded Non-Linear Elastic Beams

2017 ◽  
Vol 34 (4) ◽  
pp. 495-504
Author(s):  
V. I. Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Cross Section ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Delamination Fracture

AbstractThe present paper is focused on the delamination fracture in a multilayered two-dimensional functionally graded beam configuration which exhibits non-linear behavior of the material. The beam is loaded by two longitudinal forces applied at the beam free ends. The beam contains a delamination crack which is located symmetrically with respect to the beam mid-span. The delamination is studied analytically in terms of the strain energy release rate. TheJ-integral approach is applied for verification of the analysis of the strain energy release rate. The solution derived is valid for a beam made of an arbitrary number of layers. It is assumed that each layer has individual thickness and material properties. Also, the material is two-dimensional functionally graded in the cross-section of each layer. The solution obtained can be applied for a delamination crack located arbitrary along the height of the beam cross-section. It is shown that the solution is very convenient for investigating the influences of material gradients and crack location on the delamination fracture behavior. The results obtained can be used for optimization of multilayered two-dimensional functionally graded structural members and components with respect to their delamination fracture performance.

scholarly journals Lengthwise fracture analyses of functionally graded beams by the Ramberg-Osgood equation

2018 ◽  
Vol 38 (3) ◽  
pp. 309-320 ◽  
Author(s):  
Victor Rizov
Keyword(s):  
Energy Release Rate ◽  
Mechanical Behavior ◽  
Energy Release ◽  
Cross Section ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Functionally Graded ◽  
Non Linear

The basic purpose of the present paper is to develop lengthwise fracture analyses of the functionally graded Symmetric Split Beam (SSB) configurations which exhibit non-linear mechanical behavior of the material. The SSB is loaded in pure bending. A lengthwise crack is located symmetrically with respect to the beam's mid-span. The crack is located arbitrary along the width of the beam's cross-section. Thus, the crack arms have different widths. The material is linearly and functionally graded along the height of the beam's cross-section. The material non-linearity is treated by the Ramberg-Osgood equation (this is one of the basic novelties introduced in this paper). The fracture is analyzed in terms of the strain energy release rate by applying three approaches. First, the strain energy release rate is derived by considering the balance of the energy. The strain energy release rate is obtained also by using the complementary strain energy. The fracture is analyzed also by the J-integral. The results obtained by the three approaches are identical which proves the correctness of the lengthwise fracture analyses developed in the present paper. A parametric study is carried-out in order to examine the influences of the material gradient, the lengthwise crack location along the beam's width, and the non-linear mechanical behavior of the functionally graded material on the fracture in the SSB configuration.

Delamination of Multilayered Functionally Graded Beams with Material Nonlinearity

2018 ◽  
Vol 18 (04) ◽  
pp. 1850051 ◽  
Author(s):  
V. Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Functionally Graded ◽  
Material Nonlinearity ◽  
Functionally Graded Beam ◽  
Delamination Fracture

Delamination fracture in multilayered functionally graded, split cantilever beams is analyzed with account taken of the nonlinear behavior of the material. The fracture is studied analytically in terms of the strain energy release rate. The mechanical behavior of the material is described by a power-law stress–strain relation that is not symmetric for tension and compression. The beam can have an arbitrary number of vertical layers of different thickness. Each layer can have different material properties. Besides, the material in each layer is functionally graded along the layer thickness. Also, the delamination fracture can occur at any interface. The strain energy release rate is derived by analyzing the complementary strain energy of the beam. The solution obtained is applied to elucidating the effects of crack location, material gradient and material nonlinearity on the delamination fracture behavior of multilayered functionally graded beam configuration. It is found that the material nonlinearity leads to increase of the strain energy release rate, which implies that the material nonlinearity should be taken into account in the fracture mechanics based safety design of multilayered functionally graded structural members and components.

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