Elastodynamic Near-Tip Stress and Displacement Fields for Rapidly Propagating Cracks in Orthotropic Materials

1975 ◽  
Vol 42 (1) ◽  
pp. 183-189 ◽  
Author(s):  
J. D. Achenbach ◽  
Z. P. Bazˇant
Keyword(s):  
Crack Propagation ◽  
Numerical Procedure ◽  
Orthotropic Materials ◽  
Time Varying ◽  
Two Dimensional ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
Curved Paths ◽  
Isotropic And Orthotropic Materials ◽  
Maximum Stresses

The near-tip angular variations of elastodynamic stress and displacement fields are investigated for rapid transient crack propagation in isotropic and orthotropic materials. The two-dimensional near-tip displacement fields are assumed in the general form rp T(t, c) K(θ, c), where c is a time-varying velocity of crack propagation, and it is shown that p = 0.5. For isotropic materials, K(θ, c) is determined explicitly by analytical considerations. A numerical procedure is employed to determine K(θ, c) for orthotropic materials. The tendency of the maximum stresses to move out of the plane of crack propagation as the speed of crack propagation increases is more pronounced for orthotropic materials, for the case that the crack propagates in the direction of the larger elastic modulus. The angular variations of the near-tip fields are the same for steady-state and transient crack propagation, and for propagation along straight and curved paths, provided that the direction of crack propagation and the speed of the crack tip vary continuously.

Elastodynamic Local Fields for a Crack Running in an Orthotopic Medium

1991 ◽  
Vol 58 (4) ◽  
pp. 982-987 ◽  
Author(s):  
A. Piva ◽  
E. Radi
Keyword(s):  
Dynamic Stress ◽  
Equations Of Motion ◽  
Local Fields ◽  
Stress Fields ◽  
Orthotropic Materials ◽  
Displacement Fields ◽  
First Order ◽  
Stress And Displacement Fields ◽  
Order Elliptic System ◽  
Separated Variables

The dynamic stress and displacement fields in the neighborhood of the tip of a crack propagating in an orthotropic medium are obtained. The approach deals with the methods of linear algebra to transform the equations of motion into a first-order elliptic system whose solution is sought under the assumption that the local displacement field may be represented under a scheme of separated variables. The analytical approach has enabled the distinction between two kinds of orthotropic materials for which explicit espressions of the near-tip stress fields are obtained. Some results are presented graphically also in order to compare them with the numerical solution given in a quoted reference.

scholarly journals Surface Displacements due to a Steadily Moving Point Force

1996 ◽  
Vol 63 (2) ◽  
pp. 245-251 ◽  
Author(s):  
J. R. Barber
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Elastic Half Space ◽  
Point Force ◽  
Two Dimensional ◽  
Normal Surface ◽  
Displacement Fields ◽  
Linear Superposition ◽  
Surface Displacements ◽  
Stress And Displacement Fields

Closed-form expressions are obtained for the normal surface displacements due to a normal point force moving at constant speed over the surface of an elastic half-space. The Smirnov-Sobolev technique is used to reduce the problem to a linear superposition of two-dimensional stress and displacement fields.

Stress and Displacement Fields for Propagating the Crack Along the Interface of Dissimilar Orthotropic Materials Under Dynamic Mode I and II Load

1999 ◽  
Vol 67 (1) ◽  
pp. 223-228 ◽  
Author(s):  
K. H. Lee
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Complex Function ◽  
Orthotropic Materials ◽  
Dynamic Mode ◽  
Mode I ◽  
Intensity Factors ◽  
Displacement Fields ◽  
Crack Propagation Velocity ◽  
Stress And Displacement Fields

General stress and displacement fields are derived as a crack steadily propagates along the interface of dissimilar orthotropic materials under a dynamic mode I and II load. They are obtained from the complex function formulation of steady plane motion problems for an orthotropic material and the complex eigenexpansion function. After the relationship between stress intensity factors and stress components for a propagating crack is defined, the stress, displacement components, and energy release rate with stress intensity factors are derived. The results are useful for both dissimilar isotropic and orthotropic and isotropic-orthotropic bimaterials, and homogeneous isotropic and orthotropic materials under subsonic crack propagation velocity. [S0021-8936(00)00601-2]

A Stress Singularity Parameter Approach for Evaluating the Interfacial Reliability of Plastic Encapsulated LSI Devices

1989 ◽  
Vol 111 (4) ◽  
pp. 243-248 ◽  
Author(s):  
T. Hattori ◽  
S. Sakata ◽  
G. Murakami
Keyword(s):  
Adhesive Strength ◽  
Evaluation Method ◽  
Stress Singularity ◽  
The Finite Element Method ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
Ni Alloy ◽  
Base Resin ◽  
Interfacial Reliability ◽  
Parameter Approach

Since the stress and displacement fields near a bonding edge show singularity behaviors, the adhesive strength evaluation method, using maximum stresses calculated by a numerical stress analysis such as the finite element method, is generally not valid. In this paper, a new method, which uses two stress singularity parameters, is presented for evaluating adhesive strength. This method is applied to several kinds of molded models, composed of epoxy base resin and Fe-Ni alloy sheets, and plastic encapsulated LSI models. Predictions about the initiation and extension of delamination are compared with the results of observations made by scanning acoustic tomography on these models.

Microdeformations in Sands by Digital Image Processing and Analysis

1996 ◽  
Vol 1548 (1) ◽  
pp. 31-37 ◽  
Author(s):  
Scott A. Raschke ◽  
Roman D. Hryciw ◽  
Gregory W. Donohoe
Keyword(s):  
Image Processing ◽  
Digital Image Processing ◽  
Digital Image ◽  
Small Scale ◽  
Two Dimensional ◽  
Localized Deformation ◽  
Displacement Fields ◽  
Particulate Media ◽  
Image Processing And Analysis ◽  
Video Images

Laboratory experiments are typically performed on particulate media to study stress-deformation behavior and to verify or calibrate computer models from controlled or measured boundary stresses and displacements. However, such data do not permit the formation of shear bands, displacement fields within flowing granular media, and other small-scale localized deformation phenomena to be identified. Described are two semiautomated computer vision techniques for accurately determining the two-dimensional displacement field in granular soils from video images obtained through a transparent planar viewing window. The techniques described are applicable for studying the behavior of particulate media under plane strain and certain axisymmetric test conditions. Digital image processing and analysis routines are used in two different computer programs, Tracker and Tracer, Tracker uses a graphical user interface that allows individual particles to be selected and tracked through a sequence of digital video images. A contrast edge detection algorithm delineates the two-dimensional projected boundaries of particles. The location of the centroid of each particle selected for tracking is determined from the boundary to quantify the trajectory of each particle. Tracer maps the trace or trajectory of specially dyed fluorescent particles in a sequence of video frames. A thresholding technique segments individual particle trajectories. Together, Tracker and Tracer provide a set of tools for identifying small-scale displacement fields in particulate assemblies deforming under either quasi-static or rapid loading (such as gravity flow).

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