Transient Analysis of a Subsonic Propagating Interface Crack Subjected to Antiplane Dynamic Loading in Dissimilar Isotropic Materials

1997 ◽  
Vol 64 (3) ◽  
pp. 546-556 ◽  
Author(s):  
Yi-Shyong Ing ◽  
Chien-Ching Ma
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Fundamental Solution ◽  
Laplace Transform ◽  
Transform Domain ◽  
Full Field ◽  
Shear Wave Speed ◽  
The Laplace Transform ◽  
Crack Faces

In this study, the transient stress fields and the dynamic stress intensity factor of a semi-infinite antiplane crack propagating along the interface between two different media are analyzed in detail. The crack is initially at rest and, at a certain instant, is subjected to an antiplane uniformly distributed loading on the stationary crack faces. After some delay time, the crack begins to move along the interface with a constant velocity, which is less than the smaller of the shear wave speed of these two materials. A new fundamental solution is proposed in this study, and the solution is determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in the Laplace transform domain) on the propagating crack faces. The exact full-field solutions and the stress intensity factor are found in the time domain by using the Cagniard-de Hoop method (de Hoop, 1958) of Laplace inversion. The near-tip fields are also obtained from the reduction of the full-field solutions. Numerical results for the dynamically extending crack are evaluated in detail. The region of the stress singular field dominated in the transient process is also discussed.

Transient Analysis of a Propagating In-Plane Crack in a Finite Geometry Body Subjected to Static Loadings

1997 ◽  
Vol 64 (3) ◽  
pp. 620-628 ◽  
Author(s):  
Chwan-Huei Tsai ◽  
Chien-Ching Ma
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Dynamic Stress ◽  
Transform Domain ◽  
Free Boundaries ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Reflected Waves ◽  
The Laplace Transform

In this study, a cracked body with finite boundaries subjected to static loading and the crack propagating with a constant speed are analyzed. The interaction of the propagating crack with reflected waves generated from traction-free boundaries is investigated in detail. The methodology for constructing the scattered field by superimposing the fundamental solution in the Laplace transform domain is proposed. The fundamental solutions represent the responses of applying exponentially distributed loadings in the Laplace transform domain on the surface of a half-plane or a crack. The dynamic stress intensity factors of a propagating crack induced from the interaction with the first few reflected waves generated from the traction-free boundary are obtained in an explicit closed form. The analytical solutions of dynamic stress intensity factors are compared with available numerical and experimental results and the agreement is quite good. We find one thing very interesting: the dynamic stress intensity factor for a long time period is a universal function of the instantaneous extending rate of a crack tip times the static stress intensity factor for an equivalent stationary crack for the finite strip problem. It was also found that the reflected waves generated from free boundaries always increase the stress intensity factor, and the influence from reflected waves generated from the boundary, which is perpendicular to the crack, are weaker than those generated from the boundary, which is parallel to the crack.

scholarly journals Dynamic Crack Propagation in a Layered Medium Under Antiplane Shear

1997 ◽  
Vol 64 (1) ◽  
pp. 66-72 ◽  
Author(s):  
Chien-Ching Ma ◽  
Yi-Shyong Ing
Keyword(s):  
Stress Intensity ◽  
Fundamental Solution ◽  
Laplace Transform ◽  
Dynamic Stress ◽  
Layered Medium ◽  
Transform Domain ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Propagating Crack ◽  
The Laplace Transform

In this study, the transient analysis of dynamic antiplane crack propagation with a constant velocity in a layered medium is investigated. The individual layers are isotropic and homogeneous. Infinite numbers of reflected cylindrical waves, which are generated from the interface of the layered medium, will interact with the propagating crack and make the problem extremely difficult to analyze. A useful fundamental solution is proposed in this study, and the solution can be determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in the Laplace transform domain) on the propagating crack faces. The Cagniard’s method for Laplace inversion is used to obtain the transient solution in time domain. The exact closed-form transient solutions of dynamic stress intensity factors are expressed in compact formulations. These solutions are valid for an infinite length of time and have accounted for contributions from all the incident and reflected waves interaction with the moving crack tip. Numerical results of dynamic stress intensity factors for the propagation crack in layered medium are evaluated and discussed in detail.

Dynamic Crack Propagation in Piezoelectric Materials Subjected to Dynamic Body Forces for Vacuum Boundary

2007 ◽  
Vol 23 (3) ◽  
pp. 229-238 ◽  
Author(s):  
X.-H. Chen ◽  
C.-C. Ma ◽  
Y.-S. Ing
Keyword(s):  
Intensity Factor ◽  
Fundamental Solution ◽  
Laplace Transform ◽  
Piezoelectric Material ◽  
Electric Displacement ◽  
Dynamic Crack ◽  
Transform Domain ◽  
Electric Displacement Intensity Factor ◽  
Propagating Crack ◽  
The Laplace Transform

AbstractThe problem of a semi-infinite propagating crack in the piezoelectric material subjected to a dynamic anti-plane concentrated body force is investigated in the present study. It is assumed that between the growing crack surfaces there is a permeable vacuum free space, in which the electrostatic potential is nonzero. It is noted that this problem has characteristic lengths and a direct attempt towards solving this problem by transform and Wiener-Hopf techniques [1] is not applicable. This paper proposes a new fundamental solution for propagating crack in the piezoelectric material and the transient response of the propagating crack is determined by superposition of the fundamental solution in the Laplace transform domain. The fundamental solution represents the responses of applying exponentially distributed loadings in the Laplace transform domain on the propagating crack surface. Exact analytical transient solutions for the dynamic stress intensity factor and the dynamic electric displacement intensity factor are obtained by using the Cagniard-de Hoop method [2,3] of Laplace inversion and are expressed in explicit forms. Finally, numerical results based on analytical solutions are calculated and are discussed in detail.

The Stress Intensity Factor of Opening Mode Determined by Digital Image Correlation

2011 ◽  
Vol 83 ◽  
pp. 54-59 ◽  
Author(s):  
Rui Zhang ◽  
Ling Feng He ◽  
Chang Rong Li
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Digital Image Correlation ◽  
Intensity Factor ◽  
Digital Image ◽  
Correlation Method ◽  
Compact Tension ◽  
Image Correlation ◽  
Full Field ◽  
Opening Mode

Applications of the digital image correlation method (DIC) for the determination of the opening mode stress intensity factor (SIF) is investigated using an edge cracked aluminum plate in this paper. Standard compact tension test specimen was tested under tensile loading and the full-field displacement fields of the test sample were recorded using DIC. The SIF associated with unavoidable rigid-body displacement translation were calculated simultaneously from the experimental data by fitting the theoretical displacement field using the method of least-squares. Selection of displacement and convergence values is discussed. For validation, the SIF thus determined is compared with theoretical results, confirming the effectiveness and accuracy of the proposed technique. Therefore it reveals that the DIC is a practical and effective tool for full-field deformation and SIF measurement.

Full field measurements of anisotropic stress intensity factor ranges in fatigue

2012 ◽  
Vol 94 ◽  
pp. 13-28 ◽  
Author(s):  
Garrett J. Pataky ◽  
Michael D. Sangid ◽  
Huseyin Sehitoglu ◽  
Reginald F. Hamilton ◽  
Hans J. Maier ◽  
...  
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Field Measurements ◽  
Full Field ◽  
Anisotropic Stress

New Insights into Plasticity-Induced Crack Tip Shielding via Mathematical Modelling and Full Field Photoelasticity

2007 ◽  
Vol 345-346 ◽  
pp. 199-204
Author(s):  
K.F. Tee ◽  
Colin J. Christopher ◽  
M. Neil James ◽  
Eann A Patterson
Keyword(s):  
Growth Rate ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Applied Stress ◽  
Crack Tip ◽  
Clear Understanding ◽  
Full Field ◽  
Crack Tip Shielding

The topic of plasticity-induced closure and its role in shielding a crack tip from the full range of applied stress intensity factor has provoked considerable controversy over several decades. We are now in an era when full field measurement techniques, e.g. thermoelasticity and photoelasticity, offer a means of directly obtaining the stress field around a crack tip and hence the effective stress intensity factor. Nonetheless, without a clear understanding of the manner in which the development of plasticity around a growing crack affects the applied stress field, it will remain difficult to make crack growth rate predictions except through the use of an often highly conservative upper bound growth rate curve where closure is absent, or through semi-empirical approaches. This paper presents new evidence for an interpretation of plasticity-induced crack tip shielding as arising from two separate effects; a compatibility-induced interfacial shear stress at the elastic-plastic interface along the plastic wake of the crack, and a crack surface contact stress which will vary considerably as a function of stress state, load and material properties.

Dynamic Fracture Under Normal Impact Loading of the Crack Faces

1985 ◽  
Vol 52 (3) ◽  
pp. 585-592 ◽  
Author(s):  
K.-S. Kim
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Impact Loading ◽  
Crack Tip ◽  
Time Behavior ◽  
Crack Face ◽  
Copper Strip ◽  
Transient Stress ◽  
Crack Faces

Results of experiments on crack-face impact are presented. The transient stress-intensity factor variation of a crack has been traced by the Stress-Intensity Factor Tracer (SIFT) [1] under time-stepwise uniform pressure loading of the crack faces. To see the effects of various waves generated by the loading, part of the crack faces was left free of traction within the distance l0 from the crack tip. The crack-face impact loading was produced by an electromagnetic force induced by a square pulse of an electric current flowing through a copper strip inserted in the saw-cut crack of a Homalite 100 plate specimen. The current flowed in opposite directions in the two portions of the copper strip, between the crack faces, causing them to repel each other. The short-time and the long-time behavior of the transient stress-intensity factor variation under the impact loading have been carefully investigated. Brittle dynamic initiation of crack extension and the stress-intensity variation of a running crack have been also examined. The experimental results have been compared with theoretical predictions based on Freund’s crack-face concentrated load solution [2]. The agreement between the theory and the experiment is excellent. In this study, the various waves generated by the loading are shown to play different roles in transmitting the load to the crack tip. In addition, confirmation is given that the SIFT is excellent in tracing the stress-intensity factor regardless of the crack-tip motion.

The Extent of the Stress Intensity Factor Field During Crack Growth Under Dynamic Loading Conditions

1986 ◽  
Vol 53 (2) ◽  
pp. 303-310 ◽  
Author(s):  
C. C. Ma ◽  
L. B. Freund
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Growth ◽  
Singular Term ◽  
Dynamic Pressure ◽  
Fracture Initiation ◽  
Fracture Plane ◽  
Crack Face ◽  
Crack Faces

The phenomenon considered is fracture initiation and crack growth in a plate due to dynamic pressure loading on the faces of a pre-existing crack. The problem is formulated within the framework of two-dimensional elastodynamics, and the system is viewed as a semi-infinite crack in an otherwise unbounded body. At a certain instant of time, a spatially uniform pressure begins to act on the crack faces. The pressure magnitude increases linearly in time for a certain period (the rise time T), and it is constant thereafter. The crack begins to extend at constant speed at some time after the pressure begins to act (the delay time τ). The pressure acts only over the original crack faces, and both τ > T and τ < T are considered. The ratio of the normal stress on the fracture plane to the value due to the singular term in the stress field alone is computed for some point at a small fixed distance ahead of the crack tip, with a view toward establishing the conditions under which the stress intensity factor controlled singular term accurately describes the near tip stress distribution in this highly transient process. Measured and calculated histories compare very well for relatively low crack face pressures, but there is significant disagreement beyond crack growth initiation for higher pressures. Possible reasons for the discrepancies are discussed.

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