Determination of Plastic Zone Sizes at the Crack Tip and Naryanaswami Ranganathan

2016 ◽  
pp. 189-212
Keyword(s):  
Plastic Zone ◽  
Crack Tip

Fracture Related to a Dislocation Distribution

1979 ◽  
Vol 46 (4) ◽  
pp. 817-820 ◽  
Author(s):  
C. Vilmann ◽  
T. Mura
Keyword(s):  
Plastic Zone ◽  
Critical Stress ◽  
Continuous Distribution ◽  
Crack Tip ◽  
Plastic Zone Size ◽  
Plastic Work ◽  
Zone Size ◽  
Line Theory ◽  
Distribution Of Dislocations

The plastic flow at the crack tip is characterized by a model compatible with slip line theory. From this model it is shown that a continuous distribution of dislocations may be derived. Then assuming that these dislocations are emitted from the crack tip and move along slip lines to their final position, the Peach-Koehler force is used to calculate the plastic work involved. Since the plastic zone size is dependent on crack length, two plastic effects are present upon propagation. Primarily the distribution of dislocations present moves along with the crack tip, secondarily new dislocations are emitted to fill the larger plastic zone. These effects yield plastic work which is dependent on both σ2 and σ4, with σ being the applied stress. This dependancy yields a critical stress relationship different from that proposed by either Irwin or Orowan. It also leads to the determination of a subcritical flaw size, i.e., one which will never become unstable.

Simulation and Contrast Analysis of tem Images of Cracks

1990 ◽  
Vol 48 (1) ◽  
pp. 578-579
Author(s):  
D. Goyal ◽  
A. H. King
Keyword(s):  
Displacement Vector ◽  
Crack Tip ◽  
Perfect Crystal ◽  
Operating Conditions ◽  
Displacement Fields ◽  
Fringe Contrast ◽  
Orthogonal Geometry ◽  
Moire Fringe ◽  
Moiré Fringe

TEM images of cracks have been found to give rise to a moiré fringe type of contrast. It is apparent that the moire fringe contrast is observed because of the presence of a fault in a perfect crystal, and is characteristic of the fault geometry and the diffracting conditions in the TEM. Various studies have reported that the moire fringe contrast observed due to the presence of a crack in an otherwise perfect crystal is distinctive of the mode of crack. This paper describes a technique to study the geometry and mode of the cracks by comparing the images they produce in the TEM because of the effect that their displacement fields have on the diffraction of electrons by the crystal (containing a crack) with the corresponding theoretical images. In order to formulate a means of matching experimental images with theoretical ones, displacement fields of dislocations present (if any) in the vicinity of the crack are not considered, only the effect of the displacement field of the crack is considered.The theoretical images are obtained using a computer program based on the two beam approximation of the dynamical theory of diffraction contrast for an imperfect crystal. The procedures for the determination of the various parameters involved in these computations have been well documented. There are three basic modes of crack. Preliminary studies were carried out considering the simplest form of crack geometries, i. e., mode I, II, III and the mixed modes, with orthogonal crack geometries. It was found that the contrast obtained from each mode is very distinct. The effect of variation of operating conditions such as diffracting vector (), the deviation parameter (ω), the electron beam direction () and the displacement vector were studied. It has been found that any small change in the above parameters can result in a drastic change in the contrast. The most important parameter for the matching of the theoretical and the experimental images was found to be the determination of the geometry of the crack under consideration. In order to be able to simulate the crack image shown in Figure 1, the crack geometry was modified from a orthogonal geometry to one with a crack tip inclined to the original crack front. The variation in the crack tip direction resulted in the variation of the displacement vector also. Figure 1 is a cross-sectional micrograph of a silicon wafer with a chromium film on top, showing a crack in the silicon.

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