Mechanism for the formation of high cycle fatigue cracks at fee annealing twin boundaries
- PDF / 556,373 Bytes
- 8 Pages / 612 x 792 pts (letter) Page_size
- 40 Downloads / 191 Views
I.
INTRODUCTION
E L A S T I C interactions have recently been shown to play a major role in the onset of slip in polycrystalline alpha brass. 1.2 If the applied stress alone was used, it was possible to predict which slip systems would act in 30 pct of the cases. However, when the finite element method (FEM) was used to calculate stresses, it was possible to predict which slip system would act in nine of eleven cases. In the remaining two cases the resolved shear stresses were so close for the two highest stressed slip systems that it was not possible to tell which of these two slip systems would act. However, one of these two slip systems did operate. In effect, therefore, the slip systems with the highest resolved shear stresses were found to act in all cases. The additional stresses were thought to come only as a result of elastic interactions between grains with different orientations. ~'2 More recently, it has been shown that grain shape 3 can also play an important role in augmenting or decreasing applied stresses locally. Some years ago Thompson 4 suggested that fatigue cracking at annealing twin boundaries in fcc metals could arise as a result of elastic stresses which produced preferential slip in the vicinity of the twin boundaries. Boettner et al. 5 made a similar suggestion in 1964. In neither case was a mechanism suggested by which this preferential slip was induced by elastic stresses. A possible mechanism is suggested in the following discussion. In the generalized Hooke's law each of the six strains exx, 6yy, ezz, ,F.yz, exz, and 6xy is expressed in terms of six compliance coefficients and the corresponding stresses. Consider the strain exz Exz = S510.-xx --~ S520-yy -~- S53r
exists it will, nevertheless, produce an exz strain. Similarly, the Crzzstress will produce each of the other strains. It is this behavior which is responsible for elastic interactions between grains. Elastic interactions are more" fully discussed elsewhere. 6 Figure 1 is a schematic diagram of a twinned crystal. In Figure l(a) the stress axis, which is normal to the twin boundary, is the same crystallographic axis in both twin components. However, when the stress axis is at an angle to the twin boundary (Figure l(b)), the stress axis is no longer crystallographically the same in each crystal. This can be seen by the ~fact that the stress axis no longer makes the same angle with the planes which are in mirror image. These different stress axes are not at symmetry orientations. Consequently, different elastic strains are produced in each crystal, and each twin opposes the other's strain at the twin boundary. The elastic interactions resulting from the different elastic strains would be maximum near the boundary. The stresses, so created, would be added to those from the applied stress, and if the hypothesis is correct, would sufficiently increase the stress on slip systems parallel to the twin boundary to permit them to slip.
II.
CALCULATION PROCEDURE
To carry out the calculations to test the proposed hypothesis, a Finite
Data Loading...
