Complete theoretical analysis for higher order asymptotic terms and the HRR zone at a crack tip for Mode I and Mode II loading of a hardening material

1993 ◽  
Vol 98 (1-4) ◽  
pp. 79-98 ◽  
Author(s):  
S. Yang ◽  
Y. J. Chao ◽  
M. A. Sutton
Keyword(s):  
Theoretical Analysis ◽  
Crack Tip ◽  
Higher Order ◽  
Mode I ◽  
Mode Ii ◽  
Hardening Material ◽  
Mode Ii Loading

scholarly journals Fatigue Crack Growth under Non-Proportional Mixed Mode Loading in Rail and Wheel Steel Part 1: Sequential Mode I and Mode II Loading

2019 ◽  
Vol 9 (10) ◽  
pp. 2006 ◽  
Author(s):  
Makoto Akama
Keyword(s):  
Crack Growth ◽  
Growth Rates ◽  
Mixed Mode ◽  
Crack Tip ◽  
Wheel Steel ◽  
Mode I ◽  
Mode Ii ◽  
Mode Ii Loading ◽  
Crack Growth Rates ◽  
Branch Crack

Fatigue tests were performed to estimate the coplanar and branch crack growth rates on rail and wheel steel under non-proportional mixed mode I/II loading cycles simulating the load on rolling contact fatigue cracks; sequential and overlapping mode I and II loadings were applied to single cracks in the specimens. Long coplanar cracks were produced under certain loading conditions. The fracture surfaces observed by scanning electron microscopy and the finite element analysis results suggested that the growth was driven mainly by in-plane shear mode (i.e., mode II) loading. Crack branching likely occurred when the degree of overlap between these mode cycles increased, indicating that such degree enhancement leads to a relative increase of the maximum tangential stress range, based on an elasto–plastic stress field along the branch direction, compared to the maximum shear stress. Moreover, the crack growth rate decreased when the material strength increased because this made the crack tip displacements smaller. The branch crack growth rates could not be represented by a single crack growth law since the plastic zone size ahead of the crack tip increased with the shear part of the loading due to the T-stress, resulting in higher growth rates.

Theoretical Analysis and Engineering Implications for the High Order Term Solutions of the Mode II Type Creep Crack

2017 ◽  
Author(s):  
Yanwei Dai ◽  
Yinghua Liu ◽  
Yuh J. Chao
Keyword(s):  
Theoretical Analysis ◽  
Plane Strain ◽  
Order Term ◽  
Crack Tip ◽  
High Order ◽  
High Order Term ◽  
Mode I ◽  
Mode Ii ◽  
Mode I Crack ◽  
Creep Crack

The high order term (HOT) solutions of crack tip field should be taken into account in engineering applications due to their potential influences on the fracture toughness as well as the crack growth rate. Towards this end, the high order asymptotic analysis of mode II crack in a power-law creeping material under the plane strain condition is presented theoretically in this paper. By comparing among the three order term solution, HRR field and finite element calculations, it can be found that the proposed three order term solution is able to characterize the full field of mode II creep crack tip accurately. The high order term solution of mode II creep crack relies on the creep exponent, which is different from that of mode I crack case. There are two independent terms among these three terms of asymptotic solution for mode II creep crack, which indicates that there exists the constraint effect for the plane strain mode II creep crack though the effect of high order term may not be as significant as the mode I crack case. Based on the theoretical analysis, a modified time-dependent failure assessment diagram (TDFAD) for mode II creep crack is proposed by considering the high order term solution.

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