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Keywords: fatigue crack growth, critical damage, non-singular strain field, variable amplitude loading.

Summary

Several models have been proposed to correlate the oligocyclic fatigue crack initiation process, controlled by the strain range, with fatigue crack propagation rates controlled by the stress intensity range [1,2,3]. However, most models do not properly deal with the supposed stress field singularity at the crack tip. This singularity implies that all the damage would be caused by the last loading event. Recently, an improved model that deals with the actual elastic-plastic stresses at the crack tip has been proposed [2]. It uses epsilon N parameters and expressions of the HRR type to represent the elastic-plastic strain range inside the plastic zone ahead of the crack tip. The crack tip is modeled as a sharp notch with a very small but finite tip radius to remove the singularity issues.

This non-singular model considers that the damage zone ahead of the crack tip is composed by a sequence of very small volume elements (VE), each one loaded by a different strain range, which are broken sequentially as the crack propagates. Each of these VE will be submitted to elastic-plastic hysteresis loops of increasing amplitude as the crack tip approaches it, even in the case of constant amplitude loading. Fracturing of the VE at the crack tip (which causes the fatigue crack growth) occurs when its accumulated damage reaches a critical value, due to the summation of the damage suffered during each cycle, quantified by a damage accumulation model.

In this work, the idea that FCG is caused by the sequential failure of the VE ahead of the crack tip is extended to deal with the variable amplitude (VA) loading case, using a non-singular damage model. A cycle-by-cycle computational algorithm is proposed, to be able to calculate the variable crack increments at each cycle and to account for load sequence effects. Instead of using variable width volume elements, which would be difficult to handle computationally since such widths are not known a priori, the algorithm assumes that all the VE have constant width. However, it allows the existence of a partially cracked VE at the crack tip. The idea behind the calculations is to find at each cycle the number of fractured VE and the size of the new partially cracked element, obtaining then the crack increment. All algorithm equations are described.

Experimental results show a good agreement between measured crack growth, both under constant and variable amplitude loading, and the predictions based purely on epsilon N data.

References

1: S. Majumdar, J. Morrow, "Correlation Between Fatigue Crack Propagation and Low Cycle Fatigue Properties", ASTM STP 559, 159-182, 1974. doi:10.1520/STP38599S
2: J.A.R. Durán, J.T.P. Castro, J.C. Payão Filho,
"Fatigue Crack Propagation Prediction by Cyclic Plasticity Damage Accumulation Models", FFEMS 26, 137-150, 2003. doi:10.1046/j.1460-2695.2003.00630.x
3: J.T.P. Castro, M.A. Meggiolaro, A.C.O. Miranda, "Singular and Non-Singular Approaches for Predicting Fatigue Crack Growth Behavior", Int. J. Fatigue 27, 1366-1388, 2005. doi:10.1016/j.ijfatigue.2005.07.018

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 88 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and M. Papadrakakis Paper 242 An Efficient Computational Algorithm to Evaluate Fatigue Crack Growth under Variable Amplitude Loading from Strain-Life Data J.T.P. Castro¹, M.A. Meggiolaro¹ and A.C.O. Miranda² ¹Mechanical Engineering Department, ²Civil Engineering Department, Pontifical Catholic University of Rio de Janeiro, Brazil doi:10.4203/ccp.88.242 purchase the full-text of this paper Full Bibliographic Reference for this paper J.T.P. Castro, M.A. Meggiolaro, A.C.O. Miranda, "An Efficient Computational Algorithm to Evaluate Fatigue Crack Growth under Variable Amplitude Loading from Strain-Life Data", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 242, 2008. doi:10.4203/ccp.88.242 Keywords: fatigue crack growth, critical damage, non-singular strain field, variable amplitude loading. Summary Several models have been proposed to correlate the oligocyclic fatigue crack initiation process, controlled by the strain range, with fatigue crack propagation rates controlled by the stress intensity range [1,2,3]. However, most models do not properly deal with the supposed stress field singularity at the crack tip. This singularity implies that all the damage would be caused by the last loading event. Recently, an improved model that deals with the actual elastic-plastic stresses at the crack tip has been proposed [2]. It uses epsilon N parameters and expressions of the HRR type to represent the elastic-plastic strain range inside the plastic zone ahead of the crack tip. The crack tip is modeled as a sharp notch with a very small but finite tip radius to remove the singularity issues. This non-singular model considers that the damage zone ahead of the crack tip is composed by a sequence of very small volume elements (VE), each one loaded by a different strain range, which are broken sequentially as the crack propagates. Each of these VE will be submitted to elastic-plastic hysteresis loops of increasing amplitude as the crack tip approaches it, even in the case of constant amplitude loading. Fracturing of the VE at the crack tip (which causes the fatigue crack growth) occurs when its accumulated damage reaches a critical value, due to the summation of the damage suffered during each cycle, quantified by a damage accumulation model. In this work, the idea that FCG is caused by the sequential failure of the VE ahead of the crack tip is extended to deal with the variable amplitude (VA) loading case, using a non-singular damage model. A cycle-by-cycle computational algorithm is proposed, to be able to calculate the variable crack increments at each cycle and to account for load sequence effects. Instead of using variable width volume elements, which would be difficult to handle computationally since such widths are not known a priori, the algorithm assumes that all the VE have constant width. However, it allows the existence of a partially cracked VE at the crack tip. The idea behind the calculations is to find at each cycle the number of fractured VE and the size of the new partially cracked element, obtaining then the crack increment. All algorithm equations are described. Experimental results show a good agreement between measured crack growth, both under constant and variable amplitude loading, and the predictions based purely on epsilon N data. References 1 S. Majumdar, J. Morrow, "Correlation Between Fatigue Crack Propagation and Low Cycle Fatigue Properties", ASTM STP 559, 159-182, 1974. doi:10.1520/STP38599S 2 J.A.R. Durán, J.T.P. Castro, J.C. Payão Filho, "Fatigue Crack Propagation Prediction by Cyclic Plasticity Damage Accumulation Models", FFEMS 26, 137-150, 2003. doi:10.1046/j.1460-2695.2003.00630.x 3 J.T.P. Castro, M.A. Meggiolaro, A.C.O. Miranda, "Singular and Non-Singular Approaches for Predicting Fatigue Crack Growth Behavior", Int. J. Fatigue 27, 1366-1388, 2005. doi:10.1016/j.ijfatigue.2005.07.018 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £145 +P&P)
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