Large plasticity induced crack initiation from U-notches in thin aluminum sheets under mixed mode loading

It is shown that the experimental failure loads are well predicted by means of both the UMTS-EMC and UMS-EMC criteria. Moreover, the experimental observations and the elastic-plastic finite element analyses indicate that the U-notched aluminum sheets fail by the large-scale yielding (LSY) regime.
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Large plasticity induced crack initiation from U-notches in thin aluminum sheets under mixed mode loading Engineering Solid Mechanics (2017) 39-60 Contents lists available at GrowingScience Engineering Solid Mechanics homepage: www.GrowingScience.com/esmLarge plasticity induced crack initiation from U-notches in thin aluminum sheetsunder mixed mode loadingA. R. Torabi* and B. Mohammad HosseiniFracture Research Laboratory, Faculty of New Sciences & Technologies, University of Tehran, P.O. Box 14395-1561, Tehran, IranA R T I C L EI N F O ABSTRACT Article history: Ductile failure is investigated experimentally and theoretically in U-notched Al 7075- T6 thin Received 6 July, 2016 sheets under mixed mode I/II loading. First, several U-notched rectangular sheets are subjected Accepted 2 October 2016 to mixed mode I/II failure tests and the load-carrying capacity of the sheets are experimentally Available online recorded. Then, the Equivalent Material Concept (EMC) is employed in conjunction with the 3 October 2016 Keywords: U-notch maximum tangential stress (UMTS) and U-notch mean stress (UMS) criteria to Load-carrying capacity theoretically estimate the load-carrying capacity of the U-notched Al 7075-T6 sheets. It is Equivalent Material Concept shown that the experimental failure loads are well predicted by means of both the UMTS-EMC Ductile failure and UMS-EMC criteria. Moreover, the experimental observations and the elastic-plastic finite U-notch element analyses indicate that the U-notched aluminum sheets fail by the large-scale yielding Abrupt fracture (LSY) regime. Mixed mode I/II loading © 2017 Growing Science Ltd. All rights reserved.Nomenclature dc Critical distance of the UMS criterion measured from the notch tip dc,U Critical distance of the UMS criterion measured from the coordinate origin E Elastic modulus K Strain-hardening coefficient K IU ,  Mode I notch stress intensity factor (NSIF) for a U-notch K IIU ,  Mode II notch stress intensity factor (NSIF) for a U-notch K IcU ,  Mode I notch fracture toughness for a U-notch Kc Fracture toughness of material* Corresponding author. Tel: +98-21-61118572, Fax: +98-21-88497324E-mail addresses: a_torabi@ut.ac.ir (A. R. Torabi)© 2017 Growing Science Ltd. All rights reserved.doi: 10.5267/j.esm.2016.10.00140 K Ic Plane-strain fracture toughness of material UMS U-notch mean-stress UMTS U-notch maximum tangential stress n Strain-hardening exponent rc Critical distance of the UMTS criterion measured from the notch tip rc ,U Critical distance of the UMTS criterion measured from the coordinate origin r0 Distance between the coordinate origin and the notch tip Notch rotation angle  * f Strain at crack initiation for the equivalent material p True plastic strain u Engineering plastic strain at maximum load u ,true True plastic strain at maximum load Yp True plastic strain at yield point Y Elastic strain at yield point Notch radius  True stress c Critical stress f* Tensile strength of the equivalent material  r In-plane shear stress  Tangential stress σ θθ Mean value of tangential stress u Ultimate tensile strength Y Yield strength1. Introduction Although notches are normally fairer than sharp cracks, their fracture behavior can be similar ordissimilar to the behavior of cracks depending on the notch geometry and hence the stress concentrationand the stress gradient at the notch vicinity. For significant stress gradients, fracture assessment basedon the classic mechanics of materials, which uses the stress concentration factor (SCF) as the mainparameter of the stress field, is no longer valid because it results in considerable errors. For such cases,the principles of the notch fracture mechanics (NFM), which utilize the notch stress intensity factors(NSIFs) as the governing failure parameters, should be used instead. Indeed, cracks and notches are similar from the view point of the stress concentration; however,there is a great difference between them in definition of the fracture toughness. For a cracked member,the plane-strain fracture toughness is assumed to be a material property and denotes the ability ofwithstanding the material containing a pre-existing crack against crack propagation. However, for acomponent weakened by a notch, the notch fracture toughness (NFT) depends not only on the materialproperties, but also on the notch geometry. Physically, the NFT denotes the resistance of the notchedmember against crack initiation from the notch tip or border. For a notched member made of a brittlematerial, the crack initiation from the notch border is simultaneous with the final fracture because the ...