CTOA of a stable crack in a thin aluminum fracture specimen
Introduction
A ductile fracture criterion, which relates to the plastic strain field in the crack tip plastic zone, is the crack tip bluntness and was quantified by the crack opening displacement (COD) criterion advanced by Wells in 1963 [1]. This COD criterion, which was initially related to Irwin’s plastic zone estimate [2], ry, and later to the Dugdale plastic zone [3], was promoted mainly by The Welding Institute in the 60s and 70s [4] for fracture assessment of thick-walled pressure vessels. Since the COD along a surface crack front in a thick plate cannot be readily measured and must be computed, its acceptance was hindered by the lack of easily accessible three-dimensional (3D) elastic–plastic computer codes with the sensitivity to accurately map the crack tip bluntness. The crack tip opening angle (CTOA), which uniquely characterizes the crack tip strain field [5], is a local field parameter which in theory can be readily measured on the surface and computed in the interior of a 3D crack. Shih et al. [5] as well as Kaninnen et al. [6] in the 70s concluded that the CTOA was a computationally attractive operational parameter and an alternative to the J-integral criterion which subsequently dominated the ductile fracture research of the 80s and 90s.
The CTOA criterion was used in the 80s to analyze axial crack propagation in a subscale gas transmission line [7]. The rupturing profile of a propagating crack in a pressurized 2-in. diameter, schedule 10, carbon steel pipe was recorded with a high-speed framing camera and was processed through a special software [8] which yielded the CTOA and flap motion. The CTOA criterion was also used in a ring model of the rupturing pipe and a thermal hydraulic depressurization code to simulate the large-scale burst tests of 48-in. diameter×0.720-in. thick, X70 line pipes [9]. The excellent agreement between the measured and the computed CTOA versus crack velocity relations demonstrated that the CTOA was an effective static and dynamic fracture parameter for pipe rupture [10].
A renewed research thrust in the CTOA criterion was undertaken in the early 90s in response to the NASA Aircraft Integrity Program. The thin aluminum specimens considered were ideally suited for the CTOA criterion. Newman et al. showed that the CTOA criterion will predict the residual strength in laboratory specimens [11], [12] as well as in the FAA/NASA wide panels with multiple site damages (MSDs) [13]. In the following, the authors’ findings on the utility of CTOA in similar aluminum fracture specimens are presented.
Section snippets
SEN and CN specimens
The experimental procedure consisted of measuring the two orthogonal displacements, i.e. u- and v-fields, surrounding a stably extending crack in an aluminum specimen using moiré interferometry with a coarse cross-diffraction grating of 40 or 60 lines/mm. Single edge notch (SEN) and center notch (CN) fracture specimens as well as CN fracture specimens with multiple site damage (MSD) were machined from 2024-T3 clad aluminum sheet of thickness 0.8 mm. Starter cracks were fatigued at σmax=0.3σy
Experimental results
The curved crack paths in the biaxial fracture specimens are shown in Fig. 6. While these crack paths were not significantly influenced by the tear strap configuration, all specimens failed catastrophically when the crack penetrated into the tear strap region where the individual tear straps remained in tact. Although the machine pad-up straps failed, the failure loads of these two biaxial fracture specimens were 50% higher than those with and without tear straps.
The strength reduction plot in
Experimental procedure
In this study, dynamic moiré interferometry, which yielded the dynamic CTOA, was used to determine the transient displacement fields perpendicular and parallel to the running crack in 7075-T6 aluminum alloy, SEN specimen with a thickness of 1.6 mm. The SEN specimen was either fatigue pre-cracked or blunt notched for low- and high-crack velocity tests, respectively. Four frames of the moiré fringe patterns corresponding to either the vertical or horizontal displacements were recorded by an
Conclusions
- 1.
The CTOA resistance curve can be used to characterize stable crack growth in thin aluminum fracture specimens.
- 2.
Under mixed modes I and II crack tip deformation, the resultant CTOD remains constant.
- 3.
Dynamic ductile crack propagation can be characterize by CTOA.
Acknowledgements
This research was supported by the Office of Naval Research and the Federal Aviation Administration, all of USA.
References (18)
- et al.
An experimental and analytical investigation of axial crack propagation in long pipes
Engng. Fract. Mech.
(1986) Application of fracture mechanics at and beyond general yielding
Brit. Weld. J.
(1963)- et al.
Fracture strengths relative to onset and arrest of crack propagation
Proc. ASTM
(1958) - et al.
Plastic energy dissipation in crack propagation
- et al.
The COD approach and its application to welded structures
- et al.
Studies on crack initiation and stable crack growth
- et al.
Elastic–plastic fracture mechanics for two-dimensional stable crack growth and instability problems
- et al.
Subsize experiments and numerical modeling of axial rupture of gas transmission lines
ASME J. Press. Vess. Technol.
(1988) - Sugie E, Matsuoka M, Akiyama T, Tanaka K, Kawaguchi Y. Notch ductility requirement of line pipes for arresting...
Cited by (11)
A finite crack growth energy release rate for elastic-plastic fracture
2023, Journal of the Mechanics and Physics of SolidsNumerical investigation of speed dependent dynamic fracture toughness of line pipe steels
2013, Engineering Fracture MechanicsCitation Excerpt :Lee and Prakash [9] formulated dynamic fracture toughness in terms of critical dynamic stress intensity factor, and showed that critical dynamic stress intensity factor of 4340VAR structure steel under intense stress pulse loading increases with fracture speed, while Pandolfi et al.’s result [10] also showed that critical dynamic stress intensity factor of C300 steel increases with fracture speed. Ma et al. [11] conducted dynamic fracture experiments on thin aluminum, and showed that the CTOA of fatigue precracked aluminum specimens decreased with fracture speed. In addition, Shim et al. [2] compared the absorbed energy per fracture area, CTOA and fracture speed between standard and modified DWTT of X80 line pipes, and found that both absorbed energy per fracture area and CTOA decrease with fracture speed.
Fracture and damage mechanics modelling of thin-walled structures - An overview
2009, Engineering Fracture MechanicsA scheme for finite element analysis of mode I and mixed mode stable crack growth and a case study with AISI 4340 steel
2008, Nuclear Engineering and DesignDuctile crack growth simulations under mode-i loading using CTOA criterion
2013, 1st International and 16th National Conference on Machines and Mechanisms, iNaCoMM 2013New method for concurrent dynamic analysis and fatigue damage prognosis of bridges
2012, Journal of Bridge Engineering