D.L. Jones

An investigation of the edge-sliding mode in fracture mechanics

A boundary collocation procedure has been applied to the Williams stress function to determine the elastic stress distribution for the crack tip region of a finite, edge-cracked plate subjected to mode II loading at the crack tips. The asymmetric specimen selected was particularly suitable for the determination of plane strain fracture toughness for mode II loading. Numerical solutions for stress intensity factors for the edge-sliding mode obtained by the boundary collocation method were in close agreement with values obtained from photoelastic experiments. Fracture tests of several compact shear specimens of 2024-T4 aluminum were conducted in order to experimentally investigate the behavior of the edge-sliding mode. In each case a brittle shear failure was observed and mode II fracture toughness values were obtained. The average value for KIIc obtained from two tests was 39.5 ksi(in)12. No KIc. data for 2024-T4 were available for comparison purposes; however, KIc values for a similar alloy, 2024-T351, have been reported as 34ksi(in)12 which is only about 15 per cent below the corresponding KIIc value.

On fracture toughness in the nonlinear range

Abstract A general definition of fracture toughness, designated by G c , is developed which is appropriate to situations of subcritical crack growth and/or large-scale crack border plastic yield. The theoretical basis as well as comparisons with other proposed measures of fracture toughness are also discussed. A simple method is given for evaluating G c which is based on use of the load-displacement test record.

Load biaxiality and fracture - Synthesis and summary

Abstract In both Griffiths global energy rate theory for crack instability and Irwins local crack-tip stress intensity theory for fracture toughness, only the tensile load perpendicular to the crack influences fracture behavior of the body. Thus according to these theories, outer boundary loads applied parallel to the crack have no effect on the fracture process. This viewpoint has been widely held since its inception with the work of Griffith in 1921, and has strongly influenced the development of fracture mechanics. Investigations by the authors have shown the contrary however, in that the load biaxiality strongly affects many aspects of the fracture behavior of a cracked body. Almost all of the characteristics of brittle fracture have been shown theoretically and/or experimentally to be sensitive to load biaxiality. Specifically, this work has shown that the stress and displacement fields, the elastic strain energy density, and the maximum shear stress near the crack tip are all altered by loads applied parallel to the crack, as are the angle of initial crack extension, the strain energy of the entire body, the fracture load, and the rate of fatigue crack growth. Since the results of this research have been published piecemeal over the years, the authors are presenting, herein, a synthesis and summary of this work for the purpose of demonstrating the overall presence and consistency of the biaxial effects.

G̃c and R-curve fracture toughness values for aluminum alloys under plane stress conditions

Abstract The effect of specimen geometry and subcritical crack growth on the nonlinear energy fracture toughness, G c , has been examined for thin, center-cracked sheets of 2024-T3 and 7075-T6 aluminum alloys. The procedure followed was to independently vary the specimen length, L, width, w, andd crack length-to-specimen width ratio and to determine the toughness both at the onset of subcritical crack growth and at the initiation of unstable fracture. Comparisons were also made with the R-curve toughness, GR, evaluated at unstable fracture from which it was found that both G c and GR displayed the same trend of change with geometrical variables, with G c consistently higher than GR. When the nonlinear energy fracture toughness was evaluated at the onset of subcritical crack growth, it was found that the geometry dependence essentially disappeared. Scanning electron microscopic examination of some typical fracture surfaces showed that stable crack growth was accompanied by a gradual change of fracture mode from plane strain to plane stress. An analysis of possible errors in the experimental procedure showed that the scatter observed in G c values was not due to experimental errors, but apparently due to inhomogeneities in the materials. Several techniques were also introduced for the purpose of more directly incorporating crack growth into the G c determination, but it was found that they did not cause significant variation in the toughness values.

Fracture toughness characterization of several aluminum alloys in semi-brittle fracture

A method has recently been developed for determining a nonlinear fracture toughness parameter defined by the relation Gc = CGc where Gc is the critical elastic strain energy rate as defined by Irwin. The C term is a function of the nonlinearity of the load-displacement test record and has been evaluated using the three parameter Ramberg-Osgood approach, although other curve fitting techniques could be applied as well. The method is quite straightforward and is applicable to plane stress, plane strain and mixed mode testing although only plane stress conditions are considered in this paper. For the case of a linear load-displacement record C → 1 and Gc reduces to the linear elastic result. The toughness parameter Gc has been evaluated for a number of high strength aluminum alloys and compared with published Gc values for these materials. The tests were conducted on center-cracked sheets of 2014-T6, 2024-T81, 7075-T6 and 7475-T61 aluminum alloys under conditions of varying specimen geometry and displacement gage length. It was found that the values of Gc obtained from displacement readings with a gage length of 2 in. generally agreed with published values of Gc = Kc2E. The Gc values were found to vary inversely with gage length and a/w ratios. The variation in values for Gc is of the same order of magnitude as the scatter in published values for Gc. However, Gc appears to be less sensitive than Gc to changes in a/w.

A comparison of the geometry dependence of several nonlinear fracture toughness parameters

Abstract A number of fracture toughness tests on compact tension specimens have been performed for the purpose of comparing several nonlinear fracture toughness methods; including the nonlinear energy ( G I ), J-integral ( J I ), COD ( G δ ), and linear (– G I ) approaches. The effect of variations in specimen thickness ( B ) and width ( w ) on the fracture toughness was examined for 7075-T651, 2124-T851, 2048-T35I, and 2048-T851 aluminum alloys, Ti-6Al-4V, and 4340 steel. Fracture toughness values were evaluated at both the initiation of stable crack growth and the onset of unstable fracture (peak load). It was found that the peak load toughness values are quite geometry sensitive at thicknesses below the requirement for plane strain fracture. At the initiation of stable crack growth, the toughness values are constant over a much larger range of specimen thickness. However, the nonlinearity of the load displacement curve is quite limited at this point and the associated fracture toughness is only 30–50% of the peak-load values.

The effects of biaxial loading on the fracture characteristics of several engineering materials

Abstract A test system has been developed at The George Washington University for testing flat-sheet, center-cracked specimens over a wide range of applied biaxiality ratios. The test system provides independent control of the two perpendicular axes, with either phased static or cyclic loading (selectable phase angles) or completely independent loading functions possible. A photoelastic study was performed for several variations in specimen geometry, and the results showed good agreement with analytical predictions and other photoelastic results of similar specimen geometries. Two polymers, PMMA and PVC, and three aluminum alloys encompassing a wide range of ductility were tested. The fracture toughness values of both polymers decreased with increasing load biaxiality. The load biaxiality was found to have a strong influence on the crack growth direction in PMMA and a negligible influence on the PVC. The toughness values for 7075-T6 aluminum increased with increasing biaxiality, while for the more ductile 2024-T3 and 6061-T4 intermediate peak toughness values were observed at a biaxiality ratio of 0.5. The fracture toughnesses at the highest biaxiality ratios were approximately equal to the uniaxial results, which suggest the possibility that the tabs parallel to the cracks may have pulled off, thus releasing the biaxial constraint.

Determination of nonlinear energy toughness values for cyclic loading applications

Abstract For several years the nonlinear energy method proposed by Liebowitz and Eftis has been examined as a failure criterion for static testing of center-cracked and compact tension specimens. Since the method appears to be valid under conditions of crack-tip plasticity, subcritical crack growth and load relaxation, tests have been conducted to ascertain the merit of this method as a failure criterion under cyclic loading conditions. The nonlinear energy toughness for cyclic loading, G fc , is obtained from an envelope of the cyclic load-displacement record, which naturally imposes some restrictions on the loading program. The cyclic toughness parameter, G fc , has been evaluated for thin, center-cracked sheets of 2024-T3 and 7075-T6 aluminum alloys. The specimen dimensions were held constant and the load parameters were varied so that a significant variation of the cyclic life was obtained. Both alloys exhibited a significant reduction of G fc with increasing cyclic life in a manner similar to the classical S-N diagram. For example, the ratio of cyclic to static toughness, G fc /G c , was found to be about 0.8 when failure occurred after approximately 150 cycles. There appeared to be a tendency for the curve to level off at this point, which suggests that these curves may represent compressed S-N curves. It is felt that this method may serve the design process by allowing the establishment of a fracture toughness parameter capable of including the effects of the entire loading history of a structure into the fracture toughness requirements.

A microscopic study of crack initiation mechanisms in 7075 aluminum alloy sheets

Abstract A study of the opening mode of crack initiation in 7075-T6 aluminum alloy sheets has been conducted with the aid of a scanning electron microscope. Observations were made from several orientations including the top view of the specimen which showed the notch profile and the edge view of the specimen which showed the entire notch front along the specimen thickness. It was found that the edge view exhibited the first signs of permanent deformation at about 55 per cent of the breaking strength. These changes took the form of deformation bands which were aligned in the direction of the tensile axis and apparently defined limiting regions of homogeneous slip. It is felt that the appearance of microcracks at loads approaching the breaking strength was of fundamental importance in the formation of the final fracture surface. Many of these microcracks were initiated at intermetallic particles and other metallurgically weak regions on the notch surface. It was also possible to correlate the strain in the notch with the stress intensity factor for the various loads. Very large plastic strains were observed on the notch tip as compared to published values of elongation at fracture for unnotched specimens.