In-situ imaging of advanced materials subjected to in-plane biaxial loading using X-ray micro-computed tomography
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The effects of biaxial loading on the fracture characteristics of several engineering materials
Using the George Washington University biaxial test system, a static fracture toughness study of two polymers (PMMA and PVC) and three aluminum alloys was performed for several variations in specimen geometry. Photoelastic experiments indicate that the applied load biaxiality has a very strong influence on the size and shape of the crack-tip stress field, and fracture toughness values for both polymers were seen to decrease with increasing load biaxiality. The load biaxiality was also found to have a strong influence on the crack growth direction in PMMA and a negligible influence on the PVC. The 7075-T6 aluminum toughness values increased with biaxiality, while intermediate peak toughness values were noted at a 0.5 biaxiality ratio for the more ductile 2024-T3 and 6061-T4 alloys. Fracture toughnesses at the highest biaxiality ratios were found to be equal to the uniaxial results.
Jones, D. L.↗
Strain Measurement System Developed for Biaxially Loaded Cruciform Specimens
A new extensometer system developed at the NASA Glenn Research Center at Lewis Field measures test area strains along two orthogonal axes in flat cruciform specimens. This system incorporates standard axial contact extensometers to provide a cost-effective high-precision instrument. The device was validated for use by extensive testing of a stainless steel specimen, with specimen temperatures ranging from room temperature to 1100 F. In-plane loading conditions included several static biaxial load ratios, plus cyclic loadings of various waveform shapes, frequencies, magnitudes, and durations. The extensometer system measurements were compared with strain gauge data at room temperature and with calculated strain values for elevated-temperature measurements. All testing was performed in house in Glenn's Benchmark Test Facility in-plane biaxial load frame.
Krause, David L.↗
Biaxial load effects in the mechanics of fracture
Experimental findings on the effects of biaxial loading on fracture toughness, non-self-similar growth problems, fatigue crack propagation, and subcritical growth properties are reviewed, together with the fundamental analytical solutions for problems of crack in an elastic solid under biaxial loading. Basic asymptotic field representations, and some stress-intensity factor solutions are presented. The effects of biaxial loading on problems involving plastic deformation are illustrated with recent numerical results. Early asymptotic solutions for a nonlinear elastic solid are discussed with emphasis on the solution of problems with significant plastic deformation, and on stable crack growth. A brief survey of the applications literature, and recommendations for future studies are included.
Moyer, E. T., Jr.↗
The fracture criteria for crack growth under biaxial loading
The paper examines the fracture criteria for crack growth under biaxial loading. A finite element theory was formulated for the problem of crack propagation to failure which is based on the incremental theory of plasticity and is mathematically equivalent to that of a nonlinear moving-mixed-boundary-value problem. It was found that during the crack growth the plastic energy of the specimen and the crack size are linearly related for center-cracked specimens of an aluminum alloy subjected to uniaxial and or biaxial loading when experimental data relating applied stress and crack size have been used as input.
Liebowitz, H.↗
Damage tolerance of pressurized graphite/epoxy tape cylinders under uniaxial and biaxial loading
The damage tolerance behavior of internally pressurized, axially slit, graphite/epoxy tape cylinders was investigated. Specifically, the effects of axial stress, structural anisotropy, and subcritical damage were considered. In addition, the limitations of a methodology which uses coupon fracture data to predict cylinder failure were explored. This predictive methodology was previously shown to be valid for quasi-isotropic fabric and tape cylinders but invalid for structurally anisotropic (+/-45/90)(sub s) and (+/-45/0)(sub s) cylinders. The effects of axial stress and structural anisotropy were assessed by testing tape cylinders with (90/0/+/-45)(sub s), (+/-45/90)(sub s), and (+/-45/0)(sub s) layups in a uniaxial test apparatus, specially designed and built for this work, and comparing the results to previous tests conducted in biaxial loading. Structural anisotropy effects were also investigated by testing cylinders with the quasi-isotropic (0/+/-45/90)(sub s) layup which is a stacking sequence variation of the previously tested (90/0/+/-45)(sub s) layup with higher D(sub 16) and D(sub 26) terms but comparable D(sub 16) and D(sub 26) to D(sub 11) ratios. All cylinders tested and used for comparison are made from AS4/3501-6 graphite/epoxy tape and have a diameter of 305 mm. Cylinder slit lengths range from 12.7 to 50.8 mm. Failure pressures are lower for the uniaxially loaded cylinders in all cases. The smallest percent failure pressure decreases are observed for the (+/-45/90)(sub s) cylinders, while the greatest such decreases are observed for the (+/-45/0)(sub s) cylinders. The relative effects of the axial stress on the cylinder failure pressures do not correlate with the degree of structural coupling. The predictive methodology is not applicable for uniaxially loaded (+/-45/90)(sub s) and (+/-45/0)(sub s) cylinders, may be applicable for uniaxially loaded (90/0/+/-45)(sub s) cylinders, and is applicable for the biaxially loaded (90/0/+/-45)(sub s) and (0/+/-45/90)(sub s) cylinders. This indicates that the ratios of D(sub 16) and D(sub 26) to D(sub 11), as opposed to the absolute magnitudes of D(sub 16) and D(sub 26), may be important in the failure of these cylinders and in the applicability of the methodology. Discontinuities observed in the slit tip hoop strains for all the cylinders tested indicate that subcritical damage can play an important role in the failure of tape cylinders. This role varies with layup and loading condition and is likely coupled to the effects of structural anisotropy. Biaxial failure pressures may exceed the uniaxial values because the axial stress contributes to the formation of 0 deg ply splitting (accompanied by delamination) or similar stress-mitigating subcritical damage. The failure behavior of similar cylinders can also vary as a result of differences in the role of subcritical damage as observed for the case of a biaxially loaded (90/0/+/-45)(sub s) cylinder with a 12.7 mm slit. For this case, the methodology is valid when the initial coupon and cylinder fracture modes agree. However, the methodology underpredicts the failure pressure of the cylinder when a circumferential fracture path, suggestive of a 0 deg ply split, occurs at one slit tip. Thus, the failure behavior of some tape cylinders may be highly sensitive to the initial subcritical damage mechanism. Finite element analyses are recommended to determine how structural anisotropy and axial stress modify the slit tip stress states in cylinders from those found in flat plates since similarity of these stress states is a fundamental assumption of the current predictive methodology.
Priest, Stacy Marie↗
Biaxial load effects in fracture mechanics
It is found that the standard expressions for elastic stress and displacement in the crack-tip region (i.e., the so-called singular solution) cannot be considered to be approximations that are acceptable in a completely general sense. This conclusion is best illustrated by the instance of a biaxially loaded infinite sheet with a flat horizontal central crack, where the effect of load applied parallel to the plane of the crack appears entirely in the second terms of the series representations for local stresses and displacements. An elastoplastic finite-element analysis of the same biaxially loaded finite specimen geometry shows that the global energy release rate, the J-integral, the plastic stress and strain intensity factors (in the sense of Hilton and Hutchinson), and the size of the crack border region plastic yield, all have pronounced biaxial load dependence.
Liebowitz, H.↗
Specimen Designs for Testing Advanced Aeropropulsion Materials Under In-Plane Biaxial Loading
A design study was undertaken to develop specimen designs for testing advanced aeropropulsion materials under in-plane biaxial loading. The focus of initial work was on developing a specimen design suitable for deformation and strength tests to be conducted under monotonic loading. The type of loading initially assumed in this study was the special case of equibiaxial, tensile loading. A specimen design was successfully developed after a lengthy design and optimization process with overall dimensions of 12 by 12 by 0.625 in., and a gage area of 3.875 by 3.875 by 0.080 in. Subsequently, the scope of the work was extended to include the development of a second design tailored for tests involving cyclic loading. A specimen design suitably tailored to meet these requirements was successfully developed with overall dimensions of 12 by 12 by 0.500 in. and a gage area of 2.375 by 2.375 by 0.050 in. Finally, an investigation was made to determine whether the specimen designs developed in this study for equibiaxial, tensile loading could be used without modification to investigate general forms of biaxial loading. For best results, it was concluded that specimen designs need to be optimized and tailored to meet the specific loading requirements of individual research programs.
Ellis, John R.↗
Fracture analysis of stiffened panels under biaxial loading with widespread cracking
An elastic-plastic finite-element analysis with a critical crack-tip opening angle (CTOA) fracture criterion was used to model stable crack growth and fracture of 2024-T3 aluminum alloy (bare and clad) panels for several thicknesses. The panels had either single or multiple-site damage (MSD) cracks subjected to uniaxial or biaxial loading. Analyses were also conducted on cracked stiffened panels with single or MSD cracks. The critical CTOA value for each thickness was determined by matching the failure load on a middle-crack tension specimen. Comparisons were made between the critical angles determined from the finite-element analyses and those measured with photographic methods. Predicted load-against-crack extension and failure loads for panels under biaxial loading, panels with MSD cracks, and panels with various numbers of stiffeners were compared with test data whenever possible. The predicted results agreed well with the test data even for large-scale plastic deformations. The analyses were also able to predict stable tearing behavior of a large lead crack in the presence of MSD cracks. The analyses were then used to study the influence of stiffeners on residual strength in the presence of widespread fatigue cracking. Small MSD cracks were found to greatly reduce the residual strength for large lead cracks even for stiffened panels.
Newman, J. C., Jr.↗
Fracture analysis of stiffened panels under biaxial loading with widespread cracking
An elastic-plastic finite-element analysis with a critical crack-tip-opening angle (CTOA) fracture criterion was used to model stable crack growth and fracture of 2024-T3 aluminum alloy (bare and clad) panels for several thicknesses. The panels had either single or multiple-site damage (MSD) cracks subjected to uniaxial or biaxial loading. Analyses were also conducted on cracked stiffened panels with single or MSD cracks. The critical CTOA value for each thickness was determined by matching the failure load on a middle-crack tension specimen. Comparisons were made between the critical angles determined from the finite-element analyses and those measured with photographic methods. Predicted load-against-crack extension and failure loads for panels under biaxial loading, panels with MSD cracks, and panels with various number of stiffeners were compared with test data, whenever possible. The predicted results agreed well with the test data even for large-scale plastic deformations. The analyses were also able to predict stable tearing behavior of a large lead crack in the presence of MSD cracks. The analyses were then used to study the influence of stiffeners on residual strength in the presence of widespread fatigue cracking. Small MSD cracks were found to greatly reduce the residual strength for large lead cracks even for stiffened panels.
Newman, J. C., Jr.↗
Load biaxiality and fracture - Synthesis and summary
The question of load biaxiality strongly affecting almost all of the characteristics of brittle fracture behavior of a cracked body is investigated. Results of research published piecemeal over the years by the authors have 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. A synthesis and summary of this research is presented showing the shortcomings inherent in both Griffith's global energy rate theory for crack instability and Irwin's local crack-tip stress intensity theory for fracture toughness. In both theories only the tensile load perpendicular to the crack influences fracture behavior of the body.
Eftis, J.↗
Biaxial load effects on the crack border elastic strain energy and strain energy rate
The validity of the singular solution (first term of a series representation) is investigated for the crack tip stress and displacement field in an infinite sheet with a flat line crack with biaxial loads applied to the outer boundaries. It is shown that if one retains the second contribution to the series approximations for stress and displacement in the calculation of the local elastic strain energy density and elastic strain energy rate in the crack border region, both these quantities have significant biaxial load dependency. The value of the J-integral does not depend on the presence of the second term of the series expansion for stress and displacement. Thus J(I) is insensitive to the presence of loads applied parallel to the plane of the crack.
Eftis, J.↗
Elastic stability of biaxially loaded longitudinally stiffened composite structures.
A linear analysis method is presented for the elastic stability of structures of uniform cross section, that may be idealized as an assemblage of laminated plate-strips, flat and curved, and beams. Each plate-strip and beam covers the entire length of the structure and is simply supported on the edges normal to the longitudinal axis. Arbitrary boundary conditions may be specified on any external longitudinal side of plate-strips. The structure or selected plate-strips may be loaded in any desired combination of inplane biaxial loads. The analysis simultaneously considers all modes of instability and is applicable for the buckling of laminated composite structures. Some numerical results are presented to indicate possible applications.
Viswanathan, A. V.↗
Testing Machine for Biaxial Loading
Standard tensile-testing machine applies bending and tension simultaneously. Biaxial-loading test machine created by adding two test fixtures to commercial tensile-testing machine. Bending moment applied by substrate-deformation fixture comprising yoke and anvil block. Pneumatic tension-load fixture pulls up on bracket attached to top surface of specimen. Tension and deflection measured with transducers. Modified test apparatus originally developed to load-test Space Shuttle surface-insulation tiles and particuarly important for composite structures.
Demonet, R. J.↗
Plastic buckling of plates and shells under biaxial loading
Elastic buckling equations for calculating plastic buckling of plates and shells under biaxial loading
Peterson, J. P.↗
Inelastic response of metal matrix composites under biaxial loading
Elements of the analytical/experimental program to characterize the response of silicon carbide titanium (SCS-6/Ti-15-3) composite tubes under biaxial loading are outlined. The analytical program comprises prediction of initial yielding and subsequent inelastic response of unidirectional and angle-ply silicon carbide titanium tubes using a combined micromechanics approach and laminate analysis. The micromechanics approach is based on the method of cells model and has the capability of generating the effective thermomechanical response of metal matrix composites in the linear and inelastic region in the presence of temperature and time-dependent properties of the individual constituents and imperfect bonding on the initial yield surfaces and inelastic response of (0) and (+ or - 45)sub s SCS-6/Ti-15-3 laminates loaded by different combinations of stresses. The generated analytical predictions will be compared with the experimental results. The experimental program comprises generation of initial yield surfaces, subsequent stress-strain curves and determination of failure loads of the SCS-6/Ti-15-3 tubes under selected loading conditions. The results of the analytical investigation are employed to define the actual loading paths for the experimental program. A brief overview of the experimental methodology is given. This includes the test capabilities of the Composite Mechanics Laboratory at the University of Virginia, the SCS-6/Ti-15-3 composite tubes secured from McDonnell Douglas Corporation, a text fixture specifically developed for combined axial-torsional loading, and the MTS combined axial-torsion loader that will be employed in the actual testing.
Mirzadeh, F.↗
Plastic intensity factors for cracked plates subjected to biaxial loading
An elastic-plastic analysis is performed for an infinite plate under plane stress conditions which contains a finite line crack and is subjected to biaxial loading. In the large scale yielding range, the amplitude of the dominant singularity at the crack tip, the plastic stress (or strain) intensity factor, is found to depend on the magnitude of loading parallel to the crack direction. The predicted value for the fracture initiation stress which is based on a plastic intensity factor fracture criterion, increases under lateral, tensile loading. Compressive loading parallel to the crack has the opposite effect on the fracture initiation stress.
Hilton, P. D.↗
Comparison of polyester, film-yarn composite, balloon materials subjected to shear and biaxial loading
A series of candidate materials for use in large balloons was tested and their tensile and shear strength capabilities were compared. The tests were done in a cold box at -68 C (-90 F). Some of these materials were fabricated on a special machine called the flying thread loom. This machine laminates various patterns of polyester yarn to a thin polyester film. The results show that the shear strength of materials changes with the angle selected for the transverse yarns, and substantial increases in biaxial load carrying capabilities, compared to materials formerly used, are possible. The loom capabilities and the test methods are discussed.
Niccum, R. J.↗