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A failure criterion for notched plates in compression was developed. The criterion is based on experimentally observed kinking failure of fibers around a notch combined compressive and shear stresses. Experimental results for plates with a crack or a hole are used to verify the failure model, and design studies are performed to demonstrate the use of the model.
A large, comprehensive program is being conducted at Virginia Tech to study the effect of laminate thickness on the fracture strength of notched laminated composites. Part of this program has been the study of the chracteristics and development of subcritical crack-tip damage prior to failure. The study has concentrated on the center-cracked tension specimen geometry. Subcritical crack-tip damage has been studied using enhanced X-ray radiography and the laminate deply technique. This paper examines he role that delamination plays in affecting the fracture of (0/+ or - 45/90)ns and (0/+ or - 45)ns laminates at various values of n. The study has found that delaminations do occur in thin laminates (n = 1) and affect the strength of the laminate. However, in thick laminates such as (0/+ or 45)90ns, and (0/+ or - 45)20s, there is sufficient constraint to prevent delaminations from occurring in the interior region of he specimen. The final fracture surface is uniform in the interior and self-similar (collinear with the original starter notch), with 'shear-lip' type damage in the form of delaminations and matrix cracking in the first several plies at the surface. These differences in the type of fracture of the thin and thick laminates greatly affect the fracture strength.
Single-edge, semi-circular notched specimens of Al 2024-T3, 2.3 mm thick, were cyclicly loaded at R-ratios of 0.5, 0.0, -1.0, and -2.0. The notch roots were periodically inspected using a replica technique which duplicates the bore surface. The replicas were examined under an optical microscope to determine the initiation of very short cracks and to monitor the growth of short cracks ranging in length from a few tens of microns to the specimen thickness. In addition to short crack growth measurements, the crack opening displacement (COD) was measured for surface cracks as short as 0.035 mm and for through-thickness cracks using the Interferometric Strain/Displacement Gage (ISDG), a laser-based optical technique. The growth rates of short cracks were faster than the long crack growth rates for R-ratios of -1.0 and -2.0. No significant difference between short and long crack growth rates was observed for R = 0.0. Short cracks had slower growth rates than long cracks for R = 0.5. The crack opening stresses measured for short cracks were smaller than those predicted for large cracks, with little difference appearing for positive R-ratios and large differences noted for negative R-ratios.
The short bar chevron-notched specimen is used to measure the plane strain fracture toughness of hot pressed Si3N4. Specimen proportions and chevron-notch angle are varied, thereby varying the amount of crack extension to maximum load (upon which K sub IC is based). The measured toughness (4.68 + or 0.19 MNm to the 3/2 power) is independent of these variations, inferring that the material has a flat crack growth resistance curve.
Presented are techniques based on 3-D finite-element analysis for the examination of continuous fiber reinforced metal matrix composites. Examples are shown for specific metal matrix composites such as boron/aluminum and silicon-carbide/aluminum. Specimen stress-strain behavior and stress at first fiber failure were predicted for boron/aluminum laminates containing circular holes and crack-like slits. The predictions compared very well for (+ or - 45) sub 2s laminates. Mesh configuration was shown to have an effect on the calculation of stresses local to the notch. The presence of thin interface layers of matrix material had a significant influence on the slit-tip stress state, causing sharper stress gradients near the notch. Interface layers reduced the slit-tip fibers stresses in a (+ or - 45) sub s silicon-carbide/aluminum laminate but increased them in a (0/90) sub s laminate.
A numerical computational study was carried out to assess the effects of subcritical crack growth on crack stability in the chevron-notched three-point bend specimens. A power-law relationship between the subcritical crack velocity and the applied stress intensity were used along with compliance and stress-intensity relationships for the chevron-notched bend specimen to calculate the load response under fixed deflection rate and a machine compliance. The results indicate that the maximum load during the test occurs at the same crack length for all the deflection rates; the maximum load, however, is dependent on the deflection rate for rates below the critical rate. The resulting dependence of the apparent fracture toughness on the deflection rate is compared to experimental results on soda-lime glass and polycrystalline alumina.
The boundary-force method developed by Tan (1985) and Tan et al. (1986) is extended to two-dimensional mixed boundary-value problems in fracture mechanics. The formulation is explained in detail, and results are presented in tables and graphs for sample problems involving an edge crack emanating from a semielliptical and a semicircular notch and an edge crack emanating from a V notch. The accuracy of the approach is demonstrated by comparisons with collocation solutions for an edge-clamped center-cracked tension specimen.
This paper presents techniques based on a three-dimensional finite-element analysis for the analysis of continuous fiber reinforced metal matrix composite. Examples are shown for specific metal matrix composites such as boron/aluminum and silicon-carbide/aluminum. Specimen stress-strain behavior and stress at first fiber failure were predicted for boron/aluminum laminates containing circular holes and crack-like slits. The predictions compared very well with test data for laminates containing 0 deg fibers and reasonably well for (+/-45)2s laminates. Mesh configuration was shown to have an effect on the calculation of stresses local to the notch. The presence of thin interface layers of matrix material had a significant influence on the slit tip stress state, causing sharper stress gradients near the notch. Interface layers reduced the slit-tip fibers stress in a (+/-45)2s silicon-carbide/aluminum laminate but increased them in a (0/90)2s laminate.
A better understanding of the factors that affect the semi-circular edge-notched compressive strength is developed, and the associated failure mode(s) of thermoplastic composite laminates with multidirectional stacking sequences are identified. The primary variables in this investigation are the resin nonlinear shear constitutive behavior, stacking sequence (orientation of plies adjacent to the 0 degree plies), resin-rich regions between the 0 degree plies and the off-axis supporting plies, fiber/matrix interfacial bond strength, and initial fiber waviness. Two thermoplastic composite material systems are used in this investigation. The materials are the commercial APC-2 (AS4/PEEK) and a poor interface experimental material, AU4U/PEEK, designed for this investigation. Notched compression specimens are studied at 21, 77, and 132 C. Geometric and material nonlinear two-dimensional finite element analysis is used to model the initiation of fiber microbuckling of both the ideal straight fiber and the more realistic initially wavy fiber. The effects of free surface, fiber constitutive properties, matrix constitutive behavior, initial fiber curvature, and fiber/matrix interfacial bond strength on fiber microbuckling initiation strain levels are considered.
Two specimen configuration of a (0/90)2s SCS-6/Ti-15-3 laminate were tested and analyzed: a center hole (CH) specimen and a double edge notch (DEN) specimen. The two specimen configurations failed at similar stress levels. Two analytical techniques, a 3-D finite-element analysis and a macro-micromechanical analysis were used to predict the overall stress-deformation behavior and the notch-tip fiber-matrix interface stresses in both configurations.
While earlier studies have shown that the tensile properties and fracture test intensity factors of oxygen-strengthened Ti remain nearly unaffected by the presence of about 70 ppm (weight) hydrogen, the Charpy V-notch test-determined impact properties of oxygen-bearing Ti are strongly affected by the presence of hydrogen. The present study establishes that, concurrently with the strengthening effect of oxygen, there is a substantial lowering of ductility. The presence of hydrogen has virtually no effect on the notch strength of Ti alloys of either low or high oxygen content, where hydrogen contents lie in the 25-80 range.
Mixed-mode matrix fracture in central notched off-axis unidirectional composite laminates was investigated. A limited number of unidirectional tensile type specimens with a central, horizontal, notch were tested. Crack initiation and propagation were examined under various local stress fields that were controlled by fiber orientations. The tested specimens were simulated using a two dimensional finite element method with constant strain loading. The strain energy release rates along the crack were evaluated via crack closure technique. The variation of critical strain energy rates with off-axis angle was studied. The results from single (one-sided) and double (two-sided) crack simulations were presented and compared.
In the bulk, glassy polymers exhibit a nonlinear viscoelastic response during deformation. Stress or strain induced damage (i.e. crazing, microshear banding) results in the production of nonrecoverable work and observed nonlinearity. Stress or strain dependent shift factors have been used to mathematically model the mechanical behavior of these polymers. Glassy polymers that have been notched, may exhibit very different load displacement response compared to the same material under bulk deformation. If a sharp notch is introduced into the body then loaded, the load displacement trace may appear to be single-valued in the absence of viscoelasticity and crack growth. This suggests the volume of damaged material is small compared to the overall dimensions of the specimen. The ability to produce a single-valued load-load-line displacement trace through the use of the Correspondence Principle may prove to be useful for fracture of viscoelastic materials.
Neuber's proposed method of calculating a practical factor of stress concentration for parts containing notches of arbitrary size depends on the knowledge of a "new material constant" which can be established only indirectly. In this paper, the new constant has been evaluated for a large variety of steels from fatigue tests reported in the literature, attention being confined to stresses near the endurance limit. Reasonably satisfactory results were obtained with the assumption that the constant depends only on the tensile strength of the steel. Even in cases where the notches were cracks of which only the depth was known, reasonably satisfactory agreement was found between calculated and experimental factors. It is also shown that the material constant can be used in an empirical formula to estimate the size effect on unnotched specimens tested in bending fatigue.
The failure sequence following crack formation in a chevron-notched four-point bend 1 specimen is examined in a parametric study using the Bluhm slice synthesis model. Premature failure resulting from crack formation forces which exceed those required to propagate a crack beyond alpha (min) is examined together with the critical crack length and critical crack front length. An energy based approach is used to establish factors which forecast the tendency of such premature failure due to crack formation for any selected chevron-notched geometry. A comparative study reveals that, for constant values of alpha (1) and alpha (0), the dimensionless beam compliance and stress intensity factor are essentially independent of specimen width and thickness. The chevron tip position, alpha (0) has its primary effect on the force required to initiate a sharp crack. Small values for alpha (0) maximize the stable region length, however, the premature failure tendency is also high for smaller alpha (0) values. Improvements in premature failure resistance can be realized for larger values of alpha (0) with only a minor reduction in the stable region length. The stable region length is also maximized for larger chevron based positions, alpha (1) but the chance for premature failure is also raised. Smaller base positions improve the premature failure resistance with only minor decreases in the stable region length. Chevron geometries having a good balance of premature failure resistance, stable region length, and crack front length are 0.20 less than or equal to alpha (0) is less than or equal to 0.30 and 0.70 is less than or equal to alpha (1) is less than or equal to 0.80.
Notch antennas, also known as the tapered slot antenna (TSA), have been the topics of research for decades. TSA has demonstrated multi-octave bandwidth, moderate gain (7 to 10 dB), and symmetric E- and H- plane beam patterns and can be used for many different applications. This chapter summarizes the research activities on notch antennas over the past decade with emphasis on their most recent advances and applications. This chapter begins with some discussions on the designs of single TSA; then follows with detailed discussions of issues associated with TSA designs and performance characteristics. To conclude the chapter, some recent developments in TSA arrays and their applications are highlighted.
Two driving factors in aircraft panel design are structural efficiency and response to in-service damage. Stitching through the thickness can improve both of these considerations. Combining stitching with a post-buckling design approach can provide additional improvements. The buckling behavior of stitched structure is considered since lighter structures can be achieved if local skin buckling is allowed to occur at less than design ultimate load. Through-the-thickness stitching can suppress delamination between skin and flange, thereby allowing the structure to reliably carry load into the postbuckling range. Hat-stiffened and rod-stiffened panels in which the skin and flanges were stitched together through-the-thickness prior to curing are considered through experiment and analysis. In both types of panels no mechanical fasteners were used for the assembly. Specimens were loaded to failure in axial compression. In this study all specimens buckled in the skin between the stiffeners and continued to carry load. In addition, the behavior of panels with a severed stringer or notch are considered. Failure loads and strain distributions in the notched panel are compared to those in the unnotched panel.
Oxidation and the effects of high temperature exposures on notched fatigue life were considered for a powder metallurgy processed supersolvus heat-treated ME3 disk superalloy. The isothermal static oxidation response at 704 C, 760 C, and 815 C was consistent with other chromia forming nickel-based superalloys: a TiO2-Cr2O3 external oxide formed with a branched Al2O3 internal subscale that extended into a recrystallized - dissolution layer. These surface changes can potentially impact disk durability, making layer growth rates important. Growth of the external scales and dissolution layers followed a cubic rate law, while Al2O3 subscales followed a parabolic rate law. Cr- rich M23C6 carbides at the grain boundaries dissolved to help sustain Cr2O3 growth to depths about 12 times thicker than the scale. The effect of prior exposures was examined through notched low cycle fatigue tests performed to failure in air at 704 C. Prior exposures led to pronounced debits of up to 99 % in fatigue life, where fatigue life decreased inversely with exposure time. Exposures that produced roughly equivalent 1 m thick external scales at the various isotherms showed statistically equivalent fatigue lives, establishing that surface damage drives fatigue debit, not exposure temperature. Fractographic evaluation indicated the failure mode for the pre-exposed specimens involved surface crack initiations that shifted with exposure from predominately single intergranular initiations with transgranular propagation to multi-initiations from the cracked external oxide with intergranular propagation. Weakened grain boundaries at the surface resulting from the M23C6 carbide dissolution are partially responsible for the intergranular cracking. Removing the scale and subscale while leaving a layer where M23C6 carbides were dissolved did not lead to a significant fatigue life improvement, however, also removing the M23C6 carbide dissolution layer led to nearly full recovery of life, with a transgranular initiation typical to that observed in unexposed specimens.