Range Of Crack Lengths Research Articles

Characterization of Mode I Delamination Growth in Glass/Epoxy Composite Cylinders

Mode I delamination growth in filament wound composite cylinders has been examined analytically and experimentally. Beam specimens with the axis parallel to the cylinder axis were machined from the cylinders. The specimen contained an aluminum film at one end to define a starter delamination. A beam model incorporating elastic foundation effects and curved cross sections of the sub-beams of the delamination region was developed for the beam specimens configured for a DCB test from laminated beam theory derived from a shallow shell formulation. An experimental study on [±016 and [±0112, glass/epoxy DCB specimens employing contoured loading tabs accommodated to the curved cross-section was conducted. The delaminations were initially at the mid-surface, and the angles 0 were 300, 550 and 850. Analytical predictions of the compliance were in agreement with experimental data over the range of crack lengths, beam thicknesses, and ply angles examined. The fracture toughness corresponding to propagation straight from the insert increased slightly with increased angle 0 at the ±0 interface. The propagation fracture toughness increased steeply with crack length and then dropped. The increasing resistance, i.e., R-curve behavior, is attributed to the work associated with bridging and fracture of angle-ply fiber bundles, and the drop is attributed to crack jumping to another interface. For all laminates, the crack propagated in a non-uniform manner across the width of the specimen.

Elastic Foundation Analysis of Tilted Sandwich Debond (TSD) Specimen

The tilted sandwich debond (TSD) specimen for characterizing debonding of a sandwich structure is analyzed using elastic foundation theory. The face sheet is considered as a cantilever beam in the debonded region of the specimen and as a beam of finite length supported by an elastic foundation in the bonded region. An analytical model for the beam deflection is developed that may be utilized for design of the specimen, fracture analysis, and data reduction of face/core debond toughness. A parametric investigation was conducted to examine how material and geometrical parameters of the constituents of the sandwich and test configuration influence the compliance of the TSD specimen. Testing was performed on a sandwich consisting of glass/vinylester face sheets over a H200 PVC foam core. The compliance predictions for this and a previously examined sandwich agreed favorably with experimental data over a large range of crack lengths and tilt angles. The debond toughness reduced from experimentally calibrated compliance and from the foundation model was consistent.

Elastic Foundation Analysis of Tilted Sandwich Debond (TSD) Specimen

The tilted sandwich debond (TSD) specimen for characterizing debonding of a sandwich structure is analyzed using elastic foundation theory. The face sheet is considered as a cantilever beam in the debonded region of the specimen and as a beam of finite length supported by an elastic foundation in the bonded region. An analytical model for the beam deflection is developed that may be utilized for design of the specimen, fracture analysis, and data reduction of face/core debond toughness. A parametric investigation was conducted to examine how material and geometrical parameters of the constituents of the sandwich and test configuration influence the compliance of the TSD specimen. Testing was performed on a sandwich consisting of glass/vinylester face sheets over a H200 PVC foam core. The compliance predictions for this and a previously examined sandwich agreed favorably with experimental data over a large range of crack lengths and tilt angles. The debond toughness reduced from experimentally calibrated compliance and from the foundation model was consistent.

Fracture Analysis of Cracked Macadamia Nutshells under Contact Load between Two Rigid Plates

Fracture behaviour of Macadamia nutshells with an existing crack, compressed between two rigid plates, is investigated theoretically and numerically. In terms of a crack closure theory developed within a linearized shallow shell theory, the stress intensity factors for the cracked nutshells are determined over a range of crack lengths. Two typical crack configurations in a nutshell, defined as the vertical crack and the horizontal crack, respectively, with reference to the loading planes, are studied. The finite element analysis is carried out for comparison with the theoretical solutions, and it is shown that the shallow shell theory is valid only for a shallowness parameter up to 0·25. The linear variation of the stress intensity factor through the shell thickness, which is assumed in the shell theory, is confirmed by the finite element analysis.

Analysis of brittle fracture due to compressive loading using center-cracked Brazilian disk

The center-cracked Brazilian disk subjected to diametral compressive stress uniformly distributed along parts of its cylindrical surface is used to investigate combined mode fracture of brittle material. A fracture analysis is made of this specimen configuration. Explicit formulae for mode I and mode II stress intensity factor calculation are derived based on boundary integral equation method and related numerical solution given by Atkinson. The proposed formulae are valid in wide range of crack length a/R. This configuration can avoid splitting along load line usually occuring in Brazilian test and permit one to achieve easily pure mode II crack growth (crack coplanar extension) and any combination of KI and KII by a simple alignment of crack orientation with respect to load line. SIF values from the present calculation and finite element solution are also given for comparison.

Compliance rate change of tapered double cantilever beam specimen with hybrid interface bonds

This paper presents a combined numerical and experimental study of compliance rate change of Tapered Double Cantilever Beam (TDCB) specimens for Mode-I fracture of hybrid interface bonds. The easily machinable TDCB specimen, which is designed to achieve a constant rate of compliance change with respect to crack length, is developed for Mode-I fracture tests of hybrid material bonded interfaces, such as wood bonded to fiber-reinforced plastic (FRP) composite. The linearity of compliance crack-length relationship of the specimen is verified by both Rayleigh–Ritz method and finite element analysis. An experimental compliance calibration program for specimens with wood–wood and FRP–FRP bonded interfaces is carried out, and a constant rate change of compliance with respect to crack length is obtained for a specific range of crack length. Fracture tests are further performed using TDCB specimens for wood–wood and wood–FRP bonded interfaces to determine the critical loads for crack initiation and crack arrest, and using the constant compliance rate change of the specimens determined by experiment or analysis, the respective critical strain energy release rates, or fracture energies, are obtained. This study indicates that the constant compliance rate change obtained from experiment or finite element analysis for linear-slope TDCB specimens can be used with confidence for fracture studies of hybrid material interface bonds.

Analysis of a crack approaching a circular hole in cross-ply laminates under biaxial loading

The problem of a crack approaching a circular hole in cross-ply laminates under uniaxial and biaxial loading is investigated in this paper. The effects of material orthotropy, geometry [R/d and a/d], and loading conditions on crack tip singularity are investigated. The stress intensity factors are obtained by the modified mapping collocation method. The present results for an isotropic infinite plate show good agreement with existing solutions. The results for cross-ply laminates show that the stress intensity factors strongly depend on material orthotropy, geometry, and loading condition. The stress intensity factors for cross-ply laminates exist between those for θ=0° and those for θ=90° in the whole range of crack length and decrease as the percentage of 0° plies increases. In the range of small crack length the stress intensity factors for biaxial tension are higher than those for uniaxial tension. In the range of large crack length the stress intensity factors for uniaxial tension are higher than those for biaxial tension.

A Tapered Double-Cantilever-Beam Specimen Designed for Constant-KTesting at Elevated Temperatures

AbstractA compact, constant stress intensity factor, side grooved, tapered double-cantilever-beam (T-DCB) specimen has been designed for measuring elevated temperature creep and fatigue crack growth rates. This specimen is much smaller than the standard DCB specimen generally used for studying corrosion fatigue in airframe materials and it can be easily accommodated in standard furnaces generally used in elevated-temperature fracture mechanics testing. The specimen possesses a constant-K region of 30 mm. This constant-K crack length range was first established analytically through detailed two- and three-dimensional finite-element analyses and the finite-element calculations were further verified experimentally through quantitative fractographic analysis using the striation measurement technique.

MODE I STRESS INTENSITY FACTOR EQUATIONS FOR CRACKS AT NOTCHES AND CAVITIES

Abstract— In this paper, the notch‐crack problem is treated in two different ways: if the non‐dimensional crack length l/ρ (l= crack length; ρ= notch root radius) is smaller than the transition crack length lT/ρ, it is treated as an edge crack lying within the local stress field around the notch tip; if l/ρ is larger than lT/ρ, the notch‐crack is considered as a simple flat crack problem subjected to remote loading, the flat crack size being the sum of notch depth and the real crack length. Based on currently available numerical data, expressions for the transition crack length, lT, and for the geometric factor F=KI/(1.1215Ktσ√πl) are developed for various notch problems for the crack length range l≦lT. It is found that the stress (σyy) normalized by the peak stress (σpeak), σyy/σpeak, for the pre‐cracked component is very similar to the geometric factor for short cracks.

Characterization of crack tip and geometry induced closure

The paper presents a comprehensive series of closure measurements on a coarse grained near alpha titanium alloy. The work at room temperature involved three different monitoring techniques: DCPD, strain gauge and replicas. The information generated on part-through cracks at several stresses and over a range of crack lengths is used to assess the `3D' nature of the closure process. Particular attention is given to the cracked area in contact at each condition and crack peeling on loading. Application of the observations to a notch geometry is discussed.

A Fracture Test Method for Mode I Fracture Of Thin Metal Materials

Abstract A method of testing Mode I K dominated fractures in thin materials using a constrained short center notched tension specimen that is clamped along the loaded edge is described. Poisson's effect induces a lateral tension on the specimen that eliminates the buckling problems associated with thin materials. Furthermore, the stress intensity factor over a significant range of crack lengths and specimen geometries is dependent only on the nominal strain, making the test very suitable for crack-growth experiments under a constant-stress intensity factor. A very accurate approximate expression for the stress intensity factor is presented. A test using this method to measure the crack-growth resistance of Kapton 300HN polyimide film is described.

On the conventional K calibration equations for single-edge-cracked tension specimens

The conventional K calibration equations for single-edge-cracked tension specimens were examined by conducting constant stress intensity range fatigue tests on a 2024-T3 aluminum alloy over a range of crack lengths from 0.5 to 15 mm [corresponding to crack length-to-specimen width ratios ( a W ) of about 0.02 to 0.5] in dry oxygen at two ΔK levels. The results showed that the equations are in considerable error, ranging from less than one to over ten percent from a W of 0.05 to 0.5. These errors are attributed to the effect of bending associated with rotation at the loading pins. An empirical correction to the K calibration equations was made based on the fatigue crack growth test data in oxygen. Tests were then conducted in a different test environment (namely, deaerated 0.5M NaCl solution) to validate the modified K calibration equation and showed very satisfactory results.

Fracture analysis of semi-circular and semi-circular-bend geometries

A fracture mechanics analysis of the semi-circular (SC) and semi-circular-bend (SCB) fracture geometries is presented. The weight function method is implemented to obtain wide ranging stress intensity factor (SIF) and crack opening displacement (COD) expressions. This study has as its basis a finite element analysis of the semi-circular disk (SC) subjected to a reference loading case. The latter is required to determine both the associated reference stress intensity factor and the weight function for the base-edge-cracked semi-circular geometry. With this information, SIF and COD expressions for the full range of crack lengths are obtained. The special cases of the SC subject to a concentrated crack mouth loading and the SCB are analyzed in detail. The weight function for the SCB is fully developed, with an accurate expression for the SIF and and a numerical result for the crack mouth opening displacement (CMOD). The latter wide ranging expressions can, in turn, be applied as a reference solution. From this weight function approach, SIF's and COD's for the SC and SCB subject to any other loading can be obtained.

Fracture Resistance Behavior of Highly Anisotropic Silicon Nitride

The R‐curve behavior was characterized by the Vickers indentation flaw technique, for highly anisotropic silicon nitride, a silicon nitride whose fibrous grains are highly aligned. The measured crack lengths ranged from 30 to 500 μm. The fracture resistance of a conventional self‐reinforced silicon nitride was determined for comparison using the same procedures. While in the self‐reinforced material several hundred micrometers of crack extension were required to obtain a high fracture toughness, the highly anisotropic material exhibited a high toughness from the beginning of the measured crack length range with little increase in the following range. It is suggested that the toughness of the highly anisotropic material steeply rises in a very short crack extension, which is advantageous in avoiding catastropic fractures.

Mixed-Mode Delamination Behavior of Carbon/Epoxy Composites

The mixed-mode bending (MMB) test was employed in an investigation of delamination fracture behavior in static and fatigue loading for carbon/epoxy composites 1300/M10 and HTA/6376. As specimens were loaded at different ratios of alL for different mixed-mode ratios, both investigated composites exhibited brittle unstable or brittle stable behavior of crack growth. Mixed-mode delamination fracture toughness was determined at a IL = 0.5. Fracture surfaces of MMB specimens were examined using scanning electron microscopy to distinguish fracture features. Stable crack growth was observed over the entire range of crack lengths investigated in the cyclic tests. A consistent relation of crack growth per cycle to the cyclic strain energy release rate was obtained. The trend of reduction in crack growth rate data with diminution in cyclic strain energy release rate suggests the presence of a threshold strain energy release rate.

A Full Field DC Potential Drop Calibration for an Asymmetrically Cracked M(T) Specimen

Abstract A direct current (DC) potential drop (PD) calibration tool, in the form of a computer program, is provided that can determine the PD response at any point in an M(T) specimen containing either a symmetric or asymmetric crack. Results from the program were verified using data in the literature and results from an analog simulation. If a standard PD calibration is applied to the PD response for an asymmetric crack, the total crack length will be underestimated which leads to significant stress intensity factor errors for even small amounts of asymmetry. Using the PD response of an asymmetric crack from an analog simulation, three methods to predict individual crack lengths are evaluated. The methods use a two-dimensional (2-D) iterative procedure to solve for crack length given voltages from at least two sets of probes located at different positions on the specimen. Any of the different methods, which use different probe locations as the calibration inputs, yield good crack length predictions for crack length to specimen width ratios a/W greater than 0.25. However, the most numerically robust method resulting in the least error over a large crack length range uses the PD from a centerline probe and the PD difference from two offset probes to predict the crack length. These predictions result in a crack length error that does not exceed ±0.004 W and consequently result in insignificant stress intensity factor errors.

Back Face Strain Calibration for Crack Length Measurements

Abstract A new calibration of back face strain (BFS) versus crack length a was developed. The calibration incorporates crack closure effects and is based upon a least squares multiple curvilinear regression analysis using seven specimens. Fatigue crack growth took place over a range of crack length to width ratios a/W from 0.2 to 0.8. The information was obtained under constant change in stress intensity factor ΔK using compact fractures toughness specimens of 2024-T351 aluminum alloy. In addition, two segular fatigue life crack propagation test conditions were used in the analysis database. The calibration function A*(a/W) is presented in a tubular form as well as in a polynomial equation format. The physical crack length was measured on both surfaces and later, after fracture, corrections of crack length were made for both curvature and plastic zone size. No effect of ΔK and specimen thickness on the calibration behavior was found to occur. The calibration equation was checked against crack lengths during fatigue crack growth behavior of both HSLA steel and mechanically alloyed aluminum materials and was found to be accurate.

Boundary element weight function analysis of a strip yield crack in a rotating disk

The boundary element method combined with subtration of Bueckner singular fields are used to obtain weight functions for an internal edge crack in a rotating annular disk. A previously developed, general representation of the weight function is used which leads to integrals that can be evaluated analytically to obtain the stress intensity factor and surface displacements of the crack. The determination of crack tip opening displacements for the strip yield crack is reduced to a non-singular integral which can be evaluated in closed form. The strip yield zone length and crack tip opening displacement are determined for an internal radial crack in a rotating annular disk for a range of crack lengths and rotational speeds.

Fatigue growth of multiple-cracks near a row of fastener-holes in a fuselage lap-joint

The fatigue growth of multiple cracks, of arbitrary lengths, emanating from a row of fastener holes in a bonded, riveted, lap joint in a pressurized aircraft fuselage is studied. The effects of residual stresses due to a rivet misfit, and of plastic deformation near the hole, are included. A Schwartz-Neumann alternating method which uses the analytical solution for a row of multiple colinear cracks in an infinite sheet (the crack-faces being subject to arbitrary tractions), is developed to analyze this MSD problem on a personal computer. It is found that for a range of crack lengths, a phenomena wherein the shorter cracks may grow faster than longer cracks may exist.

A novel method to determine the R-curve behaviour of ceramic materials: Application to a ceria-partially stabilized zirconia

Abstract A new method, allowing the determination of R-curve behaviour of ceramic materials, is developed. This method, called ‘crack line wedge loading’ (CLWL), presents many advantages, especially the continuous observation of the crack growth, a mode 1 fracture specimen and plane stress, conditions favourable to show the rising R-curve effect. The R-curve behaviour of Ce-ZrO 2 is assessed by this new test procedure and the results are compared with those given by another classical method (Bluhm's slice model). The data obtained by the two methods are in close agreement. However, the new method allows a broader range of crack lengths to be covered and thus is a more accurate technique to determine the stress intensity factor corresponding to the crack initiation. It is shown that the CLWL technique gives actual values of the stress intensity factor because it is possible to take into account the main crack, together with the microcracks constituting the process zone.