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Experiments are reported which show that plasticity-induced crack closure can account for crack growth retardation following an overload. The finite element method is used to provide evidence which supports the experimental observations of crack closure. Finally, a simple model is presented which predicts with limited success the retardation transient following an overload.
The energy release rates associated with a main crack propagating into a surrounding damage zone, and a damage zone translation relative to the main crack, as well as an energy of interaction between the two are analyzed. The displacement and stress fields for the crack-damage interaction problem are reconstructed employing a semi-empirical stress analysis and experimental evaluation of the average craze density in the crazed zone.
Crack propagation mechanisms occurring at various temperatures in a single crystalline Ni-base alloy, Rene N4, were investigated. The rates of crack growth at 21, 704, 927, 1038, and 1093 C were measured in specimens with 001-line and 110-line directions parallel to the load axis and the machined notch, respectively, using a pulsed dc potential drop apparatus, and the fracture surfaces at each temperature were examined using SEM. Crack growth rates (CGRs) for specimens tested at or below 927 C were similar, while at two higher temperatures, the CGRs were about an order of magnitude higher than at the lower temperatures. Results of SEM observations showed that surface morphologies depended on temperature.
Fatigue Crack Growth (NASA/FLAGRO) computer program developed as aid in predicting growth of preexisting flaws and cracks in structural components of space systems. Is enhanced version of FLAGRO4 and incorporates state-of-the-art improvements in both fracture mechanics and computer technology. Provides fracture-mechanics analyst with computerized method of evaluating "safe-crack-growth-life" capabilities of structural components. Also used to evaluate tolerance to damage of structure of given design. Designed modular to facilitate revisions and operation on minicomputers. Written in FORTRAN 77.
An AGARD Supplemental Test Program on the growth of short fatigue cracks was conducted to allow testing of various materials and loading conditions that were of interest. Twenty-two participants from ten laboratories in eight countries contributed to the supplemental test program. The objective is to review the supplemental test program and to summarize the results obtained from all laboratories. The materials tested in the supplemental program were: 2024-T3 and 7075-T6 aluminum alloys, 2090-T8E41 aluminum-lithium alloy, Ti6Al4V titanium alloy, and 4340 steel. Tests on single-edge-notch-tension specimens were conducted under several constant-amplitude loading conditions and spectrum loading conditions (FALSTAFF, Inverted FALSTAFF, GAUSSIAN, TWIST, Felix, and the Fokker 100 spectra). The plastic-replica method was used to measure the growth of short cracks at the notch root. The results from the supplemental test program show good agreement among the several laboratories who measured short-crack growth rates on the aluminum-lithium alloy.
This paper explores the application of carbon-powder-impregnated polymeric composites for measuring crack extensions. The strain sensitivity of the gage material is shown to be very small. In the first series of tests, the gage material is characterized by measuring the change in electrical resistance due to machined slits for various gage lengths. The measured responses is compared with the response predicted from a very simple electrical model. On the basis of good correlation and repeatability, the usefulness of such gages to measure crack extensions is assessed by a second series of tests. Further work to improve the gage response by optimizing the shape of the gage and making the gage and the adhesive layer thinner is proposed. The presented concept, with improvements, can result in a reliable, inexpensive crack gage requiring inexpensive instrumentation.
The applicability of the J-integral in elasto-plastic fracture mechanics is limited to isothermal, monotonic loading conditions from the theoretical viewpoint, while in many applications, for instance gas turbine engines, crack growth occurs in the presence of cyclic inelastic loading, thermomechanical loading and temperature gradients. A number of path-independent (P-I) integrals have been proposed which do not have the restrictions of the J-integral. A review indicates that four of these integrals, although they are not the classical conservation integrals, are path-independent under these complex loading conditions. This paper describes a combined analytical and experimental effort to evaluate the ability of these four P-I integrals to correlate the crack growth data of Alloy 718 at elevated temperatures. Results for uniform temperature, 538 C, cases indicate that all these integrals are capable of correlating the crack growth data over a wide range of cyclic plasticity.
The stress intensity factor, K, has been successfully used as a measure of fracture toughness, and stress intensity factor range, Delta K, correlates well with the fatigue crack growth rate. This paper gives a deductive logic to demonstrate rigorously that, in the case of small-scale yielding, K and Delta K are capable of characterizing the elastic-plastic crack-tip field both under a monotonic loading and cyclic fatigue loading. This capability to characterize the entire crack-tip field is the underlying reason for the successful application of K and Delta K to linear fracture mechanics.
The potential application of carbon-powder impregnated polymeric gages to the measurement of crack extensions is investigated by determining whether crack lengths in Al can be inferred from resistance changes sensed by the gages. It is found that the gages can be effectively used for measuring crack extensions with a maximum error of around 12 percent. Thinner gages provide more accurate results, and the sensitivity of the device can be improved by optimizing the shape.
ZIP3D analyses cracks in three-dimensional elastic or elastic/plastic bodies. Program calculates mixed-mode fracture-mechanics parameters in cracked solids. Bodies without cracks analyzed to obtain stresses, strains, and displacement fields. Written in FORTRAN V.
A computer program that generates three-dimensional (3D) finite element models for cracked 3D solids was written. This computer program, gensurf, uses minimal input data to generate 3D finite element models for isotropic solids with elliptic or part-elliptic cracks. These models can be used with a 3D finite element program called surf3d. This report documents this mesh generator. In this manual the capabilities, limitations, and organization of gensurf are described. The procedures used to develop 3D finite element models and the input for and the output of gensurf are explained. Several examples are included to illustrate the use of this program. Several input data files are included with this manual so that the users can edit these files to conform to their crack configuration and use them with gensurf.
A simple technique was developed using conventional finite element analysis to determine stress intensity factors, K1 and K2, for interface cracks under mixed-mode loading. This technique involves the calculation of crack tip stresses using non-singular finite elements. These stresses are then combined and used in a linear regression procedure to calculate K1 and K2. The technique was demonstrated by calculating three different bimaterial combinations. For the normal loading case, the K's were within 2.6 percent of an exact solution. The normalized K's under shear loading were shown to be related to the normalized K's under normal loading. Based on these relations, a simple equation was derived for calculating K1 and K2 for mixed-mode loading from knowledge of the K's under normal loading. The equation was verified by computing the K's for a mixed-mode case with equal and normal shear loading. The correlation between exact and finite element solutions is within 3.7 percent. This study provides a simple procedure to compute K2/K1 ratio which has been used to characterize the stress state at the crack tip for various combinations of materials and loadings. Tests conducted over a range of K2/K1 ratios could be used to fully characterize interface fracture toughness.
Degradation of the material properties of the Al alloy is examined to determine the effects of moist air and predissolved hydrogen on elevated-temperature fatigue and fracture resistance. Experiments are conducted at 175 C in both moist air and high vacuum with as-processed specimens and specimens that are vacuum-heat-treated. Fracture mechanics characterizations are made for initiation and propagation fracture toughnesses during rising load, fatigue-crack propagation kinetics, and sustained-load crack-growth rates. Time-dependent embrittlement at intermediate temperatures is identified in both plate and extrusion samples of the Al-Fe-Si-V alloy 8009. Intermediate temperature cracking is found to be the same for each case in both vacuum and moist air, and the vacuum heat treatment does not significantly affect the results.
The present study proposes a mathematical model utilizing the internal state variable concept for predicting the upper bounds of the reduced axial and shear stiffnesses in cross-ply laminates with matrix cracks. The displacement components at the matrix crack surfaces are explicitly expressed in terms of the observable axial and shear strains and the undamaged material properties. The reduced axial and shear stiffnesses are predicted for glass/epoxy and graphite/epoxy laminates. Comparison of the model with other theoretical and experimental studies is also presented to confirm direct applicability of the model to angle-ply laminates with matrix cracks subjected to general in-plane loading.
The effect of the stress-free edge on the growth of local delaminations initiating from a matrix crack in (O sub 2/90 sub 4) sub s and (+/- 45.90 sub 4) sub s glass epoxy laminates is investigated using 3D finite element analysis. The presence of high interlaminar normal stresses at the intersection (corner) of the matrix crack with the stress-free edge, suggests that a mode I delamination may initiate at the corners. The strain energy release rates (G) were calculated by modeling a uniform through-width delamination and two inclined delaminations at 10.6 deg and 45 deg to the matrix crack. All components of G have high values near the free edges. The mode I component of G is high at small delamination length and becomes zero for a delamination length of one-ply thickness. The total G values near the free edge agreed well with previously derived closed form solution. The quasi-3D solutions agreed well with the 3D interior solutions.
The effect of matrix cracks on the composite delamination and interlaminar stresses is investigated in (+15/90n/-15)s glass-epoxy laminates (with values of n equal to 0, 1, 2, or 3) subjected to monotonically increasing tension loads. Three-dimensional (3D) and quasi-3D (Q3D) finite-element analyses are used to model the free-edge stress states in the laminates with and without a matrix crack, respectively. The Q3D results show that in-plane transverse tensile stresses exist in the +15 deg plies near the free edges of all of the laminates used and that only the interlaminar shear stress is high at the +15/theta interface. The results of 3D analysis indicate that large tensile interlaminar normal as well as shear stresses develop at the intersection of the matrix crack and the free edge. This suggests that the interlaminar normal stress plays a significant role in the failure of these laminates.
A model based on the micromechanical mechanism of crack growth resistance in fiber reinforced ceramics is presented. The formulation of the model is based on a small scale geometry of a macrocrack with a bridging zone, the process zone, which governs the resistance mechanism. The effect of high toughness of the fibers in retardation of the crack advance, and the significance of the fiber pullout mechanism on the crack growth resistance, are reflected in this model. The model allows one to address issues such as influence of fiber spacing, fiber flexibility, and fiber matrix friction. Two approaches were used. One represents the fracture initiation and concentrated on the development of the first microcracks between fibers. An exact closed form solution was obtained for this case. The second case deals with the development of an array of microcracks between fibers forming the bridging zone. An implicit exact solution is formed for this case. In both cases, a discrete fiber distribution is incorporated into the solution.
Simple design for fixture and specimen significantly improves crack-growth fracture testing of ceramics and other brittle materials. Makes it possible to impose crack-mouth-opening displacement that remains at or close to prescribed value even when crack extends. Important secondary advantages: geometry of specimen is simple, making specimen easy to machine; fit between pin and specimen provides self-aligning grip; contact stresses and probability of failure at or near loading spot reduced.