Fracture mechanics - The search for safety in numbers.
Safety design for high strength low toughness materials assumed to have hidden flaws, formulating stress intensity factor for fracture mechanics
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Fracture angle and strain-energy-density-factor of a crack at hole at an arbitrary angle
For both the maximum stress criterion and strain-energy-density-factor (S) theory, fracture angle (the initial angle of crack growth) is predicted by using opening and sliding mode stress intensity factors. These theoretical predictions are consistent with experimental fracture angles. For the S theory, the crack spreads in the direction of the negative fracture angle in a plane for which S is a minimum. This quantity was obtained analytically. The experimental data of the critical S on plexiglass fracture specimens remains essentially constant.
Hsu, Y. C.↗
Stress-free end problem in layered materials
In this paper the plane elastostatic problem for a medium which consists of periodically arranged two sets of bonded dissimilar layers or strips is considered. First it is assumed that one set of strips contains a crack which crosses the bimaterial interfaces. Then, by letting the collinear cracks join, the stress-free end problem is formulated. The singular behavior of the solutions at the point on intersection of the stress-free boundary and the interfaces is examined and appropriate stress intensity factors are defined. The results of some numerical examples are then presented which include the cases of both plane stress and plane strain.
Erdogan, F.↗
MSFC crack growth analysis computer program, version 2 (users manual)
An updated version of the George C. Marshall Space Flight Center Crack Growth Analysis Program is described. The updated computer program has significantly expanded capabilities over the original one. This increased capability includes an extensive expansion of the library of stress intensity factors, plotting capability, increased design iteration capability, and the capability of performing proof test logic analysis. The technical approaches used within the computer program are presented, and the input and output formats and options are described. Details of the stress intensity equations, example data, and example problems are presented.
Creager, M.↗
Fracture of composite panels
The fracture problem in panels consisting of periodically arranged load carrying and buffer strips of different materials is considered. The main emphasis is placed on the problem of a crack terminating at and crossing the interfaces and on the stress free end problem. The problem is formulated in terms of a system of singular integral equations, and numerical solutions are obtained for certain material combinations. With the study of possible crack propagation and delamination in mind, certain stress intensity factors are defined and calculated. A main result is that when the crack touches or intersects a bimaterial interface, the stress state has no longer the standard square root singularity, and, to study further propagation of the crack, the conventional fracture models need to be modified, or new models need to be developed.
Erdogan, F.↗
Elastic-Plastic Fracture Mechanics Analysis of Critical Flaw Size in ARES I-X Flange-to-Skin Welds
NASA's Ares 1 Upper Stage Simulator (USS) is being fabricated from welded A516 steel. In order to insure the structural integrity of these welds it is of interest to calculate the critical initial flaw size (CIFS) to establish rational inspection requirements. The CIFS is in turn dependent on the critical final flaw size (CFS), as well as fatigue flaw growth resulting from transportation, handling and service-induced loading. These calculations were made using linear elastic fracture mechanics (LEFM), which are thought to be conservative because they are based on a lower bound, so called elastic, fracture toughness determined from tests that displayed significant plasticity. Nevertheless, there was still concern that the yield magnitude stresses generated in the flange-to-skin weld by the combination of axial stresses due to axial forces, fit-up stresses, and weld residual stresses, could give rise to significant flaw-tip plasticity, which might render the LEFM results to be non-conservative. The objective of the present study was to employ Elastic Plastic Fracture Mechanics (EPFM) to determine CFS values, and then compare these values to CFS values evaluated using LEFM. CFS values were calculated for twelve cases involving surface and embedded flaws, EPFM analyses with and without plastic shakedown of the stresses, LEFM analyses, and various welding residual stress distributions. For the cases examined, the computed CFS values based on elastic analyses were the smallest in all instances where the failures were predicted to be controlled by the fracture toughness. However, in certain cases, the CFS values predicted by the elastic-plastic analyses were smaller than those predicted by the elastic analyses; in these cases the failure criteria were determined by a breakdown in stress intensity factor validity limits for deep flaws (a greater than 0.90t), rather than by the fracture toughness. Plastic relaxation of stresses accompanying shakedown always increases the calculated CFS values compared to the CFS values determined without shakedown. Thus, it is conservative to ignore shakedown effects.
Chell, G. Graham↗
Use of three-dimensional photoelasticity in fracture mechanics
The philosophy of fracture mechanics is reviewed and utilized to formulate a simplified approach to the determination of the stress-intensity factor photoelastically for three-dimensional problems. The method involves a Taylor Series correction for the maximum in-plane shear stress (TSCM) and does not involve stress separation. The results are illustrated by applying the TSCM to surface flaws in bending fields. Other three-dimensional problems solved by the TSCM are cited.
Smith, C. W.↗
A survey of strength analysis methods for laminates with holes
The methods for predicting the strength of composite laminates with fastener holes are reviewed for the cases of unloaded as well as loaded holes. Three categories of methods are discussed: (1) the hole-boundary stress (HBS) methods which compare the peak stresses and the laminate strength; (2) the linear elastic fracture (LEFM) methods which assume cracks emanating from the hole and predict failure when the stress intensity factor for a crack equals the laminate fracture toughness; and (3) two different two-parameter (TP) methods: the average-stress (ASTP) method, which predicts failure when the average stress over a distance from the hole equals the laminate strength; and the point-stress (PSTP) Whitney-Nuismer (1974) approach, which predicts failure when the stress near the hole equals the material strength. The PSTP is relatively accurate and is by far the most widely used of all the prediction methods. However, for large ranges of variables and cases, the current strength predictions may not always be accurate.
Crews, J. H., Jr.↗
The elasticity problem for a thick-walled cylinder containing a circumferential crack
The elasticity problem for a long hollow circular cylinder containing an axisymmetric circumferential crack subjected to general nonaxisymmetric external loads is considered. The problem is formulated in terms of a system of singular integral equations with the Fourier coefficients of the derivative of the crack surface displacement as density functions. The stress intensity factors and the crack opening displacement are calculated for a cylinder under uniform tension, bending by end couples, and self-equilibrating residual stresses.
Nied, H. F.↗
The elasticity problem for a thick-walled cylinder containing a circumferential crack
The elasticity problem for a long hollow circular cylinder containing an axisymmetric circumferential crack subjected to general nonaxisymmetric external loads is considered. The problem is formulated in terms of a system of singular integral equations with the Fourier coefficients of the derivative of the crack surface displacement as density functions. The stress intensity factors and the crack opening displacement are calculated for a cylinder under uniform tension, bending by end couples, and self-equilibrating residual stresses.
Nied, H. F.↗
Simulated Service and Stress Corrosion Cracking Testing for Friction Stir Welded Spun Form Domes
Damage tolerance testing development was required to help qualify a new spin forming dome fabrication process for the Ares 1 program at Marshall Space Flight Center (MSFC). One challenge of the testing was due to the compound curvature of the dome. The testing was developed on a sub-scale dome with a diameter of approximately 40 inches. The simulated service testing performed was based on the EQTP1102 Rev L 2195 Aluminum Lot Acceptance Simulated Service Test and Analysis Procedure generated by Lockheed Martin for the Space Shuttle External Fuel Tank. This testing is performed on a specimen with an induced flaw of elliptical shape generated by Electrical Discharge Machining (EDM) and subsequent fatigue cycling for crack propagation to a predetermined length and depth. The specimen is then loaded in tension at a constant rate of displacement at room temperature until fracture occurs while recording load and strain. An identical specimen with a similar flaw is then proof tested at room temperature to imminent failure based on the critical offset strain achieved by the previous fracture test. If the specimen survives the proof, it is then subjected to cryogenic cycling with loads that are a percentage of the proof load performed at room temperature. If all cryogenic cycles are successful, the specimen is loaded in tension to failure at the end of the test. This standard was generated for flat plate, so a method of translating this to a specimen of compound curvature was required. This was accomplished by fabricating a fixture that maintained the curvature of the specimen rigidly with the exception of approximately one-half inch in the center of the specimen containing the induced flaw. This in conjunction with placing the center of the specimen in the center of the load train allowed for successful testing with a minimal amount of bending introduced into the system. Stress corrosion cracking (SCC) tests were performed using the typical double beam assembly and with 4-point loaded specimens under alternate immersion conditions in a 3.5% NaCl environment for 90 days. In addition, experiments were conducted to determine the threshold stress intensity factor for SCC (K1SCC) of Al-Li 2195 which to our knowledge has not been determined previously. The successful simulated service and stress corrosion testing helped to provide confidence to continue to Ares 1 scale dome fabrication.
Stewart, Thomas J.↗
Stress intensity and crack displacement for small edge cracks
The weight function method was used to derive stress intensity factors and crack mouth displacement coefficients for small edge cracks (less than 20 percent of the specimen width) in common fracture specimen configurations. Contact stresses due to point application of loads were found to be small but significant for three-point bending and insignificant for four-point bending. The results are compared with available equations and numerical solutions from the literature and with unpublished boundary collocation results.
Orange, Thomas W.↗
Slow Crack Growth Analysis of Brittle Materials with Finite Thickness Subjected to Constant Stress-Rate Flexural Loading
A two-dimensional, numerical analysis of slow crack growth (SCG) was performed for brittle materials with finite thickness subjected to constant stress-rate ("dynamic fatigue") loading in flexure. The numerical solution showed that the conventional, simple, one-dimensional analytical solution can be used with a maximum error of about 5% in determining the SCG parameters of a brittle material with the conditions of a normalized thickness (a ratio of specimen thickness to initial crack size) T > 3.3 and of a SCG parameter n > 10. The change in crack shape from semicircular to elliptical configurations was significant particularly at both low stress rate and low T, attributed to predominant difference in stress intensity factor along the crack front. The numerical solution of SCG parameters was supported within the experimental range by the data obtained from constant stress-rate flexural testing for soda-lime glass microslides at ambient temperature.
Chio, S. R.↗
Fatigue life and crack growth prediction methodology
The capabilities of a plasticity-induced crack-closure model and life-prediction code to predict fatigue crack growth and fatigue lives of metallic materials are reviewed. Crack-tip constraint factors, to account for three-dimensional effects, were selected to correlate large-crack growth rate data as a function of the effective-stress-intensity factor range (delta(K(sub eff))) under constant-amplitude loading. Some modifications to the delta(K(sub eff))-rate relations were needed in the near threshold regime to fit small-crack growth rate behavior and endurance limits. The model was then used to calculate small- and large-crack growth rates, and in some cases total fatigue lives, for several aluminum and titanium alloys under constant-amplitude, variable-amplitude, and spectrum loading. Fatigue lives were calculated using the crack growth relations and microstructural features like those that initiated cracks. Results from the tests and analyses agreed well.
Newman, J. C., Jr.↗
Fatigue life and crack growth prediction methodology
This paper reviews the capabilities of a plasticity-induced crack-closure model and life-prediction code to predict fatigue crack growth and fatigue lives of metallic materials. Crack-tip constraint factors, to account for three-dimensional effects, were selected to correlate large-crack growth rate data as a function of the effective stress-intensity factor range (Delta K(sub eff)) under constant amplitude loading. Some modifications to the Delta K(sub eff)-rate relations were needed in the near threshold regime to fit small-crackgrowth rate behavior and endurance limits. The model was then used to calculate small- and large-crack growth rates, and in some cases total fatigue lives, for several aluminum and titanium alloys under constant-amplitude, variable-amplitude, and spectrum loading. Fatigue lives were calculated using the crack-growth relations and microstructural features like those that initiated cracks. Results from the tests and analyses agreed well.
Newman, J. C., Jr.↗
Fatigue Analyses Under Constant- and Variable-Amplitude Loading Using Small-Crack Theory
Studies on the growth of small cracks have led to the observation that fatigue life of many engineering materials is primarily "crack growth" from micro-structural features, such as inclusion particles, voids, slip-bands or from manufacturing defects. This paper reviews the capabilities of a plasticity-induced crack-closure model to predict fatigue lives of metallic materials using "small-crack theory" under various loading conditions. Constraint factors, to account for three-dimensional effects, were selected to correlate large-crack growth rate data as a function of the effective stress-intensity factor range (delta-Keff) under constant-amplitude loading. Modifications to the delta-Keff-rate relations in the near-threshold regime were needed to fit measured small-crack growth rate behavior. The model was then used to calculate small-and large-crack growth rates, and to predict total fatigue lives, for notched and un-notched specimens under constant-amplitude and spectrum loading. Fatigue lives were predicted using crack-growth relations and micro-structural features like those that initiated cracks in the fatigue specimens for most of the materials analyzed. Results from the tests and analyses agreed well.
Newman, J. C., Jr.↗
Analyses of Fatigue and Fatigue-Crack Growth under Constant- and Variable-Amplitude Loading
Studies on the growth of small cracks have led to the observation that fatigue life of many engineering materials is primarily crack growth from micro-structural features, such as inclusion particles, voids, slip-bands or from manufacturing defects. This paper reviews the capabilities of a plasticity-induced crack-closure model to predict fatigue lives of metallic materials using small-crack theory under various loading conditions. Constraint factors, to account for three-dimensional effects, were selected to correlate large-crack growth rate data as a function of the effective stress-intensity factor range (delta K(sub eff)) under constant-amplitude loading. Modifications to the delta K(sub eff)-rate relations in the near-threshold regime were needed to fit measured small-crack growth rate behavior. The model was then used to calculate small- and large-crack growth rates, and to predict total fatigue lives, for notched and un-notched specimens under constant-amplitude and spectrum loading. Fatigue lives were predicted using crack-growth relations and micro-structural features like those that initiated cracks in the fatigue specimens for most of the materials analyzed. Results from the tests and analyses agreed well.
Newman, J. C., Jr.↗
Limitations to the small scale yielding approximation for crack tip plasticity
Recent finite-element results by S. G. Larsson and A. J. Carlsson suggest a limited range of validity to the 'small scale yielding approximation,' whereby small crack tip plastic zones are correlated in terms of the elastic stress intensity factor. It is shown with the help of a model for plane strain yielding that their results may be explained by considering the non-singular stress, acting parallel to the crack at its tip, which accompanies the inverse square-root elastic singularity. Further implications of the non-singular stress term for crack tip deformations and fracturing are examined. It is suggested that its effect on crack tip parameters, such as the opening displacement and J-integral, is less pronounced than its effect on the yield zone size.
Rice, J. R.↗