J. C. Newman

An empirical stress-intensity factor equation for the surface crack

Abstract This paper presents an empirical stress-intensity factor equation for a surface cracks as a function of parametric angle, crack depth, crack length, plate thickness and plate width for tension and bending loads. The stress-intensity factors used to develop the equation were obtained from a previous three-dimensional, finite-element analysis of semielliptical surface cracks in finite elastic plates subjected to tension or bending loads. A wide range of configuration parameters was included in the equation. The ratios of crack length to plate thickness and the ratios of crack depth to crack length ranged from 0 to 1.0. The effects of plate width on stress-intensity variations along the crack front were also included. The equation was used to predict patterns of surface-crack growth under tension or bending fatigue loads. The equation was also used to correlate surface-crack fracture data for a brittle epoxy material within ± 10 percent for a wide range of crack shapes and crack sizes.

A Crack-Closure Model for Predicting Fatigue Crack Growth under Aircraft Spectrum Loading

Experiments on metallic materials have shown that fatigue cracks remain closed during part of the load cycle under constant- and variable-amplitude loading. These experiments have shown that crack closure is a significantfactor in causing load-interaction effects (retardation and acceleration) on crack growth rates under variable-amplitude loading. The present paper is concerned with the development and application of an analytical model of cyclic crack growth that includes the effects of crack closure. The model was based on a concept like the Dugdale model, but was modified to leave plastically deformed material in the wake of the advancing crack tip. The model was used to correlate crack growth rates under constant-amplitude loading and to predict crack growth under aircraft spectrum loading on 2219-T851 aluminum alloy plate material. The predicted crack growth lives agreed well with experimental data. The ratio of predicted-to-experimental lives ranged from 0.66 to 1.48. These predictions were made using data from an ASTM Task Group E24.06.01 round-robin analysis.

Stress-Intensity Factors for a Wide Range of Semi-Elliptical Surface Cracks in Finite-Thickness Plates

Abstract Surface cracks are among the more common flaws in aircraft and pressure vessel components. Accurate stress analyses of surface-cracked components are needed for reliable prediction of their crack growth rates and fracture strengths. Several calculations of stress-intensity factors for semi-elliptical surface cracks subjected to tension have appeared in the literature. However, some of these solutions are in disagreement by 50–100%. In this paper stress-intensity factors for shallow and deep semi-elliptical surface cracks in plates subjected to tension are presented. To verify the accuracy of the three-dimensional finite-element models employed, convergence was studied by varying the number of degrees of freedom in the models from 1500 to 6900. The 6900 degrees of freedom used here were more than twice the number used in previously reported solutions. Also, the stress-intensity variations in the boundary-layer region at the intersection of the crack with the free surface were investigated.

A finite-element analysis of fatigue crack closure

Experiments have shown that fatigue cracks close at positive loads during constant-amplitude load cycling. The crack-closure phenomenon is caused by residual plastic deformations remaining in the wake of an advancing crack tip. The present paper is concerned with the application of a two-dimensional, nonlinear, finite-element analysis using an incremental theory of plasticity to predict crack-closure and crack-opening stresses during the crack-growth process under cyclic loading. A two-dimensional finite-element computer program, which accounts for both elastic-plastic material behavior and changing boundary conditions associated with crack extension and intermittent contact of the crack surfaces under cyclic loading, has been developed. An efficient technique to account for changing boundary conditions under cyclic loading was also incorporated into the nonlinear analysis program. This program was used subsequently to study crack extension and crack closure behavior in a center-cracked panel under constant-amplitude and two-level block loading. The calculated crack-opening stresses were found to be quantitatively consistent with experimental measurements.

A review of the CTOA/CTOD fracture criterion

Abstract The crack-tip-opening angle or displacement (CTOA/CTOD) fracture criterion is one of the oldest fracture criteria applied to fracture of metallic materials with cracks. During the past two decades, the use of elastic–plastic finite-element analyses to simulate fracture of laboratory specimens and structural components using the CTOA criterion has expanded rapidly. But the early applications were restricted to two-dimensional analyses, assuming either plane-stress or plane-strain behavior, which lead to generally non-constant values of CTOA, especially in the early stages of crack extension. Later, the non-constant CTOA values were traced to inappropriate state-of-stress (or constraint) assumptions in the crack-front region and severe crack tunneling in thin-sheet materials. More recently, the CTOA fracture criterion has been used with three-dimensional analyses to study constraint effects, crack tunneling, and the fracture process. The constant CTOA criterion (from crack initiation to failure) has been successfully applied to numerous structural applications, such as aircraft fuselages and pipelines. But why does the “constant CTOA” fracture criterion work so well? This paper reviews the results from several studies, discusses the issues of why CTOA works, and discusses its limitations.

FINITE ELEMENT ANALYSIS OF PLASTICITY-INDUCED FATIGUE CRACK CLOSURE: AN OVERVIEW

Abstract Finite element analysis is perhaps the most commonly used numerical method to model plasticity-induced fatigue crack closure. The state-of-the-art is reviewed and a comprehensive overview is presented, summarizing issues which must be considered and emphasizing potential difficulties. These include mesh refinement level, crack advancement schemes, crack shape evolution, geometry effects, and crack opening value assessment techniques.

The Merging of Fatigue and Fracture Mechanics Concepts: A Historical Perspective

Abstract In this review, some of the technical developments that have occurred during the past 40 years are presented which have led to the merger of fatigue and fracture mechanics concepts. This review is made from the viewpoint of “crack propagation”. As methods to observe the “fatigue” process have improved, the formation of fatigue micro-cracks have been observed earlier in life and the measured crack sizes have become smaller. These observations suggest that fatigue damage can now be characterized by “crack size”. In parallel, the crack-growth analysis methods, using stress-intensity factors, have also improved. But the effects of material inhomogeneities, crack-fracture mechanisms, and nonlinear behavior must now be included in these analyses. The discovery of crack-closure mechanisms, such as plasticity, roughness, and oxide/corrosion/fretting product debris, and the use of the effective stress-intensity factor range, has provided an engineering tool to predict small- and large-crack-growth rate behavior under service loading conditions. These mechanisms have also provided a rationale for developing new, damage-tolerant materials. This review suggests that small-crack growth behavior should be viewed as typical behavior, whereas large-crack threshold behavior should be viewed as the anomaly. Small-crack theory has unified “fatigue” and “fracture mechanics” concepts; and has bridged the gap between safe-life and durability/damage-tolerance design concepts.

Development and Application of a Crack Tip Opening Displacement-Based Mixed Mode Fracture Criterion

Abstract Consistent with experimental observations, a crack tip opening displacement (CTOD)-based, mixed mode fracture criterion is developed for predicting the onset and direction of crack growth. The criterion postulates that crack growth occurs in either Mode I or Mode II direction, depending upon whether the maximum in either the opening or the shear component of CTOD, measured at a specified distance behind the crack tip, attains a critical value. The proposed CTOD-based fracture criterion is implemented in two finite element codes to predict the stable tearing behavior of (a) a modified Arcan test specimen made of AL 2024-T3 and (b) a double cantilever beam (DCB) specimen made of AL 7050. Using the measured load-crack extension data as input, results from simulations of stable crack growth along experimentally measured crack paths for the Arcan specimen demonstrate that the CTOD values obtained in the simulations are in excellent agreement with the proposed criterion. Then, using the CTOD criterion as input, simulations of the Arcan and DCB specimens demonstrate that the CTOD fracture criterion successfully predicts (a) load-crack path data for both specimens, (b) load-crack extension behavior for the Arcan specimen and (c) load-load point displacement data for the DCB specimen.

Finite element modeling of plasticity-induced crack closure with emphasis on geometry and mesh refinement effects

Abstract Two-dimensional, elastic–perfectly plastic finite element analyses of middle-crack tension (MT) and compact tension (CT) geometries were conducted to study fatigue crack closure and to calculate the crack-opening values under plane-strain and plane-stress conditions. The behaviors of the CT and MT geometries were compared. The loading was selected to give the same maximum stress intensity factor in both geometries, and thus approximately similar initial forward plastic zone sizes. Mesh refinement studies were performed on both geometries with various element types. For the CT geometry, negligible crack-opening loads under plane-strain conditions were observed. In contrast, for the MT specimen, the plane-strain crack-opening stresses were found to be significantly larger. This difference was shown to be a consequence of in-plane constraint. Under plane-stress conditions, it was found that the in-plane constraint has negligible effect, such that the opening values are approximately the same for both the CT and MT specimens.

Three-dimensional elastic-plastic finite-element analyses of constraint variations in cracked bodies

Abstract Three-dimensional elastic-plastic (small-strain) finite-element analyses were used to study the stresses, deformations, and constraint variations around a straight-through crack in finite-thickness plates for an elastic-perfectly plastic material under monotonie and cyclic loading. Middle-crack tension specimens were analyzed for thicknesses ranging from 1.25 to 20 mm with various crack lengths. Three local constraint parameters, related to the normal, tangential, and hydrostatic stresses, showed similar variations along the crack front for a given thickness and applied stress level. Numerical analyses indicated that cyclic stress history and crack growth reduced the local constraint parameters in the interior of a plate, especially at high applied stress levels. A global constraint factor α g was defined to simulate three-dimensional effects in two-dimensional crack analyses. The global constraint factor was calculated as an average through-the-thickness value over the crack-front plastic region. Values of α g were found to be nearly independent of crack length and were related to the stress-intensity factor for a given thickness. Using the global constraint factors, crack-tip-opening displacements calculated from a modified Dugdale model compared well with the finite-element results from small- to large-scale yielding conditions for both thin and thick bodies. An application of the global constraint factor concept to model fatigue-crack growth under aircraft spectrum loading is presented.