S.R. Daniewicz

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.

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.

Simulation of plasticity-induced fatigue crack closure in part-through cracked geometries using finite element analysis

Abstract The part-through semi-elliptical surface flaw is commonly encountered in engineering practice. Proper characterization of plasticity-induced crack closure is necessary to predict both flaw growth and flaw shape evolution under cyclic loading. Three-dimensional elastic–plastic finite element analyses are used to model the plasticity-induced closure developed along the surface flaw crack front, and the subsequent crack opening behavior under constant amplitude loading. Resulting crack opening stresses are compared with results from a strip-yield model and with experimentally measured values reported in the literature. It was found that the computed values were larger than those measured.

A new methodology for computing crack opening values from finite element analyses

Abstract Finite element analyses are frequently used to model growing fatigue cracks and the associated plasticity-induced crack closure. A new methodology is presented to calculate crack opening values in planar geometries using the crack surface nodal force distribution under minimum loading as determined from finite element analyses. The calculated crack opening values are compared with values obtained using finite element analysis and more conventional crack opening assessment methodologies, which focus on a single node near the crack tip. The new method eliminates the need to arbitrarily select a single node when defining the opening load or stress.

Analysis of crack tip plasticity for microstructurally small cracks using crystal plasticity theory

Crack tip plastic zone sizes and crack tip opening displacements (CTOD) for stationary microstructurally small cracks are calculated using the finite element method. To simulate the plastic deformation occurring at the crack tip, a two-dimensional small strain constitutive relationship from single crystal plasticity theory is implemented in the finite element code ANSYS as a user-defined plasticity subroutine. Small cracks are modeled in both single grains and multiple grains, and different crystallographic conditions are considered. The computed plastic zone sizes and CTOD are compared with those found using conventional isotropic plasticity theory, and significant differences are observed.

Three Dimensional Finite Element Analysis of a Split-Sleeve Cold Expansion Process

A cold expansion process is used to prolong the fatigue life of a structure under cyclic loadings. The process produces a beneficial compressive residual stress zone in the hole vicinity, which retards the initiation and propagation of the crack at the hole edge. In this study, a three-dimensional finite element model of the split-sleeve cold expansion process was developed to predict the resulting residual stress field. A thin rectangular aluminum sheet with a centrally located hole was considered. A rigid mandrel and an elastic steel split sleeve were explicitly modeled with the appropriate contact elements at the interfaces between the mandrel, the sleeve, and the hole. Geometrical and material nonlinearities were included. The simulation results were compared with experimental measurements of the residual stress. The influence of friction and the prescribed boundary conditions for the sheet were studied. Differences between the split-sleeve- and the non-split-sleeve model solutions are discussed.

Finite element modeling of microstructurally small cracks using single crystal plasticity

Abstract Finite element simulations of small fatigue cracks were performed using crystal plasticity theory to describe the deformation behavior near the crack tip. A rate-independent small strain formulation from crystal plasticity theory was implemented. Constant amplitude loads were applied, with a load ratio of R =0.3. Crack opening stresses and crack tip opening displacement ranges were simulated as the crack grew in a single grain, as well as when the crack grew toward a grain boundary. Crack growth in single grains indicated that stabilization of the crack opening stresses occurs relatively rapidly (5–10 μm of crack growth). Studies of crack growth toward a grain boundary revealed that, depending on the orientation of the adjacent grain, the crack growth rate is significantly affected. If the angle of misorientation between the two adjacent grains is small, the neighboring grain can increase the growth rate near the grain boundary. If the misorientation angle is high, the fatigue crack growth rate will be significantly slowed near the grain boundary.

Strip-yield and finite element analysis of part-through surface flaws

Abstract A slice synthesis methodology is developed and used to construct a weight function based strip-yield model for a semi-elliptical part-through surface flaw in an elastic–perfectly plastic body under monotonic loading. The model enables rapid approximate computation of the crack surface displacements and the crack front plastic zone size in the crack plane. A detailed mathematical description of the model is presented. Crack surface displacements from the model are shown to compare well with results from detailed three-dimensional elastic–plastic finite element analyses. From the finite element analyses, the crack plane plastic zone is shown to give an unrealistic perspective of overall crack front plasticity.

An assessment of geometry effects on plane stress fatigue crack closure using a modified strip-yield model

Using a modified strip-yield model, plane stress constant-amplitude fatigue crack growth simulations under conditions of small-scale yielding were performed for the edge-cracked strip in tension, the edge-cracked strip in bending, and the compact tension specimen with load ratios R = 0.5, 0.0, −1.0and−2.0. From these simulations, fatigue crack opening loads were predicted as a function of crack length. Geometry, loading type and crack length were observed to affect crack opening loads. The geometry-loading dependence was particularly evident for extended fatigue crack growth. Geometry-loading dependence was observed to increase for R < 0. Reductions in the crack opening loads following extended crack growth were also observed. These reductions were demonstrated to occur in the absence of large-scale plasticity in the remaining ligament. A normalized maximum applied stress intensity factor Kmax/σo√W, where σo and W represent the flow stress and specimen width respectively, was demonstrated to represent an approximate measure of small-scale yielding crack closure response similitude under plane stress conditions with R ⩾ 0. When crack opening loads were correlated in terms of this parameter, little geometry-loading dependence was observed.

Elastic-Plastic Stress Analysis of Cold-Worked Pin-Loaded Holes

A detailed two-dimensional, elastic-plastic finite element analysis of a pin-loaded hole was conducted. A thin rectangular aluminum alloy sheet (7075-T6) with a circular hole was considered under plane stress conditions. The hole was loaded purely by a rigid pin to different load magnitudes. Appropriate contact elements were used at the pin-hole interface to transfer the traction loads from one surface to another. Material nonlinearities for the sheet and friction were included in the analyses. Radial and hoop stress solutions along the pin-hole interface were compared in elastically and plastically loaded holes. The influence of friction on the stress results was studied. The locations and magnitudes of the peak hoop stresses were determined. Lastly, an initial residual field was introduced around the hole by a cold expansion simulation before a subsequent pin-loading analysis. Because the cold expansion process involves some reverse yielding, both isotropic and kinematic material hardening models were considered.