Assessment of small fatigue crack growth driving forces in single crystals with and without slip bands

Strain localization under low amplitude cyclic loading is a manifestation of plastic irreversible deformation associated with early crack growth. However, traditional constitutive models cannot usually reproduce strain localization in smooth single crystals, which can affect crack growth predictions for crystallographic fatigue cracks. This work analyzes the influence of bands of localized plastic shear strain on the cyclic crack tip displacement and on a fatigue indicator parameter by making special provision of a crack along the interface of a deformation band. Furthermore, the quality of local and volume-averaged fatigue indicator parameters are assessed using finite element models of a Cu single crystal cycled to induce plastic deformation under multiple loading conditions.     

A model of brittle fracture propagation part I—continuum aspects

The micromechanism of crack propagation in steel is described and analyzed in continuum terms and related to the macroscopic fracture behavior. It is proposed that propagation of cleavage microcracks through favorably oriented grains ahead of the main crack tip is the principal weakening mode in brittle fracture. This easy cleavage process proceeds in the Griffith manner and follows a continuous, multiply connected, nearly planar path with a very irregular front which spreads both forward and laterally and leaves behind disconnected links which span the prospective fracture surface. A discrete crack zone which extends over many grains thus exists at the tip of a running brittle crack. Final separation of the links is preceeded by plastic straining within the crack zone and occurs gradually with the increasing crack opening displacement. It is suggested that in low stress fracture, straining of the links is the only deformation mode. However, it is recognized that under certain conditions plastic enclaves may adjoin the crack zone. This deformation mode is associated with high stress fracture, energy transition and eventually with crack arrest.

Energy dissipation resulting from the two deformation mechanisms is related to crack velocity, applied load and temperature and the crack velocity in a given material is expressed as a function of the external conditions. Fracture initiation and crack arrest are then discussed in terms of the conditions which are necessary to maintain the propagation process. Finally, the dimensions of a small scale crack tip zone for a steady state, plane strain crack are evaluated as functions of material properties and the elastic stress intensity factor.

The microstructural aspects of brittle fracture will be discussed in a separate Part 2 [1].     

Fatigue crack growth in TRIP steel under positive R-ratios

Load-controlled fatigue tests are conducted for four positive R values on a low-alloy TRIP steel for two different heat treatments: an optimal treatment leading to a multiphase microstructure containing retained austenite, ferrite, bainite and martensite, and a non-optimal treatment leading to a ferritic–martensitic dual-phase microstructure. A significantly increased resistance to fatigue crack growth is found for the optimal case with respect to the non-optimal case. The amount of crack closure is found to be larger in case of the non-optimally treated (ferritic–martensitic) steel. Close to the crack tip, an increased hardness suggests martensite formation. An EBSD technique is used to quantify the volume of retained austenite ahead of the crack tip, within the plastic zone. It is found that martensite formation only occurs within the monotonic plastic zone during fatigue. By evaluation of the retained austenite fraction during straining in static tensile tests, the plastic strain levels within the plastic zone are assessed. Additionally, the effect of martensite formation on fracture toughness is estimated.     

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.     

Dislocation Behaviour near the Crack Tip in Bulk Fe-3% Si Single Crystal

An investigation has been made of the disloca-tion distribution and dislocation free zone near thecrack tip in bulk Fe-3% Si single crystal duringdeformation in SEM.It has been found that anumber of dislocations were emitted from the cracktip during deformation.After that,the dislocationsmoved rapidly away from the crack tip,which indi-cated that they were strongly repelled by the stressfield at the crack tip.Between the crack tip and theplastic zone there is a region of dislocation-free,which is referred to as dislocation-free zone (DFZ).The length of DFZs is roughly estimated 100μm which is much longer than that found in thinfoil specimen.The variation of dislocation densityas a function of the distance from the crack tip wasmeasured,which showed that the dislocations areinversely piled up in the plastic zone.The length ofDFZs increased with both the length of pre-crackand the amplitude of applied stress.     

THE EFFECT OF INTERMEDIATE HEAT TREATMENTS ON OVERLOAD INDUCED RETARDATIONS DURING FATIGUE CRACK GROWTH IN AN Al-ALLOY

Abstract— Crack growth fatigue tests were carried out on 2024-T3 specimens. Constant-amplitude loading was periodically interrupted by 10 overload cycles. Intermediate heat treatments (T4) were applied to remove the residual stress in the crack tip zone and the crack closure wake behind the crack tip. Retardation effects induced by crack closure due to the previous load history were fully erased by the heat treatments. Overload effects were easily introduced again by new overload cycles afterwards. Crack growth rate results and fractographic observations indicate that primary crack tip plastic deformation (in virgin material) is more effective for crack extension than secondary plastic deformation in an existing plastic zone. This conclusion is significant for cycle-by-cycle crack growth prediction models for variable-amplitude loading.     

Fatigue crack growth retardation inconel 600

The effect of single-cycle overloads on the subsequent fatigue crack growth behavior of Inconel 600 is studied. Overloads ranging from 10 to 50% are applied to a sample undergoing baseline fatigue crack growth at constant Δ$\text{K}$. In all cases, the crack growth rate increases slightly immediately after the overload and then decreases rapidly to a minimum value before later returning to the pre-overload value. The plastic zone size, affected crack length and the crack growth increment at minimum crack growth rate, $\text{a}\text{?}$, are measured for each overload.The affected crack length is considerably larger than the overload plastic zone size for overloads greater than 20%. Consequently, although the minimum crack growth rate occurs within the plane stress overload plastic zone, the effect of the overload extends well beyond the overload region.Within the overload plastic zone, contact occurs between the crack faces due to the excessive deformation produced during the overload cycle. The size of the contact region agrees very well with the overload plastic zone size. Beyond the overload region, Δ$\text{K}{}_{\mathrm{eff}}$ remains less than the applied Δ$\text{K}$ for some time due to the wedge action of the plastically deformed overload region, delaying recovery of the pre-overload crack growth rate. The crack growth rate recovers only after the crack grows out of the region of influence of the wedge.     

Microscale characterization of granular deformation near a crack tip

This paper presents a study of microscale plastic deformation at the crack tip and the effect of microstructure feature on the local deformation of aluminum specimen during fracture test. Three-point bending test of aluminum specimen was conducted inside a scanning electron microscopy (SEM) imaging system. The crack tip deformation was measured in situ utilizing SEM imaging capabilities and the digital image correlation (DIC) full-field deformation measurement technique. The microstructure feature at the crack tip was examined to understand its effect on the local deformation fields. Microscale pattern that was suitable for the DIC technique was generated on the specimen surface using sputter coating through a copper mesh before the fracture test. A series of SEM images of the specimen surface were acquired using in situ backscattered electronic imaging (BEI) mode during the test. The DIC technique was then applied to these SEM images to calculate the full-field deformation around the crack tip. The grain orientation map at the same location was obtained from electron backscattered diffraction (EBSD), which was superimposed on a DIC strain map to study the relationship between the microstructure feature and the evolution of plastic deformation at the crack tip. This approach enables to track the initiation and evolution of plastic deformation in grains adjacent to the crack tip. Furthermore, bifurcation of the crack due to intragranular and intergranular crack growth was observed. There was also localization of strain along a grain boundary ahead of and parallel to the crack after the maximum load was reached, which was a characteristic of Dugdale–Barenblatt strip-yield zone. Thus, it appears that there is a mixture of effects in the fracture process zone at the crack tip where the weaker aspects of the grain boundary controls the growth of the crack and the more ductile aspects of the grains themselves dissipate the energy and the corresponding strain level available for these processes through plastic work.     

The primary macrofragmentation of shear in compressed aluminum single crystals

We have experimentally studied the pattern of a deformation relief formed on the side faces of an aluminum single crystal in the initial stages of plastic straining. The single crystal sample exhibits the formation of macroscopic fragments differing by organization of the shear process. The main factors determining the character of this macrofragmentation are considered.     

Plastic deformation in a thick transversely isotropic layer containing a penny-shaped crack

Summary The width of a thin plastic annular zone formed during the deformation of a pennyshaped crack in a transversely isotropic layer of an ideal elasto-plastic material is determined. Considered are the cases where the penny-shaped crack is extended by normal stresses and by torsional stresses. The faces of the layer are shear free and deformation of the plastic zone around the penny-shaped crack occurs according to the Dugdale hypothesis. For each case, the solution of the problem is reduced to a Fredholm integral equation of the second kind. Iterative solutions are obtained for small values of the parameters and numerical results for the width of the plastic zone are determined. Graphical results showing the effect of transverse isotropy upon the width of the plastic zone are also presented.With 6 Figures     

Influence of deformation anisotropy on the size of the plastic zone at the tip of an opening mode crack

The form and dimensions of the plastic zone at the tip of an opening mode crack in a plate made of a material with deformation anisotropy were investigated within the limits of the elastic solution. The anisotropy was caused by strengthening during plastic deformation until formation of cracks by loading in a straight trajectory located in the plane of the plate. It was shown that in the case of anisotropy caused by loading in a trajectory which is oriented on a normal to the crack edges the size of the plastic zone decreases and its boundaries are rotated in the direction opposite to the crack growth. Loading in a trajectory in the direction of crack growth leads to broadening of the plastic zone in the transverse direction.Translated from Problemy Prochnosti, No. 1, pp. 73–76, January, 1990.     

Determination of the energy for crack creation using micro-hardness measures

The growth of crack is related to the existence of a plastic zone at the crack tip; whose formation and growth is accompanied by energy dissipation. The estimation of this energy is generally done by the so called global methods (hysterisis loops) or the micro-gages. In the present study, the micro-hardness measures in the plastic zone are used to evaluate the energy dissipated in the fracture process zone by plastic deformation. The obtained results on the aluminium alloy 7075 T7 and E460 steel are compared to those obtained by other methods.     

Fatigue damage in nickel and copper single crystals at nanoscale

Nanoscale fatigue damage simulations using molecular dynamics were performed in nickel and copper single crystals. Cyclic stress–strain curves and fatigue crack growth were investigated using a middle-tension (MT) specimen with the lateral sides allowing periodic boundary conditions to simulate a small region of material as a part of a larger component. The specimen dimensions were in the range of nanometers, and the fatigue loading was strain controlled under constant and variable amplitude. Four crystal orientations, [111], [100], [110] and [101] were analyzed, and the results indicated that the plastic deformation and fatigue crack growth rates vary widely from one orientation to another. Under increasing strain amplitude loading, nickel nanocrystals experienced a large amount of plastic deformation causing at least in one orientation, [101], out-of-plane crack deviation in a mixed mode I+ II growth. Under constant amplitude loading, the fatigue cracks were a planar mode I type. Double slip is observed for some orientations, while for others, many more slip systems were activated causing a more evenly distributed plastic region around the crack tip. A comparative analysis revealed that small cracks grow more rapidly in copper than in nickel single crystals.     

Effects of a single tensile overload on fatigue crack growth in a 316L steel

The aim of this study was to investigate the effects of a single tensile overload on subsequent fatigue crack growth in a 316L stainless steel. Fatigue tests were conducted under the plane stress condition, and further supplemented with compliance measurements and field emission scanning electron microscopy (FESEM) observations. Effects of a tensile overload, e.g. initial acceleration and subsequent retardation of fatigue crack growth, were explained and quantified by FESEM and compliance measurements. The FESEM observations suggest that the initial crack growth acceleration stems from void and quasi-cleavage fracture within the fatigue damage zone in the vicinity of the crack tip. Systematic compliance measurements taken during fatigue crack growth suggest that the overall crack growth retardation is related to strain hardening and residual compressive stress produced by the plastic deformation associated with the tensile overload.     

Determining the fracture toughness of metals and alloys under conditions of similarity of local failure

Conclusions The proposed criteria of similarity of local failure make it possible to compare under similar conditions the behavior of metals and alloys at the moment of occurrence of plastic instability at the apex of a crack (defect). It was established that the critical size of the zone of plastic deformation at a defect (crack) with the exceeding of which under the given loading conditions plastic instability occurs is determined by the ratio of the yield strengths of the given material in shear and in tension and depends upon the mechanism of plastic deformation realized at the moment of occurrence of plastic instability.With the use of the criteria of similarity of the constriction of plastic deformation it is fundamentally possible to convert the critical parameters controlling the occurrence of plastic instability at the apex of a crack (defect) under various loading conditions.The results obtained require further analysis and experimental confirmation.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 13, No. 5, pp. 31–45, September–October, 1977.     

Simulation of Fatigue Crack Propagation in Ductile Metals by Blunting and Re-sharpening

Laird and Smith [(1962). Philosophical Magazine 8, 847–857] proposed a plastic sliding-off mechanism for the stage II fatigue crack growth via striation formation. In their view, the fatigue crack extension results solely from the changing character of deformation at the crack tip during loading and unloading. In particular, the crack tip blunts during the loading stage and folds into a double notch during the unloading stage, resulting in striation formation. In order to verify Laird’s plastic blunting mechanism for ductile polycrystals as well as for ductile fcc single crystals, FE calculations were performed for a rectangular plate with an initially sharp crack under plane strain conditions. The plate was subjected to a fully reversed tension-to-pressure cyclic load perpendicular to the crack plane (Mode 1). In the single crystal case the crack propagation simulations were carried out for cracks with crack plane (001) for two different crack growth orientations [110] and [100]. No initial radius for the crack tip was assumed. The actual shape of the crack tip followed from an initially sharp crack by repeated remeshing. To model the constitutive behavior typical for polycrystalline ductile metals, J₂ hypo-elasto-plasticity model with Armstrong–Frederick kinematic hardening was used. To model the constitutive behavior typical for ductile fcc single crystals, a geometrically nonlinear version of Cailletaud’s model based on the multiplicative elasto-plastic decomposition of the deformation gradient was implemented into the FE program ABAQUS. For simplicity, only octahedral slip systems were considered. Using repeated remeshing for severely distorted elements at the advancing crack tip, deformation patterns in the sense of Laird’s mechanism for fatigue crack propagation with striation formation were obtained in the case of the polycrystal simulation as well as in the case of the single crystal simulation for [110] crack growth direction. The simulation for [100] crack growth direction with the same stress level as for [110] direction also yielded crack extension by progressive large deformations but without striation formation. The dependence of the fatigue striation formation on the crack growth direction as predicted by the simulation of crack propagation in single crystals is verified by the experimental results of Neumann [(1974). Acta Metallurgica 22, 1155–1165] on pure copper single crystals.     

Failure of polystyrene in tensile and cyclic deformation

The failure of polystyrene in cyclic deformation has been examined and compared with the fracture mechanisms involved in simple tension. The fatigue response can be divided into three discrete life ranges. In the short and intermediate life regions, fracture occurs by the processes of craze formation, craze growth, crack nucleation and crack propagation in a manner analogous to tensile failure. The primary influence of reversed straining is manifest as an acceleration of the crack formation stage of failure. In long life (low stress) fatigue, failure modes dissimilar to the documented craze breakdown pattern of crack nucleation are noted.     

MIXED-MODE FRACTURE MECHANISMS NEAR THE FATIGUE THRESHOLD OF AISI 316 STAINLESS STEEL

Abstract— Near threshold, mixed mode (I and II), fatigue crack growth occurs mainly by two mechanisms, coplanar (or shear) mode and branch (or tensile) mode. For a constant ratio of ΔK_I/ΔK_II the shear mode growth shows a self-arrest character and it would only start again when ΔK_I and ΔK_II are increased. Both shear crack growth and the early stages of tensile crack growth, are of a crystallographic nature; the fatigue crack proceeds along slip planes or grain boundaries. The appearance of the fracture surfaces suggest that the mechanism of crack extension is by developing slip band microcracks which join up to form a macrocrack. This process is thought to be assisted by the nature of the plastic deformation within the reversed plastic zone where high back stresses are set up by dislocation pile-ups against grain boundaries. The interaction of the crack tip stress field with that of the dislocation pile-ups leads to the formation of slip band microcracks and subsequent crack extension. The change from shear mode to tensile mode growth probably occurs when the maximum tensile stress and the microcrack density in the maximum tensile plane direction attain critical values.     

Overload effects in fatigue crack growth by crack-tip blunting

A basic mechanisms for fatigue crack growth in ductile metals is that depending on crack-tip blunting under tensile loads and re-sharpening of the crack-tip during unloading. In the present paper, the effect of an overload in one of the cycles is studied based on this mechanism. In a standard numerical analysis accounting for finite strain, it is not possible to follow the blunting/re-sharpening process during many cycles, as severe mesh distortion at the crack-tip results from the huge geometry changes developing during the cyclic plastic straining. Here, based on an elastic-perfectly plastic material model, crack growth computations are continued up to 700 full cycles by using remeshing at several stages of the plastic deformation. Crack growth results for purely cyclic loading are compared with predictions for cases where an overload is applied, and it is shown how crack growth slows down after the overload. Different load amplitudes, and an overload at different cycle numbers are considered.     

Plastic deformation and fracture in coarse-grained aluminum

Plastic deformation and fracture in aluminum polycrystalline aggregate were investigated experimentally. A series of tensile specimens with a single edge crack were made of coarse-grained aluminum plates. The in-plane moiré technique was used to quantitatively obtain the deformation field around the crack tip. The strain field ahead of the crack tip prior to crack growth, as well as grain rotations during the course of plastic deformation, were evaluated from the corresponding moiré fringe patterns. The results of this study show that for small plastic deformation, grain rotation starts to take place at the very beginning of the plastic deformation and increases proportionally with plastic strain. The plastic strain ahead of the crack tip prior to crack growth drops significantly with decreasing average grain size of the specimen. Grain boundary sliding was also observed at some of the grain boundaries where the resolved shear stress had reached a critical value. The results also show that the crack propagated with maximum velocity at the center of a grain and assumed much slower velocity near grain boundaries or grain boundary junctions. The influence of the deformation rate is also discussed in terms of the stress relaxation.