MECHANICAL REASONS FOR PLASTICITY-INDUCED CRACK CLOSURE UNDER PLANE STRAIN CONDITIONS

A mechanical explanation of plasticity-induced crack closure under plain strain conditions is given first by means of dislocation mechanics and then by the methods of continuum mechanics. In plane strain, the event of crack closure is due to transport of material from the wake to the crack tip. It is an elastic effect caused by the response of the matrix surrounding the plastic wake. The transported material produces a wedge which follows the crack tip, and unlike the plane stress condition it does not leave a remaining layer on the crack flanks. The length of the produced wedge at the crack tip is of the same scale as the plastic zone. It is then shown that in spite of its smallness this wedge is able to cause the experimentally observed shielding effect. The results also suggest that the discrepancies concerning the interpretation of fatigue crack growth and closure experiments are likely to be due to differences in accuracy in the detection of such small but nevertheless effective wedges.     

Influence of isotropic strain hardening on plane strain dynamic growth in elastic-plastic materials

In this paper, dynamic crack growth in an elastic-plastic material is analysed under mode I, plane strain, small-scale yielding conditions using a finite element procedure. The material is assumed to obey J₂ incremental theory of plasticity with isotropic strain hardening which is of the power-law type under uniaxial tension. The influence of material inertia and strain hardening on the stress and deformation fields near the crack tip is investigated. The results demonstrate that strain hardening tends to oppose the role of inertia in decreasing plastic strains and stresses near the crack tip. The length scale near the crack tip over which inertia effects are dominant also diminishes with increase in strain hardening. A ductile crack growth criterion based on the attainment of a critical crack tip opening displacement is used to obtain the dependence of the theoretical dynamic fracture toughness on crack speed. It is found that the resistance offered by the elastic-plastic material to high speed crack propagation may be considerably reduced when it possesses some strain hardening.     

The evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited

The evolution of the stress–strain fields near a stationary crack tip under cyclic loading at selected R‐ratios has been studied in a detailed elastic–plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R‐ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic–plastic finite element simulations of advancing fatigue cracks were carried out under plane‐stress, plane‐strain and generalized plane‐strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane‐strain and generalized plane‐strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane‐stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack‐closure measurement, and indeed on the role of plasticity‐induced crack closure in the reduction of the applied stress intensity factor range.     

Finite deformation cohesive polygonal finite elements for modeling pervasive fracture

In the present study, mode I crack subjected to cyclic loading has been investigated for plastically compressible hardening and hardening–softening–hardening solids using the crack tip blunting model where we assume that the crack tip blunts during the maximum load and re-sharpening of the crack tip takes place under minimum load. Plane strain and small scale yielding conditions have been assumed for analysis. The influence of cyclic stress intensity factor range (\(\Delta \hbox {K})\), load ratio (R), number of cycles (N), plastic compressibility (\({\upalpha })\) and material softening on near tip deformation, stress–strain fields were studied. The present numerical calculations show that the crack tip opening displacement (CTOD), convergence of the cyclic trajectories of CTOD to stable self-similar loops, plastic crack growth, plastic zone shape and size, contours of accumulated plastic strain and hydrostatic stress distribution near the crack tip depend significantly on \(\Delta \hbox {K}\), R, N, \({\upalpha }\) and material softening. For both hardening and hardening–softening–hardening materials, yielding occurs during both loading and unloading phases, and resharpening of the crack tip during the unloading phase of the loading cycle is very significant. The similarities are revealed between computed near tip stress–strain variables and the experimental trends of the fatigue crack growth rate. There was no crack closure during unloading for any of the load cycles considered in the present study.     

A numerical study of plasticity induced crack closure under plane strain conditions

The level of plasticity induced crack closure (PICC) is greatly affected by stress state. Under plane strain conditions, however, the level and even the existence of PICC still are controversial. The objective here is to study the influence of the main numerical parameters on plane strain PICC, namely the total crack propagation, the number of load cycles between crack increments, the finite element mesh and the parameter used to quantify PICC. The PICC predictions were included in a parallel numerical study of crack propagation, in order to quantify the impact of plane strain values on fatigue life. The results indicate that literature may be overestimating plane strain PICC due to incorrect numerical parameters. The number of load cycles usually considered is unrealistically small, and its increase was found to vanish crack closure, particularly for kinematic hardening. This effect was linked to the ratcheting effect observed at the crack tip. The total crack increment, Δa, must be large enough to obtain stabilized PICC values, but this may imply a huge numerical effort particularly for 3D models. The size of crack tip plastic zone may be overestimated in literature, which means that the meshes used may be too large. Additionally, the crack propagation study showed that the plane strain PICC has usually a dominant effect on fatigue life, and plane stress PICC is only relevant for relatively thin geometries.     

A study of the relationship between variable level fatigue crack growth and the cyclic constitutive behaviour of steel

Sensitivity of fatigue crack growth to the material behaviour was studied in two previous numerical studies (Pommier S. Plane strain crack closure and cyclic hardening. Eng Fract Mech, in press; Pommier S, Bompard P. Bauschinger effect of alloys and plasticity-induced crack-closure: a finite element analysis. Fatigue Fract Eng Mater Struct 2000;23:129–39). It was shown, in particular, that material hardening induces a rotation of the crack tip plastic zone from the front to the back of the crack, which enhances the effects of crack closure (Pommier S. Plane strain crack closure and cyclic hardening. Eng Fract Mech, in press). The type of hardening is also of key importance: Isotropic hardening is found to lower the effective part of the fatigue cycle, while kinematic hardening (Pommier S, Bompard P. Bauschinger effect of alloys and plasticity-induced crack-closure: a finite element analysis. Fatigue Fract Eng Mater Struct 2000;23:129–39) is found to increase it. This study is devoted to check the validity of those numerical results in a 0.4% C carbon steel, which displays a high Bauschinger effect and a moderate amount of isotropic hardening. The comparison between numerical results and experiments is satisfactory.     

A finite element analysis of plane strain dynamic crack growth in materials displaying the Bauschinger effect

In this paper dynamic crack growth in an elastic-plastic material is analyzed under mode I plane strain small-scale yielding conditions using a finite element procedure. The main objective of this paper is to investigate the influence of anisotropic strain hardening on the material resistance to rapid crack growth. To this end, materials that obey an incremental plasticity theory with linear isotropic or kinematic hardening are considered. A detailed study of the near-tip stress and deformation fields is conducted for various crack speeds. The results demonstrate that kinematic hardening does not oppose the role of inertia in decreasing the plastic strains and stresses near the crack tip with increase in crack speed to the same extent as isotropic strain hardening. A ductile crack growth criterion based on the attainment of a critical crack opening displacement at a small micro-structural distance behind the tip is used to obtain the dependence of the theoretical dynamic fracture toughness with crack speed. It is found that for any given level of strain hardening, the dynamic fracture toughness displays a much more steep increase with crack speed over the quasi-static toughness for the kinematic hardening material as compared to the isotropic hardening case.     

Finite element visualization of fatigue crack closure in plane stress and plane strain

Elastic-plastic finite element simulations of growing fatigue cracks in both plane stress and plane strain are used as an aid to visualization and analysis of the crack closure phenomenon. Residual stress and strain fields near the crack tip are depicted by both color fringe plots and x-y graphs. Development of the residual plastic stretch in the wake of a growing plane stress fatigue crack is shown to be associated with the transfer of material from the thickness direction to the axial direction. Finite element analyses indicate that crack closure does occur under pure plane strain conditions. The development of the residual plastic stretch in plane strain is shown to be associated with the transfer of material from the in-plane transverse direction to the axial direction. This in-plane contraction also leads to the generation of complex residual stress fields. The total length of closed crack at minimum load in plane strain is shown to be a small fraction of the total crack length, especially for positive stress ratios. This suggests that experimental measurement of plane strain closure would be extremely difficult, and may explain why some investigators have concluded that closure does not occur in plane strain.     

Computations of fatigue crack growth with strain gradient plasticity and an irreversible cohesive zone model

Computations of fatigue crack growth with a first-order strain gradient plasticity (SGP) model and an irreversible cohesive zone model are reported. SGP plays a significant role in the model predictions and leads to increased fatigue crack growth rates relative to predictions with classical plasticity. Increased magnitudes of tractions and material separation at the crack tip together with reduced crack closure appear as the cause for accelerated crack growth in SGP. Under plane strain conditions SGP appears as an essential feature of the development of the crack closure zone. Size effects are explored relative to changes in internal material length scale as well as to structural length scales.     

A537钢疲劳裂纹扩展单次拉伸超载效应及裂尖形变,裂纹闭合行为

研究了恒定ΔＫ条件下，单次拉伸超载对Ａ５３７钢疲劳裂纹扩展速率的影响，并利用激光散斑技术原位研究超载前后的裂尖应变场，裂纹闭合效应。结果表明：超载后裂纹闭合效应呈增强趋势，裂尖应变呈下降趋势。伸超载有阻滞裂纹扩展的作用。     

Prediction of crack growth following a single overload in aluminum alloy with sheet and plate microstructure

The fatigue crack growth behavior under constant amplitude and under single overload of 2024 aluminum alloy in sheet and plate product form has been investigated. Constant amplitude fatigue crack growth tests showed superior crack growth resistance of the plate attributed to a pronounced roughness induced crack closure as a result of the coarse and elongated grain structure. Crack growth tests with single overload showed that the retardation effect caused by the overload is not primarily influenced by roughness crack closure at the crack path. In this case, the sheet material with lower yield strength revealed a higher retardation effect than the plate material. The observed crack growth behavior has been simulated with the LTSM-F model, which accounts for retardation of crack growth after an overload due to material strain hardening at the crack front. Dissimilar strain hardening at the crack tip due to different yield strength for the sheet and plate has been considered by means of strength gradients inside the overload plastic zone. The analytical results confirmed the observed material crack growth trends.     

The shielding effects of the crack-tip plastic zone

In this paper we demonstrate that a plastically deformed zone around a stressed crack tip can be, mechanically, identified with an inclusion of transformation strain by means of Eshelby equivalent inclusion method. Thus, the shielding effect of the plastic zone can be quantitatively evaluated by the present transformation toughening theory. A closed-form solution to determine the change in the stress intensity factor induced by the plastic zone is given both for plane stress and plane strain mode I cracks under small-scale yielding conditions. By using the present solution, the effects of the strain-hardening behavior of the material, the plane stress and plane strain states and the T-stress on the crack-tip shielding effects are identified.     

Finite-element analysis of fatigue crack closure under plane strain conditions: stabilization behaviour and mesh size effect

An elastic–plastic finite‐element analysis of fatigue crack closure is performed for plane strain conditions. The stabilization behaviour of crack opening level and the effect of mesh size on the crack opening stress are investigated. It has been well reported that the crack opening level under plane stress conditions becomes stable after the crack advances beyond the initial monotonic plastic zone. In order to obtain a stabilized crack opening level for plane strain conditions, the crack must be advanced through approximately four times the initial monotonic plastic zone. The crack opening load tends to increase with the decrease of mesh size. The mesh size nearly equal to the theoretical plane strain cyclic plastic zone size may provide reasonable numerical results comparable with experimental crack opening data. The crack opening behaviour is influenced by the crack growth increment and discontinuous opening behaviour is observed.     

Correlation of a plastic zone length near the tip of a mode I crack in an orthotropic material with anisotropy parameters

We derived equations that relate the length of a plastic zone near a mode I crack tip in a plate made of an orthotropic material with yield strength levels in the direction of the anisotropy axes. The case of crack orientation along one of the anisotropy axes is examined, with the latter being determined by the strain hardening of a material at the stage preceding the crack nucleation. The growth of yield strength along the axes lying in the plane of the plate is shown to result in smaller sizes of the plastic zone. An increase in yield strength in the direction of the normal to the above plane leads to an increase in its length. Ukrainian Regional Research and Design Institute of Civil Engineering, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 32–37, July–August, 1999.     

CRACK CLOSURE AND PLASTIC ZONE SIZES IN FATIGUE

Abstract— An elastic-plastic finite element simulation of growing fatigue cracks which accounts for plasticity-induced crack closure is used to study the size of the forward and reversed plastic zones at the crack tip. Forward plastic zone widths for fatigue cracks and stationary, monotonically loaded cracks are compared and found to be similar. The width of the forward plastic zone at the tip of a fatigue crack is not significantly influenced by closure. The traditional Irwin-Rice estimate for crack tip plastic zone size in plane stress is found to be generally consistent with the finite element results. The width of the reversed plastic zone at the tip of a growing fatigue crack in plane stress is found to be considerably less than one-fourth the size of the forward plastic zone, the traditional Rice estimate. This decrease appears to be due to fatigue crack closure. A simple model is developed which permits estimation of the reversed plastic zone size for any stress ratio from information about maximum and minimum stresses and the closure stress. The predictions of this model agree closely with plastic zone sizes calculated by the finite element analysis. These observations appear to be consistent with experimental measurements of forward and reversed plastic zones sizes reported in the literature.     

An interface crack in a coating-substrate composite with mixed-mode Dugdale corrections

Considering both plane stress and plane strain conditions, the plastic zone size and the crack tip opening displacement of an interface crack between a coating and a semi-infinite substrate under a normal load on the crack surfaces are investigated by the mixed-mode Dugdale model. In the model, stresses applied in the plastic zones satisfy the Von Mises yield criterion. The plastic zone size can be calculated by satisfying the condition that the complex stress intensity factors vanish. After the plastic zone size is solved, the crack tip opening displacement can be obtained by dislocation theories. In numerical examples, a uniform load is considered, and the effects of the normalized elastic modulus (the ratio of the elastic modulus of the coating to the elastic modulus of the substrate) and the normalized crack depth (the ratio of the coating thickness to the interface crack length) on the normalized plastic zone size and the normalized crack tip opening displacement are examined. Numerical examples show in the case of thin coatings, the value of the normalized plastic zone size decreases with increasing the normalized elastic modulus.     

Asymptotic deformation and stress fields at the tip of a sharp notch in an elastic-plastic material

The singular elastic-plastic stress, strain and the displacement fields at the tip of a sharp notch for both plane stress and plane strain conditions are investigated analytically. The material is assumed to be governed by the deformation theory of plasticity with linear strain hardening characteristic. Since the elastic strain is retained in the analysis, the final strain and displacement fields can be separated into the elastic and the plastic parts. In the case with zero notch angle, the results reduce to the classical crack problem. The relationship of the amplitude of the near crack tip elastic-plastic field to the elastic far field is obtained. Both mode I and mode II cases are investigated. The mixed mode case is also discussed.     

Analytical study of the elastic–plastic stress fields ahead of parabolic notches under antiplane shear loading

An analytical study is carried out on the elastic–plastic stress and strain distributions and on the shape of the plastic zone ahead of parabolic notches under antiplane shear loading and small scale yielding. The material is thought of as obeying an elastic-perfectly-plastic or a strain hardening law. When the notch root radius becomes zero, the analytical frame matches the solutions for the crack case due to Hult–McClintock (elastic-perfectly-plastic material) and Rice (strain hardening material). The analytical frame provides an explicit link between the plastic stress and the elastic stress at the notch tip. Neuber’solution for blunt notches under antiplane shear is also obtained and the conditions under which such a solution is valid are discussed in detail by using elastic and plastic notch stress intensity factors. Finally, revisiting Glinka and Molski’s equivalent strain energy density (ESED), these factors are used also to give, under antiplane shear loading, the increment of the strain energy at the notch tip with respect to the linear elastic case.     

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.     

Effect of Hydrogen on Plastic Deformation near Crack-tipof A537 Steel in 3.5%NaCl Solution

A computerized digital speckle-intederometry system was set up to study in-situ the influence of cathodic hydrogen charging on the crack opening displacement and on the plastic strain distribution at corrosion fatigue crack tip for the singIe-edge notched plate specimens of structural steel in 3.5%NaCl solution with an applied potential of -1400 mV (SCE). Meanwhile, the mono-directional tension tests with smooth specimens were pedermed in both air and 3.5%NaCl solution under the hydrogen charging conditions. The fracture sudece morphology from corrosion fatigue and tension was examined by SEM. The experimental results show that the existence of hydrogen in crack tip material caused an increase of both yield strength and hardening exponent and a decrease of plastic zone size at the corrosion fatigue crack tip.