Plastic zone near the crack tip in a material with strain anisotropy caused by loading along spatial rectilinear trajectories

The equation of the boundary of the plastic zone near the tip of a mode I crack is deduced for the case of a plate made of a material with strain anisotropy. It is assumed that the anisotropy is caused by hardening in the process of plastic deformation performed prior to the appearance of the crack under loading along arbitrary rectilinear trajectories in the space of the stress tensor. An analysis of this equation demonstrates that the main factors affecting the shape and size of the plastic zone are the level of plastic strains accumulated in the process of preloading, their sign, and the orientation of the crack relative to the axes of anisotropy.     

Plastic zone near the crack tip in a material with strain anisotropy caused by loading along spatial rectilinear trajectories

The equation of the boundary of the plastic zone near the tip of a mode I crack is deduced for the case of a plate made of a material with strain anisotropy. It is assumed that the anisotropy is caused by hardening in the process of plastic deformation performed prior to the appearance of the crack under loading along arbitrary rectilinear trajectories in the space of the stress tensor. An analysis of this equation demonstrates that the main factors affecting the shape and size of the plastic zone are the level of plastic strains accumulated in the process of preloading, their sign, and the orientation of the crack relative to the axes of anisotropy. Translated from Problemy Prochnosti, No. 6, pp. 21–27, November–December, 1997.     

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 curving under mode-I loading

The whole history of failure of a rectangular panel with two symmetrical notches and a central crack subjected to a progressively increasing tension load normal to the crack plane is studied. The material of the panel exhibits substantial plastic deformation prior to fracture. An elastic-plastic analysis of the plate is first performed based on finite elements. The results of stress analysis are coupled with the strain energy density theory to determine the critical load for crack initiation and the history of stable crack growth up to the point of instability. At instability the crack runs fast through the elastic material bypassing the plastic zone near the plate boundary. The crack deviates from its initial direction and is curved even though the plate is subjected to opening-mode loading. Results for crack trajectories are given for various initial crack lengths and notch radii of the plate.Presented at Fourth Greek National Congress on Mechanics, 26–29 June 1995, held at Xanthi, Greece.     

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.     

Crystallographic analysis on small fatigue crack propagation behaviour of a nickel-based single crystal superalloy

In situ observations by scanning electron microscopy show that small fatigue cracks in a nickel-based single crystal superalloy are inclined to the loading direction and propagate in dominant crystallographic manners. In order to evaluate the driving forces for inclined crack propagation, three-dimensional anisotropic linear elastic finite-element analysis is conducted. The plastic zone size on the dominant slip plane has been calculated and proposed to correlate the fatigue crack growth. It is shown that this parameter takes into account both material anisotropy and octahedral fracture modes, and it can effectively characterize small crack propagation behaviour.     

On the effect of the residual stresses on the crack opening displacement in a cracked sheet

The residual stress and displacement fields caused by localized plastic flow near a mode I crack tip in a sheet under plane stress conditions are investigated. The present study founds on the classical Dugdale scheme of the plastic flow localization. The residual stress field is considered to be induced by reversed plastic flow near the crack tip caused by an unloading. As it is found the residual stresses around the crack compress the crack tip, while the residual tensile stresses in a distant from the crack tip zone occur. It is shown the maximum residual tensile stresses can reach the significant value of the one third of the yield limit. The length of the compressed plastic zone and the residual displacement distributions are obtained. The exact formula for the residual crack opening displacement to estimate the crack closure is found. Then the next loading of the cracked plate is considered. It is shown that the second loading causes the origin of two plastic zones localized near the crack tip and at the point, where the maximum residual tensile stresses are concentrated. Again, according to the Dugdale scheme of the plastic localization, both the plastic flow zones are modelled as narrow stripes on the line extending the crack. To determine three non-dimensional parameters, characterizing the position of the segment-like plastic flow zones, a non-linear system of equations is obtained and analyzed. The exact formula for the crack opening displacement after a loading–unloading cycle is obtained. An asymptotic analysis (as the linear dimension of the distant plastic flow zone compared with the actual crack length is small) is given. It shows that the effect of the distant plastic flow zone appears as some complementary crack closure.     

Prediction of crack growth direction under plane stress for mixed-mode I and II loading

The estimation of the plastic zone geometry ahead of a crack is fundamental to the evaluation of crack growth. Presented here is an analytical investigation for predicting crack growth direction for mixed-mode I and II loading under plane stress conditions. It is proposed that under complex loading the crack will extend in the direction where the radius of the plastic zone attains a minimum value. There is good agreement between the predicted results which are computed on the basis of this criterion and experimental data published in the literature.     

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.     

Fatigue propagation behaviour of polystyrene/polyethylene blends

Fatigue crack propagation (FCP) of injection-moulded polystyrene (PS) and 95/5, 85/15 and 70/30 PS/high-density polyethylene (HDPE) blends at loading frequencies of 2 and 20 Hz was studied. The FCP results showed that increasing the HDPE content caused a progressive reduction of the fatigue crack growth rates, especially when a styrene/ethylene– butylene/styrene (SEBS) terpolymer was added as a compatibilizer. Increasing the loading frequency also led to a fatigue crack growth rate reduction. Moreover, the fatigue crack growth rates were lower at a given cyclic stress intensity factor range, K, when the crack propagated normal, instead of parallel, to the melt-flow direction during injection moulding. Fractographic observations indicated that discontinuous growth bands (DGBs), associated with the fracture of crazes in the plastic zone, were present through most or all of the fracture surfaces of the PS/HDPE specimens. In the presence of sufficient HDPE, these DGBs were formed by the initiation, growth and coalescence of large dimples initiated at HDPE particles ahead of the microscopic crack front, similar to a multiple crazing effect. The loading frequency effect on the FCP behaviour of these blends is attributed to a time-dependent deformation process. It is concluded that the FCP behaviour of these blends is strongly affected by the loading direction with respect to the matrix and minor phase orientation, by the presence of a compatibilizer, by the composition of the blend and by the testing conditions. © Chapman & Hall.     

Ductile tearing of pipeline-steel wide plates: II. Modeling of in-plane crack propagation

The purpose of this work is to develop a finite element simulation of static ductile tearing tests carried out on pipeline-steel wide plates. Experiments have been presented in a companion paper (Part I [1]).The simulation is based on an extension of the Gurson–Tvergaard–Needleman model which includes plastic anisotropy and viscoplasticity effects. The parameters of the model are fitted using tensile specimens (smooth and notched bars). Simulated tests are used to evaluate macroscopic fracture parameters which were experimentally measured: the energy dissipation rate R and the thickness reduction Z.The simulation tool is then used to numerically investigate the effect of plate thickness, plastic anisotropy and through-thickness hardness gradients on the crack growth resistance. It is shown that with increasing thickness, the energy dissipation rate first increases and then decreases. A through-thickness hardness gradient is beneficial when the surface is harder than the bulk. Plastic anisotropy can be either detrimental or beneficial depending on the loading direction. These effects are explained in terms of plastic localization inducing necking along the crack path and in terms of stress distribution.     

Effect of mixed mode I/III loading on plastic zone in Armco Iron

Abstract

The effect of increasing loading angle or the mode III loading contribution on the size and shape of the plastic zone ahead of the crack tip were experimentally determined in Armco Iron. It was found that the shape of the experimentally measured plastic zone was in agreement with numerical prediction. However, the size of the measured plastic zones was significantly larger than the numerically predicted plastic zones for all the loading angles. The plastic zone was found to increase in the trajectory of a crack with increasing loading angle.     

Strain concentration at the crack corners in polyethylene films

The crack growth kinetics in blown low-density polyethylene film have been examined. It has been proposed from mechanical measurements that a zone of plastic deformation ahead of the crack tip acts as an obstacle to crack propagation, especially when the crack grows perpendicularly to the machine direction of the film. The existence and size of such a plastic zone have been revealed using a special microscopical method.Partly presented at the Eighth International Conference on Rheology, Naples, Italy, September 1–5, 1980.     

In situ TEM observations of fracture in nanolaminated metallic thin films

Fracture of single crystal nanolaminated thin films has been investigated through in situ straining of cross-sectional samples of Cu/Ni nanolaminates grown on Cu (001) single crystal substrates. The earlest stages of deformation exhibits a confined layer slip mechanism. With continued straining, unstable fracture occurs creating a mixed-mode crack that propagates across the nanolaminate, roughly perpendicular to the interfaces. Eventually, stable crack growth with intense plastic deformation ahead of the crack tip occurs over many bilayers in the direction of crack growth. Simultaneously, plasticity was seen to spread only 1 or 2 bilayer distances normal to the crack, creating an extremely localized plastic zone. Transmission electron microscopic (TEM) examination after the test did not reveal the presence of dislocations in the crack wake, except where severe crack deflection was observed. By comparison, the plastic zone size in the substrate was greater by several of orders of magnitude.     

The twisting mechanism of subsurface fatigue cracking in Ti-6Al-2Sn-4Zr-2Mo-0.1Si alloy

The initiation phenomenon of a subsurface fatigue crack was examined by monitoring of the acoustic emission (AE) effects revealed by the slightly surface-hardened specimens of titanium-based VT3-1 (Ti-6Al-2Sn-4Zr-2Mo-0.1Si) alloy under fatigue tests. The circumferentially notched round-bar specimens were cyclically stretched in the stress range of 720-680 MPa, with the stress ratio varying as 0.31-0.36, at 35-Hz loading frequency. The AE monitoring has shown the subsurface cracking events as concomitant with the unloading (compressive) portions of the cyclic load trajectory. In the several fractographically examined areas of subsurface fatigue fracture, mode III (rotational or twist-like) way of crack opening was found to dominate on the short-crack path; during the damage-accumulation period, creative of the first smooth crack-origin facets, such a crack-opening pattern appeared mainly related to the unloading portions of the loading trajectory. Internal residual stresses appear to control such a deformation mode in the locally compressed material. Stress-release effects should follow from the occurrence of the first crack facet favoured by gas diffusion. Therefore, the subsurface crack origination is actually a synergetic problem. The dominant mode-III deformation is also creative of a plastic zone around the now stress-released area of the first fracture facet. This plastic zone is to be involved in the mode-I (tension) opening of the subsurface crack propagating from the first subsurface crack facet. The subsurface crack opening occurs as facilitated by the dissolved-gas diffusion toward a material discontinuity. Consequently, a short crack can expand around the first facet through a combined modes III and I opening to form a growing subsurface-fracture area. Such a model of the twist-controlled subsurface cracking is proposed and discussed here in terms of the well-known numerical data on the subsurface stress-state evolution as well as on the progress of plastic mesoscopic-scale level deformation in tensile-loaded metals.     

THE SIGNIFICANCE OF CRACK TIP DEFORMATION FOR SHORT AND LONG FATIGUE CRACKS

Abstract— The behaviour of physical short mode I cracks under constant amplitude cyclic loading was investigated both numerically and experimentally. A dynamic two-dimensional elastic-plastic finite element technique was utilised to simulate cyclic crack tip plastic deformation. Different idealisations were investigated. Both stationary and artificially advanced long and short cracks were analysed. A parameter which characterises the plastically deformed crack tip zone, the strain field generated within that zone and the opening and closure of the crack tip were considered. The growth of physically short mode I cracks under constant amplitude fully reversed fatigue loading was investigated experimentally using conventional cast steel EN-9 specimens. Based on a numerical analysis, a crack tip deformation parameter was devised to correlate fatigue crack propagation rates.     

Role of plastic zone in crack growth direction criterion under mixed mode loading

An approach to determine the crack growth direction under mixed-mode loading conditions is presented. The plastic zone shape around the crack tip is applied for evaluating angle of crack propagation. It is proposed that a mixed-mode crack will extend along the plastic zone radius with a minimum value. The prediction of the proposed criterion is compared with the experimental data and other models. The agreement is fairly good.     

Plastic zones in an orthotropic plate of finite width containing a Griffith crack

The problem of an orthotropic infinite plate of finite width containing a centrally located stressed Griffith crack is considered. The crack is located perpendicular to the edges of the orthotropic plate. The crack tips are fully yielded and in the inelastic zones the material carries only constant normal stresses equal to the yield stress. Dugdale's model is employed to find the effects of the material anisotropy on the size of the plastic zones around the crack tips. Graphical results showing the effects of anisotropy on the length of the plastic zone are also presented.     

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.     

Numerical simulation of constraint effects in fatigue crack growth

The computational analysis of constraint effects on fatigue crack growth is discussed. An irreversible cohesive zone model is used in the computations to describe the processes of material separation under cyclic loading. This approach is promising for the investigation of fatigue crack growth under constraint as the energy dissipation due to the formation of new crack surface and cyclic plastic deformation is accounted for independently. Fatigue crack growth in multi-layer structures under consideration of different levels of T-stress are conducted with a modified boundary layer model. Fatigue crack growth is computed as a function of layer thickness and T-stress for constant and variable amplitude loading cases.