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.     

Elastic–plastic material response of fatigue crack surface profiles due to overload interactions

The deformation caused by single and periodic overloads on the crack surface profile is studied using finite element fatigue crack closure simulations in a material with linear kinematic hardening. Differential surface profiles (difference of crack surface displacements before and after overloads), Δu_y, are found useful in understanding the role and the interaction between overloads. Three parameters, ΔK_OL/ΔK, ΔK and R, are found necessary to characterize deformation response of a single overload on the crack surface profile. The simulation procedure and results are discussed based on experimental and numerical studies reported in literature on overload interactions.The deformation occurred on the crack surface due to an applied single overload (hump) inhibits reversed plastic deformations by acting like a spring. Therefore, a second single overload leads to a larger deformation response even if this second overload is applied outside the overload plastic zone of the first single overload. This second deformation response is found equivalent to the response of a single overload with a higher K_min value.     

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.     

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.     

A distributed dislocation stress analysis for crazes and plastic zones at crack tips

A distributed dislocation method is developed to obtain analytically the applied stress as well as the surface stress profile along narrow plastic zones at the tip of a crack in a homogeneous tensile stress field. Replacing the plastic zone by a continuous array of mathematical dislocations, the stress field solution of this mixed boundary value problem (the displacement profile of the plastic zone is fixed while the tensile stresses are zero across the crack) can be solved. A computer program based on this stress field solution has been constructed and tested using the analytical results of the Dugdale model. The method is then applied to determining the surface stress profiles of crazes and plane-stress plastic deformation zones grown from electron microprobe cracks in polystyrene and polycarbonate respectively. The necessary craze and zone surface displacement profiles are determined by quantitative analysis of transmission electron micrographs. The surface stress profiles, which show small stress concentrations at the craze or zone tip falling to an approximately constant value which is maintained to the crack tip, are compared with those previously computed using an approximate Fourier transform method involving estimation of the displacement profile in the crack. The agreement between the approximate method and the exact distributed dislocation method is satisfactory.     

Role of plastic work in fatigue crack propagation in metals

The plastic work required for a unit area of fatigue crack propagation U was measured by cementing tiny foil strain gages ahead of propagating fatigue cracks and recording the stress-strain curves as the crack approached. Measurements of U and plastic zone size in aluminum alloys 2024-T4, 2219-T861, 2219 overaged, and A1-6.3 wt% Cu-T4, and a binary Ni-base alloy with 7.2 wt% A1 are herein reported. The results are discussed along with previously reported measurements of U in three steels and 7050 aluminum alloy. When U is compared to the fatigue crack propagation rate at constant ΔK along with strength and modulus, the conclusion is drawn that U is one of the parameters which determines the rate of fatigue crack propagation. The relation of U to microstructure is also discussed. “Homogeneous” plastic deformation in the plastic zone ahead of the crack seems desirable.     

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     

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].     

Investigation of process zone structure in Fe–3Si alloy

Abstract

An in situ fracture experiment was carried out in a scanning electron microscope to investigate plastic deformation and strain distribution in the process zone (PZ) located in the immediate vicinity of the crack tip in an Fe–3Si alloy (wt-%) under mixed mode loading conditions. It was observed that plastic deformation occurred by successive activation of a number of slip systems. The strain distribution and shape of the PZ were strongly dependent on the crystallographic orientation of the grain containing the crack tip. The distribution differed from that predicted using near tip blunting calculations and was best expressed by an exponential equation. Additional strain concentrations created by surface defects caused slight perturbations in the overall distribution. Crack propagation started along a coarse slip band which possessed the highest strain. It was found that the maximum strains in the PZ exceeded the uniaxial tensile fracture strain.

MST/1404     

A FINITE ELEMENT ANALYSIS OF A CRACK GROWING UNDER CYCLIC LOADING

Abstract— Crack growth under cyclic loading has been studied by the finite element method. The calculation was made for plane stress conditions. The crack tip zone was modelled as a cohesive zone. The displacement of the free crack surface during unloading was found to be governed by the surrounding continuum and was independent of the details in the fracture zone. This means that crack closure upon unloading is directly related to the ultimate separation, of the cohesive zone, which in turn controls the residual plastic deformation left in the wake of the growing crack. If the distance over which closure takes place is rather small, closure may be very difficult to detect by the compliance technique.     

Fatigue crack closure after overload

The fatigue crack closure after overload was measured by small foil strain gages. The effect of overload on crack closure stress and crack propagation rate was observed to extend over a range several times larger than the overload plastic zone. Analysis of experimental data showed that the extra amount of plastic deformation introduced by the overload was the controlling factor. A relationshp between crack closure stress and crack length in the affected zone was found, and the amount of plastic deformation by the overload was estimated. This estimate was further confirmed by analysis of the crack closure pictures.     

TiAl基合金层状组织中裂纹扩展区的塑性变形

本文通过观察ＴｉＡｌ合金层片组织四点弯曲试样侧面裂纹扩展与滑移迹线之间的关系，分析讨论了层状组织中塑性变形对裂纹扩展的影响。发现不论层片相对于裂纹处于何种取向，沿层片方向都有一定程度的塑性变形，这种变形对于平行、倾斜、垂直于片层扩展的主裂纹都可引起裂尖钝化，从而引发构成各种韧化机制     

Fatigue crack tip plastic zone of α + β titanium alloy with Widmanstatten microstructure

The recent studies had focused on the fatigue crack propagation behaviors of α?+?β titanium alloys with Widmanstatten microstructure. The fascinated interest of this type of microstructure is due to the superior fatigue crack propagation resistance and fracture toughness as compared to other microstructures, which was believed to be related to the fatigue crack tip plastic zone (CTPZ). In this study, the plastic deformation in fatigue CTPZ of Ti-6Al-4V titanium alloy with Widmanstatten microstructure was characterized by scanning electron microscope (SEM) and electron backscatter diffraction (EBSD). The results showed that large-scale slipping and deformation twinning were generated in fatigue CTPZ due to the crystallographic feature of the Widmanstatten microstructure. The activation of twinning was related to the rank of Schmid factor (SF) and the diversity of twin variants developing behaviors reflected the influence of SF rank. The sizes of CTPZ under different stress intensity factors (K) were examined by the white-light coherence method, and the results revealed that the range of the plastic zone is enlarged with the increasing K (or crack length), while the plastic strain decreased rapidly with the increasing distance from the crack surface. The large-scale slipping and deformation twinning in Widmannstatten microstructure remarkably expanded the range of fatigue CTPZ, which would lead to the obvious larger size of the observed CTPZ than that of the theoretically calculated size.     

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.     

Measurement of fatigue-induced surface plasticity

A method is presented for measuring at a surface the localized plastic strains induced by fatigue within individual grains. The technique uses mica flakes distributed on a sample surface as reference gauges, relative to which strains in the surface can accurately be determined. An application of the method to the study of fatigue induced microplasticity in an Al 2219-T851 alloy is discussed. On an unfatigued specimen, subjected to applied stresses less than the yield strength, deformation is elastic over gauge lengths comparable with the grain size. After fully-reversed cyclic loading at a peak tensile stress of 75% of the yield strength for 20×10³ cycles, the larger grains in the alloy exhibit a residual tensile strain after a tensile loading cycle. Neighbouring smaller grains are driven into elastic compression to accommodate this tensile plastic deformation. Peak localized tensile plastic strains may exceed 0.5% at the surface. This technique will be useful in evaluating models of fatigue crack initiation and surface damage accumulation.     

A critical evaluation of superposition methods for cracks in grossly plastic gradient fields

This paper presents a critical assessment of three analytical methods in determining the crack-tip plastic deformation under large scale and gross-section yielding conditions. These theoretical approaches include two stress-based cohesive zone models and a strain-intensity factor approach, all developed on the basis of the principle of superposition. In the two stress-based cohesive zone models, the prospective stresses along the crack path are taken to be the elastic-plastic solution and the nominal elastic solution, respectively. The problem of an edge crack subjected to grossly plastic strain fields with a constant strain gradient is analysed using the finite element method. The plastic zone size and the crack-tip opening displacement determined by the finite element analysis are then compared with the analytical predictions, showing that these theoretical approaches are unable to capture the influence of gross plasticity on the plastic deformation at the crack tip. The present results highlight the deficiencies in existing stress-based superposition approaches.     

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.     

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.