Plastic Enclave Research Articles

Investigation of Plasticity Effects on Growing Fatigue Cracks Using the CJP Model of Crack Tip Fields.

A growing fatigue crack gives rise to a plastic enclave that envelops the crack and can exert a shielding effect on the crack from the global elastic stress field driving fatigue propagation. This work presents the potential of the CJP model of crack tip fields to investigate the plasticity-induced shielding effects on growing fatigue cracks as well as its ability to characterise the size and shape of the plastic zone generated at the tip of a growing fatigue crack. The model was specifically developed to consider the influence of the plastic enclave generated around a fatigue crack on the surrounding elastic material. Different aspects related to fracture mechanics and its implications for fatigue crack growth have been investigated, namely plasticity-induced crack shielding, the retardation effect induced on fatigue crack growth due to the application of an overload and the estimate of the size and shape of the crack tip plastic zone. The model has been successfully applied by analysing displacement fields experimentally measured by DIC in different CT specimens made of 2024-T3 aluminium alloy and commercially pure titanium. Results presented in this work intend to contribute to a better understanding of the shielding effects during fatigue crack growth.

Combined approach for fatigue crack characterisation in metals

In this work a comprehensive characterisation of the fatigue crack growth of an Al 2024 alloy is presented. A powerful Christopher-James-Patterson (CJP) model is used for multi-parameter characterisation of the crack state at a few different locations through the fatigue crack growth. The CJP model of crack tip displacements and stress fields was proposed in order to better capture the influences on the applied elastic stress field of the plastic enclave that is generated around a growing fatigue crack. The model does this through a set of elastic stresses applied at a notional elastic-plastic boundary, and it has been shown to accurately model plastic zone shape and size, whilst its ability to predict the effective range of stress intensity factor during a fatigue cycle has been verified. Thus, the model can predict the driving force component of the crack and additional components that account for different shielding mechanisms. CJP model is combined with full-field non-contact Digital Image Correlation (DIC) so that the model can be fed at any moment with real experimental information. The results are then correlated with Paris law data for Al 2024 alloy through Scanning Electron Microscopy (SEM) observations of the fracture surface. In this work the effect of crack length and load level are thoroughly studied and validated with fatigue crack growth rate measurements.

Investigation of effective stress intensity factors during overload fatigue cycles using photoelastic and DIC techniques

This work uses DIC and photoelastic techniques to investigate the effect of single overload cycles applied during constant amplitude fatigue. Effective values of the range of stress intensity factor were calculated using the CJP model of crack tip stress and displacement fields, as this model considers both wake contact and compatibility-induced influences on the applied elastic field arising from the plastic enclave generated around a fatigue crack. Values of the effective stress intensity factor are related to the observed crack growth acceleration and retardation. In addition, the paper compares the CJP results with those obtained using a compliance-based method. The present work demonstrates the utility of the CJP model in characterising fatigue crack growth rates during variable amplitude loading. It is also possible with the CJP model, through changes in the coefficient values and hence, for the first time, to shed explicit light on the contributions made by different mechanisms to the shielding effects of an overload.

Crack tip plastic zone evolution during an overload cycle and the contribution of plasticity‐induced shielding to crack growth rate changes

AbstractThis work explores the contribution to crack growth rate acceleration and deceleration that arises from plasticity‐induced shielding during an overload cycle. The CJP model of crack tip displacements and stress fields was proposed to better capture the influences on the applied elastic stress field of the plastic enclave that is generated around a growing fatigue crack. The model does this through a set of elastic stresses applied at a notional elastic‐plastic boundary, and it has been shown to accurately model plastic zone shape and size, whilst its ability to predict the effective range of stress intensity factor during a fatigue cycle has been independently verified. In this paper, the CJP model is used to follow plastic zone size and shape through an overload fatigue cycle and to assess the extent that plasticity‐induced shielding accounts for the observed crack growth changes. The changes in effective stress intensity factor range during the overload demonstrate that the observed growth rate changes during overload cycles can only be partially rationalised through plasticity‐induced shielding (closure).

Measurement and analysis of fatigue crack deformation at the micro-scale

This paper introduces the use of digital image correlation for the measurement of surface displacements in the neighbourhood of a crack tip, both at the macro- and micro- scale. Various methods of interpreting the measured data and producing a crack driving force are then discussed, including the use of the full CJP model. A reduced set of parameters are then proposed, corresponding to the three principal interaction forces between the plastic enclave and the surrounding elastic material. Our own results, and those of Vasco Olmo, previously reported in the literature are then reanalysed using this new framework, and excellent agreement between two independent experiments is obtained. Implications for the analysis of further data sets are then discussed.

Local crack plasticity and its influences on the global elastic stress field

This paper presents the background and development of a novel ‘plastic inclusion’ approach for dealing with the local plasticity which occurs at the tip of a growing fatigue crack. Localised plasticity arises from crack growth mechanisms and essentially blunts the crack, creates a reversed cyclic plastic zone, and induces shear along the crack flanks, along with the possible generation of wake contact stresses which act on the applied elastic stress field at the boundary of the elastic–plastic enclave surrounding the crack. The paper outlines the development of a meso-scale model of the elastic stress field around a growing crack that explicitly incorporates these interaction effects. The outcome is a modified crack tip stress intensity factor that includes some aspects of the magnitude of plastic wake-induced crack tip shielding and which the authors propose has the potential to help resolve some long-standing controversies associated with plasticity-induced closure. A full-field approach is developed for stress using photoelasticity and also for displacement using digital image correlation.

Full-Field Modelling of Crack Tip Shielding via the ‘Plastic Inclusion’ Concept

This paper presents an outline of the development, verification and application of a new model of crack tip stress fields in the presence of a plastic enclave around a growing fatigue crack. The approach taken rests on capturing the effects of this ‘plastic inclusion’, comprising the crack tip and crack wake plastic zones, via elastic stress distributions applied at the elastic-plastic boundary. The model is therefore independent of the mechanisms of plastic deformation and potentially applicable to a variety of materials. A Muskhelishvili complex potential extension to the Williams crack tip stress field is found for four stress parameters representing a K-stress, a T-stress, a crack retardation stress and a compatibility-induced shear stress at the elastic-plastic boundary. This model is validated via full field fitting to photoelastic stress fringe patterns, obtained from epoxy resin and polycarbonate specimens. It has also been extended to the strain fields measured in digital image correlation techniques, which allows its application to metallic alloys.

Synchrotron diffraction investigation of the distribution and influence of residual stresses in fatigue

ABSTRACTThis paper presents some results obtained from synchrotron diffraction investigations into two somewhat related areas of interest to the fatigue community. Firstly, the influence of fatigue cycling on the distribution and magnitude of residual strains and stresses and, secondly, the residual strains and stresses engendered around a growing fatigue crack. Its main premise is that modern tools such as automated synchrotron strain scanning offer the potential for more complete insight into the distribution of residual strains and stresses and their influence on fatigue performance. The first part of the work was accomplished using friction‐stir welded (FSW) and metal‐inert gas (MIG) welded specimens. The particular interest in these specimens was obtaining detailed knowledge regarding as‐welded variation in residual stresses between specimens, the location of peak values relative to local microstructure and stress concentrations, and of their modification during fatigue cycling. Such information may indicate a route forward to the selection of welding process parameters for optimised fatigue performance. The second part of the work considered an established fatigue crack in a compact tension (CT) specimen and examined the ability of synchrotron diffraction to characterize the stresses associated with the plastic enclave around a fatigue crack. This work is of interest in the context of better knowledge of crack‐tip shielding by plasticity‐induced closure and its incorporation into life prediction methodologies.

Characterisation of plasticity-induced closure––crack flank contact force versus plastic enclave

This paper presents some results from a totally new and powerful fusion between automated, digital photoelastic techniques and mathematical analysis of a crack experiencing closure. In essence, real-time photoelastic stress field data is acquired and fitted to a Muskhelishvili complex potential model of a loaded crack experiencing closure. The fit entails optimisation of multiple variables via a memetic algorithm, which combines a genetic algorithm and a local search. From observations made in this work, it is proposed that the plastic enclave around a crack tip will shield the crack from the full influence of the applied stress field. Furthermore, the effects of this ‘back stress’ are overcome by the applied tensile load in a way that, often, cannot be readily correlated with crack contact length, wake contact force, or with compliance.

Role of crack tip plasticity in fatigue crack growth

Abstract The effect of plasticity ahead of the crack tip as well as behind the crack tip (crack wake plasticity) on the crack tip driving force is examined using a dislocation model. The plastic zone is approximated by a superdislocation, and linear elasticity is assumed. Dislocation effects are computed using the Lin–Thomson equations. The error involved in the superdislocation approximation is shown to be small. Results indicate that the plasticity ahead of the crack tip induces a large retarding force which a crack must overcome for it to grow. The existence of a threshold in K max for fatigue crack growth as illustrated by the unified two-parameter approach can be related to this crack growth resistance. The plasticity behind the crack tip. however, has a negligible effect on the crack tip driving force and therefore has no effect on the K max threshold. Overload effects, underload effects and fatigue crack growth resistance with increasing K are all relatable to the internal stresses arising from the dislocations in the plastic zone. The two thresholds K max, th and ΔK th in the unified approach can be related to the effects of monotonic and cyclic plastic zones. Since the effects of plasticity in the wake are negligible, plasticity-induced closure due to crack wake plasticity is also negligible from the dislocation point of view. A three-zone approximation for the plastic enclave around crack tip is shown to be adequate for the description of the role of plasticity in the crack tip driving force.

An efficient procedure for modelling limited plastic flow

A degree of plasticity is often tolerated at stress raising features in severely loaded, nominally elastic, components. Conventionally, the methods available for analysis are the finite element method (FEM) or an approximate notch root plastic strain method. The method introduced here is based on the idea of distributing dislocations to form a perturbation on an elasticity solution to solve the problem for an elastic—perfectly plastic material in transverse plane strain. Specialized kernels are used to satisfy exactly the far field boundary conditions and those at the stress raiser, so that only the small plastic enclave of material need be discretized. The method is seen to follow the incremental nature of the problem and to take into account the stress redistribution in plasticity. The problem of a circular hole under remote tension is solved and good agreement with an FEM analysis of a similar problem is observed.

Photo-electrochemical imaging of hydrogen-induced damage in stainless steel

Blisters and their surrounding crack-tip areas in AISI 304 stainless steel have been imaged by Scanning Photo-Electrochemical Microscopy (SPEM), a technique providing photo-electrochemical images of hydrogen trapping and detrapping into blisters in real time, in situ and in continuous under hydrogen charging. The increased hydrogen concentration has also been imaged in the plastic enclave at the crack tip around a blister during its growth. The images acquired in time sequence can be examined as a single frame or assembled in a 2D or 3D movie, both in grey scale or false colour.

Investigation by scanning electron microscope of the effect of geometry and loading mode on blunting of copper sheets

Ductile blunting and fracture under conditions of plane stress in metals are described by two main phases: static crack growth, and slow crack propagation. In the first phase the crack tip is deformed in an elastic-plastic mode, the main characteristics of which are the formation of the plastic enclave around the crack tip, and the evolution of blunting. In the second phase the crack propagates through expansion and coalescence of microvoids and microdefects developed at the vicinity of and in front of the crack tip. Ductile blunting under plane-stress conditions in metallic plates was studied, and the influence of the geometry and the mode of loading specimens was defined. This was achieved by interrelating the amount of crack opening displacement at its tip, and its comparable effect of the crack tip advance displacement. The experimental study was executed in a scanning electron microscope with thin specimens under dominating plane-stress conditions. The mechanism of development of ductile blunting up to the point of initiation of slow crack propagation was interrelated with these characteristic quantities.

An elasto-plastic finite element and experimental study of the ironing process

This paper applies the incremental finite-element method of elasto-plastic large deformation analysis to the ironing process. In addition, an experimental test of the ironing process has been performed to verify the theoretical formulation. The paper is divided into two parts. The first part involves deriving the load correction and friction correction matrices which are indispensable for surface traction rate equilibrium in the updated Lagrangian formulation, following which the preparation and procedure of the experimental work is described. The second part involves numerical simulation and a comparison of the results of the numerical model with those of the experiment. The finite-element calculations also predict the forming load, the stress distribution, the plastic enclave, and the deformation history. The comparison shows good agreement between the load-displacement relations of the experiment and the finite-element predictions.

SEM investigations of slip-line fields around blunted cracks under mixed-mode conditions

The slip-line field around the tips of cracks was studied using extensive experimental evidence with electron scanning microscopy. Thin and thick tension specimens made of polycarbonate were edge-cracked ensuring predominant conditions of either plane stress or plane strain. The evolution of blunting and of the creation of the respective slip-line field in the intermediate phase between blunting and initiation of slow propagation of the crack were studied under a continuously increasing loading mode. It was shown that blunting depends on the type of stress state (plane stress or plane strain), on the mode of loading (mode I, mixed mode), and on the ductility of the material. Three different types of blunting were detected, the already known round-nosed and flat-nosed modes and, furthermore, an intermediate type of cornered and rounded-off front of the crack. The characteristic properties of these types are presented. The slip-line fields accompanying the phenomenon of blunting and indicating the initiation and evolution of the plastic enclaves were detected in all types of loading and specimens using the brittle-coating technique and its variations. It was shown that not only the plastic enclaves developed during this step of loading but also the significant elastic components of stresses influence the mode of development of the respective slip-line yielding a combined type corresponding in between the Rice-Johnson field for plane strain and the Theocaris field for plane stress.

Dependence of crack growth initiation on the form of the stress-strain diagram of the material in tension

The problem of growth of a crack in a plate with extensive inelastic deformation was studied by the strain energy density theory. Considered was a rectangular plate with a center through the thickness crack subjected to a uniform stress perpendicular to the crack plane. The stress, deformation and strain energy density fields of the plate were determined by a finite element code based on the incremental theory of plasticity and the von Mises yield criterion. A host of true stress-true strain diagrams representing a variety of aluminum alloys with different degrees of ductility and strain-hardening were considered in order to study the influence of material behavior on crack growth. The critical stress and the plastic enclaves at the onset of crack extension were determined for the various materials considered. From the present study the dependence of these quantities on the mechanical behavior of the material of the plate was clearly established.

FATIGUE CRACK TIP STRAINS IN 7075‐T6 ALUMINUM ALLOY

Abstract— The plastic enclave surrounding a fatigue crack in a 7075‐T6 aluminum alloy specimen is studied using moiré interferometry. Two distinct plastic zones are identified from inspection of moiré interferometric fringe patterns. The sizes and shapes of the monotonic and the cyclic plastic zones are correlated with previous theoretical and experimental results. Live load strain distributions in the plastic enclave are computed from high sensitivity (0.417 micron per fringe) full‐field in‐plane displacement contour maps. Comparison with theoretical and experimental strain distributions are included.

Displacement constraints of the faces of internal cracks due to pure shear

An analysis of the displacement field along the lips of an internal crack in an infinite elastic plate, submitted to pure shear, was undertaken, based on the exact solution. It was shown that the in-plane components of displacement of the lips of the crack consist of: (i) a linear term, normal to the initial axis of the crack, which brings this axis to its effective position. The angle λ formed by this axis and the initial axis of the crack has a tangent given by tan λ = 2σ∞ E , where σ ∞ is the normal stress applied to the plate at infinity and E the elastic modulus of the material, and (ii) a parallel to the initial axis component of displacement, which is proportional to the square of the distance from the tip of the crack. This component for pure shear is always negative, making the lips of the crack overlap each other. If to these in-plane displacements the out-of-plane component is added, the topography of the lips of the crack in pure shear is presenting a ravine with negative slopes, which terminates to two hills around the crack tips, which are sliced in halves along the crack-axis. Either half of each hill is replaced by its mirror surface, relative to the undeformed lateral faces of the plate. It was shown that the overlapping of lips starts with the application of any shearing load and develops up to an eventual creation of plastic enclaves at the tips of the crack. Conditions for zero relative displacement between the respective lips were established, which consist in adding a complementary lateral tensile load, whose magnitude depends on the applied load to the plate.

Path dependent nature of fatigue crack growth

Fatigue crack propagation is an inherently nonlinear phenomena governed by the material response to the load history. The accurate prediction of fatigue crack growth necessitates the modelling of the irreversible material damage in the neighborhood of the crack tip region. In this investigation, a two-dimensional center-cracked panel undergoing cyclic applied loading is analyzed to address the load history or path-dependency of fatigue crack growth. The crack growth process is simulated by predicting a series of crack growth steps which are assumed to occur when the material elements ahead of the crack tip accumulate a critical amount of stored strain energy density, ( dW/ dV) c . It is shown that the fatigue process is very sensitive to the choice of growth step size made in the analysis. The existing crack propagation prediction schemes based on linear elasticity are applied to the results and their inadequacies discussed. Crack growth predictions based on the nonlinear stress analysis and the Strain Energy Density Failure Criterion produce physically realistic results and also provide a method for determining the range of applicability of the linear growth laws (which are more practical for design usage). Final failure of the specimen is predicted when the strain energy density factor, S, reaches a critical value, S c ( dW/ dV) c and S c are material constants, independent of the loading and geometry. Thus, the fatigue process is characterized by these two material parameters. The crack tip yield zones (or plastic enclaves) are also shown to demonstrate the extent and influence of plasticity.

Dugdale models for two collinear unequal cracks

In this paper the Dugdale model is applied to determine the plastic zones developed in the case of two collinear and unequal cracks within an homogeneous, Isotropic, elastic-perfectly plastic infinite plate. The cracks are subjected to a normal loading, acting at the infinity. It was assumed that the type of plastic deformation was of the cross-slip mode creating narrow plastic enclaves, case for which the original Dugdale model for a single crack is valid. The case of plastic coalescence between the collinear cracks was derived as a special case of the general problem.