In‐plane and out‐of‐plane constraint parameters along a three‐dimensional crack‐front stress field under creep loading

Full‐field three‐dimensional (3D) numerical analyses was performed to determine in‐plane and out‐of‐plane constraint effect on crack‐front stress fields under creep conditions of finite thickness boundary layer models and different specimen geometries. Several parameters are used to characterize constraint effects including the non‐singular T‐stresses, the local triaxiality parameter, the T_z ‐factor of the stress‐state in a 3D cracked body and the second‐order‐term amplitude factor. The constraint parameters are determined for centre‐cracked plate, three‐point bend specimen and compact tension specimen. Discrepancies in constraint parameter distribution on the line of crack extension and along crack front depending on the thickness of the specimens have been observed under different loading conditions of creeping power law hardening material for various configurations of specimens.     

Induced out‐of‐plane mode at the tip of blunt lateral notches and holes under in‐plane shear loading

As it is well known the Poisson's effect in a cracked plate subjected to anti‐symmetric plane loading leads to the generation of a coupled out‐of‐plane singular mode. Recent theoretical and numerical analyses have shown that this effect is present also in plates weakened by sharp V‐notches and might play a role in failure initiation phenomena of notched plates subjected to Mode II loading, especially in the presence of a large notch opening angle. Dealing with blunt notches with a large notch radius, and not just with sharp notches, the presence or not of an out‐of‐plane mode does not appear to have been systematically investigated in the past. The main aim of this work is to confirm the existence of the stress field associated with the out‐of‐plane mode (Mode O) and to describe its main features in the presence of a notch radius significantly different from zero. The analyses include U‐notches, as well as circular and elliptic holes. The strain energy density in a 3D control volume is utilized to identify the most critical zone (with respect to failure initiation) through the plate thickness at the notch tip.     

On improved crack tip plastic zone estimates based on T‐stress and on complete stress fields

Cracked ductile structures yield locally to form a plastic zone (pz) around their crack tips, which size and shape controls their structural behaviour. Classical pz estimates are based solely on stress intensity factors (SIF), but their precision is limited to very low σ_n/S_Y nominal stress to yield strength ratios. T‐stresses are frequently used to correct SIF‐based pz estimates, but both SIF and SIF plus T‐stress pz estimates are based on truncated linear elastic (LE) stress fields that do not satisfy boundary conditions. Using Griffith's plate complete LE stress field to avoid such truncated pz estimates, the influence of its Williams’ series terms on pz estimation is evaluated, showing that T‐stress improvements are limited to medium σ_n/S_Y values. Then, corrections are proposed to introduce equilibrium requirements into LE pz estimates. Finally, these improved estimates are compared with pz calculated numerically by an elastic–plastic finite element analysis.     

Reduction of measured toughness due to out‐of‐plane constraint in ductile fracture of aluminium alloy specimens

It is generally believed that a lower bound on the fracture toughness of a material is obtained from a standard test, particularly in metals where yielding occurs prior to fracture. The understanding is that in such a test the material around the crack tip is highly constrained hence reducing the extent of yielding. In this paper, we report the results of fracture tests where a tensile load is applied to a biaxial aluminium alloy specimen in the direction parallel to the crack front in addition to the fracturing load normal to the crack surface. We show that in this case a lower fracture toughness is measured than that obtained from a standard test. Indeed, for the highest value of tensile load used in our tests the J‐integral at fracture was half the value measured in a standard test. It is also shown that the volume of the plastic region can be used to measure the effect of constraint, irrespective of the manner in which the constraint arises. This approach suggests an even lower fracture toughness may be obtained than that measured here in certain loading conditions.     

The effect of T‐stress on crack‐tip plastic zones under mixed‐mode loading conditions

In this paper, the influence of T‐stress on crack‐tip plastic zones under mixed‐mode I and II loading conditions is examined. The crack‐tip stress field is defined in terms of the mixed‐mode stress intensity factors and the T‐stress using William's series expansion. The crack‐tip stress field is incorporated into the Von Mises yield criteria to develop an expression that determines the crack‐tip plastic zone. Using the resultant expression, the plastic zone is plotted for various combinations of mode II to mode I stress intensity factor ratios and levels of T‐stress. The properties of the plastic zone affected by T‐stress and mixed‐mode phase angle are discussed. The observations obtained on plastic zones variations are important for further fatigue and fracture analyses for defects in engineering structures under mixed‐mode loading conditions.     

Effect of constraint on void growth near a blunt crack tip

The growth of a single cylindrical hole ahead of a blunt crack tip was studied using large deformation finite element analysis in three-point bend specimens with different precrack depth. The effect of small second phase particles was taken into account by incorporating Gurson's constitutive equation. The effects of strain hardening and the initial distance from the hole to the crack tip were also investigated. The results show that the variation of crack tip opening displacement with load is not sensitive to constraint level. The effects of constraint on the growth of hole and ductile initiation toughness are diminished with decreasing initial distance from the hole to the blunt crack tip. This revised version was published online in August 2006 with corrections to the Cover Date.     

Fatigue thresholds of holed components under in‐phase and out‐of‐phase torsional and axial loadings

The resistance‐curve (R‐curve) method was applied to the prediction of the fatigue thresholds of notched components under in‐phase and out‐of‐phase combinations of cyclic torsion and axial loadings. The prediction was compared with the experimental data obtained from thin‐walled tubular specimen of medium‐carbon steel with a hole. The stress was completely reversed and the mean stress was zero. The crack was nucleated at the position of the maximum range of the circumferential stress on the periphery of a hole, and propagated almost straight for all cases examined. The experimental data of the thresholds for crack initiation and fracture agreed well with the predictions for in‐phase and for out‐of‐phase loadings with 45° phase difference. For out‐of‐phase loading with 90°, the threshold for fracture was close to the crack initiation limit, because of the reduction of crack closure due to crack face rubbing by mode II shear cycling.     

The effect of T-stress on plane strain dynamic crack growth in elastic–plastic materials

In this paper, the effects of T‐stress on steady, dynamic crack growth in an elastic–plastic material are examined using a modified boundary layer formulation. The analyses are carried out under mode I, plane strain conditions by employing a special finite element procedure based on moving crack tip coordinates. The material is assumed to obey the J₂ flow theory of plasticity with isotropic power law hardening. The results show that the crack opening profile as well as the opening stress at a finite distance from the tip are strongly affected by the magnitude and sign of the T‐stress at any given crack speed. Further, it is found that the fracture toughness predicted by the analyses enhances significantly with negative T‐stress for both ductile and cleavage mode of crack growth.     

Effects of short cracks produced at blunted pre-crack tip on stress and strain distributions

The present work investigates problems: (1) How are the plastic strain and the stress (triaxiality) re-distributed after a short crack initiated, extended and blunted at the pre-crack tip? (2) How do the above changes put a crucial effect on the triggering of the cleavage fracture? Based on the previous observations of configuration changes and fracture surfaces of pre-crack tips, Finite element method (FEM) simulations of a short crack initiated, extended and blunted at a pre-crack tip and calculations of distributions of stress, strain and triaxiality are carried out for 3PB pre-cracked HSLA steel specimens tested at -130^°C. The results reveal that: as long as the fatigue pre-crack is only blunted, in its vicinity a region where the accumulated strain is sufficient to nucleate a crack, and a region where the stress (triaxiality) is sufficient to propagate a crack nucleus are separated by a distance. The nucleated crack cannot be propagated and the cleavage fracture cannot be triggered. While a short crack produced at the fully blunted fatigue pre-crack, the strain retains, the stress (triaxiality) is rebuilt. An initiated and significantly extended and then blunted short crack makes a tip configuration, which on one hand is much sharper than that of the fully blunted original pre-crack tip, on other hand is wide enough to spread its effects into the high stress covered region. This sharpened crack tip configuration re-builds a ‘sharper’ distribution of stress (triaxiality) and makes two regions metioned above closer. Finally the two regions overlap each other and a cleavage crack can be initiated and propagated at a distance ahead of the blunted fatigue pre-crack.     

Steady-state crack growth and fracture work based on the theory of mechanism-based strain gradient plasticity

Mode I steady-state crack growth is analyzed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by the mechanism-based strain gradient (MSG) plasticity theory [J. Mech. Phys. Solids 47 (1999) 1239, J. Mech. Phys. Solids 48 (2000) 99]. The distributions of the normal separation stress and the effective stress along the plane ahead of the crack tip are computed using a special finite element method based on the steady-state fundamental relations and the MSG flow theory. The results show that during the steady-state crack growth, the normal separation stress on the plane ahead of the crack tip can achieve considerably high value within the MSG strain gradient sensitive zone. The results also show that the crack tip fields are insensitive to the cell size parameter in the MSG theory. Moreover, in the present research, the steady-state fracture toughness is computed by adopting the embedded process zone (EPZ) model. The results display that the steady-state fracture toughness strongly depends on the separation strength parameter of the EPZ model and the length scale parameter in the MSG theory. Furthermore, in order for the results of steady crack growth to be comparable, an approximate relation between the length scale parameters in the MSG theory and in the Fleck-Hutchinson strain gradient plasticity theory is obtained.     

A three‐dimensional stress field solution for pointed and sharply radiused V‐notches in plates of finite thickness

By making use of the generalized plane strain hypothesis, an approximate stress field theory has been developed according to which the three‐dimensional governing equations lead to a system where a bi‐harmonic equation and a harmonic equation should be simultaneously satisfied. The former provides the solution of the corresponding plane notch problem, and the latter provides the solution of the corresponding out‐of‐plane shear notch problem. The system can be applied not only to pointed three‐dimensional V‐notches but also to sharply radiused V‐notches characterized by a notch tip radius small enough. Limits and degree of accuracy of the analytical frame are discussed comparing theoretical results and numerical data from FE models.     

Digital image correlation measurement of near‐tip fatigue crack displacement fields: constant amplitude loading and load history effects

Recent work by de Matos and colleagues employed digital image correlation to measure near tip displacement fields for fatigue cracks in 6082 T6 aluminium alloy. The main focus of this work was to directly measure fatigue crack closure, but the measurements can also be used to examine conditions at and ahead of the crack tip. In this paper, the results are re‐analysed and compared to two crack‐tip deformation models. The first assumes simple elastic deformation (according the Westergaard solution). This allows the history of crack‐tip stress intensity to be examined. Reasonable agreement with the elastic model is obtained, although there is a residual stress intensity caused by the plastic wake, which gives rise to crack closure. The second model examined is a simple elastic–plastic assumption, proposed by Pommier and colleagues. This can be applied to constant amplitude loading, although the results obtained here are very similar to the elastic case. A slightly more complex load case (a single overload in an otherwise constant amplitude variation of load) gives a much more complicated crack‐tip history. Here, the importance of crack‐tip plastic displacement, represented by the second term in Pommier's model becomes much clearer. Load history effects are captured by the residual value of this term and its associated displacement fields as well as by stress intensity factor. The implications for further modelling and experimental work are discussed.     

Effect of biaxial loads on elastic-plastic <Emphasis Type="Italic">J</Emphasis> and crack tip constraint for cracked plates: finite element study

Based on detailed two-dimensional (2-D) and three-dimensional (3-D) finite element (FE) analyses, this paper attempts to quantify in-plane and out-of-plane constraint effects on elastic-plastic J and crack tip stresses for a plate with a through-thickness crack and semi-elliptical surface crack under positive biaxial loading. For the plate with a through-thickness crack, plate thickness and relative crack length are systematically varied, whereas for the plate with a semi-elliptical surface crack, the relative crack depth and aspect ratio of the semi-elliptical crack are systematically varied. It is found that the reference stress based approach for uniaxial loading can be applied to estimate J under biaxial loading, provided that the limit load specific to biaxial loading is used, implying that quantification of the biaxiality effect on the limit load is important. Investigation on the effect of biaxiality on the limit load suggests that for relatively thin plates with small cracks, in particular with semi-elliptical surface cracks, the effect of biaxiality on the limit load can be neglected for positive biaxial loading, and thus elastic-plastic J for a biaxially loaded plate could be estimated, assuming that such plate is subject to uniaxial load. Regarding the effect of biaxiality on crack tip stress triaxiality, it is found that such effect is more pronounced for a thicker plate. For plates with semi-elliptical surface cracks, the crack aspect ratio is found to be more important than the relative crack depth, and the effect of biaxiality on crack tip stress triaxiality is found to be more pronounced near the surface points along the crack front.     

Intrinsic material length,Theory of Critical Distances and Gradient Mechanics: analogies and differences in processing linear‐elastic crack tip stress fields

The Theory of Critical Distances (TCD) is a bi‐parametrical approach suitable for predicting, under both static and high‐cycle fatigue loading, the non‐propagation of cracks by directly post‐processing the linear‐elastic stress fields, calculated according to continuum mechanics, acting on the material in the vicinity of the geometrical features being assessed. In other words, the TCD estimates static and high‐cycle fatigue strength of cracked bodies by making use of a critical distance and a reference strength which are assumed to be material constants whose values change as the material microstructural features vary. Similarly, Gradient Mechanics postulates that the relevant stress fields in the vicinity of crack tips have to be determined by directly incorporating into the material constitutive law an intrinsic scale length. The main advantage of such a method is that stress fields become non‐singular also in the presence of cracks and sharp notches. The above idea can be formalized in different ways allowing, under both static and high‐cycle fatigue loading, the static and high‐cycle fatigue assessment of cracked/notched components to be performed without the need for defining the position of the failure locations a priori. The present paper investigates the existing analogies and differences between the TCD and Gradient Mechanics, the latter formalized according to the so‐called Implicit Gradient Method, when such theories are used to process linear‐elastic crack tip stress fields.     

Influence of non‐proportional bending with torsion on fatigue life of 10HNAP steel within the range of crack initiation and propagation

The paper presents a precise analysis of the influence of non‐proportional loading of specimens on fatigue life during initiation and propagation of fatigue cracks. Simulation of the fatigue life of specimens was based on relations describing propagation rate of the fatigue cracks. The Paris and Forman relations were applied; they were integrated after previous introduction of relationships for the equivalent range of the stress intensity factor ΔK_eq and including the phase shift angle ? between amplitudes of the bending moment and the torsional moment. Under bending with torsion, range of the equivalent stress intensity factor ΔK_eq includes ranges of stress intensity factors for loading modes I and III, i.e. ΔK_I and Δ K_III. The performed tests of 10HNAP constructional steel under cyclic bending with torsion allowed us to determine the influence of the phase shift angle ? on the fatigue life. It has been proved that increase of the phase shift angle from ?= 0° to ?= 60° and the ratio of amplitude of the bending moment M_ag to amplitude of the torsional moment M_as equal to 1.33, 2 and 4 cause increase of the fatigue life of the tested specimens. The maximum increase of the fatigue life of specimens made of 10HNAP steel was 73% (M_ag/M_as= 2, ?= 45°).