X-ray diffraction studies on fatigue crack plastic zones developed under plane strain state conditions

An overview of the X-ray fractography technique, as performed on fatigue crack surfaces of several steels and Al-alloys under different loading conditions, is presented. The plastic zone sizes of fatigue cracks, for plane strain conditions, are measured from the in-depth distribution of residual stresses and X-ray diffraction peak broadening. In addition to the usual monotonic plastic zone size determination methodology, a model for the estimation of the reverse plastic zone size was established in the case of fatigue softening materials. Monotonic and cyclic plastic zone sizes are related to the stress intensity by, respectively, r_{pm = α (Kmax} /σ_ys )² and r_{pc = α} (ΔK/2σ′ys )2. The α-value, in the monotonic plastic zone size equation, increases as the yield strength of the material increases, following the relationship α = 0.196 [σ_ys /(129 + 0.928σ_ys )]2. The α-value versus σ_ys evolution has been understood through the influence of the hardening rate of materials on the plastic zone size. X-ray fractography has been applied to actual failure analyses to predict some aspects of the actual loadings.     

Fatigue crack growth retardation under constant amplitude and variable mean stress

Fatigue crack growth retardation under stress spectra with constant amplitude and variable mean stress, respectively, was studied. Flat specimens with a central through crack were tested under tension-tension load. The specimens were made with low alloy steel 4 mm thick, with yield strength of 625 Mpa and ultimate tensile strength of 784 MPa. Overload affected crack length increments Δa¹ were studied. The best correlation was obtained between monotonic plane stress plastic zone size 2r_y and Δa¹. The cyclic plastic zone size 2r_pc correlated with crack length increment of minimum crack growth rate after overload. Forman's equation and Willenborg's model of fatigue crack growth retardation were used for theoretical prediction of fatigue crack propagation life. The best agreement between theoretical and experimental results was also obtained using monotonic plastic zone size instead of monotonic plastic zone radius or cyclic plastic zone size. The agreement is reasonably good, even though in the case of one spectrum, cracks were arrested for several thousand cycles.     

Determination of valid R-curves for materials with large fracture toughness to yield strength ratios

Crack growth resistance curves are derived from a generalised theory of quasi-static crack propagation due to Gurney and Hunt. Both the subcritical and continuous cracking regions are investigated, where the fracture toughness of the material may depend on the cracking rate, the reacting environment at the crack tip and the mode of fracture. Precise conditions for stability of the spreading crack relative to chosen constraints of either a displacement- or load-controlled machine are formulated. Cracking of sheet materials with high fracture toughness and low yield stress, (e.g. (K/ _y )² > 200 mm), which do not satisfy certain size requirements, is often complicated by generalised yielding at regions remote from the crack tip. Complete R-curves for such materials cannot be established with conventional testpieces in the laboratory. The present paper adopts a new experimental technique [1] where a laboratory size reinforcement rig attached to the testpiece eliminates all irreversibilities caused by generalised yielding. Valid fracture toughness values and crack growth resistance curves are thereby determined, irrespective of the amount of elastic and plastic deformations occurring at the crack tip. Successful R-curve experiments are described for fracture in a few ductile and tough materials such as 7075-T3. and 1100-0 aluminium alloys, and a low carbon steel. Comparison is made with other published R-curves, and the influence of sheet thickness and (K _1c / _y ) ratio on the geometry of R-curves is investigated. A simple relationship for R-curves is suggested, viz.: R = R ₀ + (L) ^p , where, it seems, R ₀can be identified with the plane strain toughness (i.e. R ₀ = G _1c = K _1c ² /E(1 - v ²)1/2). A possible reason for this unexpected result is given in the paper. Useful estimates of K _lcmay thus be available from thin sheet tests.Paper presented in part at the 11th Annual Meeting of the Society of Engineering Science, November 11–13, 1974, Duke University, Durham, N.C., USA.     

Influence of hydrogen on the crack resistance of 10Kh15N27T3V2MR steel

In high ranges of pressure and temperature, hydrogen reduces the thresholds ∆K _th, cyclic fracture toughness K _fc , and short-term static crack resistance K _c of 10Kh15N27T3V2MR austenitic dispersion-hardened steel. Conditions of plane deformation and, correspondingly, conditions of determination of the characteristic K _Ic are maintained in testing in the range 293 – 483 K of compact specimens 20 mm thick after their preliminary hydrogenation to a hydrogen content of 8 ppm. Low-cycle fatigue and sizes of the plastic zone under static crack resistance are most sensitive to hydrogen (and decrease by 80 and 70%, respectively, against those in helium), and the cyclic crack resistance parameters ΔK _th and K _fc (decrease by 25%) are least sensitive to hydrogen. The static crack resistance K _c and the percentage reduction in the cross-sectional area ψ in short-term tension are reduced by 50%.     

The effect of microstructures on fatigue crack growth in Q345 steel welded joint

It is a traditional that the fatigue crack growth behavior is sensitive to microstructure in threshold regime, while it is sensitive to R‐ratio in Paris regime. Fatigue test is carried out for welded joints of a Q345 steel where the compact tension specimens with 3.8 and 12.5 mm thickness are used, and comparisons of fatigue crack growth behavior between base metal and a few different locations in the welded joint are considered in Paris regime. Welding residual stresses are removed by heat treatment to focus the study on the microstructural effect. It is shown that fatigue crack growth rate (FCGR) in the base metal is not sensitive to R‐ratio, but the FCGR increases in the overheated zone, the fusion zone and the weld metal zone with R‐ratio increasing. To the low R‐ratio, FCGR in the three zones is smaller than that in the base metal, but they approximate the same with base metal under the high R‐ratio. The mechanism of fatigue crack growth is analyzed through crack path in microstructures and SEM fractograph. The coarse‐grained ferrite in the base metal is of benefit to relaxation of the average stress at the crack tip, and the fatigue crack growth predicts branching and deflection within above different locations in the welded joint. These tortuous crack paths with crack branching and deflection will promote crack closure as well as crack‐tip stress shielding and then resulted in higher crack growth resistance.     

FATIGUE BEHAVIOR OF A RAIL STEEL

The fatigue behavior of a hot-rolled, control-cooled, plain carbon eutectoid rail steel has been characterized. The data include monotonic and cyclic stress-strain curves, low cycle fatigue data and near-threshold fatigue crack growth rate behavior in air and in vacuo. The effects of environment and mean stress on the near-threshold fatigue crack growth rates of rail steel are significant. At a low stress ratio (R), ΔK_o is lower in vacuum (7 MPa √m) than in moist air (10 MPa √m). At high R, ΔK_o is higher in vacuum (6 MPa √m) than in air (4 MPa √m). The beneficial effect of moist air on FCGR at low ΔK and low R is attributed to an increase in closure due to fracture surface roughness and oxide film.     

Effect of strain rate on the geometry of the plastic zone near a Mode II crack tip. Parametric analysis

We present an approximate approach to assessment of the effect of the strain rate () on the size (r_p) and shape of the plastic zone near a transverse shear crack tip. The analysis is based on including the parameters of the stress—strain diagram for the material as functions of in the quasistatic solution for r_p. We propose a two-parameter model for taking into account the effect of the magnitude of the applied shear stresses on the geometry of the plastic zone. For a crack in mild steel, we obtain estimates of the evolution of the plastic zone as the strain rate varies within the range 10^–4–10³ sec^–1.Translated from Problemy Prochnosti, No. 3, pp. 46–55, March, 1995.     

Influence of test parameters on the measurement of the essential work of fracture of zinc sheets

The Essential Work of Fracture (EWF) concept is used to characterize the fracture of thin plates of a zinc alloy. The consistency and applicability of the EWF approach are discussed. The successive stages of the fracture process were studied: the evolution of the shape of the crack tip was observed with a scanning electron microscope, the shape of the plastic zone and the evolution of necking in the ligament ahead of the crack tip were measured using a laser profilometer and the onset of cracking in the ligament was detected by means of a TV camera coupled with acoustic emission recording. The influence of both test parameters and material parameters on the Essential Work of Fracture (W _e ) and on the CTOD (_c) are elucidated. The effects of specimen geometry, deformation rate, texture and grain size are especially investigated. The main advantages and drawbacks of the EWF method are highlighted.     

LIMITATIONS ON THE USE OF THE STRESS INTENSITY FACTOR, K, AS A FRACTURE PARAMETER IN THE FATIGUE PROPAGATION OF SHORT CRACKS

Abstract— It is well known that for very short cracks the stress intensity factor K is not a suitable parameter to estimate the stress level over the small but finite Stage II process zone activation region of size r_s near the crack tip, within which crack growth events take place. A critical appreciation of the reasons for the limitations on the applicability of ΔK as a fatigue crack propagation (FCP) parameter, when the crack length a is of the same order of magnitude or smaller than the size of the ‘fatigue-fracture activation region’, r_s is presented. As an alternative to ΔK the range Δσ_s of the cyclic normal stress at a point situated at the fixed distance s=r_s/2, ahead of the crack tip, inside the fatigue-fracture activation region, is proposed. It is observed that the limitation on the use of ΔK when the crack is short, is mathematical (and not physical) but this inconvenience is easily circumvented if the stress Δσ_s at the prescribed distance is used instead of ΔK since nowadays Δσ_s can be obtained numerically by using finite element methods (FEM). It follows that the parameter Δσ_s is not restricted by the mathematical limitations on ΔK and so it would seem that there is, a priori, no reason why the validity of the parameter Δσ_s cannot be extended to short cracks. It is shown that if the Paris law is expressed in terms of Δσ_s (πrr_s)^½ instead of ΔK the validity of the modified Paris law can be extended to short cracks. A coherent estimate of the value of the fatigue-fracture activation region r_s is derived in terms of the fatigue limit Δσ_FL obtained from S-N tests and of the threshold value ΔK_th obtained from tests on long cracks where both relate to Stage II crack growth that ends in failure, namely, r_s= (ΔK_th/Δσ_FL)²/π. An overall, threshold diagram is presented based on the simple criterion that, for sustained Stage II FCP, Δσ_s must be greater than Δσ_FL. The study is based on a simple continuum mechanics approach and its purpose is the investigation of the suitability of both ΔK and Δσ_s to characterise the crack driving force that activates complex fracture processes at the microstructure's scale. The investigation pertains to conditions that lead to the ultimate failure of the component at values of Δσ_s > Δσ_FL.     

Effects of an overload event on crack closure in 3-D small-scale yielding: finite element studies

This paper describes the effects of a single overload event, within otherwise constant amplitude cycles, on the plasticity‐induced closure process for mode I fatigue crack growth in the small‐scale yielding (SSY) regime. The 3‐D finite element (FE) analyses extend the initially straight, through‐thickness crack front by a fixed amount in each load cycle, using a node release procedure. Crack closure during reversed loading occurs when nodes behind the growing crack impinge on a frictionless, rigid plane. A bilinear, purely kinematic hardening model describes the constitutive response of the elastic–plastic material. Extensive crack growth in the analyses, both before and after the overload, allows the crack to grow out of the initial and the post‐overload transient phases, respectively. The work presented here shows that the large plastic deformation in the overload cycle reduces the crack driving force through enhanced closure. Further, the residual plastic deformations due to the overload cause a disconnected pattern of closure in the wake long after the crack front passes through the overload plastic zone. The computational studies demonstrate that the 3‐D scaling relationship for crack opening loads established in our earlier work for constant amplitude cycling (with and without a T‐stress) also holds before, during and after the overload event. For a specified ratio of overload‐to‐constant amplitude loading (R_OL=K^OL_max/K_max) , the normalized opening load (K_op/K_max) at each location along the crack front remains unchanged when the constant amplitude peak load (K_max) , thickness (B) and material flow stress (σ₀) all vary to maintain a fixed value of . The paper concludes with a comparison of the post‐overload response predicted by the 3‐D analyses and by the conventional Wheeler model.     

INFLUENCE OF VARIOUS PARAMETERS ON THE DETERMINATION OF THE FATIGUE CRACK ARREST THRESHOLD Members of the Fatigue Commission of the French Metallurgical Society*

Abstract —This report presents the results of a round robin study on the fatigue crack arrest threshold (δK_th) of 2618 aluminium alloy and AISI 316 steel. The main purpose of this work was to develop a method for the determination of δK_th, and to examine the influence of various test parameters on this threshold. Among the parameters considered, only the load ratio (R) and the environment (vacuum) appear to have a significant influence on very slow fatigue crack growth rates (FCGR). Moreover, while the results obtained with the 316 steel show great scatter, the importance of the adopted procedure is pointed out.     

SHEAR LIPS ON FATIGUE FRACTURES OF ALUMINIUM ALLOY SHEETS SUBJECTED TO BIAXIAL CYCLIC LOADS AT VARIOUS R-RATIOS

An analysis is made of shear lip measurements as observed on fatigue crack surfaces of an aluminium alloy sheet material. It is shown that, for biaxial cyclic loads at stress ratios 1 and various R-ratios, shear lips were controlled by an equivalent intensity factor K_e=K₁F(λ,R). For crack growth in air the shear lip width t_s was approximately proportional to K²_e at t_s < t*_s= 2.5 × 10^?4 m and K⁴_E, at t_s > t*_s where t*_s is the critical value of the shear lip dimension. The initiation of shear lips and the orientation of crack growth for different parameters of the loading cycle are briefly considered in the discussion.     

The importance of compressive stresses on fatigue crack propagation rate

This paper is concerned with the importance of compressive stresses on crack propagation rate. In a previous paper, namely ‘Crack Closure Inadequacy at Negative Stress Ratios’, Int. Journal of Fatigue, 26, 2004, pp. 241–252, was demonstrated the inadequacy of the crack closure concept and ΔK_eff, at a negative stress ratio, R=−1, to predict crack propagation rate. It that paper was verified that, at negative stress ratios, crack closure changes with P_max, for the same R ratio. The main conclusion was about plastic properties and mainly cyclic plastic properties, the Bauschinger effect included, on crack propagation when compressive stresses exist. It was then suggested that in the place of the crack closure concept, another concept based on plasticity should be used to explain fatigue crack propagation.In this paper, instead of working with the same negative R ratio (R=−1), a study on the behavior of crack propagation rate as a function of R ratio, from negative to positive stress ratios, is made. Both the effect of P_max and of R ratio is taken into consideration. Measurements of roughness and of crack opening loads are made, in order to verify their influence on crack propagation rate. Different materials, in order to cover different cyclic plastic properties and different sensitivities to roughness are studied (Ck45-cyclic hardening; Ti6Al4V-cyclic softening, and aluminum, Al 7175-cyclically neutral) are studied. Aluminium alloys and titanium alloys are considered to be sensitive to roughness induced crack closure (RICC) while steels are more dependent on plastic properties (PICC).In this study it is emphasized the importance of the compressive part of the cycle, and of cyclic plastic properties, on crack propagation rate. It is reassessed the inadequacy of crack closure concept and ΔK_eff to describe crack propagation rate, at negative stress ratios. It is also verified that models based solely on extrinsic properties of materials, like da/dN−ΔK or da/dN−ΔK (K_max) should also incorporate intrinsic properties of the materials in order to properly correlate fatigue crack growth.     

Interface fracture analysis of joints with a ductile interlayer

Plane strain problem of an interface crack with two interface shear yield zones and one crack-face contact zone is studied. The plastic yielding of the interlayer is stimulated by the interface shear yield zones and contact zone is included near one tip of the interface crack. An interesting and important phenomenon found in this analysis is that for such an interface crack the applied compressive normal stress can increase the stress intensity factor K ₁ at one of the two crack tips, the size of the crack-face contact zone, and the maximum value of the crack opening, in a combined normal and shear stress field. Examples are given for two pairs of materials used in ceramic-metal brazed joints, Si₃N₄/Ni and Si₃N₄/Incoloy 909.     

Indentation plasticity and fracture of Si3N4 ceramic alloys

The response of a series of one- and two-phase-Si₃N₄ ceramic alloy surfaces to sharp diamond microindentation has been examined by optical and electron microscopy. The microhardness (H), which obeys the load-independent relationH=P/a ² (whereP anda are load and indent size, respectively) is nearly constant within the alloy series, indicating a retention of high covalency at large (Al and O) substitution levels. Indentation results from severe localized plasticity which is characterized by the operation of the dominant dislocation Burgers vectora[0 0 0 1] in the hexagonal lattice. The severe anisotropy in plasticity induces grain-boundary microcracking which is believed to nucleate median cracks which propagate away from the plastic zone on symmetry planes beneath the indenter. The relation between load, median crack size (c) and fracture toughness (K _c) is of the form,K _c=constant (P/c ^3/2) predicted theoretically. Values ofK _c rank correctly with those from notched-beam measurements, but there is uncertainty about the value of the constant.     

Fatigue cracking simulation based on crack closure effects in Al-based sheet materials subjected to biaxial cyclic loads

Fatigue crack growth experiments have been carried out on cruciform specimens in the range of thickness 1.2–10 mm of Al-based alloys, loaded under constant (regular) and variable (irregular) amplitudes of uniaxial and biaxial loads, including sequences of various overloads. Different cases for crack closure effects are considered because of shear lips development, crack-growth direction re-orientation after multiparameters change of cyclic loads, by examining plastic blunting effect at a crack tip during an overload and interaction effects analyzing the crack retardation length and associated parameters together with their relationships. Crack closure effect because of rotation instability of material mesovolumes under biaxial compression–tension has suggested to analyse semi-elliptical cracks. Under biaxial cyclic loads in the range of load ratio-1.4 < λ < +1.5, and R-ratios from 0.05 to 0.8, for frequency variations ?, fatigue striation formation takes place beyond a crack-growth rate close to 4 × 10⁻⁸ m/cycle. The striation spacing and the crack-growth rate increase as the ?-angle of the out-of-phase biaxial loads increases (in the range of ? from 0° to 180°). Cycle loading parameters must be taken into account in order to describe the crack growth period when using a unified method that involves an equivalent stress intensity factor K_e=K_IF(λ,R,?,?). The values of F(λ,R,?,?) are determined. The calculated crack growth period (predicted using F(λ,R,?,?)) in regular and irregular cases of cyclic loads, including material cracking after overloads, is correlated with the experimental data, and the error is of the order of 15%.     

A finite element investigation of quasi-static and dynamic asymptotic crack-tip fields in hardening elastic-plastic solids under plane stress

The asymptotic structures of crack-tip stress and deformation fields are investigated numerically for quasi-static and dynamic crack growth in isotropic linear hardening elastic-plastic solids under mode I, plane stress, and small-scale yielding conditions. An Eulerian type finite element scheme is employed. The materials are assumed to obey the von Mises yield criterion and the associated flow rule. The ratio of the crack-tip plastic zone size to that of the element nearest to the crack tip is of the order of 1.6 × 10⁴. The results of this study strongly suggest the existence of crack-tip stress and strain singularities of the type r ^s (s < 0) at r=0, where r is the distance to the crack tip, which confirms the asymptotic solutions of variable-separable type by Amazigo and Hutchinson [1] and Ponte Castañeda [2] for quasi-static crack growth, and by Achenbach, Kanninen and Popelar [3] for dynamic crack propagation. Both the values of the parameter s and the angular stress and velocity field variations from the present full-field finite element analysis agree very well with those from the analytical solutions. It is found that the dominance zone of the r ^s-singularity is quite large compared to the size of the crack-tip active plastic zone. The effects of hardening and inertia on the crack-tip fields as well as on the shape and size of the crack-tip active plastic zone are also studied in detail. It is discovered that as the level of hardening decreases and the crack propagation speed increases, a secondary yield zone emerges along the crack flank, and kinks in stress and velocity angular variations begin to develop. This dynamic phenomenon observable only for rapid crack growth and for low hardening materials may explain the numerical difficulties, in obtaining solutions for such cases, encountered by Achenbach et al. who, in their asymptotic analysis, neglected the existence of reverse yielding zones along the crack surfaces.     

Fatigue behaviour of friction stir welded AA2024‐T3 alloy: longitudinal and transverse crack growth

The fatigue crack growth properties of friction stir welded joints of 2024‐T3 aluminium alloy have been studied under constant load amplitude (increasing‐ΔK), with special emphasis on the residual stress (inverse weight function) effects on longitudinal and transverse crack growth rate predictions (Glinka's method). In general, welded joints were more resistant to longitudinally growing fatigue cracks than the parent material at threshold ΔK values, when beneficial thermal residual stresses decelerated crack growth rate, while the opposite behaviour was observed next to K_C instability, basically due to monotonic fracture modes intercepting fatigue crack growth in weld microstructures. As a result, fatigue crack growth rate (FCGR) predictions were conservative at lower propagation rates and non‐conservative for faster cracks. Regarding transverse cracks, intense compressive residual stresses rendered welded plates more fatigue resistant than neat parent plate. However, once the crack tip entered the more brittle weld region substantial acceleration of FCGR occurred due to operative monotonic tensile modes of fracture, leading to non‐conservative crack growth rate predictions next to K_C instability. At threshold ΔK values non‐conservative predictions values resulted from residual stress relaxation. Improvements on predicted FCGR values were strongly dependent on how the progressive plastic relaxation of the residual stress field was considered.     

The resistance to crack growth of asbestos cement

The crack resistance of sheet asbestos cement has been characterized in terms of anR-curve which can accomodate effects which often influence the measurement of the critical stress intensity factorK _c. The detection and location of the acoustic emission (AE) obtained from the asbestos cement has shown that it originates from microcracks in a zone just in front of the crack. The size of this zone increases to a maximum during slow propagation of the major crack and afterwards remains of constant size during the final crack growth. The form of theR-curve has been explained in terms of the mechanisms of fracture with the aid of AE and fractography studies. An analytical study has related the experimentalR-curve to a theoreticalR-curve and, hence, to the volume fraction, fibre aspect ratio and the strength of the fibre—matrix interface. It has been shown that the microcracking zone can be considered as a theoretical extension, of about one third of the zone length, to the real crack length.     

Some comments on the geometry dependence of theJ versusc relation for plane strain crack growth

Rice, Drugan, and Sham have recently presented a discussion on the elastic-plastic stress and deformation fields at the tip of a crack growing in an ideally plastic solid under plane strain small-scale yielding conditions. Coupling their asymptotic analysis results with a crack tip opening angle criterion which requires that a constant angle 0 (measured at a characteristic distancer _m behind the tip) be maintained, leads to a differential equation describing crack growth: $$\frac{{dJ}}{{dc}} = \frac{{\sigma _0 \theta }}{\alpha } - \frac{{\beta \sigma _0^2 }}{{\alpha E}}\ln \lgroup {\frac{{eR}}{{r_m }}} \rgroup,$$ wherec = crack length, σ_o = yield strength,E = Young's modulus, andJ denotes the far-field value of theJ integral: (1 ? ν²)K ²/E for small-scale yielding conditions, where ν = Poisson's ratio. The asymptotic analysis thatβ = 5.08 (for ν = 0.3), but does not give the values of the parameters α andR. However, comparisons with finite element results suggest that α has approximately the same value for stationary and growing cracks, whileR scales approximately with the plastic zone size. For large-scale yielding, Rice, Drugan, and Sham argue that a similar growth equation is expected to apply with possible variations in α and β at least in cases which maintain triaxial constraint at the crack tip. They speculate thatR increases linearly withJ at first, but then saturates in the general yield state at some fraction of the dimension of the uncracked ligament. The present paper analyses the highly idealized Dugdale-Bilby-Cottrell-Swinden model of a growing crack tip, and the results provide support for the speculations regarding the magnitude ofR in the large-scale plasticity and general yield states.