Crack growth behavior and fatigue-life prediction based on worst-case near-threshold data of a large crack for 9310 steel

ABSTRACT Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks, near‐threshold growth behavior of large cracks at constant R‐ratio/decreasing ΔK and constant K_max/decreasing ΔK, respectively, for 9310 steel. The results showed that a pronounced small‐crack effect was not observed even at R = ?1, small cracks initiated by a slip mechanism at strong slip sites. Worst‐case near‐threshold testing results for large cracks under several K_max values showed that an effect of K_max on the near‐threshold behavior does not exist in the present investigation. A worst‐case near‐threshold test for a large crack, i.e. constant K_max/decreasing ΔK test, can give a conservative prediction of growth behavior of naturally initiated small cracks. Using the worst‐case near‐threshold data for a large crack and crack‐tip constraint factor equations defined in the paper, Newman's total fatigue‐life prediction method was improved. The fatigue lives predicted by the improved method were in reasonable agreement with the experiments. A three‐dimensional (3D) weight function method was used to calculate stress‐intensity factors for a surface crack at a notch of the present SENT specimen (with r/w = 1/8) by using a finite‐element reference solution. The results were verified by limited finite‐element solutions, and agreed well with those calculated by Newman's stress‐intensity factor equations when the stress concentration factor of the present specimen was used in the equations.     

IN SITU SEM MEASUREMENTS OF CRACK CLOSURE FOR SMALL FATIGUE CRACKS IN ALUMINIUM 2024-T351

Abstract Crack closure has been measured for a range of small, self-initiated fatigue cracks using in situ SEM loading. Cracks were grown at positive R ratios in the aluminium alloy 2024-T351 and at nominal ΔK levels that extend substantially below the corresponding long crack threshold. The crack closure stress of the small cracks decreased and the K_cl level increased with increasing crack size until the long crack value near threshold was reached. For cracks of depth larger than about one grain size, a good correlation was obtained between small and long crack growth rate data in terms of ΔK_eff     

Mode I and mixed mode fracture of polysilicon for MEMS

An experimental study was carried out to investigate the local and effective fracture behaviour of polycrystalline silicon for microelectromechanical systems (MEMS). The apparent mode I critical stress intensity factor was determined from MEMS‐scale tension specimens containing atomically sharp edge pre‐cracks, while local deformation fields were recorded near the crack tip, with high resolution by the in situ Atomic Force Microscopy (AFM)/Digital Image Correlation (DIC) method previously developed by this group. The effective mode I critical stress intensity factor varied in the range 0.843–1.225 MPa√m. This distribution of values was attributed to local (in grain) cleavage anisotropy and to enhanced grain boundary toughening. The same sources resulted in very different local and macroscopic (apparent) stress intensity factors, which, combined with the small grain size of polysilicon (0.3 μm,) were the reason for subcritical crack growth that was evidenced experimentally by AFM topographic and AFM/DIC displacement measurements. The effect of local in‐grain anisotropy and granular inhomogeneity was stronger under mixed mode loading of edge cracks inclined at angles up to 55° with respect to the applied far‐field load. The K_I–K_II locus was characterized by scatter in the K_Ic values but on average it followed the curves calculated by the maximum tensile stress and the maximum energy release rate criteria calculated assuming isotropy.     

B.E. Analysis of a cracked cylindrical rod twisted by rotation of a flat annular stamp

Conclusions The use of suitable Green functions, in the BEM for axisymmetric bodies with cracks, yields accurate evaluation of the stress solution near the crack boundary. The singular character of the contact shearing stress between the stamp and the elastic medium influences the Mode III stress intensity factor for internal cracks more than for the external cracks. The validity of the numerical method has been verified through some characteristic examples. The accuracy of the results for K _IIIis displayed for internal and external cracks. Their interaction effects with the singularity due to the stamp are reflected as the geometric parameters are varied.Dedicated to G. Rieder     

Calculation of the crack tip parameters in the holed‐cracked flattened Brazilian disk (HCFBD) specimens under wide range of mixed mode I/II loading

In this paper, the crack tip parameters including the stress intensity factors (K_I and K_II), T‐stress and the third terms of the stress field (A₃ and B₃) are determined comprehensively for a disk‐type sample named holed‐cracked flattened Brazilian disk (HCFBD) under various combinations of mode I and mode II loading. The HCFBD specimen is a circular disk containing a central hole in which the initial cracks are created radially from the hole circumference. Moreover, the ends of HCFBD are flattened for the sake of convenient loading. Performing enormous finite element analyses and calculating the stress intensity factors K_I and K_II, the states of pure mode II are determined for different configurations of HCFBD. Furthermore, the sign and magnitude of parameter A₃ which plays an important role to justify the geometry and size effects on the fracture toughness of quasi‐brittle materials are also determined for HCFBD with different geometrical ratios.     

Crack-Tip Stress-Strain Fields During Cyclic Loading and Effect of Overload

Finite-deformation elastoplastic analysis of a plane-strain crack subjected to mode I cyclic loading under small scale yielding was performed. The influence of the load range, load ratio and overload on the crack tip stress-strain field is presented. Two independent parameters of cyclic loading, such as ΔK and K _max, both substantially affect the near tip evolutions of cyclic stresses and plastic strains, in agreement with typical experimental trends of fatigue cracking. This implies that the behaviour of cracks is governed by stress and strain fields ahead of the tip, via their control over the key process variables (damage accumulation and rupture, i.e., bond-breaking), so that the coupled process becomes a two-parameter one in terms of fracture mechanics variables ΔK and K _max.     

Fretting fatigue limit as a short crack problem at the edge of contact

This paper proposes a local stress concept to evaluate the fretting fatigue limit for contact edge cracks. A unique S–N curve based on the local stress could be obtained for a contact edge crack irrespective of mechanical factors such as contact pressure, relative slip, contact length, specimen size and loading type. The analytical background for the local stress concept was studied using FEM analysis. It was shown that the local stress uniquely determined the ΔK change due to crack growth as well as the stress distribution near the contact edge. The condition that determined the fretting fatigue limit was predicted by combining the ΔK change due to crack growth and the ΔK_th for a short crack. The formation of a non‐propagating crack at the fatigue limit was predicted by the model and it was experimentally confirmed by a long‐life fretting fatigue test.     

Shear mode threshold for a small fatigue crack in a bearing steel

The fatigue behaviour of small, semi‐elliptical surface cracks in a bearing steel was investigated under cyclic shear‐mode loading in ambient air. Fully reversed torsion was combined with a static axial compressive stress to obtain a stable shear‐mode crack growth in the longitudinal direction of cylindrical specimens. Non‐propagating cracks less than 1 mm in size were obtained (i) by decreasing the stress amplitude in tests using notched specimens and (ii) by using smooth specimens in constant stress amplitude tests. The threshold stress intensity factor ranges, ΔK_IIth and ΔK_IIIth, were estimated from the shape and dimensions of non‐propagating cracks. Wear on the crack faces was inferred by debris and also by changes in microstructure in the wake of crack tip. These effects resulted in a significant increase in the threshold value. The threshold value decreased with a decrease in crack size. No significant difference was observed between the values of ΔK_IIth and ΔK_IIIth.     

Contour integral method for stress intensity factors of interface crack

A general Betti's reciprocal work theorem with interface cracks of a bimaterial is established in this paper, and a path independent contour integral method for the stress intensity factor (SIF) of the interface crack was obtained. When the stress and displacement fields in a specimen are calculated by the finite element method, the SIF K _I and K _II of interface cracks can be obtained immediately by a contour integral. Some solutions of interesting examples, such as two collinear interface cracks, are also given.Presented at the Far East Fracture Group (FEFG) International Symposium on Fracture and Strength of Solids, 4–7 July 1994 in Xi'an China.     

SMALL FATIGUE CRACK GROWTH IN A LOW CARBON STEEL UNDER TENSION–COMPRESSION AND PULSATING-TENSION LOADING

The growth behaviour of small fatigue cracks has been investigated in a low carbon steel under axial loading at the stress ratios R of –1 (tension-compression) and 0 (pulsating-tension). Crack closure was measured to evaluate the effects of stress ratio and stress level on small crack growth. Except for the accelerated growth at stress levels close to the yield stress of the material, at R=–1 small cracks grow faster than large cracks below a certain crack length, but at R= 0 the crack growth rates for small cracks are coincident with those for large cracks in the whole region of crack length investigated. The critical crack length, 2c_c, above which the growth behaviour of small cracks is similar to that of large cracks depends on stress ratio, being 1–2 mm at R=–1 and smaller than 0.7 mm at R=0. The 2c_c value at R=–1 agrees with that obtained under rotating bending (R=–1). The small crack data are closely correlated with large crack growth rates in terms of the effective stress intensity range, ΔK_eff; thus ΔK_eff is found to be a characterizing parameter for small crack growth including the growth at the higher stress levels.     

Stress intensity factors for cracks initiated from a center-holed plate with unsymmetrical lengths under tension

The values of stress intensity factors of unsymmetrical cracks initiated from hole edges under tension were calculated in a center-holed plate, that is a plate having a hole in the center of a front face. The correction factor for stress intensity in the case of the holed plate with cracks was compared with that of a center-cracked plate whose crack length was equal to the total of the hole diameter and the lengths of the cracks in the case of the holed plate. In the present study, to understand the variation of the stress intensity factor, counterplots of the stress intensity factor K_I and the correction factor F_I are employed. Also, the variation of ratio R_F of correction factors between the holed plate with crack and the center-cracked plate were investigated. Where non-dimensional hole diameter a/W is smaller than 0.2, the ratio R_F is less than 1.1 after crack growth length c/W reaches 0.1. Where, 2a, 2c and 2W are hole diameter, the growth length of the crack from hole edge, and plate width, respectively. Therefore, the stress intensity factor for cracks initiated from a holed plate can be approximated within 10% error to that of a center-cracked plate where a/W is smaller than 0.2, though the unsymmetrical cracks are initiated from the edges. Where a/W is larger than 0.3, R_F becomes larger than 1.1 in the wide range of c/W.     

ESTIMATIONS OF STRESS INTENSITY FACTORS FOR SMALL CRACKS AT NOTCHES

This paper presents a simple method for determining the stress intensity factors for small notch-emanating cracks. The proposed method is based on similarities between elastic notch-tip stress fields described by two parameters; the stress concentration factor K₁, and the notch-tip radius ρ. The method developed here is rather general, and can be used for a variety of central and edge notches with through-thickness of semi-elliptical cracks. The predicted values are in good agreement with the available numerical data.     

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.     

Effects of notch length,specimen thickness,ply thickness and type of defect on the fracture behaviour of angle-ply graphite-epoxy composites

An experimental study was carried out on the effects of notch length, specimen thickness, ply thickness and type of defect (centre-notch or hole) on the fracture toughness of graphite-epoxy composites with lay-up sequences of 0/±45°/0 and 0/90°. Three fracture-mechanical concepts were applied: the Waddoups-Eisenmann-Kaminski (WEK) model, the Whitney-Nuismer model (point and average stress cirteria) and the K _R-curve method. An increase of notch length as well as an increase of ply thickness led to a higher toughness, whereas a change in specimen thickness did not noticeably affect the toughness. Furthermore, the hole caused a smaller strength reduction than a notch. The applicability of the above-mentioned concepts is probably restricted mainly because of the fact that they do not, or do only insufficiently, regard the damage zone near the border of the defect, if a large damage zone usually leads to larger material parameters of the investigated concepts, namely the inherent flaw size, the characteristic lengths of the point and average stress criterions and the K _R -value at fracture.     

Stress intensity factor K and the elastic T-stress for corner cracks

The stress intensity factor K and the elastic T-stress for corner cracks have been determined using domain integral and interaction integral techniques. Both quarter-circular and tunnelled corner cracks have been considered. The results show that the stress intensity factor K maintains a minimum value at the mid-plane where the T-stress reaches its maximum, though negative, value in all cases. For quarter-circular corner cracks, the K solution agrees very well with Pickard's (1986) solution. Rapid loss of crack-front constraint near the free surfaces seems to be more evident as the crack grows deeper, although variation of the T-stress at the mid-plane remains small. Both K and T solutions are very sensitive to the crack front shape and crack tunnelling can substantially modify the K and T solutions. Values of the stress intensity factor K are raised along the crack front due to crack tunnelling, particularly for deep cracks. On the other hand, the difference in the T-stress near the free surfaces and at the mid-plane increases significantly with the increase of crack tunnelling. These results seem to be able to explain the well-observed experimental phenomena, such as the discrepancies of fatigue crack growth rate between CN (corner notch) and CT (compact tension) test pieces, and crack tunnelling in CN specimens under predominantly sustained load.     

A New Boundary Element for Plane Elastic Problems Involving Cracks and Holes

By applying the new boundary integral formulation proposed recently by Chau and Wang (1997) for two-dimensional elastic bodies containing cracks and holes, a new boundary element method for calculating the interaction between cracks and holes is presented in this paper. Singular interpolation functions of order r^-1/2 (where r is the distance measured from the crack tip) are introduced for the discretization of the crack near the crack tips, such that stress singularity can be modeled appropriately. A nice feature for our implementation is that singular integrands involved at the element level are integrated analytically. For each of the hole boundaries, an additional unknown constant is introduced such that the displacement compatibility condition can be satisfied exactly by the complex boundary function H(t), which is a combination of the traction and displacement density. Another nice feature of the present formulation is that the stress intensity factors (both K_{_I} and K_{_II}) at crack tips are expressed in terms of the nodal unknown of H(t) exactly, and no extrapolation of numerical data is required. To demonstrate the accuracy of the present boundary element method, various crack problems are considered: (i) the Griffith crack problem, (ii) the interaction problem between a circular hole and a straight crack subject to both far field tension and compression, and (iii) the interaction problem between a circular hole and a kinked crack subject to far field uniaxial tension. Excellent agreement with existing results is observed for the first two problems and also for the last problem if the crack-hole interaction is negligible. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Fatigue life estimation after crack repair in 6005 A-T6 aluminium alloy using the cold expansion hole technique

In this paper, the hole drilling (HD) and the cold expansion (CE) processes, which were used as a technique for crack repair, were investigated in order to estimate the beneficial effects on fatigue crack initiation (FCI). The FCI life is defined as the number of cycles to initiate a new crack of 0.2 mm on the surface of the specimen. Three hole radii and three degrees of cold expansion (DCE%) values were tested after a crack propagation period. Crack retardation after the CE process was observed. This phenomenon is due to two mechanisms: retardation owing to both geometric and mechanical effects, which is produced by the stress concentration at the drilled hole, and the large strain‐induced compressive residual stresses around the hole. In this report, the influence of the loading conditions was studied. For high values of the stress intensity factor range ΔK_ρ around the hole (based on the pseudo crack length a + ρ), the number of cycles corresponding to crack initiation N_i is low. At the edge of the hole, the maximum stress range can be approximated by the following formula: Δσ_max = 2ΔK_ρ /√πρ , where ρ is the hole radius and ΔK_ρ is the related stress intensity factor range.The FCI life extension, defined by the number of cycles corresponding to crack re‐initiation N_i , is related to the relative maximum stress range ratio R_σ = [(Δσ_max )/(Δσ_max )_th ] where (Δσ_max )_th is the value of the threshold maximum stress range obtained when N_i = 2 × 10⁶ cycles. The relationship between N_i and R_σ may be written as a power function.     

On the problem of two coplanar cracks inside an infinite isotropic elastic solid

A method is proposed for the approximate evaluation of normal displacements and normal stresses on the plane of two coplanar cracks located inside an infinite isotropic elastic solid and subjected to normal internal pressure. The formulation results in a single integral equation for the unknown normal stresses on the plane of the cracks. Numerical results are given for the stress intensity factor K_I of two coplanar circular cracks and two coplanar elliptical cracks opened up under a uniform internal pressure.     

Crack veolcity and acceleration effects on dynamic stress intensity factor in polymers

Dynamic crack propagations in PMMA and epoxy specimens were studied using the method of caustics in combination with a Cranz-Schardin type high-speed camera. Single-edge-cracked tensile specimens were fractured under pin-loading conditions so that cracks could experience acceleration, deceleration and re-acceleration stages in one fracture process. The dynamic stress intensity factor K _ID, crack velocity a and acceleration a were evaluated in the course of crack propagation to examine the effects of a and a on K _ID. Results showed that a and a were important factors in changing the values of K _ID, and for constant a the decelerating crack had a larger value of K _ID than the accelerating or re-accelerating crack. Also, it was found that K _ID could be expressed as two parametric functions of and a for PMMA and epoxy specimens. This revised version was published online in August 2006 with corrections to the Cover Date.