Fatigue crack growth under non-proportional mixed-mode loading in ferritic-pearlitic steel

Mode II fatigue crack growth tests as well as tests in sequential mode I and then mode II were performed on ferritic‐pearlitic steel. For ΔK_II ranging from 7 to , bifurcation occurs after 12–450 μm of coplanar growth at a decreasing speed. By contrast, hundreds of micrometres of constant speed coplanar growth were obtained under sequential mode I and then mode II loading, for and ΔK_I ranging from 0.25 to 1.0 ΔK_II . The crack growth rate is a simple sum of the contributions of each mode for ΔK_I= 0.25 ΔK_II but above this value a synergetic effect is found. The mechanism of this fast‐propagation mode is discussed in the light of strain range maps ahead of the crack tip obtained by digital SEM image correlation and elastic–plastic finite element calculations. The stability of the crack path according to the maximum growth rate criterion is demonstrated.     

Short fatigue crack growth behavior under mixed-mode loading

Mixed-mode loading represents the true loading condition in many practical situations. In addition, most of the fatigue life of many components is often spent in the short crack growth stage. The study of short crack growth behavior under mixed-mode loading has, therefore, much practical significance. This work investigated short crack growth behavior under mixed-mode loading using a common medium carbon steel. The effects of load mixity, crack closure, and load ratio on short crack growth behavior were evaluated by conducting experiments using four-point bending specimens with several initial K _II /K _I mixed-mode ratios and two load ratios. Cracks were observed to grow along the paths with very small K _II /K _I ratios (i.e. mode I). The maximum tangential stress criterion was used to predict the crack growth paths and the predictions were found to be close to the experimental observations. Several parameters including equivalent stress intensity factor range and effective stress intensity factor range were used to correlate short crack growth rates under mixed-mode loading. Threshold values for short cracks were found to be lower than those for long cracks for all the mixed-mode loading conditions. Crack closure was observed for the entire crack length regime with all load mixity conditions at R ≈ 0.05 and for short crack regime under high load mixity condition at R = 0.5. Several models were used to describe mean stress effects and to correlate crack growth rate data.     

Mixed-mode fatigue crack growth behaviour in aluminium alloy

Fatigue crack propagation tests in compact mixed-mode specimens were carried out for several stress intensity ratios of mode I and mode II, K_I/K_II, in AlMgSi1-T6 aluminium alloy with 3 mm thickness. The tests were performed in a standard servo-hydraulic machine. A linkage system was developed in order to permit the variation of the K_I/K_II ratio by changing the loading angle. Crack closure loads were obtained through the compliance technique. A finite element analysis was also done in order to obtain the K_I and K_II values for the different loading angles. Crack closure increases under mixed-mode loading conditions in comparison to mode-I loading due the friction between the crack tip surfaces. Moreover, the crack closure level increases with the K_I/K_II ratio decrease. Correlations of the equivalent values of the effective stress intensity factor with the crack growth rates are also performed. Finally, an elastic–plastic finite element analysis was performed to obtain the plastic zones sizes and shapes and model the effect of mixed-mode loading on crack closure.     

Creep Crack Growth in Polyethylene Under Combined Mode I and Mode II Loading

Creep crack growth characteristics under various combined mode I and mode II loadings were studied using the compact tension shear (CTS) specimens of polyethylene. Creep crack growth rates da/dtunder combined mode I and mode II loading can be correlated with a single effective stress intensity factor K _Ieffderived from the combined — mode fracture toughness envelope. The steady state or constant crack growth rates which occupy the significant part of creep failure life increase with the increasing initial effective stress intensity factor.     

Mixed-mode crack growth in ductile thin-sheet materials under combined in-plane and out-of-plane loading

Ductile thin-sheet structures, such as fuselage skin or automobile panels, are widely used in engineering applications. These structures often-times are subjected to mixed mode (I/II/III) loading, with stable crack growth observed prior to final fracture. To characterize specific specimen deformations during stable tearing, a series of mixed-mode I/III stable tearing experiments with highly ductile thin-sheet aluminum alloy and steel specimens have been measured by using three-dimensional digital image correlation (3D-DIC). Measurements include (a) specimen’s deformed shape and 3D full-field surface displacement fields, (b) load-crack extension response and (c) crack path during stable tearing, (d) angular and radial distributions of strains and (e) the mixed mode crack-opening displacement (COD, measured at 1-mm from crack tip along crack surface) variation as a function of crack extension. Results indicate that for both aluminum alloy and steel at all mixed-mode I/III loading conditions (Φ = 30°, 60° and 90°), the crack tip fields have almost identical angular and radial polar strain distributions. The mixed mode I/III fields were different from those observed for the nominal Mode I loading case (Φ = 0°). The effect of the Mode III loading component is that it lowers the magnitude of the dominant strain component ε _θθ ahead of the growing crack tip and increases the singularity of the strain as compared with that in the mode I case. In addition, measurements indicate that the average mixed mode I/III stable COD for AL6061-T6 (GM6208 steel) is 4×(3×) greater than the average Mode I stable COD.     

Fracture Toughness and Creep Crack Growth in Polypropylene Under Combined Modes I and II Loading

Fracture toughness and creep crack growth characteristics under combined mode I and II loadings were studied using the compact tension shear (CTS) specimens of polypropylene. The K _I - K _II envelope for crack initiation was obtained under various combined mode loadings. The creep crack growth rates da/dt under combined mode I and mode II loadings can be correlated with a single effective stress intensity factor K _Ieff based on the combined mode fracture envelope.     

Fatigue crack growth of a railway wheel

Typically, fatigue crack propagation in railway wheels is initiated at some subsurface defect and occurs under mixed mode (I–II) conditions. For a Spanish AVE train wheel, fatigue crack growth characterization of the steel in mode I, mixed mode I–II, and evaluation of crack path starting from an assumed flaw are presented and discussed.Mode I fatigue crack growth rate measurement were performed in compact tension C(T) specimens according to the ASTM E647 standard. Three different load ratios were used, and fatigue crack growth thresholds were determined according to two different procedures. Load shedding and constant maximum stress intensity factor with increasing load ratio R were used for evaluation of fatigue crack growth threshold.To model a crack growth scenario in a railway wheel, mixed mode I–II fatigue crack growth tests were performed using CTS specimens. Fatigue crack growth rates and propagation direction of a crack subjected to mixed mode loading were measured. A finite element analysis was performed in order to obtain the K_I and K_II values for the tested loading angles. The crack propagation direction for the tested mixed mode loading conditions was experimentally measured and numerically calculated, and the obtained results were then compared in order to validate the used numerical techniques.The modelled crack growth, up to final fracture in the wheel, is consistent with the expectation for the type of initial damage considered.     

Crack growth in a mixed-mode loading on marble beams under three point bending

A combined theoretical and experimental study of a crack growth in a mixed-mode I–II loading is presented. A 160×40×20 mm marble beam, with an artificial crack 8 mm and 10 mm long each, was subjected to three point bending. The crack was located vertically to the beam's lower longitudinal fiber, through the whole width of the beam. The position of the crack was displaced from the center of the beam to one of the supporting points. The vertical force P, placed on the middle of the upper fiber of the beam, imposed the combination of the opening (mode I) and the sliding (mode II) modes on the crack mouth, creating the mixed-mode I–II loading case. The stress intensity factors K _I and K _II, which describe the local stress and strain field around the crack tip, were determined by a suitable finite element program. The crack growth was defined by two classical fracture criteria of LEFM; the minimum strain energy density and the maximum circumferential stress criteria. The initial crack growth angle () was calculated from both criteria and the critical load (P _c) from the minimum strain energy density (SED) criterion. These theoretical predictions were compared with some experimental results found from three marbles with different elastic constants; the Krystallina of Kavala, the Snow-white of Thassos and the White of Piges Drama. The theoretical results showed the same trend of and P _c as the experimental ones and they are in good agreement.Presented at Fourth Greek National Congress on Mechanics, 26–29 June 1995, held at Xanthi, Greece.     

Threshold and growth mechanism of fatigue cracks under mode II and III loadings

ABSTRACT The fatigue crack growth behaviour of 0.47% carbon steel was studied under mode II and III loadings. Mode II fatigue crack growth tests were carried out using specially designed double cantilever (DC) type specimens in order to measure the mode II threshold stress intensity factor range, ΔK_IIth. The relationship ΔK_IIth > ΔK_Ith caused crack branching from mode II to I after a crack reached the mode II threshold. Torsion fatigue tests on circumferentially cracked specimens were carried out to study the mechanisms of both mode III crack growth and of the formation of the factory‐roof crack surface morphology. A change in microstructure occurred at a crack tip during crack growth in both mode II and mode III shear cracks. It is presumed that the crack growth mechanisms in mode II and in mode III are essentially the same. Detailed fractographic investigation showed that factory‐roofs were formed by crack branching into mode I. Crack branching started from small semi‐elliptical cracks nucleated by shear at the tip of the original circumferential crack.     

CRACK FACE INTERACTIONS AND NEAR-THRESHOLD FATIGUE CRACK GROWTH

Rough fracture surfaces usually influence substantially the fatigue growth properties of materials in the regime of low growth rates. Friction, abrasion, interlocking of fracture surface asperites and fretting debris reduce the applied load amplitude to a smaller effective value at the crack tip (“sliding crack closure”, or “crack surface interaction” or “crack surface interference”). The influence of these phenomena on the fatigue crack growth properties of structural steel is discussed and compared for the two kinds of mixed mode loading employed in this work. Mixed mode loading was performed by (A): cyclic mode III + superimposed static mode I and (B): cyclic mode I + superimposed static mode III loading. Such loading cases frequently occur in rotating load-transmission devices. Several differences are typical for these two mixed-mode loading cases. A superimposed static mode I load increases the crack propagation rate under cyclic mode III loading whereas cyclic mode I fatigue crack propagation is retarded when a static mode III load is superimposed. Increase of the R -ratio (of the cyclic mode III load) leads to an insignificant increase of fracture surface interaction and subsequently to a small decrease of the crack growth rate for cyclic mode III loading, whereas higher R -values during cyclic mode I+ superimposed static mode III loading lead to a significant reduction of the crack growth rates.     

MIXED-MODE FRACTURE MECHANISMS NEAR THE FATIGUE THRESHOLD OF AISI 316 STAINLESS STEEL

Abstract— Near threshold, mixed mode (I and II), fatigue crack growth occurs mainly by two mechanisms, coplanar (or shear) mode and branch (or tensile) mode. For a constant ratio of ΔK_I/ΔK_II the shear mode growth shows a self-arrest character and it would only start again when ΔK_I and ΔK_II are increased. Both shear crack growth and the early stages of tensile crack growth, are of a crystallographic nature; the fatigue crack proceeds along slip planes or grain boundaries. The appearance of the fracture surfaces suggest that the mechanism of crack extension is by developing slip band microcracks which join up to form a macrocrack. This process is thought to be assisted by the nature of the plastic deformation within the reversed plastic zone where high back stresses are set up by dislocation pile-ups against grain boundaries. The interaction of the crack tip stress field with that of the dislocation pile-ups leads to the formation of slip band microcracks and subsequent crack extension. The change from shear mode to tensile mode growth probably occurs when the maximum tensile stress and the microcrack density in the maximum tensile plane direction attain critical values.     

A survey of failure criteria and parameters in mixed-mode fatigue crack growth

From the present survey of the mixed-mode crack growth criteria based on the fracture toughness K _Ic (critical J-integral), it follows that this concept is very extensively and variously used by different authors. The criteria discussed in the work are based on the parameters K, δ, W, and J. The most extensively applied models include the mixed mode I + II described by the stress intensity factor K. The criteria presented in the work are based on the factors affecting the fatigue crack growth during testing, namely stress, crack-tip displacement, or energy dissipation. In the case of mixed-mode cracking, special attention should be paid to the energy approach (application of the J-integral and strain energy density), which seems to be very promising for elastoplastic materials. Under mixed-mode cracking, two things should be taken into account: the rate and direction of fatigue-crack growth. Moreover, the nonproportional loading, crack closure, or overloads strongly affect the process of fatigue crack growth in the case of mixed-mode cracking.     

Finite element analysis of a subsurface crack

The problem of a subsurface crack parallel to the surface of a half space was studied by the finite element method. Without using the interface or gap elements over the crack faces, the crack faces would penetrate into each other for the traction-free boundary condition under shear loading, which is physically impossible. Using the gap elements, this problem was avoided, and a contact zone was observed near one crack tip. The size of the contact zone decreases but the maximum contact pressure at the closed crack tip increases as the crack approaches the surface. For tensile and shear loadings, both K _I (mode I stress intensity factor) and K _II (mode II stress intensity factor) increase as the crack approaches the surface. For shear loading there is no K _I at the closed tip and the K _I and K _II at the open tip are comparable as the crack approaches the surface.     

Effects of microstructure on mixed-mode, high-cycle fatigue crack-growth thresholds in Ti-6Al-4V alloy

Effect of microstructure on mixed‐mode (mode I + II), high‐cycle fatigue thresholds in a Ti‐6Al‐4V alloy is reported over a range of crack sizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditions were examined—a fine‐grained equiaxed bimodal structure (grain size ～20 µm) and a coarser lamellar structure (colony size ～500 µm). Studies were conducted over a range of mode‐mixities, from pure mode I (ΔK_II/ΔK_I = 0) to nearly pure mode II (ΔK_II/ΔK_I ～ 7.1), at load ratios (minimum load/maximum load) between 0.1 and 0.8, with thresholds characterized in terms of the strain‐energy release rate (ΔG) incorporating both tensile and shear‐loading components. In the presence of through‐thickness cracks—large (> 4 mm) compared to microstructural dimensions—significant effects of mode‐mixity and load ratio were observed for both microstructures, with the lamellar alloy generally displaying the better resistance. However, these effects were substantially reduced if allowance was made for crack‐tip shielding. Additionally, when thresholds were measured in the presence of cracks comparable to microstructural dimensions, specifically short (～200 µm) through‐thickness cracks and microstructurally small (< 50 µm) surface cracks, where the influence of crack‐tip shielding would be minimal, such effects were similarly markedly reduced. Moreover, small‐crack ΔG_TH thresholds were some 50–90 times smaller than corresponding large crack values. Such effects are discussed in terms of the dominant role of mode I behaviour and the effects of microstructure (in relation to crack size) in promoting crack‐tip shielding that arises from significant changes in the crack path in the two structures.     

FATIGUE CRACK GROWTH BEHAVIOUR OF SM45C STEEL UNDER CYCLIC MODE I WITH SUPERIMPOSED STATIC MODE II LOADINGS

Abstract— The practical applications of studies related to constant amplitude mode I loading are somewhat limited, since mode I crack growth is often influenced by mode II (sliding mode) or mode III (tearing mode) in industrial situations. For these cases, criteria, rules, and laws have to be worked out and verified by experiments. However, it is very difficult to evaluate mixed-mode fatigue cracking due to crack surface interference, crack closure, crack branching, etc. This paper, which defines the length of a branched crack as an effective slant crack with a length equal to the distance between the two crack tips, explains the influences of crack surface interference by introducing concepts of adhesive wear and scrutinizes some related researches on mixed-mode crack growth behaviour. Additionally an effective stress intensity factor range is described which considers crack closure and crack surface interference and is verified with crack growth tests under mode I fatigue loading and cyclic mode I with a superimposed static mode II loading.     

FATIGUE CRACK GROWTH UNDER MODE II LOADING

Abstract— The behavior of fatigue crack growth for low and medium carbon steels, an austenitic stainless steel and an aluminum alloy under pure Mode II loading was investigated experimentally, using cruciform specimens. The results show that under pure Mode II loading, fatigue crack propagation has three possibilities, namely, bifurcation into two branches, propagation along the original Mode II direction, and the mixture of these two situations, depending on the material. The growth rate da/dN vs. ΔK_II relation for Mode II propagation is similar to a Pans type law for Mode I growth. Fractographic observations by optical microscopy and SEM were made also on all specimens tested. When a crack branched, striations parallel to the crack front which were often associated with Mode I fatigue crack growth were observed and long marks parallel to the crack propagation direction were also found for slanted fracture surfaces. When a crack propagated along the original Mode II direction, many frictional marks parallel to the crack propagation direction were observed.     

A multi-scale approach to condense the cyclic elastic-plastic behaviour of the crack tip region into an extended constitutive model

The general idea of this paper is to model the mixed‐mode cyclic elastic‐plastic behaviour of the crack tip region at the global scale. It should be helpful, for instance, for predicting the effect of mixed mode overloads in fatigue. It is aimed at establishing a model reasonably precise (compared with elastic‐plastic finite element (FE) computations) but condensed into a set of partial derivative equations so as to avoid huge elastic‐plastic FE computations in the future. For this purpose, the kinematics of the crack tip region is characterized by a set of condensed variables. This is classical in linear elastic fracture mechanics (LEFM), the displacement field is approached by the product of spatial reference fields ( and ) and nominal stress intensity factors (K^∞_I and K^∞_II ). Therefore, in LEFM, two condensed variables only, K^∞_I and K^∞_II , fully define the kinematics in the crack tip region. So as to generalize this approach to mixed mode cyclic elastic‐plastic conditions, we define first the intensity factors ( and ) of the elastic spatial reference fields ( and ) and we introduce two additional spatial reference fields ( and ) and their intensity factors ( and ) to account for plastic deformation within the crack tip region. Such an approximation is shown to be reasonably precise using FE computations. Therefore, the velocity field in the crack tip region is fully defined by only four condensed variables ( and ). Using the multi‐scale approach proposed herein, evolutions of ρ_I and ρ_II for various mixed‐mode loading conditions defined by K^∞_I and K^∞_II were generated using the finite‐element method (FEM). Then, it was shown that we can model these evolutions at the global scale through a yield locus, a flow rule and a kinematics hardening rule. It is also suggested how this model could be employed for predicting the effects of mixed mode plasticity on fatigue crack growth.     

Experimental observation and modeling of the retardation of fatigue crack propagation under the combination of mixed-mode single overload and constant amplitude loads

It is well-known that one of the major characteristics of variable fatigue loads, especially overloads, is the retardation of the fatigue crack due to the complex interaction of many factors such as the overload ratio, the timing of overloads, the stress ratio, the yield stress of the material, the thickness of the structure, and the stress history. However, studies of the combined effect of mixed-mode I+II constant amplitude fatigue loadings and a mixed-mode I+II single overload on fatigue behavior are still scant. In this study, fatigue tests were conducted under mixed-mode I+II constant amplitude loadings with a mixed-mode I+II single overload, with reference to the variation of fatigue crack retardation. The formation of the overload plastic zone (OPZ) ahead of the crack tip under a mixed-mode I+II single overload is studied experimentally by the measurement of the shape and size of the OPZ. The behavior of fatigue crack propagation under mixed-mode loading conditions is examined by changing the loading mode of a single overload, and the relationship between the mixed-mode I+II single overload and the behavior of fatigue crack propagation in terms of the characteristics of the OPZ is evaluated. The empirical modeling of the fatigue life under mixed-mode I+II constant amplitude loadings is proposed by considering the characteristics of both the OPZ and the combination of the mode-mixity of mixed-mode I+II constant amplitude loadings and a mixed-mode I+II single overload.     

Crack-tip constraint in mode II deformation

Studies of cracked specimens loaded in mode I have shown that the stresses near the crack tip depend significantly on the level of constraint. The stresses can be determined near the crack tip using the HRR solution, but only for high constraint specimens. For other levels of constraint, O'Dowd and Shih's Q parameter may be used to adjust the stresses derived from the HRR solution. Only limited research has been carried out to study the effect of constraint in mode II. In this paper a mode II boundary layer formulation is used to study the effect of far field elastic stresses on the size and shape of the plastic zone around the crack tip and on the stresses inside the plastic zone. It is shown that in mode II, both positive and negative values of remote T-stress influence the tangential stress along the direction of maximum tangential stress. In the spirit of O'Dowd and Shih, a dimensionless parameter Q _II is introduced to quantify the constraint for mode II specimens failing by brittle fracture. The relation between Q _II and T/₀ is determined for different values of the strain hardening coefficient n. To investigate the range of validity of the Q–T diagram for real specimens, the constraint parameter Q _II is calculated directly from finite element analysis for three mode II specimens and compared with the evaluation using the Q–T diagram.     

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.