拉—拉疲劳下15MnMoVN多裂纹扩展研究

为分析单裂纹或多裂纹在裂纹面承受疲劳拉伸载荷作用下尖端应力强度因子变化规律和裂纹形貌变化以及疲劳寿命情况,以含不同初始长深比的半椭圆单裂纹或双裂纹的薄片试样为研究对象,对试样在应力比R=0.1的疲劳拉伸载荷下单裂纹或双裂纹情况进行了仿真分析。建立含裂纹试样的有限元模型,仿真分析了裂纹在扩展过程中尖端应力强度因子的分布情况,并将单裂纹扩展结果与双裂纹相互作用影响下的结果进行了对比研究;进行含裂纹试样的疲劳实验,分析了含单裂纹或双裂纹的试样的断裂面的形成原因,并验证仿真结果正确性。结果表明,裂纹面之间的相互作用会逐渐影响裂纹的扩展方向、扩展速率以及在扩展过程中尖端应力强度因子的变化趋势;而且初始形貌为半椭圆形的双裂纹在相互作用影响下会逐渐过渡到半圆形。     

Fatigue crack growth analyses of offshore structural tubular joints

This study investigated various aspects of a fatigue crack growth analysis, ranging from the stress intensity factor solutions to the simulation of a fatigue crack coalescence process of a tubular joint weld toe surface flaw. Fracture mechanics fatigue crack growth analyses for offshore structural tubular joints are not simple, because of the difficulty to calculate the stress intensity factors due to their geometric complexity. The fully mixed-mode stress intensity factors of nine weld toe surface cracks of an X-shaped tubular joint under tension loading were calculated by detailed three-dimensional finite element analyses. Using these stress intensity factor solutions, a fatigue crack growth study was performed for the X-joint until (the crack surface length grew to two times the tube thickness. Through this study, the crack shape change during the fatigue crack propagation was investigated in detail. Fatigue life calculations were also performed for a range of crack geometries using the stress intensity factor solutions of the nine flaws. These calculations indicate that the natural fatigue crack growing path for a crack is its quickest growing path. The study demonstrated that detailed fracture mechanics fatigue analyses of tubular joints can be practical using the finite element method.     

Stress intensity factors for large aspect ratio surface and corner cracks at a semi-circular notch in a tension specimen

Stress intensity factor solutions for semi-elliptic surface and quarter-elliptic corner cracks emanating from a semi-circular notch in a tension specimen are presented. A threedimensional finite-element analysis in conjunction with the equivalent domain integral was used to calculate stress intensity factors (SIF). SIF solutions for surface or corner crack (crack length to depth ratio of 2) at a notch are presented for a wide range of crack sizes and notch radii. Results showed that the SIF are larger for larger crack lengths and for larger notch radii. The SIF are nearly constant all along the crack front for deep surface cracks and for all corner cracks analysed.     

The application of asymptotic solutions to a semi-elliptical crack at the root of a notch

This paper presents an approximate method based on asymptotic solutions for estimating the stress intensity factor K for semi-elliptic surface cracks at stress concentrations. The proposed equation for estimating K makes use of the near-notch and remote-notch solution to interpolate over the entire range from shallow to deep cracks. The near-notch solution is obtained by means of the stress concentration factor. For cracks located in the remote stress field, K is obtained by considering the crack to be located in a smooth plate with a crack depth equal to the sum of the notch depth and the actual crack depth. The accuracy of the predictions is assessed using numerical calculations and solutions found in the literature.     

Approximate stress intensity factors for cracked V-notched specimens based on asymptotic solutions with application to T-joints

This paper presents an approximate method based on asymptotic solutions for estimating the stress intensity factor K for semi-elliptic surface cracks at stress concentrations. The proposed equations make use of a reference solution to interpolate over the entire range from shallow to deep cracks. The reference solution is obtained by considering the current crack emanating from the associated specimen with a sharp notch. It is shown that the proposed formulae satisfy the shallow and deep crack asymptotes. The asymptotic solutions are applied to a T-joint with a fillet-weld-shaped transition. The accuracy of the predictions is assessed using numerical calculations.     

CRACK GROWTH AND CLOSURE BEHAVIOUR OF SURFACE CRACKS UNDER AXIAL LOADING

Abstract— Crack growth and closure behaviour of surface cracks in 7075-T6 aluminium alloy are investigated under axial loading, noting the difference in fatigue growth behaviour at the maximum crack depth point and at the surface intersection point and also with through-thickness crack growth behaviour. The plane strain closure response at the point of maximum depth of a surface crack is monitored using an extensometer spanning the surface crack at the midpoint of its length. The plane stress closure at the surface intersection point is observed by multiple strain gauges placed at appropriate intervals ahead of the crack tip and continuously monitored without interrupting the fatigue test. The crack opening ratio is found to be about 10% greater at the maximum depth point than at the surface intersection point. Under axial loading, the difference in plane strain crack closure behaviour between the surface crack and the through-thickness crack is relatively small. Growth rates of surface cracks can be well described by the effective stress intensity factor range based on the closure measurements made in this study. The growth rates in terms of the effective stress intensity factor range seem to be slightly slower in surface cracks than in through-thickness cracks.     

A STUDY OF RESIDUAL CAUSTICS GENERATED FROM FATIGUE CRACKS

Abstract— The method of caustics was used to determine the stress intensity factor of fatigue cracks in steel compact tension specimens. Under zero load a residual caustic was observed at the tip of a fatigue crack indicating the presence of a residual stress field. Caustics were generated at increasing static loads and the stress intensity factors were compared with those predicted by theory. It was found that the difference between each measured stress intensity factor and its corresponding theoretical value was a constant for the range of loads. This difference was shown statistically to be equal to the stress intensity factor determined from the residual caustic. The proposed mechanism for the formation of this residual caustic was probably due to crack tip plasticity effects and not due to crack closure. It was concluded that residual caustics can be measured to quantify crack tip behaviour in fatigue cracks and have been shown to be a useful tool in the measurement of residual stress fields.     

Subcritical Crack Growth of semi-elliptical surface cracks in a turbine rotor

The subcritial growth of semi-elliptical surface cracks in the front face of a cylindrical disk was calculated. The disk represents a part of a turbine rotor. The stress intensity factors, which are the basis for the calculations presented here, were given in a former paper [1]. The loads steps considered consist of an inhomogeneous hoop stress distribution, which occurs at a distinct time-step of the start – up procedure of the turbine, and of the stress free state, respectively. By use of a Paris-law the growth of different initial cracks was evaluated under the assumption that the crack geometry remains semi-elliptic.     

喷丸强化对Ti6Al4V半椭圆表面裂纹J积分和裂纹扩展速率的影响

采用修正的J积分计算方法,考虑残余应力、残余应变和残余应变能,定量计算和分析喷丸强化对半椭圆表面裂纹前沿J积分参数的影响规律。对喷丸强化工艺进行有限元建模仿真,通过改变约束条件生成疲劳裂纹并施加远场载荷,计算J积分和裂纹扩展速率。考虑不同深度的半椭圆表面裂纹和不同丸粒速率对断裂参量的影响。结果表明:丸粒速率一定时,与未喷丸相比喷丸后J积分值的降幅随裂纹深度的增加而减小,喷丸强化有益于抑制疲劳浅裂纹的扩展。当裂纹深度为0.3mm时,裂纹最深点的J积分值由4.25N/mm降低到2.99N/mm,降幅约30.1%。裂纹深度一定时,J积分值随丸粒速率的增大而降低,提高丸粒速率对抑制裂纹扩展更有益。     

Stress distribution and fatigue crack propagation analyses in welded joints

An approach is presented, based on the weight function method to calculate the stress intensity factors of semielliptical surface cracks originating from the notch root of welded joints. The stress distribution along the potential crack plane required in the weight function method is constructed on the basis of the notch stress intensity factor approach in the highly stressed zone and of the equivalent linearized stress distribution and is compared with those determined by the finite element method and existing predictions. The stress intensity factors determined by the proposed approach are compared with available solutions. These comparisons show that the results determined by the proposed approach generally agree well with the existing solutions. For the cases where the agreement is poor, the reasons are identified. One important feature of the proposed approach is that the stress singularity at sharp notch tip can be considered, which cannot be appropriately simulated by the finite element method. Finally, to demonstrate the applicability of the proposed approach, the fatigue life and the fatigue crack shape evolution of welded joints are predicted and they are compared with experimental results.     

Stress intensity factors for three‐dimensional weld toe cracks using weld toe magnification factors

In welded components, particularly those with complex geometrical shapes, evaluating stress intensity factors is a difficult task. To effectively calculate the stress intensity factors, a weld toe magnification factor is introduced that can be derived from data obtained in a parametric study performed by finite element method (FEM). Although solutions for the weld toe magnification factor have been presented, these are applicable only to non‐load‐carrying cruciform or T‐butt joints, due possibly to the requirement of very complicated calculations. In the majority of cases for various welded joints, the currently used weld toe magnification factors do not adequately describe the behaviour of weld toe cracks. In this study, the weld toe magnification factor solutions for the three types of welded joints such as cruciform, cover plate and longitudinal stiffener joints were provided through a parametric study using three‐dimensional finite elements. The solutions were formed with exponents and fractions that have polynomial functions in terms of a/c and a/t – that is, crack depths normalised by corresponding half crack lengths and specimen thickness. The proposed weld toe magnification factors were applied to evaluate the fatigue crack propagation life considering the propagation mechanisms of multiple‐surface cracks for all welded joints. It showed good agreement within a deviation factor of two between the experimental and calculated results for the fatigue crack propagation life.     

FRACTURE MECHANICS ASSESSMENT OF PLANAR BRANCHED CRACKS IN AN EQUIBIAXIAL STRESS FIELD

Abstract A simplified fracture mechanics assessment is presented of branched planar cracks in an equibiaxial stress state. In linear-elastic fracture mechanics the stress intensity factors which characterize the load at the crack tips depend, for a given external load, only on the crack geometry. The stress intensity factors of a large number of branched cracks were evaluated using the Boundary Element method, and correlations between the stress intensity factors and the crack geometry were investigated. Formulae are presented which assign an individual effective crack length to each crack tip of a branched crack and hence allow approximate stress intensity factors to be determined for very complicated crack geometries. An algorithm is used for the stochastic simulation of an irregular crack pattern formation in thermal fatigue.     

Branch crack development from the flank of a fatigue crack propagating in mode II

The propagation of fatigue cracks in mode II often leads to the development of a branch starting from a crack flank, some distance behind the tip and not to the expected bifurcation at the crack tip. This type of branch is suggested to initiate by decohesion along a secondary slip plane and to grow in mode I due to the tensile component of the mode II stress field. Finite element calculations are performed to evaluate the stress intensity factors for the main crack and the branch as a function of the position of the latter. It is shown that the branch has a substantial shielding effect on the main crack and generates contact forces along its flanks. The simultaneous and competitive growth of the main crack and the branch in fatigue is simulated step by step using kinetic data for mode II and mode I obtained for a maraging steel.     

A fracture mechanical treatment of free edge stress singularities applied to a brazed ceramic/metal compound

The theoretical fracture mechanical treatment of craek problems in regular stress fields is extended to account for singular stresses as occur in bi-material systems whenever a discontinuity in material properties and geometry exists. The singular stress fields are derived for arbitrary material combination and geometry and the global stress state as occurs in a real compound is obtained by Finite Element (FE) calculations. Then especially the mode I stress intensity factors are calculated for semi-elliptical surface cracks in the ceramic component of a brazed ceramic/metal joint. Critical crack sizes are determined for failure analysis of the compound.     

Fatigue life prediction model for laser clad AISI 4340 specimens with multiple surface cracks

Fatigue test on laser clad AISI 4340 steel specimens show that multiple surface cracks initiate from the clad-toe region due to clad bead overlap features deposited in a raster scan pattern. A fatigue crack growth modeling algorithm capturing the observed fatigue behavior of periodic multiple co-planar semi-elliptical cracks initiating from these features was developed based on crack closure concepts for small cracks to predict the fatigue S–N curve of laser clad AISI 4340 steel specimens. New solutions for stress intensity factor and clad-toe magnification factor (Mk-factor) are presented for surface cracks propagating from the laser clad-toe region. The fatigue life prediction model is able to start from multiple clad-toe surface cracks propagating from the clad-toe region which coalesce into a dominant surface crack or edge crack before final failure. The fatigue life prediction result was compared to the experiment S–N curve test data and gave good agreement.     

SHORT AND LONG FATIGUE CRACK GROWTH IN A SiC REINFORCED ALUMINIUM ALLOY

Fatigue crack growth behaviour in a 15 wt% SiC particulate reinforced 6061 aluminium alloy has been examined using pre-cracked specimens. Crack initiation and early growth of fatigue cracks in smooth specimens has also been investigated using the technique of periodic replication. The composite contained a bimodal distribution of SiC particle sizes, and detailed attention was paid to interactions between the SiC particles and the growing fatigue-crack tip. At low stress intensity levels, the proportion of coarse SiC particles on the fatigue surfaces was much smaller than that on the metallographic sections, indicating that the fatigue crack tends to run through the matrix avoiding SiC particles. As the stress intensity level increases, the SiC particles ahead of the growing fatigue crack tip are fractured and the fatigue crack then links the fractured particles. The contribution of this monotonic fracture mode resulted in a higher growth rate for the composite than for the unreinforced alloy. An increase in the proportion of cracked, coarse SiC particles on the fatigue surface was observed for specimens tested at a higher stress ratio.     

Stress intensity factors and weight functions for deep semi-elliptical surface cracks in finite-thickness plates

ABSTRACT Three-dimensional finite element analyses have been conducted to calculate the stress intensity factors for deep semi-elliptical cracks in flat plates. The stress intensity factors are presented for the deepest and surface points on semi-elliptic cracks with a/t -values of 0.9 and 0.95 and aspect ratios ( a/c ) from 0.05 to 2. Uniform, linear, parabolic or cubic stress distributions were applied to the crack face. The results for uniform and linear stress distributions were combined with corresponding results for surface cracks with a/t = 0.6 and 0.8 to derive weight functions over the range 0.05 ≤  a/c  ≤ 2.0 and 0.6 ≤  a/t  ≤ 0.95. The weight functions were then verified against finite element data for parabolic or cubic stress distributions. Excellent agreements are achieved for both the deepest and surface points. The present results complement stress intensity factors and weight functions for surface cracks in finite thickness plate developed previously.     

AN APPROACH TO MEASURE THE SHAPES OF THREE-DIMENSIONAL SURFACE CRACKS DURING FATIGUE CRACK GROWTH

This study presents a technique for measuring shapes of three dimensional surface cracks continuously during fatigue crack growth. The technique uses a laser interferometric system to measure crack compliance and a photomicroscopic system to measure surface crack length. Using a compliance expression for surface cracks, valid for the range of crack aspect ratios (a/c) of 0.2 to 2.0, aspect ratio calculations employing compliance and surface crack length measurements are demonstrated for cracks growing from EDM notches of different geometries (shallow or deep). The experimentally determined aspect ratio variations during cyclic crack growth are shown to be in good agreement with the expected variations in aspect ratio, predicted using the stress intensity factor equations for surface cracks. The effects of deviations in the compliance measurement location from the center of the surface crack due to assymetric crack growth are also accounted for through corrections of compliance measurements for crack-asymmetry. The fatigue crack growth rates of surface cracks, after incorporating the variations in aspect ratio in the calculations, agreed with the large-crack growth data for all crack geometries.     

Multiscale continuum modeling of a crack in elastic media with microstructures

Cosserat type continuum theories have been employed by many authors to study cracks in elastic solids with microstructures. Depending on which theory was used, different crack tip stress singularities have been obtained. In this paper, a microstructure continuum theory is used to model a layered elastic medium containing a crack parallel to the layers. The crack problem is solved by means of the Fourier transform. The resulting integrodifferential equations are discretized using the Chebyshev polynomial expansion method for numerical solutions. By using the present theory, the explicit internal length effects upon the crack opening displacement and stress field can be observed. It is found that the stress field near the crack tip is not singular according to the microstructure continuum solution although the level of the opening stress shows an increasing trend until it gets very close to the crack tip. The rising portion of the near tip opening stress is used to project the stress intensity factor which agrees fairly well with that obtained using the FEM to perform stress analyses of the cracked layered medium with the exact geometry. The numerical solutions also indicate that treating the layered medium as an equivalent homogeneous classical elastic solid is not adequate if cracks are present and accurate stress intensity factors in the original layered medium is desired.     

The effect of an elliptical inclusion on a crack

The interaction between an elliptical inclusion and a crack is analyzed by body force method. The investigated stress field is simulated by superposing the fundamental solutions for a point force applied at a point in an infinite plate containing an elliptical inclusion. Based on numerical results, effects of the inclusion shape on the crack tip stress intensity factor are discussed. It is found that for small cracks emanating from a stress-higher point on the inclusion interface the stress intensity factors are mainly determined by the stresses, occurring at the crack starting point before the crack initiation, and the inclusion root radius, besides the crack length. However, for the cracks occurring in a stress-lower region around the inclusion, it is difficult to characterize the effect of the inclusion geometry on the stress intensity factors of small cracks by the inclusion root radius alone. This revised version was published online in July 2006 with corrections to the Cover Date.