Fracture analysis of multi-site cracking in fuselage lap joints

A two-dimensional plane stress elastic fracture mechanics analysis of a cracked lap joint fastened by rigid pins is presented and results are applied to the problem of multi-site damage (MSD) in riveted lap joints of aircraft fuselage skins. Two problems are addressed, the problem of equal length MSD cracks and the problem of alternating length MSD cracks. For the problem of equal length cracks, two models of rivet/skin interactions are studied and the role of residual stresses due to the riveting process is explored. Stress intensity factors are obtained as a function of normalized crack length. Also, the load distribution among rivet rows and the compliance change of the joint due to MSD cracking are obtained. For the problem of alternating length cracks, attention is focussed on how load is distributed between columns of rivets and how this load shedding can alter crack tip stress intensity factors. The equal and alternating length crack analyses reveal no clear-cut mechanism to explain the relative uniformity of fatigue cracks emerging from lap joint rivet holes in actual aircraft and in mechanical lap joint tests.     

Contact model of cracks in orthotropic materials

We consider a plane strain problem for an orthotropic half plane loaded at infinity and containing a crack along its fixed edge. To remove a singularity near the right crack tip, we introduce an artificial contact zone. The problem under consideration is reduced to the mixed Dirichlet-Riemann boundaryvalue problem. We present the exact solution of this problem and deduce formulas for stresses in the contact zone and on the continuation of the crack and for the stress intensity factors. By using both analytic and numerical methods, we prove that the energy-release rate is quasiinvariant in the process of crack propagation relative to the size of the contact zone. On the basis of these results, we propose an algorithm for the evaluation of the paramenters of fracture of composites of finite dimensions with interface cracks. As a special case, we develop a model of interface cracks with actual contact zone and establish the dependences of the length of this zone on the external load and elasticity moduli of the material. Dnepropetrovsk State University, Dnepropetrovsk. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 5, pp. 59–66, September–October, 1999     

Numerical simulation of plasticity-induced fatigue crack closure with emphasis on the crack growth scheme: 2D and 3D analyses

In this paper a numerical simulation of plasticity-induced fatigue crack closure is performed using the finite element method. Emphasis is placed on the crack growth scheme usually adopted for modelling fatigue crack growth in crack closure problems. The number of load cycles between node releases usually reported in the literature has been, in general, one or two. The present work shows that increasing the number of load cycles between node releases has a strong effect on the opening stresses, particularly, under plane strain conditions and 3D fatigue cracks, in contrast plane stress shows little variation with increasing number of load cycles. This investigation also suggests that ratchetting may take place close to the crack tip in both plane strain and 3D crack problems. The problem of discontinuous crack closure under plane strain conditions, often reported in the literature, is also addressed.     

Trifurcation of a crack due to plane SH-waves in an infinite elastic medium

The dynamic anti-plane problem of trifurcation of a semi-infinite crack due to incidence of two linearly varying plane SH-waves with non-parallel wave fronts in an infinite elastic medium has been considered. The semi-infinite crack is assumed to trifurcate when the plane waves intersect the crack tip. The problem has been solved using the self-similar technique, which is based on the observation that certain field variables show dynamic similarities. The results include the expressions for shear stress in the planes of the cracks and the stress intensity factors at the crack tips. Numerical calculations have been carried out to show the variations of stress intensity factors at the crack tips with the angle of skew for different values of the crack tip velocity and angle of incidence.     

The influence of grains’ crystallographic orientations on advancing short crack

A model of microstructurally short cracks that accounts for random grain geometry and crystallographic orientations is coupled with crystal plasticity constitutive model. A short crack is then inserted in the slip plane in one of the grains at the model top boundary and extended into one of the available slip planes of the neighboring grain at monotonic remote load of 0.96R_p0.2. Crack tip opening (CTOD) and sliding (CTSD) displacements are then calculated for several different crystallographic orientations and crack lengths. As the crack is contained in a single grain the crystallographic orientation of the neighboring grain can change the crack tip displacements by up to 26%, however, the displacements change by up to a factor of 10, once the crack is extended beyond the grain boundary into the next grain. Significant CTSD values were observed in all the analyzed cases pointing to mixed mode loading. Another important observation is that the random crystallographic orientations of grains beyond the first two crack-containing grains affect the CTOD by a factor of up to 4.4. This effect decreases slightly with increased crack length.     

Plasticity bands near the tips of edge cracks in a body with circular hole

Within the framework of the model of plasticity bands, we consider a two-dimensional elastoplastic problem of fracture mechanics for a body with one circular hole and two collinear cracks whose ends lie on the contour of the hole under the conditions of plane stressed state and plane deformation. It is assumed that plastic strains near each tip of the edge cracks are concentrated along three (for the plane stressed state) or two (under the conditions of plane deformation) plasticity bands. Their lengths and orientations are determined as a result of the solution of the problem. Numerical results are obtained for the cases of a biaxial tensile load acting at infinity and constant pressure applied to the contour of the hole and edge cracks (under the conditions of plane deformation). Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 2, pp. 79–86, March–April, 1998.     

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。     

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.     

Analysis of the dynamic behavior of two parallel symmetric cracks using the non-local theory

In this paper, the dynamic behavior of two parallel symmetric cracks under harmonic anti-plane shear waves is studied using the non-local theory. For overcoming the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the problem to obtain the stress occurs near the crack tips. The Fourier transform is applied and a mixed boundary value problem is formulated. Then a set of dual integral equations is solved using the Schmidt method. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the distance between two parallel cracks, respectively.     

VECTOR CTD CRITERION APPLIED TO MIXED MODE FATIGUE CRACK GROWTH

Abstract— This work is aimed at developing a general parameter based on the deformation intensity at a mixed mode crack tip to predict crack growth behaviour, especially in the near threshold region. Being a mechanisms-related parameter, the vector crack tip displacement (CTD) is defined as a vector summation of CTOD and CTSD_c which act, respectively in the directions of mode I and mode II fatigue crack growth. The basic assumption is that both direction and rate of mixed mode fatigue crack growth are governed by the vector ΔCTD, which represents the resultant of the "driving force"at the crack tip. The analytical predictions obtained by using the vector ΔCTD are in good agreement with the reported experimental results of mixed mode I and II fatigue cracks.     

Fracture parameters for interfacial cracks: an experimental-finite element study of crack tip fields and crack initiation toughness

Crack tip measurements and analysis of interfacial parameters for PMMA-aluminum bimaterial system are presented. A variety of crack tip mode-mixities are obtained by subjecting asymmetric four-point-bend specimens to different boundary loads. The crack tip fields are mapped using the optical method of Coherent Gradient Sensing (CGS). The complex stress intensity factors and the associated crack tip mixities () are measured from CGS fringe patterns. The asymptotic expansion field for interface cracks is used for extracting fracture parameters by accounting for higher order contributions to the experimental data. The measurements are compared with complementary finite element computations. A linear relationship between crack tip mixity and the applied load mixity is experimentally demonstrated in this large elastic mismatch system. The fracture load and hence the energy release rate G _cr () at crack initiation is measured as applied load mixities are varied. Limited discussion on the influence of surface roughness prior to bonding on the fracture toughness is included. Positive and negative shear on the crack plane produce different failure responses in this bimaterial system and the observed asymmetry is akin to the one predicted by the T&H model that includes crack tip nonlinearty.     

CRACK CLOSURE AND PLASTIC ZONE SIZES IN FATIGUE

Abstract— An elastic-plastic finite element simulation of growing fatigue cracks which accounts for plasticity-induced crack closure is used to study the size of the forward and reversed plastic zones at the crack tip. Forward plastic zone widths for fatigue cracks and stationary, monotonically loaded cracks are compared and found to be similar. The width of the forward plastic zone at the tip of a fatigue crack is not significantly influenced by closure. The traditional Irwin-Rice estimate for crack tip plastic zone size in plane stress is found to be generally consistent with the finite element results. The width of the reversed plastic zone at the tip of a growing fatigue crack in plane stress is found to be considerably less than one-fourth the size of the forward plastic zone, the traditional Rice estimate. This decrease appears to be due to fatigue crack closure. A simple model is developed which permits estimation of the reversed plastic zone size for any stress ratio from information about maximum and minimum stresses and the closure stress. The predictions of this model agree closely with plastic zone sizes calculated by the finite element analysis. These observations appear to be consistent with experimental measurements of forward and reversed plastic zones sizes reported in the literature.     

Numerical Green's functions for some electroelastic crack problems

A plane electroelastic problem involving planar cracks in a piezoelectric body is considered. The deformation of the body is assumed to be independent of time and one of the Cartesian coordinates. The cracks are traction free and are electrically either permeable or impermeable. Numerical Green's functions which satisfy the boundary conditions on the cracks are derived using the hypersingular integral approach and applied to obtain a boundary integral solution for the electroelastic crack problem considered here. As the conditions on the cracks are built into the Green's functions, the boundary integral solution does not contain integrals over the cracks. It is used to derive a boundary element procedure for computing the crack tip stress and electrical displacement intensity factors.     

The transition between stress corrosion crack growth and plastic fracture—II. The effect of loading pattern

The paper addresses the problem of predicting the onset of plastic fracture at the tip of a growing stress corrosion crack, using data from laboratory fracture mechanics tests. A theoretical analysis for a particular model: namely that of the place strain deformation of a solid with two symmetrically situated deep cracks, and with tension of the small remaining ligament, shows that plastic fracture occurs at a $\text{J}$ value that is not constant, but depends on whether the loading is load or displacement control. This result, which is valid for materials for which the onset of crack extension and unstable fracture are coincident in a rising load fracture mechanics test, provides valuable support for the view that great care must be exercised when using fracture mechanics procedures to predict the transition between stress corrosion crack growth and plastic fracture in such materials.     

The interaction of two inclined cracks with dynamic stress wave loadings

To gain insight into the phenomenon of the interaction of stress waves with material defects and the linkage of two cracks, the transient response of two semi-infinite inclined cracks subjected to dynamic loading is examined. The solutions are obtained by the linear superposition of fundamental solutions in the Laplace transform domain. The fundamental solution is the exponentially distributed traction on crack faces proposed by Tsai and Ma [1]. The exact closed form solutions of stress intensity factor histories for these two inclined cracks subjected to incident plane waves and diffracted waves are obtained explicitly. These solutions are valid for the time interval from initial loading until the first wave scattered at one crack tip returns to the same crack tip after being diffracted by another crack tip. The result shows that the contribution of diffracted waves to stress intensity factors is much less than the incident waves. The probable crack propagation direction is predicted from the fracture criterion of maximum circumferential tensile stress. The linkage of these two cracks is also investigated in detail.     

TEM observations of dislocation emission at crack tips in aluminium

Direct observations were made of the propagation of ductile cracks and associated dislocation behaviour at crack tips in aluminium during tensile deformation in an electron microscope. In the electropolished area, the cracks propagated as a Mode III shear-type by emitting screw dislocations on a plane coplanar to the crack plane. A zone free of dislocations was observed between the crack tip and the plastic zone. As the cracks propagated into thicker areas, the fracture mode changed from Mode III to predominantly Mode I. The crack top of the Mode I cracks was blunted by emitting edge dislocations on planes inclined to the crack plane. The blunted cracks did not propagate until the area ahead of the crack tip was sufficiently thinned by plastic deformation. The cracks then propagated abruptly, apparently without emitting dislocations. The stress intensity factor was measured from the crack tip geometry of Mode III cracks and it was found to be in good agreement with the critical value of the stress intensity factor required for dislocation generation.     

Constructing the weight function for flat solids with cracks

An approximated method is proposed for constructing the weight function for flat solids with a crack based on the available exact solutions for an infinite plane and the available values of the stress intensity factor at the crack tip in the examined solid for any distribution of the load at its edges. Examples are given of determining the weight function for edge and central cracks in right-angled plates and disks.Translated from Problemy Prochnosti, No. 8, pp. 10–14, August, 1990.     

A threshold fatigue crack closure model: Part I – model development

A fatigue crack closure model is developed that includes the effects of, and interactions between, the three closure mechanisms most likely to occur at threshold; plasticity, roughness, and oxide. This model, herein referred to as the CROP model (for Closure, Roughness, Oxide, and Plasticity), also includes the effects of out‐of‐plane cracking and multi‐axial loading. These features make the CROP closure model uniquely suited for, but not limited to, threshold applications. Rough cracks are idealized here as two‐dimensional sawtooths, whose geometry induces mixed‐mode crack‐tip stresses. Continuum mechanics and crack‐tip dislocation concepts are combined to relate crack face displacements to crack‐tip loads. Geometric criteria are used to determine closure loads from crack‐face displacements. Finite element results, used to verify model predictions, provide critical information about the locations where crack closure occurs. The CROP model is verified with experimental data in part II of this paper.     

A boundary integral approach for plane analysis of electrically semi-permeable planar cracks in a piezoelectric solid

A plane electro-elastostatic problem involving arbitrarily located planar stress free cracks which are electrically semi-permeable is considered. Through the use of the numerical Green's function for impermeable cracks, the problem is formulated in terms of boundary integral equations which are solved numerically by a boundary element procedure together with a predictor–corrector method. The crack tip stress and electric displacement intensity factors can be easily computed once the boundary integral equations are properly solved.     

Transient analysis of multiple parallel cracks under anti-plane dynamic loading

The problem of a homogeneous linear elastic body containing multiple non-collinear cracks under anti-plane dynamic loading is considered in this work. The cracks are simulated by distributions of dislocations and an integral equation relating tractions on the crack planes and the dislocation densities is derived. The integral equation in the Laplace transform domain is solved by the Gaussian–Chebyshev integration quadrature. The dynamic stress intensity factor associated with each crack tip is calculated by a numerical inverse Laplace scheme. Numerical results are given for one crack and two or three parallel cracks under normal incidence of a plane horizontally shear stress wave.