Effect of intercommunication between various elements of a material on its crack extension resistance: Linear intercommunication force law

A material's resistance to failure by crack extension is influenced by the characteristics of the intercommunication between the various elements that comprise the material's structure. This paper investigates in detail the case where the material consists of linear elements with the crack being transverse to these elements. Various simulation models are analysed, with consideration being focused on the case where the shear intercommunication between the elements is linearly related to the shear strain. It is shown that there is a correlation between weak intercommunication and a high crack extension resistance but that, for a wide range of situations, the strength of the shear intercommunication has relatively little effect on the crack extension resistance. This means that when seeking explanations for large differences in the crack extension resistances of various types of material, it is appropriate to look for such explanations beyond the confines of a simple linear intercommunication law.     

Analysis of Mode I and Mode II Crack Growth Arrest Mechanism with Z-Fibre Pins in Composite Laminated Joint

This paper presents the numerical study of the mode I and mode II interlaminar crack growth arrest in hybrid laminated curved composite stiffened joint with Z-fibre reinforcement. A FE model of hybrid laminated skin-stiffener joint reinforced with Z-pins is developed to investigate the effect of Z- fibre pins on mode I and mode II crack growth where the delamination is embedded inbetween the skin and stiffener interface. A finite element model was developed using S4R element of a 4-node doubly curved thick shell elements to model the composite laminates and non linear interface elements to simulate the reinforcements. The numerical analyses revealed that Z-fibre pinning were effective in suppressing the delamination growth when propagated due to applied loads. Therefore, the Z-fibre technique effectively improves the crack growth resistance and hence arrests or delays crack growth extension.     

Crack growth resistance behavior of a functionally graded material: computational studies

This paper describes crack growth resistance simulation in a ceramic/metal functionally graded material (FGM) using a cohesive zone ahead of the crack front. The plasticity in the background (bulk) material follows J₂ flow theory with the flow properties determined by a volume fraction based, elastic-plastic model (extension of the original Tamura-Tomota-Ozawa model). A phenomenological, cohesive zone model with six material-dependent parameters (the cohesive energy densities and the peak cohesive tractions of the ceramic and metal phases, respectively, and two cohesive gradation parameters) describes the constitutive response of the cohesive zone. Crack growth occurs when the complete separation of the cohesive surfaces takes place. The crack growth resistance of the FGM is characterized by a rising J-integral with crack extension (averaged over the specimen thickness) computed using a domain integral (DI) formulation. The 3-D analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates solid elements with graded elastic and plastic properties and interface-cohesive elements coupled with the functionally graded cohesive zone model. The paper describes applications of the cohesive zone model and the DI method to compute the J resistance curves for both single-edge notch bend, SE(B), and single-edge notch tension, SE(T), specimens having properties of a TiB/Ti FGM. The numerical results show that the TiB/Ti FGM exhibits significant crack growth resistance behavior when the crack grows from the ceramic-rich region into the metal-rich region. Under these conditions, the J-integral is generally higher than the cohesive energy density at the crack tip even when the background material response remains linearly elastic, which contrasts with the case for homogeneous materials wherein the J-integral equals the cohesive energy density for a quasi-statically growing crack.     

Computational modeling of the indentation of a cracked poroelastic half-space

The paper examines the computational modelling of the surface identation of a poroelastic half-space region which is weakened either by a cylindrical crack or a penny-shaped crack. The axisymmetric problems associated with those situations are examined using a finite element procedure where special singularity elements are incorporated at the crack tip and appropriate interaction conditions are incorporated on the faces of the crack. The results presented in the paper illustrate the influence of the extent of fracture and the pore pressure boundary conditions on the various surfaces, on the time dependent evolution of the stress intensity factors and the time dependent consolidation settlement of the axisymmetric indentor. The analysis is extended to the consideration of crack extension in poroelastic materials where displacement, traction and pore water pressure boundary conditions are alerted to take into account the evolving crack. The path of crack extension is established by mixed mode crack extension criteria applicable to porous fabric. The computational procedure associated with this approach is used to examine the problem of the surface indentation of a half-space by a rigid circular indentor. This revised version was published online in July 2006 with corrections to the Cover Date.     

A new subregion boundary element technique based on the domain decomposition method

A new subregion boundary element technique based on the domain decomposition method is presented in this paper. This technique is applicable to the stress analysis of multi-region elastic media, such as layered-materials. The technique is more efficient than traditional methods because it significantly reduces the size of the final matrix. This is advantageous when a large number of elements need to be used, such as in crack analysis. Also, as the system of equations for each subregion is solved independently, parallel computing can be utilized. Further, if the boundary conditions are changed the only equations required to be recalculated are the ones related to the regions where the changes occur. This is very useful for cases where crack extension is modelled with new boundary elements or where crack faces come to contact. Numerical examples are presented to demonstrate the accuracy and efficiency of the method.     

Mixed-mode crack growth predictions

The problem of slow stable growth of an inclined crack in a plate subjected to uniaxial tension is studied by the strain energy density criterion. The stable crack growth process is simulated by predicting a series of crack growth steps corresponding to a piecewise loading increase when material elements along the direction of crack extension absorb a critical amount of elastic strain energy density. Crack instability takes place when the last ligament of crack extension takes a critical value which is a material constant. The critical stress at the onset of crack initiation and unstable crack extension is determined for various crack inclination angles. Three different loading step increments corresponding to three different loading rates are considered and their effect on stable crack growth is analysed. Furthermore, the influence of loading history on the crack growth process for three different loading types is studied. The complete crack growth patterns for all types of load are determined and analysed. It is obtained that the amount of slow crack growth can be increased by lowering the rate of loading. The effect of the loading history on the failure load and the crack paths is established.     

Estimating the toughening effect of crack-bridging particles in a brittle matrix

Several toughening mechanisms for cracks in brittle solids depend on the restraining effects of material elements that bridge the faces of a crack. A standard way of quantifying the toughening effect is to smear-out the restraining stresses provided by the individual bridging elements. The present paper, by using a very simple simulation model which allows for the discreteness of the system, together with a general force-law for the behaviour of an individual bridging element, shows that the smearing-out procedure is valid if the bridging elements are ductile; however, it can underestimate the toughening effect when the elements are brittle.     

Fatigue growth prediction of center slant crack in rectangular plate

This paper presents a numerical prediction model of mixed‐mode crack fatigue growth in a plane elastic plate. It involves a formulations of fatigue growth of multiple crack tips under mixed‐mode loading and a displacement discontinuity method with crack‐tip elements (a boundary element method) proposed recently by Yan is extended to analyse the fatigue growth process of multiple crack tips. Due to an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single‐region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modelled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the present numerical approach is used to analyse the fatigue growth of a centre slant crack in a rectangular plate. The numerical results illustrate the validation of the numerical prediction model and can reveal the effect of the geometry of the cracked plate on the fatigue growth.     

The influence of crystallographic orientation on crack tip displacements of microstructurally small, kinked crack crossing the grain boundary

The paper presents an analysis of the effects of grain orientations on a short, kinked surface crack in a 316L stainless steel. The kinking of the crack is assumed to take place at the boundary between two neighbouring grains. The analysis is based on a plane-strain finite element crystal plasticity model. The model consists of 212 randomly shaped, sized and oriented grains, loaded monotonically in uniaxial tension to a maximum load of 0.96R_p0.2 (240 MPa). The influence that a random grain structure imposes on a Stage I crack is assessed by calculating the crack tip opening (CTOD) displacements for bicrystal as well as for polycrystal models, considering different crystallographic orientations. Since a Stage I crack is assumed, the crack is always placed in a slip plane. Results from a bicrystal case show that the maximal CTODs are directly related to the stiffness of the grain containing the crack extension. Anisotropic elasticity and crystal plasticity both contribute to this grain stiffness, resulting in maximal CTOD when Schmid factors are the highest on two slip planes. Such crystallographic orientation results in a soft elasto-plastic response. Anisotropic elasticity can additionally increase the softness of a grain at certain crystallographic orientations. Minimal anisotropic elasticity at the crystallographic orientations with the highest Schmid factors causes the CTOD to be maximized. Presuming that the crack will preferably follow the slip plane where the crack tip opening displacement is highest, we show that the crystallographic orientation can affect the CTOD values by a factor of up to 7.7. For a given grain orientation the maximum CTOD is attained when the crack extension deflection into a second grain is between −75.141° and 34°. For the polycrystal case we show that grains beyond the first two crack-containing grains change the CTOD by a factor of up to 3.3 and that the largest CTODs are obtained when placing the crack into a slip plane with crack extension that results in a crack extension being more perpendicular to the external load.     

Lattice modeling of aggregate interlocking in concrete

In this paper, we study a mixed-mode fracture process using a conventional two dimensional lattice model with incorporated meso-level internal material structure. Simple elasto-brittle elements of the network are divided into three phases according to a projected grain layout. The stiffness of any element that fulfils a failure criterion is removed. As a new feature of the otherwise standard lattice approach, we added the recovery of normal stiffness when a severed element enters the compressive regime. This enhancement enables capture of the shear resistance of an existing crack caused by crack roughness, i.e. what is termed aggregate interlocking. We demonstrate this enhancement via the simulation of mixed-mode experiments on concrete performed at a laboratory at the Technical University of Denmark. Double notched concrete specimens were initially pre-cracked in tension. Then, various combinations of tensile and shear load (normal and tangential to the crack plane) were applied. Simulated crack patterns and load–displacement curves are compared to the experimental observations.     

Stress intensity factor calibration for a longitudinal crack in a fuselage barrel and the bulging effect influence

Aircraft structures require minimum weight configurations with high strength in order to support all operational stresses with high reliability. Framework construction is the base of these airframes where cross sectional shapes are connected into a rigid assembly. The vertical and horizontal cross-members are arranged to withstand all structural loads and the skin to support the pressure gradient. This type of fuselage has been in use for about 80 years; it is very strong and relatively lightweight when used with materials of high specific strength.Due to the difficulty of producing defect free structures and to avoid damage during the life of a structure, damage tolerance is an important requirement. Damage tolerance is a design philosophy predominantly applied in the primary structural parts of civil airframes in order to tolerate a defect that can be detected and repaired during the next maintenance check.In this article, the stress intensity factor (SIF) for a longitudinal crack under the pressurization load was studied. For this purpose, a barrel composed of two frames with the longitudinal stiffeners and with the geometry usually found in civil airframes was chosen. A central crack, between the two frames, was simulated in a geometrically nonlinear finite element model composed by solid elements. The stress intensity factor for different crack lengths, until the crack tips reach the frame, was calculated using linear elastic fracture mechanics assumptions and the modified virtual crack closure technique. In addition, stress intensity factors along the skin thickness were determined. The variation of the SIF values along the thickness due to the bulging effect is modeled, and comparisons were made with the behavior of an equivalent reinforced flat panel.     

不同软化曲线形状对裂缝扩展阻力G_R曲线的影响

最近基于裂缝粘聚力提出了描述裂缝扩展全过程阻力变化的GR曲线,所发展的解析解相关于骨料桥联咬合作用造成的非线性断裂过程区的能量耗散,故与该区域材料使用的拉伸软化本构关系即应力-裂缝张开口位移软化曲线有密切联系。鉴于此,该文采用4种不同的软化曲线研究了软化曲线形状对裂缝扩展阻力GR的影响。结果发现,GR曲线对软化曲线敏感,GR曲线的合理性依赖于软化曲线的准确性。在使用准确软化曲线的前提下,GR曲线的特征点与软化曲线的特征点存在相对应关系。     

The effect of material combinations and relative crack size to the stress intensity factors at the crack tip of a bi-material bonded strip

Several types of singular stress fields may appear at the corner where an interface between two bonded materials intersects a traction-free edge depending on the material combinations. Since the failure of the multi-layer systems often originates at the free-edge corner, the analysis of the edge interface crack is the most fundamental to simulate crack extension. In this study, the stress intensity factors for an edge interfacial crack in a bi-material bonded strip subjected to longitudinal tensile stress are evaluated for various combinations of materials using the finite element method. Then, the stress intensity factors are calculated systematically with varying the relative crack sizes from shallow to very deep cracks. Finally, the variations of stress intensity factors of a bi-material bonded strip are discussed with varying the relative crack size and material combinations. This investigation may contribute to a better understanding of the initiation and propagation of the interfacial cracks.     

The value of the J-integral at the onset of crack extension from a weld defect: weld material is harder than parent material

The paper addresses the problem of crack extension in a weld in an engineering structure for the situation where the crack is parallel to the plane of the weld. An earlier analysis, for the case where the weld material is softer than the parent material, has demonstrated the extent to which the value of the J-integral at the onset of crack extension depends on the flow properties of the weld and parent materials, the crack size and the weld thickness. The present paper extends these earlier considerations to the case where the weld material is harder than the parent material, and again demonstrates the non-uniqueness of the value of J at the onset of crack extension.     

The criterion for the unstable failure of cracked stainless steel piping subject to a combination of applied loadings

For extreme accident conditions, the applied loadings on a cracked piping system are complex and can be a combination of loads and displacements applied to various parts of the system. In investigating the problem of crack instability for such conditions, this paper analyses the model where a straight pipe, containing a circumferential through-wall crack at its mid-length position, is subject to bending deformation as a result of rotations applied at its built-in ends through rotational springs and a transverse load applied at an intermediate position along the pipe, again through an appropriate spring system. It is thereby possible to examine the effect of a wide range of loading combinations on the crack instability criterion, as derived using the tearing modulus methodology. One important conclusion is the underscoring of the view that the loading characteristics at the pipe-ends have a very important effect on crack instability.     

Simulation of ductile crack growth in thin aluminum panels using 3-D surface cohesive elements

This work describes the formulation and application of a 3-D, interface-cohesive finite element model to predict quasi-static, ductile crack extension in thin aluminum panels for mode I loading and growth. The fracture model comprises an initially zero thickness, interface element with constitutive response described by a nonlinear traction-separation relationship. Conventional volumetric finite elements model the nonlinear (elastic-plastic) response of background (bulk) material. The interface-cohesive elements undergo gradual decohesion between faces of the volumetric elements to create new traction free crack faces. The paper describes applications of the computational model to simulate crack extension in C(T) and M(T) panels made of a 2.3 mm thick, Al 2024-T3 alloy tested as part of the NASA-Langley Aging Aircraft program. Parameters of the cohesive fracture model (peak opening traction and local work of separation) are calibrated using measured load vs. outside surface crack extensions of high constraint (T-stress > 0) C(T) specimens. Analyses of low constraint M(T) specimens, having widths of 300 and 600 mm and various a/W ratios, demonstrate the capabilities of the calibrated model to predict measured loads and outside surface crack extensions. The models capture accurately the strong 3-D effects leading to various degrees of crack front tunneling in the C(T) and M(T) specimens. The predicted crack growth response shows rapid convergence with through-thickness mesh refinement. Adaptive load increment procedures to control the rate of decohesion in the interface elements leads to stable, rapidly converging iterations in the globally implicit solution procedures.     

Crack tip opening angle measurement through a girth weld in an X100 steel pipeline section*

Crack tip opening angle (CTOA) is becoming one of the most accepted methods for characterizing fully plastic fracture. It provides a measure of the resistance to fracture for a material in cases where there is a large degree of stable‐tearing crack extension during the fracture process. Our current pipeline research uses the CTOA test as an alternative, or addition, to the CTOD (crack tip opening displacement) and the fracture energy characterization provided by the J‐integral approach. A test technique was developed for measurement of CTOA that uses a modified double cantilever beam (MDCB) specimen. A digital camera and image analysis software were used to record the progression of the crack tip and to estimate the CTOA. In this article, CTOA data on crack growth orientations perpendicular to pipeline girth welds are presented. The CTOA for X100 high strength bainitic gas pipeline steel is reported. Two different specimen gauge sections, 3 mm and 8 mm, were used and the effect of the specimen thickness on the CTOA is discussed. The results show a change in the CTOA as the crack grows into the heat affected zone (HAZ). A slight improvement in the fracture resistance is measured, and through the weld, a slight decrease in fracture resistance is observed.     

Boundary element analysis of fatigue crack propagation micromechanisms in austempered ductile iron

The Dual Boundary Element Method (DBEM) is used in this work to model the micro mechanics of fatigue crack propagation in austempered ductile iron (ADI). Emphasis is put in devising accurate procedures for the evaluation of the interaction effects between very close crack–microcrack arrays. Fracture parameters are computed via the so-called one-point displacement formula using special crack-tip elements. Crack propagation is modelled using an incremental crack extension analysis; with crack extensions calculated using a propagation law that accounts for the near-threshold regime. Obtained results are in agreement with experimental observations, providing evidence to fracture mechanics models proposed in the literature.     

A finite element treatment of ductile crack extension

Abstract

To provide a realistic analysis for fracture, this paper is devoted to finite element approaches which attempt to describe ductile crack extension. A rigorous hybrid displacement finite‐element modeling, involving the translation of entire “singular” near‐tip elements and consideration of global energy balance, is successfully developed. To investigate the variation of global energy release rate G* and J‐integral for single‐step extensions at various levels of applied loads (extension ^δa = constant), the Kfouri et al.’s center‐cracked problem together with A533B compact tension specimen are solved. In addition, an available experimental J resistance curve for the compact tension specimen (made of Ni‐Cr‐Mo‐V rotor steel) is simulated by the present finite element analysis procedure to study the actual process of ductile fracture. The effect of unloading process occurred in the plastic region behind the advancing crack‐tip is also discussed.     

PREDICTING THE EFFECTS OF CRACK TIP CONSTRAINT ON MATERIAL RESISTANCE CURVES USING DUCTILE DAMAGE THEORY

Abstract— In recent years much interest has been focused on the geometry dependence of the resistance to stable ductile crack growth of engineering materials, and in particular, in explaining this in terms of "constraint" effects. This paper describes the results of work using the Rousselier ductile damage model in finite element studies to simulate the growth and coalescence of voids, and hence the mechanics of ductile crack growth, to predict the effect of constraint on resistance to fracture. Using the modified boundary layer solution, where constraint is controlled by the application of remote displacements, it was possible to simulate resistance curves for different constraint conditions. This has produced a "net" of resistance curves, within which the curve for any specimen geometry can be found from a knowledge of the crack tip constraint for that specimen. This has been tested by comparing the results with those obtained from two specimens for which the constraint conditions are known. Good agreement has been achieved.
The results show that, although constraint has very little effect on conditions at the crack tip at initiation of crack growth, beyond that constraint plays an important part in defining the resistance curve. For low constraint geometries there is a very large loss in crack tip constraint which results in a large increase in the slope of the resistance curve. On the other hand, high constraint geometries exhibit very little dependence on crack tip constraint.