Three-dimensional stress and displacement fields near an elliptical crack front

Local stress and deformation fields for an elliptical crack embedded in an infinite elastic body subjected to normal, shear and mixed loads are considered. Particular emphasis is placed on the direction of propagation of points along the crack border. A confocal curvilinear coordinate system related to a fundamental ellipsoid, and a local spherical coordinate system attached to the crack border are adopted. Using asymptotic analysis, this paper obtains the stress and displacement fields in a plane inclined to the 3D crack front. Results show that the present solutions are independent of the curvature of the ellipse, and different from those given by Sih (1991). Based on two different fracture criteria, crack growth analysis shows that a 3D crack would propagate in the direction of the normal plane along the crack front. As a result, the fracture initiation and propagation of a 3D flat crack can be analyzed in the plane normal to the crack front, and the local fields in the normal plane are the linear superposition of the plane strain mode-I, mode-II, and mode-III crack-tip fields.     

Coupling of the BEM with the MFS for the numerical simulation of frequency domain 2-D elastic wave propagation in the presence of elastic inclusions and cracks

This paper proposes a coupling formulation between the boundary element method (BEM displacement and TBEM traction formulations) and the method of fundamental solutions (MFS) for the transient analysis of elastic wave propagation in the presence of multiple elastic inclusions to overcome the specific limitations of each of these methods. The full domain of the original problem is divided into sub-domains, which are handled separately by the BEM or the MFS. The coupling is enforced by imposing the required boundary conditions.The accuracy, efficiency and stability of the proposed algorithms, using different combinations of BEM and MFS, are verified by comparing the solutions against reference solutions. The computational efficiency of the proposed coupling formulation is illustrated by computing the CPU time and the error at high frequencies.The potential of the proposed procedures is illustrated by simulating the propagation of elastic waves in the vicinity of an empty crack, with null thickness placed close to an elastic inclusion.     

A novel boundary-domain element method of initial stress, finite deformation and discrete cracks in multilayered anisotropic elastic solids

We introduce a novel boundary-domain element method of initial stress, finite deformation (due to large rotation) and discrete cracks in multilayered anisotropic elastic solids. Because the special Green’s function that satisfies the interfacial continuity and surface boundary conditions is employed, the numerical discretization is reduced to be along one side of the cracks and over the subdomains of finite deformation. Two examples are presented. First, the process of interfacial delamination is simulated around a growing through-thickness crack in a pre-stretched film bonded to a flexible substrate. It is shown that the progression of delamination damage is stable but the initiation of delamination crack can be a snap-back instability. This simultaneous damage and fracture process is approached by the cohesive zone model. Second, the postbuckling of a circular delaminated and pre-compressed film is simulated on a flexible substrate. It is shown that the compliance of substrate can play a significant role on the critical behavior of buckling. If the substrate is more compliant or stiffer than the film, the instability initiates as a subcritical hard or a supercritical soft bifurcation. The critical magnitude of pre-strain for the initiation of buckling increases with substrate stiffness. Also, the transition of buckling from the first to the second mode is captured in the simulation.     

On improved crack tip plastic zone estimates based on T‐stress and on complete stress fields

Cracked ductile structures yield locally to form a plastic zone (pz) around their crack tips, which size and shape controls their structural behaviour. Classical pz estimates are based solely on stress intensity factors (SIF), but their precision is limited to very low σ_n/S_Y nominal stress to yield strength ratios. T‐stresses are frequently used to correct SIF‐based pz estimates, but both SIF and SIF plus T‐stress pz estimates are based on truncated linear elastic (LE) stress fields that do not satisfy boundary conditions. Using Griffith's plate complete LE stress field to avoid such truncated pz estimates, the influence of its Williams’ series terms on pz estimation is evaluated, showing that T‐stress improvements are limited to medium σ_n/S_Y values. Then, corrections are proposed to introduce equilibrium requirements into LE pz estimates. Finally, these improved estimates are compared with pz calculated numerically by an elastic–plastic finite element analysis.     

The elastic displacement and stress in a material to promote reflection and transmission of an incoming wave

The conditions on elastic displacement and stress in a material that will promote reflection and transmission of an incoming wave are calculated. It is found, for example, that to optimize reflection and transmission, scalar potentials of the displacement in the wave and in the material will be related to rotations in planes perpendicular and parallel to the direction of propagation to the wave. When a pulse is constructed and its path analyzed through short distances, it is shown that abrupt transitions in tension and compression in a material will maximize reflection of the pulse. When strain energy is minimized where reflection and refraction are to occur, differences in tension and compression become prominent again. Finally, an approximate volume of material is calculated for an electron to harness the restoring forces in a material to balance the energy lost in inelastic scattering.     

Acoustic measurements of stress fields and microstructure

A very precise system for measuring two-dimensional velocity fields in solid samples has been used for nondestructive measurements of both externally applied and residual inhomogeneous stresses in solids,J integrals, stress intensity factors of cracks, and hardness of quenched steel. The longitudinal velocity measurement is based on precise determination of the propagation transit time through the stressed solid specimen using a small diameter, water-coupled acoutic transducer, which is scanned mechanically over the sample. Changes in velocity are then related to changes of stress in the sample by the theory of acoustoelasticity. Similar measurements show a high degree of correlation between longitudinal velocity changes and changes in microstructure in steel samples. Applications to problems of solid mechanics and material science illustrate the utility of this nondestructive measuring technique.     

The numerical solution of boundary-value problems for an elastic body with an elliptic hole and linear cracks

Using the boundary-element method which is a combination of a fictitious load and a displacement discontinuity, numerical solutions are obtained for two-dimensional (plane deformation) boundary-value problems for the elastic equilibrium of infinite and finite homogeneous isotropic bodies having elliptic holes with cracks and cuts of finite length. Using the method of separation of variables, the boundary-value problem is solved in the case of an infinite domain containing an elliptic hole with a linear cut on whose contour the symmetry conditions are fulfilled.     

The optimal control of fracture and stress parameters in a piezoceramic halfspace with cracks

An approach to the determination of the optimal control of fracture and strength parameters in a piezoceramic halfspace with cracks under antiplane deformation conditions is proposed. The distribution over certain part of the halfspace boundary, harmonically changing with time under the influence of axial forces or electric charges is analyzed as a control interaction. The solution of the inverse problem in fracture mechanics is obtained from the solution of the corresponding direct boundary value problem; in this case, the optimization problem is reduced to the momentum problem. The solution of the direct electroelastic problem using the method of the boundary integral equations is obtained. Various control functions permitting to realize the optimal process of control, i.e. the minimal energetic expenses, are given.     

Numerical simulation of fatigue crack propagation in compressive residual stress fields of notched round bars

In this paper, the influence of the residual compressive stresses induced by roller burnishing on fatigue crack propagation in the fillet of notched round bar is investigated. A 3D finite element simulation model of rolling has allowed to introduce a residual stress profile as an initial condition. After the rolling process, fatigue loading has been applied to three‐point bending specimens in which an initial crack has been introduced. A numerical predictive method of crack propagation in roller burnished specimens has also been implemented. It is based on a step‐by‐step process of stress intensity factor calculations by elastic finite element analyses. These stress intensity factor results are combined with the Paris law to estimate the fatigue crack growth rate. In the case of roller burnished specimens, a numerical modification concerning experimental crack closure has to be considered. This method is applied to three specimens: without roller burnishing, and with two levels of roller burnishing (type A and type B). In all these cases, the computational finite element predictions of fatigue crack growth rate agree well with the experimental measurements. The developed model can be easily extended to crankshafts in real operating conditions.     

The finite element absolute nodal coordinate formulation incorporated with surface stress effect to model elastic bending nanowires in large deformation

Surface stress was incorporated into the finite element absolute nodal coordinate formulation in order to model elastic bending of nanowires in large deformation. The absolute nodal coordinate formulation is a numerical method to model bending structures in large deformation. The generalized Young-Laplace equation was employed to model the surface stress effect on bending nanowires. Effects from surface stress and large deformation on static bending nanowires are presented and discussed. The results calculated with the absolute nodal coordinate formulation incorporated with surface stress show that the surface stress effect makes the bending nanowires behave like softer or stiffer materials depending on the boundary condition. The surface stress effect diminishes as the dimensions of the bending structures increase beyond the nanoscale. The developed algorithm is consistent with the classical absolute nodal coordinate formulation at the macroscale.     

Relaxation element method in calculations of stress state of elastic plane with the plastic deformation band

On the basis of relaxation element method an analytical representation of the band of localized plastic deformation, as the defect with its own internal stress field in the plane under tensile loading, is given. The influence of orientation of the band with respect to tensile axis on the stress concentration in the plane is analyzed.     

The behavior of statically-indeterminate structural members and frames with cracks present

Crack stability is discussed as affected by their presence in statically-indeterminate beams, frames, rings, etc. loaded into the plastic range. The stability of a crack in a section, which has become plastic, is analyzed with the remainder of the structure elastic and with subsequent additional plastic hinges occurring. The reduction of energy absorption characteristics for large deformations is also discussed. The methods of elastic-plastic tearing instability are incorporated to show that in many cases the fully plastic collapse mechanism must occur for complete failure.     

The influence of Al2O3 particulate reinforcement on cyclic stress response and fracture behavior of 6061 aluminum alloy

The cyclic stress response characteristics and cyclic fracture behavior of aluminum alloy 6061 discontinuously reinforced with particulates of Al₂O₃ are presented and discussed. The 6061/Al₂O₃ composite specimens and the unreinforced 6061 aluminum alloy were cyclically deformed using tension-compression loading under constant total strain amplitude control. Both the composite and the unreinforced alloy exhibited softening to failure from the onset of cyclic deformation. The degree of softening was observed to increase at the elevated test temperature for both the composite and the unreinforced counterpart. The intrisic micromechanisms controlling the stress response characteristics during fully-reversed cyclic straining are highlighted and rationale for the observed behavior is discussed. The cyclic fracture behavior of the composite is discussed in terms of the competing influences of intrinsic microstructural effects, deformation characteristics arising from a combination of mechanical and microstructural contributions, cyclic stress response, and test temperature.     

The dependence of stress intensity factors and weight functions on elastic constants

We investigate the dependence of stress intensity factors (SIFs) on elastic constants in two-dimensional elastic isotropic bodies. Bueckners weight function theory is used for the derivation of the dependence of SIFs on elastic constants. The dependence of SIFs on Poissons ratio shows up when the resultant tractions on each of the contours L _k separately is not zero in multiply connected bodies. As an example we calculate K ₁ for Griffith crack under concentrated loading applied on the upper crack face.     

The coupling effect of punch shape and residual stress on measuring adhesion work of membrane by pull-off test

The adhesion work of thin film, such as membrane, can be measured by pull-off test. In this kind of experiments, the residual stress in film due to pretension during sample preparation plays an important role in experimental results. Moreover, the effect of residual stress on results varies greatly depending on different punch shapes. The coupling effect of punch shape and residual stress is studied in the framework of plate theory and energy principle. The analytical expressions for the effect parameters are obtained on the basis of the energy criterion. From our study, it is found that the effect of residual stress is more significant for a circular punch than the one for a rectangular punch. For future pull-off experiments, the coupling effect should be taken into account and the rectangular punch instead of a circular punch should be prioritized in experiments to mitigate the effect of residual stress.     

非圆形磁性颗粒对磁流变脂剪切应力的影响及其计算模型研究

磁流变脂是继磁流变液和磁流变弹性体之后,又一个具有巨大发展潜力的磁流变智能材料。参照作者提出的圆形颗粒的建模过程,建立了非圆形磁性颗粒磁流脂的剪切应力模型,并以六边形磁性颗粒磁流变脂为例,推导出六边形磁性颗粒磁流变脂剪切应力公式。该模型对半径和边长相同时剪切屈服应力与磁场强度的关系,体积相同时剪切屈服应力与磁场强度的关系,零场下的剪切力应力进行了模拟计算。结果表明同体积下的非圆形磁性颗粒磁流变脂的剪切应力比圆形磁性颗粒磁流变脂大,且随接触边长的减少剪切应力亦减少,但都比圆形磁性颗粒磁流变脂的剪切应力大。即使零场条件下,非圆形磁性颗粒磁流变脂的剪切应力比圆形磁性颗粒磁流变脂大,说明球形磁流变液不是最佳选择。所以,非圆形磁性颗粒的磁流变脂机理研究对高性能磁流变液制备及其应用具有极其重要的指导意义。     

The in-plane and out-of-plane stress constraint factors and K-T-Tz description of stress fields near the border of a quarter-elliptical corner crack

The elastic T-stress and stress intensity factor K for quarter-elliptical corner cracks have been investigated in elastic plates by detailed three-dimensional finite-element calculations. The distributions of normalized K and T-stress have been obtained along the crack front with aspect ratios (a/c) of 0.2, 0.3, 0.4, 0.5, 0.6, 0.8 and 1.0, and far-field tension and the effect of Poisson's ratio have also been considered. The normalized K increases and the normalized T-stress decreases with the increase of Poisson's ratio v. For v= 0.3, the normalized K gradually increases in the range of crack-face angle φ≥ 22.5° and decreases in the range of φ≤ 22.5° with the increase of a/c. The normalized T-stress increases in the beginning and then decreases with increasing φ except for a/c= 0.2 and a/c= 0.3. By fitting the numerical results with the least squares method, empirical formulae have been given for the convenience of engineering applications. Combining with the corresponding out-of-plane constraint factor T_z, the three-parameter K-T-T_z approach has been provided, which can accurately describe the stress field around the crack front.     

The elastic interaction of screw dislocations and a star crack with a central hole

The elastic interaction of screw dislocations and a star crack with a central hole was investigated. The complex potential of the present problem was obtained from that of an internal crack in an infinite medium using the conformal mapping technique. The stress field, image force and strain energy of dislocation, and stress intensity factor at the crack tip were derived. The critical stress intensity factor for dislocation emission was calculated based on the spontaneous dislocation emission criterion. The influence of the ratio of crack length to hole radius, crack number, and dislocation source on the above mechanical variables were studied. The present solution was reduced to several special cases previously reported in the literature.     

The mechanism of hydrogen embrittlement: the stress interaction between a crack, a hydrogen cluster, and moving dislocations

Mechanisms of dissolvent anodic chemical reaction and hydrogen embrittlement have been proposed as stress corrosion cracking (SCC) mechanisms. The former is feasible for the case of plastic deformation dominant metals (low-yield stress), and the latter is for high-strength metals such as high-strength steels. However, in spite of low-yield stress, a discontinuous cleavage-like fracture is sometimes observed during SCC for ductile fcc alloys, which concerns the interaction between dislocations and the hydrogen cluster. The problem of when these mechanisms will be dominant remains. In this paper, the stress corrosion cracking model on the basis of hydrogen diffusion and concentration toward the elastic-plastic stress field around a crack and the interaction of dislocations and hydrogen around a crack tip are proposed to clarify the mechanism of stress corrosion cracking for ductile and brittle materials. We conducted numerical analyses using these proposed models.