A methodology for thermomechanical fatigue crack growth testing in MMCs

This paper describes the experimental techniques used in an investigation of the crack growth characteristics of a four-ply, unidirectional, silicon carbide fiber reinforced, titanium matrix composite (SCS-6/Ti–6Al–2Sn–4Zr–2Mo) subjected to thermomechanical fatigue. A mechanical test system was assembled which is capable of conducting fully automated, computer-controlled thermomechanical fatigue crack growth tests. The system is able to simultaneously impose operator-defined arbitrary mechanical and thermal histories on the specimen. Crack lengths in single-edge tension [SE(T)] or middle tension [M(T)] specimens are measured by the direct-current electric potential method and optically using a unique telemicroscope system. A series of isothermal, in-phase and out-of-phase crack growth tests was conducted to obtain baseline data for material modeling purposes. The test temperatures ranged from 150°C to 538°C, and the highest thermal frequency was 0.0083 Hz.     

A numerical method for crack growth analysis in linearly viscoelastic materials

This paper presents a numerical method for the analysis of crack initiation and extension in linearly viscoelastic materials undergoing Mode I plane stress deformation. Plastic deformation near the crack tip is considered by a strip-yielding model. The crack initiation and growth are taken to follow a critical energy release rate fracture criterion, and the plastic work per unit crack extension is included in the calculation of the total energy release rate. The resulting numerical method is presented in algorithmic form and two example problems are solved to demonstrate its application. The two example problems represent unstable and stable crack propagations respectively. The results obtained lend insight into the effect of creep deformation on the initiation and growth of a crack.     

A simple method for crack growth in mixed mode with X-FEM

In this paper, a new method for level set update is proposed, in the context of crack propagation modeling with the extended finite element method (X-FEM) and level sets. Compared with the existing methods, such as the resolution of the Hamilton–Jacobi equations, this new method is much simpler because it does not required complex manipulations of the level sets. This method, called the “projection” method, uses both a classical discretization of the surface of the crack (segments for 2d cracks and triangles for 3d cracks) and a level set representation of the crack. This discretization is updated with respect to the position of the new crack front. Then the level sets are re-computed using the true distance to the new crack, by an orthogonal projection of each node of the structure onto the new crack surface. Then, numerical illustrations are given on 2d and 3d academic examples. Finally, three illustrations are given on 3d industrial applications.     

A stress criterion for crack growth

A stress criterion for crack growth was developed from test results with 7075-T6 aluminum-sheet specimens containing transverse machined cracks. Stress distributions near the crack tip were obtained using strain gages and by reducing the strain data to stresses with the aid of Reuss plasticity theory. These distributions indicated the biaxial nature of stress at the crack tip, the high stress gradients a short distance from the tip, and the variation in stress-concentration factor with crack length. Crack growth was found to occur when the effective stress at the crack root reached the engineering ultimate strength.     

Computer-controlled elastic-plastic fatigue crack growth testing using multi-task programming

Experimental Techniques - The automated test system for computer-controlled low-cycle fatigue crack growth can be achieved using multi-task programming. The results of constant ΔJ test show...     

A cohesive zone model for fatigue crack growth allowing for crack retardation

A damage-based cohesive model is developed for simulating crack growth due to fatigue loading. The cohesive model follows a linear damage-dependent traction–separation relation coupled with a damage evolution equation. The rate of damage evolution is characterized by three material parameters corresponding to common features of fatigue behavior captured by the model, namely, damage accumulation, crack retardation and stress threshold. Good agreement is obtained between finite element solutions using the model and fatigue test results for an aluminum alloy under different load ratios and for the overload effect on ductile 316 L steel.     

A damage model for crack initiation and growth

A damage accumulation model is presented for the study of the problem of crack initiation and stable growth in an elastic-plastic material. A centre-cracked specimen subjected to a uniform stress perpendicular to the crack plane is considered. A coupled stress and failure analysis is performed by using a finite element computer program based on J₂-plasticity theory in conjunction with the strain energy density theory. After initial yielding, each material element follows a different equivalent uniaxial stress-strain behavior depending on the amount of energy dissipation by permanent deformation. A host of uniaxial stress-strain curves constituting parts of the same stress-strain curve were assigned to material elements for each increment of loading. The path-dependent nature of the onset of crack initiation and growth was revealed. The proposed model predicts faster crack growth rates than those obtained on the basis of a single uniaxial stress-strain curve and is closer to experimental observation.     

A new direct biaxial testing machine for anisotropic materials

A screw-driven new biaxial testing machine for the realization of experimental investigations on anisotropic sheet materials, such as composite plates or rolled sheet metals, is presented. The described mechanical concept and servocontrol system allow cruciform specimens to be subjected to large strain biaxial tensile and compressive tests without kinematic incompatibilities. Moreover, for the proper implementation of biaxial tensile tests, the specific problems linked to the anisotropic properties of the investigated materials are taken into account; therefore, for the first time, the biaxial machine is supplied with the original ‘off-axes testing device,’ consisting of hinged fixtures with knife-edges at each arm of the cruciform specimen. A recently developed optimization method for the optimal design of flat tensile cruciform specimens is shortly reviewed. Numerical simulations illustrate the decisive superiority of the optimized specimen compared with specimen designs proposed in the literature, as well as the necessity to use the ‘off-axes’ testing technique in biaxial tests on anisotropic materials.     

A direct method for non-linear normal modes

This paper presents a direct method for locating normal modes in certain holonomic, scleronomous, conservative non-linear two degree of freedom dynamical systems. The method does not require that the system studied be close to a linear system.     

A generalized Paris’ law for fatigue crack growth

An extension of the celebrated Paris law for crack propagation is given to take into account some of the deviations from the power-law regime in a simple manner using the Wöhler SN curve of the material, suggesting a more general “unified law”. In particular, using recent proposals by the first author, the stress intensity factor K(a) is replaced with a suitable mean over a material/structural parameter length scale Δa, the “fracture quantum”. In practice, for a Griffith crack, this is seen to correspond to increasing the effective crack length of Δa, similarly to the Dugdale strip-yield models. However, instead of including explicitly information on cyclic plastic yield, short-crack behavior, crack closure, and all other detailed information needed to eventually explain the SN curve of the material, we include directly the SN curve constants as material property. The idea comes as a natural extension of the recent successful proposals by the first author to the static failure and to the infinite life envelopes. Here, we suggest a dependence of this fracture “quantum” on the applied stress range level such that the correct convergence towards the Wöhler-like regime is obtained. Hence, the final law includes both Wöhler's and Paris’ material constants, and can be seen as either a generalized Wöhler's SN curve law in the presence of a crack or a generalized Paris’ law for cracks of any size.     

A NEW CYCLIC J-INTEGRAL FOR LOW-CYCLE FATIGUE CRACK GROWTH

The constitutive equation under the low-cycle fatigue (LCF) was discussed, and a two-dimensional (2-D) model for simulating fatigue crack extension was put forward in order to propose a new cyclic J-integral. The definition, primary characteristics, physical interpretations and numerical evaluation of the new parameter were investigated in detail. Moreover, the new cyclic J-integral for LCF behaviors was validated by the compact tension (CT) specimens. Results show that the calculated values of the new parameter can correlate well with LCF crack growth rate, during constant-amplitude loading. In addition, the phenomenon of fatigue retardation was explained through the viewpoint of energy based on the concept of the new parameter.     

平面偏心结构的三维能力谱方法

基于单自由度模型的性态评估方法,无法考虑偏心结构平扭耦联效应且不便于考虑双向地震动输入,存在很大的局限性.本文在对水平偏心结构模态分析的基础上,利用OpenSees构建等效三自由度模型(ETDOF),将该模型用于双向地震动作用下偏心结构平扭耦联简化计算和性态评估.在对ETDOF模型进行振动特性分析的基础上,基于等位移原...     

A non-intrusive methodology for the representation of crack growth stochastic processes

In this paper, we present a methodology to pursue the uncertainty quantification of the stochastic process that represents the crack growth problem. The main idea of this methodology is to discretize the crack growth process in a sequence of random variables and then, approximate each of them using a stochastic polynomial approach. This methodology is non-intrusive, i.e. it is based on the representation of random variables using stochastic polynomials, whose coefficients are evaluated using a least squares method and only a few realizations of the stochastic process. The Paris–Erdogan law was used as crack growth model in order to focus the reader's attention on the uncertainty quantification methodology. We modeled the parameters of the Paris–Erdogan law as random variables, i.e. the initial crack length and the coefficients of the Paris–Erdogan model are treated as random variables. Two numerical examples are presented in order to shown the effectiveness and accuracy of the proposed methodology. From the results of these examples, it is shown that the proposed methodology is able to successfully approximate the stochastic process that represents the crack growth for the Paris–Erdogan model, with a much lower computational cost than the MCS. The main limitation of the proposed approach is that, in the form it was presented, it is not able to handle random processes as input parameters.     

D-c electric-potential method applied to thermal/mechanical fatigue crack growth

The paper describes a d-c electric potential system for measuring crack length under thermal/mechanical fatigue-crack-growth (TMFCG) test conditions. A programmable d-c current supply and precision multimeter produce reliable electric-potential readings. H.H. Johnson's formula is used to calculate crack length from electric potential for the center-crack-tensionM(T) geometry. Calibration constants for the formula are determined from an initial optical crack-length measurement. The resolution of the system is 1.0 microvolt which corresponds to a crack extension of approximately 0.002 mm for the center-crack-tension geometry using a current of 10.00 amps. Good crack-length accuracy and low data scatter are achieved by taking special precautions to minimize or eliminate errors in potential measurement due to thermal effects. Material resistivity changes are identified as the cause of short and long term changes in the measured electric potential for uncracked specimens. Crack-length accuracy is discussed in terms of short-term scatter and longterm drift.     

Fatigue crack growth behavior of Al7050-T7451 attachment lugs under flight spectrum variation

This paper discusses an analytical and experimental investigations of the fatigue crack growth behavior in attachment lugs subjected to a randomized flight-by-flight spectrum. In the analysis, the stress intensity factors for through-the-thickness cracks initiating from lug holes were compared by weight function method, boundary element method (BEM), the interpolation of Brussat’s solution. The stress intensity factors of a corner crack at a transition region were obtained using two parameter weight function method and correction factors. Fatigue life under a load spectrum was predicted using stress intensity factors and Willenborg retardation model considering the effects of a tensile overload. Experiments were performed under a load spectrum and compared with the fatigue life prediction using the stress intensity factors by different methods. Changes of fatigue life and aspect ratio according to the clipping level of the spectrum were discussed through experiment and prediction. Effect of the spectrum clipping level on the fatigue life was experimentally evaluated by using beach marks of fractured surface.     

An electro-optical system for crack growth characterization

Experimental Techniques -     

求解混合型裂纹应力强度因子的围线积分法

本文用复变函数理论推导出裂纹的辅助场，并用Betti功互等定理给出求解混合型裂纹应力强度因子的远场围绕积分法．此方法与积分路径的选择无关，用有限元法计算出远离裂纹尖端的位移场和应力场，就可通过计算绕裂端的围线积分，精确地给出混合型裂纹的应力强度因子KⅠ和KⅡ的数值解．