The temperature field induced by the dynamic stresses of a transverse crack in periodically layered composites

The temperature field induced by the dynamic application of a far-field mechanical loading on a periodically layered material with an embedded transverse crack is investigated. To this end, the thermoelastically coupled elastodynamic and energy (heat) equations are solved by combining two approaches. In the first one, the dynamic representative cell method is employed for the construction of the time-dependent Green’s functions generated by the displacement jumps along the crack line. This is performed in conjunction with the application of the double finite discrete Fourier transform on the thermomechanically coupled equations. Thus the original problem for the cracked periodic composite is reduced to the problem of a domain with a single period in the transform space. The second approach is based on wave propagation analysis in composites where full thermomechanical coupling in the constituents exists. This analysis is based on the coupled elastodynamic-energy continuum equations where the transformed time-dependent displacement vector and temperature are expressed by second-order expansions, and the elastodynamic and energy equations and the various interfacial and boundary conditions are imposed in the average (integral) sense. The time-dependent thermomechanically coupled field at any observation point in the plane can be obtained by the application of the inverse transform. Results along the crack line as well as the full temperature field are given for cracks of various lengths for Mode I and Mode II deformations. In particular the temperature drops (cooling) at the vicinity of the crack’s tip and the heating zones at its surroundings are generated and discussed.     

Investigations on the stress intensity factor field for unstable dynamic crack growth

In this study, the unstable dynamic crack propagation due to static loading in an elastic material is analyzed for both antiplane and inplane conditions. Of particular concern is the investigation of limitations on the assumption that the stress intensity factor field is fully established over a region of given size near the tip of a growing crack. The transient analysis of the stress for a material particle at a small fixed distance from the moving crack tip is examined in detail. Some estimations are made of the time required for the stress at a point near the moving crack tip to reach the value it would have if the stress field were actually given by the near tip stress intensity factor field. In addition, a simple formulation obtained from the equivalent static problem is proposed which can be used as a good approximation to the associated complicated dynamic transient problem.     

焊接动态位移场的激光电子散斑法测量

为提供一种能够全场测量整个焊接过程动态位移场的工具,建立了激光电子散斑法测量系统.应用于实际TIG焊接过程中,获得了焊接位移场的散斑原始图像.利用自开发软件,对图像进行灰度变换和直方图均衡化处理后,采用频域同态滤波的方法对图像进行降噪滤波处理.经降噪、二值化、细化、平整、拟合、标定等一系列处理后,即可自动生成相对动态位移场.结果表明,激光电子散斑法能够胜任焊接动态位移场的测量,且具有非接触、测量精度高、对环境的防震要求低、可在明光下操作、能进行全场测量的特点.     

Numerical study of dynamic crack growth by the finite element method

Recent developments in numerical techniques for dynamic transient stress analysis have ensured that realistic models can now be employed in crack propagation studies. In this paper transient dynamic finite element solutions are undertaken for both double cantilever beam (DCB) and pipeline problems with propagation of the crack being permitted. Standard parabolic isoparametric elements are employed for spatial discretization with an explicit (central difference) scheme being employed for time integration. Both critical stress and energy balance crack propagation criteria are considered.The pressurised pipeline problem is solved for as a fully three-dimensional solid. Firstly, a stationary crack is considered and both large deformations and plasticity effects are accounted for. The transient case of a dynamically propagating crack is then modelled, employing both a stress and energy criterion. Elastic large deformation behaviour is permitted for this case.

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Résumé Des développements récents dans les techniques numériques pour l'analyse des contraintes dynamiques transitoires ont permis d'utiliser à présent des modèles réalistes dans les études de propagation des fissures. Dans ce mémoire, on envisage des solutions par éléments finis pour les transitoires dynamiques dans les cas de la poutre double cantilever et de problèmes de pipelines où l'on autorise la propagation d'une fissure. On recourt aux éléments paramétriques paraboliques standards pour réaliser une division discrète de l'espace, et l'on utilise pour l'intégration dans le temps un schéma explicite à différence centrale. On considére à la fois les critères de contraintes critiques et d'équilibre d'énergie lors de la propagation de la fissure. Le problème du pipeline pressurisé est solutionné en considérant ce dernier comme un solide tridimensionnel. En premier lieu, on considère une fissure stationnaire et l'on tient compte des effets des grandes déformations et de la plasticité. On met ensuite en équation le cas transitoire d'une fissure en propagation dynamique, en utilisant un critère de contrainte et un critère d'énergie. Ce cas permit d'envisager le comportement sous des déformations élastiques importantes.

     

Numerical simulations of dynamic interfacial crack growth allowing for crack growth away from the bond line

Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack subject to impact tensile loading. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. Potential surfaces of decohesion are interspersed in the material on either side of the bond line and along the bond line. The cohesive surface constitutive relation allows for the creation of new tree surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. The resistance to crack initiation, the crack speed history and the crack path are predicted without invoking any ad hoc failure criterion. Three calculations are carried out for a PMMA/Al bimaterial. The imposed loading and the properties of the adjacent materials are kept fixed, while the bond line strength is taken to be 1/4, 1/2, and 3/4 of the strength of PMMA. The nominal crack speed decreases with increasing bond line strength. When the bond line strength is 1/4 that of PMMA, the crack remains on the bond line although there is an attempt at branching off the bond line. For the intermediate case, a bond line strength 1/2 that of PMMA, repeated branching of the main crack off the bond line into the PMMA occurs, together with micro-crack nucleation on the bond line. The crack branches off the bond line into the PMMA when its strength is 3/4 that of PMMA, with the main direction of growth being parallel to the bond line, but with the crack progressively drifting further into the PMMA.     

Measurement of fatigue crack growth in large compact tension specimens using an AC magnetic field method

Fatigue crack growth rate data are required in order to carry out a numerical analysis of the fatigue performance of complex structural components. These data are obtained by measuring crack growth in standard fracture mechanics specimens. A new method for measuring fatigue crack growth in compact tension specimens has been developed. The technique is based on the measurement of the surface magnetic fields produced when passing a high-frequency alternating current through the specimen. Fatigue crack growth data recorded using this method indicated an accuracy of ±0.02 mm when compared with optical measurements. The technique is suitable for computer-controlled operation and could easily be applied to other standard specimen geometries.     

Fatigue crack closure and crack growth behaviour in a titanium alloy with different microstructures

Fatigue crack closure and crack growth behaviour in Ti–2.5 wt % Cu alloy with two equiaxed and two lamellar microstructures have been investigated by constant-load amplitudetests. Plasticity-induced crack closure and roughness-induced crack closure have been characterized separately by experimental methods. A change in closure mechanism from plasticity-induced crack closure at high K values (region of high stress intensity ranges)to roughness-induced crack closure at low K values occurs in a solution-annealed equiaxed microstructure, while plasticity-induced crack closure is the operative closure mechanism in an over-aged equiaxed microstructure over the whole range of K and roughness-induced crack closure occurs in two lamellar microstructures. The crack closing stress intensity factor for plasticity-induced crack closure increases continuously with increasing maximum stress intensity. The crack closing stress intensity factor for roughness-induced crack closure increases with increasing maximum stress intensity at low K, and remains constant at high K. Crack closure and crack path deflection have a significant influence on the crack growth rates. © 1998 Kluwer Academic Publishers     

Slow crack growth and failure induced by manufacturing defects in HDPE-tubes

Medium-diameter pipelines produced from High Density Polyethylene are an economic and generally reliable solution for the transportation of potable water in large infrastructure works. However, in the present case, widespread fracture occurred after a few months of operation. Semi-elliptical cracks ran out from multiple initiation points at the inner radius of tubes, without piercing the outer surface, instead connecting sideward by absorbing other crack initiation zones. Longitudinal crack extension was followed by sudden crack propagation at the moment of catastrophic failure. Cracks were stopped or deviated at the welds between tube sections. Some information on fracture toughness was inferred from compact tensile specimens, complemented by direct observation of the crack surface. The latter indicated excessive brittleness of the tube material, accelerating the process of slow crack growth at low stress intensity. Numerous extrusion defects were found to be responsible for crack initiation; an excessive amount of recycled resin may have increased crack propagation velocity.     

An asymptotic analysis of dynamic crack growth in rubber

Asymptotic analyses of the mechanical fields in front of stationary and propagating cracks are important for several reasons. For example, they facilitate the understanding of the mechanical and physical state in front of crack tips, and they enable prediction of crack growth. Furthermore, efficient modelling of arbitrary crack growth by use of XFEM (extended finite element method) requires accurate knowledge of the asymptotic crack tip fields. The present study focuses on the asymptotic fields in front of a crack that propagates dynamically in rubber. Static analyses of this type of problem have been made in previous studies. In order to be able to compare the present results with these earlier studies, the constitutive model from Knowles and Sternberg (J. Elast. 3:67–107, 1973) was adopted. It is assumed that viscoelastic stresses become negligible compared with the singular elastic stresses close to the crack tip. The present analysis shows that in materials with a significant hardening, the inertia term in the equations of motion becomes negligible in the asymptotic analysis. However, for a neoHookean type of model, inertia comes into play and causes a maximum theoretical crack speed that equals the shear wave speed.     

A COD fracture model of ferroelectric ceramics with applications in electric field induced fatigue crack growth

In this paper, Crack Opening Displacement (COD) is introduced to study the fracture and fatigue of ferroelectrics. A fundamental solution for the COD of ferroelectrics is derived considering both the piezoelectric effect and ferroelectric effect. Bases on this solution, a nonlinear COD fracture model of ferroelectrics, which takes into account the effect of domain switching, is developed and accords well with the experimental results. Furthermore, fatigue crack growth in ferroelectrics is analytically investigated using this COD model. Comparison between the experimental results and the predicted electric-field-induced fatigue crack growth shows the applicability of the proposed COD model.     

High temperature fatigue crack growth in Inconel 718

Abstract

The nickel base superalloys are extensively used in high temperature applications, so it is important to know their behaviour under conditions of high-temperature fatigue. This paper studies the influence of ΔK, loading frequency, stress ratio and temperature on the high temperature fatigue crack growth rate of nickel base superalloys. This study is based on fatigue tests carried out in corner crack specimens of Inconel 718 at 600°C and at room temperature. Three stress ratios (R = 0.05, 0.5 and 0.8) and loading frequencies ranging from 0.0017 to 15 Hz were considered in the tests. For frequencies below 0.25 Hz, the load wave shape was trapezoidal with different dwell times at maximum load. At relatively high frequencies the propagation is cycle dependent, while for lower frequencies it is time dependent. At intermediate frequencies a mixed crack growth occurs. The transition frequencies from cycle dependent to mixed regime and from mixed to time dependent regime were obtained for each R. The increase of R increases the transition frequencies, i.e., extends the time dependent crack growth to higher frequencies. The increase of R also produces an increase of cyclic crack growth rate for all regimes of crack growth. In the time dependent regime, a higher variation is observed, that can be explained by an acceleration of oxidation damage promoted by the increase of maximum stress. An approach for modelling the high-temperature fatigue crack growth in nickel base superalloys is presented. A good agreement was observed between time dependent fatigue results and mathematical models based on static load results.     

Measurement of the dynamic elastic moduli of porous titanium aluminide compacts

The dynamic elastic moduli of the porous alpha-two titanium aluminide compacts are measured using an ultrasonic technique. Both shear and longitudinal velocities are measured for compacts of different densities, making computation of all the four elastic constants, namely, the Young’s modulus, shear modulus, bulk modulus and Poisson’s ratio. The dependence of these on the relative density are correlated and compared with some earlier models, and some of the uncertainties in the earlier models are discussed. This revised version was published online in November 2006 with corrections to the Cover Date.     

Three-dimensional mixed-mode fatigue crack growth in a functionally graded titanium alloy

The implementation of unitized structure in the aerospace industry has resulted in complex geometries and load paths. Hence, structural failure due to three-dimensional mixed-mode fatigue crack growth is a mounting concern. In addition, the development of functionally graded materials has further complicated structural integrity issues by intentionally introducing material variability to create desirable mechanical behavior. Ti-6Al-4V β-STOA (solution treated over-aged) titanium is a functionally graded metallic alloy that has been tailored for superior fatigue crack growth and fracture response compared with traditional titanium alloys. Specifically, the near-surface material of Ti β-STOA is resistant to fatigue crack incubation and the interior is more resistant to fatigue crack growth and fracture. Therefore, Ti β-STOA is well suited for applications where surface cracking is a known failure mode. Advances in experimental testing have shown that complex loading conditions and multi-faceted materials can be tested reliably. In this paper, the authors will experimentally generate three-dimensional mixed-mode surface crack data in functionally graded Ti-6Al-4V β-STOA and comment on the effect of the material tailoring.