Crack patterns corresponding to the residual strength plateau of ceramics subjected to thermal shock

The formation mechanism of the residualstrength plateau of ceramics subjected to thermal shockis addressed.A set of thermal shock experimentsof 99Al2O3 are conducted,where the thin specimensof 1 mm × 10 mm × 50 mm exhibit parallel through edgecracks,and thus permit quantitative measurements of thecrack patterns.The cracks evolve with the severity of thermal shock.It is found that there is a correlation between thelength and density of the thermal shock cracks.The increaseof crack length weakens the residual strength,whereas theincrease of crack density improves it.In a considerably widetemperature range,the two contrary effects just counteracteach other;consequently a plateau appears in the variationcurve of the residual strength.A comparison between thenumerical and experimental results of the residual strengthis made,and they are found in good agreement.This work ishelpful to a deep understanding of the thermal shock failureof ceramics.     

3D numerical simulation of drilling residual stresses

Drilling can affect the integrity of the surface of a mechanical component and reduce its fatigue life. Thus, drilling parameters such as lubrication or drilling velocity must be optimized to ensure a satisfactory residual mechanical state of the hole surfaces. Unfortunately, experimental tests are time consuming and it is not easy to observe the cutting process because of the confinement of the drill zone. The literature does not exhibit any numerical simulation capable of simulating 3D thermomechanical phenomena in the drill zone for large depth holes. Therefore, residual stresses cannot be easily simulated by means of the sole drilling parameters. The aim of this article is to propose a new numerical approach to compute drilling residual stresses for large-depth holes. A first simulation is developed to simulate heat transfer by means of a 3D thermoviscoplastic simulation in a new Rigid-ALE framework allowing the use of large calculation time steps. Then, a time interpolation and a spatial projection are implemented to rebuild the Lagrangian thermal history of the machined component. Finally, a thermo-elastoplastic simulation is carried out to compute residual stresses in the final workpiece. In this paper, the method is applied to a 316L austenitic stainless steel in the case of an unlubricated hole. The computed residual stresses are compared to experimental measurements.     

Analytical solution for bending stress intensity factor in an orthotropic elastic plate containing a crack and subjected to concentrated moments

The problem of estimating the bending stress distribution in the neighborhood of a crack located on a single line in an orthotropic elastic plate of constant thickness subjected to out-of-plane concentrated moments is examined. Using classical plate theory and integral transform techniques, the general formulae for the bending moment and twisting moment in an elastic plate containing cracks located on a single line are derived. The solution is obtained in a closed form for the case in which there is a single crack in an infinite plate subjected to symmetric concentrated moments.     

New stress intensity factor solutions of a periodic array of cracks in residual stress field

Many important applications of crack mechanics involve self-equilibrating residual or thermal stress fields. For these types of problems, the traditional fracture mechanics approach based on the superposition principle has ignored the effect of crack surface contact when the crack-tip propagates into the residual compressive region. Contact between the crack faces and the wedging action are responsible for subsequent crack-tip reopening, which often leads to a much larger mode I stress intensity factor. In this study, an analytical approach is used to study the effect of crack face contact for a period array of collinear cracks embedded in several typical residual stress fields. It is found that the nonlinear contact between crack surfaces dominates the cracking behavior in residual/thermal stress fields, which is responsible for crack coalescence.     

Effect of plastic zone on the fatigue crack propagation behavior between two fatigue cracks

In this study, the fatigue crack propagation behavior in the stress interaction field between two different fatigue cracks is studied by experiment and finite element analysis. In the experiment, the offset distance between two cracks and the applied stress are varied to create different stress interaction fields. The size of the plastic zone area is used to examine the crack propagation path and rate. Three types of crack propagation in the interaction field were found by experiment, and the crack propagation behavior of two cracks was significantly changed as different stresses were applied. The size of the plastic zone obtained by finite element analysis can be used to explain crack propagation behavior qualitatively.     

Use of the hole-drilling method for measuring residual stresses in highly stressed shot-peened surfaces

The same shot-peening treatment was applied to five steels with different mechanical properties. The induced residual stress profiles were analyzed using X-ray diffraction and incremental hole drilling (IHD). The results of both techniques showed that IHD can still be successfully used for measuring shot-peening residual stresses, even if these exceed the yield strength of the bulk material. Expected errors due to the plasticity effect are reduced by the strain hardening of the surface. For an assessment of the reliability of IHD data, strain-hardening variation was quantified by microhardness measurements to estimate the yield strength of the plastified layer. All the main calculation methods for IHD were applied. The results were compared and discussed with respect to the characteristics of each method.     

Dynamic crack tip fields and dynamic crack propagation characteristics of anisotropic material

Based on mechanics of anisotropic material, the dynamic crack propagation problem of I/II mixed mode crack in an infinite anisotropic body is investigated. Expressions of dynamic stress intensity factors for modes I and II crack are obtained. Components of dynamic stress and dynamic displacements around the crack tip are derived. The strain energy density theory is used to predict the dynamic crack extension angle. The critical strain energy density is determined by the strength parameters of anisotropic materials. The obtained dynamic crack tip fields are unified and applicable to the analysis of the crack tip fields of anisotropic material, orthotropic material and isotropic material under dynamic or static load. The obtained results show Crack propagation characteristics are represented by the mechanical properties of anisotropic material, i.e., crack propagation velocity M and fiber direction α. In particular, the fiber direction α and the crack propagation velocity M give greater influence on the variations of the stress fields and displacement fields. Fracture angle is found to depend not only on the crack propagation but also on the anisotropic character of the material.     

Predicting the fatigue life and crack aspect ratio evolution in complex structures

This paper discusses a computationally efficient method for determining the behaviour of complex structures containing three-dimensional cracks. A simple method is presented for calculating the mode I stress intensities for semi-elliptical cracks emanating from the saddle point of two intersecting tubular members. This method, which gives results in good agreement with published values, uses the finite element technique, but does not require the crack to be modelled explicitly. The technique is then used, in conjunction with FASTRAN II, to study fatigue crack growth and the results are compared to experimental data. Good agreement is achieved between both the predicted and measured fatigue crack growth and the evolution of the crack aspect ratios.     

The effect of indentation sequence on rock breakages: A study based on laboratory and numerical tests

Rock may response differently to external loads applied in different sequences. Thus, we conducted indentation tests to investigate the effect of the indentation sequence on rock breakages. Sequential indentations, consuming less indentation energy, usually resulted in larger and deeper grooves and then led to lower specific energies. Thus, we conclude that sequential indentations occur instead of simultaneous indentations form larger grooves with the same indentation energy. To further validate this conclusion, we performed a series of numerical tests. The numerical analysis of stress evolution shows that, for simultaneous indentations, the propagation of an internal crack from an inner rim restrained the propagation of the other internal crack from the other inner rim. However, the chipping pattern varied for sequential indentations. In the first indentation process, an internal crack, initiating from an inner rim, is usually connected with an internal crack caused by the second indentation. The deflection angles of the internal cracks for the sequential indentations were smaller because of the lower compressive stress in the horizontal direction. Then, these smaller deflection angles led to larger chips.     

Remarques sur les contraintes résiduellesSome comments on residual stresses

Residual stresses which are currently observed in solid bodies can result from non-compatible initial strains. Theses stresses can then be determined, in general, from the incompatibility tensor associated to the initial strains tensor. However, even if the incompatibility tensor is zero, residual stresses may exist, when the solid is not simply-connected or when discontinuity surfaces are present. Several examples are provided. To cite this article: P. Bérest, G. Vouille, C. R. Mecanique 331 (2003).     

An asymptotic approach to crack initiation in fretting fatigue of complete contacts

The stress state near the corner of a complete contact subject to fretting action is studied using an asymptotic analysis. The spatial distribution of stress, together with the generalised stress intensity factor defining the severity of the stress state are found, and the implications for experimental determination of crack initiation conditions discussed.     

Interacting cracks and ellipsoidal inhomogeneities by the equivalent inclusion method

Based on the Eshelby's equivalent inclusion method (EIM) and Hill's theorem on discontinuities of elastic fields across the interfaces, a theory for the determination of the stress intensity factors (SIFs) of arbitrarily oriented interacting cracks under non-uniform far-field applied stress (strain) is developed. As shown in this investigation the EIM proposed by Moschovidis and Mura can be extended for treatment of such problems, but their formulations are quite cumbersome and computationally inefficient. An alternative analytical approach is proposed that is computationally more efficient, and unlike the method of Moschovidis and Mura can easily handle complex problems of interacting inhomogeneities and cracks. It is seen that as the interaction between the inhomogeneities becomes stronger, this method yields results that are closer to the solutions reported in the literature than the solutions obtained using the extended EIM of Moschovidis and Mura, which is developed herein. Problems involving combinations of interacting elliptic and penny shape cracks and inhomogeneities are excellent candidates for demonstration of the accuracy and robustness of the present theory, for which the previous EIM produces less accurate results. Due to the limitations imposed on the existing methods, every reported treatment has been tailored for a certain category of problems, and only uniform far-field loadings have been remedied. In contrast, the present theory is more general than the previously reported theories and it encompasses interacting cracks having a variety of geometries subjected to non-uniform far-field applied stress (strain); moreover, it is applicable to modes, I, II, III, and mixed mode fracture.     

Simulation of edge dislocation emission from a crack under in-plane shear

Considered is the tandem emission of dislocations and dislocation dipoles from a crack under in-plane shear in one slip system as well as multiple slip systems. Effective stress intensity factors are determined by considering zones of local distortion similar to that in macro-plasticity. The dislocation free zone (DFZ) is also obtained which is analogous to the core region in fracture mechanics. Studied are effects of dislocation emission or development of plastic zone in front of the crack tip on the potential crack propagation based on the strain energy density factor criterion.     

Convergence of local atomistic stress based on periodic lattice

Local stress in an atomic system, which provides an average stress measurement within a spatial volume containing a collection of atoms, is essential for determining the mechanical properties of a nanoscale structure as well as developing a proper multiscale modeling technique. Theoretically, the smaller averaging volume where a local stress can converge, the closer this atomistic stress definition can approach the ideal continuum stress. As a result, the more accurate stress concentration can be evaluated for the inhomogeneous case. With reference to the previous studies focusing on the spherical averaging volume, dependent on the type of crystals, the convergent radius of the virial stress or Hardy stress usually spans the size of several lattice constants. In this paper, we find that, once the averaging volume is periodic, the convergence of the virial stress and Hardy stress can be accomplished within one single lattice, which is much smaller than what is required by other non-periodic volumes such as a sphere. In the final section, a cracked sodium chloride crystal is considered to demonstrate that the crack opening stress described by the periodic lattices captures the stress concentration near the crack tip.     

A numerical analysis of perpendicular cracks under general in-plane loading with a hybrid displacement discontinuity method

In this paper, a numerical analysis of perpendicular cracks under general in-plane loading is performed by using a hybrid displacement discontinuity method which consists of the non-singular displacement discontinuity element presented by Crouch and Starfied and the crack tip displacement discontinuity elements by the author. In the boundary element implementation the left or the right crack tip displacement discontinuity element is placed locally at corresponding left or right crack tip on top of the ordinary non-singular displacement discontinuity elements that cover the entire crack surface and the other boundary. The present numerical results show that the numerical approach is simple, yet very accurate for calculating numerically stress intensity factors for perpendicular cracks under general in-plane loading.     

Thermal shock analyses for a strip containing an infinite row of periodically distributed cracks normal to its edge

The transient thermal stress problem of a semi-infinite plate containing an infinite row of periodically distributed cracks normal to its edge is investigated in this paper. The elastic medium is assumed to be cooled suddenly on the crack-containing edge. By the superposition principle, the formulation leads to a mixed boundary value problem, with the negating tractions arisen from the thermal stresses for a crack-free semi-infinite plate. The resulting singular integral equation is solved numerically. The effects on the stress intensity factors due to the presence of periodically distributed cracks in a semi-infinite plate are illustrated. For both the edge crack and the embedded crack arrays, the stress intensity factors increase, due to the reduction of the shielding effect, as the stacking cracks are more separated. For the case of embedded crack array, one has the further conclusion that the stress intensity factors decline as the crack array shifts from the plate edge.     

The analysis of thermal stresses in thermopiezoelastic semi-infinite body with an edge crack

Summary  Thermopiezoelastic materials have recently attracted considerable attention because of their potential use in intelligent or smart structural systems. The governing equations of a thermopiezoelastic medium are more complex due to the intrinsic coupling effects that take place among mechanical, electrical and thermal fields. In this analysis, we deal with the problem of a crack in a semi-infinite, transversely isotropic, thermopiezoelastic material by means of potential functions and Fourier transforms under steady heat-flux loading conditions. The problem is reduced to a singular integral equation that is solved. The thermal stress intensity factor for a crack situated in a cadmium selenide material is calculated. Received 20 March 2001; accepted for publication 18 October 2001     

Impulse response model of thermal striping for hollow cylindrical geometries

The impulse response method is applied to the analysis of the thermally striped internal surface of a hollow cylinder containing a circumferential crack on this surface. Stress intensity factor and strain energy density factor ranges as functions of crack depth for various sinusoidal striping frequencies are calculated. Good agreement is found with both the frequency response and finite element methods. Results for stress intensity factor fluctuations have been applied to the calculation of maximum allowable temperature striping amplitudes. Solutions for striping on the external surface are also presented.     

Unsteady Dynamic Crack Propagation in a Brittle Polymer

Dynamic crack propagation in a brittle polymer, poly(methyl-methacrylate) (PMMA), was studied using the method of caustics in combination with a Cranz–Schardin high-speed camera. Four different types of specimen geometry and loading method were employed to achieve the crack acceleration, deceleration, and/or reacceleration processes in one fracture event. The dynamic stress intensity factor K _ID and crack velocity were obtained in the course of the crack propagation and the corresponding relationship was determined. The effect of the crack acceleration and deceleration on the K _ID-velocity relationships was as follows: (1) the variations of K _ID and the velocity were strongly influenced by the specimen geometry and loading method; (2) the velocity change was qualitatively in accord with K _ID; (3) K _ID for a constant crack velocity was larger when the crack decelerated than it was when the crack accelerated or reaccelerated; (4) K _ID for an acceleration-free crack was uniquely related to the velocity; and (5) K _ID could be expressed as two parametric functions of the velocity and acceleration.     

Anti-plane problem of periodic cracks in a functionally graded coating–substrate structure

The static and dynamic anti-plane problem for a functionally graded coating–substrate structure containing a periodic array of parallel cracks, which are perpendicular to the boundary, is considered. Integral-transform techniques are employed to reduce the problem to the solution of an integral equation with hypersingular kernels. Numerical results are presented to show the influence of geometry, material properties and material gradient parameter on the fracture behavior.