Thermal Stresses and Cracks During the Growth of Large-sized Sapphire with SAPMAC Method

The finite-element method has been used to study the thermal stress distribution in large-sized sapphire crystals grown with the sapphire growth technique with micro-pulling and shoulder-expanding at cooled center （SAPMAC） method. A critical defect model has been established to explain the growth and propagation of cracks during the sapphire growing process. It is demonstrated that the stress field depends on the growth rate, the ambient temperature and the crystallizing direction. High stresses always exist near the growth interfaces, at the shoulder-expanding locations, the tailing locations and the sites where the diameters undergo sharp changes. The maximum stresses always occur at the interface of seeds and crystals. Cracks often form in the critical defect region and spread in the m-planes and a-planes under applied tensile stresses during crystal growth. The experimental results have verified that with the improved system of crystal growth and well-controlled techniques, the large-sized sapphire crystals of high quality can be grown due to absence of cracks.

Measuring internal residual stress in Al-Cu alloy forgings by crack compliance method with optimized parameters

Measuring the internal stress of Al alloy forgings accurately is critical for controlling the deformation during the subsequent machine process.In this work,the crack compliance method was used to calculate the internal residual stress of Al-Cu high strength alloys,and the effect of various model parameters of crack compliance method on the calculated precision was studied by combining the numerical simulation and experimental method.The results show that the precision first increased and then decreased with increasing the crack range.The decreased precision when using a high crack range was due to the strain fluctuation during the machining process,and the optimized crack range was 71%of the thickness of forgings.Low orders of Legendre polynomial can result in residual stress curve more smooth,while high orders led to the occurrence of distortion.The Tikhonov regularization method effectively suppressed the distortion of residual stress caused by the fluctuation of strain data,which significantly improved the precision.In addition,The crack compliance method with optimized parameters was used to measure the residual stress of Al-Cu alloy with different quenching methods.The calculated results demonstrated that the distribution of residual stress was obtained accurately.

Crack propagation simulation in brittle elastic materials by a phase field method

To overcome the difficulties of re-meshing and tracking the crack-tip in other computational methods for crack propagation simulations,the phase field method based on the minimum energy principle is introduced by defining a continuous phase field variable(x)∈[0,1]to characterize discontinuous cracks in brittle materials.This method can well describe the crack initiation and propagation without assuming the shape,size and orientation of the initial crack in advance.In this paper,a phase field method based on Miehe's approach[Miehe et al.,Comp.Meth.App.Mech.Eng.(2010)]is applied to simulate different crack propagation problems in twodimensional(2D),isotropic and linear elastic materials.The numerical implementation of the phase field method is realized within the framework of the finite element method(FEM).The validity,accuracy and efficiency of the present method are verified by comparing the numerical results with other reference results in literature.Several numerical examples are presented to show the effects of the loading type(tension and shear),boundary conditions,and initial crack location and orientation on the crack propagation path and force-displacement curve.Furthermore,for a single edge-cracked bi-material specimen,the influences of the loading type and the crack location on the crack propagation trajectory and force-displacement curve are also investigated and discussed.It is demonstrated that the phase field method is an efficient tool for the numerical simulation of the crack propagation problems in brittle elastic materials,and the corresponding results may have an important relevance for predicting and preventing possible crack propagations in engineering applications.

Cracking Propagation of Hardening Concrete Based on the Extended Finite Element Method

Self-deformation cracking is the cracking caused by thermal deformation, autogenous volume deformation or shrinkage deformation. In this paper, an extended finite element calculation method was deduced for concrete crack propagation under a constant hydration and hardening condition during the construction period, and a corresponding programming code was developed. The experimental investigation shows that initial crack propagation caused by self-deformation loads can be analyzed by this program. This improved algorithm was a preliminary application of the XFEM to the problem of the concrete self-deformation cracking during the hydration and hardening period. However, room for improvement exists for this algorithm in terms of matching calculation programs with mass concrete temperature fields containing cooling pipes and the influence of creep or damage on crack propagation.

Simulation of crack coalescence mechanism underneath single and double disc cutters by higher order displacement discontinuity method

The present research is focused on the numerical crack coalescence analysis of the micro-cracks and cracks produced during the cutting action of TBM disc cutters. The linear elastic fracture mechanics(LEFM) concepts and the maximum tangential stress criterion are used to investigate the micro crack propagation and its direction underneath the excavating discs. A higher order displacement discontinuity method with quadratic displacement discontinuity elements is used to estimate the stress intensity factors near the crack tips. Rock cutting mechanisms under single and double type discs are simulated by the proposed numerical method.The main purposes of the present modeling are to simulate the chip formation process of indented rocks by single and double discs.The effects of specific disc parameters(except speed) on the thrust force Ft, the rolling force Fr, and the specific energy ES are investigated. It has been shown that the specific energy(energy required to cut through a unit volume of rock) of the double disc is less than that of the single disc. Crack propagation in rocks under disc cutters is numerically modeled and the optimum ratio of disc spacing S to penetration depth Pd(i.e. S/Pd ratio) of about 10 is obtained, which is in good agreement with the theoretical and experimental results cited in the literature.

Crack stop holes in steel bridge decks:Drilling method and effects

Force analysis using a compact tension model, as recommended by ASTM, was carried out on a crack stop hole. The stress before, and after, drilling the hole was compared in terms of stress concentration and stress gradient. The optimum drilling location and diameter were studied through analysis of different locations and diameters. By analyzing the effects of flank holes and an additional hole, drilling advice was proposed and fatigue testing of the cracks in a steel bridge deck with a crack stop hole was conducted. The results show that the stress at the crack tip with a crack stop hole decreased, and the major principal stress around the hole was distributed accordingly. The optimum position of the crack stop hole centre was where the centre of the crack stop hole was situated behind the crack and the hole edge coincided with the crack tip. Therefore, hole diameters larger than 8 mm, or those weakening the section by 10%, were suggested as the best diameters. In terms of multi-hole crack stopping, a flank hole was not recommended. The optimum horizontal position of flank holes was at a distance of 1/4 of a single hole diameter from, and in front of, the single hole. Besides, the experiment showed that crack stop hole could only prevent cracks from growing and had no influence on crack growth rate.

Cracking analysis of fracture mechanics by the finite element method of lines(FEMOL)

The Finite Element Method of Lines （FEMOL） is a semi-analytic approach and takes a position between FEM and analytic methods. First, FEMOL in Fracture Mechanics is presented in detail. Then, the method is applied to a set of examples such as edge-crack plate, the central-crack plate, the plate with cracks emanating from a hole under tensile or under combination loads of tensile and bending. Their dimensionless stress distribution, the stress intensify factor （SIF） and crack opening displacement （COD） are obtained, and comparison with known solutions by other methods are reported. It is found that a good accuracy is achieved by FEMOL. The method is successfully modified to remarkably increase the accuracy and reduce convergence difficulties. So it is a very useful and new tool in studying fracture mechanics problems.

Evaluation method of cracking resistance of lightweight aggregate concrete

The cracking behavior of lightweight aggregate concrete(LWAC) was investigated by mechanical analysis, SEM and cracking-resistant test where a shrinkage-restrained ring with a clapboard was used. The relationship between the ceramsite type and the cracking resistance of LWAC was built up and compared with that of normal-weight coarse aggregate concrete(NWAC). A new method was proposed to evaluate the cracking resistance of concrete, where the concepts of cracking coefficient ζt(t) and the evaluation index Acr(t) were proposed, and the development of micro-cracks and damage accumulation were recognized. For the concrete with an ascending cracking coefficient curve, the larger Acr(t) is, the lower cracking resistance of concrete is. For the concrete with a descending cracking coefficient curve, the larger Acr(t) is, the stronger the cracking resistance of concrete is. The evaluation results show that in the case of that all the three types of coarse aggregates in concrete are pre-soaked for 24 h, NWAC has the lowest cracking resistance, followed by the LWAC with lower water absorption capacity ceramsite and the LWAC with higher water absorption capacity ceramsite has the strongest cracking resistance. The proposed method has obvious advantages over the cracking age method, because it can evaluate the cracking behavior of concrete even if the concrete has not an observable crack.

STUDY ON THREE-DIMENSIONAL FINITE BODIES CONTAINING CRACKS USING THE FINITE ELEMENT METHOD OF LINES

The three-dimensional finite element method of lines is presented, and the basic processing description of 3D FEMOL in cracking questions is given in detail. Applications to 3D bodies with cracks indicate that good accuracy can be obtained with relatively coarse girds. In particular, application to the tension specimen shows very good agreement with the evaluation of stress intensity factors, which is better than the results of other methods. This implies a considerable potential for using this method in the 3D analysis of finite geometry solids and suggests a possible extension of this technique to nonlinear material behavior.

MESHLESS METHOD FOR 2D MIXED-MODE CRACK PROPAGATION BASED ON VORONOI CELL

A meshless method integrated with linear elastic fracture mechanics(LEFM)is presented for 2D mixed-mode crack propagation analysis.The domain is divided automatically into sub-domains based on Voronoi cells,which are used for quadrature for the potential energy. The continuous crack propagation is simulated with an incremental crack-extension method which assumes a piecewise linear discretization of the unknown crack path.For each increment of the crack extension,the meshless method is applied to carry out a stress analysis of the cracked structure.The J-integral,which can be decomposed into mode Ⅰ and mode Ⅱ for mixed-mode crack,is used for the evaluation of the stress intensity factors(SIFs).The crack-propagation direction,predicted on an incremental basis, is computed by a criterion defined in terms of the SIFs. The flowchart of the proposed procedure is presented and two numerical problems are analyzed with this method.The meshless results agree well with the experimental ones,which validates the accuracy and efficiency of the method.

INVESTIGATION OF ANTI-PLANE SHEAR BEHAVIOR OF TWO COLLINEAR CRACKS IN PIEZOELECTRIC MATERIALS BY A NEW METHOD

In this paper, the interaction between two collinear cracks inpiezoelectric materials under anti-plane shear loading wasinvestigated for the impermeable crack face conditions. By using theFourier transform, the problem can be solved with two pairs of tripleintegral equations. These equations are solved using Schmidt'smethod. This process is quite different from that adopted previously.This makes it possible to understand the two collinear cracksinteraction in piezoelectric materials.

A SELF-SIMILAR CRACK EXPANSION METHOD FOR THREE-DIMENSIONAL CRACKS IN AN INFINITE OR SEMI-INFINITE MEDIUM

The Self-Similar Crack Expansion (SSCE) method is used to calculate stress intensity factors for three-dimensional cracks in an infinite medium or semi-infinite medium by the boundary integral element technique, whereby, the stress intensity factors at crack tips are determined by calculating the crack-opening displacements over the crack surface. For elements on the crack surface, regular integrals and singular integrals are precisely evaluated based on closed form expressions, which improves the accuracy. Examples shaw that this method yields very accurate results for stress intensity factors of penny-shaped cracks and elliptical cracks in the full space, with errors of less than 1% as compared with analytical solutions. The stress intensity factors of subsurface cracks ate in good agreement with other analytical solutions.

SELF-SIMILAR CRACK EXPANSION METHOD FOR THE STRESS INTENSITY FACTOR ANALYSIS

The Self-Similar Crack Expansion (SSCE) method is proposed to evaluate stress intensity factors at crack tips, whereby stress intensity factors of a crack can be determined by the crack opening displacement over the crack, not just by the local displacement around the crack tip. The crack expansion rate is estimated by taking advantage of the crack self-similarity. Therefore, the accuracy of the calculation is improved. The singular integrals on crack tip elements are also analyzed and are precisely evaluated in terms of a special integral analysis. Combination of these two techniques greatly increases the accuracy in estimating the stress distribution around the crack tip. A variety of two-dimensional cracks, such as subsurface cracks, edge cracks, and their interactions are calculated in terms of the self-similar expansion rate. Solutions are satisfied with errors less than 0.5% as compared with the analytical solutions. Based on the calculations of the crack interactions, a theory for crack interactions is proposed such that for a group of aligned cracks the summation of the square of SIFs at the right tips of cracks is always equal to that at the left tips of cracks. This theory was proved by the mehtod of Self-Similar Crack Expansion in this paper.

METHOD TO CALCULATE BENDING CENTER AND STRESS INTENSITY FACTORS OF CRACKED CYLINDER UNDER SAINT_VENANT BENDING

Using the single crack solution and the regular solution of plane harmonic function, the problem of Saint_Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross_section is not thin_walled, but of small torsion rigidity is proposed. Some numerical examples are given.

COMBINED DELAUNAY TRIANGULATION AND ADAPTIVE FINITE ELEMENT METHOD FOR CRACK GROWTH ANALYSIS

The paper presents the utilization of the adaptive Delaunay triangulation in the finite element modeling of two dimensional crack propagation problems, including detailed description of the proposed procedure which consists of the Delaunay triangulation algorithm and an adaptive remeshing technique. The adaptive remeshing technique generates small elements around crack tips and large elements in the other regions. The resulting stress intensity factors and simulated crack propagation behavior are used to evaluate the effectiveness of the procedure. Three sample problems of a center cracked plate, a single edge cracked plate and a compact tension specimen, are simulated and their results assessed.

METHOD OF STRONGLY SINGULAR INTEGRAL EQUATION FOR THE TORSION OF CYLINDER WITH EDGE CRACK

From the dislocation type solution of the torsion of single crack, by using the concept of finite part integrals. The torsion problem of cylinder with a single crack was reduced into an integral equation with strong singularity. The numerical method was also obtained and several numerical examples were calculated successfully at the end of this paper.,

A WEIGHTED RESIDUAL METHOD FOR ELASTIC-PLASTIC ANALYSIS NEAR A CRACK TIP AND THE CALCULATION OF THE PLASTIC STRESS INTENSITY FACTORS

In this paper, a weighted residual method for the elastic-plastic analysis near a crack tip is systematically given by taking the model of power-law hardening under plane strain condition as a sample. The elastic-plastic solutions of the crack lip field and an approach based on the superposition of the nonlinear finite element method on the complete solution in the whole crack body field, to calculate the plastic stress intensity factors, are also developed. Therefore, a complete analvsis based on the calculation both for the crack tip field and for the whole crack body field is provided.

A new method--the inverse strain method(ISM)for preventing welding hot cracking of high strength aluminium alloy LY12CZ

In this paper a new method for preventing welding hot cracking—the inverse strain method(ISM)is developed on the principle of welding mechan- ics.Effectiveness and feasiblity of method in preventing welding hot cracking of high strength aluminum alloy LY12CZ by synchronous rolling during welding (SRDW)along both sides of the weld at a suitable distance behind the welding arc are examined.Experimental resulte indicate that welding hot cracking of LY12CY can be effectively prevented and the mechanical properties of welded joint can also be improved by the method.It is an important new solution for preventing hot cracking in welding of sheet metal.

A NEW METHOD OF ANALYZING SURFACE CRACKS

The authors have developed a new line-spring boundary element method in the present paper, which combines the advantage of the line-spring model with that of the boundary element method. This method reduces the three-dimension problem of the surface cracks into a quasi-one-dimension problem and can be used to analyze the surface cracked plate under various loading conditions. In this paper theoretical analyses and numerical verifications are carried out. The calculated results are reported, which indicate that the present method is efficient and can be used to analyze the surface crack problem on a personal computer.

A linearly-independent higher-order extended numerical manifold method and its application to multiple crack growth simulation

The numerical manifold method(NMM)can be viewed as an inherent continuous-discontinuous numerical method,which is based on two cover systems including mathematical and physical covers.Higher-order NMM that adopts higher-order polynomials as its local approximations generally shows higher precision than zero-order NMM whose local approximations are constants.Therefore,higherorder NMM will be an excellent choice for crack propagation problem which requires higher stress accuracy.In addition,it is crucial to improve the stress accuracy around the crack tip for determining the direction of crack growth according to the maximum circumferential stress criterion in fracture mechanics.Thus,some other enriched local approximations are introduced to model the stress singularity at the crack tip.Generally,higher-order NMM,especially first-order NMM wherein local approximations are first-order polynomials,has the linear dependence problems as other partition of unit(PUM)based numerical methods does.To overcome this problem,an extended NMM is developed based on a new local approximation derived from the triangular plate element in the finite element method(FEM),which has no linear dependence issue.Meanwhile,the stresses at the nodes of mathematical mesh(the nodal stresses in FEM)are continuous and the degrees of freedom defined on the physical patches are physically meaningful.Next,the extended NMM is employed to solve multiple crack propagation problems.It shows that the fracture mechanics requirement and mechanical equilibrium can be satisfied by the trial-and-error method and the adjustment of the load multiplier in the process of crack propagation.Four numerical examples are illustrated to verify the feasibility of the proposed extended NMM.The numerical examples indicate that the crack growths simulated by the extended NMM are in good accordance with the reference solutions.Thus the effectiveness and correctness of the developed NMM have been validated.