Critical stress intensity factors for cracked hollow pipes under transient thermal loads

Finite element analyses of a long hollow cylinder having an axisymmetric circumferential internal edge crack, subjected to convective cooling on the inner surface are performed. The transient thermal stress intensity factor is estimated using a domain version of the J-integral method. The effect of the thickness of the cylinder, crack length, and heat transfer coefficient on the stress intensity factor history are studied. The variations of critical normalized stress intensity factor with crack length-to-thickness ratio for different parameters are presented. The results show that if a small inner surface crack begins to grow, its stress intensity factor will increase with increase in crack length, reach a maximum, and then begin to drop. Based on the results, a fracture-based design methodology for cracked hollow pipes under transient thermal loads is discussed.

A general methodology for calculating mixed mode stress intensity factors and fracture toughness of solder joints with interfacial cracks

Solder joints in electronic packages undergo thermo-mechanical cycling, resulting in nucleation of micro-cracks, especially at the solder/bond-pad interface, which may lead to fracture of the joints. The fracture toughness of a solder joint depends on material properties, process conditions and service history, as well as strain rate and mode-mixity. This paper reports on a methodology for determining the mixed-mode fracture toughness of solder joints with an interfacial starter-crack, using a modified compact mixed mode (CMM) specimen containing an adhesive joint. Expressions for stress intensity factor (K) and strain energy release rate (G) are developed, using a combination of experiments and finite element (FE) analysis. In this methodology, crack length dependent geometry factors to convert for the modified CMM sample are first obtained via the crack-tip opening displacement (CTOD)-based linear extrapolation method to calculate the under far-field mode I and II conditions (f(1a) and f(2a)), (ii) generation of a master-plot to determine a(c), and (iii) computation of K and G to analyze the fracture behavior of joints. The developed methodology was verified using J-integral calculations, and was also used to calculate experimental fracture toughness values of a few lead-free solder-Cu joints. (C) 2014 Elsevier Ltd. All rights reserved.

Dynamic SIF of interface crack between two dissimilar viscoelastic bodies under impact loading

In this paper, the transient dynamic stress intensity factor (SIF) is determined for an interface crack between two dissimilar half-infinite isotropic viscoelastic bodies under impact loading. An anti-plane step loading is assumed to act suddenly on the surface of interface crack of finite length. The stress field incurred near the crack tip is analyzed. The integral transformation method and singular integral equation approach are used to get the solution. By virtue of the integral transformation method, the viscoelastic mixed boundary problem is reduced to a set of dual integral equations of crack open displacement function in the transformation domain. The dual integral equations can be further transformed into the first kind of Cauchy-type singular integral equation (SIE) by introduction of crack dislocation density function. A piecewise continuous function approach is adopted to get the numerical solution of SIE. Finally, numerical inverse integral transformation is performed and the dynamic SIF in transformation domain is recovered to that in time domain. The dynamic SIF during a small time-interval is evaluated, and the effects of the viscoelastic material parameters on dynamic SIF are analyzed.

Semi-weight function method on computation of stress intensity factors in dissimilar materials

Semi-weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi-weight functions were obtained as virtual displacement and stress fields with eigenvalue-lambda. Integral expression of fracture parameters, K-I and K-II, were obtained from reciprocal work theorem with semi-weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi-weight function method is a simple, convenient and high precision calculation method.

Elastodynamic stress-intensity factors for a semiinfinite crack under 3-d combined mode loading

The dynamic stress intensity factor histories for a half plane crack in an otherwise unbounded elastic body are analyzed. The crack is subjected to a traction distribution consisting of two pairs of suddenly-applied shear point loads, at a distance L away from the crack tip. The exact expression for the combined mode stress intensity factors as the function of time and position along the crack edge is obtained. The method of solution is based on the direct application of integral transforms together with the Wiener-Hopf technique and the Cagniard-de Hoop method, which were previously believed to be inappropriate. Some features of solutions are discussed and the results are displayed in several figures.

Laser shock peening treatment to control and moderate fatigue crack growth in aircraft structure based on residual stress engineering approach

Laser Shock Peening (LSP) is a surface enhancement treatment which induces a significant layer of beneficial compressive residual stresses of up to several mm underneath the surface of metal components in order to improve the detrimental effects of the crack growth behavior rate in it. The aim of this thesis is to predict the crack growth behavior in metallic specimens with one or more stripes which define the compressive residual stress area induced by the Laser Shock Peening treatment. The process was applied as crack retardation stripes perpendicular to the crack propagation direction with the object of slowing down the crack when approaching the peened stripes. The finite element method has been applied to simulate the redistribution of stresses in a cracked model when it is subjected to a tension load and to a compressive residual stress field, and to evaluate the Stress Intensity Factor (SIF) in this condition. Finally, the Afgrow software is used to predict the crack growth behavior of the component following the Laser Shock Peening treatment and to detect the improvement in the fatigue life comparing it to the baseline specimen. An educational internship at the “Research & Technologies Germany – Hamburg” department of AIRBUS helped to achieve knowledge and experience to write this thesis. The main tasks of the thesis are the following: •To up to date Literature Survey related to “Laser Shock Peening in Metallic Structures” •To validate the FE model developed against experimental measurements at coupon level •To develop design of crack growth slowdown in Centered Cracked Tension specimens based on residual stress engineering approach using laser peened strip transversal to the crack path •To evaluate the Stress Intensity Factor values for Centered Cracked Tension specimens after the Laser Shock Peening treatment via Finite Element Analysis •To predict the crack growth behavior in Centered Cracked Tension specimens using as input the SIF values evaluated with the FE simulations •To validate the results by means of experimental tests

Crack propagation in non-homogenous materials: Evaluation of mixed-mode SIFs, T-stress and kinking angle using a variant EFG method

A new variant of the Element-Free Galerkin (EFG) method, that combines the diffraction method, to characterize the crack tip solution, and the Heaviside enrichment function for representing discontinuity due to a crack, has been used to model crack propagation through non-homogenous materials. In the case of interface crack propagation, the kink angle is predicted by applying the maximum tangential principal stress (MTPS) criterion in conjunction with consideration of the energy release rate (ERR). The MTPS criterion is applied to the crack tip stress field described by both the stress intensity factor (SIF) and the T-stress, which are extracted using the interaction integral method. The proposed EFG method has been developed and applied for 2D case studies involving a crack in an orthotropic material, crack along an interface and a crack terminating at a bi-material interface, under mechanical or thermal loading; this is done to demonstrate the advantages and efficiency of the proposed methodology. The computed SIFs, T-stress and the predicted interface crack kink angles are compared with existing results in the literature and are found to be in good agreement. An example of crack growth through a particle-reinforced composite materials, which may involve crack meandering around the particle, is reported.

New a posteriori error estimator and adaptive mesh refinement strategy for 2-D crack problems

A posteriori error estimation and adaptive refinement technique for fracture analysis of 2-D/3-D crack problems is the state-of-the-art. The objective of the present paper is to propose a new a posteriori error estimator based on strain energy release rate (SERR) or stress intensity factor (SIF) at the crack tip region and to use this along with the stress based error estimator available in the literature for the region away from the crack tip. The proposed a posteriori error estimator is called the K-S error estimator. Further, an adaptive mesh refinement (h-) strategy which can be used with K-S error estimator has been proposed for fracture analysis of 2-D crack problems. The performance of the proposed a posteriori error estimator and the h-adaptive refinement strategy have been demonstrated by employing the 4-noded, 8-noded and 9-noded plane stress finite elements. The proposed error estimator together with the h-adaptive refinement strategy will facilitate automation of fracture analysis process to provide reliable solutions.

Fracture Analysis of Concrete Structural Components Accounting for Tension Softening Effect

This paper presents methodologies for fracture analysis of concrete structural components with and without considering tension softening effect. Stress intensity factor (SIF) is computed by using analytical approach and finite element analysis. In the analytical approach, SW accounting for tension softening effect has been obtained as the difference of SIP obtained using linear elastic fracture mechanics (LEFM) principles and SIP due to closing pressure. Superposition principle has been used by accounting for non-linearity in incremental form. SW due to crack closing force applied on the effective crack face inside the process zone has been computed using Green's function approach. In finite element analysis, the domain integral method has been used for computation of SIR The domain integral method is used to calculate the strain energy release rate and SIF when a crack grows. Numerical studies have been conducted on notched 3-point bending concrete specimen with and without considering the cohesive stresses. It is observed from the studies that SW obtained from the finite element analysis with and without considering the cohesive stresses is in good agreement with the corresponding analytical value. The effect of cohesive stress on SW decreases with increase of crack length. Further, studies have been conducted on geometrically similar structures and observed that (i) the effect of cohesive stress on SW is significant with increase of load for a particular crack length and (iii) SW values decreases with increase of tensile strength for a particular crack length and load.

Analysis of a cracked lug loaded by an interference fit pin

In the present study, a lug joint fitted with an interference fit (oversized) pin is considered with radial through cracks situated at diametrically opposite points perpendicular to the loading direction. A finite element contact stress algorithm is developed with linear elastic assumptions to deal with varying partial contact/separation at the pin-plate interface using a marching solution. Stress Intensity Factor (SIF) at the crack tips is evaluated using the Modified Crack Closure Integral (MCCI) method. The effect of change in crack length and edge distance on the load-contact relation, SIFs and stress distributions are studied. A rigorous plane stress elasticity solution of the pin-plate interface at the crack mouth confirmed the existence of the stress concentration leading to a local peak in the radial stress at the crack mouth and provided a method of estimating it quantitatively. Copyright (C) 1996 Elsevier Science Ltd.

Experimental Study of the Earthquake Recurrence Period and the Trend of Post-Seismic Development

In order to study the earthquake recurrence and the characteristics of earthquake series, rupture tests of rock samples and plexiglass samples were made. On rock samples, a number of acoustic emission (AE) and strain measuring points were deployed; the load was one side direct shear. The variation characteristics of AE and strain at different detecting points around the extra large fracture were observed and studied. On plexiglass samples, a series of inclined cracks were prefabricated by a small-scale compressive testing machine. The samples were then loaded on a shockproof platen, when the samples were loaded, the stress intensity factor (SIF) was determined by the laser interferometric technique and shadow optical method of caustics. The fracture conditions such as material toughness around the extra large fracture were also studied. From those experimental results and the theory of fracture mechanics, the earthquake recurrence period and the trend of post-seismic development were studied.

Multiple Axial Cracks in A Coated Hollow Cylinder due to Thermal Shock

The transient thermal stress problem of an inner-surface-coated hollow cylinder with multiple pre-existing surface cracks contained in the coating is considered. The transient temperature, induced thermal stress, and the crack tip stress intensity factor (SIF) are calculated for the cylinder via finite element method (FEM), which is exposed to convective cooling from the inner surface. As an example, the material pair of a chromium coating and an underlying steel substrate 30CrNi2MoVA is particularly evaluated. Numerical results are obtained for the stress intensity factors as a function of normalized quantities such as time, crack length, convection severity, material constants and crack spacing. (c) 2005 Elsevier Ltd. All rights reserved.

Molecular dynamics studies of brittle fracture of SiO2

By applying for molecular dynamics (MD) simulation and Griffith fracture criterion, the brittle behavior of crack extension of mode I type is investigated. The critical stress intensity factor (SIF)K-Ic(MD) of crack extension is calculated, and the evolution of atoms near crack tip is observed. It is found that K-Ic(MD) is in good agreement with the Griffith ftacture criterion K-Ic(Griffith).

Hybrid special finite element method for bi-material crack

In the paper, two novel 2-D hybrid special finite elements each containing an interfacial edge crack, which lies along or vertical to the interface between two materials, are developed. These proposed elements can assure the high precision especially in the vicinity of crack tip and provide a better description of its singularity with only one hybrid element surrounding one interfacial crack, thus, the numerical modeling of fracture analysis on bi-material crack can be greatly simplified. Numerical examples are provided to demonstrate the validity and versatility of the proposed method.

Time–Harmonic Behaviour of a Cracked Piezoelectric Solid by BIEM

ACM Computing Classification System (1998): J.2, G.1.9