Elastodynamic Interaction of Two Offset Interfacial Cracks in Bonded Dissimilar Media With a Functionally Graded Interlayer Under Antiplane Shear Impact

2014 ◽  
Vol 81 (8) ◽  
Author(s):  
Hyung Jip Choi
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Functionally Graded ◽  
Inverse Laplace Transform ◽  
Dynamic Mode ◽  
Cauchy Type ◽  
Intensity Factors ◽  
Interfacial Cracks ◽  
Graded Interlayer ◽  
The Impact

The impact response of bonded media with a functionally graded interlayer weakened by a pair of two offset interfacial cracks is investigated under the condition of antiplane deformation. The material nonhomogeneity in the graded interlayer is represented in terms of power-law variations of shear modulus and mass density between the dissimilar, homogeneous half-planes. Laplace and Fourier integral transforms are employed to reduce the crack problem to solving a system of Cauchy-type singular integral equations in the Laplace domain. The crack-tip behavior in the physical domain is recovered through the inverse Laplace transform to evaluate the dynamic mode III stress intensity factors as a function of time. As a result, the transient interaction of the offset interfacial cracks spaced apart by the graded interlayer is illustrated. The peak values of the dynamic stress intensity factors are also presented versus offset crack distance, elaborating the effects of various material and geometric parameters of the bonded system on the overshoot characteristics of the transient behavior in the near-tip regions, owing to the impact-induced interaction of singular stress fields between the two cracks.

Interfacial cracking in a graded coating/substrate system loaded by a frictional sliding flat punch

2009 ◽  
Vol 466 (2115) ◽  
pp. 853-880 ◽  
Author(s):  
Hyung Jip Choi ◽  
Glaucio H. Paulino
Keyword(s):  
Stress Intensity ◽  
Stress Field ◽  
Contact Pressure ◽  
Contact Stress ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Functionally Graded ◽  
Cauchy Type ◽  
Intensity Factors ◽  
Flat Punch

An analysis of a coupled plane elasticity problem of crack/contact mechanics for a coating/substrate system with functionally graded properties is performed, where the rigid flat punch slides over the surface of the coated system that contains a crack. The graded material is treated as a non-homogeneous interlayer between dissimilar, homogeneous phases of the coated medium and the crack is assumed to exist along the interface between the interlayer and the substrate. Based on the Fourier integral transform method and the transfer matrix approach, formulation of the current coupled mixed boundary value problem lends itself to the derivation of a set of three simultaneous Cauchy-type singular integral equations. In the numerical results, the emphasis is placed on the investigation of interactions between the contact stress field and the crack-tip behaviour for various combinations of material, geometric and loading parameters of the coated system. Specifically, effects of interfacial cracking on the distributions of the contact pressure and the in-plane stress component along the coating surface are examined and the mixed-mode stress intensity factors evaluated from the crack-tip stress field with the square-root singularity are provided as a function of punch location. Further addressed is the quantification of the singular character of contact pressure distributions at the trailing and leading edges of the flat punch in terms of the punch-edge stress intensity factors. Implicit in this particular analysis of the coupled crack/contact problem presented henceforth is that the crack closure behaviour under the compressive contact stress field is not taken into account, ignoring the influence of crack-face contact and friction.

scholarly journals A Numerical Evaluation of SIFs of 2-D Functionally Graded Materials by Enriched Natural Element Method

2019 ◽  
Vol 9 (17) ◽  
pp. 3581 ◽  
Author(s):  
Jin-Rae Cho
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Materials ◽  
Displacement Field ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Graded Materials ◽  
Natural Element Method ◽  
Natural Element

This paper presents the numerical prediction of stress intensity factors (SIFs) of 2-D inhomogeneous functionally graded materials (FGMs) by an enriched Petrov-Galerkin natural element method (PG-NEM). The overall trial displacement field was approximated in terms of Laplace interpolation functions, and the crack tip one was enhanced by the crack-tip singular displacement field. The overall stress and strain distributions, which were obtained by PG-NEM, were smoothened and improved by the stress recovery. The modified interaction integral M ˜ ( 1 , 2 ) was employed to evaluate the stress intensity factors of FGMs with spatially varying elastic moduli. The proposed method was validated through the representative numerical examples and the effectiveness was justified by comparing the numerical results with the reference solutions.

Consideration of Reduction in Stiffness due to Cracking and the Impact on Standard Stress Intensity Factor Solutions

2017 ◽  
Author(s):  
Daniel M. Blanks
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Intensity Factors ◽  
Nozzle Geometry ◽  
Intensity Factors ◽  
Factor Solution ◽  
Small Component ◽  
Embedded Crack ◽  
The Impact

An API 579-1/ASME FFS-1 Failure Assessment Diagram based Fitness-for-Service assessment was carried out on an embedded crack-like flaw found in a nozzle to shell weld in a pressure vessel. Stress intensity factors were initially calculated by utilizing stress results from a Finite Element Analysis (FEA) of an uncracked configuration, with the standard embedded crack stress intensity factor solution given in API 579-1/ASME FFS-1. Due to the complex nozzle geometry and flaw size, a second analysis was carried out, incorporating a crack into the FEA model, to calculate the stress intensity factors and evaluate if the standard solution could be applied to this geometry. A large difference in the resulting stress intensity factors was observed, with those calculated by the FEA with the crack incorporated into the model to be twice as high as those calculated by the standard solutions, indicating the standard embedded crack stress intensity factor solution may be non-conservative in this case. An investigation was carried out involving a number of studies to determine the cause of the difference. Beginning with an elliptical shaped embedded crack in a plate, the stress intensity factor calculated with an idealized 3D crack mesh agreed with the API 579-1/ASME FFS-1 solution. Examining other crack locations, and crack shapes, such as a constant depth embedded crack, revealed how the solution began to differ. The greatest difference was found when considering a crack mesh with a small component height (i.e. the distance measured perpendicular from the crack face to the top of the mesh). A close agreement was then found between the stress intensity factors calculated in the nozzle model and an idealized crack mesh with component heights representative of the true geometry. This revealed that reduced structural stiffness is a key factor in the calculation of the stress intensity factors for this geometry, due to the close proximity of the embedded crack to the inner surface of the nozzle. It was found that this reduction is potentially significant even with relatively small crack sizes. This paper details the investigation, and aims to provide the reader with an awareness of situations when the standard stress intensity factor solutions may no longer be valid, and offers general recommendations to consider when calculating stress intensity factors in these situations.

Improved crack analysis of two-dimensional functionally graded materials by enriched natural element method

2020 ◽  
Vol 234 (10) ◽  
pp. 2012-2023
Author(s):  
Jin-Rae Cho
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Materials ◽  
Displacement Field ◽  
Stress Intensity Factors ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Graded Materials ◽  
Natural Element Method ◽  
Natural Element

The numerical calculation of stress intensity factors of two-dimensional functionally graded materials is introduced by an enriched Petrov–Galerkin natural element method (enriched PG-NEM). The overall trial displacement field is basically approximated in terms of Laplace interpolation functions and it is enriched by the near-tip asymptotic displacement field. The overall strain and stress fields which were approximated by PG-NEM were smoothened and enhanced by the patch recovery. The modified interaction integral [Formula: see text] is used to evaluate the stress intensity factors of functionally graded materials with the spatially varying elastic modulus. The validity of present method is justified through the evaluation of crack-tip stress distributions and the stress intensity factors of four numerical examples. It has been found that the proposed method effectively and successfully captures the near-tip stress singularity with a remarkably improved accuracy, even with the remarkably coarse grid, when compared with an extremely fine grid and the analytical and numerical reference solutions.

Sign in / Sign up

Export Citation Format

Share Document