Modified Boundary Layer Model Research Articles

J resistance behavior in functionally graded materials using cohesive zone and modified boundary layer models

This paper describes elastic–plastic crack growth resistance simulation in a ceramic/metal functionally graded material (FGM) under mode I loading conditions using cohesive zone and modified boundary layer (MBL) models. For this purpose, we first explore the applicability of two existing, phenomenological cohesive zone models for FGMs. Based on these investigations, we propose a new cohesive zone model. Then, we perform crack growth simulations for TiB/Ti FGM SE(B) and SE(T) specimens using the three cohesive zone models mentioned above. The crack growth resistance of the FGM is characterized by the J-integral. These results show that the two existing cohesive zone models overestimate the actual J value, whereas the model proposed in the present study closely captures the actual fracture and crack growth behaviors of the FGM. Finally, the cohesive zone models are employed in conjunction with the MBL model. The two existing cohesive zone models fail to produce the desired K–T stress field for the MBL model. On the other hand, the proposed cohesive zone model yields the desired K–T stress field for the MBL model, and thus yields JR curves that match the ones obtained from the SE(B) and SE(T) specimens. These results verify the application of the MBL model to simulate crack growth resistance in FGMs.

A boundary layer framework considering material gradation effects

This paper describes the development and application of a novel modified boundary layer (MBL) model for graded nonhomogeneous materials, e.g. functionally graded materials (FGMs). The proposed model is based on a middle-crack tension, M(T), specimen with traction boundary conditions applied to the top and lateral edges of the model. Finite element analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates elements with graded elastic and plastic properties. Elastic crack-tip fields obtained from the proposed MBL model show excellent agreement with those obtained from full models of the cracked component for homogeneous and graded nonhomogeneous materials. The K– T dominance of FGMs is investigated by comparing the actual stress fields with the asymptotic stress fields (the Williams’ solution). The examples investigated in the present study consider a crack parallel to the material gradient. Results of the present study provide insight into the K– T dominance of FGMs and also show the range of applicability of the proposed MBL model. The MBL model is applied to analyze the elastic–plastic crack-tip response of a Ti/TiB FGM SE(T) specimen. The numerical results demonstrate that the proposed MBL model captures the effect of T-stress on plastic zone size and shape, constraint effects, etc. for such configurations.

Numerical simulation of constraint effects in fatigue crack growth

The computational analysis of constraint effects on fatigue crack growth is discussed. An irreversible cohesive zone model is used in the computations to describe the processes of material separation under cyclic loading. This approach is promising for the investigation of fatigue crack growth under constraint as the energy dissipation due to the formation of new crack surface and cyclic plastic deformation is accounted for independently. Fatigue crack growth in multi-layer structures under consideration of different levels of T-stress are conducted with a modified boundary layer model. Fatigue crack growth is computed as a function of layer thickness and T-stress for constant and variable amplitude loading cases.

Unbiased membrane permeability parameters for gabapentin using boundary layer approach

The present study was performed to determine the relative contribution of both passive and nonpassive transport processes in jejunal absorption of gabapentin. The oral absorption of gabapentin was studied using in situ single pass intestinal perfusion technique in fasted rats. Unbiased intrinsic membrane absorption parameters such as maximal flux, Michaelis constant, carrier permeability, and membrane permeability were calculated using a modified boundary layer model. Gabapentin intestinal perfusion results indicate that its jejunal absorption in rats occurs via a nonpassive process, with no significant passive absorption component, as demonstrated by saturable absorption kinetics and its concentration-dependent permeability. A good correlation (r2 = 0.88) between observed human absorption fraction and calculated (from in situ rat intestine) human absorption fraction was obtained.

A numerical analysis of constraint effects in fatigue crack growth by use of an irreversible cohesive zone model

The analysis of constraint effects in fatigue crack growth in multi-layer structures is discussed. The process of material separation under cyclic loading is described by a cohesive zone model (CZM) with an irreversible constitutive relationship. The traction–separation behavior does not follow a predefined path, but is dependent on the evolution of the damage dependent cohesive zone properties. A modified boundary layer model is used in simulations of fatigue crack growth along the centerline crack of the metal layer sandwiched between two elastic substrates. Fatigue crack growth is computed for a series of values of metal layer thickness under constant and variable amplitude loading conditions. The results of the computations demonstrate that certain combinations of load magnitude, layer thickness and material properties results in significant constrain effects in fatigue crack growth. The influence of these constraint effects on fatigue crack growth rates and on crack closure processes is determined. The evolutions of the traction–separation law, the accumulated and current plastic zones, as well as the stress fields during the crack propagation are discussed.

Effect of T-stress on fatigue crack closure in 3-D small-scale yielding

This paper investigates the effects of in-plane constraint on 3-D fatigue crack closure in the small-scale yielding regime. The finite element analyses grow a sharp, straight-through crack in a modified boundary layer model under mode I, constant amplitude cyclic loading with prescribed but independent peak values of stress intensity factor, K max, and the T-stress, T max. A purely kinematic hardening law with constant modulus represents the material constitutive behavior. The computational results demonstrate that a two parameter characterization of crack tip fields in terms of K max /σ 0 B and T max/ σ 0, where σ 0 denotes the yield stress of the material, correlates successfully the normalized opening load K op/ K max across variations of thickness ( B), constraint level and material flow properties. Both negative and positive T-stress reduce the through-thickness variation in local opening load levels along the crack front. A negative T-stress increases K op/ K max values, particularly at low peak loads where the plastic zone size remains a fraction of the thickness; a positive T-stress has limited effect on K op/ K max values. The fringe plots of individual plastic strain components reveal (a) in the absence of T-stress ( T max/ σ 0=0), plastic contraction in the thickness direction compensates primarily for permanent stretching in the direction normal to the crack plane required for closure, (b) for negative T-stress ( T max/ σ 0<0), plastic contraction in the in-plane transverse direction contributes the larger share of material flowing into the normal direction, and (c) for positive T-stress ( T max/ σ 0>0), both in-plane directions experience permanent stretching and the thickness direction alone undergoes plastic contraction.

Kinetics and rate-limiting mechanisms of dolomite dissolution at various CO 2 partial pressures

Techniques of rotating-disk and catalyst were used in investigating the kinetics of dolo- mite dissolution in flowing CO2-H2O system. Experiments run in the solutions equilibrated with various CO2 partial pressures ( 2 CO P ) from 30 to 100000 Pa. It shows that dissolution rates of dolomite are related with rotating speeds at conditions far from equilibrium. This was explained by modified diffusion boundary layer (DBL) model. In addition, the dissolution rates increase after ad- dition of carbonic anhydrase (CA) to solutions, where the CA catalyzes CO2 conversion. However, great differences occur among various CO2 partial pressures. The experimental observations give a conclusion that the modified DBL model enables one to predict dissolution rates and their be- haviour at various 2 CO P with satisfactory precision at least far from equilibrium.

A complete Gurson model approach for ductile fracture

Recently, a complete Gurson model has been introduced by the authors. The complete Gurson model is a combination of the modified Gurson model which deals with microvoid nucleation and growth, and a physical microvoid coalescence criterion based on the plastic limit load model by Thomason. By comparing finite element cell modeling analyses, the complete Gurson model is accurate for both non-hardening and hardening materials. One attractive feature of the complete Gurson model is that material ductile failure is exclusively linked to the microvoid nucleation parameter, and the nucleation parameter in many cases can be determined without metallurgical examinations. Furthermore, the so-called critical void volume fraction f c, has been eliminated from material constants. In this paper, two simple microvoid nucleation models for modeling ductile fracture are discussed, and a method which applies multitension specimens including both smooth and notched cylindrical specimens for determining the microvoid nucleation parameter is introduced. Once the microvoid nucleation parameter has been determined from the tension specimens, the characteristic length parameter which describes the stress/strain gradient effect can be fitted from fracture mechanics tests. Material ductile crack resistance behavior is then a function of the microvoid nucleation parameter, the length parameter and the specimen geometry. For modified boundary layer models, it has been found that the crack resistance curves can be normalized by the T stress, and the T stress can be possibly taken as the geometry controlling parameter for ductile crack growth.

Quantification of Geometry and Material Mismatch Constraint in Steel Weldments with Fusion Line Cracks

Finite element analyses of an idealised steel weldment show that the constraint caused by geometry and material mismatch can be separated in a Modified Boundary Layer (MBL) model. The MBL model was loaded by a KI+T displacement field. Analyses of four fracture mechanics specimens revealed that the loss of constraint in the investigated weldments was different from the corresponding loss of constraint in a homogeneous reference case. Therefore, it was not possible to use the homogeneous reference to predict the development of constraint in the investigated weldments. In the fracture mechanics specimens the analyses show that the mismatch constraint is slightly reduced together with the loss of geometry constraint as large scale yielding develops in the specimens. By using the mismatch constraint determined from the MBL model, good predictions of the constraint in the specimens were obtained. In order to predict the fracture toughness in steel weldments with varying material mismatch and geometry constraint, three failure criteria have been compared. The results show that the RKR failure criterion by Ritchie et al. (1973) is applicable to the inhomogeneous material in this study. The study reveals that the mismatch effect on the failure predictions is influenced by the critical threshold stress used in the failure criteria. For all the investigated criteria, the mismatch effect on the predicted toughness was amplified by an elevation of the threshold stress. The constraint description has been used together with the RKR failure criterion to predict the required toughness (Jref) as a function of J for all the investigated geometries and mismatch cases.

Characterization of the oral absorption of several aminopenicillins: Determination of intrinsic membrane absorption parameters in the rat intestine in situ

The absorption mechanism of several penicillins was characterized using in situ single-pass intestinal perfusion in the rat. The intrinsic membrane absorption parameters were determined using a modified boundary layer model (fitted value ± S.E.): J ∗ max = 11.78 ± 1.88 mM, K m = 15.80 ± 2.92 mM, P ∗ m = 0, J ∗ c = 0.75 ± 0.04 for ampicillin; J ∗ max = 0.044 ± 0.018 mM, K m = 0.058 ± 0.026 mM , P ∗ m = 0.558 ± 0.051, P ∗ c = 0.757 ± 0.088 for amoxicillin; and J ∗ max = 16.30 ± 3.40 mM, K m = 14.00 ± 3.30 mM, P ∗ m = 0 , P ∗ c = 1.14 ± 0.05 for cyclacillin. All of the aminopenicillins studied demonstrated saturable absorption kinetics as indicated by their concentration-dependent wall permeabilities. Inhibition studies were performed to confirm the existence of a nonpassive absorption mechanism. The intrinsic wall permeability ( P ∗ w ) of 0.01 mM ampicillin was significantly lowered by 1 mM amoxicillin and the P ∗ w of 0.01 mM amoxicillin was reduced by 2 mM cephradine consistent with competitive inhibition.

On the Use of Boundary Layer Theory to Determine the Internal Circulation of Falling Drops

Abstract The standard boundary layer model for the flow past a circulating drop neglects the stress reduction caused by motion of the drop surface. A modified boundary layer model which incorporates this effect is presented, and is shown to yield good agreement with a numerical solution for the strength of the drop internal circulation.