On Crack-Tip Stresses as Crack-Tip Radii Decrease

2010 ◽  
Vol 78 (1) ◽  
Author(s):  
G. B. Sinclair ◽  
G. Meda ◽  
B. S. Smallwood
Keyword(s):  
Crack Tip ◽  
Physical Reality ◽  
Test Problems ◽  
Crack Plane ◽  
Elasticity Analysis ◽  
Stress Singularities ◽  
Classical Elasticity ◽  
Cohesive Stress ◽  
Elliptical Holes ◽  
Numerical Approaches

In classical elasticity, when cracks are modeled with stress-free elliptical holes, stress singularities occur as crack-tip root radii go to zero. This raises the question of when crack-tip stresses first start to depart from physical reality as radii go to zero. To address this question, here, cohesive stress action is taken into account as radii go to zero. To obtain sufficient resolution of the key crack-tip fields, two highly focused numerical approaches are employed: finite elements with successive submodeling concentrated on the crack-tip and numerical analysis of a companion integral equation with considerable discretization refinement at the crack-tip. Both numerical approaches are verified with convergence checks and test problems. Results show that for visible cracks, classical elasticity analysis leads to physically sensible stresses, provided that crack-tip radii are accounted for properly. For microcracks with smaller crack-tip radii, however, cohesive stress action also needs to be included if accurate crack-tip stresses are to be obtained. For cracks with yet smaller crack-tip radii, cracks close and stresses throughout the crack plane become uniform.

Atomistic Study of Cleavage and Dislocation Emission in NiAl

1994 ◽  
Vol 364 ◽  
Author(s):  
M. Ludwig ◽  
P. Gumbsch
Keyword(s):  
Finite Element ◽  
Mixed Mode ◽  
Crack Tip ◽  
Mode I ◽  
Crack Plane ◽  
Dislocation Emission ◽  
Dislocation Generation ◽  
Embedded Atom ◽  
Atomistic Study ◽  
Eam Potential

AbstractThe atomistic processes during fracture of NiAl are studied using a new embedded atom (EAM) potential to describe the region near the crack tip. To provide the atomistically modeled crack tip region with realistic boundary conditions, a coupled finite element - atomistic (FEAt) technique [1] is employed. In agreement with experimental observations, perfectly brittle cleavage is observed for the (110) crack plane. In contrast, cracks on the (100) plane either follow a zig-zag path on (110) planes, or emit dislocations. Dislocation generation is studied in more detail under mixed mode I/II loading conditions.

scholarly journals Critical value of the generalized stress intensity factor for a crack perpendicular to an interface

2015 ◽  
Vol 471 (2183) ◽  
pp. 20150571 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Crack Tip ◽  
Critical Value ◽  
Zone Model ◽  
Cohesive Stress ◽  
Generalized Stress Intensity Factor

When a crack tip impinges upon a bi-material interface, the order of the stress singularity will be equal to, less than or greater than one-half. The generalized stress intensity factors have already been determined for some such configurations, including when a finite-length crack is perpendicular to the interface. However, for these non-square-root singular stresses, the determination of the conditions for crack growth are not well established. In this investigation, the critical value of the generalized stress intensity factor for tensile loading is related to the work of adhesion by using a cohesive zone model in an asymptotic analysis of the separation near the crack tip. It is found that the critical value of the generalized stress intensity factor depends upon the maximum stress of the cohesive zone model, as well as on the Dundurs parameters ( α and β ). As expected this dependence on the cohesive stress vanishes as the material contrast is reduced, in which case the order of the singularity approaches one-half.

Brittle-Ductile Transition in Heterogeneous Metallic Materials [PowerPoint Submission]

2006 ◽  
Vol 978 ◽  
Author(s):  
Silvester John Noronha ◽  
Nasr M Ghoniem
Keyword(s):  
Fracture Toughness ◽  
Tensile Stress ◽  
Size Distribution ◽  
Crack Tip ◽  
Transition Curve ◽  
Crack Plane ◽  
Metallic Materials ◽  
Brittle Ductile Transition ◽  
Discrete Dislocation ◽  
The Matrix

AbstractWe present a model for the brittle - ductile transition in heterogenous metallic materials based on two dimensional discrete dislocation simulations of crack-tip plasticity. The sum of elastic fields of the crack and the emitted dislocations defines an elasto-plastic crack field. Effects of crack-tip blunting of the macrocrack are included in the simulations. The plastic zone characteristics are found to be in agreement with continuum models, with the added advantage that the hardening behavior comes out naturally in our model. The present model is composed of a macrocrack with microcracks ahead of its tip. These microcracks represent potential fracture sites at internal inhomogenities, such as brittle precipitates. Dislocations that are emitted from the crack-tip account for plasticity. When the tensile stress at the microcrack situated along the crack plane attains a critical value over a distance fracture is assumed to take place. The brittle-ductile transition curve is obtained by determining the fracture toughness at various temperatures. Factors that contribute to the sharp upturn in fracture toughness with temperature are found to be: the decrease in tensile stress ahead of the crack tip due to increase in blunting, and the increase in dislocation mobility. The inherent scatter in fracture toughness measurements are studied by using a size distribution for microcracks, distributed on the crack plane of the macrocrack. The scatter in fracture toughness measurements is found to be an effect of the size distribution of microcracks rather than their spatial distribution on the matrix ahead of the crack plane. When compared, the obtained results are in agreement with the existing experimental data.

Quantification of Residual Stresses Induced by Prior Loading at High Temperatures

2011 ◽  
Author(s):  
Ali N. Mehmanparast ◽  
Catrin M. Davies ◽  
Robert C. Wimpory ◽  
Kamran M. Nikbin
Keyword(s):  
Fracture Toughness ◽  
Residual Stress ◽  
Residual Stresses ◽  
Crack Growth ◽  
Creep Crack Growth ◽  
Crack Tip ◽  
Crack Plane ◽  
Residual Stress Field ◽  
Compression Direction ◽  
Fracture Specimen

High temperature components generally undergo cyclic loading conditions. Prior tensile/compressive loading of a fracture specimen can induce compressive/tensile residual stress fields at the crack tip. These residual stresses will influence the subsequent fracture behaviour of the cracked body. This work forms part of a project to examine the influence of creep induced damage at a crack tip on subsequent fatigue crack growth and fracture toughness properties of austenitic type 316H stainless steel. Creep damage is introduced local to the crack tip of a fracture specimen by interrupting a creep crack growth test, performed at 550 °C. Prior to testing, the material was pre-compressed in order to strain harden the material. The compact tension, C(T), specimen geometry has been considered in this work. Since residual stresses are known to influence fatigue and fracture toughness properties of a cracked body, it is important that the residual stress levels at the crack tip are quantified. Neutron diffraction (ND) measurements have therefore been performed to quantify the extent of residual stress in these samples after initial loading, and compared to finite element model predictions. Two specimens have been considered with the crack plane orientated in parallel and perpendicular to the pre-compression direction. Compressive residual stresses of around 100 MPa have been measured directly ahead of the crack tip. Reasonable predictions of the principal residual stress distributions have been obtained by the simplified FE analysis. Though the tensile properties differ significantly in for specimens orientated parallel and perpendicular to the pre-compression direction, no significant differences in the residual stress field are predicted in the C(T) specimens orientated in both directions.

Stress singularities in classical elasticity–I: Removal, interpretation, and analysis

2004 ◽  
Vol 57 (4) ◽  
pp. 251-298 ◽  
Author(s):  
GB Sinclair
Keyword(s):  
Stress Intensity ◽  
Structural Integrity ◽  
Review Article ◽  
Stress Fields ◽  
General Context ◽  
Stress Singularities ◽  
Classical Elasticity ◽  
Linear Elastostatics ◽  
Present Part ◽  
Asymptotic Analyses

This review article has two parts, published in separate issues of this journal, which consider the stress singularities that occur in linear elastostatics. In the present Part I, after a brief review of the singularities that attend concentrated loads, attention is focused on the singularities that occur away from such loading, and primarily on 2D configurations. A number of examples of these singularities are given in the Introduction. For all of these examples, it is absolutely essential that the presence of singularities at least be recognized if the stress fields are to be used in attempts to ensure structural integrity. Given an appreciation of a stress singularity’s occurrence, there are two options open to the stress analyst if the stress analysis is to actually be used. First, to try and improve the modeling so that the singularity is removed and physically sensible stresses result. Second, to try and interpret singularities that persist in a physically meaningful way. Section 2 of the paper reviews avenues available for the removal of stress singularities. At this time, further research is needed to effect the removal of all singularities. Section 3 of the paper reviews possible interpretations of singularities. At this time, interpretations using the singularity coefficient, or stress intensity factor, would appear to be the best available. To implement an approach using stress intensity factors in a general context, two types of companion analysis are usually required: analytical asymptotics to characterize local singular fields; and numerical analysis to capture participation in global configurations. Section 4 of the paper reviews both types of analysis. At this time, methods for both are fairly well developed. Studies in the literature which actually effect asymptotic analyses of specific singular configurations will be considered in Part II of this review article. The present Part I has 182 references.

scholarly journals Dislocations emission and crack extension at the atomistic crack tip in body-centered-cubic metal Mo

1999 ◽  
Vol 14 (10) ◽  
pp. 4035-4043 ◽  
Author(s):  
Qiheng Tang ◽  
Tzuchiang Wang
Keyword(s):  
Crystal Orientation ◽  
Crack Extension ◽  
Crack Tip ◽  
Crack Plane ◽  
Body Centered Cubic ◽  
Dislocation Emission ◽  
Slip Direction ◽  
Loading Modes ◽  
Mode Ii Loading ◽  
Dynamics Method

The behaviors of a crack in body-centered-cubic metal Mo under different loading modes were studied using the molecular dynamics method. Dislocation emission was observed near the crack tip in response to mode II loading with θ = 0° in which θ is the inclination angle of the slip plane with respect to the crack plane, and two full dislocations were observed at the stress level of KII = 1.17 MPa m1/2 without any evidence of crack extension. Within the range of 0° ≤ θ ≤ 45°, crack extension was observed in response to mode I loading, and the effect of crystal orientation on the crack propagation was studied. The crack propagated along the [111] slip direction without any evidence of dislocations emission.

The r−1/2 (ln r) Singularities at Interface Cracks in Monoclinic and Isotropic Bimaterials due to Heat Flow

1993 ◽  
Vol 60 (2) ◽  
pp. 432-437 ◽  
Author(s):  
G. Yan ◽  
T. C. T. Ting
Keyword(s):  
Heat Flow ◽  
Interface Crack ◽  
Simple Form ◽  
Crack Tip ◽  
Higher Order ◽  
Stress Singularities ◽  
Interface Cracks ◽  
Existence Conditions

It is known that the stress singularities at an interface crack tip of bimaterials with the effects of heat flow may have the form r−1/2 (ln r). The existence conditions of the higher order singularitiy r−1/2 (ln r) are studied for monoclinic bimaterials whose plane of symmetry is at x3 = 0. It is shown that the higher order singularity does not exist if the bimaterial is mismatched. If the bimaterial is non-mismatched, the higher order singularity does not exist when a certain condition is satisfied. This condition is given explicitly for monoclinic bimaterials with the plane of symmetry of x3 = 0 and in a simple form for isotropic bimaterials.

Sign in / Sign up

Export Citation Format

Share Document