The Nature of Crack Tip Fields in Atomic Scale Models of Aluminum

1990 ◽  
Vol 193 ◽  
Author(s):  
R. G. Hoagland ◽  
M. S. Daw ◽  
S. M. Foiles ◽  
M. I. Baskes
Keyword(s):  
Surface Energy ◽  
Crack Tip ◽  
Atomic Scale ◽  
Dislocation Emission ◽  
Linear Elastic ◽  
Path Independence ◽  
Scale Models ◽  
Sharp Crack ◽  
Good Agreement ◽  
M Integral

ABSTRACTThe stresses, displacement gradients, and Eshelby's F and M integrals are obtained for two crack orientations in an EAM atomic model of aluminum. For a sharp crack, the stresses are shown to agree quite well with the linear elastic prediction, and F is essentially path independent and also in good agreement with the linear elastic prediction. When dislocation emission and blunting ensues, the path independence of F disappears. In addition, for circular contours with origin at the crack tip, the M-integral is linear in contour radius with slope equal to twice the surface energy and zero intercept for a sharp crack, but acquires a nonzero intercept as blunting occurs. The shift in intercept is related to the movement of singularities away from the origin.

Some aspects of forces and fields in atomic models of crack tips

1991 ◽  
Vol 6 (12) ◽  
pp. 2565-2577 ◽  
Author(s):  
R.G. Hoagland ◽  
M.S. Daw ◽  
J.P. Hirth
Keyword(s):  
Crack Tip ◽  
Lattice Parameter ◽  
Crack Model ◽  
Dislocation Emission ◽  
Linear Elastic ◽  
Partial Dislocations ◽  
Atomistic Models ◽  
Crack Tips ◽  
Eam Potential ◽  
Crack Faces

This paper examines the stresses and displacement gradients in atomistic models of cracks based on an EAM potential devised for aluminum. Methods for computing these quantities are described. Results are presented for two models differing in terms of the orientations of the crack relative to the crystal, a [100] (010) orientation that behaves in a brittle fashion and a [111] (110) orientation that emits partial dislocations prior to extending. Both models display lattice trapping. The stresses in the brittle crack model are compared with the linear elastic prediction and found to be in remarkably good agreement to within distances of about one lattice parameter of the crack tip and at the free surface where contributions from sources other than strain energy (e.g., surface tension) influence the results. Similar results are observed for the ductile model until dislocation emission occurs. The largest stresses that develop just prior to crack extension or dislocation emission are used to estimate the ratio of theoretical tensile strength to shear strength in this material. Eshelby's conservation integrals, F and M, are also computed. F is found to be essentially contour independent and in agreement with the linear elastic prediction in both models until dislocation emission occurs, at which point a large screening contribution arises from the emitted partials. The contour size dependence of M reveals some interesting features of the crack tip including a slight wobble of the crack tip inside its potential well with changing applied K and the existence of forces acting to move the crack faces apart as blunting occurs.

A completely meshless analysis of cracks in isotropic functionally graded materials

2009 ◽  
Vol 224 (3) ◽  
pp. 581-590 ◽  
Author(s):  
H Koohkan ◽  
G H Baradaran ◽  
R Vaghefi
Keyword(s):  
Functionally Graded Materials ◽  
Crack Tip ◽  
Functionally Graded ◽  
Least Squares Approximation ◽  
Equilibrium Equations ◽  
Graded Materials ◽  
Linear Elastic ◽  
Support Domain ◽  
A New Technique ◽  
Good Agreement

In the present study, a completely meshless analysis of two-dimensional cracks in non-homogeneous, isotropic, and linear elastic functionally graded materials (FGMs) is developed. The meshless local Petrov—Galerkin method is applied and the equilibrium equations are considered to drive the local symmetric weak formulations. The moving least-squares approximation is used to interpolate the solution variables and the penalty method is applied to impose the essential boundary conditions. Also, a new technique for defining local sub-domain and support domain is proposed. Using the technique, more nodes are considered in the direction of material variation and extra nodes are located near the crack tip of the FGM body to obtain an accurate meshless model. The based functions are also enriched in order to capture singularities around the crack tip. Several numerical examples containing both mode-I and mixed-mode conditions are presented and the results are compared with the available solutions in the literature which shows a good agreement.

Influence of Surface Tension on Mixed-Mode Cracks

2015 ◽  
Vol 07 (05) ◽  
pp. 1550070 ◽  
Author(s):  
Yuan Li ◽  
Gang-Feng Wang
Keyword(s):  
Surface Tension ◽  
Mixed Mode ◽  
Crack Tip ◽  
Critical Stress Intensity Factor ◽  
Stress Fields ◽  
Strengthening Effect ◽  
J Integral ◽  
Mode Ii Crack ◽  
Sharp Crack ◽  
Good Agreement

Surface tension inherently exists on free surface, and its effect becomes quite important at sharp crack tip. In the present paper, we investigate the influence of surface tension on mixed-mode cracks by finite element method. It is found that surface tension significantly alters the stress fields and J-integral around crack tip, depending on the profile of crack tip. Generally, surface tension decreases the J-integral and thus enhances material toughness, especially for sharp crack. Based on the criteria of energy release rate, the critical stress intensity factor (SIF) for brittle materials is also determined. Surface tension yields an enhanced critical SIF for mixed-mode cracks, and more significant strengthening effect is obtained for Mode-I crack than for Mode-II crack. Moreover, an analytical expression is advanced to characterize the influence of surface tension on fracture, which shows a good agreement with numerical calculations.

An atomic model of crack tip deformation in aluminum using an embedded atom potential

1990 ◽  
Vol 5 (2) ◽  
pp. 313-324 ◽  
Author(s):  
R. G. Hoagland ◽  
M. S. Daw ◽  
S. M. Foiles ◽  
M. I. Baskes
Keyword(s):  
Crack Tip ◽  
Atomic Displacement ◽  
Crack Plane ◽  
Dislocation Emission ◽  
Displacement Fields ◽  
Linear Elastic ◽  
Embedded Atom ◽  
Equilibrium Configurations ◽  
Field Dislocation ◽  
Atom Potential

The atomic configuration at the tip of a mode 1 crack in aluminum is modeled by means of molecular dynamics calculations using an embedded atom potential. This potential intrinsically incorporates many-body contributions. This paper is concerned with the characteristics of the atomic displacement fields in comparison to the linear elastic predictions and dislocation emission phenomena. Three crack/crystal orientations are examined in which the crack plane–crack propagation directions are (010)-[100], (10)-[110], and (10)-[111]. The first two models behaved in a brittle fashion as dislocation emission did not occur for reasons associated with the use of periodic boundary conditions parallel to the crack front. For the models which remained atomically sharp, the positions of the atoms near the crack tip in equilibrium configurations are different from the linear elastic predictions but, to first order, retain an r1/2 dependence, with smaller K, and with the origin displaced behind the physical crack tip. This near tip region is also observed to be elastically softer than in the far field. Dislocation emission readily proceeds in the (10)-[111] model by the sequential emission of partials with attendant nonzero uz displacements. The blunting is characterized by the creation of two corner defects that separate as emission occurs and relaxation of the strains in the region initially confronted by the crack tip. Additional features of the results are discussed.

Finite Element Analysis of the Cohesive Zone across a Strength Mismatched Bimetallic Interface

2007 ◽  
Vol 348-349 ◽  
pp. 85-88
Author(s):  
Vijay G. Ukadgaonker ◽  
Sunil Bhat
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cohesive Zone ◽  
Crack Tip ◽  
Element Analysis ◽  
Linear Elastic ◽  
Parent Alloy ◽  
Cohesive Stresses ◽  
Steel Body ◽  
Good Agreement

When a Mode I crack in soft steel body grows and reaches near the perpendicular interface of ultra strong steel body, its cohesive zone penetrates into the interface body which influences the crack tip parameter. The paper presents finite element analysis of the cohesive zone across the interface of such elastically matched but strength mismatched bodies in linear elastic regime. Parent alloy steel (ASTM 4340) body and interface maraging steel (MDN 250) body are considered for analysis. The cohesive zone is modeled in accordance with the Dugdale criterion. J integral is evaluated over the path around the interface to examine the effect of cohesive stresses on the crack tip. The results are compared vis-à-vis those obtained from the theoretical model. The two are in very good agreement with each other.

scholarly journals Constitutive Modeling of the Densification Behavior in Open-Porous Cellular Solids

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2731
Author(s):  
Ameya Rege
Keyword(s):  
Constitutive Model ◽  
Cell Walls ◽  
Compressive Strain ◽  
Pore Collapse ◽  
Compressive Response ◽  
Linear Elastic ◽  
Nonlinear Springs ◽  
Different Types ◽  
Point Of Intersection ◽  
Good Agreement

The macroscopic mechanical behavior of open-porous cellular materials is dictated by the geometric and material properties of their microscopic cell walls. The overall compressive response of such materials is divided into three regimes, namely, the linear elastic, plateau and densification. In this paper, a constitutive model is presented, which captures not only the linear elastic regime and the subsequent pore-collapse, but is also shown to be capable of capturing the hardening upon the densification of the network. Here, the network is considered to be made up of idealized square-shaped cells, whose cell walls undergo bending and buckling under compression. Depending on the choice of damage criterion, viz. elastic buckling or irreversible bending, the cell walls collapse. These collapsed cells are then assumed to behave as nonlinear springs, acting as a foundation to the elastic network of active open cells. To this end, the network is decomposed into an active network and a collapsed one. The compressive strain at the onset of densification is then shown to be quantified by the point of intersection of the two network stress-strain curves. A parameter sensitivity analysis is presented to demonstrate the range of different material characteristics that the model is capable of capturing. The proposed constitutive model is further validated against two different types of nanoporous materials and shows good agreement.

Investigation on Stress and Strain Singularity in LEFM

2006 ◽  
Vol 306-308 ◽  
pp. 31-36
Author(s):  
Zheng Yang ◽  
Wanlin Guo ◽  
Quan Liang Liu
Keyword(s):  
High Stress ◽  
Crack Tip ◽  
Plane Stress State ◽  
Stress And Strain ◽  
Linear Elastic ◽  
Geometrical Nonlinear ◽  
Maximum Crack ◽  
Elastic Fracture ◽  
Plain Strain ◽  
Strain Singularity

Stress and strain singularity at crack-tip is the characteristic of Linear Elastic Fracture Mechanics (LEFM). However, the stress, strain and strain energy at crack-tip may be infinite promoting conflicts with linear elastic hypothesis. It is indicated that the geometrical nonlinear near the crack-tip should not be neglected for linear elastic materials. In fact, the crack-tip blunts under high stress and strain, and the singularity vanishes due to the deformation of crack surface when loading. The stress at crack-tip may still be very high even though the singularity vanishes. The low bound of maximum crack-tip stress is the modulus of elastic in plane stress state, while in plain strain state, it is greater than the modulus of elastic, and will increase with the Poisson’s ratio.

Crack-Path Effect on Material Toughness

1990 ◽  
Vol 57 (1) ◽  
pp. 97-103 ◽  
Author(s):  
Asher A. Rubinstein
Keyword(s):  
Crack Path ◽  
Numerical Procedure ◽  
Crack Tip ◽  
Elastic Solid ◽  
Singular Integral Equations ◽  
Length Change ◽  
Curvilinear Crack ◽  
Linear Elastic ◽  
System Of Cracks ◽  
Remote Stress

The material-toughening mechanism based on the crack-path deflection is studied. This investigation is based on a model which consists of a macrocrack (semi-infinite crack), with a curvilinear segment at the crack tip, situated in a brittle solid. The effect of material toughening is evaluated by comparison of the remote stress field parameters, such as the stress intensity factors (controlled by a loading on a macroscale), to effective values of these parameters acting in the vicinity of a crack tip (microscale). The effects of the curvilinear crack path are separated into three groups: crack-tip direction, crack-tip geometry pattern-shielding, and crack-path length change. These effects are analyzed by investigation of selected curvilinear crack patterns such as a macrocrack with simple crack-tip kink in the form of a circular arc and a macrocrack with a segment at the crack tip in the form of a sinusoidal wave. In conjunction with this investigation, a numerical procedure has been developed for the analysis of curvilinear cracks (or a system of cracks) in a two-dimensional linear elastic solid. The formulation is based on the solution of a system of singular integral equations. This numerical scheme was applied to the cases of finite and semi-infinite cracks.

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.

Influence of the Interface and Residual Stresses on the Apparent Fracture Toughness of Layered Ceramic Composites Based on Alumina-Zirconia

2014 ◽  
Vol 606 ◽  
pp. 209-212
Author(s):  
Luboš Náhlík ◽  
Bohuslav Máša ◽  
Pavel Hutař
Keyword(s):  
Residual Stresses ◽  
Crack Propagation ◽  
Ceramic Composites ◽  
Layered Composites ◽  
Material Interfaces ◽  
Linear Elastic ◽  
Apparent Fracture Toughness ◽  
Elastic Fracture ◽  
Layered Ceramic ◽  
Good Agreement

This paper deals with the fracture behaviour of layered ceramic composite with residual stresses. The main goal is to investigate the effect of residual stresses and material interfaces on crack propagation by more complex 3D finite element models. The crack behaviour was described by analytical procedures based on linear elastic fracture mechanics (LEFM) and generalized LEFM. The influence of laminate composition with residual stresses on critical values for crack propagation through the laminate interfaces was also determined. Good agreement has been found to exist between numerical results and experimental data. The results obtained can be used for a design of new layered composites with improved resistance against crack propagation.

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