fracture mechanics ppt
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Computational Fracture Mechanics
COMPUTATIONAL FRACTURE MECHANICS:
Overview:
Computers have had an enormous influence in virtually all branches
of engineering, and fracture mechanics is no exception.
Finite element modeling has become an indispensable step in
computational fracture mechanic problems since few cracked body
Problems! have closed form analytical solutions. (K, G, J, CTOD)
Stress Intensity Factor solutions for literally hundreds of cracked
body problems have been compiled, the majority of which were
inferred from Finite Element Analysis. Elastic-Plastic FEA to
compute the the J-integral and Crack Tip Opening
Displacement(CTOD) are also quite common.
Researches are developing Advanced Numerical Techniques to
special problems; such as fracture at interfaces, dynamic fracture
ductile crack growth,etc.
Rapid advances in computer hardware technology are primarily
responsible for exponential growth in Application of Computational
Fracture Mechanics.
Commercial FEM systems are highly user friendly and have
incorporated Computational Fracture Mechanics capabilities.
example:ANSYS with K-CAL command.
Experimental stress analysis methods such as photo elasticity, Moire
Interferrometry and Caustics are available, but even these techniques
require a numerical analysis to interpret experimental measurements/
observations.
A variety of numerical methods have been applied to problems in Solid
Mechanics including the FDM, FEM, and BEM. In recent years, the
FEM has been applied almost exclusively for the analysis for cracked
body problems. However, a number of special techniques are necessary
to compute fracture mechanics parameters (K, J, G, CTOD) from the
results of FEA (nodal displacements/element stresses).
Accurate SIF solutions for through cracks in plates and shells can be
obtained from Finite Element Analysis only.
Early researchers in CFM attempted to introduce “special finite
elements” at the crack tip that exhibit the 1/ singularity.
• Tracey,D.M. Finite elements for determination of crack tip
stress intensity factors, Engineering Fracture Mechanics,
vol.3,1971, pp.255-266
r
Barsoum later achieved the same effect by using doubly distorted
Quadratic Isoparametric element.This approach is now universal for FE
modeling of cracked solid /structures, since commercial FEM system
can be directly used.
Barsoum,R.S. On the use of isoparametric finite elements in LEFM, IJNME,
vol.10,1976.pp25-37.
However, there is real need to develop and add post processing programs to compute
the SIF’s / Energy released rates / J / CTOD / using standard output
from a FEA program.
More recent formulations of J computation apply an area integration for
2D problems and volume integration for 3D problems.This approach
provide much better accuracy than contour and surface integrals and
also much easier to implement in the post processor of FEA programs.
J-evaluation by the virtue crack extension(VCE) technique is an
example.
For crack problems, the design of a finite element mesh is as much
an art form as it is a science.Many commercial FEA codes have
automatic mesh generation modification commands. However,
realization of an appropriate FE mesh invariably requires some
human intervention. In particular, require a certain amount of
judgment on the part of the analyst.
8 noded quadrilateral 2D elements and 20 noded hexahedral 3D
elements are widely used in FE Modeling of cracked bodies. At the
cracktip, the quadrilateral elements are degenerated to triangular
elements.Note that the three nodes at the crack tip occupy the same
point in space.
In LEFM, the 3 nodes at the crack tip normally tied and mid nodes
moved to quarter point locations.such modifications results in a 1/
strain singularity within the element.Use of such singular elements
enhance accuracy of computed SIF’s / ERR’s.
When a plastic zone forms, the 1/ strain singularity is no longer valid at
the crack tip.Consequently use of elastic singular elements is not
appropriate for EPFM.Figure 11.15(b) shows a special element that
exhibits the desired strain singularity under fully plastic conditions.
The element is degenerated to a triangle shape as before, but the crack
tip nodes are untied and the location of mid-side nodes unchanged.This
element produces a 1/ r strain singularity, which corresponds to the crack
tip strain field for fully plastic, non-hardening materials.
r
r
(a) Elastic singularity element (b) Plastic singularity element
Fig.11.15. Crack tip elements for elastic and elastic-plastic analysis
Element (a) produces a 1/√r strain singularity, while (b) exhibits
a 1/r strain singularity
Fig.11.13. Degeneration of quadrilateral element in to a triangle at the crack tip
Fig11.14 Degeneration of a brick element in to wedge
One side benefit of the use of plastic singularity elements is that it
allows the Crack Tip Opening Displacement (CTOD) to be
computed from the deformed mesh as fig 11.16 illustrates.The
CTOD can be inferred from the deformed crack profile by means
of 90º intercept mesh.
Fig. 11.16. Deformed shape of plastic singularity elements ( fig. 11.15(b))
The crack tip elements model blunting and it is possible to measure CTOD
The most efficient mesh design for the crack tip region has proven
to be “spider web” configuration, which consist of concentric rings
of quadrilateral elements that are focused towards the crack tip.The
innermost ring are degenerated to triangular elements.Since the
crack tip region features steep stress and strain gradients, the mesh
refinement should be greatest at the crack tip.The “spider web”
design facilitates a smooth transition from a fine mesh at the crack
tip region to coarser mesh remote to the crack tip. Fig 11.17 shows
a half-symmetry FE Model of a single edge cracked panel.
Fig. 11.17. Half-symmetry model of a cracked panel
COMPUTATIONAL FRACTURE MECHANICS:
Benchmark for Mixed Mode Membrane Stress Intensity Factor Evaluation
Central circular arc crack in a rectangular panel:
Target SIF solution:
KI/σ0 , KII/σ0 α (0<α<90)
FE Modeling: Using singular and regular isoparametric elements
(STRIA6,QUAD8)
SIF evaluation : using K-VALUES a post processing subprogram
Convergence study: Model #1 NS=36, =a/100
Model #2 NS=72, =a/100
Results:
1)crack tip stress field
2)crack tip SIF’s
3)crack tip plastic zone(shape and size)
a a
aa
Vs
COMPUTATIONAL FRACTURE MECHANICS:
Limitations
FE Modeling of a cracked body can compute the crack tip FM
parameters. But this alone cannot predict when fracture will occur.
To predict fracture,we need a validated fracture criterion and
associated material property data (Fracture Toughness, etc.,.)
FEA relies on continuum mechanics which cannot model voids, micro
cracks, second phase particles, grain boundaries, dislocations, or any
other microscopic or submicroscopic features that in reality control the
fracture behavior of engineering materials.
Fracture process by itself can be modeled, but a separate
FRACTURE CRITERION is required. For example, one might
model cleavage fracture by using a stress based fracture criterion
in which FEA would predict fracture when user specified stress is
reached at a specified point ahead of crack tip.
FEA will undoubtedly play a major role in developing
micro mechanical models for fracture. Numerical simulation of
processes such as micro-crack nucleation,void growth, and
interface fracture should lead to new insights into fracture /damage
mechanisms. Such research may then lead to rational fracture
criteria that can be incorporated into global continuum models of
cracked bodies.