ch6-EPFM2

ch6-EPFM2 - HRR Integral Recall with I n 1 n +1 EJ % ij = 0...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
HRR Integral Recall with is the integration constant. ( 29 1 1 0 2 0 , n ij n EJ n I r σ θ ασ + = % ( 29 1 0 2 0 , n n ij n EJ n E I r ε + = % n I Recall the material equation, Now the singularity, unlike varies as a function of n and state of stress. 0 0 0 n α = + I K
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
HRR Integral Recall with is the integration constant, as shown in the Figure below. ( 29 1 1 0 2 0 , n ij n EJ n I r σ θ ασ + = % ( 29 1 0 2 0 , n n ij n EJ n E I r ε + = % n I Recall the material equation, Now the singularity, unlike , varies as a function of n and state of stress. 0 0 0 n α = + I K
Background image of page 2
HRR Integral, cont. Angular variation of dimensionless stress for n=3 and n=13.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
HRR Integral, cont. Note the singularity is of the strenth . For the specific case of n=1 (linearly elastic), we have singularity. Note also that the HRR singularity still assumes that the strain is infinitesimal, i.e., , and not the finite strain . Near the tip where the strain is finite, (typically when ), one needs to use the strain measure . ( 29 1 1 1 n r + 1 r ( 29 1 , , 2 ij i j j i u u ε= + ( 29 1 , , , , 2 ij i j j i k i k j E u u u u = + + 0.1 ij ε< E Some consequences of HRR singularity In elastic-plastic materials, the singular field is given by (with n=1 it is LEFM) stress is still infinite at . the crack tip were to be blunt then since it is now a free surface. This is not the case in HRR field. HRR is based on small strain theory and is not thus applicable in a region very close to the crack tip. 1 1 1 1 1 2 n ij n ij J k r J k r σ ε + + = = 0 r = 0 at 0 xx r = =
Background image of page 4
HRR Integral, cont. Large-strain crack tip finite element results of McMeeking and Parks. Blunting causes the stresses to deviate from the HRR solution close to the crack tip.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
HRR Integral, cont. Some additional notes on CTOD and J-integral CTOD is based on Irwin’s formulation Or based on strip yield (Dugdale’s model) 2 1 2 2 1 2 2 4 4 2 I p YS p y I I y YS YS K r r K u K K G u E π σ μ δ π σ = + = = = = 8 ln sec 2 ys ys ys a E G = = CTOD is generally determined by three point bend test.
Background image of page 6
HRR Integral, cont. 0 ( ) with and ij x i ij ij i ij j u J wdy t ds x w dV t n ε σ ε σ Γ = - = = J-Integral Derived for non-linear elastic material and hence is not valid directly for elasto- plastic material during unloading part.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/11/2011 for the course EML 3004c taught by Professor Staff during the Fall '11 term at FSU.

Page1 / 28

ch6-EPFM2 - HRR Integral Recall with I n 1 n +1 EJ % ij = 0...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online