STRESS INTENSITY FACTORS

1

• STRESS INTENSITY FACTORS
• FOR COLDWORKED HOLES
• USING THE WEIGHT FUNCTION TECHNIQUE

Pedro M G P Moreira, Paulo F P de
Matos, Silvestre T Pinho, Stefan D Pastrama,
Paulo M S T de Castro IDMEC, Universidade do
Porto, Portugal University Politehnica of
Bucharest, Romania
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• objectives

- determination of the stress intensity factor
in an infinite plate, subjected to a remote
uniform stress and having a cracked cold-worked
hole, using the weight function technique - a
parametric study is carried out for establishing
the variation of the stress intensity factor with
the crack length and initially applied pressure
- different polynomial expressions are used for
the residual stress field, in order to observe
the influence of the polynomial approximation on
the stress intensity factor
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geometry
an infinite plate with a central hole of
diameter D 20 mm, with pressure acting on the
hole surface to create a compressive residual
stress field
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crack lengths
two symmetrical cracks a/R 1.25, 1.3, 1.35,
1.4, 1.45, 1.475, 1.5, 1.55, 1.6
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loading

• residual stress due to cold-work remote uniform
  traction ? 100 MPa
• three values of the internal pressure pi
• - elastic-perfectly plastic material, with
  plastic extension 6.5 (pi 0.65?y)
• - elastic-perfectly plastic material, with
  plastic extension 16.5 (pi 0.75?y)
• - elastic-perfectly plastic material, with
  plastic extension 26.5 (pi 0.85?y)

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the weight function method
a method for calculating K in a cracked
structure, if one already knows KIr(a) stress
intensity factor for a reference loading
case uIr(x,a) half of the crack face
displacement field in the reference case
h(x,a) the weight function independent of the
loading ?(x) crack line stress in the uncracked
structure in the case for which K is calculated
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the coordinate system
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application for cold worked cracked hole
- the reference case is uniform remote loading
for which values of the reference stress
intensity factor can be taken from handbooks -
the reference crack face displacement is
calculated using the approximate expression of
Petroski and Achenbach - ?(x) is determined by
adding the expressions of the residual stress and
the stress due to remote traction
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Petroski Achenbach approximation

• ?0 characteristic stress for the reference
  case (remote stress)
• F(a/L) correction factor in the expression of
  Kir taken from handbooks
• G(a/L) function obtained from the equation of
  self consistency K Kir
• L characteristic dimension L R (hole
  radius)

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determination of G(a/R)
can be obtained from the weight function equation
written for the reference case K KIr in which
G(a/L) is the only unknown
?r(x) reference stress variation on the crack
line, obtained from theory of elasticity
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equations of G(a/L)
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the reference stress intensity factor
reference loading uniform remote stress values
of K from the handbook of Murakami polynomial
interpolation for obtaining the reference K
solution
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the residual stress field
resulting stress for a plastic extension 6.5
(pi 0.75 ?y)
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the residual stress field
hoop stress constant remote stress variable
hole expansion
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the residual stress field
hoop stress constant hole expansion variable
remote stress
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the residual stress field polynomial interpolation
- two different equations for the rising and
decreasing parts of the residual circumferential
stress curve - both equations are in the general
form
- equations are derived separately for each
value of pi - values of the coefficients are
listed in the report
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results for pi 0.65 ?y
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plastically deformed region in the case of
elastic-perfectly plastic material
plast ext 6.5 (pi 0.65 ?y)
plast ext 26.5 (pi 0.85 ?y)
plast ext 16.5 (pi 0.75 ?y)
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results (W.F.T. weight function tech.)
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results for different polynomial residual stress
equations
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conclusions

• - stress intensity factors for an infinite plate
  with a cold worked cracked hole were determined
  using the weight function technique
• - the residual stress due to coldworking,
  superimposed with a uniform tensile stress was
  considered as loading
• - results were compared with those obtained by
  FEM accuracy was excellent except in one case
  (6) where the crack tip was inside the plastic
  zone created by cold work and the FEM results can
  not be considered as reliable
• - different polynomial fits (4th and 12th
  degree) for the residual stress field give
  practically the same value of the stress
  intensity factor.