Chapter 6: Failure Prediction for Static Loading

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Chapter 6 Failure Prediction for Static Loading
The concept of failure is central to the design
process, and it is by thinking in terms of
obviating failure that successful designs are
achieved. Henry Petroski, Design Paradigms
Image The Liberty Bell, a classic case of
brittle fracture.
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Axial Load on Plate with Hole
Figure 6.1 Rectangular plate with hole subjected
to axial load. (a) Plate with cross-sectional
plane. (b) Half of plate with stress
distribution.
Text Reference Figure 6.1, page 221
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Stress Concentrations for Plate with Hole
Figure 6.2 Stress concentration factor for
rectangular plate with central hole. (a) Axial
Load. Adapted from Collins (1981).
Text Reference Figure 6.2, page 222
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Stress Concentrations for Plate with Hole (cont.)
Figure 6.2 Stress concentration factor for
rectangular plate with central hole. (b)
Bending. Adapted from Collins (1981).
Text Reference Figure 6.2, page 222
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Stress Concentrations for Plate with Fillet
Figure 6.3 Stress concentration factor for
rectangular plate with fillet. (a) Axial Load.
Adapted from Collins (1981).
Text Reference Figure 6.3, page 223
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Stress Concentrations for Plate with Fillet
(cont.)
Figure 6.3 Stress concentration factor for
rectangular plate with fillet. (b) Bending Load.
Adapted from Collins (1981).
Text Reference Figure 6.3, page 223
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Stress Concentrations for Plate with Groove
Figure 6.4 Stress concentration factor for
rectangular plate with groove. (a) Axial Load.
Adapted from Collins (1981).
Text Reference Figure 6.4, page 224
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Stress Concentrations for Plate with Groove
(cont.)
Figure 6.4 Stress concentration factor for
rectangular plate with groove. (b) Bending.
Adapted from Collins (1981).
Text Reference Figure 6.4, page 224
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Stress Concentrations for Bar with Fillet
Figure 6.5 Stress concentration factor for round
bar with fillet. (a) Axial load. Adapted from
Collins (1981).
Text Reference Figure 6.5, page 225
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Stress Concentrations for Bar with Fillet (cont.)
Figure 6.5 Stress concentration factor for round
bar with fillet. (b) Bending. Adapted from
Collins (1981).
Text Reference Figure 6.5, page 225
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Stress Concentrations for Bar with Fillet (cont.)
Figure 6.5 Stress concentration factor for round
bar with fillet. (c) Torsion. Adapted from
Collins (1981).
Text Reference Figure 6.5, page 225
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Stress Concentrations for Bar with Groove
Figure 6.6 Stress concentration factor for round
bar with groove. (a) Axial load. Adapted from
Collins (1981).
Text Reference Figure 6.6, page 226
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Stress Concentrations for Bar with Groove (cont.)
Figure 6.6 Stress concentration factor for round
bar with groove. (b) Bending. Adapted from
Collins (1981).
Text Reference Figure 6.6, page 226
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Stress Concentrations for Bar with Groove (cont.)
Figure 6.6 Stress concentration factor for round
bar with groove. (c) Torsion. Adapted from
Collins (1981).
Text Reference Figure 6.6, page 226
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Concentración de tensiones Barra circular
con agujero
Figura Caso de flexión
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Concentración de tensiones Barra circular
con agujero
Figura Caso de Torsión.
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Stress Contours in Bar
Figure 6.7 Bar with fillet axially loaded
showing stress contours through a flat plate for
(a) square corners, (b) rounded corners (c) small
groove, and (d) small holes.
Text Reference Figure 6.7, page 229
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Modes of Crack Displacement
Figure 6.8 Three modes of crack displacement.
(a) Mode I, opening (b) mode II, sliding (c)
mode III, tearing.
Text Reference Figure 6.8, page 231
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Tenacidad a la fractura
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Yield Stress and Fracture Toughness Data
Table 6.1 Yield stress and fracture toughness
data for selected engineering materials at room
temperature From ASM International (1989).
Text Reference Table 6.1, page 232
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Criterios de Fallo estático

• Teoría del esfuerzo normal máximo.
• Teoría de la deformación normal máxima.
• Teoría de la energía de deformación total.
• Teoría de la energía de distorsión(Von
  Mises-Hencky).
• Teoría del esfuerzo cortante máximo(Tresca).

Text Reference Figure 6.9, page 236
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Criterios de Fallo estático

• Teoría del esfuerzo normal máximo.
• Teoría de la deformación normal máxima.
• Teoría de la energía de deformación total.
• Teoría de la energía de distorsión(Von
  Mises-Hencky).
• Teoría del esfuerzo cortante máximo(Tresca).

Text Reference Figure 6.9, page 236
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Three Dimensional Yield Locus
Figure 6.9 Three dimensional yield locus for
MSST and DET. Adapted from Popov (1968).
Text Reference Figure 6.9, page 236
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MSST for Biaxial Stress State
Coulomb(1773) Tresca(1868)
Figure 6.10 Graphical representation of
maximum-shear-stress theory (MSST) for biaxial
stress state (?z0)
Teoría del cortante máximo La falla ocurre cuando
el esfuerzo cortante máximo en una pieza excede
el esfuerzo cortante en una probeta a tensión en
el punto de fluencia (la mitad del límite de
fluencia elástico a tensión).
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DET for Biaxial Stress State
Coulomb(1773) Tresca(1868)
Figure 6.11 Graphical representation of
distortion-energy-theory (DET) for biaxial stress
state (?z0)
Esfuerzo efectivo de Von Mises. Se define como
aquel esfuerzo a tensión uniaxial que generaría
la misma energía de distorsión que la que se
produciría por la combinación real de los
esfuerzos aplicados.
Cortante puro (torsión pura)
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Examen Septiembre 2009

• Que carga estática es capaz de transmitir la
  llave de la figura con un n 1,7.
• b) que sucedería si la carga fluctua entre un
  30-90 de la carga de diseño.
• Datos AISI 1080(380-615) Fiabilidad 90 a T
  50ºC.

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Example 6.6
Figure 6.12 Rear wheel suspension used in
Example 6.6.
Text Reference Figure 6.12, page 238
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Example 6.7
Figure 6.13 Cantilevered, round bar with torsion
applied to free end (used in Example 6.7). (a)
Bar with coordinates and load (b) stresses
acting on element (c) Mohrs circle
representation of stresses.
Text Reference Figure 6.13, page 240
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Example 6.8
Figure 6.14 Cantilevered, round bar with torsion
and transfer force applied to free end (used in
Example 6.8). (a) Bar with coordinates and loads
(b) stresses acting on top of bar and at wall
(c) Mohrs circle representation of stresses.
Text Reference Figure 6.14, page 241
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MNST Theory for Biaxial Stress State
Figure 6.15 Graphical representation of
maximum-normal-stress theory (MNST) for biaxial
stress state (?z0)
Text Reference Figure 6.15, page 243
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Internal Friction and Modified Mohr Theory
Figure 6.16 Internal friction theory and
modified Mohr theory for failure prediction of
brittle materials.
Text Reference Figure 6.16, page 244
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Comparison of Failure Theories to Experiments
Figure 6.17 Comparison of experimental results
to failure criterion. (a) Brittle fracture. (b)
ductile yielding.
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Inserted Total Hip Replacement
Figure 6.18 Inserted total hip replacement.
Text Reference Figure 6.18, page 247
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Dimensions of Femoral Implants
Figure 6.19 Dimensions of femoral implants (in
inches).
Text Reference Figure 6.19, page 248
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Sections of Implant Analyzed for Static Failure
Figure 6.20 Section of femoral stem analyzed for
static failure.
Text Reference Figure 6.20, page 248