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.

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

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

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

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

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

Stress Concentrations for Plate with Fillet (cont.)

Stress Concentrations for Plate with Groove

Text Reference: Figure 6.4, page 224

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

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 6.5, page 225

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

Figure 6.5 Stress concentration factor for round bar with fillet. (b) Bending. [Adapted from Collins (1981).]

Stress Concentrations for Bar with Fillet (cont.)

Text Reference: Figure 6.5, page 225

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 6.6, page 226

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

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

Stress Concentrations for Bar with Groove (cont.)

Figure 6.6 Stress concentration factor for round bar with groove. (c) Torsion. [Adapted from Collins (1981).]

Concentración de tensiones: Barra circular con agujero

Figura: Caso de flexión

Concentración de tensiones: Barra circular con agujero

Figura: Caso de Torsión.

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

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

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)].

Material Yield Stress , S y Fracture Toughness , K ciks i Mpa ksi in1 /2 Mpa m1 /2

MetalsAluminum alloy

2024-T35147 325 33 36

Aluminum alloy7075-T651

73 505 26 29

Alloy steel 4340tempered at 260°C

238 1640 45.8 50.0

Alloy steel 4340tempered at 425°C

206 1420 80.0 87.4

Titanium alloyTi-6Al-4V

130 910 40-60 44-66

CeramicsAluminum oxide 2.7-4.8 3.0-5.3Soda-lime glass 0.64-0.73 0.7-0.8Concrete 0.18-1.27 0.2-1.4

PolymersPolymethyl methacrylate 0.9 1.0Polystyrene 0.73-1.0 0.8-1.1

Text Reference: Table 6.1, page 232

Criterios de Fallo estático

Text Reference: Figure 6.9, page 236

-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).

Criterios de Fallo estático

Text Reference: Figure 6.9, page 236

-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).

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

MSST for Biaxial Stress State

Figure 6.10 Graphical representation of maximum-shear-stress theory (MSST) for biaxial stress state (z=0)

Teoría del cortante máximoLa 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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Coulomb(1773)Tresca(1868)

DET for Biaxial Stress State

Figure 6.11 Graphical representation of distortion-energy-theory (DET) for biaxial stress state (z=0)

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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Coulomb(1773)Tresca(1868)

Examen Septiembre 2009

a) 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.

Example 6.6

Figure 6.12 Rear wheel suspension used in Example 6.6.

Text Reference: Figure 6.12, page 238

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) Mohr’s circle representation of stresses.

Text Reference: Figure 6.13, page 240

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) Mohr’s circle representation of stresses.

Text Reference: Figure 6.14, page 241

MNST Theory for Biaxial Stress State

Figure 6.15 Graphical representation of maximum-normal-stress theory (MNST) for biaxial stress state (z=0)

Text Reference: Figure 6.15, page 243

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

Comparison of Failure Theories to Experiments

Figure 6.17: Comparison of experimental results to failure criterion. (a) Brittle fracture. (b) ductile yielding.

Inserted Total Hip Replacement

Figure 6.18 Inserted total hip replacement.

Text Reference: Figure 6.18, page 247

Dimensions of Femoral Implants

Figure 6.19 Dimensions of femoral implants (in inches).

Text Reference: Figure 6.19, page 248

Sections of Implant Analyzed for Static Failure

Text Reference: Figure 6.20, page 248

Figure 6.20 Section of femoral stem analyzed for static failure.