Chapter 6: Failure Prediction for Static Loading

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1 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.

2 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

3 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

4 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

5 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

6 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

7 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

8 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

9 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

10 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

11 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

12 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

13 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

14 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

15 Concentración de tensiones: Barra circular con agujero
Figura: Caso de flexión

16 Concentración de tensiones: Barra circular con agujero
Figura: Caso de Torsión.

17 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

18 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

19 Tenacidad a la fractura

20 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

21 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

22 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

23 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

24 MSST for Biaxial Stress State
Coulomb(1773) Tresca(1868) Figure Graphical representation of maximum-shear-stress theory (MSST) for biaxial stress state (z=0) 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).

25 DET for Biaxial Stress State
Coulomb(1773) Tresca(1868) Figure 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)

26 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( ) Fiabilidad 90% a T= 50ºC.

27 Example 6.6 Figure 6.12 Rear wheel suspension used in Example 6.6.
Text Reference: Figure 6.12, page 238

28 Example 6.7 Figure 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

29 Example 6.8 Figure 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

30 MNST Theory for Biaxial Stress State
Figure Graphical representation of maximum-normal-stress theory (MNST) for biaxial stress state (z=0) Text Reference: Figure 6.15, page 243

31 Internal Friction and Modified Mohr Theory
Figure Internal friction theory and modified Mohr theory for failure prediction of brittle materials. Text Reference: Figure 6.16, page 244

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

33 Inserted Total Hip Replacement
Figure Inserted total hip replacement. Text Reference: Figure 6.18, page 247

34 Dimensions of Femoral Implants
Figure Dimensions of femoral implants (in inches). Text Reference: Figure 6.19, page 248

35 Sections of Implant Analyzed for Static Failure
Figure Section of femoral stem analyzed for static failure. Text Reference: Figure 6.20, page 248