Chapter 6: Failure Prediction for Static Loading

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. 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

16. 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

17. 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

18. 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

19. MSST for Biaxial Stress State Figure 6.10 Graphical representation of maximum-shear-stress theory (MSST) for biaxial stress state (z=0) Text Reference: Figure 6.10, page 237

20. DET for Biaxial Stress State Figure 6.11 Graphical representation of distortion-energy-theory (DET) for biaxial stress state (z=0) Text Reference: Figure 6.11, page 238

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

22. 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

23. 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

24. 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

25. 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

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

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

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

29. 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