Stress concentrations produced by discontinuities in structures such as holes, notches, and fillets will be introduced in this section. The stress concentration factor will be defined. The concept of fracture toughness will also be introduced.

1. Section 7 Stress Concentration Stress concentrations produced by discontinuities in structures such as holes, notches, and fillets will be introduced in this section. The stress concentration factor will be defined. The concept of fracture toughness will also be introduced. © Loughborough University 2010. This work is licensed under a Creative Commons Attribution 2.0 Licence .

4. Stress Concentration Abrupt change Stress “flow lines” crowd together causing high stress concentration in transition zone Smooth change “ Flow lines” more evenly distributed causing lower stress concentration in transition zone Fillet

5. Stress Concentration (Thickness h) P P b d

7. Stress Concentration Chart – Central hole P P d b

8. Stress Concentration Factor Formulae

9. Basic Design Rule – Yield Limited Design If limit load is reached we will get permanent deformation. Note that the holes, notches and fillets are being discussed in a structural sense. In reality we can get holes and notches through surface defects and manufacturing defects. These can become an issue in fatigue related issues. There are several examples of structural failure occurring relating to fatigue. P P b d

10. Example 1: Stress Concentration A stepped flat bar of 6 mm thick has a hole of 18 mm diameter. It has three widths of b 1 =40 mm, b 2 =50 mm and b 3 =36 mm. Stress concentration factors for the left fillet, hole and the right fillet are 1.24, 2.28 and 1.31, respectively. The allowable stress is 41 MPa. What is the permissible load P max ? b 1 d b 2 P P b 3

11. Example 1: Stress Concentration b 1 d b 2 P P b 3

13. Example 2: Stress Concentration A round straight bar with a diameter of d 1 = 20 mm is being compared with a bar of the same diameter, which has an enlarged portion with a diameter of d 2 = 25 mm. The radius of the fillets is 2.5 mm and the associated stress concentration factor is 1.74. Does enlarging the bar in this manner make it stronger? Justify the answer by determining the maximum permissible load P 1 for the straight bar and the maximum permissible load P 2 for the enlarged bar if an allowable tensile stress of the material is 80 MPa. d 1 d 2 P 2 P 2 d 1 P 1 P 1 d 1

14. Example 2: Stress Concentration P 1 P 1 d 1 d 1 d 2 P 2 P 2 d 1

18. Fracture Toughness The term  crops up quite frequently in fast fracture mechanics and is usually given the symbol K. The units of K are MN m -3/2 . It is called the stress intensity factory (!) G c : Toughness – strain energy release rate K c : Fracture toughness – critical stress intensity release factor If K<K c then crack is stable If K=K c then crack will propagate (at speed of sound in material 1 mile s -1 !!) K c is material property To measure K c , (Gc): experimental set up for mode I: (Caution: a is length of edge crack or a is half length of central crack)   a   2a

19. Example: Fracture Toughness A sheet of aluminium alloy has a 4mm central crack through the thickness. If a stress of 200 MPa is reached on the point of fast fracture, determine the fracture toughness of the sheet. If the Young’s Modulus is 70 GPa what is its toughness G C ?

20. Example: Fracture Toughness A sheet of aluminium alloy has a 4mm central crack through the thickness. If a stress of 200 MPa is reached on the point of fast fracture, determine the fracture toughness of the sheet. If the Youngs Modulus is 70 GPa what is its toughness G C ? Solution:

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