Download presentation

Presentation is loading. Please wait.

Published byHaley Edgerton Modified about 1 year ago

1
Fracture, Toughness and Strength by Gordon Williams

2
Introduction Strength is not a material property For ductile materials we have flow and necking For brittle materials we have failure from flaws Surface polishing, a transition from brittle to ductile Griffith ideas

3
Griffith(1922) All bodies contain flaws Fracture is from these flaws Used “Energy Release Rate” (see later) Defined as “G” G>G c, energy per unit of created surface area (J/m^2) G c is a basic material property

4
Fig 1 W 2a2a H b

5
Griffith at fracture In general, Y 2 is a geometric factor, Y 2 = for an infinite plate To find G c vary a, measure , calculate Y 2 hence EG c From E find G c

6
Griffith From E find G c If only stresses needed use K c G c preferred, better physics The strength problem “ a ” exists, flaws, hence is determined

7
Compliance Method (Composites) F dd F+dF F o C C( a +d a ) b F ada

8
Initial Energy: Work done on a a+da, Final Energy: Change in energy=U 1 +U 2 -U 3 (Shaded area) ie Compliance Method (Composites)

9
Compliance: Hence Energy release rate Compliance Method (Composites)

10
Energy form:

11
Used in impact For DCB F a b hh

12
Experimental Method i)Measure C( a ) ii)Measure F at fracture G c iii)True for any form

13
Compliance Method From Griffith Solution in General

14
Plasticity and Size Effects Basic method is elastic (LEFM) All cracks have a local plastic/damage zone Let c be the zone stress rr a r xx

15
Plasticity and Size Effects Local stresses,(singular) » (const., 2 can change) r makes response non-linear, Must be within limits, e.g F 5%, F max

16
G c & K c are dependent on Constraint Lowest values are for Plane strain, z =0 in the plastic zone, i.e. lateral constraint. Highest values are for Plane stress, z =0 Plasticity and Size Effects

17
z rbrb b Plane stress Plane strain bcbc KcKc

18
Plasticity and Size Effects For b >> r z plane strain For b ≈ r z =0, plane stress Transition: b**
**

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google