Fracture, Toughness and Strength by Gordon Williams

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

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

Fig 1 W 2a2a  H b

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

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

Compliance Method (Composites) F dd  F+dF F o C C( a +d a ) b F ada 

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)

Compliance: Hence Energy release rate Compliance Method (Composites)

Energy form:

Used in impact For DCB F a  b hh

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

Compliance Method From Griffith Solution in General

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

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

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

z rbrb b Plane stress Plane strain bcbc KcKc

Plasticity and Size Effects For b >> r   z  plane strain For b ≈ r   z =0, plane stress Transition: b<b c high value