Chapter 9 mechanical failure
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CHAPTER 9: MECHANICAL FAILURE. ISSUES TO ADDRESS. • How do flaws in a material initiate failure?. • How is fracture resistance quantified; how do different material classes compare?. • How do we estimate the stress to fracture?.

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CHAPTER 9: MECHANICAL FAILURE

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Chapter 9 mechanical failure

CHAPTER 9:MECHANICAL FAILURE

ISSUES TO ADDRESS...

• How do flaws in a material initiate failure?

• How is fracture resistance quantified; how do different

material classes compare?

• How do we estimate the stress to fracture?

• How do loading rate, loading history, and temperature

affect the failure stress?

Computer chip-cyclic

thermal loading.

Hip implant-cyclic

loading from walking.

Ship-cyclic loading

from waves.

1


Ex failure of a pipe

EX: FAILURE OF A PIPE

• Ductile failure:

--one piece

--large deformation

• Brittle failure:

--many pieces

--small deformation

3


Moderately ductile failure

MODERATELY DUCTILE FAILURE

• Evolution to failure:

50 mm

50 mm

• Resulting

fracture

surfaces

(steel)

100 mm

particles

serve as void

nucleation

sites.

4


Brittle fracture surfaces

BRITTLE FRACTURE SURFACES

• Intragranular

(within grains)

• Intergranular

(between grains)

304 S. Steel (metal)

316 S. Steel (metal)

160mm

4 mm

Polypropylene

(polymer)

Al Oxide

(ceramic)

3mm

1 mm

5


Ideal vs real materials

IDEAL VS REAL MATERIALS

TS << TS

engineering

materials

perfect

materials

• Stress-strain behavior (Room T):

• DaVinci (500 yrs ago!) observed...

--the longer the wire, the

smaller the load to fail it.

• Reasons:

--flaws cause premature failure.

--Larger samples are more flawed!

6


Flaws are stress concentrators

FLAWS ARE STRESS CONCENTRATORS!

• Elliptical hole in

a plate:

• Stress distrib. in front of a hole:

• Stress conc. factor:

• Large Kt promotes failure:

7


Engineering fracture design

ENGINEERING FRACTURE DESIGN

• Avoid sharp corners!

8


When does a crack propagate

WHEN DOES A CRACK PROPAGATE?

• rt at a crack

tip is very

small!

• Result: crack tip

stress is very large.

• Crack propagates when:

the tip stress is large

enough to make:

K ≥ Kc

9


Geometry load material

GEOMETRY, LOAD, & MATERIAL

• Condition for crack propagation:

K ≥ Kc

Stress Intensity Factor:

--Depends on load &

geometry.

Fracture Toughness:

--Depends on the material,

temperature, environment, &

rate of loading.

• Values of K for some standard loads & geometries:

10


Fracture toughness

FRACTURE TOUGHNESS

increasing

Based on data in Table B5,

Callister 6e.

Composite reinforcement geometry is: f = fibers; sf = short fibers; w = whiskers; p = particles. Addition data as noted (vol. fraction of reinforcement):

1. (55vol%) ASM Handbook, Vol. 21, ASM Int., Materials Park, OH (2001) p. 606.

2. (55 vol%) Courtesy J. Cornie, MMC, Inc., Waltham, MA.

3. (30 vol%) P.F. Becher et al., Fracture Mechanics of Ceramics, Vol. 7, Plenum Press (1986). pp. 61-73.

4. Courtesy CoorsTek, Golden, CO.

5. (30 vol%) S.T. Buljan et al., "Development of Ceramic Matrix Composites for Application in Technology for Advanced Engines Program", ORNL/Sub/85-22011/2, ORNL, 1992.

6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci. Proc., Vol. 7 (1986) pp. 978-82.

11


Design against crack growth

DESIGN AGAINST CRACK GROWTH

K ≥ Kc

• Crack growth condition:

• Largest, most stressed cracks grow first!

--Result 2: Design stress

dictates max. flaw size.

--Result 1: Max flaw size

dictates design stress.

12


Design ex aircraft wing

DESIGN EX: AIRCRAFT WING

• Material has Kc = 26 MPa-m0.5

• Two designs to consider...

Design B

--use same material

--largest flaw is 4 mm

--failure stress = ?

Design A

--largest flaw is 9 mm

--failure stress = 112 MPa

• Use...

• Key point: Y and Kc are the same in both designs.

--Result:

112 MPa

9 mm

4 mm

Answer:

• Reducing flaw size pays off!

13


Loading rate

LOADING RATE

• Increased loading rate...

--increases sy and TS

--decreases %EL

• Why? An increased rate

gives less time for disl. to

move past obstacles.

• Impact loading:

--severe testing case

--more brittle

--smaller toughness

14


Temperature

TEMPERATURE

• Increasing temperature...

--increases %EL and Kc

• Ductile-to-brittle transition temperature (DBTT)...

15


Design strategy stay above the dbtt

DESIGN STRATEGY:STAY ABOVE THE DBTT!

• Pre-WWII: The Titanic

• WWII: Liberty ships

• Problem: Used a type of steel with a DBTT ~ Room temp.

16


Summary

SUMMARY

• Engineering materials don't reach theoretical strength.

• Flaws produce stress concentrations that cause

premature failure.

• Sharp corners produce large stress concentrations

and premature failure.

• Failure type depends on T and stress:

-for noncyclic s and T < 0.4Tm, failure stress decreases with:

increased maximum flaw size,

decreased T,

increased rate of loading.

-for cyclic s:

cycles to fail decreases as Ds increases.

-for higher T (T > 0.4Tm):

time to fail decreases as s or T increases.

26


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