chap 1 strength

7/25/2019 Chap 1 Strength

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Chap 1:Introduction, Strength,

Processing, structure, properties


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What material should be chosen for a nuclear

pressure vessels to ensure 40 years of safe

operation?

How can an aircraft wing skin be made ligher

without compromising its load bearing

capacity?

Why did a particular power plant generator

shaft break in service?

Introduction


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Need to understand the interplay between:

Material properties

Design choices

=> Path to safe, efficient and effective engineered

structures


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Material properties are determined using a

wide variety of mechanical tests

Variety of specimen shapes and test

conditions

2 mechanical tests:

Control the load and measure the displacement

Control the displacement and measure the load

Mechanical testing


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Which test to use is determined by the

objective of the test

One may wish to evaluate the fundamental

material properties

Compare different type of materials

Use simple, standardized specimen shapes and

simple loading conditions


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a) Cellular phone testing by bending b) Tensile testing for fundamental material properties using a

standardized tensile specimen c) Bend testing using a standardized fracture speciment


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3 basics categories of mechanical response to

an applied load:

Elasticity

Plasticity

Failure

Elasticity: fully recoverable response

No permanent change of the shape or integrity

when loading is removed


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Plasticity and fracture: involve permanent

shape changes under load but their are

distinct

Plasticity: shape change without cracking

Fracture: involves the creation or propagation

of a crack that separates a portion of the

component to the remainder


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Schematic depictions of typical engineering stress-strain curves for (a) Ceramic and glass, (b-d)metals, (e-h)

polymer -

Polymer: 4 distinct curvese: brittle, f: plastic but limited ductility, g: plastic with significant ductility and strengthening, h: elastic (but

nonlinear) to large strains.

Metals: (b-d) different metal or alloys but polymer curves (e-g) could be different polymer or the same polymer

tested under different strain rates or temperature conditions


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Strength of materials

Strength of materials

Relationship between internal forces,deformation and external loads

Assume equilibrium and continuous body with novoids: Identical properties at all points

Most engineering materials:

More than one phase Different mechanical properties

Heterogeneous


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Even single-phase metal exhibit chemical

segregation

Metals are made up of an aggregate of crystal

grains having different properties in different

crystallographic structures


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Isotropic: the mechanical properties does

not vary with direction or orientation

Anisotropic: Property varies with

orientation with respect to some system of

axes

Reasons why the equations of strength ofmaterials describe the behavior of metals

The crystal grains are so small that for

specimen of any macroscopic volume, thematerials are statistically homogenous and

isotropic

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However, when metals are deformed in a

particular direction (example in rolling,

forging), mechanical properties may be

anisotropic on a macro scale

Other examples of anisotropy:

Fiber reinforced composite, single crystal


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Elastic and plastic behavior

Experience shows that all solids materials can

be deformed when subjected to an external

load

At certain limiting loads, a solid will recover its

original dimensions when the load is removed

Elastic behavior

Limiting load beyond which the material no

longer behaves elastically is the elastic limit


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If elastic limit is exceed

Permanent change of shape or deformation when theload is removed

Plastic deformation

For most material, as long as the load does notexceed the elastic limit The deformation is proportional to the load

Known as Hooks law

Stress is proportional to strain

For most metals, there is a narrow range of loadsover which Hookes law strictly applies


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Average stress and strain

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Average Linear strain

Stress Derived from


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In general the stress is not uniform therefore thestress equation represents an average stress

Anisotropy between grains in a polycrystallinemetal rules out the possibility of a completeuniformity of stress over a body of macroscopicsize

Presence of more than one phase gives rise tononuniformity

Nonuniformity occurs if the bar is not straight ,

not centrally loaded, or with the presence ofstress raisers or stress concentration.

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Below the elastic limit, Hooks Law can be

considered valid so that the average stress is

proportional to the average strain:

The constant E is the modulus of elasticity or YoungModulus

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Tensile deformation of ductile metal

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Point A is the elastic limit:

Greatest stress that the metal can withstand withoutexperiencing a permanent strain when the load is removed

Point A is the proportional limit

The stress at which the stress-strain curve deviates fromlinearity.

The yield strength is defined as the stress which willproduce a small amount of permanent deformation,

equal to a strain of 0.002 (OC)

Plastic deformation begins when the limit is exceeded


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Ductile versus Brittle behaviour

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The general behavior of materials can beclassified as:

Ductile

brittle


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Ductile versus Brittle behaviour

Ductility is an important material characteristic

Allows the material to redistribute localized stresses

(at notches or other points of stress concentrations)

With brittle materials, localized stresses continueto build up when there is no local yielding

Cracks will form at one or more points of stress

concentrations and spread rapidly over the section


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Brittleness is not an absolute metal property Tungsten is brittle at room temperature but

ductile at an elevated temp.

A metal which is brittle in tension may be ductile

under hydrostatic compression

A metal which is ductile in tension at RT can

become brittle in the presence of notches, low

temperature, high rates of loading or embrittlingagents (hydrogen)

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Resilience

Resilience: amount of energy per unit volumeThat can be absorbed under elastic loading and

That is completely released when the load is removed.


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Toughness

Toughness is another measure of resistance to

fracture

Measured in units of energy

Brittle material absorbs little energy while a

touch material would require a large

expenditure of energy in the fracture process


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What constitutes failure?

Structural members and machines can failfor perform their intended function in three

general ways:

Excessive elastic deformation Yielding or excessive plastic deformation

Fracture

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Two general types of excessive elastic deformation

Excessive deflection

Sudden deflection or buckling

Yield occurs when the elastic limit of the material

has been exceeded

Permanent change of shape

In a ductile metal, yielding rarely results in fracture

under static loading at RT because the metal strain

hardens as it deforms and an increased stress isrequired to produce further deformation

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Failure by excessive plastic deformation is

controlled by the yield strength of the metal for

a uniaxial loading condition At temperature significantly greater that RT,

metals can continuously deform at constant

stress in a time dependant yielding known asCREEP

Failure criterion under creep conditions is

complicated by: Stress and strain are not proportional

Mechanical properties may change

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Metal fail by fracture in three ways

Sudden Brittle fracture (DTBT)

Fatigue (failure under cyclic loading)

Delayed fracture (stress-rupture in creep or

hydrogen embrittlement at RT)

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All engineering materials show a variabilityin mechanical properties

Mechanical properties can be influenced by

change in heat treatment or fabrication

Provide a margin of safety and protect

again failure from unpredictable cause

Safe stress or Working stress

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Values of the working stress are set by local, federal

and technical agencies (ASME).

For static applications, the working stress of ductilemetals is based on the yield strength and for brittlematerials on the ultimate tensile strength

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Concept of Stress and type of Stress

Stress:

is force per unit area

not uniformly distributed

Surface forces:

Hydrostatic pressure

Body forces encountered in engineering practice

Centrifugal forces due to high speed rotation Thermal stresses due to temperature differential over

the body

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Stress at the point O on plane mmOf body 2


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The total stress can be resolved in:

Normal stress Shear stress

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Normal stress

Shear stress

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Concept of Strain and type of Strain

Linear strain

True strain

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Elastic deformation may result in a change of

any initial angle between 2 lines

Shear strain: angular change

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Example

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Elastic Stress-Strain relationship


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Strain Energy


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ex: hardness vs structure of steel

Properties depend onstructure

ex: structure vs cooling rate of steel

Processing can changestructure

Structure, Processing, & Properties

H

ardness(BHN)

Cooling Rate (C/s)

100

2 00

3 00

4 00

5 00

6 00

0.01 0.1 1 10 100 1000

(d)

30mm(c)

4mm

(b)

30mm

(a)

30mm


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1.

Pick Application Determine required Properties

2.

Properties Identify candidate Material(s)

3.

Material Identify required Processing

Processing: changes structureand overall shapeex: casting, sintering, vapor deposition, doping

forming, joining, annealing.

Material: structure, composition.

The Materials Selection Process

chap 1 strength

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