Chapter 7

How do we measure mechanical responses of brittle materials

Bend testing

Why is stress at fracture lower than tensile strength?

Necking - the material no longer has the initial cross-sectional area

Yield Stress

The stress at which a material begins to deform plastically, and where the graph deviates from linear elastic regime (aka yield strength) Where we measure strength of a material

Torsion

Twisting in a plane Related to shear - kind of gradient shear in a circular, twisting pattern

What is the Poisson ratio of most materials and what does it imply

0.25 < v < 0.35 (particularly metals) Implies that most materials are not isotropic and do not conserve volume

Poisson ratio in isotropic material

0.25 because response is same in every direction Positive ratio means x,y shrinks when z increases

Poisson ratio when volume is conserved in a material

0.5 (maximum possible value)

How do you describe the load on a material?

1) Stress on the material 2) Orientation of the load Ex. for uniaxial tension is a load perpendicular to a plane

What factors influence how we observe polymers?

1. Water is small enough to fit inside (between chains) of most polymer materials which changes mechanical behavior 2. Arrangement of chains matters! (amorphous vs crystalline)

Shear loading

A load parallel to a plane Load is in the surface and opposite force is applied on opposite side of material in order to maintain mechanical equilibrium

Rockwell Hardness

A method of determining hardness of a metal by applying pressure on the surface of metal being tested. A small diamond pyramid or tungsten ball is forced against the surface (10 kg load usually) for minor load, then a major load applied for a fixed time at fixed rate (60, 100, 150kg). The hardness value number is the depth of penetration

3 classes of polymer mechanical responses

A-Brittle polymer (no evidence of any kind of yield, just a linear elastic region and then fracture) B-Elastomer polymer* (most common and most characteristic stress strain curve, traditional linear elastic regime, then plastic deformation before fracture) C-Elastomer polymer (linear elastic regime dominates)

Ductile

Allows a lot of plastic deformation before fracture

ASTM

American Society Testing and Materials - Lays out how to describe and measure mechanical properties

What happens to the chains in polymers during necking?

Amorphous chains untangle and align with each other to form new crystalline regions, allowing the material to elongate

Viscous (flow)

Anelastic (time-dependent) plastic deformation

Situations where plastic deformation does not occur

Brittle material, ceramics, covalent bonds (due to directionality), ionic bonds (looking for cations or anions specifically)

Glassy

Brittle/stiff - expect cross-linked or networked polymers For non-polymers, this implies non crystalline

Brittle polymer makeup

Crosslinked/networked - covalent bonds start to stretch a little then the whole thing comes apart

What is the shape/cut of material used for tensile testing called?

Dog-bone

0.2% Strain offset method

Draw a line parallel to linear elastic regime from 0.2% strain and point it intersects on stress strain curve is yield Used for finding yield stress for a gradual transition from elastic to plastic deformation

Materials Properties

E - Elastic modulus v - Poisson ratio G - shear modulus All specific to unique materials and for linear elastic response should stay the same so long as composition stays the same, ie., processing doesn't matter

Hardness testing benefits

Fast, cheap, easy, non-destructive since load and response is localized

Relaxation modulus

For viscoelastic polymers, the time-dependent modulus of elasticity. It is determined from stress relaxation measurements as the ratio of stress (taken at some time after the load application—normally 10 s) to strain Measuring how material responds to strain over time

How is plastic deformation temperature dependent?

Higher temperature makes plastic deformation easier

Poisson Effect

If length of a material increases when stretched, cross-sectional area should decrease

Fracture toughness

Integral from 0 to strain at fracture of sigma d epsilon How much energy a material can absorb before it breaks

Tensile testing

It determines the failure of ductile materials in tension or compression below the elastic limit

Shear Modulus

Linear elastic limit for shear stress where shear stress (tao) is equal to shear modulus (G) times shear strain (gamma) The ratio of shear stress to strain

Rubbery

Lots of elastic or plastic deformation

Brittle

Material that has no plastic deformation meaning that fracture toughness is low

Isotropic material

Material that has the same response/properties in all directions

Tensile strength

Maximum stress that can be applied to a material (maximum on plastic deformation curve) Inevitably leads to fracture

Stress for flexural loading

Mc/I where Mc is the bending moment, c is distance from center of specimen, and I is moment of inertia of cross-section

What kind of deformation of the dog bone happens beyond ultimate tensile strength?

Necking

What is the scale of hardness

No absolute scale, just saying "something is harder than something else Mohs scale: talc is 1 (softest) to diamond as 10 (hardest)

Elastomer polymer makeup

No/few crosslinks, amorphous, giving lots of room to move around and recover

Engineering Strain

Normalized deformation (change in size/shape) Epsilon = delta(l)/l_0 l_0 = initial length Only for tensile loading

Engineering Stress

Normalized load (sigma = F/A_0) A_0 = initial cross-sectional area Can be applied to tensile or shear load

What is the elastic modulus?

Numerical value characterizing response to a load in the elastic limit Elastic response (initial linear response) of a material to applied stress/strain Slope of stress/strain curve

Why do we not measure strength of a material by its tensile strength?

Once a material reaches tensile strength, enough plastic deformation has occurred that fracture is inevitable and the material is useless for its purpose

Uniaxial compression

Opposite of uniaxial tension - pushing material together along one axis

What factors change polymer mechanical properties?

Past processing and current conditions

Fracture

Physical separation of a part

Why are polymers/soft materials so hard to test?

Range of bond types: secondary (van der Waals) bonds between chains, primary bonds (cross links) sometimes between chains, and primary bonds (covalent bonds!) along C-chain

Poisson Ratio

Reaction perpendicular to applied load

Hardness

Resistance to localized deformation (scratching, gouging)

Viscoelastic creep

Resistance to stress and strain as a function of time but now applied a fixed load (stress) and watch material stretch out Most commonly observed in metals but also present in polymers

Mechanical properties

Response of materials to applied loads Depends on both details of load and details about material

Plastic polymer makeup

Semicrystalline/crystallizable with some cross links

In what orientations does tensile load resolve into within uniaxial tension?

Shear and tensile load components (sigma prime and tao prime), one parallel and one perpendicular to the plane

Load displacement curve

Similar to stress strain curve but length continues to increase as force is applied until fracture True stress looks the same since it is over instantaneous area and the ratio keeps increasing

Viscoelasticity

Simplest form of anelasticity, time-dependent elastic response When anelasticity is significant in a material (Think a ball of taffy slowly spreading out on a counter)

Uniaxial tension

Simplest load - tension applied along one axes (pulling material apart)

What is the response of material to a load?

Simplest response: elastic deformation (bonds stretching, where stress is equal to Young's Modulus times Hooke's Law of linear elasticity) Slope of stress strain graph is young's modulus

How to determine Young's Modulus given a stress/strain graph with a linear elastic response

Slope of the stress strain graph

Percent Elongation (%EL)

Strain at specific points

Fracture stress

Stress at fracture Usually lower than tensile strength At end of stress strain curve

How is stress and strain graphed?

Stress is dependent variable (y axis) and strain is independent variable (x axis)

Resilience

Stress times strain - area under the curve of linear elastic regime Integral from 0 to strain at yield of sigma d epsilon If force is below resilience, it won't get to yielding

Yield Point Phenomenon

Sudden onset of plastic deformation in some crazy metals - creates an upper and lower yield point Yield stress is measured at lower yield point (average value)

How to determine Young's Modulus given a stress/strain graph with a nonlinear elastic response

Take local slopes - either the slope of the secant or tangent line

Formula given for shear stress

Tao = F/A_0 Same formula as tensile stress, but clearer because of different symbols

What represents yield on a polymer stress/strain curve

The highest point on the curve

Poisson's Ratio

The negative ratio of lateral strain to the corresponding longitudinal strain in an elastic body under longitudinal stress (nu = -stress in x or y/ stress in z)

Why aren't brittle materials tensile tested?

They are hard to form into tensile specimens, hard to grip, and hard to measure strain

Anelasticity/viscoelasticity

Time dependent response to elastic deformation

Anelasticity

Time-dependent elastic (nonpermanent) deformation Most often observed in polymers and ignored in metals

Leathery

Tough but plastic deformation possible, less cross-links or higher temperature

Why is tensile testing not performed on a material of uniform thickness?`

When the cross-sectional area is the same everywhere, you can't predict where it will break because the stress is the same throughout the material. The thin part of the dog bone where A is a minimum maximizes the stress in that area, assuring most stress can be measured