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Mechanical Properties Chapter 4. Professor Joe Greene CSU, CHICO. MFGT 041. Chapter 4 Objectives. Objectives Mechanical properties in solids (types of forces, elastic behavior and definitions) Mechanical properties of liquids_ viscous flow (viscous behavior and definitions)

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Mechanical properties chapter 4 l.jpg
Mechanical PropertiesChapter 4

Professor Joe Greene


MFGT 041

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Chapter 4 Objectives

  • Objectives

    • Mechanical properties in solids (types of forces, elastic behavior and definitions)

    • Mechanical properties of liquids_ viscous flow (viscous behavior and definitions)

    • Viscoelastic materials (viscoelastic behavior and definitions, time dependent)

    • Plastic stress-strain behavior (plastic behavior and definitions, interpretation and mechanical model of plastic behavior)

    • Creep and Toughness

    • Reinforcements and Fillers

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Viscoelastic Materials

  • Polymers are Viscoelastic materials that exhibit

    • liquid (viscous) or

    • solid (elastic) properties

    • Depending upon the time scale of the event;

      • Short time (fast) event will act like a solid;

      • Long time (slow) event will act like a liquid.

    • Depending upon the temperature of the event

      • Example, Silly Putty

        • Roll into a ball and drop it to the ground and it BOUNCES like a solid

        • Place it on a table and leave overnight and it will FLOW and flatten out into a puddle like a liquid.

        • Heat up the silly putty and the drop it and it will STICK to the ground like a liquid.

        • Chill silly putty to bellow room temperature and leave rolled up on a table and it will STAY rolled up at that cold temperature

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Fundamentals of Mechanical Properties

  • Mechanical Properties

    • Deal directly with behavior of materials under applied forces.

    • Properties are described by applied stress and resulting strain, or applied strain and resulting stress.

      • Example: 100 lb force applies to end of a rod results in a stress applied to the end of the rod causing it to stretch or elongate, which is measured as strain.

    • Strength: ability of material to resist application of load without rupture.

      • Ultimate strength- maximum force per cross section area.

      • Yield strength- force at yield point per cross section area.

      • Other strengths include rupture strength, proportional strength, etc.

    • Stiffness: resistance of material to deform under load while in elastic state.

      • Stiffness is usually measured by the Modulus of Elasticity (Stress/strain)

      • Steel is stiff (tough to bend). Some beds are stiff, some are soft (compliant)

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Fundamentals of Mechanical Properties

  • Mechanical Properties

    • Hardness: resistance of materials to surface indentation or abrasion.

      • Example, steel is harder than wood because it is tougher to scratch.

    • Elasticity: ability of material to deform without permanent set.

      • Rubber band stretches several times and returns to original shape.

    • Plasticity: ability of material to deform outside the elastic range and yet not rupture,

      • Bubble gum is blown up and plastically deforms. When the air is removed it deflates but does not return to original shape.

      • The gum has gone beyond its elastic limit when it stretches, set it remains plastic, below the breaking strength of the material.

    • Energy capacity: ability of material to absorb energy.

      • Resilience is used for capacity in the elastic range.

      • Toughness refers to energy required to rupture material

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Mechanical Test Considerations


  • Principle factors are in three main areas

    • manner in which the load is applied

    • condition of material specimen at time of test

    • surrounding conditions (environment) during testing

  • Tests classification- load application

    • kind of stress induced. Single load or Multiple loads

    • rate at which stress is developed: static versus dynamic

    • number of cycles of load application: single versus fatigue

  • Primary types of loading





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Standardized Testing Conditions

  • Moisture

    • 100F, 100% R.H.

    • 1 Day, 7 Days, 14 Days

  • Temperature

    • Room Temperature: Most common

    • Elevated Temperature: Rocket engines

    • Low Temperature: Automotive impact

  • Salt spray for corrosion

    • Rocker Arms on cars subject to immersion in NaCl solution for 1 Day and 7 Days at Room Temperature and 140 F.

  • Acid or Caustic environments

    • Tensile tests on samples after immersion in acid/alkaline baths.

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  • Stress: Intensity of the internally distributed forces or component of forces that resist a change in the form of a body.

    • Tension, Compression, Shear, Torsion, Flexure

  • Stress calculated by force per unit area. Applied force divided by the cross sectional area of the specimen.

  • Stress units

    • Pascals = Pa = Newtons/m2

    • Pounds per square inch = Psi Note: 1MPa = 1 x106 Pa = 145 psi

  • Example

    • Wire 12 in long is tied vertically. The wire has a diameter of 0.100 in and supports 100 lbs. What is the stress that is developed?

    • Stress = F/A = F/r2 = 100/(3.1415927 * 0.052 )= 12,739 psi = 87.86 MPa

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0.1 in

1 in


  • Example

    • Tensile Bar is 10in x 1in x 0.1in is mounted vertically in test machine. The bar supports 100 lbs. What is the stress that is developed? What is the Load?

      • Stress = F/A = F/(width*thickness)= 100lbs/(1in*.1in )= 1,000 psi = 1000 psi/145psi = 6.897 Mpa

      • Load = 100 lbs

    • Block is 10 cm x 1 cm x 5 cm is mounted on its side in a test machine. The block is pulled with 100 N on both sides. What is the stress that is developed? What is the Load?

      • Stress = F/A = F/(width*thickness)= 100N/(.01m * .10m )= 100,000 N/m2 = 100,000 Pa = 0.1 MPa= 0.1 MPa *145psi/MPa = 14.5 psi

      • Load = 100 N

100 lbs

1 cm



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  • Strain: Physical change in the dimensions of a specimen that results from applying a load to the test specimen.

  • Strain calculated by the ratio of the change in length and the original length. (Deformation)

  • Strain units (Dimensionless)

    • When units are given they usually are in/in or mm/mm. (Change in dimension divided by original length)

  • % Elongation = strain x 100%



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Stress-Strain Diagrams







  • Stress-strain diagrams is a plot of stress with the corresponding strain produced.

  • Stress is the y-axis

  • Strain is the x-axis

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  • Stiffness is a measure of the materials ability to resist deformation under load as measured in stress.

    • Stiffness is measures as the slope of the stress-strain curve

    • Hookean solid: (like a spring) linear slope

      • steel

      • aluminum

      • iron

      • copper

    • All solids (Hookean and viscoelastic)

      • metals

      • plastics

      • composites

      • ceramics

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  • Modulus of Elasticity (E) or Young’s Modulus is the ratio of stress to corresponding strain (within specified limits).

    • A measure of stiffness

      • Stainless Steel E= 28.5 million psi (196.5 GPa)

      • Aluminum E= 10 million psi

      • Copper E= 16 million psi

      • Molybdenum E= 50 million psi

      • Nickel E= 30 million psi

      • Titanium E= 15.5 million psi

      • Tungsten E= 59 million psi

      • Carbon fiber E= 40 million psi

      • Glass E= 10.4 million psi

      • Composites E= 1 to 3 million psi

      • Plastics E= 0.2 to 0.7 million psi

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Modulus Types

Initial Modulus

Tangent Modulus

Secant Modulus



  • Modulus: Slope of the stress-strain curve

    • Initial Modulus: slope of the curve drawn at the origin.

    • Tangent Modulus: slope of the curve drawn at the tangent of the curve at some point.

    • Secant Modulus: Ratio of stress to strain at any point on curve in a stress-strain diagram. It is the slope of a line from the origin to any point on a stress-strain curve.

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Testing Procedure

  • Tensile tests yield a tensile strain, yield strength, and a yield stress

  • Tensile modulus or Young’s modulus or modulus of elasticity

    • Slope of stress/strain

    • Yield stress

    • point where plastic

      deformation occurs

    • Some materials do

      not have a distinct yield point

      so an offset method is used

Yield stress

1000 psi


Yield strength


0.002 in/in


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Expected Results

  • Stress is measured load / original cross-sectional area.

  • True stress is load / actual area.

  • True stress is impractical to use since area is changing.

  • Engineering stress or stress is most common.

  • Strain is elongation / original length.

  • Modulus of elasticity is stress / strain in the linear region

  • Note: the nominal stress (engineering) stress equals true stress, except where large plastic deformation occurs.

  • Ductile materials can endure a large strain before rupture

  • Brittle materials endure a small strain before rupture

  • Toughness is the area under a stress strain curve

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Energy Capacity



  • Energy Capacity: ability of a material to absorb and store energy. Energy is work.

  • Energy = (force) x (distance)

  • Energy capacity is the area under the stress-strain curve.

  • Hysteresis: energy that is lost after repeated loadings. The loading exceeds the elastic limit.



Elastic strain

Inelastic strain

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Creep Testing

  • Creep

    • Measures the effects of long-term application of loads that are below the elastic limit if the material being tested.

    • Creep is the plastic deformation resulting from the application of a long-term load.

    • Creep is affected by temperature

  • Creep procedure

    • Hold a specimen at a constant elevated temperature under a fixed applied stress and observe the strain produced.

    • Test that extend beyond 10% of the life expectancy of the material in service are preferred.

    • Mark the sample in two locations for a length dimension.

    • Apply a load

    • Measure the marks over a time period and record deformation.

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Creep Results




Tertiary Creep



Secondary Creep



Primary Creep

Time (hours)

  • Creep versus time

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Mechanical Properties in Liquids (Viscous Flow)

  • Polymer Flow in Pressure Flow (Injection Molding)

FIGURE 2. (a) Simple shear flow. (b) Simple extensional flow. (c) Shear

flow in cavity filling.(d) Extensional flow in cavity filling.

Ref: C-MOLD Design Guide

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Viscous Flow

  • Viscosity is a measure of the material’s resistance to flow

    • Water has low viscosity = easy to flow

    • Syrup has higher viscosity = harder to flow

  • Viscosity is a function of Shear Rate, Temp, and Pressure

    • increase Shear Rate = Viscosity Decreases

    • Increase Temperature = Viscosity Decreases

Ref: C-MOLD Design Guide

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Newtonian and Non-Newtonian Flow


Shear Thickening



or Pa-sec



Shear Thinning

Shear Rate, sec -1

  • Viscosity is a measure of the material’s resistance to flow.

    • Newtonian Material. Viscosity is constant

    • Non-Newtonian: Viscosity changes with shear rate, temperature, or pressure

    • Polymers are non-Newtonian, usually shear thinning

Fig 4.4

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Viscosity Measurements

  • Viscosity is a measure of the material’s resistance to flow.

    • Liquids: (paints, oils, thermoset resins, liquid organics) Measured with rotating spindle in a cup of fluid, e.g., Brookfield Viscometer

      • Resistance to flow is measured by torque.

      • The spindle is rotated at several speeds.

      • The fluid is heated to several temperatures.

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Viscosity Measurements

Cone, radius r




  • Melts: (plastic pellets, solid particles)

    • Resistance to flow is measured by torque in cone-and-plate, e.g., Rheometrics viscometer

    • The plates are heated and the toque is measured

    • Resistance to flow is measured by flow through tube

      • Capillary rheometer

      • Melt Indexer

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Viscosity Testing

  • Melt Flow Index

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Melt Index

  • Melt index test measure the ease of flow for material

  • Procedure (Figure 3.6)

    • Heat cylinder to desired temperature (melt temp)

    • Add plastic pellets to cylinder and pack with rod

    • Add test weight or mass to end of rod (5kg)

    • Wait for plastic extrudate to flow at constant rate

    • Start stop watch (10 minute duration)

    • Record amount of resin flowing on pan during time limit

    • Repeat as necessary at different temperatures and weights

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Viscoelastic models

  • Plastics exhibit viscoelastic behavior, to an applied stress

    • Viscous liquid: Continuously deform while shear stress is applied

    • Elastic solid: Deform while under stress and recover to original shape

Ref: C-MOLD Design Guide

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Viscoelastic models

  • Plastics exhibit viscoelastic behavior, to an applied stress

    • Viscous liquid: Simple dashpot

    • Viscoelastic liquid: Spring and Dashpot in series (Maxwell model)

    • Viscoelastic solid: Spring and Dashpot in Parallel (Voight model)

    • Elastic solid: Simple Spring

    • Figure 4-6

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Viscoelastic models

  • Time Dependence of Viscoelastic properties

    • Viscous liquid: Constant viscosity: Newtonian

    • Viscoelastic liquid: Viscosity changes at different rates, e.g., higher shear rate reduces viscosity or Shear thinning plastics

    • Viscoelastic solid: Solid part has a memory to applied stress and needs time for the stress to reach zero after an applied load.

    • Elastic solid: Simple Spring: Hook’s Law on spring constant

    • Figure 4-7