unit 5.2: materials testing -...

POE@BHS-TOPIC 5: Material Properties and Testing, UNIT 5.2: Material Testing

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UNIT 5.2: Materials Testing

Preface

Material Testing is a critical process that determines whether a product is reliable, safe, and predictable in function. Material testing is basically divided into two major categories: destructive testing and nondestructive testing. Destructive testing is defined as a process where a material is subjected to a load in a manner that will ultimately cause the material to fail. Machines have been developed specifically to conduct destructive testing. These machines exert force on the sample and record information such as resulting deformation, the amount of stress that builds up inside the sample, elastic behavior, strength, etc. When non-destructive testing is performed on a material, the part is not permanently affected by the test. The part is usually still serviceable. The purpose of non-destructive testing is to determine whether the material contains imperfections.

Over many years, tests have been developed for measuring the common properties of engineering materials, including acoustical, electrical, magnetic, physical, optical, and thermal properties. But why is material testing so significant?

Concepts

1. Engineers utilize a design process and mathematical formulas to solve and document

design problems.

2. Material testing aids in determining a product’s reliability, safety, and predictability in

function.

3. Engineers perform destructive and non-destructive tests on material specimens for the

purpose of identifying and verifying the properties of various materials.

4. Material testing provides a reproducible evaluation of material properties.

5. Tensile testing data is used to create a test sample stress strain curve.

6. Stress strain data points are used to identify and calculate sample material properties

including elastic range, proportional limit, modulus of elasticity, elastic limit, resilience, yield point, plastic deformation, ultimate strength, failure, and ductility.

Performance Objectives

It is expected that students will:

Utilize a five-step technique to solve word problems.

Obtain measurements of material samples.

Tensile test a material test sample.

Identify and calculate test sample material properties using a stress strain curve.

Assessment

Explanation

1. Students will explain the importance of material testing as a verification process.

Application

2. Students will tensile test a material sample and identify and calculate material properties.

Interpretation


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3. Students will write journal entries reflecting on their learning and experiences. An example

writing prompt: What is something you learned today about material testing, manufacturing processes, or engineering problem solving that you did not understand or know before?

Self-Knowledge

4. Students will reflect on their work by recording their thoughts and ideas in journals. They

may use self-assessments as a basis for improvement. Ideas and questions students may pose and answer in their journals are:

Today the hardest concept for me to understand was . . .

When I work in a group, I find that . . .

When I work by myself, I find that . . .

What did I accomplish today?

Now that I have completed this task, what is next?

Essential Questions

1. Why is it critical for engineers to document all calculation steps when solving problems?

2. How is material testing data useful?

3. Stress strain curve date points are useful in determining what specific material properties?

Source: http://www.docstoc.com/docs/49617062/Material-Testing-Laboratory


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Lesson 5.2.1: Engineering Calculations

Purpose

Engineers are technical problem solvers. The way in which engineers solve problems varies. In general engineers implement a logical approach, or method, in solving the problems that they encounter. The purpose of this activity is to refresh yourself with the important steps to effective problem solving and to apply those steps to questions related to problems involving the variables related to certain types of materials testing.

Procedure

Important Definitions: Stress: The term stress (s) is used to express the loading in terms of force applied to a certain cross-

sectional area of an object. From the perspective of loading, stress is the applied force or system of forces

that tends to deform a body. From the perspective of what is happening within a material, stress is the

internal distribution of forces within a body that balance and react to the loads applied to it. A bar loaded

in pure tension will essentially have a uniform tensile stress distribution.

Source: http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Mechanical/StressStrain.htm

Strain: Strain is the response of a system to an applied stress. When a material is loaded with a force,

it produces a stress, which then causes a material to deform. Engineering strain is defined as the amount

of deformation in the direction of the applied force divided by the initial length of the material. This

results in a unitless number, such as inches per inch or meters per meter. For example, the strain in a bar

that is being stretched in tension is the amount of elongation or change in length divided by its original

length.

If the stress is small, the material may only strain a small amount and the material will return to its

original size after the stress is released. This is called elastic deformation. Like a rubber band, it returns

to its unstressed state. Elastic deformation only occurs in a material when stresses are lower than a

critical stress called the yield strength. If a material is loaded beyond it elastic limit, the material will

remain in a deformed condition after the load is removed. This is called plastic deformation.

Source: http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Mechanical/StressStrain.htm


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Axial stress is symbolized by the Greek letter sigma (). Axial stress is defined as the force perpendicular to the cross-sectional area of the member divided by the cross-sectional area.

Shear stress is symbolized by the Greek letter Tau (). It is defined as the force parallel to the cross-sectional area of the member divided by the cross-sectional area. Strain is the ratio of the change in length of an object (its elongation) as a result of an applied stress to the original length of the object. If we assume a homogenous material with uniform

cross section, the normal strain (epsilon) is defined as the elongation per unit length. Elastic region is the region of stress that is directly proportional to the strain. The slope of the straight line fitted through two points is called the modulus of elasticity. The point at which the elastic region ends is called the elastic limit. The elastic limit is the point at which permanent deformation occurs. If the force is taken off of the sample, the sample will not return to its original size and shape. The proportional limit is the point at which the deformation is no longer directly proportional to the applied force. Hooke’s law does not apply anymore and the graph becomes parabolic in nature. At the yield point, considerable elongation of the test specimen occurs with no increase in loading. Beyond this theoretical point, the material becomes perfectly plastic since it deforms without an increase in stress. Strain hardening of the material occurs after the yield point is passed and the material undergoes change that causes it to actually become harder. At the maximum stress, called the ultimate stress, any further stretching would lead to fracture and the failure point where the sample fails. Hooke’s Law – Robert Hooke stated in 1676 that “There is a linear relationship between stress and strain for a bar in simple tension or compression.” This relationship is expressed by the equation:

= E

Symbols – is the axial stress, is the axial strain, and E is the constant of proportionality. This constant is called the modulus of elasticity. E is often referred to as Young’s modulus, after the scientist Thomas Young (1773-1829) who introduced the idea of the modulus of elasticity. Prismatic Bars – A prismatic bar is defined as a structural member having a straight longitudinal axis and constant cross section throughout its length. Elongation caused by a tensile load F on a prismatic bar, assuming linear elasticity, can be calculated using Hooke’s

law (= E ). By combining the formulas for stress ( = F/A ) and strain ( = /L), we can

determine deformation ( = FL/EA).


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Source: http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Mechanical/Tensile.htm

Variables: Δx (delta x) = the change in x (units are the units of x) δ (delta) = total deformation or elongation (in.) σ (sigma) = stress (force per unit area, psi or lb/in.2) ε (epsilon) = strain or unit elongation E = modulus of elasticity P or F = axial force (lb) A = cross-sectional area (in²), Ao = original area (in2) L = length (in.), Lo = original length (in) r = radius (in.) d = diameter (in.) p= Pressure (psi or lb/in.2)

Equations/Formulas (what’s the difference?:

𝜺 =𝜹

𝑳 𝝈 =

𝑷

𝑨 𝝈 = 𝑬𝜺 => 𝜹 =

𝑷𝑳

𝑬𝑨

𝑨 = 𝝅𝒓𝟐 =𝝅𝒅𝟐

𝟒


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Five Step Problem-Solving Method

STEP1-Organize the information provided in the problem statement: Begin by drawing a picture. Identify knowns (what you’re given) and unknowns (what you want to find out). Assign variable names to the knowns and unknowns and specify each using the correct number and unit name.

STEP2-Derive a set of equations (or find a set of formulas) that relate your knowns to your unknowns. You will know that you have a sufficient number of equations/formulas when the number of unknowns is equal to the number of equations/formulas.

STEP3-Manipulate the equations/formulas using algebraic principles, if necessary.

STEP4-Substitute numbers and units into the equations/formulas using “railroad tracks” and solve. Write your answer in terms of the variable name that you chose previously. Be sure to specify not only the numeric answer but the units as well.

STEP5-Check the reasonableness of your answer and your units. Convert units using “railroad tracks” if necessary.

Examples

Example#1: A force of 150 lb pushes on a round plate with an area of 30. in.2. What is the normal stress that the plate applies to the ground?


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Example#2: A 35 ft long solid steel rod is subjected to a tensile load of 8,000. lb. This load causes the rod to stretch 0.266 in. The modulus of elasticity of the steel is 3.0 x 107 psi. Determine the diameter of the rod.

Practice Problems: Solve at least four of the following problems using the method described above.

A ¼ in. diameter rod must be machined on a lathe to a smaller diameter for use as a specimen in a tension test. The rod material is expected to break at a normal stress of 63,750 psi. If the tension testing machine can apply no more than 925 lb of force to the specimen, what is the maximum rod diameter that should be used for the specimen?

A 4.0 in. wide by 1.125 in. thick rectangular steel bar supports a load of P in tension. Determine:

The stress in the bar for P = 32,000 lb. The load P that can be supported by the bar if the axial stress must not exceed 25,000 psi.


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A 35 ft long solid steel rod is subjected to a tensile load of 8,000. lb. This load causes the rod to stretch 0.266 in. The modulus of elasticity of the steel is 3.0 x 107 psi. Determine the diameter of the rod.

A 1.25 in. by 3.0 in. rectangular steel bar is used as a diagonal tension member in a bridge truss. The diagonal member is 20. ft long, and its modulus of elasticity is 3.0 x 107 psi. If the strain in the diagonal member is measured as 0.001200, determine:

The axial stress The tension force in the bar The elongation of the member

A 9.0 x 103 lb load is suspended from the roof in a shopping mall with a 16 ft long solid aluminum rod. The modulus of elasticity of the aluminum is 1.0 x.107 psi. If the maximum rod elongation must be limited to 0.50 in. and the maximum normal stress must be limited to 3.0 x 103 psi, determine the minimum diameter that may be used for the rod. In your answer demonstrate that both the elongation and stress limits are satisfied.


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Lesson 5.2.2: Tensile Testing

Purpose:

To use the PASCO Stress-Strain Testing Apparatus to collect data for the elastic deformation, plastic deformation, and failure of a provided sample and to determine a number of important parameters for that sample.

Definitions:

Consider the stress-strain diagram provided below. For each of the terms listed on this and the next page, indicate how the terms relate to the diagram for Stainless steel (18-8) and estimate their values from the data provided for Stainless steel (18-8) to the best of your ability:

o Proportional Limit Stress [𝜎𝑃𝐿]

o Yield Point Stress [𝜎𝑌𝑃]

o Ultimate Stress [𝜎𝑈𝐿𝑇]

o Rupture Stress [𝜎𝑅𝑈𝑃𝑇]

o Total Strain [𝜀𝑇𝑂𝑇]


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o Modulus of Elasticity [𝐸]

o Modulus of Resilience [𝑀𝑅]

o Modulus of Toughness [𝑀𝑇]


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Data Collection: Sample material being tested:_______________________________________________________ Class members analyzing this sample:________________________________________________ Photographs or tracings of pre- and post-test sample (place broken ends together if sample failed) and the PASCO Stress-Strain Apparatus AP-8216A

Stress-Strain Diagram (created using PASCO Data Studio software:


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Data Analysis:

Illustrate the following parameters for your sample on the Stress-Strain Diagram and estimate their numerical values for your sample. Include all calculations.

a. Proportional Limit Stress [𝜎𝑃𝐿]

b. Yield Point Stress [𝜎𝑌𝑃]

c. Ultimate Stress [𝜎𝑈𝐿𝑇]

d. Rupture Stress [𝜎𝑅𝑈𝑃𝑇]

e. Modulus of Elasticity [𝐸]

f. Modulus of Resilience [𝑀𝑅 =1

2𝜀𝑃𝐿𝜎𝑃𝐿]

g. Modulus of Toughness [𝑀𝑇]

h. Total Strain [𝜀𝑇𝑂𝑇]

i. % Elongation [100 ∗ 𝜀𝑇𝑂𝑇]


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Lesson 5.2 Key Term Crossword

1 2 3 4

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9 10

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14 15

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18 19

20

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22 23

24

25

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27 28

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32

www.CrosswordWeaver.com


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ACROSS

3 The law stating that the stress of a solid is directly

proportional to the strain applied to it.

6 Method of prestressing concrete w hereby the

tendons are elongated and anchored w hile the

concrete in the member is cast, and released w hen

the concrete is strong enough to receive the forces

from the tendon through bond.

7 The fractional increase in a material's length due to

stress in tension or to thermal expansion.

9 The ratio of actual strength to required strength.

11 An influence on a body w hich causes it to

accelerate; quantitatively it is a vector, equal to the

body's time rate of change of momentum.

15 Refers to reinforcing concrete in w hich internal

stresses have been introduced to reduce potential

tensile stresses in the concrete resulting from loads.

16 Any alteration of shape or dimensions of a body

caused by stresses, thermal expansion or

contraction, chemical or metallurgical

transformations, or shrinkage and expansions due to

moisture change.

22 The probability that a component part, equipment, or

system w ill satisfactorily perform its intended

function under given circumstances, such as

environmental conditions, limitations as to operating

time, and frequency and thoroughness of

maintenance for a specif ied period of time.

24 The ratio of the increment of some specif ied form of

stress to the increment of some specif ied form of

strain, such as Young's modulus, the bulk modulus,

or the shear modulus. Also know n as coeff icient of

elasticity, elasticity modulus, elastic modulus.

27 Maximum stress that a material w ill w ithstand

w ithout permanent deformation.

29 The stress required to fracture a material w hether by

compression, tension, or shear.

30 Mechanical property of a material that indicates the

ability of the material to handle overloading before it

fractures.

31 Test methods used to examine an object, material,

or system causing permanent damage to its

usefulness.

32 Sometimes referred to as Tensile Strength;

determined by measuring the maximum load a

material specimen can carry w hen in the shape of a

rectangular bar or cylindrical can.

DOWN

1 Operational techniques necessary to satisfy all

quality requirements; includes process monitoring

and the elimination of root causes of unsatisfactory

product or service quality performance.

2 A measure of how easily a material can be tw isted.

4 A force w ith its resultant passing through the

centroid of a particular section and being

perpendicular to the plane of the section. A force in

a direction parallel to the long axis of the structure.

5 The condition of a string, w ire, or rod that is

stretched betw een tw o points.

8 Test methods used to examine an object, material,

or system w ithout impairing its future usefulness.

10 The loss of the load-bearing ability of a material

under repeated load application, as opposed to a

single load.

12 The average of the squared differences from the

mean.

13 Graphical representation of a material's mechanical

properties.

14 Point at w hich the deformation is no longer directly

proportional to the applied force. Hooke's Law no

longer applies.

17 When a material is reduced in volume by the

application of pressure; the reciprocal of the bulk

modulus.

18 A statistical measurement of variability.

19 The ability to get answ ers to questions through a

conscious, organized process. The answ ers are

usually, but not necessarily, quantitative.

20 Change in the length of an object in some direction

per unit.

21 The collection and analysis of numerical data in

large quantities.

23 Nominal stress developed in a material at rupture.

Not necessarily equal to ultimate strength. Since

necking is not taken into account in determining

rupture strength, seldom indicates true stress at

rupture.

25 A mechanical property of a material that show s how

effective the material is absorbing mechanical

energy w ithout sustaining any permanent damage.

26 The force acting across a unit area in a solid

material resisting the separation, compacting, or

sliding that tends to be induced by external forces.

28 Condition caused by collapse, break, or bending, so

that a structure or structural element can no longer

fulf ill its purpose.

unit 5.2: materials testing -...

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