tensile test

Technology 25 San Jose State University LabNotes

Tensile Test LN 9-1

Tensile & Fracture Tests

1.0 Learning Objectives

After successfully completing this laboratory workshop, including the assigned reading, the lab

bluesheets, the lab quizzes, and any required reports, the student will be able to:

• Relate the bonding type to the materials’ mechanical properties.

• Generate a stress/strain diagram from experimental data.

• Use a stress/strain diagram to determine yield point, ultimate tensile strength, Young’s modulus, ductility, and toughness.

• Demonstrate the large variation in breaking stress for glass specimens from a common source and similar process history.

• Show how the critical stress to break glass by bending can be determined from the load at fracture.

• Indicate a statistical method for analyzing the breaking stress which provides a meaningful `materials parameter' to characterize the glass; a parameter on which the engineer can base a design-allowable stress.

2.0 Resources

Callister, Materials Science and Engineering: An Introduction, Chapter 6.1-6.8 and Chapter 13.7-13.8

Links on Tensile Test and Properties:

http://www.shodor.org/~jingersoll/weave/tutorial/tutorial.html

Online Tensile Test Experiment: [this link to be updated]. http://www.menet.umn.edu/~klamecki/Forming/tensileexercise.html

3.0 Materials Applications

Mechanical testing is critical when designing and evaluating materials for most any application.

Obviously the strength of a material is important for applications such as mountain bikes and hip

implants - applications that see a lot of repeated, aggressive loading. However, mechanical

strength is also important for less obvious things such as the layers in a computer chip that are

exposed to mechanical stress from the surrounding layers due to the fact that the layers expand

and contract at different rates during heating. Mechanical tests can be designed to investigate

either how much load a material can withstand during one application and the affect of cyclic

(repeated) stress.

http://www.shodor.org/~jingersoll/weave/tutorial/tutorial.html

http://www.menet.umn.edu/~klamecki/Forming/tensileexercise.html


Tensile Test LN 9-2

4.0 Background on Tensile Test

Engineered structures and components are subjected to various loads and displacements during

service. When the applied forces (or displacements) are relatively low, unloading causes the

structure to return to its original size and shape. This type of mechanical response is described

as ‘elastic’ (elastic deformation). However, at some increased level of load, the material may

not return to its original shape when unloaded, and permanent, or plastic deformation is said to

have taken place. Most engineering materials function under anticipated, elastic loading.

Clearly, one must know at what load or stress level the transition from elastic to plastic behavior

occurs in order to set "design limits"; and one must know how "forgiving" the material is if elastic

loads are exceeded. This information is available, in large part, from a standard tensile test. The

standard tensile test is the subject of this experiment. It is described in ASTM Method E8

(Standard Methods for Tension Testing of Metallic Materials).

A simple tensile test consists of slowly applying an axial force or load to a standard specimen by

means of a suitable testing machine and measuring the corresponding dimensional changes.

The stretching, deformation, or elongation in the direction of the applied load is of particular

interest. The deformation per standard unit of length in this direction is called the longitudinal

strain, e. The ‘engineering stress’, s, is defined as is the force per unit area, is based on the

original cross-sectional area of the specimen, the area perpendicular to the applied force.

When a specimen is pulled to failure in a tensile testing machine, the calculated stress values

(ordinate) and corresponding strains (abscissa) are typically plotted on graph paper to produce a

stress-strain diagram. Analysis of this diagram will determine the key mechanical properties.

The properties commonly considered are the ultimate tensile strength, Su; the yield strength

Sy (or yield point, depending on the type of material tested); the total elongation to failure, %El

and the % reduction-of-area, %RA. For a more complete understanding of the mechanical

properties, Young's modulus of elasticity, E, must be added to the list.

In the most general way, we may define the mechanical strength of engineering materials as their

ability to withstand loads without excessive distortion or failure. The simplest type of mechanical

loading to analyze is static tension, and it is also commonly encountered in engineering

structures. Too, the information from the tensile test helps predict the effects of other more

complex types of loading. For all of these reasons, the static tension test is a good place to begin

the study of mechanical properties of materials.


4.1 Elastic Behavior

Elastic deformation is said to have occurred when a material, which has deformed under load,

returns to its original shape and dimensions when the load is removed. Elastic deformation in

metals or ceramics occurs as the result of a temporary extension of the interatomic bonds during

the application of the load. In other materials, such as polymers, elastic deformation may involve

the stretching and kinking of long chain molecules, or more complex phenomena. Within the

elastic range of deformation for metals, the strain is, essentially, linearly proportional to the

applied stress. The proportionality constant is called Young's modulus of elasticity, E

(sometimes called the elastic modulus).

At the same time as interatomic bonds in the general direction of the applied force are elongated,

the atoms are forced closer together laterally. The ratio between lateral and longitudinal strain is

called Poisson's ratio. For metals, Poisson's ratio generally varies somewhere between 0.25 and

0.40. The relation is ordinarily written:

ν = −εxεz

= −εyεz

where ν is Poisson's ratio, εy and εx are the lateral strain, and εz is the longitudinal strain. The

negative sign is present in the equation because the lateral strain under tensile load is

compressive.

4.2 Plastic Behavior

When stress-strain data are plotted for engineering materials tested in tension, they generally

tend to behave in one of three ways (see Figure 1):

(1) some materials will fail after exhibiting only elastic deformation with relatively small strains (‘brittle’ materials such as glass)

(2) some materials show large, fully elastic strains (‘elastic’ materials such as rubber)

(3) some materials deform plastically after an initial elastic deformation (‘ductile’ metals and alloys).

There may be large variations within these primary categories. Most common engineering metals

and alloys (with a few exceptions, such as cast iron and some hardened high-strength steels)

deform plastically after an initial elastic response.

Plastic deformation is irrecoverable. After it has occurred, the material will not return to its

original dimensions. The mechanism by which plastic yielding takes place in metals is called slip.

Essentially, all slip processes can be related to dislocation motion in the crystal structure. These

linear imperfections in the crystal structure determine the plastic deformation characteristics of a

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material. Under elastic loading, dislocations remain motionless, and deformation occurs at the

interatomic level only. When loading is sufficient to "move" dislocations, slip is said to have taken

place and plastic deformation begins.

As slip begins, dislocations will start to move in certain favorably oriented crystal planes in

polycrystalline metals. The dislocations will eventually begin to pile-up at the grain boundaries

and, in order for slip to continue, dislocations must move in less favorably oriented slip planes in

adjacent crystals. A greater stress is required for this to happen, and so the material is said to

become harder, or to ‘strain-harden’ (see Figure 2).

The stress at which plastic deformation begins is of particular importance. When properly defined,

it gives a useful indication of allowable deformation for certain engineering structures. The most

commonly used term for this stress is the yield stress (or yield strength), which is defined as the

stress at which a certain small amount of plastic deformation takes place. This strain is typically

taken to be 0.2% and the yield strength is then termed to be the 0.2% offset yield strength, sy.

To obtain the value of yield strength from a stress-strain curve, one may draw a line parallel to the

elastic part of the curve at the point of 0.2% offset on the strain axis. The yield stress (strength) is

determined by the intersection of this line with the plotted curve (Figure 3).

There are other measures of departure from elastic behavior, such as the elastic limit (EL) or the

proportional limit (PL), but they are not ordinarily used in commercial testing of metals as they are

very difficult to measure accurately. The value PL is the stress value at which the stress-strain

curve becomes non-linear. This is, of course, difficult to ascertain as the curve only gradually

changes to non-linear behavior (see Figure 3). The elastic limit (EL) is the stress value at which

the stress-strain behavior is no longer fully elastic. Fully elastic behavior does not necessarily

imply a linear stress-strain response, so the value of EL is usually slightly greater (or equal) to PL.

In some materials, most particularly in certain types of "mild" structural steel, plastic yielding

occurs very suddenly rather than gradually (see Figure 4). The result is that a rather large plastic

deformation is observed without any increase in stress such as would be encountered with strain-

hardening. Occasionally, yielding is followed by a sharp drop in stress. The theoretical reason

usually advanced for this discontinuous plastic flow (generally referred to in steels as the yield

point slip phenomenon) is that it represents a tearing away of dislocations from an ‘atmosphere’

of impurity atoms, which at lower stresses had anchored the dislocations against movement. The

dislocations available to accommodate slip are not all "freed" at one initial stress value. The

release of the dislocations from the impurity atom atmospheres is a sequential process. This may

result in a rather substantial strain accumulation at a lower stress than that initially involved in

releasing the first dislocations. After some time (or strain) at this lower stress, work-hardening will


begin again and the stress value will start to climb. The stress at which dislocations are first

released is called the Upper Yield Point (Suy): The strain-independent stress value is the Lower

Yield Point (siy).

Figure 1: The stress-strain behavior of: (1) a material that fails after exhibiting only a small elastic deformation (graphite fiber/epoxy composite); (2) a material showing elastic response over an extensive range of strain (rubber); and (3) a material exhibiting elastic/plastic deformation (most polycrystalline commercial metal alloys).

Figure 2. The manner by which the 0.2% offset yield strength (Sy) of a material showing continuous plastic flow is determined, and graphic representations of the proportional and elastic limits, PL and EL, respectively.

Tensile Test LN 9-5


Figure 3. The yield point slip phenomenon - discontinuous deformation.

The tensile properties previously discussed (strain-hardening, the yield strength, and the yield-

point slip phenomenon) describe the early stages of plastic behavior in polycrystalline metals. Let

us now consider events that occur near (just before) the final fracture of a specimen tested in

uniaxial tension.

Eventually a point of plastic instability is reached in the stress-strain curve. At plastic instability

(and as a result of eccentricities of loading, points of local weakness, or other stress

concentrations in the specimen) a highly localized straining event, called ‘necking-down’, occurs.

The cross-sectional area starts to decreases rapidly at some point along the gage section of the

specimen. Since the original cross-sectional area Ao is used for calculating stress, this point

represents a peak in the stress-strain curve (Figure 4, below).

The associated "maximum" stress is called the ultimate tensile strength (su), where

σu=Fmax/Ao

This is sometimes called the UTS. Note that the “engineering” stress-strain diagram is based on

the original length and the original cross-sectional area of the test specimen.

A practical and direct measurement of the diameter, once necking-down occurs, is usually not

available. Nevertheless, the concepts of "true" stress and strain, which are based on

instantaneous measurements of specimen geometry, are fundamental. The concept of true

stress is fairly simple, and will be used at the fracture point after the tests are concluded.

However, true strain and how it applies to the mechanical behavior of materials is beyond the

scope of this introductory course. Tensile Test LN 9-6


Figure 4. Stress-Strain diagram showing the ultimate tensile strength, where necking begins, and the percent elongation at that point.

Other mechanical properties of engineering interest include measures of ductility. The most

common measure of ductility is the percent elongation to failure, % EL:

% EL = [(Lf - Lo)/Lo] x 100]

where Lf is the final length of the specimen at fracture and Lo is the original gage length (the

length of the reduced, uniform load-bearing area of the specimen). The percent reduction-of-

area, %RA, at the necked region of the specimen, measured after fracture, is another measure of

ductility. The applicable relation is:

% RA = [(Ao -Af)/Ao] x 100

Where Ao is the original cross-sectional area and Af is the reduced area at the neck.

Toughness is another measure of the durability of a material when plastically deformed. It is the

ability of a material to absorb energy and deform plastically before fracture. It is usually

measured by calculating the area under the stress-strain curve in a tensile test or by the energy

absorbed in a notch-impact test. Resilience is the capacity of a material to absorb energy in the

elastic range and is measured by the area under the elastic portion of the stress-strain curve.

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5.0 Tensile Test Experiment

Several specimens will be tested. Obtain sample details from your instructor before proceeding.

1. Measure and record the specimen width and thickness (or diameter, for cylindrical specimens). Carefully mark a 2-inch guage section on one face of the samples, using a scratch awl or prick punch. If the punch marks are too deep, you will damage the sample.

2. Position the specimen in the testing machine. Position the extensometer, and engage the data acquisition system per the laboratory director's instruction. Apply continuous loading to the specimen and the extension and load data will be recorded automatically.

3. Continue the test until the specimen breaks. Note both the maximum and breaking loads.

4. Reset the cross-head on the load frame.

5. Measure the final width and thickness (or diameter for cylindrical specimens) at the necked-down region. Fit the halves of the specimen together carefully to determine the final specimen elongation. Note that all plastic deformation is assumed to have taken place in the uniform gage section of the specimen (practically speaking, this may not be true, if the fracture or part of the necked-down region falls beyond the marked guage section.)

5.1 Safety Precautions

Follow the testing machine procedure sheet carefully! Use safety glasses during all phases of

testing.

6.0 Theory on the Fracture Strength of Glass

Glass and ceramic materials in general behave in a brittle manner when bearing heavy loads.

Anyone who has thrown or hit a baseball at a glass window, or who has dropped a dinner plate in

the sink, is well aware of this behavior. Of course, as you will learn in class, advanced ceramics

are being designed and processed to be more resistant to impact fracture (ie, to be more tough).

But, nevertheless, brittle ceramics and brittle glasses are the rule, not the exception. The issue in

this laboratory activity is how the engineer characterizes the breaking strength of brittle materials.

The use of Weibull statistics applied to bend data to establish the breaking strength of glass will

be explored in this experiment.

6.1 The Bend Test

The bend test is one common method to obtain meaningful mechanical strength data to

characterize brittle engineering materials. The three-point bend test of a rectangular section

beam of a ceramic material is illustrated in Figure 7. One simply places the beam (or sometimes

rod) specimen across the lower knife edges, and then applies ever increasing load through the


upper fulcrum. At some point, the specimen breaks and the load to break the specimen is

recorded.

6.2 The Breaking Strength in Bending

The bend test establishes the load to break the specimen. But, how is this used to determine the

`stress' at which failure occurred? A simple relation from a `strength of materials' course will

provide the answer. Most of you have not, and will not be taking this course. So here we provide

this most important relation:

σ = 3

2PLwt2

where ... σ is the applicable stress P is the maximum load to break the specimen t is the thickness of the beam specimen (in M) w is the width of the beam specimen (in M) and L is the distance (in M) between the lower pair of knife-edges

Figure 5 The three-point bend testing of a glass microscope slide or flat plate.

As can be seen from the formula, the thickness of such a sample is much more important than its

width, in this kind of loading. Tensile Test LN 9-9


6.3 Weibull Statistics

Fracture in brittle materials is dependent on the presence of internal cracks, voids and other

defects (or flaws) which result from processing. The larger the flaw, the lower the fracture stress.

Since the flaw size and distribution is random, the fracture stress will exhibit much scatter.

Statistical methods are required to analyze the stress required for fracture of brittle materials.

The statistical method applied in this experiment is the Weibull method. W. Weibull is a

contemporary Swedish research engineer who originally proposed a distribution function that is

widely used in the analysis of the strength of brittle materials and in the analysis of fatigue and

fracture data. A simplified version of the Weibull function is as follows:

Pf = 1 - exp[ ]-V*( )σσ0

m

where ... V is the volume of the part bearing the load m is the Weibull modulus σ is the stress of interest σo is a `characteristic' strength of the material and Pf is the probability of failure at a given strength level, σ.

For the simplified Weibull method, the material parameters we will focus on are the Weibull

modulus and the characteristic strength. The Weibull modulus is a measure of the degree of

scatter of the breaking strength data. When the Weibull modulus is low (~5), there is much

scatter; and this statistical method must be applied. When the Weibull modulus is high (~50),

there is little scatter in the data, and the normal distribution (average value and standard

deviation) can be used to characterize the data. The typical strength values for metals and

alloys, the yield and ultimate tensile strengths, follow the normal distribution. The Weibull

modulus for some engineering materials is tabulated in Table 1.

Material Weibull Modulus, m

Glass 2 to 3

SiC 4 to 10

Si3N4 6 to 15

Graphite 12

Cast Iron 38

Table 1. The Weibull Modulus, m, for Some Brittle Engineering Materials

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The characteristic strength from the Weibull analysis can be taken to be a measure of the

horizontal displacement on what is called the `Weibull plot' (see Figure 6). A plot of failure data

for two materials that differ only in Weibull modulus are plotted in Figure 8a. A logarithmic plot of

similar data is schematically illustrated in Figure 8b. This is the Weibull plot. The slope of this

best straight-line fit to the data is m, the Weibull modulus; and the horizontal position of the line is

proportional to the characteristic strength. Materials exhibiting a higher Weibull modulus (steeper

slope) and/or a greater characteristic strength (line shifted to the right) are `best' from a design

standpoint!

Figure 6: Typical Weibull logarithmic plot.

7.0 Glass Fracture Experiment

Fracture data can be used to establish design allowable stresses to which a structural material

can be safely loaded, with some acceptable failure probability assumed. Remember this: it is

appropriate for the engineer to assume that what they design will fail! What is the consequence

of failure? Is the failure rate acceptable? How does one keep the rate of failure `under control'?

Obviously the engineer needs to quantify the stress (i.e., load) at which failure probably will occur

to arrive at a suitable design allowable stress. The design allowable stress considers the degree

of scatter of all available strength data and a presumed level of risk (economic, safety, and

otherwise). Establishing a design allowable is beyond the scope of this course. However, we will Tensile Test LN 9-11


test glass microscope slides in a simple 3-point bend test, then calculate the stress necessary to

break the slides, and then apply Weibull statistics to the data to arrive at an appropriate and

meaningful breaking strength parameter. After all, it is a strength parameter on which the design

allowable must be based.

1. Position a glass slide over the two lower knife edges on the three-point bend fixture as indicated below (see also figure 5). .

↓ Reading

P

∇

∆ ∆

: :

←⎯⎯⎯→

L

L = 2.54 cm

P(N) = reading (in kgF) x 9.81 (N)


2. Turn on the testing unit (switch in back, NOT on the left side front). Important system parameters will be set for you by the laboratory instructor.

3. Set the loading rate knob on the testing unit to maximum. The rate must remain fixed for a given evaluation.

4. Press the start button. The upper fulcrum will lower at a given rate until the specimen breaks. The bending load increases until the slide breaks. The load given by the machine is in kg. You must multiply by 9.81m/s2 to obtain the force in Newtons.

5. Record the actual peak-load (in Kgf) as read in the liquid crystal display on the control panel of the Sebastiani V.

6. Remove all major broken glass pieces, using tweezers, that may interfere with motion of the 3-point fixture on a subsequent test.

7. Return to step 1a, and continue testing the rest of the slides. Twenty glass slides are needed for a `good' Weibull plot for a given condition.



8.0 Report

Your written report should include the following sections (see instructor, if a modified version of

either of these tests was performed):

1. Title Page

2. Abstract 3. Introduction: Explain why mechanical testing is important to materials design. Discuss the

theory behind tensile and fracture tests..

4. Procedure: Explain what you did in your own words. Include sketches. Be very careful not to plagiarize the lab notes!

5. Data Analysis and Results: Include all your data collection, calculations, and plots specified on the lab bluesheets.

6. Discussion of results: Determine whether the results of your data are appropriate, i.e. whether the values make sense.

7. Summary/ conclusions: Summarize what you did and your results. Comment on the importance/ relevance of the experiment.

8. References

See the grading criteria on the next page.



Grading Guidelines for Laboratory Report Tensile & Fracture Tests

Student Name

Score (6) Weak

(7) (8) (9) (10) Effective

Writing Style & Structure Total: /50

Sentence structure

Spelling &Neatness

Paragraph structure, logical flow

Clarity of writing (Gives ideas directly, does not complicate ideas)

Voice (Creativity, Originality) (uses original voice, text not copied from outside source)

Technical Content & Structure Total: /120

Abstract

Introductory (Background) Section [Overall]

• Theory on tensile test

• Theory on fracture test

Results [Overall]:

• Figures (use appropriate Graphics, Labels, etc)

• Distinguishes data from results and shows all plots mentioned in Bluesheets

• Shows all calculations and how data is analyzed

Discussion [Overall]

• Makes some attempt to determine whether results are correct or sensible, links results to theory presented earlier

Conclusion

References

Total Report Score = Sum of above/170



Lab Bluesheet: Tensile Test Data Collection

Specimen #1, Type: ______________ Initial Width: ______________

Thickness: ______________ Guage Length: ______________

Property Experimental Value

Young’s Modulus, E (GPa)

Ultimate Tensile Strength, (MPa)

Yield Stress, (MPa)

Percent Elongation, %

True Stress at fracture, (MPa)






Yield Stress, (MPa)










Yield Stress, (MPa)








Yield Stress, (MPa)




Lab Bluesheet: Fracture Test Data Collection

For each run:

1. Using the data tabulation sheet attached, transfer the respective load data for the test condition of interest. You must record the load data in order of increasing load to break. This is important in the determination of the probability of failure, Pf. The `n' in the data table is the total number of specimens tested for a given condition (it should normally be 20). Record the load to failure in Kgf and then convert it to (N) by multiplying by 9.81.

2. Calculate δ in Pa (or Mpa = 106 Pa) by using:

δ =3

2 PL

wt2

Where w = width of slide, and t = thickness of slide

To simplify calculate the constant part of the formula first:

3

2 L

wt2= (all in meters)

3. Then calculate Ln (δ)

4. Calculate Pf (see Section 6.3 Weibull Statistics).

5. Calculate

ln ln 1

1− Pf

⎛ ⎝ ⎜ ⎞

⎠ ⎟ ⎛

⎝ ⎜

⎞ ⎠ ⎟

and make a linear plot of that quantity vs. Ln (δ). Determine the slope, m.



THE FRACTURE STRENGTH OF GLASS - DATA TABLE

LOAD (Kg)

i FORCE (N)

σf (MPa)

ln σf Pf = i

n + 1

1

(1 − Pf )

In{In(1/1-Pf)}

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20


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