PART A - MATERIAL PROPERTIES IN UNIAXIAL TENSION
Objective
To demonstrate the behaviour of brittle and ductile materials in uniaxial tension.
Introduction to the Tension Test
The term tension test is usually taken to refer to a test in which a prepared
specimen is subjected to gradually increasing (i.e. "static") uniaxial load until failure
occurs. In a simple tension test, the operation is accomplished by gripping opposite ends
of the specimen and pulling it apart. The test specimen elongates in a direction parallel
to the applied load.
The specimens are typically cylindrical or prismatic in form and of approximately
constant cross section over the length within which measurements of extension are made.
Within the limits of practicability, the resultant of the load coincides with the longitudinal
axis of the specimen. Thus (with certain exceptions), an attempt is made to obtain a
uniform distribution of direct stress over cross sections normal to the direction of the load.
The static tension test is one of the most commonly performed and simplest of all
the mechanical tests. Static compression tests are also simple and easy to perform for
many materials. Which test is most appropriate is largely determined by the nature of the
material in terms of brittleness or ductility and by the type of service to which the material
is subjected. For example, steel generally exhibits relatively high ductility and is therefore
one of the best materials for resisting tensile loads.
Brittle materials such as cast iron, concrete and mortar, which have low tensile
strengths compared with their compressive strengths, are principally employed to resist
compressive forces, so compression tests are more important.
Wood is an example of a material where both tensile and compressive strengths
are relatively high, but it cannot always be effectively utilized in structural members
because of low shear strength which causes failure before the full tensile resistance of
the member can be developed. With this material the choice between tension or
compression tests is more difficult. The compression test is usually considered of greater
practical significance than the tension test, and it is also easier to perform.
 

 

The Stress-Strain Diagram:
It is often necessary to relate the loads on a structure, or on a member in a
structure, to the deflection which the loads produce. Such information can be obtained
by plotting diagrams showing loads and deflections for each member and the type of
loading in a structure, but such diagrams vary with the dimensions of the loaded member.
By plotting the load per unit cross-sectional area (stress) against the elongation
per unit length (strain), the behaviour of each specimen may be represented on a "stress-
strain diagram" which has the great advantage that the plotted quantities are essentially
independent of the size and shape of the specimen.
The stress-strain diagram for a particular material is found to be a reproducible
relationship that is characteristic of that material. It is therefore possible to describe, both
qualitatively and quantitatively, the differences in behaviour between materials subjected
to tension by comparing their stress-strain diagrams.
The Modulus of Elasticity:
The slope of the linear portion of the stress-strain diagram is the modulus of
elasticity, E.
Therefore: E  = tan ? = ??? / ??          Equation (1)
Where,
E = modulus of elasticity, MPa
??= stress, MPa
?? = strain
Stress is a defined concept and is not directly measurable. Consequently,
experimental determination of the stresses in a complex structural member ordinarily
requires measurement of the strain and subsequent calculation of the stress from Hooke's
Law. For uniaxial stress, Hooke's Law is simply a revised form of equation (1):??
??
?? = E?                                Equation (2)
??
From the form of this equation, it is obvious that the percentage error in s will be
the same as the error in E. Therefore, accurate values of the elastic modulus for structural
materials are of considerable importance to engineers.
Apparatus
Tinius Olsen testing machine consisting of
(a) Loading Unit
The loading unit is a universal hydraulic testing machine with a load capacity
of 600kN, capable of performing static tension, compression, and transverse
tests on prepared test specimens. A built-in servo control provides continuous
feedback signals for precision control testing.
(b) Data System
The data system is on personal computer with related components that can be
programmed to control tests and record data. Load-deformation or stress-
strain curves can be generated on the display screen.
Load-deformation information is obtained with the aid of an extensometer,
which consists of a main frame complete with knife-edge measuring points, a
linear variable differential transformer (LVDT), and a spring clamping device for
attaching the extensometer to round or rectangular specimens.
Summary of Objectives and Methods:

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Procedure
During the laboratory period, two materials will be tested with a Tinius-Olson
Tension Test Apparatus. One material will be cast-iron and the other mild steel. The
amount of elongation will be measured by the extensometer. Observe the generation of
a continuous load-deformation relationship as each specimen is loaded and note
differences in the failure of the two materials. You will be provided with a graph for each
type of material where the y-axis is Load (kN) and the x-axis is elongation (mm).
The results recorded refer only to these particular specimens and, in the absence
of reliable data from other sources, it would be necessary to test additional specimens
before one could safely conclude that the results were an accurate measure of the
performance of the material.
The particular aspects of interest are those which tell us how close the material
comes to some idealization of its properties which may be used in design calculations of
strength or deformation.
Discussion
From the plots obtained for mild steel and cast-iron specimens, re-label and
renumber the y and x axes to read stress and strain on the handout.
PLEASE NOTE: the original graph paper was 25cm on the y-axis but has
been reduced to fit standard letter size paper.
Mild Steel:
I. The initial y-axis full scale is 0-300kN.
a. Convert the y-axis to stress by dividing the load by the cross
sectional area of the specimen.
b. Re-label the axis as stress with appropriate units (MPa).
c. Renumber the axis with the values as stress. Label every
second centimetre of chart paper within the elastic range.
II. The x-axis is elongation in 0.05mm increments per centimetre of
chart paper.
a. Convert the x-axis to strain by dividing each increment by the
Gauge Length (50mm)
b. Re-label the axis as strain.
c. Renumber the axis with the values as strain. Label only the
elastic range.
Cast Iron:
I. The initial y-axis full scale is 0-150kN.
a. Convert the y-axis to stress by dividing the load by the cross-
sectional area of the specimen.
b. Re-label the axis as stress with appropriate units (MPa)
c. Renumber the axis with the values as stress in the elastic
range.
II. The x-axis is elongation in 0.05mm per centimetre of chart paper.
a. Convert the x-axis by dividing each increment by the Gauge
Length (50mm)
b. Re-label the axis as strain.
c. Renumber the axis with the values as strain in the elastic
range.
1) Does each material obey Hooke's Law? If so, at what stage of loading does it
cease to obey Hooke's Law?
2) Calculate E for both materials, please show calculations
3) In which manner does each material fail (ductile or a brittle) and describe the
failure?
4) Does each material exhibit a "yield plateau"? Explain.
 

Image transcription text

2 28.72 152.48 3#14.96 Theit 0. 007 300 KN RANGE 0. 00 3 0.064 0. 005 0.00 6 YIELD POINT MILD STEEL 0.008 0. 009 0.01 YIELD
PLATEAU 0.017 0.012 T.SCSI 50 KN RANGE 0.001 FOO O - Ww OS / wwgo'0 - NIHALS 0.002 0.003 0.004 0. 005 CAST IRON 0.006 0-007
0.00 8