# Alloys' Constituents Are Usually Measured by Masssteel Is a Metal Alloy Whose Major Component

Introduction

Alloy:

An alloy is a partial or complete solid solution of one or more elements in a metallic matrix. Complete solid solution alloys give single solid phase microstructure, while partial solutions give two or more phases that may be homogeneous in distribution depending on thermal (heat treatment) history. Alloys usually have different properties from those of the component elements.

Alloys' constituents are usually measured by massSteel is a metal alloy whose major component is iron, with carbon content between 0.02% and 2.14% by mass

Theory:

Alloying one metal with other metal(s) or non-metal(s) often enhances its properties. For example, steel is stronger than iron, its primary element. The physical properties, such as density, reactivity, Young's modulus, and electrical and thermal conductivity, of an alloy may not differ greatly from those of its elements, but engineering properties such as tensile strength[1] and shear strength may be substantially different from those of the constituent materials. This is sometimes due to the sizes of the atoms in the alloy, since larger atoms exert a compressive force on neighboring atoms, and smaller atoms exert a tensile force on their neighbors, helping the alloy resist deformation. Sometimes alloys may exhibit marked differences in behavior even when small amounts of one element occur. For example, impurities in semi-conducting ferromagnetic alloys lead to different properties, as first predicted by White, Hogan, Suhl, Tian Abrie and Nakamura.[2][3] Some alloys are made by melting and mixing two or more metals. Bronze, an alloy of copper and tin, was the first alloy discovered, during the prehistoric period now known as the bronze age; it was harder than pure copper and originally used to make tools and weapons, but was later superseded by metals and alloys with better properties. In later times bronze has been used for ornaments, bells, statues, and bearings. Brass is an alloy made from copper and zinc.

Unlike pure metals, most alloys do not have a single melting point, but a melting range in which the material is a mixture of solid and liquid phases. The temperature at which melting begins is called the solidus, and the temperature when melting is just complete is called the liquidus. However, for most alloys there is a particular proportion of constituents (in rare cases two) the eutectic mixture which gives the alloy a unique melting point

**Tensile Testing:**

Tensile test data have many uses. Tensile properties are used in selecting materials for various applications. And they are also used in research and development to compare new materials or processes. With plasticity theory, tensile stress-strain curve can be used to predict a material's behavior under forms of loading other than un-axial tension.

Often the primary concern is strength. The level of stress that causes appreciable plastic deformation of material is called its Yield stressσy. The maximum tensile stress that a material carries is called its ultimate stressσu. Both of these measures are used with appropriate caution, in engineering design.

Stress-strain Diagram:

Suppose that a metal specimen be placed in tension-compression-testing machine. As the axial load is gradually increased in increments, the total elongation over the gauge length is measured at each increment of the load and this is continued until failure of the specimen takes place. Knowing the original cross-sectional area and length of the specimen, the normal stress and the strain can be obtained. The graph of these quantities with the stress along the y-axis and the strain along the x-axis is called the stress-strain diagram. The **stress-strain diagram** differs in form for various materials. The diagram shown below is that for a medium-carbon structural steel. Metallic engineering materials are classified as either **ductile or brittle** materials. A ductile material is one having relatively large tensile strains up to the point of rupture like structural steel and aluminum, whereas brittle materials has a relatively small strain up to the point of rupture like cast iron and concrete. An arbitrary strain of 0.05 mm/mm is frequently taken as the dividing line between these two classes.

fig1: Stress-strain diagram of a medium-carbon structural steel

#### Proportional Limit (Hooke's Law):

From the origin O to the point called proportional limit, the stress-strain curve is a straight line. This linear relation between elongation and the axial force causing was first noticed by **Sir Robert Hooke** in 1678 and is called Hooke’s Law that within the proportional limit, the stress is directly proportional to strain or

or =k

The constant of proportionality k is called the **Modulus of Elasticity E or Young’s Modulus** and is equal to the slope of the stress-strain diagram from O to P. Then

=E

#### Elastic Limit:

The elastic limit is the limit beyond which the material will no longer go back to its original shape when the load is removed, or it is the maximum stress that may e developed such that there is no permanent or residual deformation when the load is entirely removed.

#### Elastic and Plastic Ranges:

The region in stress-strain diagram from O to P is called the elastic range. The region from P to R is called the plastic range.

#### Yield Point:

Yield point is the point at which the material will have an appreciable elongation or yielding without any increase in load.

#### Ultimate Strength:

The maximum ordinate in the stress-strain diagram is the ultimate strength or tensile strength.

#### Rapture Strength:

Rapture strength is the strength of the material at rupture. This is also known as the breaking strength.

#### Modulus of Resilience:

Modulus of resilience is the work done on a unit volume of material as the force is gradually increased from O to P, in N⋅m/m3. This may be calculated as the area under the stress-strain curve from the origin O to up to the elastic limit E (the shaded area in the figure). The resilience of the material is its ability to absorb energy without creating a permanent distortion.

#### Modulus of Toughness:

Modulus of toughness is the work done on a unit volume of material as the force is gradually increased from O to R, in N⋅m/m3. This may be calculated as the area under the entire stress-strain curve (from O to R). The toughness of a material is its ability to absorb energy without causing it to break.

#### Working Stress, Allowable Stress, and Factor of Safety:

Working stress is defined as the actual stress of a material under a given loading. The maximum safe stress that a material can carry is termed as the allowable stress. The allowable stress should be limited to values not exceeding the proportional limit. However, since proportional limit is difficult to determine accurately, the allowable tress is taken as either the yield point or ultimate strength divided by a factor of safety. The ratio of this strength (ultimate or yield strength) to allowable strength is called the factor of safety.

**Engineering” Stress-Strain Curves:**

Perhaps the most important test of a material’s mechanical response is the tensile test1, in which one end of a rod or wire specimen is clamped in a loading frame and the other subjected to a controlled displacement δ (see Fig. 2). A transducer connected in series with the specimen provides an electronic reading of the load P(δ) corresponding to the displacement. Alternatively, modern servo-controlled testing machines permit using load rather than displacement as the controlled variable, in which case the displacement δ(P) would be monitored as a function of load.

The engineering measures of stress and strain, denoted in this module as σe and ɛe respectively, are determined from the measured the load and deflection using the original specimen cross-sectional area A0 and length L0 as

σe =P/A0

ɛe =δ/L0

When the stress σe is plotted against the strain εe, fig2 the modulus of elasticity or Young’s modulus, denoted E

σe = Eɛe

in Fig. 2, in which a line of slope E is drawn from the strain axis at ɛe = 0.2%; this is the unloading line that would result in the specified permanent strain. The stress at the point of intersection with the σe- ɛe curve is the offset yield stress

Figure 3: Full engineering stress-strain curve for annealed polycrystalline copper.

In Figure 3 shows the engineering stress-strain curve for copper with an enlarged scale, now showing strains from zero up to specimen fracture. Here it appears that the rate of strain hardening2 diminishes up to a point labeled UTS, for Ultimate Tensile Strength (denoted σf in these modules). Beyond that point, the material appears to strain soften, so that each increment of additional strain requires a smaller stress.

**True” Stress-Strain Curve:**

Using the true stress σt = P/A rather than the engineering stress σe = P/A0 can give a more direct measure of the material’s response in the plastic flow range.

A measure of strain often used in conjunction with the true stress takes the increment of strain to be the incremental increase in displacement dL divided by the current length L:

This is called the “true” or “logarithmic” strain. During yield and the plastic-flow regime following yield, the material flows with negligible change in volume; increases in length are offset by decreases in cross-sectional area. Prior to necking, when the strain is still uniform along the specimen length, this volume constraint can be written:

L/L0=A/A0

The ratio L/L0 is the extension ratio, denoted as λ. Using these relations, it is easy to develop relations between true and engineering measures of tensile stress and strain;

σt = σe (1 +ɛe)

These equations can be used to derive the true stress-strain curve from the engineering curve, up to the strain at which necking begins.

Fig. (4)

Figure 4 Comparison of engineering and true stress-strain curves for copper. An arrow indicates the position on the “true” curve of the UTS on the engineering curve

Figure 5: Power-law representation of the plastic stress-strain relation for copper.

Strain energy:

The area under the σe−ɛe curve up to a given value of strain is the total mechanical energy per unit volume consumed by the material in straining it to that value. This is easily shown in Fig. (6).

**Modulus of Resilience:**

Resilience is the property of a material to absorb energy when it is deformed elastically and then, upon unloading to have this energy recovered. In other words, it is the maximum energy per unit volume that can be elastically stored. It is represented by the area under the curve in the elastic region in the stress-strain curve.

**Modulus of Toughness:**

Modulus of toughness is the work done on a unit volume of material as the force is gradually increased from O to R, in N⋅m/m3. This may be calculated as the area under the entire stress-strain curve (from O to R). The toughness of a material is its ability to absorb energy without causing it to break

Fig. (7) Resilience and Toughness Moduli

In the elastic range, these areas are equal and no net energy is absorbed. But if the material is loaded into the plastic range as shown in Fig. The energy absorbed exceeds the energy released and the difference is dissipated as heat.

Procedure

1- Measure the length and diameter of the sample and then fix the sample to the device Measure the diameter and length again after fixing the sample.

2- Edit the test program to suite your experiment.

3- Run the test and transfer data to any graphic program like Excel or origin.

4- Using the graphic program features draw the Engineering Stress-Strain Curve and calculate Young’s modulus Y, Yield stress **σy, Ultimate Stress σu, Fracture stress σf** and the Maximum strain (ductility) εmax.

5- Plot the relation between True strain and True Stress.

6- Sketch the ln εt and ln σt and calculate both n and A.

References:

· Tensile testing,second edition J.R. Pavis & Associates.2004

· Mechanical properties of ductile materials by the tension test

· . Boyer, H.F., Atlas of Stress-Strain Curves, ASM International, Metals Park, Ohio, 1987.

· Courtney, T.H., Mechanical Behavior of Materials, McGraw-Hill, New York, 1990..

· Hayden;H.W., W.G. Moffatt and J. Wulff, The Structure and Properties of Materials:

Vol. III Mechanical Behavior, Wiley, New York, 1965

· Wikipedia, the free encyclopedia.