SOM Lab Manual - Modified PDF

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I am poor in the strength of materials...

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STRENGTH OF MATERIALS

LAB MANUAL

Department of Mechanical Engineering

List of Experiments: S. No

Name of the experiment

Page Number

1

The tension test

1

2

The compression test

6

3

Poisson’s ratio test

9

4

Hardness test

12

5

Estimation of Moment of Inertia of a simply supported beam

17

6

Estimation of Moment of Inertia of a cantilever beam

19

7

Deflection test on simply supported and cantilever beams

21

8

Impact strength test

24

9

Buckling test

27

10

Fatigue test

30

11 12 13

Wear Strength test Spring compression test VIVA Questions Appendix – Hardness conversion tables

36 39 41

14

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Associated ASTM standards ASTM D638- Plastic, ASTM D575-Rubber, ASTM D4761- Wood, ASTM B209M Aluminium. Concrete, masonry, ASTM D575-Rubber. ASTM D6641-polymer matrix composite. ASTM D4761- Wood. ASTM D575-Rubber, ASTM D4761- Wood, ASTM A276- Stainless steel. ASTM B152 –Copper, ASTM A276- Stainless steel, ASTM B209M-Aluminium, ASTM A295High carbon steel, ASTM A36 - Mild steel, ASTM B927-Brass & Hardness conversion charts Cylindrical, Rectangular, Hollow Cylindrical, Hollow Rectangular, ASTM A276- Stainless steel Cylindrical, Rectangular, Hollow Cylindrical, Hollow Rectangular ASTM B209M-Aluminium, ASTM A295-High carbon steel, ASTM A36Mild steel ASTM D7565-Composites ASTM D256- Izod Test, ASTM E23, ASTM A370- Charpy Test. ASTM A591-Light Weight steel, ASTM B209M-Aluminium Structures. Circular Notched and Rectangular bars, ASTM A276-Stainless steels ASTM F1108-Titanium alloys ASTM A53 –Carbon alloy steels ---

1. THE TENSION TEST AIM: The main objective of this experiment is to;  Perform an ASTM standard tensile test.  Collect load vs. elongation data, plot engineering stress vs. engineering strain, determine the modulus of elasticity, 0.2% offset yield strength, ultimate tensile strength, ductility, resilience, and toughness.  Plot true stress Vs. true strain curve and obtaining a relation between them.  Study the fracture mechanics of broken tensile surface. EQUIPMENT: 1. Universal Testing Machine 2. ASTM standard specimen 3. Vernier caliper/micrometer ASTM E8M STANDARD TENSILE SPECIMEN (ROUND):

Fig.1: Tensile Specimen G = Gage length = 62.5 mm ± 0.1 mm D= Diameter = 12.5 mm ± 0.2 mm R = Fillet radius = 10 mm A = Length of Reduced section =75 mm Length of grip = about 100 mm (this can vary slightly) Overall length of specimen = about 300mm (this can vary slightly)

THEORY : Various machine and structure components are subjected to tensile loading in numerous applications. For safe design of these components, their ultimate tensile strength and ductility is to be determined before their actual use. Tensile test can be conducted on Universal Testing Machine (UTM). A material when subjected to a tensile load resists the applied load by developing internal resisting force. These resistances come due to atomic bonding between atoms of the material. The resisting force for unit normal cross-section area is known as stress.

1

Fig. 2: Typical Engineering Stress-Strain Diagram for Ductile Material 1. Elastic limit: It is the maximum stress within which there is no suitable amount of permanent strain remains inside the material. 2. Proportional limit: It is the greatest stress up to which the stress is directly proportional to strain. It is the stress at which there is a deviation of stress-strain curve from linearity. 3. Yield strength: It is the stress required to produce a small specified amount of plastic deformation. Offset yield strength: In many materials, the yield stress is not very well defined and for this reason a standard has been developed to determine its value. The standard procedure is to project a line parallel to the initial elastic region starting at a strain of 0.2 percent offset (engineering strain e =0.002). The intersection of this new line with the stress-strain curve then defines the yield strength. So= Py/Ao, Py = Load corresponding to offset 4. Ductility: Deformation of a material under tension. Ease in wire drawing operation. Mathematically ductility defines as; Elongation at fracture, ef = (Lf – Lo)/Lo Reduction of area at fracture, Ar = (Ao – Af)/Ao 5. Tensile strength or Ultimate tensile strength (UTS): It is the maximum stress in the stress-strain curve of a tensile specimen. It is obtained in dividing the maximum load by the original cross-sectional area. UTS: Su = Pmax/ Ao 6. Modulus of elasticity or Young’s modulus of elasticity (E): It is the slope of initial linear portion of the stress-strain curve. Modulus of elasticity is the measure of stiffness of the material. E = stress/strain

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Fracture at broken surface of the tensile specimen:

Fig. 3: Different tensile fracture In brittle fracture, no apparent plastic deformation takes place before fracture. In brittle crystalline materials, fracture can occur by cleavage as the result of tensile stress acting normal to crystallographic planes. In ductile fracture, extensive plastic deformation (necking) takes place before fracture. The terms rupture or ductile rupture describes the ultimate failure of tough ductile materials loaded in tension. Rather than cracking, the material "pulls apart," generally leaving a rough surface. In this case there is slow propagation and absorption of large amount energy before fracture.

Fig.4: Schematic Representation of the Steps in Ductile Fracture (Pure Tension) Many ductile metals, especially materials with high purity, can sustain very large deformation of 50–100% or more strain before fracture under favorable loading condition and environmental condition. UNIVERSAL TESTING MACHINE (UTM) & ITS SPECIFICATIONS: The tensile test is conducted on UTM. It is hydraulically operates a pump, oil in oil sump, load dial indicator and central buttons. The left has upper, middle and lower cross heads i.e.; specimen grips (or jaws). Idle cross head can be moved up and down for adjustment. The pipes connecting the lift and right parts are oil pipes through which the pumped oil under pressure flows on left parts to more the cross-heads. PROCEDURE: 3

1. The load pointer is set at zero by adjusting the initial setting knob. 2. Measuring the diameter of the test piece by Vernier caliper at least at three places and determine the mean value also mark the gauge length. 3. Now the specimen is gripped between upper and middle cross head jaws of the m/c. 4. Set the automatic graph recording system. 5. Start the m/c and take the reading. 6. The specimen is loaded gradually and the elongation is noted until the specimen breaks. OBSEVATIONS: i. ii. iii. iv. v. vi. vi. vii. viii.

Initial diameter of specimen d1 = Initial gauge length of specimen L1 = Initial cross-section area of specimen A1 = Load of yield point Py = Ultimate tensile load Pmax= Ultimate load after specimen breaking P = Final gauge length after specimen breaking L2 = Dia. of specimen at breaking place d2 = Cross section area at breaking place A2 =

_____ _____ _____ _____ _____ _____ _____ _____ _____

TABLE:1 Load

Load Points

Elongation

Load

1

Elongation 2

Load

Elongation 3

Elastic limit Proportional limit Yield strength Ultimate Strength Failure Point

OBSERVATIONS: The primary output from a tensile test is the load vs. elongation (change in length) curve of the specimen, which is recorded in real-time using a load cell and an extensometer. This curve is then used to determine two types of stress-strain curves:  Engineering stress-strain.  True stress-strain Calculate the following from engineering stress-strain curve; (i) (ii) (iii)

Ultimate tensile strength = Percentage elongation % at fracture= % reduction in area at fracture = 4

_____ _____ _____

(iv) Resilience = _____ (v) Yield stress = _____ (vi) Modulus of elasticity = _____ (vii) Toughness = _____ Also calculate ‘n’ and ‘K’ value from true stress-strain plot using power law. CONCLUSIONS: 1. Yield point elongation is observed (write if you have observed) 2. Mechanical properties have been determined. PRECAUTIONS: 1. 2. 3. 4.

The specimen should be prepared in proper dimensions. The specimen should be properly to get between the jaws. Take reading carefully. After breaking specimen stop to m/c.

5

2. THE COMPRESSION TEST AIM:  To perform compression test on a given ASTM standard specimen on UTM.  To collect the load vs. contraction data and draw the engineering stress-strain and true stress-strain curves for the specimen.  To calculate the young’s modulus, ductility, yield strength and ultimate compressive strength from engineering stress-strain curve for the specimen.  To compare the tensile and compressive properties of the specimen. EQUIPMENT: 1. 2. 3. 4. 5.

UTM or Compression testing machine Cylindrical or cube shaped specimen of cast iron/mild steel Vernier caliper Linear scale Dial gauge (or Compressometer)

THEORY: Several machine and structure components such as columns and struts are subjected to compressive loads in their applications. These components are made of high compressive strength materials. Several materials, which are good in tension, are poor in compression. Contrary to this, many materials poor in tension but very strong in compression. Cast iron is one such example. That is why, determination of ultimate compressive strength is essential before using a material which is determined by conducting of a compression test. By definition, the ultimate compressive strength of a material is that value of uniaxial compressive stress reached when the material fails completely. Compression test is just opposite in nature to tensile test. Nature of deformation and fracture is quite different from that of tensile test. Compressive load tends to squeeze the specimen. During a typical compression test, data are collected regarding the applied load, resultant deformation or deflection, and condition of the specimen. For brittle materials, the compressive strength is relatively easy to obtain, showing marked failure. However, for ductile materials, the compressive strength is generally based on an arbitrary deformation value. Ductile materials do not exhibit sudden fractures that brittle materials present. They tend to buckle and "barrel out". Hence this test is generally performed on cast iron, cement, concrete etc. But ductile materials like aluminum and mild steel which are strong in tension are also tested in compression.

Fig. 1: Typical stress-strain diagram in a compression test

6

Fig. 2: Comparison of Stress-Strain Diagrams in Compression & Tension for CI TEST SET-UP, SPECIFICATION OF M/C AND SPECIMEN DETAILS: A compression test can be performed on UTM by keeping the test-piece on base block and moving down the central grip to apply load. It can also be performed on a compression testing machine. A compression testing machine has two compression plates/heads. The upper head moveable while the lower head is stationary. One of the two heads is equipped with a hemispherical bearing to obtain. Uniform distribution of load over the test-piece ends. A load gauge is fitted for recording the applied load. SPECIMEN:

In cylindrical specimen, it is essential to keep h/d ≤ 2 to avoid lateral instability due to bucking action. Specimen size = h ≤ 2d

Fig. 3: Standard Test Specimen PROCEDURE: 1. Dimension of test piece is measured at three different places along its height/length to determine the average cross-section area. 2. Ends of the specimen should be plane. 3. The specimen is placed centrally between the two compressions plates, such that the centre of moving head is vertically above the centre of specimen. 4. Load is applied on the specimen by moving the movable head. 5. The load and corresponding contraction are measured at different intervals. The load interval may be as 500 kg. Load is applied until the specimen fails. OBSERVATIONS: Initial height and diameter of specimen ‘h’ & ‘do’ = 7

TABULATION: S. No.

Applied load ‘P’ (N)

Recorded change in length, mm

CALCULATIONS: For compression test, we can  Draw stress-strain (σ-ε) curve in compression, (both engineering and true stressstrain),  Determine Young’s modulus in compression,  Determine ultimate (maximum) compressive strength, and  Determine percentage reduction in length (or height) of the specimen. PRECAUTIONS: 1. The specimen should be prepared in proper dimensions. 2. The specimen should be properly to get between the compression plates. 3. Take reading carefully. 4. After failed specimen, stop the m/c. RESULT: The compressive strength of given specimen = ______N/mm2 OBSERVATIONS:

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3. POISSON’S RATIO TEST AIM:  To evaluate the Poisson’s Ratio of the given beam by loading it as a cantilever.  To understand elastic constants and their relations. EQUIPMENT: Cantilever beam, weights, strain gauges or extensometer. THEORY: Poisson’s ratio, ν, of a material is defined as the ratio of transverse strain, εtran, to longitudinal strain, εlon, or:



 tran long

(1)

Fig.1 Cantilever beam along with position of strain gauges. Poisson’s Ratio is a material property and it is dimensionless. Suppose if two strain gauges positioned on a cantilever beam (as shown in Fig. 1). One is positioned on the top of the beam in the longitudinal or axial direction. The longitudinal gauge will provide the longitudinal strain reading as the beam deflects downward when a point load is applied. The other gauge is positioned on the bottom of the beam in the lateral, or transverse, direction and will provide the lateral strain reading. When a point load is applied on the top surface of the beam, top surface will elongate in the axial or longitudinal direction. The top surface will also contract in transverse or lateral direction. This phenomenon is known as Poisson’s effect. Likewise, the bottom surface will contract longitudinally and expand laterally. Quantitatively, the longitudinal elongation or contraction is much larger than the lateral contraction or expansion. Therefore, Poisson’s Ratio is a value less than one. Poisson’s Ratio is also a positive value since the longitudinal and lateral strain should be measured at the same point on the beam. For example, if measuring the strains on the top surface of the beam the longitudinal strain would be positive (beam elongates longitudinally) and the lateral strain would be negative (beam contracts laterally). Therefore, according to Eq. (1) these values result in a positive value of Poisson’s ratio. In this experiment it would be impossible to position both the longitudinal and the lateral strain gauges at the same point on the beam. Therefore, the longitudinal gauge is positioned on the top surface and the lateral gauge is positioned at the same location on the 9

bottom of the beam. Because of the unique positioning in this experiment, a negative sign is artificially added to the calculation of Poisson’s Ratio since both the longitudinal and lateral gauges will measure positive strain readings. Apart from using strain gauges, one may use extensometers to measure elongations or contractions and there by calculate corresponding longitudinal and transverse strains and there by Poisson’s ratio. The Poisson's ratio of a stable, isotropic, linear elastic material will be greater than −1.0 or less than 0.5 because of the requirement for Young's modulus, the shear modulus and bulk modulus to have positive values. Most materials have Poisson's ratio values ranging between 0.0 and 0.5. Poisson’s ratio for various materials is tabulated as follows: Material Rubber Indium Gold Lead Copper Aluminium Copper Polystyrene Brass Ice Polystyrene foam Stainless Steel Steel Tungsten Zinc Fused quartz Boron Beryllium Re-entrant foam

Poisson's ratio 0.48 - 0.5 0.45 0.42 0.44 0.37 0.34 0.35 0.34 0.33 0.33 0.3 0.3 0.29 0.3 0.25 0.17 0.08 0.03 -0.7

Table 1. Poisson’s ratio values of various materials Elastic constants & their relations: Young’s Modulus or Modulus of elasticity: It is the ratio between compressive stress and compressive strain or tensile stress and tensile strain. It is denoted by ‘E’. Its units are N/m2. E = stress/stain = σ/ε = σt/εt = σc/εc Modulus of Rigidity or Shear Modulus of Elasticity: It is the ratio of shear stress (τ) to shear strain (γ). It is represented by ‘G’ and its units are N/m2. G = τ/γ Bulk Modulus or Volume Modulus of elasticity: It is defined as the ratio of applied pressure (on each face of solid cube) to volumetric strain. It is represented by ‘K’. Its units are N/m2. K = p/εv Relation between E and G: E = 2G [1+ µ], relation between E and K: E = 3K (1-2µ) and relation between E, G and K: E=9KG/ (3K+G). 10

PROCEDURE: 1. Take a cantilever beam made with required material and attach strain gauges at required locations as shown in Fig.1 or extensometer if not working with strain gauges. 2. Apply point loads at the end of cantilever and make a note of longitudinal and transverse strain values or displacements if using extensometer. 3. Evaluate the value of Poisson’s ratio from longitudinal and transverse strains. 4. Repeat these steps for different materials. RESULT: Poisson’s ratio of the given material is: ___. OBSERVATIONS & CONCLUSIONS:

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4. HARDNESS TEST AIM:  To learn about principles and different methods of hardness measurement.  To learn about the correlations among different types of hardness measurement and correlations of hardness with tensile strength.  Performing micro Vickers hardness test. EQUIPMENT: Micro hardness tester (Vickers) and various test samples. THEORY: Hardness is generally considered as resistance to penetration. Harder the materials, greater the resistance to penetration. Hardness is directly related to the mechanical properties of the material. Factors influencing hardness include microstructure, grain size, strain hardening, etc. Generally as hardness increases yield strength and ultimate tensile strength (UTS) also increases, thus specifications often require the results of hardness tests rather than tensile tests. The most popular methods are Brinell, Vickers and Rockwell hardness tests for metals and alloys. All these hardness measurement techniques adopt static indentation method. Static indentation involves pressing a ball, diamond, or other types of indenter under a specified constant load into the surface of material and measuring the length, width, or depth of the indentation. Each hardness test method, or scale, is defined with a particular type of indenter, a specified minor load, and a specified major load. The measured indentation size is then converted to a hardness number specific to the scale adopted. In general harder the material, the better the resistance, and thus the smaller the indentation. In general, a material will scratch another material of lesser hardness. The Mohs scale is a semi-quantitative scale designed to take advantage of this fact. Ten minerals are numbered from one to ten in order of increasing hardness: 1. Talc, 2. Gypsum, 3. Calcite, 4. Fluorite, 5. Apatite, 6. Orthoclase, 7. Quartz, 8. Topaz, 9. Corundum, 10. Diamond. However, the hardness of these ten minerals is not regularly spaced. The numbers serve only to designate hardness relative to the hardness of a set of minerals. A substance that scratches quartz but not topaz, for example, has a Mohs hardness between 7 and 8. Since the Mohs testing does not provide sufficient accuracy, i...