Strength of materials Lab 3- Bending Test PDF

Preview

Summary

Bending Test...

Description

Faculty of Engineering and Design 2310 – Strength of materials I Technical Report Formatting SECTION#1

Bending Test Universal Testing Machine

Made by: Farida Ashraf Wafik ID number: 0321141

1|P age

Abstract lskdnskdnaskdnskdnskadnandaskdnaskdaskdnaskldnaskdnaskdnskdnksdnskndaklsdn Bend testing, sometimes called flexure testing or transverse beam testing, measures the behavior of materials subjected to simple beam loading. If a piece of material is subjected to forces which induce compression stress over one part of a cross section of the material and tension stress on the remaining part, the piece is known to be in a bending condition. It is commonly performed on relatively flexible materials such as polymers, wood, and composites. At its most basic level a bend test is performed on a universal testing machine by placing a specimen on two support anvils and bending it through applied force on 1 or 2 loading anvils in order to measure its properties. The test specimens are loaded in a way that creates a concave surface at the midpoint with a specified radius of curvature according to the standard in relation to which the test is performed. A bending test is carried out to ensure that a material has sufficient ductility to stand bending without fracturing. A standard specimen is bent through a specified arc and in the case of strip, the direction of grain flow is noted and whether the bend is with or across the grain. In this experiment, a bending test is done to evaluate the specimens’ (aluminum and copper) mechanical properties such as modulus of rupture, modulus of elasticity and stiffness. (1)

2|P age

Table of cont contents: ents:

Table of contents: ......................................................................................................................................... 3 List of figures: ................................................................................................................................................ 4 Nomenclature: .............................................................................................................................................. 5 Introduction: ................................................................................................................................................. 6 Objectives: .................................................................................................................................................... 7 Specimen:...................................................................................................................................................... 7 Theory: .......................................................................................................................................................... 9 Description of the machine:........................................................................................................................ 11 .................................................................................................................................................................... 11 .................................................................................................................................................................... 11 .................................................................................................................................................................... 11 .................................................................................................................................................................... 11 .................................................................................................................................................................... 11 .................................................................................................................................................................... 11 Procedures: ................................................................................................................................................. 12 Results and calculations: ............................................................................................................................. 13 Conclusions and Recommendations: .......................................................................................................... 16 References: .................................................................................................................................................17

3|P age

List of ffigures: igures: Figure 1: Bending test ................................................................................................................................... 6 Figure 2: aluminum bending ......................................................................................................................... 7 Figure 3: aluminum bending (zoomed in) ..................................................................................................... 7 Figure 4: copper bending .............................................................................................................................. 8 Figure 5: copper specimen............................................................................................................................ 8 Figure 6: modulus of rupture ........................................................................................................................ 9 Figure 7: bending test ................................................................................................................................. 11 Figure 8: Universal testing machine............................................................................................................ 11 Figure 9: vernier caliper .............................................................................................................................. 12 Figure 10: aluminum bending graph ........................................................................................................... 13 Figure 11: copper bending graph................................................................................................................ 14 Figure 12: aluminum tensile graph ............................................................................................................. 15 Figure 13: aluminum vs copper...................................................................................................................15

Equation 1 ..................................................................................................................................................... 9 Equation 2 ..................................................................................................................................................... 9 Equation 3 ..................................................................................................................................................... 9 Equation 4 ..................................................................................................................................................... 9 Equation 5 ..................................................................................................................................................... 9 Equation 6 ..................................................................................................................................................... 9 Equation 7 ................................................................................................................................................... 10 Equation 8 ................................................................................................................................................... 10 Equation 9 ................................................................................................................................................... 10 Equation 10 ................................................................................................................................................. 10 Equation 11 ................................................................................................................................................. 10 Equation 12 ................................................................................................................................................. 10 Equation 13 ................................................................................................................................................. 11

Table 1........................................................................................................................................................... 5

4|P age

Nomenclatu Nomenclature: re: Quantity Stress Pressure Force Bending moment Cross-sectional area Strain Extension diameter deflection load Initial area Final area Modulus of elasticity Initial length Final length Fracture stress Ultimate stress Yield Stress Moment of Inertia Base

Symbol σ P F M A

𝜀 k d

𝛿 L

𝐴𝑜 𝐴𝑓 E 𝐿𝑜 𝐿𝑓 𝜎𝑓 𝜎𝑈 𝜎𝑌 I b Table 1

5|P age

Unit pascal pascal newton Newton per millimetre square metres millimetres millimetres millimetres newton square metres Square metres

Symbol MPa Pa N N/mm

gigapascal

GPa

millimetres millimetres

mm mm

Megapascal

MPa

Megapascal Megapascal Double square millimetres millimetres

MPa MPa mm4

m2 mm mm mm N m2 m2

mm

Introduction Introduction:: Engineers often want to understand various aspects of material’s behavior, but a simple uniaxial tension or compression test may not provide all necessary information. As the specimen bends or flexes, it is subjected to a complex combination of forces including tension, compression, and shear. For this reason, bend testing is commonly used to evaluate the reaction of materials to realistic loading situations. Flexural test data can be particularly useful when a material is to be used as a support structure. For example, a plastic chair needs to give support in many directions. While the legs are in compression when in use, the seat will need to withstand flexural forces applied from the person seated. Not only do manufacturers want to provide a product that can hold expected loads, but the material also needs to return to its original shape if any bending occurs. One of the more popular uses of bend testing is in the area of welds. The purpose of bend testing welds is to make sure that the weld has properly fused to the parent metal and that the weld itself does not contain any defects that may cause it to fail when it experiences bending stresses. The sample weld is deformed using a guided bend test so that it forms a “U” subjecting the material on the outer surface to a tensile force and the material on the inside to a compressive force. If the weld holds and shows no sign of fracture it has passed the test and is deemed an acceptable weld. (6)

Figure 1: Bending test

6|P age

Objective Objectives: s: • • • • • • •

To investigate the relationship between load, span, width, height, and deflection of a beam, placed on two bears affected by a concentrated load at the center To ascertain the coefficient of elasticity aluminum and copper To determine mechanical properties of aluminum specimen Compare between bending and tension Study stress contribution on cross-sectional area To know the effect of length or cross-sectional area on stiffness Study the ductility of structural steel by cold bending test.

Specim Specimen: en: 1. Aluminum specimen Aluminum is ductile and has a low melting point and density. It can be processed in several ways in a molten condition. Its ductility allows aluminum products to be formed close to the end of the product's design. Ductility is the ability of a material to be drawn or plastically deformed without fracture. It is therefore an indication of how ‘soft’ or malleable the material is. aluminum is resistant to corrosion and oxidation. Aluminum is very malleable, meaning it is easy to bend, so it is an unsuitable direct replacement for steel. Aluminum alloys harden and become stronger during the bending process. As a result, thickness and bend radius are factors that need to be considered. (5)

Figure 2: aluminum bending

Figure 3: aluminum bending (zoomed in)

The sample exhibits bending without fracturing, since there was no room inside the machine for the sample to deform before it breaks, this property indicates that the sample is ductile, so it absorbs the stress first until it cracks from the force being applied and the specimen 's form changed from a straight specimen to an arc like shape due to cold bending. 7|P age

2. Copper specimen It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkish-orange color. Copper is soft. It bends easily. Unlike aluminum, it doesn’t “spring” back. Worked by hands lacking sufficient experience and expertise, copper is easily overbent and ruined. Because of its exceptional Figure 5: copper specimen Figure 4: copper bending formability, copper can be formed as desired at the job site. Copper tube, properly bent, will not collapse on the outside of the bend, and will not buckle on the inside of the bend. (2)

8|P age

Theory: •

Stress: The ratio of load to the initial area 𝜎=

𝑃 𝐴𝑜

Equation 1

•

Strain: The ratio of deflection to the initial length 𝜀=

𝛿 𝐿𝑜

Equation 2

• Modulus of Elasticity: Is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it. The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region: A stiffer material will have a higher elastic modulus. 𝐸=

𝜎 𝜀

Equation 3

•

Modulus of Rupture: Flexural strength, also known as modulus of rupture, or bend strength, or transverse rupture strength is a material property, defined as the stress in a material just before it yields in a flexure test. σr = 3Fx / yz2 Equation 4

αx = (Y/C) αm Equation 5

αm = MC/I Equation 6

9|P age

Figure 6: modulus of rupture

αx = Mx/I Equation 7

•

Stiffness: is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. Stiffness= Modulus of elasticity x Moment of inertia Equation 8

•

Moment of Inertia: The moment of inertia, otherwise known as the mass moment of inertia, angular mass or rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration. (3) Moment of Inertia= Angular moment/ Angular velocity Equation 9

Ix = (bh^3)/12 Equation 10

Iy= (b^3h)/12 Equation 11

If a beam is simply supported at the ends and carries a concentrated load at the center, the beam bends concave upwards. The distance between the original position of the beam and its position after bending is different at different points along the length if the beam, being maximum at the center in this case. This difference is called ‘deflection’. In this type of loading the maximum amount of deflection (δ) is given by the relation. In this type of loading the maximum amount of deflection ( δ ) is given by the relation, δ = Wl3/48EI Equation 12

10 | P a g e

As per bending equation,

𝑴 𝝈 = 𝒀 𝑰 Equation 13

Figure 7: bending test

Descript Description ion of the machine: Load Frame

Cross Head Conditioning

Output Device

Test Fixtures

Figure 8: Universal testing machine

The testing machine is hydraulically operated with 400 kN maximum, the machine also allows the performance of compression and bending tests. The load is measured by the load cell and displayed on a dial and a digital display. The displacement of the lower 11 | P a g e

head is transmitted by the cord to the recording drum which is rotated with a cord slung around it. Afterwards, a pen fixed at that point draws a graph in a circumferential direction of the drum which is equivalent to the graph of force against elongation of the length of the specimen. Once the machine is started it begins to apply an increasing load on specimen. Throughout the tests the control system and its associated software record the load and extension or compression of the specimen. (4)

Figure 9: vernier caliper

A vernier caliper is a visual aid to take an accurate measurement reading between two graduation markings on a linear scale by using mechanical interpolation; thereby increasing resolution and reducing measurement uncertainty by using vernier acuity to reduce human estimation error. It has an accurate scale of 0.01 mm.

Procedures Procedures:: 1. By use of a vernier caliper, the thickness and width of each sample of aluminum and copper were measured. 2. This bend testing is carried out using a universal testing machine; adjust the supports along the UTM bed by drawing a 3 cm clearness line from the right and from the left to align it with the supporters, then adjusting the specimen between the cross heads so that they are symmetrical with respect to the length of the bed. 3. Place the beam on the two blocks so as to project equally beyond each block from each end. Check if the load is applied at the center of the beam. 4. Measure the initial reading of the distance between a fixed part on the machine above the specimen and the upper edge of the beam specimen, in order to calculate the total final deflection after fracture. 5. Apply the load up to fracture. 12 | P a g e

6. After fracture, record the final readings of both copper and aluminum using a vernier caliper

Results and calculations: Regarding the aluminum specimen,

Aluminum Bending Test 2.5

Young’s Modulus =

2

Force

(0.949-0.5480)/ (470.582 259.659) = 0.00190 GPa

1.5

1 0.5

Bend Depth

0 0

Moment of Inertia: 3

Figure 10: aluminum bending graph 2

Ix= (3*(18) )/12 = 1458 KN.cm

Stiffness: Young’s Modulus * Moment of Inertia = 1458*0.00190 = 2.7702 KN/cm

modulus of rupture: αx = Mx/I = 23676.8/1458 =16 KN/mm3

13 | P a g e

200

400

600

800

1000

1200

Regarding the copper specimen,

Copper bending test

Young’s Modulus = (9.944-5.39) / (4707.242-2628.881) = 0.00219 GPa

Moment of Inertia: Ix= (3*(18)3)/12 = 1458 KN.cm2

Figure 11: copper bending graph

Stiffness: = Young’s Modulus * Moment of Inertia = 1458*0.00219 = 3.19302 KN/cm

modulus of rupture: αx = Mx/I = 1039400/1458 =712.9 KL/mm3

14 | P a g e

Load

Aluminum Tension Test 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 0

2

4

6

8

10

Deflection Figure 12: aluminum tensile graph

• Concerning bending, the specimen only had room to move by Yield power.But to achieve its ultimate tensile strength and fracture strength, there was not enough room. •

Con...