OBJECTIVE To determine the value of flexural strength ( modulus (Ef) of materials.
), maximum flexural strain ( ) and flexural
INTRODUCTION This mechanical testing method measures the behaviour of materials subjected to simple bending loads. Like tensile modulus, flexural modulus (stiffness) is calculated from the slope of the bending load vs. deflection curve. Flexural testing involves the bending of a material, rather than pushing or pulling, to determine the relationship between bending stress and deflection. Flexural testing is commonly used on brittle materials such as ceramics, stone, masonry and glasses. It can also be used to examine the behaviour of materials which are intended to bend during their useful life, such as wire insulation and other elastomeric products The three point bending flexural test provides values for the modulus of elasticity in bending , flexural stress , flexural strain and the flexural stress-strain response of the material. The main advantage of a three point flexural test is the ease of the specimen preparation and testing. However, this method has also some disadvantages: the results of the testing method are sensitive to specimen and loading geometry and strain rate.
Flexural stress ( ) can be calculated on any point on the load deflection curve by using following equation 1. - (1) where; p L b d
: flexural stress (MPa) : the load at a given point on the load-deflection curve (N) : the length of the support span (mm) : width of the specimen (mm) : thickness of the specimen (mm)
Flexural strength ( ) is the maximum capability of a material to resist the plastic deformation. Equation 2 is used to calculate the value of flexural strength ( ). - (2) where; : flexural strength (MPa) Y : yield point which the load does not increase with an increase in strain (N) L : the length of the support span (mm) b : width of the specimen (mm) d : thickness of the specimen (mm) Flexural strain ( ) is nominal fractional change in the length of an element of the outer surface of the specimen at middle of span, where the maximum strain occurs. Equation 3 is used to calculate the value of flexural strain ( ). - (3) where; D L d
: flexural strain : maximum deflection of the centre of the beam (mm) : the length of the support span (mm) : thickness of the specimen (mm)
Modulus of Elasticity (MOE) is the ratio, within the elastic limit, of stress to corresponding strain. Equation 4 is used to calculate the value of Modulus of Elasticity (MOE).
- (4) where; m L b d
: modulus of elasticity (MPa) : slope of the tangent to the initial straight-line portion of the load deflection curve (N/mm) : the length of the support span (mm) : width of the specimen (mm) : thickness of the specimen (mm)
SPECIMEN AND EQUIPMENTS 1. Instron Series 8500 (5kN) 2. Vernier caliper 3. Test jig 4. Loading block 5. Flexural specimens
PROCEDURES 1) The thickness and width of the beam are measured. 2) The loading block is gripped and test jig in the upper and lower gripping head, respectively. 3) The specimen is located so that the upper surface is to the side and centered in loading assembly. 4) The machine is operated until the loading block was bought into contact with the upper surfaces of the specimen. Full contact between the load (and supporting) surfaces and the specimen is ensured to secure. 5) The required parameters are set on the control panel. 6) The load recorder is adjusted on the front panel controller to zero, to read load applied. 7) Start button is pressed to start the flexural test. 8) The specimen is observed, as the load was gradually applied. 9) The maximum load is recorded and loading is continued until complete failure.
Results 1. Show all the measurements of beams.
Beam length L [mm]
Beam width
Beam thickness
Beam working length
Aluminium
150.04
24.92
2.06
70
Steel
150.00
24.94
1.96
70
2. Plot the load- deflection graph for the tested specimen.
Aluminium
Graph 1: load – deflection of aluminium
Steel
Graph 2: load – deflection of steel
3. Complete the table below. For Aluminium
Flexural strength Maximum flexural strain Flexural modulus Ef [GPa]
Experimental
Theory
13.688
613.636
0.169
8.074
69.099
76
For Steel
Flexural strength Maximum flexural strain Flexural modulus Ef [GPa]
Calculation
Experimental
Theory
9.469
451.963
0.169
0.458
56.034
207
DISCUSSIONS
1. Discuss on the shape of obtained load–deflection graph. The flexure test method measures behaviour of materials subjected to simple beam loading. This is calculated at the surface of the specimen on the convex or tension side. Flexural modulus is calculated from the slope of the stress vs. deflection curve. If the curve has no linear region, a secant line is fitted to the curve to determine slope.
According to the aluminium graph:-
C B
D
A
From 0 to 300 (N) “A to B” – the aluminium was elastic deformation From 300 to 510 (N) “B to C” – the aluminium was plastic deformation From 500 to 450 (N) “C to D” – the aluminium was strain hardening or it can call necking At point D = 450 (N) “D” – the aluminium was fracture
According to Steel Graph
C D B
A
From 0 to 250 (N) “A to B” – the steel was elastic deformation From 250 to 400 (N) “B to C” – the steel was plastic deformation From 400 to 380 (N) “C to D” – the steel was strain hardening or it can call necking At point D = 380 (N) “D” – the steel was fracture
2. What is the percentage error (%) between experiment results with the theory? Why? For aluminium the percentage was at 65 % to 70 % For steel the percentage was at 60 % to 75 % It is because the graph it makes from the parallel line and the theory we use the calculations
3. What is the critical application of the experiment in industry? Flexural testing is predominately used in industries where materials are subject to some form of bending force. The construction industry is a typical example in that the most common test for structural steels, concrete beams, timber joists, GRC panels, ceramic tiles etc is flexural testing. Flexural testing is also widely used to evaluate materials that can be difficult to test in tensile mode. This technique requires specialised fixtures and precision displacement measurement coupled with advanced flexural testing software. Test metric offer a comprehensive range of 3 and 4 point bend fixtures, displacement systems and dedicated software to suit all applicable materials.
Conclusions The system functions by using metal bending bars of varying thickness and stiffness to deform the test specimen. The force applied is measured by use of a built-in calibration and calculation system. Due to the large margin of error from the measured and calculated results, the experimental results are not acceptable for practical application. At maximum deflection, the percentage of error of the experimental result for aluminium is 65% - 70%. One cause for this error occurs because the equations used are a c c u r a t e i n s m a l l d e f l e c t i o n s a n d l o a d s e a s i l y h a n d l e d b y t h e m a t e r i a l t e s t e d . T h e p e r c e n t a g e e r r o r f o r s t e e l i s 60 % to 75 %. A l s o , Hooke's law is only valid for a portion of the elastic range for some materials, including aluminium.
References
Gilbert, J. A and C. L. Carmen. "Chapter 8 –Flexure Test." MAE/CE 370 – Mechanics of Materials Laboratory Manual. June 2000
Dowling, N.E., Mechanical behaviour of materials: Engineering methods for deformation, fracture and fatigue, 2nd edition, 1999, Prentice Hall, ISBN-0-13010989-4.
Hibbleler, R.C., Mechanics of Materials, SI second edition, 2005, Prentice Hall, ISBN 0-13-186-638-9.
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