Introduction
Bend (flexure) testing is often done in springs as well in brittle materials whose behaviors of failure are linear like concrete, wood, plastic, glass and ceramics. Bend testing is suitable for evaluating the strength of brittle materials where the results of tensile tests aren’t easy to interpret due to the breaking of specimens around the gripping (Schoffstall, Charles, and Robert 234). In bend testing experiment, smooth rectangular specimens without notches are recommended under three or four point bend arrangements. Figure I below illustrates three point and four point bend arrangements respectively.
Figure 1. Bend testing of a smooth rectangular bar a) three-point bend test; b) four-point bend test
Considering the three-point bend analysis of an elastic material, a load P is applied at the middle of a specimen on the x-y plane. The distribution of stress across the width of the specimen is demonstrated as shown in figure 1 a. at neutral axis N-N, the stress is essentially zero. Stresses on the y-axis in positive direction indicate tensile stresses while stresses in negative direction indicate compressive stresses. Brittle materials show a linear relationship between the load and deflection where there is yielding on the thin layer of the surface of the specimen at the middle. Crack initiation leads to the failure of the specimen. Ductile materials provide load versus deflection curves that deviate from a linear relationship just before failure occurs.
A three-point bend test is used in mechanics to determine the Young’s modulus of the material. A beam of length L rests on two roller supports and load P at the center. The deflection who at the midspan of the beam is represented as:
..1 where E represents the Young’s Modulus, I represents the second moment of area. I is defined as:
.2 Where a is the depth of the beam and b is the width.
Figure 2. Schematic diagram of a three point bend test with graphs of bending moment M, shear moment Q, and deflection w.
In a bend test, P is plotted against the central displacement (two) to yields a straight line with the elastic limit of the material is reached. After a deflection, the beam returns to its initial flat shape. The gradient of the linear relationship is: to obtain the gradient, a line of best fit is drawn to attain a linear relationship.
.3
The purpose of undertaking this lab experiment was aimed at achieving several objectives. Firstly, to study the principles of bend testing, practice testing skills and interpreting the results of the experiment of the materials. Secondly, to investigate the responses of materials when bending is subjected to them. Thirdly, to determine bend test parameters such as the bending strength, elastic modulus, and yield strength. Lastly, interpret the data form the bend test and select the best engineering materials for purposed use to avoid creep failures. In this lab, part I involved three-points bending test using a tensile testing machine by Instron. Part II of the lab involved bending a cantilever beams using a typical benchtop apparatus.
Procedure
The apparatus were arranged as shown in figure 3 below.
Figure 3. Three point diagram
All the dimensions needed to determine second moment, I of the beam and support distance, L on the Instron machine were measured. The rate of deformation of an Instron machine was set to 3 mm/minute and the beam mounted on the machine, the load cell was balanced, and the gauge length reset. The 3-point test was run until the beam ceased to be useful.
The apparatus used in this experiment included two-meter aluminum rules, two C-clamps, one short piece of wood clamping, and a spring scale.
One of the 36-inch meter rules was clamped to one corner of the workbench so that it overhung by 21 inches by the use a piece of wood and the two C-clamps. The c-clamp was made to spread a few inches away from the each other to ensure a firm clamp as shown in figure 4 below.
Figure 4
The ruler with initial pre-curvature deflected vertically under its weight, the position was recorded as the non-deflected position. The other rule was made to stand vertically on the lower end of the chair. The vertical position of the non-deflected ruler was measured at a point one inch from the free end.
The spring scale was used to load one end of the cantilever beam upwards. The load was applied at the same point where the vertical position of the non-deflected beam was measured. Four different values of the load were applied to get a reasonable range of deflections. The four different values of the loads and resulting deflections were recorded.
A vertical ruler was used to measure the deflected position of the load point. The above procedure was repeated using an effective ruler of 10-inch length.
Results
Cold rolled steel dimensions
a)
b)
Data analysis
Using the relationships;;
The value of P can be calculated where a = 6.37 mm, 0.00637 meters; b = 25.33 mm, 0.02533 meters; E = 207 GPa; L = 10 inches; 10*2.5/100=0.25 meters, maximum deflection, Ymax = 15 mm, 0.015 meters
The second moment of area is;
The load P will be given as;
A diagram of shear force, V, and bending moment of a three-point bend test is shown in the figure 5 a) and b) below.
Figure 5 a) shear force, V, for loading condition
Figure 5 b) bending moment, M, for loading condition
Maximum deflection is attained at 15 millimeters, maximum bending moment was.
Maximum deflection occurred at the middle of the beam; L/2 from each end.
The graphs of load, P against the deflection are shown below.
Graph 1. Vertical deflection versus vertical force (p) of 10-inch meter rule
Graph 2. Vertical deflection versus vertical force (p) of 21-inch meter rule
Discussion
The three-point bending tests were conducted with the Instron machine. The applied velocity of the bending load was 3 mm/min. Different stacking sequence laminate types were done. Load-displacement plots were attained for the test specimens. Four specimens were tested in the experiment. In this experiment, the results were plotted regarding the applied load against the center displacement of the specimen under test in the Instron machine. The four loading in two specimens produced two similar relationships when the vertical deflection was plotted against vertical force.
The two graphs illustrate the load displacement plots for the specimens. From the plot, it can be seen that the specimen’s stiffness remained linear up to the peak value. The linear relationship of the curve explains the elastic deformation of the material. The deformation represented when the displacement was affected in the upper surface as a result of some imperfections on the surface of the specimen. As shown in the illustration, the behavior of the specimen in the experiment was bending stiffness. The stacking sequence showed very little oscillations before peak load that may result from the supports’ vibration. Some defects in the composite, dents and delamination in the bottom and top faces of the specimen could cause damage to the specimen.
If the microscopic view of the structure was done, the following composite would be seen. The figure below shows the transverse view of the specimen in microscopic analysis.
Figure 6 a) Optical microscope photos for specimen 1. b) Optical microscope photos for specimen 2
Figure 7 a) Optical microscope photos for a damaged specimen 1. b) Optical microscope photos for a damaged specimen 2
The determination of the yield strength was carried out by replacing the load P at the yielding point. The yielding load is determined at a certain percentage offset. It is critical to understand that the yield strength obtained from the bend test is not varied from the yield strength achieved from another tensile test. To support this, it is proved that the relationship between the load P and deflection remain linear at the yielding point. From the bend test experiment, it is possible to calculate and obtain the elastic modulus of the beam.
Elastic modulus can be calculated from the gradient of load deflection graph (dP/dv) in the linear region. ..4
Or
.5
In equation (5), m is the gradient of the straight line portion of a load versus deflection beam. The elastic moduli from the test is close to the on obtained from tension and compression of the same material. Some factors affect the elastic stimuli in three-point bend test; elastic deformation at the rollers in the supports, the loading points might not be sufficiently enough compared to the deflection of the beam. If a short specimen is used, deformation due shear stress occurs. Also, some materials have different elastic moduli under bending, tension, and compression. Due to these uncertainties, the elastic moduli in a bend test should be identified to eliminate confusions from the interpretation of the mechanical behavior of the specimen.
Conclusion
The result of a bend test is a plot of load versus displacement. Since the amount of load need to stretch the specimen depend on the shape and size of the specimen – and, of course, the properties of the specimen, the comparison between the materials can sometimes be difficult. Making proper comparison is the main issue for someone to design structural applications for the material to withstand certain loads.
The strength of equipment is a widely used and recognized property. Bend test ensures comparisons of strengths of different materials are tested. The material that shows the best strength property is useful than that one that implicates little deflection with a fracture. The bend test in the experiment is a superb method of verifying the strength of material. This lab satisfies the objectives of the experiment.
Work cited
Schoffstall, Charles W, and Robert C. Boyden. Development of a Standard Bending Test for a Rope Yarns. Washington: Government Printing Office, 1925. Print.
